The effects of fiscal targets in a monetary union: a Multi-Country Agent-Based Stock Flow Consistent model

The effects of fiscal targets in a monetary union: a Multi-Country Agent-Based Stock Flow... Abstract We present an Agent Based-Stock Flow Consistent Multi-Country model of a Monetary Union to analyze the impact of a change in the fiscal regime of member countries, modeled as a permanent change in the deficit-to-gross domestic product (GDP) target that governments are committed to comply. Simulations are performed under three scenarios, differentiated by the number of countries considered (2, 6, 10). The parametric configuration employed yields economically reasonable values for the dynamics and relative dimension of key variables, broadly comparable with historical data and available stylized facts. Our policy experiments show that fiscal expansions generally allow to improve the dynamics of real GDP, labor productivity, and employment, though being generally associated with higher levels of public debt. Conversely, permanent fiscal contractions always exert strong recessionary effects, exacerbate real GDP volatility, and tend to be self-defeating in the long run. In scenarios where the Monetary Union includes a greater number of countries and the common market is bigger, fiscal austerity raises—rather than decreasing—average public debt-to-GDP ratios. We show that this is mainly related to a raise of debt-to-GDP in poorer and less productive countries mirrored by a reduction of their net foreign asset position. 1. Introduction The article presents an Agent Based-Stock Flow Consistent (AB-SFC) Multi-Country model to analyze the impact of different fiscal regimes on the long-term economic dynamics of a Monetary Union broadly comparable to the European Economic and Monetary Union (EMU). The computational framework proposed is at once simple in its behavioral assumptions and sophisticated in its interaction structure. Agents’ behaviors are based on relatively simple adaptive heuristics. We consider a pure labor economy where there is no capital accumulation and only final goods are produced. Money is endogenous to the system, but only credit to firms is modeled. Finally, public expenditure takes the form of a lump-sum monetary transfer to households. Yet the model is sophisticated in several other respects: first, its dynamics endogenously emerges from the decisions undertaken by many heterogeneous agents, interacting in a decentralized way on several types of markets (i.e., labor, tradable and nontradable consumption goods, credit, deposit, and bond markets). Furthermore, the model accounts for international flows of real and financial assets, arising from trade and credit flows between member countries. Consumers’ preferences and firms’ products are differentiated using Salop’s (1979) circular specification of Hotelling’s (1929) locational model. Technological change and sectoral technological spillovers, affecting the evolution of labor productivity across firms and countries, are modeled as an endogenous process driven by firms’ investment in R&D. In addition to this, the model displays several important add-ons to the current AB macro-modeling literature: to our knowledge, this is one of the first, if not the very first, fully fledged multi-country AB macroeconomic model presented in the literature. Indeed, models developed within this stream of research either displayed a closed-economy or, at most, a two-country economy. Our model instead can be initialized with a variable number of countries: for the present work experiments have been performed with 2, 6, and 10 countries. Second, the model aims at integrating the real and financial spheres of the economy along the line traced by Caiani et al. (2016, 2018); Deissenberg et al. (2008), thanks to the adoption of the SFC framework which provides a rigorous and exhaustive accounting of financial flows and stocks (Godley, 1997; Godley and Lavoie, 2007). Third, instead of assuming that the number of firms is fixed and that defaulted firms (or banks) are immediately replaced by an equal number of new entrants, we endogenize the entry–exit process of firms and banks by introducing a stylized mechanism to model households’ equity investment. The creation of new businesses thus depends on households’ financial wealth portfolio allocation between equity participations in new firms (banks) and deposit accounts at banks, based on their relative rates of return and their perceived riskiness. Finally, we propose a simple “generative” procedure to initialize the model in an SFC manner, inspired by the “SIM model” presented by Godley and Lavoie (2007). For the sake of analyzing the impact on our artificial Monetary Union of a permanent change in countries’ fiscal policy, we first combined the empirical information at our disposal with a preliminary investigation of the parameter space so to identify a baseline parametric configuration yielding realistic and relatively stable systemic dynamics. Then, we introduced a fiscal policy regime switch occurring at period 500, modeled as a variation of the common fiscal target for countries’ public deficit. Results were first analyzed looking at variations induced by the policy change in the average values and volatility of main economic aggregates, both in the short and long run. Then, we differentiated between high- and low-income countries to assess if changes in the policy regime affect richer and poorer countries in the same way, or if instead asymmetric effects arise. Results show that fiscal expansions generally tend to boost economic growth, technological change, and employment, at the cost of higher debt-gross domestic product (GDP) ratios. Instead, permanent reductions of fiscal targets exert significant depressing effects on real GDP, labor productivity dynamics, unemployment, and prices. More important, the efficacy of permanent fiscal contractions in reducing the burden of public debt seems to be limited, at least in the long run, to the two-country scenario. On the contrary, in the more realistic scenarios where the Monetary Union includes more countries and the common market is wider, fiscal contractions tend to be self-defeating in the long run increasing, rather than decreasing, average debt-GDP ratios. In these cases fiscal austerity tends to exacerbate recessions, amplifying economic fluctuations. We also show that fiscal contractions tend to impact more on the public finance of poorer and generally less productive countries causing a remarkable increase of their public debt burden, which explains much of the observed rise in the average debt-to-GDP ratios of the Union. Finally, we show that the increased public debt of less productive countries is generally associated with a deterioration of their net foreign asset position in favor of richer countries. 1.1 Euro imbalances and fiscal consolidation in the EMU: empirical and theoretical disputes The Great Recession begun in 2007 revealed the vulnerability of the EMU. The global economic turmoil displayed very peculiar traits in Europe, compared to the US case, manifesting itself not only as a real and banking crisis but also as a sovereign debt crisis. Policy interventions launched by European institutions and national governments have mainly gone in two directions: on the monetary policy side, the European Central Bank was called to play a more active role as lender of last resort, both for private banks in distress and for countries experiencing severe financing problems which threatened the financial stability of the Euro area.1 On the fiscal side, if severe fiscal contractions were the distinctive trait of Macroeconomic Adjustment Programmes undertaken by countries in distress, fiscal austerity measures have been also exacerbated in other countries under the Stability and Growth Pact and the Fiscal Compact additional provisions. This latter, in particular, has bound signatory countries to transpose into their legal order the provision of the treaty for a balanced national budget. However, the efficacy of these measures have been put seriously into question as a consequence of the deflationary spiral which invested many southern countries, of the rising imbalances between core and peripheral economies, and of the endemic fragility affecting both private credit institutions and countries’ public finance. The resurgence of the economic debate on the sustainability of the European Monetary Union project had profound implications on the political debate, and its topicality grew dramatically after the “Brexit.” Admittedly, fiscal austerity entered the scene way before the Euro Crisis. The principle of limiting as much as possible the discretion of member countries in conducting fiscal policy, by setting strict bounds to public deficits, has been at the very core of the European integration process since the Maastricht Treaty. The corollary aspiration for a completely independent Central Bank found its institutional transposition in the Treaty on the Functioning of the European Union which prohibited the ECB from buying government bonds in the primary market. Such an enduring position in favor of fiscal consolidation policies finds its theoretical roots in the traditional Neoclassical postulate that public spending would exert direct and indirect crowing out effects on private expenditure, in particular on investment. The modern refinement of this idea is the so-called “Expansionary Fiscal Contraction Hypothesis,” originally proposed by Giavazzi and Pagano (1990) and Alesina and Perotti (1995) and brought back in vogue after Reinhart and Rogoff (2010) contended the existence of a negative relationship between high levels of public debt and economic growth in advanced countries. These authors argued that discretionary fiscal expansions may undermine the solidity of public finance and of the overall financial system, eventually depressing private spending: for example, if consumers behave in a Ricardian way, they will abstain from consumption when fiscal deficits are perceived as unsustainable making future tax hikes more likely. Vice-versa, well-designed fiscal consolidations, that is, deep, persistent, and credible cuts in public expenditures, may stimulate private consumption and investment, and even improve export dynamics. The empirical ground of these claims has been harshly criticized by several authors. Herndon et al. (2014), for example, rose serious doubts on Reinhart and Rogoff’s work focusing on the alleged arbitrariness of their data sampling procedure and pointing out serious flaws—and even trivial coding mistakes—in their data elaboration. Others, as Guajardo et al. (2011), pointed out that the cyclically adjusted primary balance measures employed in the Expansionary Austerity literature do not completely remove the effects of economic cycles on the evolution of public finances, so that the positive correlation between fiscal restrictions and economic expansions would be the consequence of a biased measure of fiscal balances. Furthermore, since the causal link between fiscal balances and economic growth is likely to go in both directions, they point out that cyclically adjusted primary balance cannot be treated as an exogenous explicative variable. When a more correct estimation methodology is adopted, fiscal contractions end up to be consistently recessionary. Much of the debate on the role of fiscal stimuli has been geared around the estimation of the magnitude of fiscal multipliers. Gechert and Rannenberg (2014), in an attempt to review the ever-growing literature on “state-contingent” fiscal multipliers, provided a meta-regression analysis of fiscal multipliers from a broad set of empirical reduced-form models. Their meta-analysis found that fiscal multipliers are significantly higher during recessions than during boom phases, and that spending multipliers significantly exceed tax multipliers, so that fiscal consolidation should take place during recoveries, being instead avoided during recessions, and should be based on taxes rather than on public spending cuts. Similar results were achieved by Auerbach and Gorodnichenko (2012); Blanchard and Leigh (2013), while Ferraresi et al. (2014) found that the response of output to fiscal policy shocks is stronger and more persistent when the economy is in a “tight” credit regime. Finally, De Grauwe and Ji (2013) highlighted that government bond markets in the Eurozone, where countries lost their ability to issue debt in a currency over which they had full control, are more fragile and more susceptible to self-fulfilling liquidity crises than in stand-alone countries. This in turn has fostered a “panic-driven” austerity in the south having a self-defeating character, while failing to induce offsetting stimulus in the north. On a different level, Botta (2015) pointed out the theoretical inconsistency of the “Expansionary Fiscal Contraction Hypothesis,” going through a detailed analysis of the policy measures advocated by its supporters and showing that fiscal consolidation might have expansionary outcomes only under extreme, very specific, and uncertain conditions. Post-Keynesian scholars have opposed the view that fiscal profligacy by southern countries, paired with excessive wage growth, was the major cause of the Euro Crisis, as well as its implications that austerity and labor market deregulation were essential to restoring order. On the contrary, they traced the origin of the global crisis in the emergence of a debt-driven growth model, which resulted in a rapid increase in private debt ratios and eventually inflated a real estate bubble. These authors considered the escalation of the crisis into a sovereign debt crisis, and a depression in Southern Europe, as the outcome of the European Union’s peculiar institutional and policy setup, based on the separation of the fiscal and monetary spaces and designed to impose fiscal discipline and pro-cyclical austerity (Stockhammer et al., 2016). In particular, they insisted on the role played by the institutional framework in amplifying trade and Balance of Payment imbalances between core and peripheral European countries (Hein et al., 2011; Semieniuk et al., 2011; Perez-Caldentey and Vernengo, 2012; Zezza, 2012b).2 1.2 Euro imbalances and fiscal consolidation in the EMU: simulation approaches Besides the empirical and analytical levels, the impact of alternative fiscal regimes has been widely explored also by means of computational methods based on computer simulations. Within the DSGE literature, a vision strongly in favor of fiscal consolidation measures has been proposed by Cogan et al. (2010): building on an empirically estimated version of the Smets and Wouters’ (2007) New Keynesian model of the US economy, they argued that fiscal multipliers are significantly lower than those estimated with traditional structural macroeconomic models which do not account for forward looking rational expectations by individuals and firms, and are consequently unable to grasp the change in economic actors’ behavior in response to policy shocks. Christiano et al. (2011), on the contrary, found that fiscal multipliers can be much larger than one when the zero lower bound on the nominal interest rate binds and stressed that fiscal multipliers are significantly larger when higher spending is coupled with monetary accommodation. Fiscal stimuli were seen as potentially useful also in Corsetti et al. (2009), who showed that crowding-in effects on consumption become possible when increases in government spending are carried out under a plausible debt-stabilizing policy that links current stimulus to a subsequent period of spending restraint. Finally, Coenen et al. (2012) proposed an interesting comparison between results of the former three DSGE models developed in the academia and those obtained by seven structural models employed by major policymaking institutions. The policy experiments with seven different fiscal instruments showed that the seven models—six DSGE and a PAC—display large fiscal multipliers, and that temporary expansionary fiscal policies are most effective when accommodated by the monetary policy, whereas permanent fiscal stimuli (i.e., permanent increases in deficits) have significantly lower multipliers, possibly reducing output in the long run. Our work aims at giving a contribution to another stream of research in macroeconomic modeling. The economic debate emerged in the aftermath of the Great Recession has casted serious doubts on the theoretical and empirical foundation of DSGE models, questioning the reliability of their policy prescriptions (Trichet, 2010; Blanchard et al., 2012) and fostering a quest for alternative macroeconomic modeling tools: Agent-Based models (Delli Gatti et al., 2010), which conceive the economy as a “complex evolving system” (Esptein, 2006), have proven to be well suited to explain the endogenous nature of economic growth, the generation of business cycles, and the emergence of real and financial fragility, possibly culminating in severe recessions. This approach provides an alternative way to micro-found models (Gaffeo et al., 2008) where emergent dynamics are the result of the decentralized interaction between heterogeneous, boundedly rational, adaptive agents. Agent-Based models provide a powerful framework to test a wide variety of policy schemes. A detailed comparison between the DSGE and ABM approaches can be found in Caiani et al. (2016) and Fagiolo and Roventini (2016). As a consequence of the encouraging results within this nascent research field, in recent years AB models are blossoming. Several applications have been proposed to analyze the effects of fiscal and monetary policies and to tackle the macroeconomic imbalances affecting the EMU. For example, Dosi et al. (2013), using a refined version of Dosi et al. (2010), studied the interactions between income distribution and monetary and fiscal policies. They found that accomodative fiscal policies dampen the amplitude of business cycles, reduce the likelihood of huge crises, and may exert a positive effect on long-term growth. Vice-versa, fiscal restrictions negatively affect the economic performance. Furthermore, the positive impact of fiscal policies is greatly enhanced when the distribution of income is skewed toward profits. Dosi et al. (2015) further extended the model to analyze the effects of alternative combinations of fiscal and monetary policies, reaching the conclusion that the most appropriate policy mix to stabilize the economy requires unconstrained countercyclical fiscal policies coupled with a monetary policy targeting also employment. On the contrary, fiscal policies comparable to those proposed in the Fiscal Compact have a strong depressing impact which is exacerbated when the monetary policy targets only price stability. Similar conclusions were reached by Teglio et al. (2015), building upon Cincotti et al. (2010) and Raberto et al. (2012). Riccetti et al. (2013) proposed an AB model with decentralized matching on all the simulated markets, finding that an increase in public employment significantly stabilizes the economy at the expense of a slight increase of the deficit-to-GDP ratio, which can be almost eliminated through a modest increase of tax rates. Dawid et al. (2016a) employed a two-country extension of Deissenberg et al. (2008) as a laboratory to analyze several types of fiscal policies aiming to revert Euro imbalances. They found that policies asking core countries to share the debt-burden of peripheral countries are not effective in promoting a convergence. On the contrary, fiscal transfers in favor of households in peripheral regions do exert a positive effect. However, technology-oriented subsidies to firms, aiming to improve labor productivity in peripheral regions, are the most effective tool to improve their competitiveness. By employing the closed-economy version of the same model Harting (2015) showed that distinct fiscal policies, such as demand-oriented and supply(technology)-oriented fiscal policies may exert very different effects on the long-run economic performance of the economic system, even though they can have similar effects in reducing business cycle volatility. Our contribution also points to the so-called Stock Flow Consistent approach (Godley and Lavoie, 2007) which stems from the accounting-based modeling tradition started by Brainard and Tobin (1968) and later refined by Godley and Cripps (1983). This modeling approach aims at providing a comprehensive and fully integrated representation of the economy, including all financial transactions. At its base we find the idea that real and financial flows, and the stocks on which they impact, must always satisfy given accounting identities in a social accounting perspective. These identities ensure that there are no black holes in the representation of (real and nominal) stocks and flows, acting as a “conservation of energy principle for economic theory” (Godley and Cripps, 1983). In the recent years SFC models have been extensively employed to analyze fiscal, monetary, and macroprudential policies, in particular in the context of a Monetary Union. Adopting an SFC framework, Zezza (2012a) suggested that fiscal austerity in the presence of large public debts tends to redistribute income from taxpayers to the owners of such debt: when public debt has been financed by financial markets in foreign countries, interest payments on bonds will redistribute income to foreigners, thereby exacerbating the contractionary effect of austerity on domestic growth. Eventually, this would make the target of achieving a lower debt-to-GDP ratio unfeasible. This result suggests that, since public debt is held abroad when a country has been running a current account deficit, the primary concern of policymakers should be to introduce mechanisms for correcting, or at least financing, trade imbalances within the EMU. Duwicquet et al. (2013) presented an SFC two-country model where the southern country is suffering from an overvalued currency, while the northern country enjoys an undervalued currency, boosting its exports. The authors then test different institutional reforms at the Monetary Union level to counter these implicit transfers from the South to the North, finding that both fiscal transfers based on a federal budget and a system of eurobonds help to dampen trade imbalances. Mazier and Valdecantos (2015) extended the previous work proposing a four-country SFC model to study the effects of different exchange-rate arrangements. Among the proposed arrangements, the adoption of a double-Euro currency is shown to be potentially effective in reducing Eurozone imbalances. Though accounting-based models have found fertile soil in the Post-Keynesian tradition (see Dos Santos (2006) and Caverzasi and Godin (2015) for a literature review), in recent years they gained more and more interest also outside this community. Caiani et al. (2014a,b) for example, presented two applications of the SFC methodology to the study of Great Surges of Development in an evolutionary–Neo-Schumpeterian perspective, stressing the interdependency between innovation and finance. In 2011, the Bank of England used a similar accounting-based approach to analyze the mechanics of financial instability. Barwell and Burrows (2011) advocated the diffusion of macroeconomic approaches stressing the importance of balance sheet linkages. On a similar ground (though in a general equilibrium framework), Duca and Muellbauer (2013) revisited Tobin’s efforts to understand financial–real linkages, and proposed a modeling framework for analyzing households’ flows-off-fund and consumption in an integrated way. Finally, the Bank of England has recently presented a Stock Flow Consistent Model to perform scenario analysis on the UK economy (Burgess et al., 2016): their fiscal expansion experiment considered an increase of 10% in government spending, phased over 3 years, finding a fiscal multiplier around one. AB and SFC models may greatly benefit from a mutual integration (Deissenberg et al., 2008; Caiani et al., 2014a, 2016, 2018). In particular, the adoption of an AB-SFC framework provides a powerful tool to check the internal theoretical consistency of an AB model and an effective expedient to discipline AB practitioners (Caiani and Caverzasi, 2017). A fusion of the two approaches could help AB macroeconomic models to set themselves as a credible alternative to DSGE models (Farmer and Foley, 2009) responding to the call recently made by FED chair Jellen (Jellen, 2016) for models capable of addressing the role of agents’ heterogeneity and real–financial linkages. The rest of the article is structured as follows: the next section goes through the behavioral equations of the model and explains the logic employed to define the initial setup of our simulation experiments. Section 3.2 first checks the consistency of our results with available empirical stylized facts, and then displays and discusses the results of our policy experiments. Finally, Section 4 considers the limits of the present work and briefly sketches out future applications and refinements. 2. The model The artificial economy depicted in the model is a Monetary Union composed of K countries. Each country k is populated by the same number H of households and by an endogenously varying number of firms (Ikt) and banks (Zkt). Firms produce their output out of labor only and are differentiated between “tradable,” producing final goods to be sold on the common internationally integrated market, and “nontradable,” producing for the domestic market. The process of entry and exit of firms and banks is shaped so to avoid the emergence of excessive imbalances in the relative dimension of the manufacturing and banking sectors, and in the proportion between tradable and nontradable firms. International trade between countries gives rise to international transfers of goods, deposits, and bank reserves. Firms, when needed, can demand loans to both domestic and foreign banks. Commercial banks are allowed to purchase bonds issued by any member country. On the contrary, for simplicity reasons, we assume that there is no international labor mobility and that households invest only in domestic firms and banks. Governments collect taxes on households’ income and on profits of firms and banks. Public spending takes the form of a lump-sum monetary transfer to households. Countries are subject to the same regulatory framework being committed to not exceeding a common deficit-to-GDP threshold. For this purpose they can adaptively modify tax rates and the level of public spending. The System of Central Banks of the Monetary Union operates under the control of the Union Central Bank and includes K national Central Banks, one for each country. The Union Central Bank employs a Taylor rule to set the common discount interest rate applied on cash advances. National Central Banks accommodate commercial banks’ demand for cash advances through the marginal lending facility. Furthermore, they buy the residual amount of their country’s public debt bonds which have not been purchased by private banks. In this way they also inject reserves into the economic system (Caiani et al., 2016). The model endogenizes technological change, arising from firms’ R&D investment directed to increase the productivity of their employees, thereby reducing unit costs of production and increasing profit margins. Productivity enhancing innovations can be achieved in two ways: through direct incremental innovations, or by exploiting sectoral spillovers through imitation, which allows less productive firms to catch up with the sectoral productive standards (Dosi et al., 2010). Together with aggregate demand, technological change is the fundamental engine of long-term real growth in the model and plays a crucial role in determining firms’ and countries’ international competitiveness, thereby impacting on international trade patterns and countries’ differentiation. Finally, we follow Riccetti et al. (2015) and Caiani et al. (2016) in assuming that agents interact on all markets in a decentralized way, following specific matching protocols. The structure of our artificial economy encompasses six types of market: national “nontradable” good markets, national labor markets, national deposit markets, a common “tradable” good market, a common credit market, and a common bond market. The following two subsections describe in details agents’ behaviors and interactions. 2.1 Agents 2.1.1 Households Households are at the same time workers, equity holders, and consumers. Each worker supplies a given quantity of labor ( lS=1) in each period of the simulation to ψ randomly sampled potential employers (see Section 2.1.2). Since firms formulate their demand for labor in real terms, rather than in integer units, some workers will be part-time employed, being able to sell only a portion of their unitary labor supply. The same occurs if a firm is prevented from employing a worker at full-time by liquidity shortages. Part-time workers can return on the labor market to offer their residual labor force to the other ψ−1 potential employers. As a consequence, they may be employed in different firms at the same time, selling to each of them quantity of labor force lhit (where i is one employer out of the n employers of the household h) and receiving from each of them a different wage whit. Yet, the worker may remain unemployed, or part-time employed, if total labor actually sold to firms lht=∑i,lhit>0Iktlhit is still lower than the quantity supplied lS. Workers choose the potential employer offering the highest wage, but they do not accept vacant positions below their reservation wage wht. This latter is adaptively modified depending on the worker’s past employment situation. Workers lower their reservation wage by a stochastic amount if they were not fully employed in the last period. U[0,δ] indicates a random sample from a Uniform distribution defined between 0 and δ. If instead lS=lh,t−1, they increase their reservation wage with a positive probability Pr(wht+) which is inversely related to the aggregate rate of unemployment, as shown in equation (1). Workers’ wage claims are negatively affected by higher levels of unemployment, with the parameter υ>0 shaping the strength of this relationship: the higher υ, the lower the probability of increasing demanded wages for given levels of unemployment.   wht={wh,t−1(1+U[0,δ]), iflS−lh,t−1=0withPr(wht+)=e−υut−1wh,t−1(1−U[0,δ]), iflS−lh,t−1>0. (1) Furthermore, we assume that firms employ workers for production and R&D activities indifferently and that financial resources devoted to innovative investments ( R&Dit, see Section 2.1.2) add on to workers’ wages, being distributed across workers according to their individual contribution (lhit) to the total quantity of labor employed by the firm (lit). Investment in R&D thus generates additional wages for workers. Besides labor income households also receive interests on their deposits Dht from banks (computed at the interest rate rdt), dividends from participated firms and banks (Divht), and a tax-exempt monetary transfer ( Gkt/H) by the government of their country k. All in all, households’ gross and disposable income after taxation, indicated, respectively, by yht and yhtD, are expressed by:   yht=∑i,lhit>0Iktwhitlhit+rdtDht+Divht+∑i,lhit>0IktR Ditlhitlit, (2)  yhtD=(1−τt)yht+GktH, (3) where τt is the tax rate in the current period. Desired nominal consumption ( CitD) is a linear function of current disposable income and current wealth held in the form of deposits, with fixed marginal propensities cy and cd:   ChtD=cyyhtD+cdDht, (4) where 0<cy<1 and 0<cd<1.3 Consumers then distribute their demand between tradables ( ChtDT) and nontradables ( ChtDNT) with fixed proportions cT and 1−cT, respectively.4  ChtDT=cTChtD. (5)  ChtDNT=(1−cT)ChtD. (6) Households enter the tradable and nontradable markets in a random order. Each consumer samples ψ potential suppliers, and rank them from the most to the least preferred. The model employs a circular Hotelling’s locational specification (Salop, 1979) of consumers’ preferences and firms’ offered varieties, assuming that good varieties produced by firms’ and consumers’ preferences are randomly located on a circle (Figure 1) with unitary diameter. According to this approach, a random radian value is associated to each firm (ωi) and to each consumer (ωh). Consumers rank suppliers based on a mechanism which takes into account both the price competitiveness, expressed as the ratio between the price pit of a firm i and the sector average price Pit, and the distance dhi between the firm and the consumer. The lower the price and the distance, the higher will tend to be the position of the supplier in the consumer’s ranking. Formally, firm i will be preferred to firm j if:   1dhiβPtpit>1dhjβPtpjt, (7) where β≥0 is a parameter weighting households’ preferences for variety: the lower β, the more consumer perceive consumption goods as homogeneous, thereby giving more weight to price differences in sorting consumption alternatives. The distance between firms’ offered varieties and consumers’ preferences coincides with the length of the chord between their locations. Since the diameter of the circle is set equal to 1, this can be computed as:   dhi= sin(min[|ωh−ωi|,2π−(|ωh−ωi|)]/2). (8) Figure 1. View largeDownload slide Hotelling circle example. The point H, identified by the angle ωh, expresses the preferences of household h. The point I, associated to angle ωi, indicates the variety produced by firm i. The distance dhi between the household’s preferences and the firm’s variety is equal to the arch HI¯. Figure 1. View largeDownload slide Hotelling circle example. The point H, identified by the angle ωh, expresses the preferences of household h. The point I, associated to angle ωi, indicates the variety produced by firm i. The distance dhi between the household’s preferences and the firm’s variety is equal to the arch HI¯. Figure 2. View largeDownload slide Cyclical components of simulated times series for real output (y), consumption, export, import, and unemployment rate. Figure 2. View largeDownload slide Cyclical components of simulated times series for real output (y), consumption, export, import, and unemployment rate. Consumers first try to satisfy their demand at the preferred supplier. If supply constraints are present, consumers can turn to the second, third, fourth, etc., supplier in the ranking to exhaust their residual demand. Households hold their wealth (NWht) partly in the form of deposit accounts at commercial banks Dht, which yield a positive interest rate, and partly as participations in the equity of firms and banks Aht, yielding dividends when profits of participated firms are positive. Therefore, in every period households must choose how to allocate their financial wealth between these two types of assets. This allocation is based on an endogenously determined “liquidity preference”5lpht, depending on the risk-weighted past rates of return yielded by the two types of assets. Deposits are a risk-free asset. On the contrary, the rate of return on equity investment is weighted by its perceived riskiness, proxied by the past extinction rate of firms and banks. Indicating by Itdefault and Ztdefault, respectively, the number of firms and banks defaulting in period t, we define this latter as: Prtdefault=It−1default+Zt−1defaultIt−1+Zt−1. The liquidity preference of each household is then expressed as:   lph,t={λe−(Divh,t−1Ah,t−1(1−Prtdefault)−rdt) if Divh,t−1Ah,t−1≥rdt and Ah,t−1≥0λ if Divh,t−1Ah,t−1<rdt or Ah,t−1=0, (9) with 0<λ<1 representing the maximum liquidity preference, attained when the return on equity investment was lower than the interest rate paid on deposits, or if the household did not own any equity in the previous period. If we indicate by NWhtD=NWht−1+yhtD−ChtD households’ expected level of net worth based on their planned consumption, we can derive the desired level of equity and deposits as:   AhtD=max{Aht−1,(1−lph,t)NWhtD}, (10)  DhtD=NWhtD−(AhtD−Aht−1), (11) where AhtD−Aht−1 is the desired investment in equity, which is bound to be nonnegative.6 However, since consumption may be frustrated by supply constraints, actual consumption (Cit) may be lower than desired ( CitD), so that NWht may end up being greater than planned ( NWhtD), due to “forced” savings: Sht=yhtD−Cht. In this case deposits act as a buffer stock, absorbing the discrepancy, while investment in equity sticks to its planned level AhtD. In other words: Dht=NWht−(AhtD−Aht−1)>NWhtD. Households having a positive desired investment gather in the attempt to set up a new firm (or a new bank). Investors act as an equity fund, gathering their invested resources so to raise the funds required to start the new business. These funds must be greater than a threshold level determined in the entry procedure explained in Section 2.1.6. If the level of investment is not sufficient, no firm (bank) is created and households abstain from investing in the current period. Deposits are again the buffer stock, ending up to be higher than originally planned. Conversely, if desired investment by households is high enough, more than one firm (bank) can enter the market. Finally, in each period households choose their deposit bank randomly, since every bank offers the same interest rate rdt for simplicity reasons. 2.1.2 Firms Firms are classified into “tradables,” selling their products in the common-internationally integrated market, and “nontradables,” producing for the domestic market. Labor is the sole productive factor and is employed both for production and R&D purposes. Firms’ production plans depend on their sales expectations and the level of inventories inherited from the past. Furthermore, we assume that firms desire to hold a level of inventories invit equal to a given share θ of expected sales, as a buffer against unexpected demand swings (Steindl, 1952) and possibly to avoid frustrating customers with supply constraints (Lavoie, 1992). We indicate by qit the (real) output produced by firm i in period t, by q^it the quantities sold, by pit their selling price, by qite firm’s (real) sales expectations, and by qittot=qit+invit the total amount of goods available for sales, equal to current production plus inventories. Prices and sales expectations are revised adaptively from period to period according to the following scheme:   if  q^i,t−1≥q^i,t−1e:{q^ite=q^ite(1+U[0,δ])pit=pi,t−1(1+U[0,δ]). (12)  if  q^i,t−1<q^i,t−1e  and   qi,t−1tot>q^i,t−1:{q^ite=q^ite(1−U[0,δ])pit=pi,t−1(1−U[0,δ]). (13)  if  q^i,t−1<q^i,t−1e   and  qi,t−1tot=q^i,t−1:{q^ite=q^i,t−1epit=pit−1. (14) Equation (12) states that if past sales exceeded expectations, firms adaptively increase both sales expectations and their selling price. By increasing prices they aim to increase their profit margin. When instead past sales were below their expected value and no supply constraint was binding [equation (13)], both expectations and prices are revised downwardly. By reducing prices firms aim to make their output more attractive to consumers, thereby improving their sales performance. Finally, when firms’ past sales were below expectations due to the presence of a supply constraint [i.e., despite firms had exhausted all their available supply, see equation (14)], firms postpone any revision of prices and expectations to the next periods. Prices have a lower bound represented by unit costs of production, that is, pit≥witφit, where φit is firm’s i current level of labor productivity. The desired amount of goods to be produced for the current period is then determined as:   qitD=qite(1+θ)−invit. (15) The demand for labor can be obtained by dividing planned output for the firm’s labor productivity level: litD=qitD/φit. However, if firms have not enough funds to pay wages ( witlitD), labor demand is reduced accordingly. Firms’ labor demand can be also frustrated by other factors, for example, if the economy is already at full employment or if the salary offered is too low to cover vacant positions. Since production depends on the quantity of labor actually employed, which can differ from demanded quantities for the reasons explained above, also actual output may be lower than originally planned. The salary wit offered by firm i changes according to the difference between labor demanded li,t−1D and labor actually employed in the previous period li,t−1. If the firm was not able to cover all vacant positions, i.e., labor employed was below labor demanded, it increases the salary so to attract workers. When all vacant positions were covered, firms consider the possibility to reduce wage so to increase their profit margins. The lower the unemployment, the lower is the probability of such a revision, since reducing wages increases the risk of ending up being labor constrained.   wit={wi,t−1(1+U[0,δ]), ifli,t−1D−li,t−1>0wi,t−1(1−U[0,δ]), ifli,t−1D−li,t−1=0withPr(wit−)=1−e−υut−1. (16) Firms can increase their profit margin also by improving their productivity φit, thereby reducing unit labor costs. Labor productivity can be enhanced either through incremental innovations or by exploiting spillovers at the sectoral level through imitation, which allows less productive firms to catch up with sector production standards. Innovations and imitations can be achieved through firms’ investment in R&D. Firms invest in each period a given share of its expected wage bill in R&D, as follows:7  R&DitD=γwitlitD. (17) Actual investment R&Dit will be equal to R&DitD only if the firm does not face any financial or labor constraint; otherwise, it will be lower than desired. The amount of resources invested in R&D, in turn, determines the probabilities of enhancing firm’s productivity through either incremental innovations or sectoral spillovers (Dosi et al., 2010). These two probabilities are assumed to be equal. For firms producing tradable goods, they are defined as:   PrsuccessitT=1−e−νR&DitΦtTPtT, (18) where PtT is the average international price of tradables, and ΦtT is the average labor productivity of tradable firms in the Monetary Union. Both are calculated as a weighted average, with weights represented by firms’ market shares. Similarly, for nontradable firms:   PrsuccessitNT=1−e−νR&DitΦtNTPtNT, (19) where PtNT is the average domestic price of nontradable goods, and ΦtNT is the national average labor productivity of nontradable firms, both being weighted for firms’ market shares. Equations (18) and (19) show that the two probabilities of success are a nonlinear increasing function of the real investment on productivity-enhancing activities ( R&Dit/PtT and R&Dit/PtNT for tradable and nontradable firms), divided by the sector average level of productivity ( ΦtT and ΦtNT, respectively).8 If firms result to be successful in innovating, their firm-specific labor productivity is then increased by a stochastic amount, as described in equation (20):   φi,t+1=φit(1+U[0,δ]). (20) Firms having productive standards below the sector average (i.e., a level of productivity below the average) can also try to exploit sectoral spillovers through imitation in an attempt to catch up with leading firms. The probability of success in imitating is the same as for innovations. If successful, firms are enabled to narrow the gap with the standards of production in the sector extracting a new productivity level in a range between their current one, possibly updated according to equation (20) if they have already achieved an innovation, and the sector average. For tradable firms the new level is formally determined as:   φi,t+1=φit+U[0,(ΦtT−φit)]ifφit<ΦtT. (21) For nontradable producers:   φi,t+1=φit+U[0,(ΦtNT−φit)]ifφit<ΦtNT. (22) The new level of productivity achieved thanks to an innovation and/or an imitation is embedded in the production process starting from the following period. Firms’ production and R&D investment can be financed using both internal funds accumulated through time (Dit) and external funding in the form of loans asked to domestic and foreign banks (Lit). Following a well-established assumption in AB modeling, inspired by the “Pecking Order Theory of Finance” (Myers, 1984), firms in the model resort to external financing after internal funding possibilities have been exhausted, since the cost of external finance is usually higher due to market imperfections and information asymmetries. Accordingly, the demand for loans by firms can be expressed as:   LitD={witlitD+R&DitD−Dit, if witlitD+R&DitD>Dit0, if witlitD+R&DitD≤Dit. (23) However, given the cost of external finance the demand for loans is positive only if the expected revenues generated by employing these funds are greater than the cost of financing.9 Firms are financially constrained if the amount of credit received (Lit) is lower than demanded (see Section 2.1.3): Lit≤LitD. This happens when banks have already exhausted the total amount of loans they were willing to supply in a given period or if none of them is willing to provide credit to the firm, if it is perceived as too risky (see Section 2.1.3). Yet, firms can try to fulfill their financing needs asking credit to different banks. When financially constrained, firms prioritize production over R&D. For simplicity reasons, in this first version of the model, loans are assumed to be granted and repaid within the same period, similarly to the monetary circuit theory (Graziani, 2003).10 As for households, also firms randomly choose their deposit bank, receiving an interest rdt on the amounts deposited. Profits are then computed as the sum of revenues from sales ( pitqit), interests received on deposits held at banks ( rdtDit), and the nominal variation of inventories ΔINVit11, minus labor expenditure for production ( witlit) and R&D activities( R&Dit), and credit costs ( ritLit):   πit=pitqit+rdtDit+ΔINVit−witlit−R&Dit−ritLit. (24) If we omit the variation of inventories from equation (24), we obtain a measure of the net operating cash flows generated by the firm, which we indicate by πit*. When πit*>0, firms pay taxes ( Titπ) and distribute dividends ( Divitπ) to equity holders, expressed as a share ρ of their residual net cash inflow. Since profits are generated at the end of period t—when public spending, tax payments on income of households, and consumption have already taken place—taxes on profits generated in period t are paid in period t + 1. Accordingly, also dividends generated in period t are paid to equity holders in period t + 1.   Titπ={τtπit*, if πit*>00, if πit*≤0. (25)  Divitπ={ρ(πit*−Titπ), if πit*>00, if πit*≤0. (26) Dividends are distributed to equity holders proportionally to their participation share. Retained net profits increase firms’ net worth:   Ai,t+1=Ait+πit*−Titπ−Divitπ. (27) Since firms belong to households who originally invested in their creation, as Ai,t+1 increases also equity holders’ participations are increased accordingly. 2.1.3 Banks Banks offer demand deposit accounts to households and firms, paying an interest rdt equal to a constant fraction ζ of the discount rate rt fixed by the Central Bank of the Monetary Union. In addition, banks endogenously create means of payment by providing credit to firms. As it happens in reality, every new loan granted by a bank, which is an asset for it, is immediately balanced by the creation of a matching liability in the form of a deposit for the borrower, both being created exnihilo. This implies that banks’ credit supply is not constrained by the amount of deposits already in circulation nor by the amount of reserves they hold. However, we assume that to avoid taking excessive risks, the maximum amount of credit that banks are willing to supply in any given period is a multiple μ1 of their equity Azt: LztDS=μ1Azt. Banks receive credit applications from both domestic and foreign firms. For each loan application received, banks compute a probability Pr(Loanit) to grant it. Furthermore, banks also discriminate borrowers by applying different interest rates (rit). The probability Pr(Loanit) and the interest rate charged rit are, respectively, a decreasing and increasing function of the borrowers’ target leverage, computed as the ratio between their demand for loans ( LitD) and their net worth (Ait):   Pr(Loanit)=e−ιlLitDAit. (28)  rit=χLitDAit+rt. (29) Banks are subject to minimal reserve requirements, expressed as a share μ2 of their deposits:   RztM=μ2Dzt. (30) Reserves are held at the national Central Bank and yield a fixed interest rate rre. Whenever reserves RztM are below the minimum level, banks apply to the Central Bank lending facility, asking cash advances (LzCBt) to restore the mandated liquidity ratio. National Central Banks accommodate these requests, receiving the discount rate rt on funds lent to banks. If instead banks have reserves in excess with respect to the mandatory level, these can be invested in the purchase of bonds ( BztD) issued by any member country k, which bring an interest rate rbkt computed following equation (45). In each period of the simulation, all the bond tranches issued by governments of the Monetary Union (Section 2.1.5) are piled up and shuffled. Then, commercial banks enter the bond market in a random order and go through this pile, having a probability of purchasing each tranche which depends on the riskiness associated to the country and defined as:   Pr(bkt)=e−ιbBktYkt. (31) Each bank goes through the pile of bond tranches till it eventually exhausts its demand, or there are no tranches to be sold. Therefore banks’ profits (πzt) are equal to:   πzt=∑i,Lizt>0IktritLizt+rbtBzt+rreRzt−BDizt−rdtDzt−rtLzCBt, (32) where (BDizt) indicates “bad debt,” that is, loans not (entirely) repaid as a consequence of a borrower’s default. When profits are positive ( πzt>0), banks pay taxes ( Titπ) and distribute to equity holders a share ρ of net profits ( Divztπ). As for firms, dividends are distributed among investors proportionally to the share of the bank’s equity they own.   Tztπ={τtπzt, if πzt>00, if πzt≤0. (33)  Divztπ={ρ(πzt−Tztπ), if πzt>00, if πzt≤0. (34) Retained profits after taxes then increase banks’ net worth:   Az,t+1=Azt+πzt−Tztπ−Divztπ. (35) As Az,t+1 varies, also households’ participation in the bank, and thus households’ net worth, is revised accordingly. 2.1.4 Central Banks The Central Bank of the Monetary Union operates through the System of Central Banks which it heads. This is composed by national Central Banks in charge of enforcing the Union Central Bank policies at the country (indexed by k) level. National Central Banks hold reserves of commercial banks (RCBkt), accommodate their requests for cash advances (LCBkt), and possibly buy bonds issued by the country government (BCBkt) which remain unsold after private banks’ purchases. At the beginning of the simulation, when no commercial banks are present (see Section 2.3), Central Banks directly collect money of households and purchase the entire amount of bonds issued by governments.12 However, in this transitory phase they cannot offer credit to firms. National Central Banks’ profits (πCBkt) derive from interests on cash advances and bonds, from which we shall subtract interests paid on banks’ reserve accounts.   πCBkt=rbktBCBkt+rtLCBkt−rreRCBkt. (36) For simplicity reasons, we assume that national Central Banks’ profits are automatically redistributed to the national government. The Union Central Bank is in charge of implementing the common monetary policy. For this sake it sets the discount interest rate following a Taylor rule based on the average level of inflation across member countries (Taylor, 1993; Smets and Wouters, 2007; Gerali et al., 2010):   rt=r¯(1−ξ)+ξ*rt−1+(1−ξ)*ξΔP(ΔPt−1−ΔP¯), (37) where r¯ is the exogenous long-run interest rate, ξ is the parameter defining the speed of the adjustment, ξΔP is the sensitivity to inflation, ΔPt−1 is the average level of inflation, and ΔP¯ is the inflation target. 2.1.5 Government The government of each country collects income taxes from households (h) and taxes on past period profits from firms (i) and banks (z). Therefore, total taxes Tkt of country k are equal to:   Tkt=∑h,yht>0Hkτktyht+∑i,π*>0Ikτktπit−1+∑z,π>0Zkτktπzt−1. (38) Government public expenditure Gkt takes the form of a lump-sum transfer which is equally distributed among households ( Gkt/H), thus providing additional purchasing power. The public balance in a given period is the difference between revenues from taxes and government expenses, including also interests paid on public debt. When negative, we have a deficit DEFkt. In the opposite case the government attains a budget surplus SUkt−1. Possible budget surpluses are set aside to fund public expenditure in the next periods, thereby reducing the quantity of bonds to be issued. Countries’ public deficit (DEFkt) and debt (Bkt) are then given by:   DEFkt=Gkt+rbkt−1Bkt−1−Tkt. (39)  Bkt=Bkt−1−DEFkt−SUkt−1. (40) The government employs two instruments to implement its fiscal policy: the level of public spending (Gkt) and the tax rate (τkt). These are adaptively revised from period to period based on the discrepancy between desired and past levels of public expenditure on the one hand, and expected and admissible levels of public deficit on the other hand. The desired level of public expenditure GktD is simply defined as the initial (exogenous) real value of public spending G, adjusted for the country average level of prices Pkt and average productivity Φkt, so to ensure that the dimension of the public sector remains roughly stable compared to aggregate GDP: GktD=PktΦktG. In addition, governments are committed to keep their deficit-to-GDP ratios ( dkt=DEFkt/Ykt) below a given threshold value indicated by dmax. Public expenditure and tax rates are then revised according to the following scheme:13  if dkt−1≥dmax   and   GktD≤Gkt−1:{Gkt=Gkt−1(1−U[0,δ])τkt+1=τkt(1+U[0,δ]) (41)  if  dkt−1≥dmax  and   GktD>Gkt−1:{Gkt=Gkt−1τkt+1=τkt(1+U[0,δ]). (42)  if  dkt−1<dmax  and   GktD≤Gkt−1:{Gkt=Gkt−1(1−U[0,δ])τkt+1=τkt(1−U[0,δ]). (43)  if  dkt−1<dmax  and  GktD>Gkt−1:{Gkt=Gkt−1(1+U[0,δ])τkt+1=τkt. (44) However, to avoid unreasonable high or low values, the tax rate is bound to vary within the range {τmin,τmax}, whereas Gkt is bound between a minimum and maximum share of GDP: {gminYkt,gmaxYkt}. Bonds last for one period. In each period, the government repays bonds previously issued and pays interests to bond holders. The interest rate on bonds is set as a premium on the Central Bank discount rate (rkt) depending on the debt-to-GDP ratio of the country ( Bkt/Ykt) and:   rbkt=χBkt/Ykt+rt. (45) Newly issued bonds (for a total value of Bkt) are split into 100 tranches ( bkt=Bkt/100) and put on the bond market where they can be purchased by commercial banks (both national and foreign), and by the national Central Bank for the possible residual part. Finally, the government steps in to guarantee depositors in case of a bank default. For this sake, the government issues an additional batch of bonds, which is directly purchased by the Central Bank, and uses the liquidity collected to reimburse households and firms who lost their deposits in the default. 2.1.6 Firms’ and banks’ endogenous entry and exit As discussed in Section 2.1.1 households’ savings are partly invested in the creation of new firms and new banks. A minimum level of investment, equal to a share ϖ of the country average wage, is required to allow an individual household to participate in the creation of a new business, regardless its type. Furthermore, there is a maximum number of businesses in which an individual household can invest, equal to ψ. To avoid excessive imbalances in the the dimension of the banking sector relative to the productive one, we assume that the new entrant will be a bank when either the ratio between banks’ and firms’ number or the ratio between banks’ and firms’ total net worth is below a given percentage η. Otherwise, the new entrant will be a firm. The new firm will be a tradable with probability cT, or a nontradable with probability 1−cT. The initial equity of the new entrant is determined as a random sample between the net worth of the smallest and larger incumbents in the sector14: when funds collectively invested by households are greater or equal to this random equity level, the new organization is created and the first h randomly chosen investors required to collect this level of funds become its shareholders. Otherwise, no firm (bank) enters the market and the funds originally allocated by households to equity investment are deposited at banks, being available to fund households’ investment in the next period.15 If instead funds allocated to equity investment are not exhausted by the creation of the new enterprise, the remaining part can be employed to set up other businesses, their type and dimension being determined according to the procedure explained above. As for new entrants’ initial dimension, also their initial productivity ( φ), price (pit), and wage offered (wit) are randomly extracted within a range going from the lowest to the highest values of incumbent firms in the sector. Their sales expectations ( qite) are instead the maximum between the random value sampled between the lowest and highest values of incumbents and Aitwitφit, this latter representing the amount of goods feasibly producible, given the values of equity, wage, and productivity sampled by the entrant. Firms whose net worth is below a threshold level, defined as the wage they offer to workers Ft=wit, default. Similarly, banks having a net worth below the national average wage default. This threshold level of internal funding has a technical reason, being meant to avoid the unnecessary computational burden required to keep track of extremely small firms and banks, almost negligible in terms of their contribution to the dynamics of the model. A default by a firm implies a nonperforming loan for creditors. The larger the bad debt suffered by banks, the worse the effect on their balance sheet [through equation (32)], which negatively affect their credit supply. In addition, defaults will generally increase unemployment. Therefore, firms’ failures may impact on the business cycle both directly, reducing employment and the potential output of the economy, and indirectly, by reducing the amount of credit banks are willing to supply. Defaults by banks instead do not directly affect households and firms, as the government totally bears the loss by issuing additional bonds to reimburse depositors (Section 2.1.5). However, in this way banks’ failures affect public debt dynamics. In addition, banks’ failures may eventually cause a reduction of the total credit supply in the economy. Finally, even before causing a default, negative profits of firms and banks prevent them from paying dividends and decrease their equity, thereby affecting the net worth of equity holders. 2.2 Simulation scheduling We conclude this section dedicated to agents’ behaviors by sketching out the sequence of events taking place during each round of the simulation. Firms determine their desired production, their labor demand, the price of their output, the wage offered, and their desired R&D investment. Firms interact with banks on the credit market and possibly receive loans. Banks possibly ask cash advances to the Central Bank to satisfy the mandatory liquidity ratio. Firms interact with workers on the labor market. Workers are paid and employed to produce firms’ output and to perform R&D. Dividends generated in the previous period are distributed to equity holders, summing up to their current income. Governments calculate revenues from taxes (on past period profits and current period households’ income), determine the level of public spending and the tax rate for the next period, repay bonds plus interests to bond holders, and determine the quantity of bonds to be issued. Bonds are put on the bond market where commercial banks buy it. The possible residual part is purchased by national Central Banks. After having paid taxes and received the tax-exempt monetary transfer from the government, households compute their demand for consumption goods and interact with tradable and nontradable firms on the correspondent good markets. Firms and banks compute their profits and update their net worth and shareholders’ equity accordingly. Taxes and dividends to be paid in the next period to the government and to equity holders, respectively, are then computed. Defaulted firms and banks exit the market. Household equity investment takes place and, if enough financial resources are collected, new firms and banks are created. 2.3 Simulations setup Table A1 provides a summary of the parameter values employed for the model. Each simulation period ideally represents a quarter. Simulations have been run for 1000 periods. For each simulation setup we run 25 Monte Carlo repetitions. In addition, for all simulation experiments we consider three different specifications regarding the number of countries belonging to the Monetary Union: a traditional two-country model, and then a 6-country and a 10-country cases. Besides the setting of behavioral parameters, one of the most tricky aspects of the model calibration procedure concerns the setup of initial values of stocks and flows. Caiani et al. (2016) point out that this aspect has been quite neglected within the AB macro literature, and very few models provide a detailed discussion of the logic followed to address this task. Initial stocks and flows across agents must be mutually compatible from a social accounting point of view, respecting Copeland’s quadruple entry principle (Copeland, 1949; Godley and Lavoie, 2007). A calibration affected by possible accounting flaws can be a major source of logical and accounting inconsistencies, building up throughout the simulation rather than fading away thus compromising the reliability of results. In addition, the calibration of initial values should be such to allow the model to reach, after the initial burn-in phase, a reasonable configuration regarding stocks and flows absolute and relative dimension. Within the AB-SFC literature, Caiani et al. (2016) present a sophisticated procedure to carry out this task. Dawid et al. (2016b) and Teglio et al. (2015) also provide an overview of the calibration method employed for the “EURACE” AB-SFC model (Deissenberg et al., 2008; Holcombe et al., 2013). The present article provides a simple and intuitive alternative to these procedures, inspired by the logic adopted by Godley and Lavoie (2007) in presenting the “SIM” model. The fundamental feature of this procedure is that, instead of setting exogenously the initial values for each type of stocks, and then distributing them across agents, we start from a situation where there are no stocks in the economy, and we let them to be progressively created and accumulated as time goes by. To be more precise, not only real and financial stocks are initially absent but firms and banks as well. Everything starts with public spending, as the government makes an initial transfer to resident households. Given that there are no private banks in this initial phase, the national Central Banks buy government bonds, providing in this way the legal currency which funds public expenditure. Since no firms, production, and goods are present, this lump-sum transfer is completely saved by households. However, part of these savings (see Sections 2.1.1 and 2.1.6) are invested in the creation of new firms which start to employ workers and produce consumption goods to be sold to households on either the tradable or nontradable markets. Firms also start to invest in R&D, thus possibly increasing their level of productivity. As their number increases also banks will be created: households and firms then deposit their holdings of legal currency at the newly created banks. Banks start to grant credit to firms, creating loans and matching deposits ex nihilo, thus triggering the process of endogenous creation of money. At the same time banks use their reserves in excess to buy bonds issued by the government and, conversely, as cash advances to their Central Bank when needed. At this stage, the system is already characterized by the presence of two interdependent monetary circuits, since both legal money, created by the public authority, and private money, created by banks through credit, are present. As soon as households receive an income, and firms and banks realize positive profits, taxes start to be collected by the government. With rising tax revenues and GDP increasing—as more and more firms are in business—the debt-to-GDP ratio rapidly declines to reasonable levels. Since tradable firms sell their output on the common integrated market, international flows of goods, deposits, and reserves between countries arise. Supranational debt–credit relationships, generating international flows of interests, also arise because commercial banks grant loans to foreign firms and purchase public debt bonds of foreign countries. The number of firms and banks quickly increases in the initial phase until new businesses and defaults start offsetting each other, stabilizing their number. In the meanwhile, firms and countries become more and more heterogeneous as a consequence of their R&D performance which drives technological progress and impact on their competitiveness. In turn, international trade and labor productivity dynamics affect the evolution of employment, wages, prices, profits, aggregate demand, and GDP in the Monetary Union, thereby possibly impacting also on public finance, and on R&D investment by firms as well. The model thus progressively exits its transition phase and starts to display regular patterns and quite stable properties. The next section is dedicated to their analysis. 3. Simulation results 3.1 Overview and consistency with international stylized facts The dashboards in Figures 6–8 present the dynamics of several important variables in a typical simulation executed under the 2 (left column), 6 (center), and 10 (right) country scenarios, while Table 1 provides some synthetic statistics on the 25 simulation runs performed under the three baseline scenarios. Table 1. Average simulated and empirical macro-variables in percentage values. Simulated averages and standard error from 25 Monte Carlo simulation runs. Empirical averages of Euro Area countries Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    Table 1. Average simulated and empirical macro-variables in percentage values. Simulated averages and standard error from 25 Monte Carlo simulation runs. Empirical averages of Euro Area countries Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    As we mentioned in the introduction, we tried to identify a baseline configuration of our artificial economy capable of yielding realistic and relatively stable dynamics. The adjective “realistic” indicates a specification in which the properties of key economic variables—real GDP and productivity growth rates, inflation rates, unemployment rates, debt-to-GDP ratios, exports and imports, etc.—are economically reasonable and broadly comparable to historical data for advanced countries, in particular for the Euro Area which constitutes the natural point of reference for our work.16Table 1 highlights that our artificial Monetary Union is broadly comparable to the EMU (last column) under many respects. Admittedly, the dimension of private debt over GDP is substantially lower than its empirical counterpart, whereas average public debt is relatively higher. The first discrepancy can be partly explained by the fact that no other form of credit than to firms is modeled. The greater debt-GDP ratio may be instead related to the initialization procedure, which requires the government to trigger the development process through its initial public expenditure: at the beginning public debt considerably increases, since taxes are lower than public spending given the low number of firms and banks in business. However, the average debt-GDP ratio is not unreasonably high compared to historical experience of many countries—in particular in the two scenarios with more countries—and remains quite stable after the initial transition phase. Finally, the dimension of imports and exports relative to GDP in the two-country case looks lower than its empirical counterpart. This is likely to be caused by the smaller dimension of the international market for tradable goods in this scenario, where domestic firms account for a significant share of the common market. On the contrary, in the other two cases, the higher number of countries implies that domestic tradable firms account for a smaller portion of the total number of firms producing for the common tradable goods market, so that the demand by domestic consumers is more likely to be addressed to foreign firms.17 The panel in Figure 6 displays that the model generates exponential growth of real GDP, coupled with an exponential increase in labor productivity. However, the process of development does not unfold in a smooth way, but rather through a succession of economic cycles. Figures in Panel 2 (Figure 2) display the cyclical component of main economic aggregates, each one normalized by the trend component to allow a comparison on the same scale: in accordance with the empirical evidence, the volatility of consumption is slightly below the volatility of real GDP, whereas exports, imports, and unemployment are significantly more volatile than real GDP. Figures 3 and 4 show the artificial cross-correlations with the cyclical component of real GDP of the cyclical components of consumption, exports, imports, public expenditure, public expenditure on GDP, and unemployment. The left, center, or right position of the peak in each correlation figure indicates whether the variable is lagged, coincident, or leading with respect to GDP. The darker bars indicate correlations significantly different from 0. In accordance with the empirical stylized facts on the co-movements of main aggregates within and across countries (Uribe and Schmitt-Grohé, 2017), consumption, exports, and imports are positively correlated with GDP, with the only exception of imports in the two-country case; real public expenditure is pro-cyclical in levels, whereas public expenditure over GDP is strongly countercyclical; finally, unemployment is strongly countercyclical. The pro-cyclical character of consumption, exports, and public expenditure is not surprising, since the former two are direct components of real GDP, while public expenditure increases the available income of households, and thus aggregate demand and real GDP. Similarly, the positive correlation of imports is not surprising because increments of real GDP generally increase the demand for both nontradables and tradables, and thus imports. However, in the two-country case, the fact that domestic firms account for a significant share of the market for tradables tend to dampen the impact of real GDP increments on imports. This possibly explains the nonsignificance of the correlation of imports with current output in this case. Finally, the positive correlation of G and the countercyclical character of G/GDP imply that government expenditure increases with GDP, but less than proportionally. Figure 3. View largeDownload slide Simulated data average cross correlations of aggregate consumption (c), export (x), and import (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figure 3. View largeDownload slide Simulated data average cross correlations of aggregate consumption (c), export (x), and import (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figure 4. View largeDownload slide Simulated data average cross correlations of public expenditure (g), public expenditure over GDP (g/y), and unemployment (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figure 4. View largeDownload slide Simulated data average cross correlations of public expenditure (g), public expenditure over GDP (g/y), and unemployment (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figures in Panel 6 and 7 also highlight that our results are consistent with other two important empirical regularities observed in international trade data: inflation in nontradable goods is higher than in tradables, whereas labor productivity growth in nontradables is lower than in tradables (De Gregorio et al., 1993; Bernard and Jensen, 1999; Bernard et al., 2003, 2007). In our model, prices in the tradable sector tend to be lower first of all as a consequence of the greater competitive pressure faced by tradable firms, which are compelled to face more competitors on the international common market for tradables. For the same reason, international spillovers in the tradable sector tend to be greater than national spillovers in nontradable industries, providing a possible explanation for the enhanced productivity dynamics in the tradable sector. In turn, since higher productivity levels imply lower unit costs of production in the tradable sector, this concurs to keep prices of tradables lower. Figure 5 provides the log-log plot of firm and bank size distribution with the log-normal (green line) and Pareto (red) fits of the upper tails: firms and banks significantly differ with respect to their size, and their size distributions is right skewed and display excess kurtosis and fat tails under all scenarios. Tests based on Clauset et al. (2009) show that both the power law and log-normal hypothesis on the shape of the right tails are plausible, though the former is to be preferred according to Vuong’s likelihood ratio test, in line with the empirical evidence in the wake of Gibrat’s contribution (Stanley et al., 1995).18 Figure 5. View largeDownload slide Firm and Bank size distributions. The figure also displays the log-normal (green) and power law (red) fits of the right tails of the sample distributions. Colour figures available in the online version. Figure 5. View largeDownload slide Firm and Bank size distributions. The figure also displays the log-normal (green) and power law (red) fits of the right tails of the sample distributions. Colour figures available in the online version. Finally, figures in Panel 6 also show that in all scenarios countries may significantly and persistently diverge in terms of real GDP and productivity levels, as observed in reality. In these simulations, some countries achieve a sufficiently high competitive advantage thanks to R&D and tend to keep it over the simulation, whereas some others are affected by persistent technological gaps, though the magnitude of these differences may widen or shrink over the simulation time span. The dynamics of technological change in different countries is crucial to understand the evolution of the system. Figures 6–8 allow to get a first general idea about the interactions between technological change and several other important processes undergoing in the real and financial sphere of the economy. Figure 6. View largeDownload slide Country dynamics of real GDP (y) and average productivity in the tradable and nontradable sectors. Colour figures available in the online version. Figure 6. View largeDownload slide Country dynamics of real GDP (y) and average productivity in the tradable and nontradable sectors. Colour figures available in the online version. Figure 7. View largeDownload slide Country dynamics of unemployment and average price in the tradable and nontradable sectors. Figure 7. View largeDownload slide Country dynamics of unemployment and average price in the tradable and nontradable sectors. Figure 8. View largeDownload slide Country dynamics of debt over GDP (Debt/GDP), Current Account over GDP (CA/Y), and Net Foreign Asset Position over GDP. Colour figures available in the online version. Figure 8. View largeDownload slide Country dynamics of debt over GDP (Debt/GDP), Current Account over GDP (CA/Y), and Net Foreign Asset Position over GDP. Colour figures available in the online version. In the firms’ perspective, an increase in productivity allows firms to produce more goods at a lower cost of production, thereby improving their competitiveness on the national (nontradable) or international (tradable) markets: more productive firms can sell their output at a lower price without eroding their profit margin. The two bottom lines of Panel 7 show that countries characterized by higher levels of productivity tend to have also lower price levels. Therefore, more productive firms are able to attract more consumers, increasing sales and revenues. The consequent increase of their sales expectations induces an output expansion, possibly to an extent which increases their demand for labor, despite the labor-saving effect of technological change. As long as their increasing output finds an outlet on the market, they make higher profits, they are relatively less financially constrained, and they invest more on R&D. Higher R&D investments in turn enhance further their probability of achieving innovations, thereby widening the productivity advantage over competitors. This is the multiplicative engine which tends to foster firms’ productivity differentiation. However, this process can be hindered by several counterforces: first, rising sales can induce firms to increase prices to an excessive extent eroding their price competitiveness; second, sectoral spillovers can allow firms suffering a productivity gap to catch up; finally, the economic conjuncture plays an important role in determining whether the advantages of an innovation are quickly reabsorbed or translate into a durable competitive advantage. When demand is growing firms suffering a productivity gap have greater chances to find an outlet for their production despite their competitive disadvantage thus keeping enough resources to invest in R&D, possibly catching up with leading firms. On the contrary, economic downturns tend to exacerbate the Schumpeterian selection mechanism of firms, since less productive firms tend to suffer more from the fall in aggregate demand, having less room to adapt prices. While their need for external finance to fund production and R&D investment is likely to increase, the fall in revenues, negatively impacting on their net worth, reduces banks’ willingness to satisfy their requests. Eventually, less productive firms reduce or even abstain from investing in R&D, thus becoming doomed to failure. However, also leading firms may go into troubles during downturns if, for example, they have excessively increased their production and borrowed too much during the previous upward phase of the cycle. In the countries’ perspective, an increase in productivity obviously tends to exert direct labor-saving effects for given values of output. However, unemployment may remain stable, or even decrease if aggregate demand grows, inducing firms to expand their production. On the domestic markets for nontradables more innovative and productive firms tend to increase their market share at the expense of less productive competitors. Much of the net effect of technological change on total labor demand thus depends on whether the positive effect caused by the rising output of more productive firms, or the negative effect due to the shrinking output of less productive ones, is dominating. If we consider the common market for tradable goods on the contrary, innovations achieved by a country are more likely to exert a positive effect on its employment levels. Indeed, higher productivity levels translate into greater international competitiveness, possibly enhancing exports and the GDP of the country. The raise of output thus tends to sterilize the labor-saving effect of technological change, preventing unemployment from rising and wages from declining (or slowing down). As a consequence, also demand for nontradables can possibly grow, leading to further improvements of employment and output dynamics. Achieving a competitive advantage thanks to innovation can trigger an expansion phase in the country. The enhanced GDP dynamics, in turn, may increase tax revenues and reduce public deficits, so that the government may consider to cut tax rates and increase public spending, further boosting GDP growth. In addition, since default rates tend to be lower and profit margins greater and more stable, households’ investment in equity increases: new firms are created leading to further increases of employment and output, though their entrance may also exacerbate the competitive pressure on incumbent firms in the following periods, in particular on less productive ones. Finally, as long as productivity, wages, and prices are such to give the country a competitive advantage, the ensuing current account surplus causes a net inflow of financial resources, improving the net lending position of the country. This explains how differentiation between countries endogenously arises in the model. However, these tendencies may be dampened and partially reverted by several counterforces. First, rising output in countries experiencing a competitive advantage may counteract the reduction of unit costs of production in the measure in which firms, in response to the increase of their sales, decide to rise prices.19 In addition, if the rise of output is such to reduce unemployment, workers’ bargaining power increases, pushing up wages. On the one hand, this tends to increase aggregate demand and output levels further. However, if the faster growth of wages is not offset by further increases in productivity levels, unit costs raise as well. This either narrows firms’ profit margins or lead to an increase of prices, eroding the country price competitiveness on the tradable market. Finally, the rise of households’ disposable income in countries having a competitive advantage increases imports of tradable goods from abroad, partly compensating for the higher exports. This not only impacts directly on the country Current Account but also indirectly on the country intenrational competitiveness, since imports from foreign firms will possibly allow them to fund more investment in R&D. Since the long-run dynamics of the model emerges from the chain of successive short-run cycles, each one building on the previous one, the long-term system dynamics and the observed degree of convergence or divergence across countries can be seen as the path-dependent output of these conflicting forces. Figures 6 and 7 show that in the long run, countries with higher productivity levels tend to be characterized by higher real GDP and lower inflation, whereas unemployment levels are quite similar. Plots also show that there is a tight relationship between productivity and GDP levels in the long run. On the contrary, even though more productive countries tend to have, on average, also more solid public finance, countries with higher Debt/GDP ratios can sometimes outperform countries with lower public debt levels. Similarly, though countries benefiting from a productivity advantage tend on average to have a better international position, this does not necessarily imply that their Current Account will always be in surplus nor that they will always be net lenders (bottom line in Panel 8). Finally, there is a clear inverse relationship between the public debt and the net foreign asset position of countries (top and bottom lines of Panel 8, respectively). In Section 3.2 we will discuss in details the relationship between fiscal and trade balances. 3.2 Policy experiments on fiscal targets To assess the impact of a change in the fiscal targets that governments are committed to comply, we run six experiments assuming a change in the value of dmax, which was originally set at 0.03, occurring at period 500. More precisely, we test the following values of the parameter: dmax={0.0,0.01,0.02,0.025,0.035,0.04}. The first four scenarios, implying a fiscal policy contraction, correspond to the “austerity” case, whereas the other two correspond to a fiscal expansion. In particular, the first scenario corresponds to the “balanced budget” provision of the Fiscal Compact. It must be stressed that, since actual public deficits can be computed only after public spending and tax payments have taken place, actual deficits may be temporarily higher than dmax, so that this latter should be interpreted as a fiscal target rather than as an inviolable upper bound. In addition, given governments’ behavioral rules specified in Section 2.1.5, tax rates and public spending are progressively revised in an adaptive way. The panel of Figures 9 displays the impact of the fiscal regime switch on a selection of key macroeconomic aggregates in the 2 (left), 6 (center) and 10-country (right) cases. Values plotted are the Monte Carlo means of the across-country averages under the baseline case (black line) and the other six policy scenarios. Dotted lines are the across-runs standard deviations of mean values. The plots in the first two lines show that all scenarios characterized by a permanent fiscal restriction generate a significant drop of both real GDP and real productivity levels, associated with remarkable increases of unemployment rates. Expansionary policies instead tend to increase both real GDP and real productivity levels, though the improvement in the two-country case is almost negligible. Furthermore, permanent expansionary changes in fiscal targets always allow to reduce unemployment. Figure 9. View largeDownload slide Effects of different fiscal targets on real GDP (y), average productivity, unemployment, debt over GDP (Debt/Y), and average prices (P). The black line corresponds to the simulation baseline specification with dmax=0.03, the red one to dmax=0.025, the green to dmax=0.02, the blue to dmax=0.01, the light blue to dmax=0.0, the violet to dmax=0.035, and the yellow to dmax=0.04. The policy change occurs at period 500. Lines are average values from 25 Monte Carlo runs. Colour figures available in the online version. Figure 9. View largeDownload slide Effects of different fiscal targets on real GDP (y), average productivity, unemployment, debt over GDP (Debt/Y), and average prices (P). The black line corresponds to the simulation baseline specification with dmax=0.03, the red one to dmax=0.025, the green to dmax=0.02, the blue to dmax=0.01, the light blue to dmax=0.0, the violet to dmax=0.035, and the yellow to dmax=0.04. The policy change occurs at period 500. Lines are average values from 25 Monte Carlo runs. Colour figures available in the online version. If we look at the dynamics of nominal variables, there is a tight positive relationship between fiscal targets and the dynamics of prices: fiscal contractions are associated to very low levels of inflation, which is almost 0 in the two most restrictive cases. Vice-versa, a permanent increase of dmax generates higher levels of inflation. Finally the dynamics of the debt-GDP ratio across scenarios is particularly interesting, revealing a nonlinear relationship with fiscal targets. While increases of dmax seem to be connected with greater public debt ratios in the two expansionary cases analyzed, the impact of restriction policies is less trivial. Results highlight that in the two-country case fiscal contractions are able to effectively reduce the burden of public debt both in the medium and long run: average public debt-to-GDP ratios are indeed lower in all the austerity scenarios considered. However, strong fiscal contractions tend to be more effective in the short–medium run, but less effective in the long run compared to milder contractions, the levels of debt/GDP ending up to be lower in the dmax={0.025,0.02} cases than in the dmax={0.01,0.0} scenarios. In fact, in the long run the depressing effect on GDP levels partially compensates for the reduction of nominal public debt, so that the efficacy of strong and permanent reductions of fiscal targets in abating the debt burden is significantly dampened. This effect is exacerbated in the 6 and 10-country cases: the plots referring to these scenarios show that all austerity policies are effective only in the short–medium run, while being self-defeating in the long run. Debt-GDP ratios end up to be higher in these scenarios than in the baseline: in the most restrictive cases, debt-GDP ratios end up to be comparable to those obtained in the first expansionary case. An initial raise in taxes (or a cut in spending), possibly occurring in more than one country as a consequence of the tighter fiscal targets, reduces the disposable income available for consumption, triggering a reduction in aggregate demand for domestic and foreign goods. The reduction of dmax, however, exerts another important effect: during recessions, when deficit-GDP ratios tend to raise as a consequence of the fall in GDP, tax rates increase, and public spending cuts become more likely than in the baseline scenario, thereby exacerbating the ongoing recessionary dynamics. As a consequence, an initial increase of unemployment and default rates is now more likely to lead to an increase of tax rates, which tends to further depress demand, employment, wages, and prices. This in turn increases default rates. If the fall of taxable income and profits is very pronounced, the ensuing drop of tax revenues will likely increase deficit-GDP ratios further even if tax rates are raising and public spending is constant or decreasing. Fiscal policy becomes very pro-cyclical during recessions, since an initial drop of GDP induces further fiscal contractions, which eventually depress the economy further. However, a point will be reached when the slowdown of inflation (or deflation in extreme cases) caused by the recession will be such to stop the fall of workers’ real disposable income, allowing firms to unload the stock of inventories accumulated during the recession, thereby improving their expectations, and making a recovery possible. Wages and prices adjustments have two other important consequences: first, they reduce unit costs of production. This gives tradable firms more room to maneuver in reducing prices in response to the drop of their sales. Second, as a country disposable income declines, also its imports start falling. Even though these two adjustment processes can contribute to revert the recession in a single country, they can be effective only in the measure in which they reduce the country’s demand for tradables and increase domestic firms’ market share on the tradable market, at the expense of other countries. In other words these two latter effects can help to trigger a recovery in a country only in the measure in which they contribute to jeopardize other countries. Obviously the dimension of this effect is narrow when international trade is small compared to domestic markets, as it happens in the two-country case, or if only one country finds itself in the situation depicted above. But when instead the size of the tradable market is greater and all countries follow a fiscal rule which tends to be more pro-cyclical during recession, this contagion channel becomes prominent, amplifying the recessionary effects of fiscal contractions through negative feedbacks between member countries, as observed in the 6 and 10-country scenarios of Panel 9. All in all, the stricter fiscal goal does not only trigger a contraction of GDP but also tends to increase the instability of the system amplifying fluctuations of real GDP, unemployment, and nominal variables both in the short and long run, as one can observe in Figure 10. In these cases austerity tends to be self-defeating. On the contrary, fiscal expansions tend to reduce the volatility of main economic aggregates, so that the process of development proceeds along a smoother trajectory. Figure 10. View largeDownload slide Country real GDP dynamics under different fiscal target scenarios: austerity dmax=0.02, baseline dmax=0.03, and expansion dmax=0.04. The policy change occurs at period 500. Top line: two-country case. Center line: six-country case. Bottom line: 10-country case. Colour figures available in the online version. Figure 10. View largeDownload slide Country real GDP dynamics under different fiscal target scenarios: austerity dmax=0.02, baseline dmax=0.03, and expansion dmax=0.04. The policy change occurs at period 500. Top line: two-country case. Center line: six-country case. Bottom line: 10-country case. Colour figures available in the online version. We also noticed that, when the Monetary Union is bigger, encompassing a higher number of countries, the regime switch does not impact on them in the same way. To perform such an analysis we divide countries into two groups: countries with a level of real GDP higher than the median level and countries with a lower real GDP at the period when the permanent policy change occurs (i.e., period 500). For space and explanatory reasons we present the case of the fiscal contraction with dmax=0.02 and the case of a fiscal expansion with dmax=0.04. The effects discussed for these two scenarios are reinforced under more extreme cases. Even though real GDP and productivity differentials do not seem to be significantly different across scenarios, at least on average, the increase of debt-to-GDP levels observed in the austerity case is largely related to a remarkable increase of the average debt-GDP ratio in poorer-less productive countries, whereas it remains almost stable in richer ones. In low-income countries, the increase of the public debt burden is accompanied by a deterioration of their net foreign asset position, as shown in Figures 12 and 13. Indeed, as discussed above higher-income levels are associated with higher average productivity levels. Although wages may vary in a way that tends to mitigate unit costs ( w/φ) differences between tradable firms of high- and low-income countries, their dynamics is largely affected also by what happens in domestic markets. As a consequence, Figures 11–13 display that under all cases, unit costs of production tend to be higher in less productive countries than in more productive ones. Therefore, tradable firms in poorer countries have lower profit margins and less room to manouvre when setting prices compared to their competitors in rich countries. Less productive tradable firms are thus less equipped to face recessions, when firms tend to lower prices to recover sales. Default rates turn out to be higher in less productive countries where tradable firms either see their profit margin rapidly evaporating, when forced to reduce prices, or experience a dramatic drop of sales if their price has already hit the unit cost lower bound. In this latter case, firms must wait for wages to fall due to rising unemployment before being able to recover some competitiveness, thereby being more exposed to defaults. Figure 11. View largeDownload slide Two-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 11. View largeDownload slide Two-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 12. View largeDownload slide Six-country case —high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average Productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 12. View largeDownload slide Six-country case —high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average Productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 13. View largeDownload slide Ten-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 13. View largeDownload slide Ten-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. In the recessionary and volatile context triggered by the austerity turn in fiscal policy, less productive tradable firms will thus be more fragile and less flexible in adjusting prices. This implies that poorer-less productive country has more difficulties and need more time to adapt during recessions, experiencing on average deeper and more frequent current account deficits compared to the baseline scenario. These deficits then translate into a reduction of tax revenues, culminating in higher public deficits and explaining the raise of debt-GDP levels, which is associated with the worsening of the net foreign asset position in poor countries relative to richer ones. 4. Conclusions The article presents an Agent-Based Stock Flow Consistent Multi-Country model of a Monetary Union. Besides the possibility of running simulations with a variable number of countries, which is per se a major novelty in the AB macroeconomic literature, the model displays several other important features. In particular, we adopt an SFC framework (Godley and Lavoie, 2007) on the top of the AB structure, along the line traced by Caiani et al. (2016, 2018), to ensure the accounting consistency of the model and to provide a fully integrated representation of the real and financial sides of the economic system depicted. In this respect, we also present an innovative procedure to initialize stocks and flows in an SFC manner, where initial injections of money through public spending allow households to create firms and banks, thus letting the economy to emerge from 0 in a “generative” perspective. The model features endogenous technological change in an evolutionary flavor, following the long-lasting tradition on the wake of the seminal contribution of Nelson and Winter (1977, 1982). Innovation dynamics plays a crucial role, allowing firms and countries to differentiate from each other, and concurring with aggregate demand and international trade to steer the economic dynamics in the short and long run. Finally, the endogenization of the entry–exit process of firms, depending on households’ equity investment decisions, is another important add-on to the current AB macroeconomic literature. After a preliminary validation, the model was employed to assess the effect of a change in the fiscal regime of member countries, modeled as a permanent variation of the maximum deficit-to-GDP ratio allowed. Each policy experiment was performed under three scenarios, differentiated for the number of countries belonging to the Monetary Union. In this way, we were able to asses how the dimension of the Monetary Union, and in particular the dimension of the common market for tradables, affects the efficacy of the policies tested. Policy experiments show that fiscal expansions tend to improve the dynamics of real GDP, labor productivity, and employment, though being generally associated to higher levels of public debt and higher levels of inflation. On the contrary, permanent fiscal contractions have strong recessionary effects which attenuate their efficacy in reducing public debt-GDP ratios in the long run. When the Monetary Union encompasses a higher number of countries, and international trade between member countries is more prominent, permanent fiscal contractions are self-defeating in the medium and long run, as public debt ends up being higher than in the baseline. Public debt increases in poorer and less productive countries mirrored by a corresponding deterioration of their net foreign asset position, suggesting that permanent fiscal contraction exert an asymmetric impact on more and less productive countries. Finally, fiscal contractions tend to exacerbate the volatility of main economic aggregates both in the short and long run, whereas fiscal expansions tend to dampen it. Our assessment of the effects of different fiscal policies in the context of a Monetary Union characterized by strong trade linkages is thus generally consistent with the conclusions of De Grauwe and Ji (2013), Hein et al. (2011),Semieniuk et al. (2011), and Perez-Caldentey and Vernengo (2012), and with results obtained by Dosi et al. (2013, 2015), and Teglio et al. (2015) using similar modeling approaches: with respect to these works our results distinguish themselves for the asymmetric impact of fiscal restrictions on high and low productivity countries, and for the scale-dependent efficacy of fiscal austerity in the long run, depending on the size of the common market for tradables. Our analysis is susceptible of being enlarged, deepened, and refined under many respects. First, while the present work focused on the impact of permanent policy changes in the fiscal targets of all member countries, one may wonder what would be the effects of fiscal consolidations implemented through temporary fiscal interventions, or through state-contingent policies, or yet through asymmetric policies in different countries. In addition, the interaction between monetary and fiscal policies should be addressed as well. Finally, whereas in the current article we let heterogeneity between firms and countries emerge endogenously starting from symmetric initial conditions, the model can be calibrated using more realistic initial conditions where countries are differentiated under several important respects such as their dimension, productivity level, income, and public and private debt levels. On the modeling side, the framework proposed can be largely improved on the financial side which at this stage presents simplified matching procedures on the international credit and bond markets, and totally neglects the role of foreign direct investments. As a consequence, most of the dynamics of international financial flows across countries is determined by international trade (i.e., by the trade balance), whereas in reality autonomous international financial transactions can be of topical importance as well. Finally, given the crucial role played in the model by international trade and unit costs asymmetries between firms and countries, also the possible interaction between fiscal policies and labor market regulation should be explored. Funding The research leading to these results has received funding from the European Union, Seventh Framework Programme FP7, under grant agreement FinMaP numver 612955. Footnotes 1 Under the first respect, unconventional and unprecedented forms of monetary policy, such as the Quantitative Easing, were adopted. As for the latter, ECB President Draghi’s famous claim in the apex of the sovereign debt crisis to do “whatever it takes to save the Euro” then culminated in the launch of European Financial Stability Facility (EFSF) and the European Financial Stabilisation Mechanism (EFSM), then replaced in 2012 by the European Stability Mechanism (ESM). 2 Although moving from a different theoretical perspective, also Holinski et al. (2012) stressed the potential risks associated to persistent trade and financial imbalances between the North and South of Europe, advocating better coordinated policies to prevent the emergence of unsustainable imbalances in the Euro area. 3 This specification of the consumption function ensures that the level of desired consumption chosen by households is always financially feasible, given the amount of deposits at their disposal. 4 Please notice that cT is also the exogenous probability that a newly created firm will be a tradable, as later explained in Section 2.1.6. 5 The term liquidity preference is employed here to indicate the share or wealth that households desire to hold in the form of liquid assets, that is, deposits. 6 Indeed, for simplicity reasons, we prevent households from liquidating their participations in firms and banks. 7 As explained before, financial resources dedicated to R&D are distributed across employees, summing up to their wages. 8 This correction for the sector average productivity is required to prevent Prsuccessit from increasing with the higher levels of productivity Φt achieved, as the simulation time goes by: indeed, higher levels of labor productivity allow to produce increasing quantities of goods with the same amount of labor. A stable or increasing pattern of real output, and a non-exploding pattern of unemployment can then be achieved if the purchasing power of households grows faster than prices, allowing the greater productive capacity to find an outlet on the market. Since most of this purchasing power is represented by wages paid by firms, and given that innovative efforts are proportional to the expected wage bill of firms, R&Dit/Pt will generally increase with Φt. This asks to correct real investment in innovation for Φt, so to avoid an unreasonable and unjustified continuous rise of the probability of success Prsuccessit. 9 Formally, LitD>0 if pit(LitDwit)φit≥ritLitD. 10 Though very common in the AB literature, we are aware that this represents a strong simplification, as thoroughly explained in Caiani et al. (2016). To avoid excessive complications, however, in this first application of the multi-country model we decided to keep the financial side relatively simple. 11 These latter are evaluated at their unit cost of production, in accordance with accounting standards: ΔINVit=(invit−invi,t−1)witφit. 12 In this way Central Banks inject in the system the initial amount of legal currency that, saved and invested by households in the creation of banks and firms, will eventually become banks’ initial stock of consolidated reserves. In the Monetary Union depicted in this article total banks’ consolidated reserves should coincide with total Central Banks’ holdings of countries’ public debt for accounting reasons, whereas at the country level the amount of reserves held by domestic commercial banks also depends on the international flows of deposits arising, for example, from international trade. 13 Admittedly, public expenditure and the tax rate on income and profits are kept constant in the very first periods of the simulation till the first firm is created, since the fiscal scheme proposed in equations (41)–(44) can be employed only when at least one firm is present; otherwise no employment, output, income, and profit are generated. This takes just one period in the setup employed in the article. 14 Given that this stochastic rule can operate only when some organization is already present, the first tradable and nontradable firms to enter the market have an exogenous initial net worth equal to A0. In addition, to ensure that banks will be big enough to provide credit to firms, whose number is by far higher, the initial equity of banks has a lower bound defined as a multiple σ of the country’s median dimension of firms. 15 The same occurs when households’ individual investment does not exceed the minimum participation level. 16 This objective was pursued through a combination of empirically grounded calibration and tentative investigation of the parameter space, whereas we did not employ recursive calibration or estimation methods aiming to minimize the distance between the properties (e.g., moments) of the artificial and real time series. 17 Similarly, production of tradable goods by domestic firms is more likely to be purchased by foreign consumers, since the domestic demand for tradable goods accounts for a smaller share of the total demand coming from the Monetary Union as a whole. 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Parameters K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      View Large Table A1. Parameters K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      View Large © The Author(s) 2018. Published by Oxford University Press on behalf of Associazione ICC. All rights reserved. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Industrial and Corporate Change Oxford University Press

The effects of fiscal targets in a monetary union: a Multi-Country Agent-Based Stock Flow Consistent model

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Oxford University Press
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© The Author(s) 2018. Published by Oxford University Press on behalf of Associazione ICC. All rights reserved.
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0960-6491
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1464-3650
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10.1093/icc/dty016
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Abstract

Abstract We present an Agent Based-Stock Flow Consistent Multi-Country model of a Monetary Union to analyze the impact of a change in the fiscal regime of member countries, modeled as a permanent change in the deficit-to-gross domestic product (GDP) target that governments are committed to comply. Simulations are performed under three scenarios, differentiated by the number of countries considered (2, 6, 10). The parametric configuration employed yields economically reasonable values for the dynamics and relative dimension of key variables, broadly comparable with historical data and available stylized facts. Our policy experiments show that fiscal expansions generally allow to improve the dynamics of real GDP, labor productivity, and employment, though being generally associated with higher levels of public debt. Conversely, permanent fiscal contractions always exert strong recessionary effects, exacerbate real GDP volatility, and tend to be self-defeating in the long run. In scenarios where the Monetary Union includes a greater number of countries and the common market is bigger, fiscal austerity raises—rather than decreasing—average public debt-to-GDP ratios. We show that this is mainly related to a raise of debt-to-GDP in poorer and less productive countries mirrored by a reduction of their net foreign asset position. 1. Introduction The article presents an Agent Based-Stock Flow Consistent (AB-SFC) Multi-Country model to analyze the impact of different fiscal regimes on the long-term economic dynamics of a Monetary Union broadly comparable to the European Economic and Monetary Union (EMU). The computational framework proposed is at once simple in its behavioral assumptions and sophisticated in its interaction structure. Agents’ behaviors are based on relatively simple adaptive heuristics. We consider a pure labor economy where there is no capital accumulation and only final goods are produced. Money is endogenous to the system, but only credit to firms is modeled. Finally, public expenditure takes the form of a lump-sum monetary transfer to households. Yet the model is sophisticated in several other respects: first, its dynamics endogenously emerges from the decisions undertaken by many heterogeneous agents, interacting in a decentralized way on several types of markets (i.e., labor, tradable and nontradable consumption goods, credit, deposit, and bond markets). Furthermore, the model accounts for international flows of real and financial assets, arising from trade and credit flows between member countries. Consumers’ preferences and firms’ products are differentiated using Salop’s (1979) circular specification of Hotelling’s (1929) locational model. Technological change and sectoral technological spillovers, affecting the evolution of labor productivity across firms and countries, are modeled as an endogenous process driven by firms’ investment in R&D. In addition to this, the model displays several important add-ons to the current AB macro-modeling literature: to our knowledge, this is one of the first, if not the very first, fully fledged multi-country AB macroeconomic model presented in the literature. Indeed, models developed within this stream of research either displayed a closed-economy or, at most, a two-country economy. Our model instead can be initialized with a variable number of countries: for the present work experiments have been performed with 2, 6, and 10 countries. Second, the model aims at integrating the real and financial spheres of the economy along the line traced by Caiani et al. (2016, 2018); Deissenberg et al. (2008), thanks to the adoption of the SFC framework which provides a rigorous and exhaustive accounting of financial flows and stocks (Godley, 1997; Godley and Lavoie, 2007). Third, instead of assuming that the number of firms is fixed and that defaulted firms (or banks) are immediately replaced by an equal number of new entrants, we endogenize the entry–exit process of firms and banks by introducing a stylized mechanism to model households’ equity investment. The creation of new businesses thus depends on households’ financial wealth portfolio allocation between equity participations in new firms (banks) and deposit accounts at banks, based on their relative rates of return and their perceived riskiness. Finally, we propose a simple “generative” procedure to initialize the model in an SFC manner, inspired by the “SIM model” presented by Godley and Lavoie (2007). For the sake of analyzing the impact on our artificial Monetary Union of a permanent change in countries’ fiscal policy, we first combined the empirical information at our disposal with a preliminary investigation of the parameter space so to identify a baseline parametric configuration yielding realistic and relatively stable systemic dynamics. Then, we introduced a fiscal policy regime switch occurring at period 500, modeled as a variation of the common fiscal target for countries’ public deficit. Results were first analyzed looking at variations induced by the policy change in the average values and volatility of main economic aggregates, both in the short and long run. Then, we differentiated between high- and low-income countries to assess if changes in the policy regime affect richer and poorer countries in the same way, or if instead asymmetric effects arise. Results show that fiscal expansions generally tend to boost economic growth, technological change, and employment, at the cost of higher debt-gross domestic product (GDP) ratios. Instead, permanent reductions of fiscal targets exert significant depressing effects on real GDP, labor productivity dynamics, unemployment, and prices. More important, the efficacy of permanent fiscal contractions in reducing the burden of public debt seems to be limited, at least in the long run, to the two-country scenario. On the contrary, in the more realistic scenarios where the Monetary Union includes more countries and the common market is wider, fiscal contractions tend to be self-defeating in the long run increasing, rather than decreasing, average debt-GDP ratios. In these cases fiscal austerity tends to exacerbate recessions, amplifying economic fluctuations. We also show that fiscal contractions tend to impact more on the public finance of poorer and generally less productive countries causing a remarkable increase of their public debt burden, which explains much of the observed rise in the average debt-to-GDP ratios of the Union. Finally, we show that the increased public debt of less productive countries is generally associated with a deterioration of their net foreign asset position in favor of richer countries. 1.1 Euro imbalances and fiscal consolidation in the EMU: empirical and theoretical disputes The Great Recession begun in 2007 revealed the vulnerability of the EMU. The global economic turmoil displayed very peculiar traits in Europe, compared to the US case, manifesting itself not only as a real and banking crisis but also as a sovereign debt crisis. Policy interventions launched by European institutions and national governments have mainly gone in two directions: on the monetary policy side, the European Central Bank was called to play a more active role as lender of last resort, both for private banks in distress and for countries experiencing severe financing problems which threatened the financial stability of the Euro area.1 On the fiscal side, if severe fiscal contractions were the distinctive trait of Macroeconomic Adjustment Programmes undertaken by countries in distress, fiscal austerity measures have been also exacerbated in other countries under the Stability and Growth Pact and the Fiscal Compact additional provisions. This latter, in particular, has bound signatory countries to transpose into their legal order the provision of the treaty for a balanced national budget. However, the efficacy of these measures have been put seriously into question as a consequence of the deflationary spiral which invested many southern countries, of the rising imbalances between core and peripheral economies, and of the endemic fragility affecting both private credit institutions and countries’ public finance. The resurgence of the economic debate on the sustainability of the European Monetary Union project had profound implications on the political debate, and its topicality grew dramatically after the “Brexit.” Admittedly, fiscal austerity entered the scene way before the Euro Crisis. The principle of limiting as much as possible the discretion of member countries in conducting fiscal policy, by setting strict bounds to public deficits, has been at the very core of the European integration process since the Maastricht Treaty. The corollary aspiration for a completely independent Central Bank found its institutional transposition in the Treaty on the Functioning of the European Union which prohibited the ECB from buying government bonds in the primary market. Such an enduring position in favor of fiscal consolidation policies finds its theoretical roots in the traditional Neoclassical postulate that public spending would exert direct and indirect crowing out effects on private expenditure, in particular on investment. The modern refinement of this idea is the so-called “Expansionary Fiscal Contraction Hypothesis,” originally proposed by Giavazzi and Pagano (1990) and Alesina and Perotti (1995) and brought back in vogue after Reinhart and Rogoff (2010) contended the existence of a negative relationship between high levels of public debt and economic growth in advanced countries. These authors argued that discretionary fiscal expansions may undermine the solidity of public finance and of the overall financial system, eventually depressing private spending: for example, if consumers behave in a Ricardian way, they will abstain from consumption when fiscal deficits are perceived as unsustainable making future tax hikes more likely. Vice-versa, well-designed fiscal consolidations, that is, deep, persistent, and credible cuts in public expenditures, may stimulate private consumption and investment, and even improve export dynamics. The empirical ground of these claims has been harshly criticized by several authors. Herndon et al. (2014), for example, rose serious doubts on Reinhart and Rogoff’s work focusing on the alleged arbitrariness of their data sampling procedure and pointing out serious flaws—and even trivial coding mistakes—in their data elaboration. Others, as Guajardo et al. (2011), pointed out that the cyclically adjusted primary balance measures employed in the Expansionary Austerity literature do not completely remove the effects of economic cycles on the evolution of public finances, so that the positive correlation between fiscal restrictions and economic expansions would be the consequence of a biased measure of fiscal balances. Furthermore, since the causal link between fiscal balances and economic growth is likely to go in both directions, they point out that cyclically adjusted primary balance cannot be treated as an exogenous explicative variable. When a more correct estimation methodology is adopted, fiscal contractions end up to be consistently recessionary. Much of the debate on the role of fiscal stimuli has been geared around the estimation of the magnitude of fiscal multipliers. Gechert and Rannenberg (2014), in an attempt to review the ever-growing literature on “state-contingent” fiscal multipliers, provided a meta-regression analysis of fiscal multipliers from a broad set of empirical reduced-form models. Their meta-analysis found that fiscal multipliers are significantly higher during recessions than during boom phases, and that spending multipliers significantly exceed tax multipliers, so that fiscal consolidation should take place during recoveries, being instead avoided during recessions, and should be based on taxes rather than on public spending cuts. Similar results were achieved by Auerbach and Gorodnichenko (2012); Blanchard and Leigh (2013), while Ferraresi et al. (2014) found that the response of output to fiscal policy shocks is stronger and more persistent when the economy is in a “tight” credit regime. Finally, De Grauwe and Ji (2013) highlighted that government bond markets in the Eurozone, where countries lost their ability to issue debt in a currency over which they had full control, are more fragile and more susceptible to self-fulfilling liquidity crises than in stand-alone countries. This in turn has fostered a “panic-driven” austerity in the south having a self-defeating character, while failing to induce offsetting stimulus in the north. On a different level, Botta (2015) pointed out the theoretical inconsistency of the “Expansionary Fiscal Contraction Hypothesis,” going through a detailed analysis of the policy measures advocated by its supporters and showing that fiscal consolidation might have expansionary outcomes only under extreme, very specific, and uncertain conditions. Post-Keynesian scholars have opposed the view that fiscal profligacy by southern countries, paired with excessive wage growth, was the major cause of the Euro Crisis, as well as its implications that austerity and labor market deregulation were essential to restoring order. On the contrary, they traced the origin of the global crisis in the emergence of a debt-driven growth model, which resulted in a rapid increase in private debt ratios and eventually inflated a real estate bubble. These authors considered the escalation of the crisis into a sovereign debt crisis, and a depression in Southern Europe, as the outcome of the European Union’s peculiar institutional and policy setup, based on the separation of the fiscal and monetary spaces and designed to impose fiscal discipline and pro-cyclical austerity (Stockhammer et al., 2016). In particular, they insisted on the role played by the institutional framework in amplifying trade and Balance of Payment imbalances between core and peripheral European countries (Hein et al., 2011; Semieniuk et al., 2011; Perez-Caldentey and Vernengo, 2012; Zezza, 2012b).2 1.2 Euro imbalances and fiscal consolidation in the EMU: simulation approaches Besides the empirical and analytical levels, the impact of alternative fiscal regimes has been widely explored also by means of computational methods based on computer simulations. Within the DSGE literature, a vision strongly in favor of fiscal consolidation measures has been proposed by Cogan et al. (2010): building on an empirically estimated version of the Smets and Wouters’ (2007) New Keynesian model of the US economy, they argued that fiscal multipliers are significantly lower than those estimated with traditional structural macroeconomic models which do not account for forward looking rational expectations by individuals and firms, and are consequently unable to grasp the change in economic actors’ behavior in response to policy shocks. Christiano et al. (2011), on the contrary, found that fiscal multipliers can be much larger than one when the zero lower bound on the nominal interest rate binds and stressed that fiscal multipliers are significantly larger when higher spending is coupled with monetary accommodation. Fiscal stimuli were seen as potentially useful also in Corsetti et al. (2009), who showed that crowding-in effects on consumption become possible when increases in government spending are carried out under a plausible debt-stabilizing policy that links current stimulus to a subsequent period of spending restraint. Finally, Coenen et al. (2012) proposed an interesting comparison between results of the former three DSGE models developed in the academia and those obtained by seven structural models employed by major policymaking institutions. The policy experiments with seven different fiscal instruments showed that the seven models—six DSGE and a PAC—display large fiscal multipliers, and that temporary expansionary fiscal policies are most effective when accommodated by the monetary policy, whereas permanent fiscal stimuli (i.e., permanent increases in deficits) have significantly lower multipliers, possibly reducing output in the long run. Our work aims at giving a contribution to another stream of research in macroeconomic modeling. The economic debate emerged in the aftermath of the Great Recession has casted serious doubts on the theoretical and empirical foundation of DSGE models, questioning the reliability of their policy prescriptions (Trichet, 2010; Blanchard et al., 2012) and fostering a quest for alternative macroeconomic modeling tools: Agent-Based models (Delli Gatti et al., 2010), which conceive the economy as a “complex evolving system” (Esptein, 2006), have proven to be well suited to explain the endogenous nature of economic growth, the generation of business cycles, and the emergence of real and financial fragility, possibly culminating in severe recessions. This approach provides an alternative way to micro-found models (Gaffeo et al., 2008) where emergent dynamics are the result of the decentralized interaction between heterogeneous, boundedly rational, adaptive agents. Agent-Based models provide a powerful framework to test a wide variety of policy schemes. A detailed comparison between the DSGE and ABM approaches can be found in Caiani et al. (2016) and Fagiolo and Roventini (2016). As a consequence of the encouraging results within this nascent research field, in recent years AB models are blossoming. Several applications have been proposed to analyze the effects of fiscal and monetary policies and to tackle the macroeconomic imbalances affecting the EMU. For example, Dosi et al. (2013), using a refined version of Dosi et al. (2010), studied the interactions between income distribution and monetary and fiscal policies. They found that accomodative fiscal policies dampen the amplitude of business cycles, reduce the likelihood of huge crises, and may exert a positive effect on long-term growth. Vice-versa, fiscal restrictions negatively affect the economic performance. Furthermore, the positive impact of fiscal policies is greatly enhanced when the distribution of income is skewed toward profits. Dosi et al. (2015) further extended the model to analyze the effects of alternative combinations of fiscal and monetary policies, reaching the conclusion that the most appropriate policy mix to stabilize the economy requires unconstrained countercyclical fiscal policies coupled with a monetary policy targeting also employment. On the contrary, fiscal policies comparable to those proposed in the Fiscal Compact have a strong depressing impact which is exacerbated when the monetary policy targets only price stability. Similar conclusions were reached by Teglio et al. (2015), building upon Cincotti et al. (2010) and Raberto et al. (2012). Riccetti et al. (2013) proposed an AB model with decentralized matching on all the simulated markets, finding that an increase in public employment significantly stabilizes the economy at the expense of a slight increase of the deficit-to-GDP ratio, which can be almost eliminated through a modest increase of tax rates. Dawid et al. (2016a) employed a two-country extension of Deissenberg et al. (2008) as a laboratory to analyze several types of fiscal policies aiming to revert Euro imbalances. They found that policies asking core countries to share the debt-burden of peripheral countries are not effective in promoting a convergence. On the contrary, fiscal transfers in favor of households in peripheral regions do exert a positive effect. However, technology-oriented subsidies to firms, aiming to improve labor productivity in peripheral regions, are the most effective tool to improve their competitiveness. By employing the closed-economy version of the same model Harting (2015) showed that distinct fiscal policies, such as demand-oriented and supply(technology)-oriented fiscal policies may exert very different effects on the long-run economic performance of the economic system, even though they can have similar effects in reducing business cycle volatility. Our contribution also points to the so-called Stock Flow Consistent approach (Godley and Lavoie, 2007) which stems from the accounting-based modeling tradition started by Brainard and Tobin (1968) and later refined by Godley and Cripps (1983). This modeling approach aims at providing a comprehensive and fully integrated representation of the economy, including all financial transactions. At its base we find the idea that real and financial flows, and the stocks on which they impact, must always satisfy given accounting identities in a social accounting perspective. These identities ensure that there are no black holes in the representation of (real and nominal) stocks and flows, acting as a “conservation of energy principle for economic theory” (Godley and Cripps, 1983). In the recent years SFC models have been extensively employed to analyze fiscal, monetary, and macroprudential policies, in particular in the context of a Monetary Union. Adopting an SFC framework, Zezza (2012a) suggested that fiscal austerity in the presence of large public debts tends to redistribute income from taxpayers to the owners of such debt: when public debt has been financed by financial markets in foreign countries, interest payments on bonds will redistribute income to foreigners, thereby exacerbating the contractionary effect of austerity on domestic growth. Eventually, this would make the target of achieving a lower debt-to-GDP ratio unfeasible. This result suggests that, since public debt is held abroad when a country has been running a current account deficit, the primary concern of policymakers should be to introduce mechanisms for correcting, or at least financing, trade imbalances within the EMU. Duwicquet et al. (2013) presented an SFC two-country model where the southern country is suffering from an overvalued currency, while the northern country enjoys an undervalued currency, boosting its exports. The authors then test different institutional reforms at the Monetary Union level to counter these implicit transfers from the South to the North, finding that both fiscal transfers based on a federal budget and a system of eurobonds help to dampen trade imbalances. Mazier and Valdecantos (2015) extended the previous work proposing a four-country SFC model to study the effects of different exchange-rate arrangements. Among the proposed arrangements, the adoption of a double-Euro currency is shown to be potentially effective in reducing Eurozone imbalances. Though accounting-based models have found fertile soil in the Post-Keynesian tradition (see Dos Santos (2006) and Caverzasi and Godin (2015) for a literature review), in recent years they gained more and more interest also outside this community. Caiani et al. (2014a,b) for example, presented two applications of the SFC methodology to the study of Great Surges of Development in an evolutionary–Neo-Schumpeterian perspective, stressing the interdependency between innovation and finance. In 2011, the Bank of England used a similar accounting-based approach to analyze the mechanics of financial instability. Barwell and Burrows (2011) advocated the diffusion of macroeconomic approaches stressing the importance of balance sheet linkages. On a similar ground (though in a general equilibrium framework), Duca and Muellbauer (2013) revisited Tobin’s efforts to understand financial–real linkages, and proposed a modeling framework for analyzing households’ flows-off-fund and consumption in an integrated way. Finally, the Bank of England has recently presented a Stock Flow Consistent Model to perform scenario analysis on the UK economy (Burgess et al., 2016): their fiscal expansion experiment considered an increase of 10% in government spending, phased over 3 years, finding a fiscal multiplier around one. AB and SFC models may greatly benefit from a mutual integration (Deissenberg et al., 2008; Caiani et al., 2014a, 2016, 2018). In particular, the adoption of an AB-SFC framework provides a powerful tool to check the internal theoretical consistency of an AB model and an effective expedient to discipline AB practitioners (Caiani and Caverzasi, 2017). A fusion of the two approaches could help AB macroeconomic models to set themselves as a credible alternative to DSGE models (Farmer and Foley, 2009) responding to the call recently made by FED chair Jellen (Jellen, 2016) for models capable of addressing the role of agents’ heterogeneity and real–financial linkages. The rest of the article is structured as follows: the next section goes through the behavioral equations of the model and explains the logic employed to define the initial setup of our simulation experiments. Section 3.2 first checks the consistency of our results with available empirical stylized facts, and then displays and discusses the results of our policy experiments. Finally, Section 4 considers the limits of the present work and briefly sketches out future applications and refinements. 2. The model The artificial economy depicted in the model is a Monetary Union composed of K countries. Each country k is populated by the same number H of households and by an endogenously varying number of firms (Ikt) and banks (Zkt). Firms produce their output out of labor only and are differentiated between “tradable,” producing final goods to be sold on the common internationally integrated market, and “nontradable,” producing for the domestic market. The process of entry and exit of firms and banks is shaped so to avoid the emergence of excessive imbalances in the relative dimension of the manufacturing and banking sectors, and in the proportion between tradable and nontradable firms. International trade between countries gives rise to international transfers of goods, deposits, and bank reserves. Firms, when needed, can demand loans to both domestic and foreign banks. Commercial banks are allowed to purchase bonds issued by any member country. On the contrary, for simplicity reasons, we assume that there is no international labor mobility and that households invest only in domestic firms and banks. Governments collect taxes on households’ income and on profits of firms and banks. Public spending takes the form of a lump-sum monetary transfer to households. Countries are subject to the same regulatory framework being committed to not exceeding a common deficit-to-GDP threshold. For this purpose they can adaptively modify tax rates and the level of public spending. The System of Central Banks of the Monetary Union operates under the control of the Union Central Bank and includes K national Central Banks, one for each country. The Union Central Bank employs a Taylor rule to set the common discount interest rate applied on cash advances. National Central Banks accommodate commercial banks’ demand for cash advances through the marginal lending facility. Furthermore, they buy the residual amount of their country’s public debt bonds which have not been purchased by private banks. In this way they also inject reserves into the economic system (Caiani et al., 2016). The model endogenizes technological change, arising from firms’ R&D investment directed to increase the productivity of their employees, thereby reducing unit costs of production and increasing profit margins. Productivity enhancing innovations can be achieved in two ways: through direct incremental innovations, or by exploiting sectoral spillovers through imitation, which allows less productive firms to catch up with the sectoral productive standards (Dosi et al., 2010). Together with aggregate demand, technological change is the fundamental engine of long-term real growth in the model and plays a crucial role in determining firms’ and countries’ international competitiveness, thereby impacting on international trade patterns and countries’ differentiation. Finally, we follow Riccetti et al. (2015) and Caiani et al. (2016) in assuming that agents interact on all markets in a decentralized way, following specific matching protocols. The structure of our artificial economy encompasses six types of market: national “nontradable” good markets, national labor markets, national deposit markets, a common “tradable” good market, a common credit market, and a common bond market. The following two subsections describe in details agents’ behaviors and interactions. 2.1 Agents 2.1.1 Households Households are at the same time workers, equity holders, and consumers. Each worker supplies a given quantity of labor ( lS=1) in each period of the simulation to ψ randomly sampled potential employers (see Section 2.1.2). Since firms formulate their demand for labor in real terms, rather than in integer units, some workers will be part-time employed, being able to sell only a portion of their unitary labor supply. The same occurs if a firm is prevented from employing a worker at full-time by liquidity shortages. Part-time workers can return on the labor market to offer their residual labor force to the other ψ−1 potential employers. As a consequence, they may be employed in different firms at the same time, selling to each of them quantity of labor force lhit (where i is one employer out of the n employers of the household h) and receiving from each of them a different wage whit. Yet, the worker may remain unemployed, or part-time employed, if total labor actually sold to firms lht=∑i,lhit>0Iktlhit is still lower than the quantity supplied lS. Workers choose the potential employer offering the highest wage, but they do not accept vacant positions below their reservation wage wht. This latter is adaptively modified depending on the worker’s past employment situation. Workers lower their reservation wage by a stochastic amount if they were not fully employed in the last period. U[0,δ] indicates a random sample from a Uniform distribution defined between 0 and δ. If instead lS=lh,t−1, they increase their reservation wage with a positive probability Pr(wht+) which is inversely related to the aggregate rate of unemployment, as shown in equation (1). Workers’ wage claims are negatively affected by higher levels of unemployment, with the parameter υ>0 shaping the strength of this relationship: the higher υ, the lower the probability of increasing demanded wages for given levels of unemployment.   wht={wh,t−1(1+U[0,δ]), iflS−lh,t−1=0withPr(wht+)=e−υut−1wh,t−1(1−U[0,δ]), iflS−lh,t−1>0. (1) Furthermore, we assume that firms employ workers for production and R&D activities indifferently and that financial resources devoted to innovative investments ( R&Dit, see Section 2.1.2) add on to workers’ wages, being distributed across workers according to their individual contribution (lhit) to the total quantity of labor employed by the firm (lit). Investment in R&D thus generates additional wages for workers. Besides labor income households also receive interests on their deposits Dht from banks (computed at the interest rate rdt), dividends from participated firms and banks (Divht), and a tax-exempt monetary transfer ( Gkt/H) by the government of their country k. All in all, households’ gross and disposable income after taxation, indicated, respectively, by yht and yhtD, are expressed by:   yht=∑i,lhit>0Iktwhitlhit+rdtDht+Divht+∑i,lhit>0IktR Ditlhitlit, (2)  yhtD=(1−τt)yht+GktH, (3) where τt is the tax rate in the current period. Desired nominal consumption ( CitD) is a linear function of current disposable income and current wealth held in the form of deposits, with fixed marginal propensities cy and cd:   ChtD=cyyhtD+cdDht, (4) where 0<cy<1 and 0<cd<1.3 Consumers then distribute their demand between tradables ( ChtDT) and nontradables ( ChtDNT) with fixed proportions cT and 1−cT, respectively.4  ChtDT=cTChtD. (5)  ChtDNT=(1−cT)ChtD. (6) Households enter the tradable and nontradable markets in a random order. Each consumer samples ψ potential suppliers, and rank them from the most to the least preferred. The model employs a circular Hotelling’s locational specification (Salop, 1979) of consumers’ preferences and firms’ offered varieties, assuming that good varieties produced by firms’ and consumers’ preferences are randomly located on a circle (Figure 1) with unitary diameter. According to this approach, a random radian value is associated to each firm (ωi) and to each consumer (ωh). Consumers rank suppliers based on a mechanism which takes into account both the price competitiveness, expressed as the ratio between the price pit of a firm i and the sector average price Pit, and the distance dhi between the firm and the consumer. The lower the price and the distance, the higher will tend to be the position of the supplier in the consumer’s ranking. Formally, firm i will be preferred to firm j if:   1dhiβPtpit>1dhjβPtpjt, (7) where β≥0 is a parameter weighting households’ preferences for variety: the lower β, the more consumer perceive consumption goods as homogeneous, thereby giving more weight to price differences in sorting consumption alternatives. The distance between firms’ offered varieties and consumers’ preferences coincides with the length of the chord between their locations. Since the diameter of the circle is set equal to 1, this can be computed as:   dhi= sin(min[|ωh−ωi|,2π−(|ωh−ωi|)]/2). (8) Figure 1. View largeDownload slide Hotelling circle example. The point H, identified by the angle ωh, expresses the preferences of household h. The point I, associated to angle ωi, indicates the variety produced by firm i. The distance dhi between the household’s preferences and the firm’s variety is equal to the arch HI¯. Figure 1. View largeDownload slide Hotelling circle example. The point H, identified by the angle ωh, expresses the preferences of household h. The point I, associated to angle ωi, indicates the variety produced by firm i. The distance dhi between the household’s preferences and the firm’s variety is equal to the arch HI¯. Figure 2. View largeDownload slide Cyclical components of simulated times series for real output (y), consumption, export, import, and unemployment rate. Figure 2. View largeDownload slide Cyclical components of simulated times series for real output (y), consumption, export, import, and unemployment rate. Consumers first try to satisfy their demand at the preferred supplier. If supply constraints are present, consumers can turn to the second, third, fourth, etc., supplier in the ranking to exhaust their residual demand. Households hold their wealth (NWht) partly in the form of deposit accounts at commercial banks Dht, which yield a positive interest rate, and partly as participations in the equity of firms and banks Aht, yielding dividends when profits of participated firms are positive. Therefore, in every period households must choose how to allocate their financial wealth between these two types of assets. This allocation is based on an endogenously determined “liquidity preference”5lpht, depending on the risk-weighted past rates of return yielded by the two types of assets. Deposits are a risk-free asset. On the contrary, the rate of return on equity investment is weighted by its perceived riskiness, proxied by the past extinction rate of firms and banks. Indicating by Itdefault and Ztdefault, respectively, the number of firms and banks defaulting in period t, we define this latter as: Prtdefault=It−1default+Zt−1defaultIt−1+Zt−1. The liquidity preference of each household is then expressed as:   lph,t={λe−(Divh,t−1Ah,t−1(1−Prtdefault)−rdt) if Divh,t−1Ah,t−1≥rdt and Ah,t−1≥0λ if Divh,t−1Ah,t−1<rdt or Ah,t−1=0, (9) with 0<λ<1 representing the maximum liquidity preference, attained when the return on equity investment was lower than the interest rate paid on deposits, or if the household did not own any equity in the previous period. If we indicate by NWhtD=NWht−1+yhtD−ChtD households’ expected level of net worth based on their planned consumption, we can derive the desired level of equity and deposits as:   AhtD=max{Aht−1,(1−lph,t)NWhtD}, (10)  DhtD=NWhtD−(AhtD−Aht−1), (11) where AhtD−Aht−1 is the desired investment in equity, which is bound to be nonnegative.6 However, since consumption may be frustrated by supply constraints, actual consumption (Cit) may be lower than desired ( CitD), so that NWht may end up being greater than planned ( NWhtD), due to “forced” savings: Sht=yhtD−Cht. In this case deposits act as a buffer stock, absorbing the discrepancy, while investment in equity sticks to its planned level AhtD. In other words: Dht=NWht−(AhtD−Aht−1)>NWhtD. Households having a positive desired investment gather in the attempt to set up a new firm (or a new bank). Investors act as an equity fund, gathering their invested resources so to raise the funds required to start the new business. These funds must be greater than a threshold level determined in the entry procedure explained in Section 2.1.6. If the level of investment is not sufficient, no firm (bank) is created and households abstain from investing in the current period. Deposits are again the buffer stock, ending up to be higher than originally planned. Conversely, if desired investment by households is high enough, more than one firm (bank) can enter the market. Finally, in each period households choose their deposit bank randomly, since every bank offers the same interest rate rdt for simplicity reasons. 2.1.2 Firms Firms are classified into “tradables,” selling their products in the common-internationally integrated market, and “nontradables,” producing for the domestic market. Labor is the sole productive factor and is employed both for production and R&D purposes. Firms’ production plans depend on their sales expectations and the level of inventories inherited from the past. Furthermore, we assume that firms desire to hold a level of inventories invit equal to a given share θ of expected sales, as a buffer against unexpected demand swings (Steindl, 1952) and possibly to avoid frustrating customers with supply constraints (Lavoie, 1992). We indicate by qit the (real) output produced by firm i in period t, by q^it the quantities sold, by pit their selling price, by qite firm’s (real) sales expectations, and by qittot=qit+invit the total amount of goods available for sales, equal to current production plus inventories. Prices and sales expectations are revised adaptively from period to period according to the following scheme:   if  q^i,t−1≥q^i,t−1e:{q^ite=q^ite(1+U[0,δ])pit=pi,t−1(1+U[0,δ]). (12)  if  q^i,t−1<q^i,t−1e  and   qi,t−1tot>q^i,t−1:{q^ite=q^ite(1−U[0,δ])pit=pi,t−1(1−U[0,δ]). (13)  if  q^i,t−1<q^i,t−1e   and  qi,t−1tot=q^i,t−1:{q^ite=q^i,t−1epit=pit−1. (14) Equation (12) states that if past sales exceeded expectations, firms adaptively increase both sales expectations and their selling price. By increasing prices they aim to increase their profit margin. When instead past sales were below their expected value and no supply constraint was binding [equation (13)], both expectations and prices are revised downwardly. By reducing prices firms aim to make their output more attractive to consumers, thereby improving their sales performance. Finally, when firms’ past sales were below expectations due to the presence of a supply constraint [i.e., despite firms had exhausted all their available supply, see equation (14)], firms postpone any revision of prices and expectations to the next periods. Prices have a lower bound represented by unit costs of production, that is, pit≥witφit, where φit is firm’s i current level of labor productivity. The desired amount of goods to be produced for the current period is then determined as:   qitD=qite(1+θ)−invit. (15) The demand for labor can be obtained by dividing planned output for the firm’s labor productivity level: litD=qitD/φit. However, if firms have not enough funds to pay wages ( witlitD), labor demand is reduced accordingly. Firms’ labor demand can be also frustrated by other factors, for example, if the economy is already at full employment or if the salary offered is too low to cover vacant positions. Since production depends on the quantity of labor actually employed, which can differ from demanded quantities for the reasons explained above, also actual output may be lower than originally planned. The salary wit offered by firm i changes according to the difference between labor demanded li,t−1D and labor actually employed in the previous period li,t−1. If the firm was not able to cover all vacant positions, i.e., labor employed was below labor demanded, it increases the salary so to attract workers. When all vacant positions were covered, firms consider the possibility to reduce wage so to increase their profit margins. The lower the unemployment, the lower is the probability of such a revision, since reducing wages increases the risk of ending up being labor constrained.   wit={wi,t−1(1+U[0,δ]), ifli,t−1D−li,t−1>0wi,t−1(1−U[0,δ]), ifli,t−1D−li,t−1=0withPr(wit−)=1−e−υut−1. (16) Firms can increase their profit margin also by improving their productivity φit, thereby reducing unit labor costs. Labor productivity can be enhanced either through incremental innovations or by exploiting spillovers at the sectoral level through imitation, which allows less productive firms to catch up with sector production standards. Innovations and imitations can be achieved through firms’ investment in R&D. Firms invest in each period a given share of its expected wage bill in R&D, as follows:7  R&DitD=γwitlitD. (17) Actual investment R&Dit will be equal to R&DitD only if the firm does not face any financial or labor constraint; otherwise, it will be lower than desired. The amount of resources invested in R&D, in turn, determines the probabilities of enhancing firm’s productivity through either incremental innovations or sectoral spillovers (Dosi et al., 2010). These two probabilities are assumed to be equal. For firms producing tradable goods, they are defined as:   PrsuccessitT=1−e−νR&DitΦtTPtT, (18) where PtT is the average international price of tradables, and ΦtT is the average labor productivity of tradable firms in the Monetary Union. Both are calculated as a weighted average, with weights represented by firms’ market shares. Similarly, for nontradable firms:   PrsuccessitNT=1−e−νR&DitΦtNTPtNT, (19) where PtNT is the average domestic price of nontradable goods, and ΦtNT is the national average labor productivity of nontradable firms, both being weighted for firms’ market shares. Equations (18) and (19) show that the two probabilities of success are a nonlinear increasing function of the real investment on productivity-enhancing activities ( R&Dit/PtT and R&Dit/PtNT for tradable and nontradable firms), divided by the sector average level of productivity ( ΦtT and ΦtNT, respectively).8 If firms result to be successful in innovating, their firm-specific labor productivity is then increased by a stochastic amount, as described in equation (20):   φi,t+1=φit(1+U[0,δ]). (20) Firms having productive standards below the sector average (i.e., a level of productivity below the average) can also try to exploit sectoral spillovers through imitation in an attempt to catch up with leading firms. The probability of success in imitating is the same as for innovations. If successful, firms are enabled to narrow the gap with the standards of production in the sector extracting a new productivity level in a range between their current one, possibly updated according to equation (20) if they have already achieved an innovation, and the sector average. For tradable firms the new level is formally determined as:   φi,t+1=φit+U[0,(ΦtT−φit)]ifφit<ΦtT. (21) For nontradable producers:   φi,t+1=φit+U[0,(ΦtNT−φit)]ifφit<ΦtNT. (22) The new level of productivity achieved thanks to an innovation and/or an imitation is embedded in the production process starting from the following period. Firms’ production and R&D investment can be financed using both internal funds accumulated through time (Dit) and external funding in the form of loans asked to domestic and foreign banks (Lit). Following a well-established assumption in AB modeling, inspired by the “Pecking Order Theory of Finance” (Myers, 1984), firms in the model resort to external financing after internal funding possibilities have been exhausted, since the cost of external finance is usually higher due to market imperfections and information asymmetries. Accordingly, the demand for loans by firms can be expressed as:   LitD={witlitD+R&DitD−Dit, if witlitD+R&DitD>Dit0, if witlitD+R&DitD≤Dit. (23) However, given the cost of external finance the demand for loans is positive only if the expected revenues generated by employing these funds are greater than the cost of financing.9 Firms are financially constrained if the amount of credit received (Lit) is lower than demanded (see Section 2.1.3): Lit≤LitD. This happens when banks have already exhausted the total amount of loans they were willing to supply in a given period or if none of them is willing to provide credit to the firm, if it is perceived as too risky (see Section 2.1.3). Yet, firms can try to fulfill their financing needs asking credit to different banks. When financially constrained, firms prioritize production over R&D. For simplicity reasons, in this first version of the model, loans are assumed to be granted and repaid within the same period, similarly to the monetary circuit theory (Graziani, 2003).10 As for households, also firms randomly choose their deposit bank, receiving an interest rdt on the amounts deposited. Profits are then computed as the sum of revenues from sales ( pitqit), interests received on deposits held at banks ( rdtDit), and the nominal variation of inventories ΔINVit11, minus labor expenditure for production ( witlit) and R&D activities( R&Dit), and credit costs ( ritLit):   πit=pitqit+rdtDit+ΔINVit−witlit−R&Dit−ritLit. (24) If we omit the variation of inventories from equation (24), we obtain a measure of the net operating cash flows generated by the firm, which we indicate by πit*. When πit*>0, firms pay taxes ( Titπ) and distribute dividends ( Divitπ) to equity holders, expressed as a share ρ of their residual net cash inflow. Since profits are generated at the end of period t—when public spending, tax payments on income of households, and consumption have already taken place—taxes on profits generated in period t are paid in period t + 1. Accordingly, also dividends generated in period t are paid to equity holders in period t + 1.   Titπ={τtπit*, if πit*>00, if πit*≤0. (25)  Divitπ={ρ(πit*−Titπ), if πit*>00, if πit*≤0. (26) Dividends are distributed to equity holders proportionally to their participation share. Retained net profits increase firms’ net worth:   Ai,t+1=Ait+πit*−Titπ−Divitπ. (27) Since firms belong to households who originally invested in their creation, as Ai,t+1 increases also equity holders’ participations are increased accordingly. 2.1.3 Banks Banks offer demand deposit accounts to households and firms, paying an interest rdt equal to a constant fraction ζ of the discount rate rt fixed by the Central Bank of the Monetary Union. In addition, banks endogenously create means of payment by providing credit to firms. As it happens in reality, every new loan granted by a bank, which is an asset for it, is immediately balanced by the creation of a matching liability in the form of a deposit for the borrower, both being created exnihilo. This implies that banks’ credit supply is not constrained by the amount of deposits already in circulation nor by the amount of reserves they hold. However, we assume that to avoid taking excessive risks, the maximum amount of credit that banks are willing to supply in any given period is a multiple μ1 of their equity Azt: LztDS=μ1Azt. Banks receive credit applications from both domestic and foreign firms. For each loan application received, banks compute a probability Pr(Loanit) to grant it. Furthermore, banks also discriminate borrowers by applying different interest rates (rit). The probability Pr(Loanit) and the interest rate charged rit are, respectively, a decreasing and increasing function of the borrowers’ target leverage, computed as the ratio between their demand for loans ( LitD) and their net worth (Ait):   Pr(Loanit)=e−ιlLitDAit. (28)  rit=χLitDAit+rt. (29) Banks are subject to minimal reserve requirements, expressed as a share μ2 of their deposits:   RztM=μ2Dzt. (30) Reserves are held at the national Central Bank and yield a fixed interest rate rre. Whenever reserves RztM are below the minimum level, banks apply to the Central Bank lending facility, asking cash advances (LzCBt) to restore the mandated liquidity ratio. National Central Banks accommodate these requests, receiving the discount rate rt on funds lent to banks. If instead banks have reserves in excess with respect to the mandatory level, these can be invested in the purchase of bonds ( BztD) issued by any member country k, which bring an interest rate rbkt computed following equation (45). In each period of the simulation, all the bond tranches issued by governments of the Monetary Union (Section 2.1.5) are piled up and shuffled. Then, commercial banks enter the bond market in a random order and go through this pile, having a probability of purchasing each tranche which depends on the riskiness associated to the country and defined as:   Pr(bkt)=e−ιbBktYkt. (31) Each bank goes through the pile of bond tranches till it eventually exhausts its demand, or there are no tranches to be sold. Therefore banks’ profits (πzt) are equal to:   πzt=∑i,Lizt>0IktritLizt+rbtBzt+rreRzt−BDizt−rdtDzt−rtLzCBt, (32) where (BDizt) indicates “bad debt,” that is, loans not (entirely) repaid as a consequence of a borrower’s default. When profits are positive ( πzt>0), banks pay taxes ( Titπ) and distribute to equity holders a share ρ of net profits ( Divztπ). As for firms, dividends are distributed among investors proportionally to the share of the bank’s equity they own.   Tztπ={τtπzt, if πzt>00, if πzt≤0. (33)  Divztπ={ρ(πzt−Tztπ), if πzt>00, if πzt≤0. (34) Retained profits after taxes then increase banks’ net worth:   Az,t+1=Azt+πzt−Tztπ−Divztπ. (35) As Az,t+1 varies, also households’ participation in the bank, and thus households’ net worth, is revised accordingly. 2.1.4 Central Banks The Central Bank of the Monetary Union operates through the System of Central Banks which it heads. This is composed by national Central Banks in charge of enforcing the Union Central Bank policies at the country (indexed by k) level. National Central Banks hold reserves of commercial banks (RCBkt), accommodate their requests for cash advances (LCBkt), and possibly buy bonds issued by the country government (BCBkt) which remain unsold after private banks’ purchases. At the beginning of the simulation, when no commercial banks are present (see Section 2.3), Central Banks directly collect money of households and purchase the entire amount of bonds issued by governments.12 However, in this transitory phase they cannot offer credit to firms. National Central Banks’ profits (πCBkt) derive from interests on cash advances and bonds, from which we shall subtract interests paid on banks’ reserve accounts.   πCBkt=rbktBCBkt+rtLCBkt−rreRCBkt. (36) For simplicity reasons, we assume that national Central Banks’ profits are automatically redistributed to the national government. The Union Central Bank is in charge of implementing the common monetary policy. For this sake it sets the discount interest rate following a Taylor rule based on the average level of inflation across member countries (Taylor, 1993; Smets and Wouters, 2007; Gerali et al., 2010):   rt=r¯(1−ξ)+ξ*rt−1+(1−ξ)*ξΔP(ΔPt−1−ΔP¯), (37) where r¯ is the exogenous long-run interest rate, ξ is the parameter defining the speed of the adjustment, ξΔP is the sensitivity to inflation, ΔPt−1 is the average level of inflation, and ΔP¯ is the inflation target. 2.1.5 Government The government of each country collects income taxes from households (h) and taxes on past period profits from firms (i) and banks (z). Therefore, total taxes Tkt of country k are equal to:   Tkt=∑h,yht>0Hkτktyht+∑i,π*>0Ikτktπit−1+∑z,π>0Zkτktπzt−1. (38) Government public expenditure Gkt takes the form of a lump-sum transfer which is equally distributed among households ( Gkt/H), thus providing additional purchasing power. The public balance in a given period is the difference between revenues from taxes and government expenses, including also interests paid on public debt. When negative, we have a deficit DEFkt. In the opposite case the government attains a budget surplus SUkt−1. Possible budget surpluses are set aside to fund public expenditure in the next periods, thereby reducing the quantity of bonds to be issued. Countries’ public deficit (DEFkt) and debt (Bkt) are then given by:   DEFkt=Gkt+rbkt−1Bkt−1−Tkt. (39)  Bkt=Bkt−1−DEFkt−SUkt−1. (40) The government employs two instruments to implement its fiscal policy: the level of public spending (Gkt) and the tax rate (τkt). These are adaptively revised from period to period based on the discrepancy between desired and past levels of public expenditure on the one hand, and expected and admissible levels of public deficit on the other hand. The desired level of public expenditure GktD is simply defined as the initial (exogenous) real value of public spending G, adjusted for the country average level of prices Pkt and average productivity Φkt, so to ensure that the dimension of the public sector remains roughly stable compared to aggregate GDP: GktD=PktΦktG. In addition, governments are committed to keep their deficit-to-GDP ratios ( dkt=DEFkt/Ykt) below a given threshold value indicated by dmax. Public expenditure and tax rates are then revised according to the following scheme:13  if dkt−1≥dmax   and   GktD≤Gkt−1:{Gkt=Gkt−1(1−U[0,δ])τkt+1=τkt(1+U[0,δ]) (41)  if  dkt−1≥dmax  and   GktD>Gkt−1:{Gkt=Gkt−1τkt+1=τkt(1+U[0,δ]). (42)  if  dkt−1<dmax  and   GktD≤Gkt−1:{Gkt=Gkt−1(1−U[0,δ])τkt+1=τkt(1−U[0,δ]). (43)  if  dkt−1<dmax  and  GktD>Gkt−1:{Gkt=Gkt−1(1+U[0,δ])τkt+1=τkt. (44) However, to avoid unreasonable high or low values, the tax rate is bound to vary within the range {τmin,τmax}, whereas Gkt is bound between a minimum and maximum share of GDP: {gminYkt,gmaxYkt}. Bonds last for one period. In each period, the government repays bonds previously issued and pays interests to bond holders. The interest rate on bonds is set as a premium on the Central Bank discount rate (rkt) depending on the debt-to-GDP ratio of the country ( Bkt/Ykt) and:   rbkt=χBkt/Ykt+rt. (45) Newly issued bonds (for a total value of Bkt) are split into 100 tranches ( bkt=Bkt/100) and put on the bond market where they can be purchased by commercial banks (both national and foreign), and by the national Central Bank for the possible residual part. Finally, the government steps in to guarantee depositors in case of a bank default. For this sake, the government issues an additional batch of bonds, which is directly purchased by the Central Bank, and uses the liquidity collected to reimburse households and firms who lost their deposits in the default. 2.1.6 Firms’ and banks’ endogenous entry and exit As discussed in Section 2.1.1 households’ savings are partly invested in the creation of new firms and new banks. A minimum level of investment, equal to a share ϖ of the country average wage, is required to allow an individual household to participate in the creation of a new business, regardless its type. Furthermore, there is a maximum number of businesses in which an individual household can invest, equal to ψ. To avoid excessive imbalances in the the dimension of the banking sector relative to the productive one, we assume that the new entrant will be a bank when either the ratio between banks’ and firms’ number or the ratio between banks’ and firms’ total net worth is below a given percentage η. Otherwise, the new entrant will be a firm. The new firm will be a tradable with probability cT, or a nontradable with probability 1−cT. The initial equity of the new entrant is determined as a random sample between the net worth of the smallest and larger incumbents in the sector14: when funds collectively invested by households are greater or equal to this random equity level, the new organization is created and the first h randomly chosen investors required to collect this level of funds become its shareholders. Otherwise, no firm (bank) enters the market and the funds originally allocated by households to equity investment are deposited at banks, being available to fund households’ investment in the next period.15 If instead funds allocated to equity investment are not exhausted by the creation of the new enterprise, the remaining part can be employed to set up other businesses, their type and dimension being determined according to the procedure explained above. As for new entrants’ initial dimension, also their initial productivity ( φ), price (pit), and wage offered (wit) are randomly extracted within a range going from the lowest to the highest values of incumbent firms in the sector. Their sales expectations ( qite) are instead the maximum between the random value sampled between the lowest and highest values of incumbents and Aitwitφit, this latter representing the amount of goods feasibly producible, given the values of equity, wage, and productivity sampled by the entrant. Firms whose net worth is below a threshold level, defined as the wage they offer to workers Ft=wit, default. Similarly, banks having a net worth below the national average wage default. This threshold level of internal funding has a technical reason, being meant to avoid the unnecessary computational burden required to keep track of extremely small firms and banks, almost negligible in terms of their contribution to the dynamics of the model. A default by a firm implies a nonperforming loan for creditors. The larger the bad debt suffered by banks, the worse the effect on their balance sheet [through equation (32)], which negatively affect their credit supply. In addition, defaults will generally increase unemployment. Therefore, firms’ failures may impact on the business cycle both directly, reducing employment and the potential output of the economy, and indirectly, by reducing the amount of credit banks are willing to supply. Defaults by banks instead do not directly affect households and firms, as the government totally bears the loss by issuing additional bonds to reimburse depositors (Section 2.1.5). However, in this way banks’ failures affect public debt dynamics. In addition, banks’ failures may eventually cause a reduction of the total credit supply in the economy. Finally, even before causing a default, negative profits of firms and banks prevent them from paying dividends and decrease their equity, thereby affecting the net worth of equity holders. 2.2 Simulation scheduling We conclude this section dedicated to agents’ behaviors by sketching out the sequence of events taking place during each round of the simulation. Firms determine their desired production, their labor demand, the price of their output, the wage offered, and their desired R&D investment. Firms interact with banks on the credit market and possibly receive loans. Banks possibly ask cash advances to the Central Bank to satisfy the mandatory liquidity ratio. Firms interact with workers on the labor market. Workers are paid and employed to produce firms’ output and to perform R&D. Dividends generated in the previous period are distributed to equity holders, summing up to their current income. Governments calculate revenues from taxes (on past period profits and current period households’ income), determine the level of public spending and the tax rate for the next period, repay bonds plus interests to bond holders, and determine the quantity of bonds to be issued. Bonds are put on the bond market where commercial banks buy it. The possible residual part is purchased by national Central Banks. After having paid taxes and received the tax-exempt monetary transfer from the government, households compute their demand for consumption goods and interact with tradable and nontradable firms on the correspondent good markets. Firms and banks compute their profits and update their net worth and shareholders’ equity accordingly. Taxes and dividends to be paid in the next period to the government and to equity holders, respectively, are then computed. Defaulted firms and banks exit the market. Household equity investment takes place and, if enough financial resources are collected, new firms and banks are created. 2.3 Simulations setup Table A1 provides a summary of the parameter values employed for the model. Each simulation period ideally represents a quarter. Simulations have been run for 1000 periods. For each simulation setup we run 25 Monte Carlo repetitions. In addition, for all simulation experiments we consider three different specifications regarding the number of countries belonging to the Monetary Union: a traditional two-country model, and then a 6-country and a 10-country cases. Besides the setting of behavioral parameters, one of the most tricky aspects of the model calibration procedure concerns the setup of initial values of stocks and flows. Caiani et al. (2016) point out that this aspect has been quite neglected within the AB macro literature, and very few models provide a detailed discussion of the logic followed to address this task. Initial stocks and flows across agents must be mutually compatible from a social accounting point of view, respecting Copeland’s quadruple entry principle (Copeland, 1949; Godley and Lavoie, 2007). A calibration affected by possible accounting flaws can be a major source of logical and accounting inconsistencies, building up throughout the simulation rather than fading away thus compromising the reliability of results. In addition, the calibration of initial values should be such to allow the model to reach, after the initial burn-in phase, a reasonable configuration regarding stocks and flows absolute and relative dimension. Within the AB-SFC literature, Caiani et al. (2016) present a sophisticated procedure to carry out this task. Dawid et al. (2016b) and Teglio et al. (2015) also provide an overview of the calibration method employed for the “EURACE” AB-SFC model (Deissenberg et al., 2008; Holcombe et al., 2013). The present article provides a simple and intuitive alternative to these procedures, inspired by the logic adopted by Godley and Lavoie (2007) in presenting the “SIM” model. The fundamental feature of this procedure is that, instead of setting exogenously the initial values for each type of stocks, and then distributing them across agents, we start from a situation where there are no stocks in the economy, and we let them to be progressively created and accumulated as time goes by. To be more precise, not only real and financial stocks are initially absent but firms and banks as well. Everything starts with public spending, as the government makes an initial transfer to resident households. Given that there are no private banks in this initial phase, the national Central Banks buy government bonds, providing in this way the legal currency which funds public expenditure. Since no firms, production, and goods are present, this lump-sum transfer is completely saved by households. However, part of these savings (see Sections 2.1.1 and 2.1.6) are invested in the creation of new firms which start to employ workers and produce consumption goods to be sold to households on either the tradable or nontradable markets. Firms also start to invest in R&D, thus possibly increasing their level of productivity. As their number increases also banks will be created: households and firms then deposit their holdings of legal currency at the newly created banks. Banks start to grant credit to firms, creating loans and matching deposits ex nihilo, thus triggering the process of endogenous creation of money. At the same time banks use their reserves in excess to buy bonds issued by the government and, conversely, as cash advances to their Central Bank when needed. At this stage, the system is already characterized by the presence of two interdependent monetary circuits, since both legal money, created by the public authority, and private money, created by banks through credit, are present. As soon as households receive an income, and firms and banks realize positive profits, taxes start to be collected by the government. With rising tax revenues and GDP increasing—as more and more firms are in business—the debt-to-GDP ratio rapidly declines to reasonable levels. Since tradable firms sell their output on the common integrated market, international flows of goods, deposits, and reserves between countries arise. Supranational debt–credit relationships, generating international flows of interests, also arise because commercial banks grant loans to foreign firms and purchase public debt bonds of foreign countries. The number of firms and banks quickly increases in the initial phase until new businesses and defaults start offsetting each other, stabilizing their number. In the meanwhile, firms and countries become more and more heterogeneous as a consequence of their R&D performance which drives technological progress and impact on their competitiveness. In turn, international trade and labor productivity dynamics affect the evolution of employment, wages, prices, profits, aggregate demand, and GDP in the Monetary Union, thereby possibly impacting also on public finance, and on R&D investment by firms as well. The model thus progressively exits its transition phase and starts to display regular patterns and quite stable properties. The next section is dedicated to their analysis. 3. Simulation results 3.1 Overview and consistency with international stylized facts The dashboards in Figures 6–8 present the dynamics of several important variables in a typical simulation executed under the 2 (left column), 6 (center), and 10 (right) country scenarios, while Table 1 provides some synthetic statistics on the 25 simulation runs performed under the three baseline scenarios. Table 1. Average simulated and empirical macro-variables in percentage values. Simulated averages and standard error from 25 Monte Carlo simulation runs. Empirical averages of Euro Area countries Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    Table 1. Average simulated and empirical macro-variables in percentage values. Simulated averages and standard error from 25 Monte Carlo simulation runs. Empirical averages of Euro Area countries Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    Variable  2 countries  6 countries  10 countries  Euro area (years)  Real GDP growth  1.20  1.20  1.20  0.98 (04–15)  (0.041)  (0.039)  (0.039)    Labor productivity growth  1.19  1.19  1.19  0.90 (04–13)  (0.045)  (0.042)  (0.039)    Inflation  2.72  2.26  2.26  1.74 (04–15)  (0.067)  (0.101)  (0.078)    Unemployment  10.7  13.5  13.5  9.6 (98–15)  (0.795)  (1.208)  (0.918)    Public debt/GDP  121.7  108.5  107.7  81.3 (06–15)  (12.121)  (23.514)  (22.645)    Private loans/GDP  68.7  68.7  68.2  104.6 (06–15)  (5.732)  (7.857)  (6.798)    Public deficit/GDP  1.2  1.0  1.0  3.2 (06–15)  (0.139)  (0.229)  (0.225)    Exports/GDP  19.5  32.0  34.5  40.0 (04–15)  (0.606)  (0.323)  (0.227)    Imports/GDP  19.5  32.0  34.5  38.1 (04–15)  (0.612)  (0.282)  (0.212)    Public expenditure/GDP  44.1  46.2  46.3  48.6 (06–15)  (0.588)  (0.920)  (0.869)    R&D investment/GDP  3.3  3.1  3.1  2.0 (06–15)  (0.082)  (0.012)  (0.099)    Household investment to GDP ratio  6.2  6.2  6.2  6.1 (06–15)  (0.176)  (0.136)  (0.173)    As we mentioned in the introduction, we tried to identify a baseline configuration of our artificial economy capable of yielding realistic and relatively stable dynamics. The adjective “realistic” indicates a specification in which the properties of key economic variables—real GDP and productivity growth rates, inflation rates, unemployment rates, debt-to-GDP ratios, exports and imports, etc.—are economically reasonable and broadly comparable to historical data for advanced countries, in particular for the Euro Area which constitutes the natural point of reference for our work.16Table 1 highlights that our artificial Monetary Union is broadly comparable to the EMU (last column) under many respects. Admittedly, the dimension of private debt over GDP is substantially lower than its empirical counterpart, whereas average public debt is relatively higher. The first discrepancy can be partly explained by the fact that no other form of credit than to firms is modeled. The greater debt-GDP ratio may be instead related to the initialization procedure, which requires the government to trigger the development process through its initial public expenditure: at the beginning public debt considerably increases, since taxes are lower than public spending given the low number of firms and banks in business. However, the average debt-GDP ratio is not unreasonably high compared to historical experience of many countries—in particular in the two scenarios with more countries—and remains quite stable after the initial transition phase. Finally, the dimension of imports and exports relative to GDP in the two-country case looks lower than its empirical counterpart. This is likely to be caused by the smaller dimension of the international market for tradable goods in this scenario, where domestic firms account for a significant share of the common market. On the contrary, in the other two cases, the higher number of countries implies that domestic tradable firms account for a smaller portion of the total number of firms producing for the common tradable goods market, so that the demand by domestic consumers is more likely to be addressed to foreign firms.17 The panel in Figure 6 displays that the model generates exponential growth of real GDP, coupled with an exponential increase in labor productivity. However, the process of development does not unfold in a smooth way, but rather through a succession of economic cycles. Figures in Panel 2 (Figure 2) display the cyclical component of main economic aggregates, each one normalized by the trend component to allow a comparison on the same scale: in accordance with the empirical evidence, the volatility of consumption is slightly below the volatility of real GDP, whereas exports, imports, and unemployment are significantly more volatile than real GDP. Figures 3 and 4 show the artificial cross-correlations with the cyclical component of real GDP of the cyclical components of consumption, exports, imports, public expenditure, public expenditure on GDP, and unemployment. The left, center, or right position of the peak in each correlation figure indicates whether the variable is lagged, coincident, or leading with respect to GDP. The darker bars indicate correlations significantly different from 0. In accordance with the empirical stylized facts on the co-movements of main aggregates within and across countries (Uribe and Schmitt-Grohé, 2017), consumption, exports, and imports are positively correlated with GDP, with the only exception of imports in the two-country case; real public expenditure is pro-cyclical in levels, whereas public expenditure over GDP is strongly countercyclical; finally, unemployment is strongly countercyclical. The pro-cyclical character of consumption, exports, and public expenditure is not surprising, since the former two are direct components of real GDP, while public expenditure increases the available income of households, and thus aggregate demand and real GDP. Similarly, the positive correlation of imports is not surprising because increments of real GDP generally increase the demand for both nontradables and tradables, and thus imports. However, in the two-country case, the fact that domestic firms account for a significant share of the market for tradables tend to dampen the impact of real GDP increments on imports. This possibly explains the nonsignificance of the correlation of imports with current output in this case. Finally, the positive correlation of G and the countercyclical character of G/GDP imply that government expenditure increases with GDP, but less than proportionally. Figure 3. View largeDownload slide Simulated data average cross correlations of aggregate consumption (c), export (x), and import (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figure 3. View largeDownload slide Simulated data average cross correlations of aggregate consumption (c), export (x), and import (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figure 4. View largeDownload slide Simulated data average cross correlations of public expenditure (g), public expenditure over GDP (g/y), and unemployment (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figure 4. View largeDownload slide Simulated data average cross correlations of public expenditure (g), public expenditure over GDP (g/y), and unemployment (m) with real GDP (y), computed from 25 Monte Carlo simulation runs. Figures in Panel 6 and 7 also highlight that our results are consistent with other two important empirical regularities observed in international trade data: inflation in nontradable goods is higher than in tradables, whereas labor productivity growth in nontradables is lower than in tradables (De Gregorio et al., 1993; Bernard and Jensen, 1999; Bernard et al., 2003, 2007). In our model, prices in the tradable sector tend to be lower first of all as a consequence of the greater competitive pressure faced by tradable firms, which are compelled to face more competitors on the international common market for tradables. For the same reason, international spillovers in the tradable sector tend to be greater than national spillovers in nontradable industries, providing a possible explanation for the enhanced productivity dynamics in the tradable sector. In turn, since higher productivity levels imply lower unit costs of production in the tradable sector, this concurs to keep prices of tradables lower. Figure 5 provides the log-log plot of firm and bank size distribution with the log-normal (green line) and Pareto (red) fits of the upper tails: firms and banks significantly differ with respect to their size, and their size distributions is right skewed and display excess kurtosis and fat tails under all scenarios. Tests based on Clauset et al. (2009) show that both the power law and log-normal hypothesis on the shape of the right tails are plausible, though the former is to be preferred according to Vuong’s likelihood ratio test, in line with the empirical evidence in the wake of Gibrat’s contribution (Stanley et al., 1995).18 Figure 5. View largeDownload slide Firm and Bank size distributions. The figure also displays the log-normal (green) and power law (red) fits of the right tails of the sample distributions. Colour figures available in the online version. Figure 5. View largeDownload slide Firm and Bank size distributions. The figure also displays the log-normal (green) and power law (red) fits of the right tails of the sample distributions. Colour figures available in the online version. Finally, figures in Panel 6 also show that in all scenarios countries may significantly and persistently diverge in terms of real GDP and productivity levels, as observed in reality. In these simulations, some countries achieve a sufficiently high competitive advantage thanks to R&D and tend to keep it over the simulation, whereas some others are affected by persistent technological gaps, though the magnitude of these differences may widen or shrink over the simulation time span. The dynamics of technological change in different countries is crucial to understand the evolution of the system. Figures 6–8 allow to get a first general idea about the interactions between technological change and several other important processes undergoing in the real and financial sphere of the economy. Figure 6. View largeDownload slide Country dynamics of real GDP (y) and average productivity in the tradable and nontradable sectors. Colour figures available in the online version. Figure 6. View largeDownload slide Country dynamics of real GDP (y) and average productivity in the tradable and nontradable sectors. Colour figures available in the online version. Figure 7. View largeDownload slide Country dynamics of unemployment and average price in the tradable and nontradable sectors. Figure 7. View largeDownload slide Country dynamics of unemployment and average price in the tradable and nontradable sectors. Figure 8. View largeDownload slide Country dynamics of debt over GDP (Debt/GDP), Current Account over GDP (CA/Y), and Net Foreign Asset Position over GDP. Colour figures available in the online version. Figure 8. View largeDownload slide Country dynamics of debt over GDP (Debt/GDP), Current Account over GDP (CA/Y), and Net Foreign Asset Position over GDP. Colour figures available in the online version. In the firms’ perspective, an increase in productivity allows firms to produce more goods at a lower cost of production, thereby improving their competitiveness on the national (nontradable) or international (tradable) markets: more productive firms can sell their output at a lower price without eroding their profit margin. The two bottom lines of Panel 7 show that countries characterized by higher levels of productivity tend to have also lower price levels. Therefore, more productive firms are able to attract more consumers, increasing sales and revenues. The consequent increase of their sales expectations induces an output expansion, possibly to an extent which increases their demand for labor, despite the labor-saving effect of technological change. As long as their increasing output finds an outlet on the market, they make higher profits, they are relatively less financially constrained, and they invest more on R&D. Higher R&D investments in turn enhance further their probability of achieving innovations, thereby widening the productivity advantage over competitors. This is the multiplicative engine which tends to foster firms’ productivity differentiation. However, this process can be hindered by several counterforces: first, rising sales can induce firms to increase prices to an excessive extent eroding their price competitiveness; second, sectoral spillovers can allow firms suffering a productivity gap to catch up; finally, the economic conjuncture plays an important role in determining whether the advantages of an innovation are quickly reabsorbed or translate into a durable competitive advantage. When demand is growing firms suffering a productivity gap have greater chances to find an outlet for their production despite their competitive disadvantage thus keeping enough resources to invest in R&D, possibly catching up with leading firms. On the contrary, economic downturns tend to exacerbate the Schumpeterian selection mechanism of firms, since less productive firms tend to suffer more from the fall in aggregate demand, having less room to adapt prices. While their need for external finance to fund production and R&D investment is likely to increase, the fall in revenues, negatively impacting on their net worth, reduces banks’ willingness to satisfy their requests. Eventually, less productive firms reduce or even abstain from investing in R&D, thus becoming doomed to failure. However, also leading firms may go into troubles during downturns if, for example, they have excessively increased their production and borrowed too much during the previous upward phase of the cycle. In the countries’ perspective, an increase in productivity obviously tends to exert direct labor-saving effects for given values of output. However, unemployment may remain stable, or even decrease if aggregate demand grows, inducing firms to expand their production. On the domestic markets for nontradables more innovative and productive firms tend to increase their market share at the expense of less productive competitors. Much of the net effect of technological change on total labor demand thus depends on whether the positive effect caused by the rising output of more productive firms, or the negative effect due to the shrinking output of less productive ones, is dominating. If we consider the common market for tradable goods on the contrary, innovations achieved by a country are more likely to exert a positive effect on its employment levels. Indeed, higher productivity levels translate into greater international competitiveness, possibly enhancing exports and the GDP of the country. The raise of output thus tends to sterilize the labor-saving effect of technological change, preventing unemployment from rising and wages from declining (or slowing down). As a consequence, also demand for nontradables can possibly grow, leading to further improvements of employment and output dynamics. Achieving a competitive advantage thanks to innovation can trigger an expansion phase in the country. The enhanced GDP dynamics, in turn, may increase tax revenues and reduce public deficits, so that the government may consider to cut tax rates and increase public spending, further boosting GDP growth. In addition, since default rates tend to be lower and profit margins greater and more stable, households’ investment in equity increases: new firms are created leading to further increases of employment and output, though their entrance may also exacerbate the competitive pressure on incumbent firms in the following periods, in particular on less productive ones. Finally, as long as productivity, wages, and prices are such to give the country a competitive advantage, the ensuing current account surplus causes a net inflow of financial resources, improving the net lending position of the country. This explains how differentiation between countries endogenously arises in the model. However, these tendencies may be dampened and partially reverted by several counterforces. First, rising output in countries experiencing a competitive advantage may counteract the reduction of unit costs of production in the measure in which firms, in response to the increase of their sales, decide to rise prices.19 In addition, if the rise of output is such to reduce unemployment, workers’ bargaining power increases, pushing up wages. On the one hand, this tends to increase aggregate demand and output levels further. However, if the faster growth of wages is not offset by further increases in productivity levels, unit costs raise as well. This either narrows firms’ profit margins or lead to an increase of prices, eroding the country price competitiveness on the tradable market. Finally, the rise of households’ disposable income in countries having a competitive advantage increases imports of tradable goods from abroad, partly compensating for the higher exports. This not only impacts directly on the country Current Account but also indirectly on the country intenrational competitiveness, since imports from foreign firms will possibly allow them to fund more investment in R&D. Since the long-run dynamics of the model emerges from the chain of successive short-run cycles, each one building on the previous one, the long-term system dynamics and the observed degree of convergence or divergence across countries can be seen as the path-dependent output of these conflicting forces. Figures 6 and 7 show that in the long run, countries with higher productivity levels tend to be characterized by higher real GDP and lower inflation, whereas unemployment levels are quite similar. Plots also show that there is a tight relationship between productivity and GDP levels in the long run. On the contrary, even though more productive countries tend to have, on average, also more solid public finance, countries with higher Debt/GDP ratios can sometimes outperform countries with lower public debt levels. Similarly, though countries benefiting from a productivity advantage tend on average to have a better international position, this does not necessarily imply that their Current Account will always be in surplus nor that they will always be net lenders (bottom line in Panel 8). Finally, there is a clear inverse relationship between the public debt and the net foreign asset position of countries (top and bottom lines of Panel 8, respectively). In Section 3.2 we will discuss in details the relationship between fiscal and trade balances. 3.2 Policy experiments on fiscal targets To assess the impact of a change in the fiscal targets that governments are committed to comply, we run six experiments assuming a change in the value of dmax, which was originally set at 0.03, occurring at period 500. More precisely, we test the following values of the parameter: dmax={0.0,0.01,0.02,0.025,0.035,0.04}. The first four scenarios, implying a fiscal policy contraction, correspond to the “austerity” case, whereas the other two correspond to a fiscal expansion. In particular, the first scenario corresponds to the “balanced budget” provision of the Fiscal Compact. It must be stressed that, since actual public deficits can be computed only after public spending and tax payments have taken place, actual deficits may be temporarily higher than dmax, so that this latter should be interpreted as a fiscal target rather than as an inviolable upper bound. In addition, given governments’ behavioral rules specified in Section 2.1.5, tax rates and public spending are progressively revised in an adaptive way. The panel of Figures 9 displays the impact of the fiscal regime switch on a selection of key macroeconomic aggregates in the 2 (left), 6 (center) and 10-country (right) cases. Values plotted are the Monte Carlo means of the across-country averages under the baseline case (black line) and the other six policy scenarios. Dotted lines are the across-runs standard deviations of mean values. The plots in the first two lines show that all scenarios characterized by a permanent fiscal restriction generate a significant drop of both real GDP and real productivity levels, associated with remarkable increases of unemployment rates. Expansionary policies instead tend to increase both real GDP and real productivity levels, though the improvement in the two-country case is almost negligible. Furthermore, permanent expansionary changes in fiscal targets always allow to reduce unemployment. Figure 9. View largeDownload slide Effects of different fiscal targets on real GDP (y), average productivity, unemployment, debt over GDP (Debt/Y), and average prices (P). The black line corresponds to the simulation baseline specification with dmax=0.03, the red one to dmax=0.025, the green to dmax=0.02, the blue to dmax=0.01, the light blue to dmax=0.0, the violet to dmax=0.035, and the yellow to dmax=0.04. The policy change occurs at period 500. Lines are average values from 25 Monte Carlo runs. Colour figures available in the online version. Figure 9. View largeDownload slide Effects of different fiscal targets on real GDP (y), average productivity, unemployment, debt over GDP (Debt/Y), and average prices (P). The black line corresponds to the simulation baseline specification with dmax=0.03, the red one to dmax=0.025, the green to dmax=0.02, the blue to dmax=0.01, the light blue to dmax=0.0, the violet to dmax=0.035, and the yellow to dmax=0.04. The policy change occurs at period 500. Lines are average values from 25 Monte Carlo runs. Colour figures available in the online version. If we look at the dynamics of nominal variables, there is a tight positive relationship between fiscal targets and the dynamics of prices: fiscal contractions are associated to very low levels of inflation, which is almost 0 in the two most restrictive cases. Vice-versa, a permanent increase of dmax generates higher levels of inflation. Finally the dynamics of the debt-GDP ratio across scenarios is particularly interesting, revealing a nonlinear relationship with fiscal targets. While increases of dmax seem to be connected with greater public debt ratios in the two expansionary cases analyzed, the impact of restriction policies is less trivial. Results highlight that in the two-country case fiscal contractions are able to effectively reduce the burden of public debt both in the medium and long run: average public debt-to-GDP ratios are indeed lower in all the austerity scenarios considered. However, strong fiscal contractions tend to be more effective in the short–medium run, but less effective in the long run compared to milder contractions, the levels of debt/GDP ending up to be lower in the dmax={0.025,0.02} cases than in the dmax={0.01,0.0} scenarios. In fact, in the long run the depressing effect on GDP levels partially compensates for the reduction of nominal public debt, so that the efficacy of strong and permanent reductions of fiscal targets in abating the debt burden is significantly dampened. This effect is exacerbated in the 6 and 10-country cases: the plots referring to these scenarios show that all austerity policies are effective only in the short–medium run, while being self-defeating in the long run. Debt-GDP ratios end up to be higher in these scenarios than in the baseline: in the most restrictive cases, debt-GDP ratios end up to be comparable to those obtained in the first expansionary case. An initial raise in taxes (or a cut in spending), possibly occurring in more than one country as a consequence of the tighter fiscal targets, reduces the disposable income available for consumption, triggering a reduction in aggregate demand for domestic and foreign goods. The reduction of dmax, however, exerts another important effect: during recessions, when deficit-GDP ratios tend to raise as a consequence of the fall in GDP, tax rates increase, and public spending cuts become more likely than in the baseline scenario, thereby exacerbating the ongoing recessionary dynamics. As a consequence, an initial increase of unemployment and default rates is now more likely to lead to an increase of tax rates, which tends to further depress demand, employment, wages, and prices. This in turn increases default rates. If the fall of taxable income and profits is very pronounced, the ensuing drop of tax revenues will likely increase deficit-GDP ratios further even if tax rates are raising and public spending is constant or decreasing. Fiscal policy becomes very pro-cyclical during recessions, since an initial drop of GDP induces further fiscal contractions, which eventually depress the economy further. However, a point will be reached when the slowdown of inflation (or deflation in extreme cases) caused by the recession will be such to stop the fall of workers’ real disposable income, allowing firms to unload the stock of inventories accumulated during the recession, thereby improving their expectations, and making a recovery possible. Wages and prices adjustments have two other important consequences: first, they reduce unit costs of production. This gives tradable firms more room to maneuver in reducing prices in response to the drop of their sales. Second, as a country disposable income declines, also its imports start falling. Even though these two adjustment processes can contribute to revert the recession in a single country, they can be effective only in the measure in which they reduce the country’s demand for tradables and increase domestic firms’ market share on the tradable market, at the expense of other countries. In other words these two latter effects can help to trigger a recovery in a country only in the measure in which they contribute to jeopardize other countries. Obviously the dimension of this effect is narrow when international trade is small compared to domestic markets, as it happens in the two-country case, or if only one country finds itself in the situation depicted above. But when instead the size of the tradable market is greater and all countries follow a fiscal rule which tends to be more pro-cyclical during recession, this contagion channel becomes prominent, amplifying the recessionary effects of fiscal contractions through negative feedbacks between member countries, as observed in the 6 and 10-country scenarios of Panel 9. All in all, the stricter fiscal goal does not only trigger a contraction of GDP but also tends to increase the instability of the system amplifying fluctuations of real GDP, unemployment, and nominal variables both in the short and long run, as one can observe in Figure 10. In these cases austerity tends to be self-defeating. On the contrary, fiscal expansions tend to reduce the volatility of main economic aggregates, so that the process of development proceeds along a smoother trajectory. Figure 10. View largeDownload slide Country real GDP dynamics under different fiscal target scenarios: austerity dmax=0.02, baseline dmax=0.03, and expansion dmax=0.04. The policy change occurs at period 500. Top line: two-country case. Center line: six-country case. Bottom line: 10-country case. Colour figures available in the online version. Figure 10. View largeDownload slide Country real GDP dynamics under different fiscal target scenarios: austerity dmax=0.02, baseline dmax=0.03, and expansion dmax=0.04. The policy change occurs at period 500. Top line: two-country case. Center line: six-country case. Bottom line: 10-country case. Colour figures available in the online version. We also noticed that, when the Monetary Union is bigger, encompassing a higher number of countries, the regime switch does not impact on them in the same way. To perform such an analysis we divide countries into two groups: countries with a level of real GDP higher than the median level and countries with a lower real GDP at the period when the permanent policy change occurs (i.e., period 500). For space and explanatory reasons we present the case of the fiscal contraction with dmax=0.02 and the case of a fiscal expansion with dmax=0.04. The effects discussed for these two scenarios are reinforced under more extreme cases. Even though real GDP and productivity differentials do not seem to be significantly different across scenarios, at least on average, the increase of debt-to-GDP levels observed in the austerity case is largely related to a remarkable increase of the average debt-GDP ratio in poorer-less productive countries, whereas it remains almost stable in richer ones. In low-income countries, the increase of the public debt burden is accompanied by a deterioration of their net foreign asset position, as shown in Figures 12 and 13. Indeed, as discussed above higher-income levels are associated with higher average productivity levels. Although wages may vary in a way that tends to mitigate unit costs ( w/φ) differences between tradable firms of high- and low-income countries, their dynamics is largely affected also by what happens in domestic markets. As a consequence, Figures 11–13 display that under all cases, unit costs of production tend to be higher in less productive countries than in more productive ones. Therefore, tradable firms in poorer countries have lower profit margins and less room to manouvre when setting prices compared to their competitors in rich countries. Less productive tradable firms are thus less equipped to face recessions, when firms tend to lower prices to recover sales. Default rates turn out to be higher in less productive countries where tradable firms either see their profit margin rapidly evaporating, when forced to reduce prices, or experience a dramatic drop of sales if their price has already hit the unit cost lower bound. In this latter case, firms must wait for wages to fall due to rising unemployment before being able to recover some competitiveness, thereby being more exposed to defaults. Figure 11. View largeDownload slide Two-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 11. View largeDownload slide Two-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 12. View largeDownload slide Six-country case —high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average Productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 12. View largeDownload slide Six-country case —high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average Productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 13. View largeDownload slide Ten-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. Figure 13. View largeDownload slide Ten-country case—high- vs. low-income countries: the green lines correspond to average values for high-income countries, and blue lines are averages of low-income countries. In the baseline dmax=0.03 for the whole simulation time span, in the austerity case dmax=0.02 after period 500, and in the expansionary case dmax=0.04 after period 500. Figures display the results for real GDP (y), debt over GDP (Debt/Y), Net Foreign Asset Position over GDP, and average nominal wages over average productivity (Wage/Productivity). Average values are computed from 25 Monte Carlo runs. Colour figures available in the online version. In the recessionary and volatile context triggered by the austerity turn in fiscal policy, less productive tradable firms will thus be more fragile and less flexible in adjusting prices. This implies that poorer-less productive country has more difficulties and need more time to adapt during recessions, experiencing on average deeper and more frequent current account deficits compared to the baseline scenario. These deficits then translate into a reduction of tax revenues, culminating in higher public deficits and explaining the raise of debt-GDP levels, which is associated with the worsening of the net foreign asset position in poor countries relative to richer ones. 4. Conclusions The article presents an Agent-Based Stock Flow Consistent Multi-Country model of a Monetary Union. Besides the possibility of running simulations with a variable number of countries, which is per se a major novelty in the AB macroeconomic literature, the model displays several other important features. In particular, we adopt an SFC framework (Godley and Lavoie, 2007) on the top of the AB structure, along the line traced by Caiani et al. (2016, 2018), to ensure the accounting consistency of the model and to provide a fully integrated representation of the real and financial sides of the economic system depicted. In this respect, we also present an innovative procedure to initialize stocks and flows in an SFC manner, where initial injections of money through public spending allow households to create firms and banks, thus letting the economy to emerge from 0 in a “generative” perspective. The model features endogenous technological change in an evolutionary flavor, following the long-lasting tradition on the wake of the seminal contribution of Nelson and Winter (1977, 1982). Innovation dynamics plays a crucial role, allowing firms and countries to differentiate from each other, and concurring with aggregate demand and international trade to steer the economic dynamics in the short and long run. Finally, the endogenization of the entry–exit process of firms, depending on households’ equity investment decisions, is another important add-on to the current AB macroeconomic literature. After a preliminary validation, the model was employed to assess the effect of a change in the fiscal regime of member countries, modeled as a permanent variation of the maximum deficit-to-GDP ratio allowed. Each policy experiment was performed under three scenarios, differentiated for the number of countries belonging to the Monetary Union. In this way, we were able to asses how the dimension of the Monetary Union, and in particular the dimension of the common market for tradables, affects the efficacy of the policies tested. Policy experiments show that fiscal expansions tend to improve the dynamics of real GDP, labor productivity, and employment, though being generally associated to higher levels of public debt and higher levels of inflation. On the contrary, permanent fiscal contractions have strong recessionary effects which attenuate their efficacy in reducing public debt-GDP ratios in the long run. When the Monetary Union encompasses a higher number of countries, and international trade between member countries is more prominent, permanent fiscal contractions are self-defeating in the medium and long run, as public debt ends up being higher than in the baseline. Public debt increases in poorer and less productive countries mirrored by a corresponding deterioration of their net foreign asset position, suggesting that permanent fiscal contraction exert an asymmetric impact on more and less productive countries. Finally, fiscal contractions tend to exacerbate the volatility of main economic aggregates both in the short and long run, whereas fiscal expansions tend to dampen it. Our assessment of the effects of different fiscal policies in the context of a Monetary Union characterized by strong trade linkages is thus generally consistent with the conclusions of De Grauwe and Ji (2013), Hein et al. (2011),Semieniuk et al. (2011), and Perez-Caldentey and Vernengo (2012), and with results obtained by Dosi et al. (2013, 2015), and Teglio et al. (2015) using similar modeling approaches: with respect to these works our results distinguish themselves for the asymmetric impact of fiscal restrictions on high and low productivity countries, and for the scale-dependent efficacy of fiscal austerity in the long run, depending on the size of the common market for tradables. Our analysis is susceptible of being enlarged, deepened, and refined under many respects. First, while the present work focused on the impact of permanent policy changes in the fiscal targets of all member countries, one may wonder what would be the effects of fiscal consolidations implemented through temporary fiscal interventions, or through state-contingent policies, or yet through asymmetric policies in different countries. In addition, the interaction between monetary and fiscal policies should be addressed as well. Finally, whereas in the current article we let heterogeneity between firms and countries emerge endogenously starting from symmetric initial conditions, the model can be calibrated using more realistic initial conditions where countries are differentiated under several important respects such as their dimension, productivity level, income, and public and private debt levels. On the modeling side, the framework proposed can be largely improved on the financial side which at this stage presents simplified matching procedures on the international credit and bond markets, and totally neglects the role of foreign direct investments. As a consequence, most of the dynamics of international financial flows across countries is determined by international trade (i.e., by the trade balance), whereas in reality autonomous international financial transactions can be of topical importance as well. Finally, given the crucial role played in the model by international trade and unit costs asymmetries between firms and countries, also the possible interaction between fiscal policies and labor market regulation should be explored. Funding The research leading to these results has received funding from the European Union, Seventh Framework Programme FP7, under grant agreement FinMaP numver 612955. Footnotes 1 Under the first respect, unconventional and unprecedented forms of monetary policy, such as the Quantitative Easing, were adopted. As for the latter, ECB President Draghi’s famous claim in the apex of the sovereign debt crisis to do “whatever it takes to save the Euro” then culminated in the launch of European Financial Stability Facility (EFSF) and the European Financial Stabilisation Mechanism (EFSM), then replaced in 2012 by the European Stability Mechanism (ESM). 2 Although moving from a different theoretical perspective, also Holinski et al. (2012) stressed the potential risks associated to persistent trade and financial imbalances between the North and South of Europe, advocating better coordinated policies to prevent the emergence of unsustainable imbalances in the Euro area. 3 This specification of the consumption function ensures that the level of desired consumption chosen by households is always financially feasible, given the amount of deposits at their disposal. 4 Please notice that cT is also the exogenous probability that a newly created firm will be a tradable, as later explained in Section 2.1.6. 5 The term liquidity preference is employed here to indicate the share or wealth that households desire to hold in the form of liquid assets, that is, deposits. 6 Indeed, for simplicity reasons, we prevent households from liquidating their participations in firms and banks. 7 As explained before, financial resources dedicated to R&D are distributed across employees, summing up to their wages. 8 This correction for the sector average productivity is required to prevent Prsuccessit from increasing with the higher levels of productivity Φt achieved, as the simulation time goes by: indeed, higher levels of labor productivity allow to produce increasing quantities of goods with the same amount of labor. A stable or increasing pattern of real output, and a non-exploding pattern of unemployment can then be achieved if the purchasing power of households grows faster than prices, allowing the greater productive capacity to find an outlet on the market. Since most of this purchasing power is represented by wages paid by firms, and given that innovative efforts are proportional to the expected wage bill of firms, R&Dit/Pt will generally increase with Φt. This asks to correct real investment in innovation for Φt, so to avoid an unreasonable and unjustified continuous rise of the probability of success Prsuccessit. 9 Formally, LitD>0 if pit(LitDwit)φit≥ritLitD. 10 Though very common in the AB literature, we are aware that this represents a strong simplification, as thoroughly explained in Caiani et al. (2016). To avoid excessive complications, however, in this first application of the multi-country model we decided to keep the financial side relatively simple. 11 These latter are evaluated at their unit cost of production, in accordance with accounting standards: ΔINVit=(invit−invi,t−1)witφit. 12 In this way Central Banks inject in the system the initial amount of legal currency that, saved and invested by households in the creation of banks and firms, will eventually become banks’ initial stock of consolidated reserves. In the Monetary Union depicted in this article total banks’ consolidated reserves should coincide with total Central Banks’ holdings of countries’ public debt for accounting reasons, whereas at the country level the amount of reserves held by domestic commercial banks also depends on the international flows of deposits arising, for example, from international trade. 13 Admittedly, public expenditure and the tax rate on income and profits are kept constant in the very first periods of the simulation till the first firm is created, since the fiscal scheme proposed in equations (41)–(44) can be employed only when at least one firm is present; otherwise no employment, output, income, and profit are generated. This takes just one period in the setup employed in the article. 14 Given that this stochastic rule can operate only when some organization is already present, the first tradable and nontradable firms to enter the market have an exogenous initial net worth equal to A0. In addition, to ensure that banks will be big enough to provide credit to firms, whose number is by far higher, the initial equity of banks has a lower bound defined as a multiple σ of the country’s median dimension of firms. 15 The same occurs when households’ individual investment does not exceed the minimum participation level. 16 This objective was pursued through a combination of empirically grounded calibration and tentative investigation of the parameter space, whereas we did not employ recursive calibration or estimation methods aiming to minimize the distance between the properties (e.g., moments) of the artificial and real time series. 17 Similarly, production of tradable goods by domestic firms is more likely to be purchased by foreign consumers, since the domestic demand for tradable goods accounts for a smaller share of the total demand coming from the Monetary Union as a whole. 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Parameters K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      View Large Table A1. Parameters K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      K: Number of countries  2, 6, 10  μ2: Minimal reserve requirement parameter  0.1  H: Number of households  500  ιl: Loan probability parameter  1.0  lS: Workers’ labor supply  1.0  χ: Loan interest parameter  0.003  ψ: Matching parameter  10  ιb: Bond probability parameter  0.1  υ: Wage revision probability parameter  1.0  rre: Interest paid on banks’ reserves  0.0  w0: Initial wage  1.0  rb0: Initial interest on bonds  0.001  ϕ0: Initial productivity  1.0  r¯: Taylor rule long run interest rate  0.0075  τ0: Initial tax rate  0.4  ξ: Taylor rule adjustment speed parameter  0.8  cy: Propensity to consume out of income  0.9  ξΔP: Taylor rule sensitivity to inflation  2  cD: Propensity to consume out of wealth  0.2  ΔP¯: Inflation target  0.005  δ: Adaptive parameter  0.03  dmax: Maximum deficit-GDP ratio  0.03  cT: Share of tradable  0.4  taumin: Minimum tax rate  0.35  β: Hotelling circle parameter  2.0  taumax: Maximum tax rate  0.45  λ: Liquidity preference parameter  0.2  gmin: Minimum G/GDP  0.4  θ: Share of sales as inventories  0.2  gmax: Maximum G/GDP  0.6  γ: R&D expenditure parameter  0.03  η: Banks–firms minimum proportion  0.03  ν: R&D success probability parameter  1.5  ϖ: Minimum investment threshold parameter  0.1  ρ: Share of profits distributed  0.95  A0: First firms’ initial net worth  10.0  ζ: Deposit interest–discount rate ratio  0.1  σ: Banks’ minimum dimension relative to firms  4  μ1: Total credit supply parameter  20      View Large © The Author(s) 2018. Published by Oxford University Press on behalf of Associazione ICC. All rights reserved. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

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Industrial and Corporate ChangeOxford University Press

Published: Apr 7, 2018

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