Heterogeneous firms and informality: the effects of trade liberalization on labour markets

Heterogeneous firms and informality: the effects of trade liberalization on labour markets Abstract The informal sector is often seen as a way for firms to evade regulation. In this paper, I therefore investigate the role of the informal sector in the impact of trade liberalization on employment, wage inequality and welfare in a model of trade with heterogeneous firms and endogenous wage dispersion. The findings suggest that trade liberalization reduces informal employment unambiguously. Contrary to the extant literature, however, its impact on total salaried employment, wage inequality and welfare is country-specific. 1. Introduction In the seminal heterogeneous firm trade model by Melitz (2003), trade liberalization induces firm selection on productivity into exporting and forces the least-productive firms to exit the market. The result is improved welfare and higher than average productivity. Yet, empirical studies provide suggestive evidence that informality can act as a channel of distortion to the resource allocation process among firms (La Porta and Shleifer, 2008; Hsieh and Klenow, 2009; McCaig and Pavcnik, 2013), which might affect the welfare gains from trade. Further, informal workers make up a large portion of the workforce particularly in developing countries (Schneider et al., 2010). Yet, the empirical evidence on the impact of trade on informal employment remains conflicting (Goldberg and Pavcnik, 2003; Fiess and Fugazza, 2012; Acosta and Montes-Rojas, 2014; McCaig and Pavcnik, 2014), and the mechanisms through which workers might be affected in the presence of informality are unclear. Thus, in this paper I introduce informality into a trade model of heterogeneous firms to address two important questions: How does trade liberalization affect employment and wages in the presence of an informal sector? What is the effect of trade liberalization on welfare in the presence of an informal sector? To answer the first question, the model predicts that trade liberalization leads to a reduction in informal sector employment, consistent with empirical work by Fiess and Fugazza (2012) and McCaig and Pavcnik (2014), and ambiguously affects formal sector employment in line with Davidson and Matusz (2009), Dutt et al. (2009), Felbermayr et al. (2011ba) and Menezes-Filho and Muendler (2011). This result derives not just from export selection and firm exit, both well known from Melitz (2003), but a new adjustment mechanism—the informalization of firms. Intuitively, trade liberalization induces the selection of high-productivity formal firms into exporting and hiring more workers, while lower-productivity formal firms switch to informal production to remain profitable, and accordingly shed formal labour. Depending on the characteristics of the economy, such as the cost of exporting, the additional hires by exporting firms may or may not compensate for the labour shedding in the formal sector. Furthermore, the lowest-productivity informal firms are forced to exit the market, resulting in a reduction in informal sector employment. The net effect on total employment is ambiguous. Additionally, the model is the first informality model to allow studying both trade liberalization and endogenous wage dispersion. Wage inequality is caused by a wage gap between informal and formal workers, as frequently found in empirical studies (Bargain and Kwenda, 2011; de Paula and Scheinkman, 2011; Günther and Launov, 2012), and workers’ fair wage preferences with respect to firm productivity that lead to within-group inequality. The model predicts that liberalizing trade increases wage inequality between informal and formal workers. Because of the reduction in informal sector employment and sector switching, the increase of the informal sector average wage is lower than the increase in the formal sector average wage and the average wages of both sectors diverge. Hence, between-group wage inequality, as measured by the ratio of the formal sector relative to the informal sector average wage, increases. Wage inequality among all employed workers, as measured by the Gini-coefficient, is ambiguously affected through the above employment effect and depends on the proportion of formal sector firms, and hence formal workers, prior to trade liberalization. To answer the second question, trade liberalization leads to an ambiguous change in aggregate output, and hence welfare. Similar to the employment effect, the increase in aggregate output by shifting resources towards the highest-productivity exporting firms may or may not compensate for the loss in aggregate output due to the exit of the least-productive informal firms and the informalization of the least-productive formal firms. Therefore, the informal sector plays a role in the resource allocation process, as found by Bruhn (2013), and trade liberalization can either increase aggregate output (McCaig and Pavcnik, 2013), and hence welfare, or reduce it by affecting informal sector participation. This result is particularly interesting, as it stands in contrast to the clear increase in welfare that is commonly established in the theoretical literature on trade with heterogeneous firms (e.g. Egger and Kreickemeier, 2009). Lastly, a simple numerical simulation indicates that liberalizing trade is close in effectiveness to improving contract enforcement in reducing informal employment and increasing welfare, given reasonable economy parameters from the empirical literature. Notably, trade liberalization has a stronger impact than improving access to the formal sector, which substantiates the relevance of trade liberalization in curbing informality. The model derives from introducing informality into Egger and Kreickemeier (2009), which is a heterogeneous firm trade model à la Melitz (2003) with a fair wage specification along the lines of Akerlof and Yellen (1990). It consists of three crucial pieces. First, firms are heterogeneous in productivity. Second, informality is an active entrepreneurial choice given the costs and benefits of informal and formal sector participation, as shown by Maloney (2004), and in line with the seminal work by de Soto (1989) is defined as firm-level non-compliance with registration. I therefore follow the strain of literature that shows informality as the result of excessive regulatory burden in the formal sector, and a profit-maximizing strategy for entrepreneurs (Djankov et al., 2002; Auriol and Warlters, 2005; Antunes and de V. Cavalcanti, 2007; Ulyssea, 2010; de Paula and Scheinkman, 2011). Recent research by Bruhn (2013) finds that in addition to the here modelled entrepreneurial segment, there exists a segment of self-employed informal entrepreneurs that see informality only as a last resort and would rather work as salaried workers in the formal sector. This type of subsistence informality is featured in this model as a residual to salaried employment in informal and formal multi-worker firms. Third, labour markets are imperfect and labour market frictions are caused by workers’ fair wage expectations.1 Given that workers are randomly matched to firms in this model, informal workers are excluded from higher-wage formal employment. Accordingly, I model informal employment corresponding to what is considered the exclusion view of informal employment. Current research indicates, however, that additionally there exists a segment of workers that voluntarily choose informality, rather than being excluded from formal work (Günther and Launov, 2012; Radchenko, 2014). Given the model’s focus, the voluntary informal workforce is not part of the present analysis. This paper is related to several lines of previous research. First, it contributes to heterogeneous firm trade models, particularly the work featuring labour market frictions arising from search-and-matching (Helpman and Itskhoki, 2010; Felbermayr et al., 2011ab) and fair wage (Egger and Kreickemeier, 2009; Davis and Harrigan, 2011; Amiti and Davis, 2012) specifications. Additionally, it is related to Bustos (2011), who studies technology upgrading of exporters modelled in a similar fashion to formality here. Second, the paper follows a long list of models of the informal economy. Fields (1975) uses a Harris-Todaro-type model to analyse unemployment, whereas Rauch (1991) provides a rationale for size-dualism with large formal and small informal firms. Loayza (1996) examines the interaction of tax evasion and public good congestion. The link between trade reform, corruption and informality is studied by Marjit et al. (2007). El Badaoui et al. (2010) demonstrate the link between firm size, wages and informality. Wage dualism between formal and informal firms, and workers is explained by Basu et al. (2011). Prado (2011) examines general equilibrium government decisions on regulation and enforcement in a heterogeneous firm model where informal firms evade taxes. Arias et al. (2013) take a labour market focus of informality and model workers’ decisions to move between the informal and formal sector. Heid et al. (2013) construct a heterogeneous firm trade model with labour market frictions to analyse the rise of the maquiladora sector on employment, welfare and wage inequality in the presence of informality. The model, however, considers heterogeneous workers and a small open economy setting that features a fixed formality wage premium. Both Aleman-Castilla (2006) and Paz (2014) consider trade and informality from a labour market perspective by defining informality as payroll tax evasion, where Aleman-Castilla (2006) models a world without labour market frictions and full employment, and Paz (2014) features labour market imperfections, but only examines informal employment and average wages in a small open economy. Heid (2015) studies the impact of regional trade agreements on welfare, employment and informality in a structural gravity framework and similarly finds that trade reduces informal employment. Fiess et al. (2010) take yet another direction by combining macroeconomic fluctuations and informal self-employment in a small open economy model. Lastly, the most closely related work comes from Davies and Paz (2011), who also study the impact of trade liberalization on informality in a model of heterogeneous firms and endogenous entry. While they similarly find that a tariff reduction decreases the size of the informal sector, their model defines informality as tax evasion, contrasts the effect of tariffs to VAT on the informal sector, employs a quasi-linear utility function and assumes a perfect labour market. Therefore, this is the first paper that presents a unified theory of trade and the informal sector that accommodates five important points: (i) informality defined as regulation non-compliance; (ii) heterogeneous firms; (iii) a large open economy setting; (iv) formal and informal salaried employment, and informal self-employment; and (v) endogenous wage dispersion in both formal and informal sector. Through combining all these elements, this model complements earlier work by providing a tractable setup that allows policymakers a rich look at the labour market implications of trade liberalization, including an analysis of between-sector and within-economy wage inequality that previous work did not offer. I proceed as follows. Section 2 characterizes the closed economy specification of the model. Section 3 extends the model to an open economy and discusses the impact of trade liberalization. Section 4 concludes the paper. 2. The closed economy model The economy consists of L units of labour, the only factor of production. There are two types of goods: a final output and intermediate goods. The final output is homogeneous and its market is in perfect competition. The intermediate goods are differentiated and produced under monopolistic competition by a mass of heterogeneous firms (Melitz, 2003). 2.1 The final output The final output Y is an aggregate of all intermediate goods and is characterized by the following constant-elasticity-of-substitution (CES) production function (Blanchard and Giavazzi, 2003):2  Y=[M−(1−ρ)∫v∈Vq(v)ρdv]1ρ,0<ρ<1. (1) Intermediate good varieties are indexed with v and V is the set representing the mass of available intermediate goods M. q(v) and p(v) are the quantity and the price of variety v. σ≡11−ρ is the elasticity of substitution between the varieties of intermediate goods. The final output market is under perfect competition and the final output acts as numeraire. The resulting CES-price index P is thus normalized to 1. The price index is described by:   P=[M−1∫v∈Vp(v)1−σdv]11−σ. (2) Through profit maximization of the producer of the final good, the demand for variety v of the intermediate good is   q(v)=YMp(v)−σ. (3) 2.2 The intermediate goods: informal and formal sector The intermediate goods are produced under monopolistic competition by firms in two sectors: an informal and a formal sector. Henceforth all informal sector variables feature subscript i and formal sector variables subscript f. The firms are heterogeneous in their productivity and every firm produces one unique variety of input for the final output production. Hence, M can interchangeably be used to account for the number of firms or total number of input varieties v. M=Mi+Mf is the number of domestically active firms, which consists of all informal sector firms, Mi, and formal sector firms, Mf. Firms face fixed costs of production in terms of final output Y and variable costs that are directly related to the firm’s productivity ϕ. Firm output is linear in labour inputland productivity ϕ, that is q=ϕl. Firms with the same productivity behave in the same manner. Therefore, I index firms solely in terms of their productivity ϕ. Firms voluntarily choose to become either informal or formal producers. Informal producers face fixed cost fi and formal producers face ff to start production. I assume ff > fi, to reflect that formality generates an additional registration cost on top of the basic capital cost fi required from any entrepreneur to start a business (Auriol and Warlters, 2005; Antunes and de V. Cavalcanti, 2007). As Djankov et al. (2002) points out, the registration cost usually is not an efficient transfer to the government, but rather red tape caused by bureaucratic hurdles and complex registration procedures. Corresponding to Antunes and de V. Cavalcanti (2007) and Quintin (2007), who show that imperfect contract enforcement in the formal sector and lack thereof in the informal sector are main drivers of informality, I assume that contracts can only be enforced in the formal sector, albeit limited to an exogenous fraction λ∈(0,1). The effective productivity of a firm in the formal sector is described by ϕ1−λ.3 No contracts can be enforced in the informal sector. The profit maximizing price of both types of firms is a constant markup 1/ρ over marginal cost, where w(ϕ) denotes the wage paid by a firm with productivity ϕ and ε is the effort level of workers:   pi(ϕ)=wi(ϕ)ρϕε and pf(ϕ)=wf(ϕ)ρϕ1−λε. (4) In combination, demand for the individual input variety (3) and the profit-maximizing price (4) lead to the informal and formal revenues   ri(ϕ)=YM(wi(ϕ)ρϕε)1−σ and rf(ϕ)=YM(wf(ϕ)ρϕ1−λε)1−σ, (5) and profits:   πi(ϕ)=YσM(wi(ϕ)ρϕε)1−σ−fi and πf(ϕ)=YσM(wf(ϕ)ρϕ1−λε)1−σ−ff. (6) Besides firm productivity and wages, firm revenue depends on two factors. First, the number of firms operating in the domestic market M (and hence the number of varieties sold in the domestic market) influence the demand for each individual variety. A strong domestic competition (thus, a high M) reduces the demand for each variety and therefore the profitability of each firm’s operation. Second, the demand for each firm’s variety rises with the aggregate revenue in the economy (here Y, as P is normalized to 1). 2.3 The labour market and wage determination with informality There are three groups of workers: informal salaried workers Li, formal salaried workers Lf and informal self-employed workers Ls. Together they make up the total labour force in the economy L≡Li+Lf+Ls. The informal salaried employment share, formal salaried employment share and share of self-employed informal workers are described by Ei=(Li/L), Ef=(Lf/L) and S=(Ls/L). E≡Ei+Ef=1−S is the fraction of salaried workers employed by multi-worker firms. Workers are identical and have a preference for fair wages along the lines of Akerlof and Yellen (1990). As workers are identical, they are randomly selected by employers in the hiring process and can become either informal or formal salaried workers or become self-employed. Without loss of generality, I assume that self-employed workers just receive a subsistence wage, which is normalized to 0. Moreover, henceforth I consider only informal salaried workers as informal workers, because self-employed informal workers as residual of salaried employment are not the focus of the present analysis. I distinguish the informal sector average wage wi¯ from the formal sector average wage wf¯. The average wages are calculated as follows. The wage bill of the informal sector Wi, i.e. the sum of all wages wi(ϕ) paid in the informal sector, is divided by the amount of informal employment Li. This provides the informal sector average wage wi¯=(Wi/Li). The calculation of the formal sector average wage follows the same procedure. Taking the potential informal self-employment that provides only a subsistence wage of 0 into account, the average wage income per worker in the economy (Eiwi¯+Efwf¯) consists of the two average wages weighted by the respective salaried employment shares, that is:   Eiwi¯+Efwf¯=Wi+WfL. (7) The reference wage of workers w(ϕ) consists of two parts: a firm-internal and a firm-external factor (Howitt, 2002; Bewley, 2005; Danthine and Kurmann, 2007). The firm-internal component captures the economic success of the firm as measured by the firm’s productivity ϕ. When hired by a formal firm, workers are aware of the productivity bonus that firms experience due to enforceable contacts in the formal sector and take the firm’s effective productivity ϕ1−λ into account. In line with Kreickemeier and Nelson (2006), the firm-external component relates to the labour market and is the outside option of workers. The external reference point is therefore described by the average wage income per worker: (Eiwi¯+Efwf¯). The workers’ fairness consideration between firm-internal and -external reference points is a geometric average weighted by the fairness parameter θ∈(0,1). Through the firm-internal component that relates the wage to firm productivity, the fair wage setup induces heterogeneous wages among workers that are identical before the hiring process. The informal and formal reference wages take the following functional form:   wi^(ϕ)=ϕθ(Eiwi¯+Efwf¯)1−θandwf^(ϕ)=(ϕ1−λ)θ(Eiwi¯+Efwf¯)1−θ. (8) Workers exert effort level ε relative to what they perceive to be a fair wage w^. For w(ϕ)≥w^ workers effort their maximum effort level ε = 1, that is ε=min⁡{w(ϕ)/w^,1}. Additionally, I assume that worker effort level ε cannot be contracted and the only mechanism to induce effort is a wage offer. Therefore, outside workers are not able to underbid the wage of currently employed workers, all firms pay the firm-specific reference wage w^ and all employed workers exert effort ε = 1.4 This is supported by the experimental evidence of Fehr and Falk (1999), who show that worker effort level is positively related to their wage and that employers are not interested in wage underbidding by outside workers in a world of incomplete contracts. With all employed workers exerting full effort ε = 1, I henceforth ignore ε. The presence of two sectors leads to two crucial differences of this model’s wages to the wage specification of Egger and Kreickemeier (2009). First, the firm-external reference point depends on both informal and formal sector wages. Due to the random selection of workers, both employment types are viable options for workers. Second, workers are aware of the productivity bonus that formal sector firms experience and adjust their firm-internal reference point accordingly. 2.4 The firm’s decision to enter the informal or formal sector A firm’s decision to become informal or formal is established as follows. Before the start of the operation, the firm pays a fixed cost fe and draws a productivity ϕ, a mechanism explained in detail in subsection 2.6. A firm’s productivity influences its variable costs, but not the fixed cost it faces for entering either the informal or formal sector. Having full information over entry costs and productivity bonus due to contract enforcement in the formal sector, firms choose the sector in which they can produce the most profitable or do not produce at all, that is max⁡{πi(ϕ),πf(ϕ),0}. Corresponding to empirical evidence, I assume that informal firms are low-productivity and formal firms are high-productivity firms (La Porta and Shleifer, 2008; Dabla-Norris et al., 2008; de Paula and Scheinkman, 2011). That is ϕf*>ϕi*, where ϕi* and ϕf* are the cutoff productivity levels at which informal and formal firms start profitably operating. The sorting is achieved if   (1−λ)−ξ<fffi (9) with ξ≡(1−σ)(θ−1), which I assume henceforth holds. Figure 1 visualizes this sorting of sectors along the productivity spectrum. Fig. 1 View largeDownload slide Sector sorting along the productivity spectrum according if (9) holds Fig. 1 View largeDownload slide Sector sorting along the productivity spectrum according if (9) holds The intuition for condition (9) is as follows. If the benefit of formality relative to informality is less than the relative formal sector entry cost, then only high-productivity firms enter formal production and informal firms break even at a lower productivity level than formal firms do.5 If the condition holds, the combination of the fixed costs fi and ff and the fact that relative revenue of formal to informal firms is increasing ensures a single crossing of the informal and formal profit functions.6 Thus, only formal sector firms can be found at higher productivity levels. ϕi* and ϕf* are determined by two conditions:   πi(ϕi*)=0 (10) and:   πf(ϕf*)=πi(ϕf*). (11) Notably, for the extreme case of λ = 0, i.e. contracts are not enforceable in the formal sector, firms would have no incentive to join the formal sector and the model would collapse to the one-sector specification in Egger and Kreickemeier (2009). If on top of that, θ = 0 holds, that is workers only value the expected wage in the economy and wages are not firm-specific, labour markets would clear and the model would further collapse to the model described in Melitz (2003). 2.5 Firm-specific variables The relative difference between any two firms can entirely be described by their productivity ϕ, the share of enforceable contracts λ and their resulting formality status, as in Melitz (2003) and Egger and Kreickemeier (2009). To begin with, using (4) and (8) results in:   wi(ϕi)wf(ϕf)=(ϕiϕf)θ(1−λ)θ<1 and pi(ϕi)pf(ϕf)=(ϕiϕf)θ−1(1−λ)θ−1>1. (12) Consistent with the empirical literature, informal wages are lower than formal wages for two reasons. First, wages are a function of firm productivity and formal sector firms are high-productivity firms. Second, a higher share of enforceable contracts entails higher firm profitability and accordingly acts as a wage premium for formal sector employment. This results in an informal wage gap as empirically found by Bargain and Kwenda (2011), de Paula and Scheinkman (2011) and Günther and Launov (2012). Similarly, (12) allows for a comparison of the relative prices pi(ϕi)/pf(ϕf), and shows that formal firms charge lower prices than informal firms. Intuitively, due to their productivity bonus and higher productivity level, formal firms are able to translate lower marginal costs into lower prices for their products. This is in line with the findings of Foster et al. (2008), who show a negative correlation between physical firm productivity and output prices. While firms produce symmetric varieties at different costs, as mentioned in Melitz (2003) an alternative interpretation is that firms produce varieties of different quality at the same cost. Given this interpretation, the model implicitly reflects the lower quality of informal sector products, which has empirically found to be the case by La Porta and Shleifer (2011).7 In addition, using (3) and (5), I can compare the quantities and revenues between firms in the two sector:   qi(ϕi)qf(ϕf)=(ϕiϕf)σ(1−θ)(1−λ)σ(1−θ)<1 and ri(ϕi)rf(ϕf)=(ϕiϕf)ξ(1−λ)ξ<1. (13) Formal firms are not just able to translate higher productivity into lower prices, but they also produce larger quantities than their informal counterparts (La Porta and Shleifer, 2008). In combination, the revenue of firms in the formal sector is higher than in the informal sector (Fajnzylber et al., 2011). Lastly, (14) illustrates the labour demand of an informal sector firm li(ϕ) relative to the labour demand of a formal sector firm lf(ϕ):   li(ϕi)lf(ϕf)=(ϕiϕf)σ(1−θ)−1(1−λ)σ(1−θ)−1<1. (14) To capture the positive correlation between productivity level and employment (Brown and Medoff, 1989), that is li(ϕ)<lf(ϕ), I assume:   σ(1−θ)−1>0, (15) analogous to Egger and Kreickemeier (2009).8 In this setup the assumption is relevant for another reason. Given this assumption, formal firms hire more labour than informal firms due to the productivity bonus they receive (La Porta and Shleifer, 2008; de Paula and Scheinkman, 2011; Fajnzylber et al., 2011). Notably, this is not a strong assumption. The empirical literature indicates σ in the range of 2 to 5 (see for example, Head and Mayer, 2014), which implies reasonable fairness parameters of θ<0.5 to θ<0.8, respectively. Using the zero profit conditions for both sectors (10) and (11), I can specify the distance of informal to formal sector cutoff productivity level relative to the formal sector cutoff productivity level ϕf*−ϕi*ϕf*.   ϕf*−ϕi*ϕf*=1−(fiff−fi)1ξ((1−λ)−ξ−1)1ξ. (16) This allows the analysis of inter-firm productivity differences between the marginal informal and the marginal formal firm with regard to policy changes.9 Higher informal firm capital requirements fi or a higher share of enforceable contracts λ raises ϕi* relative to ϕf* and thereby diminishes the distance in relative productivity levels. It increases for a higher formal sector entry cost ff, because a higher ff reduces formal sector profitability. 2.6 Firm productivity distribution and free entry Firms are indexed by their productivity ϕ, hence firm size distribution, aggregate employment and aggregate output of the economy hinge on the productivity distribution. A commonly used distribution in Melitz-type models (2003) is the Pareto distribution. It is both tractable and fits empirical findings on firm size and the productivity distribution well (Axtell, 2001). The distribution is given by G(ϕ) with density g(ϕ) and shape parameter:   k>ξ.10 (17) The lower bound of productivities is normalized to 1:   G(ϕ)=1−ϕ−k and g(ϕ)=kϕ−(k+1). (18) There exists a mass Me of prospective entrants, all identical ex-ante, to the intermediate sector.1011 Entering entails a fixed cost of fe>0 and allows firms to draw a productivity ϕ from the distribution G(ϕ). Firms only start producing if the expected profit of production is non-negative. In equilibrium, the average profit of active firms, conditional on successful market entry, is equal to the sunk cost fe. This is described by the free entry condition:   ∫ϕi*ϕf*πi(ϕ)g(ϕ)dϕG(ϕf*)−G(ϕi*)+∫ϕf*∞πf(ϕ)g(ϕ)dϕ1−G(ϕf*)=fe. (19) Using the cutoff productivity levels and wage equations for both sectors, I can describe (7), the average wage income per worker in the economy, as:   Eiwi¯+Efwf¯=L−1[∫ϕi*ϕf*li(ϕ)wi(ϕ)g(ϕ)dϕ+∫ϕf*∞lf(ϕ)wf(ϕ)g(ϕ)dϕ]. (20) As firms price their goods with a constant markup 1/ρ over marginal costs, the wage income of employed workers is equal to a constant share of output (Eiwi¯+Efwf¯)L=ρY.12 Through (19), the expected profits of all firms equal their initial investment fe. Therefore, the workers’ income is the only disposable income for consumption and a natural utilitarian measure for welfare, as in Egger and Kreickemeier (2009), and can be written as:   YL=(Eiwi¯+Efwf¯)ρ. (21) 2.7 Employment The share of salaried employment in the economy consists of two parts: informal sector salaried employment share Ei and formal sector salaried employment share Ef. The salaried employment share can be written as:   E=Ei+Ef=L−1[∫ϕi*ϕf*li(ϕ)g(ϕ)dϕ+∫ϕf*∞lf(ϕ)g(ϕ)dϕ]. (22) Using this, I derive the relative salaried employment share (Ei/Ef) to determine the effect of policy changes:   EiEf=(1−λ)χ+k[(ϕi*ϕf*)χ−1], (23) where χ≡σ(1−θ)−k−1<0.13 The ratio of informal employment share to formal employment share EiEf is increasing in ff, and decreasing in fi and λ.14 This sheds light on the mechanics of the economy. A higher share of enforceable contracts λ leads to a relatively smaller informal sector, as found by Antunes and de V. Cavalcanti (2007) and Quintin (2007). A higher informal sector start-up cost fi similarly decreases the relative size of the informal sector. A decrease in formal sector profitability (i.e. increase in ff) increases relative informal sector salaried employment. Intuitively, reducing informal sector profitability or increasing formal sector profitability drives the least-productive informal sector firms out of the market. As a result, the informal sector sheds labour and informal sector average productivity increases. This extends Egger and Kreickemeier (2009) to a new adjustment margin. Informal and formal sector salaried employment are affected differently by changes in the economy. The employment effect of one sector can buffer the employment effect of the other one. 2.8 Wage inequality Prior to the hiring process workers are identical and subsequently can be employed in either the informal or formal sector. Additionally, wages in this model are firm-specific. Therefore, two types of wage inequality can be disentangled. First, given the productivity difference between the two sectors and the informal sector wage gap, I consider the wage inequality between informal and formal workers. Second, as all workers are identical in skill level, I analyse wage inequality among all employed workers similar in spirit to Egger and Kreickemeier (2012).15 The measure of between-group wage inequality is the ratio of the formal sector average wage relative to the informal sector average wage:   wf¯wi¯=(1−λ)−θ[1−(ϕi*ϕf*)χ][1−(ϕi*ϕf*)ξ−k]−1>1. (24) Given the informal sector wage gap and informal firms being low-productivity types, the average wage in the informal sector is lower than in the formal sector and the ratio is strictly greater than one. Second, I measure the wage inequality among all employed workers using the Gini-coefficient. Calculating the Gini-coefficient for the two-sector economy requires two steps. First, I calculate the Lorenz curve Q(γ) by relating the share of employment to the share of wage bill for firms with productivity below ϕ¯∈[ϕi*,∞]. Because employment and wages in the informal sector differ from the formal sector, the Lorenz curve consists of two segments and requires lengthy calculations that can be found in online Appendix B. Second, I derive the Gini-coefficient G(a), where subscript (a) stands for autarky, from the Lorenz curve through G(a)=1−2∫01Q(γ)dγ. G(a) is described by:   G(a)=Gf[1+2(ϕi*ϕf*)k−ξθΓΔ{χ[ϒ−Ξ(ϕi*ϕf*)θ+[Ξ−ϒ](ϕi*ϕf*)−χ]         +θϒ[1−(ϕi*ϕf*)−χ]}], (25) where Gf≡θθ−2(ξ−k),16 Γ≡1−[1−(1−λ)−ξ+θ](ϕi*ϕf*)−χ, Δ≡1−[1−(1−λ)−ξ](ϕi*ϕf*)k−ξ, ϒ≡1−(1−λ)−ξ and Ξ≡1−(1−λ)−ξ+θ. The Gini-coefficient in the two-sector economy G(a) depends on the ratio of the two cutoff productivity levels (ϕi*/ϕf*), which is a proxy for the relative sector size. For the extreme cases of (ϕi*/ϕf*)=1, i.e. all firms are formal, and (ϕi*/ϕf*)=0, i.e. all firms are informal, the specification collapses to the single-sector economy Gini-coefficient Gf.17 In the two-sector economy, that is (ϕi*/ϕf*)∈(0,1), G(a)>Gf holds and the wage distribution is more unequal than in the single-sector economy. Moreover, for θ∈(0,1), i.e. workers value firm-specific wages, the Gini-coefficient is strictly greater than 0.18 3. The open economy To explore how the presence of an informal sector may mediate the impact of trade liberalization, I extend the closed economy specification by adding international trade with n symmetric countries. The symmetry assumption allows me to focus on firm-level effects and renders country indices obsolete. Moreover, a world in which every country is characterized by sector dualism is sensible, since informality is a global phenomenon (Schneider et al., 2010). Two types of costs are distinguished for firms participating in international trade. As has been empirically shown by Roberts and Tybout (1997), sunk costs of exporting critically determine export participation. Firms have to cover a fixed exporting cost fx > ff, in addition to the domestic entry cost, to participate in trade. The fixed cost fx can be interpreted as a one-time expense for knowledge or infrastructure needed to engage in international trade and allows firms to access all n markets. Subscript x is used henceforth to describe variables related to export activities. In addition, firms face a variable trade cost that is modelled in the form of an iceberg trade cost τ>1, i.e. for one unit to arrive at the destination market, τ units have to be shipped. 3.1 The firm’s decision to export Given the previous constraint on informal firms being characterized by lower productivities than formal firms, it is never profitable for informal firms to export.19 Intuitively, informal firms decide against formality out of profitability considerations arising from the formal sector fixed cost ff. Exporting induces an even higher fixed cost fx than the formal sector participation already does. Hence, the same profitability considerations will lead informal sector firms to not be able to profitably export. The complete exclusion of informal sector firms from exporting is stylized. Yet, this model result is supported by the empirical literature that finds that informal firms rarely export (Batra et al., 2003; Bigsten et al., 2004; La Porta and Shleifer, 2008). Notably, the exclusion of informal firms from international trade arises as a model result in this setup, opposed to being an assumption as in the related work by Davies and Paz (2011). Lemma 1 Informal sector firms do not find it profitable to export. In regards to the formal sector, empirical studies find a clear correlation between export participation and firm productivity, i.e. the highest-productivity firms in an economy self-select into exporting (Bernard and Jensen, 1995; Roberts and Tybout, 1997). Hence, I focus on parameters that satisfy ϕx*>ϕf*, where ϕx* stands for the cutoff productivity level at which exporting becomes profitable. That is, I assume that exporters are characterized by a higher productivity level than non-exporters. Upon drawing a productivity ϕ, a firm in the open economy therefore decides on its formality status and export participation according to max⁡{πi(ϕ),πf(ϕ),πf(ϕ)+πx(ϕ),0}. The number of firms operating in the domestic market then consists of informal sector firms and formal sector firms, which are domestic, as well as foreign exporters, i.e. M=Mi+Mf+(1+n)Mx. The sorting ϕx*>ϕf*, is ensured if:   fxτξ1−θn(1−λ)−ξ>ff−fi(1−λ)−ξ−1, (26) which I assume henceforth holds.20 The sorting depends on the entry costs to the informal and formal sector (fi and ff), the share of enforceable contacts (λ) and the variables determining the costs and benefits of trade (fx, τ and n). Intuitively, the inequality compares two cost–benefit ratios. If the cost–benefit ratio of exporting fxτξ1−θn(1−λ)−ξ is higher than the cost–benefit ratio of domestic production ff−fi(1−λ)−ξ−1, then a higher productivity is required to be able to profit from exporting. Given the variable and fixed cost, the formal sector firm revenue function is:   r(ϕ)={rf(ϕ) if the firm sells domestically ,rf(ϕ)+nτ1−σrf(ϕ) if the firm exports.  (27) A firm’s profit from exporting is described by:   πx(ϕ)=rf(ϕ)nτ1−σσ−fx. (28) In addition to (10) and (11), there is a new condition to determine the export participation productivity cutoff level ϕx*:   πx(ϕx*)=0. (29) In summary, to achieve the productivity sorting of firms in the open economy according to the empirical literature, the model builds on (9) and (26). If they hold, informal sector firms are assumed to be the lowest-productivity firms followed by domestic formal firms. Lastly, formal firms that export are the highest-productivity firms and there are no informal sector exporters. 3.2 Firm-specific variables I can express the relationship between formal firms and formal exporting firms as ratios solely in terms of their productivity levels, variable trade costs τ and the number of countries n, independent of assumptions on the distribution of firm productivity. Notably, the price and quantity with subscript x refer solely to the export markets, but the revenue and labour demand below refer to both domestic and export markets. Exporters pay the same wage as formal sector producers conditional on productivity, i.e. wf(ϕ). However, if (26) holds, exporters are more productive than non-exporting formal firms, wf(ϕx*)>wf(ϕf*) and the model captures the empirical observation that exporting firms pay higher wages than non-exporting firms (Bernard and Jensen, 1995):   pf(ϕf)px(ϕx)=(ϕfϕx)θ−1τ−1<1 and qf(ϕf)qx(ϕx)=(ϕfϕx)σ(1−θ)τσ>1. (30) Given the same productivity, firms charge a higher price and sell a lower quantity abroad than at home:   rf(ϕf)rx(ϕx)=(ϕfϕx)ξ11+nτ1−σ<1 and lf(ϕf)lx(ϕx)=(ϕfϕx)σ(1−θ)−111+nτ1−σ<1. (31) With regard to revenue and labour demand, both are increasing in the number of countries n and decreasing in the variable trade cost τ for exporters relative to formal non-exporters. These model results are in line with the commonly stated firm-level evidence on exporters being characterized by higher employment and higher revenues than their non-exporting counterparts (Bernard and Jensen, 1995). Equation (32) allows me to analyse the distance between formal sector productivity cutoff ϕf* and exporting cutoff productivity level ϕx* relative to the exporting cutoff productivity level ϕx*:   ϕx*−ϕf*ϕx*=1−((ff−fi)nτ1−σ)fx)1ξ((1−λ)−ξ−1)−1ξ(1−λ)−1. (32) The results can be separated into two groups.21 First, variables increasing the attractiveness of international trade (increase in n or decrease in fx or τ) close the relative distance between the productivities, as trade liberalization increases the profitability of exporting firms and decreases the required productivity level for participation. For non-exporting formal sector firms, an increased number of foreign competitors in the domestic market drives down profitability and increases productivity requirements. Second, factors increasing the profitability of formal relative to informal sector participation (increase in fi and λ, decrease in ff) lower the productivity threshold of becoming formal, but affect export participation only indirectly. Lastly, comparing ϕx*=(fx/fi)1ξ(nτ1−σ)−1ξ(1−λ)ϕi*, i.e. the cutoff productivity level of the marginal exporting and informal sector firms highlights what drives their difference. The ratio of sector entry costs, trade variables and the share of enforceable contracts lead to a higher productivity requirement for exporting firms relative to informal sector producers. To derive the new free entry condition in the open economy, I extend (19) to include potential exporting profit:   ∫ϕi*ϕf*πi(ϕ)g(ϕ)dϕG(ϕf*)−G(ϕi*)+∫ϕf*ϕx*πf(ϕ)g(ϕ)dϕG(ϕx*)−G(ϕf*)+∫ϕx*∞[πf(ϕ)+πx(ϕ)]g(ϕ)dϕ1−G(ϕx*)=fe. (33) 3.3 Employment Salaried employment at multi-worker firms in the open economy consists of three segments: informal, formal and formal exporter employment. The employment share in the economy is:   E=L−1[∫ϕi*ϕf*li(ϕ)g(ϕ)dϕ+∫ϕf*ϕx*lf(ϕ)g(ϕ)dϕ+∫ϕx*∞lx(ϕ)g(ϕ)dϕ]. (34) In analysing the impact of trade liberalization on salaried employment, I first separately study the impact on the formal and informal sectors. Formal sector employment adjusts along two margins. The high-productivity formal firms become exporters and hire additional workers to be able to serve the foreign demand. After trade liberalization, foreign competitors enter the domestic market and more varieties of the intermediate good are sold domestically (increase in M). As competitive pressure rises, the demand for each variety decreases and the profitability of all firms is reduced. Low-productivity formal firms informalize to remain profitable. As a result, formal sector employment is affected negatively, dampening total salaried employment. Informal sector firms do not experience the productivity bonus λ due to enforceable contracts and thus hire fewer workers than formal sector firms at the same productivity level. This is obvious when comparing the labour demand ratio li(ϕ1)/lf(ϕ2)=(ϕ1/ϕ2)σ(1−θ)−1(1−λ)σ(1−θ)−1. Whether the hiring effect of exporting firms or the labour shedding of informalized firms dominates depends on the key characteristics of the economy. Thus, the effect of trade liberalization on formal sector employment is ambiguous. Informal sector employment is also affected along two margins. With falling demand for each input variety, the lowest-productivity informal producers are forced out of the market and release labour. Along the other margin, the least-productive formal sector firms become informal and thereby increase informal sector employment. Given the Pareto productivity distribution, the labour releasing effect is stronger than the labour hiring and therefore informal sector salaried employment unambiguously decreases upon trade liberalization.22 This result provides theoretical support for decreasing informal sector employment upon trade liberalization (Fiess and Fugazza, 2012; McCaig and Pavcnik, 2014) amidst conflicting empirical evidence with a wide range of definitions of informality and data sets in use. Alternatively, Goldberg and Pavcnik (2003) and Attanasio et al. (2004) find an increase in informal employment upon trade liberalization. However, they define workers as informal if no social security contributions for them are made. Accordingly, firms can hire both informal and formal workers by evading social security contributions for only some of their workers, whereas in this model all workers at a firm that evades regulations are considered informal. Within their framework, formal firms can substitute formal for informal workers, while remaining formal at the firm-level. Accordingly, workers would be considered formal from the firm-level perspective of this work, but informal from their labour market perspective, which can explain the diverging results on informal employment upon trade liberalization. Lastly, I analyse the total salaried employment in the economy as a combination of the employment adjustments of both sectors. As illustrated in Fig. 2, liberalizing trade changes the position of both sectors along the productivity distribution. Three forces determine the change in total salaried employment: an employment gain as a result of exporter hiring, an employment loss caused by the informalization of the least-productive formal sector firms and an employment loss that occurs as the least-productive informal sector firms exit the market. While there are unambiguously fewer informal salaried workers in the economy, the effect of trade liberalization on formal sector employment is ambiguous, thus rendering the total salaried employment effect ambiguous. Given that informal self-employment is a last resort and residual to salaried employment, also informal self-employment is impacted ambiguously by trade liberalization. The magnitude of each sectoral adjustment and accordingly the direction of total salaried employment adjustment is determined by the economy’s characteristics, such as entry costs to both sectors. The move from autarky to full integration is stylized. However, the aforementioned results hold also for gradual trade integration, as measured by a reduction in τ or fx.23 Fig. 2 View largeDownload slide Sector sorting along the productivity distribution in autarky and the open economy Fig. 2 View largeDownload slide Sector sorting along the productivity distribution in autarky and the open economy This highlights a key contribution of this model. In Egger and Kreickemeier (2009) there are only two forces at work. The highest-productivity firms become exporters and hire additional workers; the lowest-productivity firms exit the market and shed labour. In sum, Egger and Kreickemeier (2009) find an unambiguous decrease in salaried employment. The existence of an informal sector gives rise to a third force, i.e. the informalization of low-productivity formal firms, which dampens the reallocation of labour towards more productive firms. The economy’s characteristics affect the three forces and accordingly the magnitude of each. This result, as summarized in Proposition 1, bridges the gap between the original model of Egger and Kreickemeier (2009) and the mixed empirical evidence on the relationship between trade liberalization and formal salaried employment (Davidson and Matusz, 2009; Dutt et al., 2009; Felbermayr et al., 2011ba; Menezes-Filho and Muendler, 2011). Moreover, the finding that trade liberalization reduces informal employment, complements the related work by Davies and Paz (2011), who show a reduction of both the number of informal firms, and accordingly informal employment, as well as informal output through the same pro-competitive effect of trade liberalization, albeit in a setup without labour market frictions. Proposition 1 Trade liberalization reduces informal salaried employment unambiguously and can either reduce or increase formal salaried employment. In combination, the effect of trade liberalization on total salaried employment and informal self-employment in the economy is ambiguous. Proof See online Appendix D. □ To gain further insight into the mechanics of the model, analogously to the closed economy case, I can describe the informal salaried employment share relative to the formal salaried employment share:   (EiEf)(t)=η(EiEf)(a), (35) where η≡[1+nτ1−σ(ϕf*ϕx*)−χ]−1<1. Subscript (a) and (t) stand for autarky and trade. The intuition follows from the earlier result. Informal salaried employment unambiguously decreases, while formal sector employment may either increase or decrease. In combination, trade liberalization unambiguously reduces the informal salaried employment share relative to the formal salaried share. 3.4 Wage inequality Trade liberalization affects wage inequality indirectly by adjusting the number of workers employed in the informal and formal sector.24 Thus, the model introduces a novel impact of trade liberalization in the presence of informality that is not featured in the related work, such as Davies and Paz (2011), without labour market frictions. Between-group wage inequality in the open economy is higher than under autarky:   (wf¯wi¯)(t)=ω(wf¯wi¯)(a), (36) where ω≡[1+nτ1−σ(ϕx*ϕf*)ξ−k][1+nτ1−σ(ϕx*ϕf*)χ]−1>1. Intuitively, trade liberalization raises the competitive pressure in the economy and forces the least-productive informal firms to exit and the lowest-productivity formal firms to informalize. The informal firms paying the lowest wages exit and higher-wage formal firms start informal production. This raises the informal sector average wage. With regard to the formal sector, the highest-wage exporters hire more workers and the lowest-wage formal firms informalize. The average wage of the formal sector increases and does so at a greater magnitude than the informal sector average wage. Hence, the average wages diverge and between-group inequality increases. This corresponds to the empirical work of Attanasio et al. (2004), who document an increase in the average wage of formal relative to informal workers in the years following Colombia’s tariff reductions in 1990–1991. Similarly, wage inequality among all employed workers measured by the Gini-coefficient hinges on the share of employment in both sectors. The derivation of the Gini-coefficient is analogous to the closed economy, albeit more complicated.25 The Lorenz curve consists of not just informal and formal workers, but also workers employed by exporting firms.26 Trade liberalization affects wage inequality indirectly through the employment shares and can either increase or decrease wage inequality. The intuition for this result derives from section 3.3. Both a purely-formal and a purely-informal economy feature the same Gini-coefficient, which is strictly lower than that of an economy featuring both sectors.27 Trade liberalization increases the formal sector employment share relative to informal sector employment share. If initially formal sector employment is large relative to informal sector employment, a relative increase in the formal labour share pushes the economy closer to a purely formal economy. Hence, wage inequality decreases. The opposite holds true if the formal sector is relatively small before trade trade liberalization. Due to the relative formalization of labour through trade, the economy diverges from a purely-informal economy. Trade then increases wage inequality.28 Proposition 2 Trade liberalization increases between-group wage inequality and has an ambiguous effect on wage inequality among all employed workers. Proof See online Appendix D. □ 3.5 Welfare The average wage income per worker (Eiwi¯+Efwf¯) in the open economy is described by all three cutoff productivities and, in combination with (21), determines the aggregate output in the open economy:   (Eiwi¯+Efwf¯)=L−1[∫ϕi*ϕf*li(ϕ)wi(ϕ)g(ϕ)dϕ+∫ϕf*ϕx*lf(ϕ)wf(ϕ)g(ϕ)dϕ+∫ϕx*∞lx(ϕ)wf(ϕ)g(ϕ)dϕ]. (37) The effect of trade liberalization on welfare, as measured by the aggregate output of the economy per capita, is similar to the employment effect. The intuition is as follows. Trade liberalization allows the highest-productivity firms to become exporters and shifts resources towards the most-productive firms in the economy. Thereby aggregate formal sector output is increased. The lowest-productivity formal firms, however, switch to informal sector production. The result is a reduction in aggregate formal sector output through the loss of the formal sector productivity bonus. In sum, the effect of trade on the aggregate formal sector output is ambiguous. The informal sector is affected along two margins, as well. The lowest-productivity informal sector firms cease production and decrease aggregate informal sector output, while the informalization of the lowest-productivity formal firms increases the aggregate output of the informal sector. Depending on the economy’s characteristics the former may or may not compensate for the latter, rendering the effect on aggregate informal sector output ambiguous. As before, depending on the key parameters of the economy, the net effect of trade liberalization on the aggregate output of the whole economy can be positive or negative. This result also holds for gradual trade liberalization (decrease in τ or fx).29 The effect of trade on aggregate output in this model is more nuanced than in Egger and Kreickemeier (2009), who find an unambiguous increase in aggregate output through trade liberalization. The ambiguous result highlights the effect of the informal sector on resource allocation, as suggested by Hsieh and Klenow (2009) and Bruhn (2013), that can either lead to an increase in aggregate output (McCaig and Pavcnik, 2013), and hence welfare, or decrease in aggregate output upon trade liberalization. Moreover, this result underlines the ambiguous welfare effect of trade liberalization in the presence of informality shown by Davies and Paz (2011), which in this model also arises without the shift from tariffs to VAT.30 Proposition 3 Trade liberalization in the presence of informality has an ambiguous effect on the aggregate output of the informal sector, the formal sector and in sum on the welfare of the economy. Proof See online Appendix D. □ 3.6 Numerical Simulation To substantiate the policy relevance of the model, I proceed with a numerical simulation to: (i) compare the effectiveness of different policy instruments on welfare; and (ii) size the impact of trade liberalization on informal employment. Table 1 lays out the baseline scenario with parameters that either stem from empirical literature or follow from model conditions.31 The respective constraints and equations to derive these results, as well as additional scenarios to highlight the ambiguity of the effect of trade on welfare and total salaried employment, can be found in online Appendix D. First, I compare the impact of liberalizing trade (decreasing τ), improving access to the formal sector (decreasing ff) and improving contract enforcement in the formal sector (increasing λ) in their impact on welfare captured by Y(t). More specifically, I estimate the required change in each of the parameters to increase welfare by 5%. The results listed in table 2 indicate that increasing contract enforceability in the formal sector is the most effective in achieving this goal, closely followed by decreasing trade costs with implied welfare elasticities of 1.2 and –1.1, respectively. Additionally, both have a similar impact on informal employment with informal salaried employment elasticities of –0.7 for λ and 0.6 for τ. To achieve the same welfare gain, the formal sector entry costs needs to be decreased to a larger extent (11.7%) implying lower welfare and informal salaried employment elasticities. Table 1 Parameter values for the baseline scenario     Baseline  Source  Elasticity of substitution  σ  5.0  Head and Mayer (2014)  Pareto distribution parameter  k  3.0    Formal fixed cost  ff  1.4  Ulyssea (2010)  Informal fixed cost  fi  0.3  Ulyssea (2010)  Exporting fixed cost  fx  2.0    Fairness parameter  θ  0.7    Share of enforceable contracts  λ  0.47  World Bank (2016)  Iceberg transportation cost  τ  1.1    Number of foreign countries  n  1        Baseline  Source  Elasticity of substitution  σ  5.0  Head and Mayer (2014)  Pareto distribution parameter  k  3.0    Formal fixed cost  ff  1.4  Ulyssea (2010)  Informal fixed cost  fi  0.3  Ulyssea (2010)  Exporting fixed cost  fx  2.0    Fairness parameter  θ  0.7    Share of enforceable contracts  λ  0.47  World Bank (2016)  Iceberg transportation cost  τ  1.1    Number of foreign countries  n  1    Table 2 Simulation results.   λ  ff  τ  Change in parameter  4.1%  –11.7%  –4.6%  Change in Y(t)  5.0%  5.0%  5.0%  Implied elasticity  1.2  –0.4  –1.1  Change in Ei  –2.9%  –4.6%  –2.8%  Implied elasticity  –0.7  0.4  0.6    λ  ff  τ  Change in parameter  4.1%  –11.7%  –4.6%  Change in Y(t)  5.0%  5.0%  5.0%  Implied elasticity  1.2  –0.4  –1.1  Change in Ei  –2.9%  –4.6%  –2.8%  Implied elasticity  –0.7  0.4  0.6  Lastly, I size the reduction of informal employment upon trade liberalization, as shown in Fig. 3. For the baseline value of τ=1.1, moving from autarky to trade reduces informal salaried employment by –1.9%. Abolishing all tariffs and going from autarky to τ = 1, leads to a –4.7% reduction in informal employment. In sum, the numerical simulation substantiates trade liberalization as an effective policy instrument in both increasing welfare and curbing informality at a level comparable to improving contract enforcement, and more effective than alleviating barriers to formality. Fig. 3 View largeDownload slide The effect of moving from autarky to trade on informal employment Ei Fig. 3 View largeDownload slide The effect of moving from autarky to trade on informal employment Ei 4. Conclusion Previous trade models did not reconcile heterogeneous firms, labour market frictions and informality in the form of registration non-compliance. By introducing informality into heterogeneous firm trade models with labour market frictions, this paper shows analytically how informality distorts resource allocation in an economy and trade can affect total salaried employment, wage inequality and welfare ambiguously. A numerical simulation corroborates trade liberalization as an effective tool in curbing informality and potentially raising welfare in the process. Therefore, the implication of this framework for policymakers is clear. While trade liberalization achieves the often-targeted reduction in informal employment, the economic conditions in a country ultimately determine whether trade is beneficial or detrimental in regard to employment, welfare and wage inequality in the presence of informality. Hence, this setup emphasizes the need to consider the existence of an informal sector and the economic environment jointly in policy decisions on trade. However, using reasonable parameters, a numerical simulation demonstrates that informal employment can be reduced, while increasing welfare, through trade liberalization and that liberalizing trade is a more effective tool than reducing entry costs to the formal sector. Several extensions of this work would provide for interesting future research endeavours. First, replacing the productivity sharing motif of the fair wage specification with revenue sharing would lead to a wage premium for exporters from foreign sales conditional on firm productivity, and can possibly entail different distributional consequences than the present work. Second, including heterogeneous workers and allowing firms to hire both informal and formal workers is a useful extension to capture the empirical findings of works with labour market-specific definitions of informality. Lastly, introducing informality with a broader definition as tax evasion and registration non-compliance and in a public finance framework would inform optimal taxation and enforcement decisions in the presence of an informal sector. Supplementary material Supplementary data are available at OEP online. Funding This work was supported by the Cornell Population Center. Footnotes 1 Several empirical studies find wage curves, that is the negative relationship between regional unemployment and wages, for informal and formal salaried workers (Bucheli and González, 2007; Ramos et al., 2010; Baltagi et al., 2013), which is consistent with my model setup of the labour market frictions arising from fair wage preferences in both sectors (Blanchflower and Oswald, 1995). 2 This CES-specification ensures that the unemployment rate is independent of the size of the economy, as there is no evidence on the correlation between the two, and prevents an increase in aggregate output due to an increase in the number of input varieties. If, for example, equal amounts of every input q(v)=qM were to be used in the final good production process, the production function would imply Y = q. External scale effects are well understood from previous literature, e.g. Ethier (1982), and through this specification the focus lies purely on the selection effect of trade liberalization. 3 Recent empirical work that examines the effect of formality on firm performance, controlling for firm characteristics and self-selection into the formal sector, finds a significant effect of formality, particularly of increasing firm profits (Fajnzylber et al., 2011; McKenzie and Sakho, 2010; Rand and Torm, 2012). λ can be seen to capture this effect of formality on firm performance. 4 If an outsider were to be hired for a lower wage, she would adjust her reference wage w^ and, given the wage below reference level, decrease her effort level accordingly. Therefore, in equilibrium wage underbidding is not attractive to firms. 5 Breaking even at a lower productivity requires that ϕi*<ϕf* for ϕi* from πi(ϕi*)=0 & ϕf* from πf(ϕf*)=0. From eq. (6): ϕi*=[fiσMY]1ξ(Eiwi¯+Efwf¯)ρ1θ−1 and ϕf*=[ffσMY]1ξ(Eiwi¯+Efwf¯)ρ1θ−1(1−λ). Hence, (1−λ)−ξ<fffi. 6 Mathematically, [rf(ϕi)/ri(ϕf)]=(ϕf/ϕi)ξ(1−λ)−ξ and ∂[rf(ϕi)/ri(ϕf)]/∂(ϕf/ϕi)=ξ(ϕf/ϕi)ξ−1(1−λ)−ξ>0. 7 Verhoogen (2008) models product quality explicitly, albeit by using heterogeneous workers. 8 An interpretation of the condition comes from rewriting it as 1/ρ<1/θ, that is the love of variety 1/ρ needs to be greater than the inverse of the fairness consideration parameter θ. Intuitively, for a lower love of variety 1/ρ, the cheaper varieties are demanded relatively more, which are produced by higher-productivity firms. Hence, higher-productivity firms hire more workers. On the other hand, a higher fairness preference θ raises the wages paid by high-productivity firms and accordingly a decrease in those firms’ hiring. 9 See online Appendix A.1. 10 A Pareto distributions has a finite mean only if its shape parameter k > 1. Productivity is Pareto distributed and labour as well as revenue are power functions of productivity. Therefore, also firm size and revenue are Pareto distributed. For the distributions of firm size and revenue to have a finite mean: kξ−θ>1 and kξ>1, respectively, have to hold. Thus, as in Egger and Kreickemeier (2009), k>ξ is assumed. 11 Me is exogenously given and without loss of generality normalized to 1. 12 The aggregate revenue in the economy is described by Y, because P = 1. It consists of both the firms’ and the workers’ share of the aggregate revenue. Due to the monopolistic competition assumption and resulting prices characterized by a constant markup 1/ρ over marginal costs, the shares are constant proportions. A constant fraction 1/σ of the firm revenue accrues to the firm and (σ−1)/σ=ρ accrues to the workers of the firm. Hence, the wage income of all employed workers (Eiwi¯+Efwf¯)L has to equal their constant share of the aggregate revenue ρY. 13 k>ξ is assumed. This implies σ(1−θ)−k−1+θ<0 and thus σ(1−θ)−k−1<0. 14 For proof see online Appendix A.2. 15 The analysis in this model differs to the one in Egger and Kreickemeier (2012) in two ways. First, Egger and Kreickemeier (2012) consider heterogeneous individuals and examine wage inequality between self-selected entrepreneurs and salaried workers. Second, workers consider firm revenue in their fair wage preference, which leads to an exporter wage premium. Opposed to that, I examine wage inequality among identical workers that can be employed in the informal or formal sector and workers consider firm productivity in their fair wage preference. 16 Gf is the Gini-coefficient of a purely-formal or purely-informal economy. This result is derived in online Appendix B. 17 Wage inequality being exactly the same in a purely informal and a purely formal economy is a stylized result. However, some support for this result comes from Saavedra (2001), who finds that the coefficient of variation for the hourly wage of salaried informal workers is comparable to the one of salaried formal workers. 18 For the extreme case of θ = 0, i.e. all workers receive the same wage, Gf = 0 and the economy would be perfectly equal. 19 What is required for informal exporting to be profitable at a lower productivity level than formal exporting, i.e. ϕi<ϕf from: πix(ϕi)=nYσM{ϕiθ−1(Eiwi¯+Efwf¯)1−θρ−1τ}1−σ−fx=0 & πfx(ϕf)=nYσM{(ϕf1−λ)θ−1(Eiwi¯+Efwf¯)1−θρ−1τ}1−σ−fx=0. The resulting requirement is 1>(1−λ)−1, which is a contradiction given that λ∈(0,1). 20 Ensuring ϕx*>ϕf* for ϕf* from πi(ϕf*)=πf(ϕf*) and ϕx* from πx(ϕx*)=0 is sufficient to sort domestic productivity levels below export productivity levels. This results in: ϕf*=[(ff−fi)MσY((1−λ)−ξ−1)]1ξ(Eiwi¯+Efwf¯)ρ1θ−1 and: ϕx*=[fxnσMY]1ξ(Eiwi¯+Efwf¯)(ρτ)1θ−1(1−λ). In combination, fxτξ1−θn(1−λ)−ξ>ff−fi(1−λ)−ξ−1. 21 See online Appendix A.3. 22 Ei(t)Ei(a)=[1+n(fxfinτ1−σ)−kξ(1−λ)−k]−θξ[1+(1−λ)−k(nτ1−σ)kξ(fxfi)ξ−kξ((1−λ)−ξ−1)kξ(fiff−fi)k−ξξ+1]θξ−1, where the subscript (a) and (t) stand for autarky and trade. (Ei(t)Ei(a))<1 because −θξ<0 and θξ−1<0. Hence, informal sector employment unambiguously decreases upon trade liberalization. 23 Proof available on request. 24 The model focuses on the interaction between the informal and formal sector and accordingly ignores an exporter wage premium conditional on firm productivity. The model can be extended to include a fair wage constraint that uses firm revenue and not firm productivity as firm-internal reference point. This would lead to an exporter wage premium and could provide another source for wage inequality, even among formal workers. 25 Given its complicated nature, the Gini-coefficient for the open economy is derived in online Appendix C. 26 For the extreme case of (ϕi*/ϕx*)=0, i.e. no firm exports, the open economy Gini-coefficient collapses to the autarky specification. If in addition to that, (ϕi*/ϕf*)=0 or (ϕi*/ϕf*)=1 are imposed, the coefficient further collapses to the formal-sector-only specification. 27 For a derivation of this result, see online Appendix B. As shown by Helpman et al. (2010), the Gini-coefficient depends only on the shape parameter of the wage distribution, but not its lower limit. Both informal and formal sector wage distribution feature the same shape parameter and thus the same inequality. 28 The intuition here is similar to the effect of a conditional exporter wage premium on wage inequality, as shown empirically by Akerman et al. (2013) and theoretically by Helpman et al. (2010). The findings suggest that a major share of overall wage inequality arises from the wage differences between firms in the same industry paid to workers with similar characteristics, i.e. within-industry wage inequality. Moreover, wage inequality is driven by the employment adjustments of these firms upon trade liberalization. 29 Proof for this is available from the author upon request. 30 Recent work by Dhingra and Morrow (2014) shows that the pro-competitive effect of trade can decrease welfare when market allocations or firm entry are not inefficient, as is the case here in the presence of informality. 31 For the share of enforceable contacts I employ quality of judicial processes index for Latin American & Caribbean, which is 8.4/16=0.47. Acknowledgements I am grateful to Nancy Chau, Ravi Kanbur, Ankita Patnaik, Joel Landry, the 2013 NEUDC, 2013 ISI conference, 2014 Midwest International Trade and 2014 ThReD participants, as well as two anonymous referees for helpful comments and suggestions. References Acosta P., Montes-Rojas G. ( 2014) Informal jobs and trade liberalisation in Argentina, Journal of Development Studies , 50, 1104– 18. Google Scholar CrossRef Search ADS   Akerlof G.A., Yellen J.L. ( 1990) The fair wage-effort hypothesis and unemployment, Quarterly Journal of Economics , 105, 255– 83. Google Scholar CrossRef Search ADS   Akerman A., Helpman E., Itskhoki O., Muendler M.-A., Redding S. ( 2013) Sources of wage inequality, American Economic Review , 103, 214– 19. Google Scholar CrossRef Search ADS   Aleman-Castilla B. ( 2006) The effect of trade liberalization on informality and wages: evidence from Mexico. CEP Discussion Paper 763, Centre for Economic Performance, London School of Economics, London. Amiti M., Davis D.R. ( 2012) Trade, firms, and wages: theory and evidence, Review of Economic Studies , 79, 1– 36. Google Scholar CrossRef Search ADS   Antunes A.R., de V., Cavalcanti T.V. ( 2007) Start up costs, limited enforcement, and the hidden economy, European Economic Review , 51, 203– 24. Google Scholar CrossRef Search ADS   Arias J., Artuc E., Lederman D., Rojas D. ( 2013) Trade, informal employment and labor adjustment costs. Policy Research Working Paper 6614, World Bank, Washington, DC. Google Scholar CrossRef Search ADS   Attanasio O., Goldberg P.K., Pavcnik N. ( 2004) Trade reforms and wage inequality in Colombia, Journal of Development Economics , 74, 331– 66. Google Scholar CrossRef Search ADS   Auriol E., Warlters M. ( 2005) Taxation base in developing countries, Journal of Public Economics , 89, 625– 46. Google Scholar CrossRef Search ADS   Axtell R.L. ( 2001) Zipf distribution of U.S. firm sizes, Science , 293, 1818– 20. Google Scholar CrossRef Search ADS PubMed  Baltagi B.H., Baskaya Y.S., Hulagu T. ( 2013) How different are the wage curves for formal and informal workers? Evidence from Turkey, Papers in Regional Science , 92, 271– 83. Google Scholar CrossRef Search ADS   Bargain O., Kwenda P. ( 2011) Earnings structures, informal employment, and self-employment: new evidence from Brazil, Mexico, and South Africa, Review of Income and Wealth , 57, 100– 22. Google Scholar CrossRef Search ADS   Basu A.K., Chau N.H., Kanbur R. ( 2011) Contractual dualism, market power and informality. IZA Discussion Papers 5845, Institute for the Study of Labor (IZA), Bonn. Google Scholar CrossRef Search ADS   Batra G., Kaufmann D., Stone A.H.W. ( 2003) Investment climate around the world: Voices of the firms from the world business environment survey . The World Bank, Washington, DC. Google Scholar CrossRef Search ADS   Bernard A.B., Jensen J.B. ( 1995) Exporters, jobs, and wages in U.S. manufacturing: 1976–1987. Brookings Papers on Economic Activity. Microeconomics , 1995: 67– 112. Google Scholar CrossRef Search ADS   Bewley T. ( 2005) Fairness, reciprocity, and wage rigidity, in Gintis H., Bowles S., Boyd R., Fehr E. (eds) Moral Sentiments and Material Interests: The Foundations of Cooperation in Economic Life , MIT Press, Cambridge, MA, 303– 8. Google Scholar CrossRef Search ADS   Bigsten A., Kimuyu P., Lundvall K. ( 2004) What to do with the informal sector?, Development Policy Review , 22, 701– 15. Google Scholar CrossRef Search ADS   Blanchard O., Giavazzi F. ( 2003) Macroeconomic effects of regulation and deregulation in goods and labor markets, Quarterly Journal of Economics , 118, 879– 907. Google Scholar CrossRef Search ADS   Blanchflower D.G., Oswald A.J. ( 1995) An introduction to the wage curve, Journal of Economic Perspectives , 9, 153– 67. Google Scholar CrossRef Search ADS   Brown C., Medoff J. ( 1989) The employer size-wage effect, Journal of Political Economy , 97, 1027– 59. Google Scholar CrossRef Search ADS   Bruhn M. ( 2013) A tale of two species: revisiting the effect of registration reform on informal business owners in Mexico, Journal of Development Economics , 103, 275– 83. Google Scholar CrossRef Search ADS   Bucheli M., González C. ( 2007) An estimation of the wage curve for Uruguay. Documentos de Trabajo 11/07, Departamento de Economía, Facultad de Ciencias Sociales. Universidad de la República, Montevideo. Bustos P. ( 2011) Trade liberalization, exports, and technology upgrading: evidence on the impact of MERCOSUR on Argentinian firms, American Economic Review , 101, 304– 40. Google Scholar CrossRef Search ADS   Dabla-Norris E., Gradstein M., Inchauste G. ( 2008) What causes firms to hide output? The determinants of informality, Journal of Development Economics , 85, 1– 27. Google Scholar CrossRef Search ADS   Danthine J.-P., Kurmann A. ( 2007) The macroeconomic consequences of reciprocity in labor relations, Scandinavian Journal of Economics , 109, 857– 81. Google Scholar CrossRef Search ADS   Davidson C., Matusz S.J. ( 2009) International Trade with Equilibrium Unemployment , Princeton University Press, Princeton, NJ. Google Scholar CrossRef Search ADS   Davies R.B., Paz L.S. ( 2011) Tariffs versus vat in the presence of heterogeneous firms and an informal sector, International Tax and Public Finance , 18, 533– 54. Google Scholar CrossRef Search ADS   Davis D.R., Harrigan J. ( 2011) Good jobs, bad jobs, and trade liberalization, Journal of International Economics , 84, 26– 36. Google Scholar CrossRef Search ADS   de Paula A., Scheinkman J.A. ( 2011) The informal sector: an equilibrium model and some empirical evidence from Brazil, Review of Income and Wealth , 57, 8– 26. Google Scholar CrossRef Search ADS   de Soto H. ( 1989) The Other Path , Harper and Row, New York, NY. Dhingra S., Morrow J. ( 2014) Monopolistic competition and optimum product diversity under firm heterogeneity. Mimeo, London School of Economics, London. Djankov S., La Porta R., Lopez-De-Silanes F., Shleifer A. ( 2002) The regulation of entry, Quarterly Journal of Economics , 117, 1– 37. Google Scholar CrossRef Search ADS   Dutt P., Mitra D., Ranjan P. ( 2009) International trade and unemployment: theory and cross-national evidence, Journal of International Economics , 78, 32– 44. Google Scholar CrossRef Search ADS   Egger H., Kreickemeier U. ( 2009) Firm heterogeneity and the labor market effects of trade liberalization, International Economic Review , 50, 187– 216. Google Scholar CrossRef Search ADS   Egger H., Kreickemeier U. ( 2012) Fairness, trade, and inequality, Journal of International Economics , 86, 184– 96. Google Scholar CrossRef Search ADS   El Badaoui E., Strobl E., Walsh F. ( 2010) The formal sector wage premium and firm size, Journal of Development Economics , 91, 37– 47. Google Scholar CrossRef Search ADS   Ethier W.J. ( 1982) National and international returns to scale in the modern theory of international trade, American Economic Review , 72, 389– 405. Fajnzylber P., Maloney W.F., Montes-Rojas G.V. ( 2011) Does formality improve micro-firm performance? Evidence from the Brazilian SIMPLES program, Journal of Development Economics , 94, 262– 76. Google Scholar CrossRef Search ADS   Fehr E., Falk A. ( 1999) Wage rigidity in a competitive incomplete contract market, Journal of Political Economy , 107, 106– 34. Google Scholar CrossRef Search ADS   Felbermayr G., Prat J., Schmerer H.-J. ( 2011a) Trade and unemployment: what do the data say?, European Economic Review , 55, 741– 58. Google Scholar CrossRef Search ADS   Felbermayr G., Prat J., Schmerer H.-J. ( 2011b) Globalization and labor market outcomes: wage bargaining, search frictions, and firm heterogeneity, Journal of Economic Theory , 146, 39– 73. Google Scholar CrossRef Search ADS   Fields G.S. ( 1975) Rural-urban migration, urban unemployment and underemployment, and job-search activity in LDCs, Journal of Development Economics , 2, 165– 87. Google Scholar CrossRef Search ADS PubMed  Fiess N.M., Fugazza M. ( 2012) Informality and openness to trade: insights from cross-sectional and panel analyses, Margin: The Journal of Applied Economic Research , 6, 235– 75. Google Scholar CrossRef Search ADS   Fiess N.M., Fugazza M., Maloney W.F. ( 2010) Informal self-employment and macroeconomic fluctuations, Journal of Development Economics , 91, 211– 26. Google Scholar CrossRef Search ADS   Foster L., Haltiwanger J., Syverson C. ( 2008) Reallocation, firm turnover, and efficiency: selection on productivity or profitability?, American Economic Review , 98, 394– 425. Google Scholar CrossRef Search ADS   Goldberg P.K., Pavcnik N. ( 2003) The response of the informal sector to trade liberalization, Journal of Development Economics , 72, 463– 96. Google Scholar CrossRef Search ADS   Günther I., Launov A. ( 2012) Informal employment in developing countries: opportunity or last resort?, Journal of Development Economics , 97, 88– 98. Google Scholar CrossRef Search ADS   Head K., Mayer T. ( 2014) Chapter 3 – gravity equations: workhorse, toolkit, and cookbook, in Gita Gopinath E.H., Rogoff K. (eds) Handbook of International Economics , vol. 4, Elsevier, Amsterdam, 131– 95. Heid B. ( 2015) Regional trade agreements, unemployment, and the informal sector. Working paper, CESifo Area Conference on Global Economy Working Paper, Munich. Heid B., Larch M., Riaño A. ( 2013) The rise of the maquiladoras: a mixed blessing, Review of Development Economics , 17, 252– 67. Google Scholar CrossRef Search ADS   Helpman E., Itskhoki O. ( 2010) Labour market rigidities, trade and unemployment, Review of Economic Studies , 77, 1100– 37. Google Scholar CrossRef Search ADS   Helpman E., Itskhoki O., Redding S.J. ( 2010) Inequality and unemployment in a global economy, Econometrica , 78, 1239– 83. Google Scholar CrossRef Search ADS   Howitt P. ( 2002) Looking inside the labor market: a review article, Journal of Economic Literature , 40, 125– 38. Hsieh C.-T., Klenow P.J. ( 2009) Misallocation and manufacturing TFP in China and India, Quarterly Journal of Economics , 124, 1403– 48. Google Scholar CrossRef Search ADS   Kreickemeier U., Nelson D. ( 2006) Fair wages, unemployment and technological change in a global economy, Journal of International Economics , 70, 451– 69. Google Scholar CrossRef Search ADS   La Porta R., Shleifer A. ( 2008) The unofficial economy and economic development, Brookings Papers on Economic Activity , 2008, 275– 352. Google Scholar CrossRef Search ADS   La Porta R., Shleifer A. ( 2011) The unofficial economy in Africa. Working Paper 16821, National Bureau of Economic Research, Cambridge, MA. Loayza N.V. ( 1996) The economics of the informal sector: a simple model and some empirical evidence from Latin America, Carnegie-Rochester Conference Series on Public Policy , 45, 129– 62. Google Scholar CrossRef Search ADS   Maloney W.F. ( 2004) Informality revisited, World Development , 32, 1159– 78. Google Scholar CrossRef Search ADS   Marjit S., Ghosh S., Biswas A. ( 2007) Informality, corruption and trade reform, European Journal of Political Economy , 23, 777– 89. Google Scholar CrossRef Search ADS   McCaig B., Pavcnik N. ( 2013) Moving out of agriculture: structural change in Vietnam. Working Paper 19616, National Bureau of Economic Research, Cambridge, MA. McCaig B., Pavcnik N. ( 2014) Export markets and labor allocation in a low-income country. Working Paper 20455, National Bureau of Economic Research, Cambridge, MA. McKenzie D., Sakho Y.S. ( 2010) Does it pay firms to register for taxes? The impact of formality on firm profitability, Journal of Development Economics , 91, 15– 24. Google Scholar CrossRef Search ADS   Melitz M.J. ( 2003) The impact of trade on intra-industry reallocations and aggregate industry productivity, Econometrica , 71, 1695– 725. Google Scholar CrossRef Search ADS   Menezes-Filho N.A., Muendler M.-A. ( 2011) Labor reallocation in response to trade reform. Working Paper 17372, National Bureau of Economic Research, Cambridge, MA. Paz L.S. ( 2014) The impacts of trade liberalization on informal labor markets: a theoretical and empirical evaluation of the Brazilian case, Journal of International Economics , 92, 330– 48. Google Scholar CrossRef Search ADS   Prado M. ( 2011) Government policy in the formal and informal sectors, European Economic Review , 55, 1120– 36. Google Scholar CrossRef Search ADS   Quintin E. ( 2007) Contract enforcement and the size of the informal economy, Economic Theory , 37, 395– 416. Google Scholar CrossRef Search ADS   Radchenko N. ( 2014) Heterogeneity in informal salaried employment: evidence from the Egyptian labor market survey, World Development , 62, 169– 88. Google Scholar CrossRef Search ADS   Ramos R., Duque J.C., Surinach J. ( 2010) Is the wage curve formal or informal? Evidence for Colombia, Economics Letters , 109, 63– 65. Google Scholar CrossRef Search ADS   Rand J., Torm N. ( 2012) The benefits of formalization: evidence from Vietnamese manufacturing SMEs, World Development , 40, 983– 98. Google Scholar CrossRef Search ADS   Rauch J.E. ( 1991) Modelling the informal sector formally, Journal of Development Economics , 35, 33– 47. Google Scholar CrossRef Search ADS   Roberts M.J., Tybout J.R. ( 1997) The decision to export in Colombia: an empirical model of entry with sunk costs, American Economic Review , 87, 545– 64. Saavedra L.A. ( 2001) Female wage inequality in Latin American labor markets. Policy Research Working Paper 2741, World Bank, Washington, DC. Google Scholar CrossRef Search ADS   Schneider F., Buehn A., Montenegro C.E. ( 2010) New estimates for the shadow economies all over the world, International Economic Journal , 24, 443– 61. Google Scholar CrossRef Search ADS   Ulyssea G. ( 2010) Regulation of entry, labor market institutions and the informal sector. Journal of Development Economics , 91, 87– 99. Google Scholar CrossRef Search ADS   Verhoogen E.A. ( 2008) Trade, quality upgrading, and wage inequality in the Mexican manufacturing sector, Quarterly Journal of Economics , 123, 489– 530. Google Scholar CrossRef Search ADS   World Bank ( 2016) Doing Business 2016: Measuring Regulatory Quality and Efficiency. The World Bank, Washington, DC. © Oxford University Press 2017 All rights reserved http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Oxford Economic Papers Oxford University Press

Heterogeneous firms and informality: the effects of trade liberalization on labour markets

Loading next page...
 
/lp/ou_press/heterogeneous-firms-and-informality-the-effects-of-trade-muAL47FUk6
Publisher
Oxford University Press
Copyright
© Oxford University Press 2017 All rights reserved
ISSN
0030-7653
eISSN
1464-3812
D.O.I.
10.1093/oep/gpx029
Publisher site
See Article on Publisher Site

Abstract

Abstract The informal sector is often seen as a way for firms to evade regulation. In this paper, I therefore investigate the role of the informal sector in the impact of trade liberalization on employment, wage inequality and welfare in a model of trade with heterogeneous firms and endogenous wage dispersion. The findings suggest that trade liberalization reduces informal employment unambiguously. Contrary to the extant literature, however, its impact on total salaried employment, wage inequality and welfare is country-specific. 1. Introduction In the seminal heterogeneous firm trade model by Melitz (2003), trade liberalization induces firm selection on productivity into exporting and forces the least-productive firms to exit the market. The result is improved welfare and higher than average productivity. Yet, empirical studies provide suggestive evidence that informality can act as a channel of distortion to the resource allocation process among firms (La Porta and Shleifer, 2008; Hsieh and Klenow, 2009; McCaig and Pavcnik, 2013), which might affect the welfare gains from trade. Further, informal workers make up a large portion of the workforce particularly in developing countries (Schneider et al., 2010). Yet, the empirical evidence on the impact of trade on informal employment remains conflicting (Goldberg and Pavcnik, 2003; Fiess and Fugazza, 2012; Acosta and Montes-Rojas, 2014; McCaig and Pavcnik, 2014), and the mechanisms through which workers might be affected in the presence of informality are unclear. Thus, in this paper I introduce informality into a trade model of heterogeneous firms to address two important questions: How does trade liberalization affect employment and wages in the presence of an informal sector? What is the effect of trade liberalization on welfare in the presence of an informal sector? To answer the first question, the model predicts that trade liberalization leads to a reduction in informal sector employment, consistent with empirical work by Fiess and Fugazza (2012) and McCaig and Pavcnik (2014), and ambiguously affects formal sector employment in line with Davidson and Matusz (2009), Dutt et al. (2009), Felbermayr et al. (2011ba) and Menezes-Filho and Muendler (2011). This result derives not just from export selection and firm exit, both well known from Melitz (2003), but a new adjustment mechanism—the informalization of firms. Intuitively, trade liberalization induces the selection of high-productivity formal firms into exporting and hiring more workers, while lower-productivity formal firms switch to informal production to remain profitable, and accordingly shed formal labour. Depending on the characteristics of the economy, such as the cost of exporting, the additional hires by exporting firms may or may not compensate for the labour shedding in the formal sector. Furthermore, the lowest-productivity informal firms are forced to exit the market, resulting in a reduction in informal sector employment. The net effect on total employment is ambiguous. Additionally, the model is the first informality model to allow studying both trade liberalization and endogenous wage dispersion. Wage inequality is caused by a wage gap between informal and formal workers, as frequently found in empirical studies (Bargain and Kwenda, 2011; de Paula and Scheinkman, 2011; Günther and Launov, 2012), and workers’ fair wage preferences with respect to firm productivity that lead to within-group inequality. The model predicts that liberalizing trade increases wage inequality between informal and formal workers. Because of the reduction in informal sector employment and sector switching, the increase of the informal sector average wage is lower than the increase in the formal sector average wage and the average wages of both sectors diverge. Hence, between-group wage inequality, as measured by the ratio of the formal sector relative to the informal sector average wage, increases. Wage inequality among all employed workers, as measured by the Gini-coefficient, is ambiguously affected through the above employment effect and depends on the proportion of formal sector firms, and hence formal workers, prior to trade liberalization. To answer the second question, trade liberalization leads to an ambiguous change in aggregate output, and hence welfare. Similar to the employment effect, the increase in aggregate output by shifting resources towards the highest-productivity exporting firms may or may not compensate for the loss in aggregate output due to the exit of the least-productive informal firms and the informalization of the least-productive formal firms. Therefore, the informal sector plays a role in the resource allocation process, as found by Bruhn (2013), and trade liberalization can either increase aggregate output (McCaig and Pavcnik, 2013), and hence welfare, or reduce it by affecting informal sector participation. This result is particularly interesting, as it stands in contrast to the clear increase in welfare that is commonly established in the theoretical literature on trade with heterogeneous firms (e.g. Egger and Kreickemeier, 2009). Lastly, a simple numerical simulation indicates that liberalizing trade is close in effectiveness to improving contract enforcement in reducing informal employment and increasing welfare, given reasonable economy parameters from the empirical literature. Notably, trade liberalization has a stronger impact than improving access to the formal sector, which substantiates the relevance of trade liberalization in curbing informality. The model derives from introducing informality into Egger and Kreickemeier (2009), which is a heterogeneous firm trade model à la Melitz (2003) with a fair wage specification along the lines of Akerlof and Yellen (1990). It consists of three crucial pieces. First, firms are heterogeneous in productivity. Second, informality is an active entrepreneurial choice given the costs and benefits of informal and formal sector participation, as shown by Maloney (2004), and in line with the seminal work by de Soto (1989) is defined as firm-level non-compliance with registration. I therefore follow the strain of literature that shows informality as the result of excessive regulatory burden in the formal sector, and a profit-maximizing strategy for entrepreneurs (Djankov et al., 2002; Auriol and Warlters, 2005; Antunes and de V. Cavalcanti, 2007; Ulyssea, 2010; de Paula and Scheinkman, 2011). Recent research by Bruhn (2013) finds that in addition to the here modelled entrepreneurial segment, there exists a segment of self-employed informal entrepreneurs that see informality only as a last resort and would rather work as salaried workers in the formal sector. This type of subsistence informality is featured in this model as a residual to salaried employment in informal and formal multi-worker firms. Third, labour markets are imperfect and labour market frictions are caused by workers’ fair wage expectations.1 Given that workers are randomly matched to firms in this model, informal workers are excluded from higher-wage formal employment. Accordingly, I model informal employment corresponding to what is considered the exclusion view of informal employment. Current research indicates, however, that additionally there exists a segment of workers that voluntarily choose informality, rather than being excluded from formal work (Günther and Launov, 2012; Radchenko, 2014). Given the model’s focus, the voluntary informal workforce is not part of the present analysis. This paper is related to several lines of previous research. First, it contributes to heterogeneous firm trade models, particularly the work featuring labour market frictions arising from search-and-matching (Helpman and Itskhoki, 2010; Felbermayr et al., 2011ab) and fair wage (Egger and Kreickemeier, 2009; Davis and Harrigan, 2011; Amiti and Davis, 2012) specifications. Additionally, it is related to Bustos (2011), who studies technology upgrading of exporters modelled in a similar fashion to formality here. Second, the paper follows a long list of models of the informal economy. Fields (1975) uses a Harris-Todaro-type model to analyse unemployment, whereas Rauch (1991) provides a rationale for size-dualism with large formal and small informal firms. Loayza (1996) examines the interaction of tax evasion and public good congestion. The link between trade reform, corruption and informality is studied by Marjit et al. (2007). El Badaoui et al. (2010) demonstrate the link between firm size, wages and informality. Wage dualism between formal and informal firms, and workers is explained by Basu et al. (2011). Prado (2011) examines general equilibrium government decisions on regulation and enforcement in a heterogeneous firm model where informal firms evade taxes. Arias et al. (2013) take a labour market focus of informality and model workers’ decisions to move between the informal and formal sector. Heid et al. (2013) construct a heterogeneous firm trade model with labour market frictions to analyse the rise of the maquiladora sector on employment, welfare and wage inequality in the presence of informality. The model, however, considers heterogeneous workers and a small open economy setting that features a fixed formality wage premium. Both Aleman-Castilla (2006) and Paz (2014) consider trade and informality from a labour market perspective by defining informality as payroll tax evasion, where Aleman-Castilla (2006) models a world without labour market frictions and full employment, and Paz (2014) features labour market imperfections, but only examines informal employment and average wages in a small open economy. Heid (2015) studies the impact of regional trade agreements on welfare, employment and informality in a structural gravity framework and similarly finds that trade reduces informal employment. Fiess et al. (2010) take yet another direction by combining macroeconomic fluctuations and informal self-employment in a small open economy model. Lastly, the most closely related work comes from Davies and Paz (2011), who also study the impact of trade liberalization on informality in a model of heterogeneous firms and endogenous entry. While they similarly find that a tariff reduction decreases the size of the informal sector, their model defines informality as tax evasion, contrasts the effect of tariffs to VAT on the informal sector, employs a quasi-linear utility function and assumes a perfect labour market. Therefore, this is the first paper that presents a unified theory of trade and the informal sector that accommodates five important points: (i) informality defined as regulation non-compliance; (ii) heterogeneous firms; (iii) a large open economy setting; (iv) formal and informal salaried employment, and informal self-employment; and (v) endogenous wage dispersion in both formal and informal sector. Through combining all these elements, this model complements earlier work by providing a tractable setup that allows policymakers a rich look at the labour market implications of trade liberalization, including an analysis of between-sector and within-economy wage inequality that previous work did not offer. I proceed as follows. Section 2 characterizes the closed economy specification of the model. Section 3 extends the model to an open economy and discusses the impact of trade liberalization. Section 4 concludes the paper. 2. The closed economy model The economy consists of L units of labour, the only factor of production. There are two types of goods: a final output and intermediate goods. The final output is homogeneous and its market is in perfect competition. The intermediate goods are differentiated and produced under monopolistic competition by a mass of heterogeneous firms (Melitz, 2003). 2.1 The final output The final output Y is an aggregate of all intermediate goods and is characterized by the following constant-elasticity-of-substitution (CES) production function (Blanchard and Giavazzi, 2003):2  Y=[M−(1−ρ)∫v∈Vq(v)ρdv]1ρ,0<ρ<1. (1) Intermediate good varieties are indexed with v and V is the set representing the mass of available intermediate goods M. q(v) and p(v) are the quantity and the price of variety v. σ≡11−ρ is the elasticity of substitution between the varieties of intermediate goods. The final output market is under perfect competition and the final output acts as numeraire. The resulting CES-price index P is thus normalized to 1. The price index is described by:   P=[M−1∫v∈Vp(v)1−σdv]11−σ. (2) Through profit maximization of the producer of the final good, the demand for variety v of the intermediate good is   q(v)=YMp(v)−σ. (3) 2.2 The intermediate goods: informal and formal sector The intermediate goods are produced under monopolistic competition by firms in two sectors: an informal and a formal sector. Henceforth all informal sector variables feature subscript i and formal sector variables subscript f. The firms are heterogeneous in their productivity and every firm produces one unique variety of input for the final output production. Hence, M can interchangeably be used to account for the number of firms or total number of input varieties v. M=Mi+Mf is the number of domestically active firms, which consists of all informal sector firms, Mi, and formal sector firms, Mf. Firms face fixed costs of production in terms of final output Y and variable costs that are directly related to the firm’s productivity ϕ. Firm output is linear in labour inputland productivity ϕ, that is q=ϕl. Firms with the same productivity behave in the same manner. Therefore, I index firms solely in terms of their productivity ϕ. Firms voluntarily choose to become either informal or formal producers. Informal producers face fixed cost fi and formal producers face ff to start production. I assume ff > fi, to reflect that formality generates an additional registration cost on top of the basic capital cost fi required from any entrepreneur to start a business (Auriol and Warlters, 2005; Antunes and de V. Cavalcanti, 2007). As Djankov et al. (2002) points out, the registration cost usually is not an efficient transfer to the government, but rather red tape caused by bureaucratic hurdles and complex registration procedures. Corresponding to Antunes and de V. Cavalcanti (2007) and Quintin (2007), who show that imperfect contract enforcement in the formal sector and lack thereof in the informal sector are main drivers of informality, I assume that contracts can only be enforced in the formal sector, albeit limited to an exogenous fraction λ∈(0,1). The effective productivity of a firm in the formal sector is described by ϕ1−λ.3 No contracts can be enforced in the informal sector. The profit maximizing price of both types of firms is a constant markup 1/ρ over marginal cost, where w(ϕ) denotes the wage paid by a firm with productivity ϕ and ε is the effort level of workers:   pi(ϕ)=wi(ϕ)ρϕε and pf(ϕ)=wf(ϕ)ρϕ1−λε. (4) In combination, demand for the individual input variety (3) and the profit-maximizing price (4) lead to the informal and formal revenues   ri(ϕ)=YM(wi(ϕ)ρϕε)1−σ and rf(ϕ)=YM(wf(ϕ)ρϕ1−λε)1−σ, (5) and profits:   πi(ϕ)=YσM(wi(ϕ)ρϕε)1−σ−fi and πf(ϕ)=YσM(wf(ϕ)ρϕ1−λε)1−σ−ff. (6) Besides firm productivity and wages, firm revenue depends on two factors. First, the number of firms operating in the domestic market M (and hence the number of varieties sold in the domestic market) influence the demand for each individual variety. A strong domestic competition (thus, a high M) reduces the demand for each variety and therefore the profitability of each firm’s operation. Second, the demand for each firm’s variety rises with the aggregate revenue in the economy (here Y, as P is normalized to 1). 2.3 The labour market and wage determination with informality There are three groups of workers: informal salaried workers Li, formal salaried workers Lf and informal self-employed workers Ls. Together they make up the total labour force in the economy L≡Li+Lf+Ls. The informal salaried employment share, formal salaried employment share and share of self-employed informal workers are described by Ei=(Li/L), Ef=(Lf/L) and S=(Ls/L). E≡Ei+Ef=1−S is the fraction of salaried workers employed by multi-worker firms. Workers are identical and have a preference for fair wages along the lines of Akerlof and Yellen (1990). As workers are identical, they are randomly selected by employers in the hiring process and can become either informal or formal salaried workers or become self-employed. Without loss of generality, I assume that self-employed workers just receive a subsistence wage, which is normalized to 0. Moreover, henceforth I consider only informal salaried workers as informal workers, because self-employed informal workers as residual of salaried employment are not the focus of the present analysis. I distinguish the informal sector average wage wi¯ from the formal sector average wage wf¯. The average wages are calculated as follows. The wage bill of the informal sector Wi, i.e. the sum of all wages wi(ϕ) paid in the informal sector, is divided by the amount of informal employment Li. This provides the informal sector average wage wi¯=(Wi/Li). The calculation of the formal sector average wage follows the same procedure. Taking the potential informal self-employment that provides only a subsistence wage of 0 into account, the average wage income per worker in the economy (Eiwi¯+Efwf¯) consists of the two average wages weighted by the respective salaried employment shares, that is:   Eiwi¯+Efwf¯=Wi+WfL. (7) The reference wage of workers w(ϕ) consists of two parts: a firm-internal and a firm-external factor (Howitt, 2002; Bewley, 2005; Danthine and Kurmann, 2007). The firm-internal component captures the economic success of the firm as measured by the firm’s productivity ϕ. When hired by a formal firm, workers are aware of the productivity bonus that firms experience due to enforceable contacts in the formal sector and take the firm’s effective productivity ϕ1−λ into account. In line with Kreickemeier and Nelson (2006), the firm-external component relates to the labour market and is the outside option of workers. The external reference point is therefore described by the average wage income per worker: (Eiwi¯+Efwf¯). The workers’ fairness consideration between firm-internal and -external reference points is a geometric average weighted by the fairness parameter θ∈(0,1). Through the firm-internal component that relates the wage to firm productivity, the fair wage setup induces heterogeneous wages among workers that are identical before the hiring process. The informal and formal reference wages take the following functional form:   wi^(ϕ)=ϕθ(Eiwi¯+Efwf¯)1−θandwf^(ϕ)=(ϕ1−λ)θ(Eiwi¯+Efwf¯)1−θ. (8) Workers exert effort level ε relative to what they perceive to be a fair wage w^. For w(ϕ)≥w^ workers effort their maximum effort level ε = 1, that is ε=min⁡{w(ϕ)/w^,1}. Additionally, I assume that worker effort level ε cannot be contracted and the only mechanism to induce effort is a wage offer. Therefore, outside workers are not able to underbid the wage of currently employed workers, all firms pay the firm-specific reference wage w^ and all employed workers exert effort ε = 1.4 This is supported by the experimental evidence of Fehr and Falk (1999), who show that worker effort level is positively related to their wage and that employers are not interested in wage underbidding by outside workers in a world of incomplete contracts. With all employed workers exerting full effort ε = 1, I henceforth ignore ε. The presence of two sectors leads to two crucial differences of this model’s wages to the wage specification of Egger and Kreickemeier (2009). First, the firm-external reference point depends on both informal and formal sector wages. Due to the random selection of workers, both employment types are viable options for workers. Second, workers are aware of the productivity bonus that formal sector firms experience and adjust their firm-internal reference point accordingly. 2.4 The firm’s decision to enter the informal or formal sector A firm’s decision to become informal or formal is established as follows. Before the start of the operation, the firm pays a fixed cost fe and draws a productivity ϕ, a mechanism explained in detail in subsection 2.6. A firm’s productivity influences its variable costs, but not the fixed cost it faces for entering either the informal or formal sector. Having full information over entry costs and productivity bonus due to contract enforcement in the formal sector, firms choose the sector in which they can produce the most profitable or do not produce at all, that is max⁡{πi(ϕ),πf(ϕ),0}. Corresponding to empirical evidence, I assume that informal firms are low-productivity and formal firms are high-productivity firms (La Porta and Shleifer, 2008; Dabla-Norris et al., 2008; de Paula and Scheinkman, 2011). That is ϕf*>ϕi*, where ϕi* and ϕf* are the cutoff productivity levels at which informal and formal firms start profitably operating. The sorting is achieved if   (1−λ)−ξ<fffi (9) with ξ≡(1−σ)(θ−1), which I assume henceforth holds. Figure 1 visualizes this sorting of sectors along the productivity spectrum. Fig. 1 View largeDownload slide Sector sorting along the productivity spectrum according if (9) holds Fig. 1 View largeDownload slide Sector sorting along the productivity spectrum according if (9) holds The intuition for condition (9) is as follows. If the benefit of formality relative to informality is less than the relative formal sector entry cost, then only high-productivity firms enter formal production and informal firms break even at a lower productivity level than formal firms do.5 If the condition holds, the combination of the fixed costs fi and ff and the fact that relative revenue of formal to informal firms is increasing ensures a single crossing of the informal and formal profit functions.6 Thus, only formal sector firms can be found at higher productivity levels. ϕi* and ϕf* are determined by two conditions:   πi(ϕi*)=0 (10) and:   πf(ϕf*)=πi(ϕf*). (11) Notably, for the extreme case of λ = 0, i.e. contracts are not enforceable in the formal sector, firms would have no incentive to join the formal sector and the model would collapse to the one-sector specification in Egger and Kreickemeier (2009). If on top of that, θ = 0 holds, that is workers only value the expected wage in the economy and wages are not firm-specific, labour markets would clear and the model would further collapse to the model described in Melitz (2003). 2.5 Firm-specific variables The relative difference between any two firms can entirely be described by their productivity ϕ, the share of enforceable contracts λ and their resulting formality status, as in Melitz (2003) and Egger and Kreickemeier (2009). To begin with, using (4) and (8) results in:   wi(ϕi)wf(ϕf)=(ϕiϕf)θ(1−λ)θ<1 and pi(ϕi)pf(ϕf)=(ϕiϕf)θ−1(1−λ)θ−1>1. (12) Consistent with the empirical literature, informal wages are lower than formal wages for two reasons. First, wages are a function of firm productivity and formal sector firms are high-productivity firms. Second, a higher share of enforceable contracts entails higher firm profitability and accordingly acts as a wage premium for formal sector employment. This results in an informal wage gap as empirically found by Bargain and Kwenda (2011), de Paula and Scheinkman (2011) and Günther and Launov (2012). Similarly, (12) allows for a comparison of the relative prices pi(ϕi)/pf(ϕf), and shows that formal firms charge lower prices than informal firms. Intuitively, due to their productivity bonus and higher productivity level, formal firms are able to translate lower marginal costs into lower prices for their products. This is in line with the findings of Foster et al. (2008), who show a negative correlation between physical firm productivity and output prices. While firms produce symmetric varieties at different costs, as mentioned in Melitz (2003) an alternative interpretation is that firms produce varieties of different quality at the same cost. Given this interpretation, the model implicitly reflects the lower quality of informal sector products, which has empirically found to be the case by La Porta and Shleifer (2011).7 In addition, using (3) and (5), I can compare the quantities and revenues between firms in the two sector:   qi(ϕi)qf(ϕf)=(ϕiϕf)σ(1−θ)(1−λ)σ(1−θ)<1 and ri(ϕi)rf(ϕf)=(ϕiϕf)ξ(1−λ)ξ<1. (13) Formal firms are not just able to translate higher productivity into lower prices, but they also produce larger quantities than their informal counterparts (La Porta and Shleifer, 2008). In combination, the revenue of firms in the formal sector is higher than in the informal sector (Fajnzylber et al., 2011). Lastly, (14) illustrates the labour demand of an informal sector firm li(ϕ) relative to the labour demand of a formal sector firm lf(ϕ):   li(ϕi)lf(ϕf)=(ϕiϕf)σ(1−θ)−1(1−λ)σ(1−θ)−1<1. (14) To capture the positive correlation between productivity level and employment (Brown and Medoff, 1989), that is li(ϕ)<lf(ϕ), I assume:   σ(1−θ)−1>0, (15) analogous to Egger and Kreickemeier (2009).8 In this setup the assumption is relevant for another reason. Given this assumption, formal firms hire more labour than informal firms due to the productivity bonus they receive (La Porta and Shleifer, 2008; de Paula and Scheinkman, 2011; Fajnzylber et al., 2011). Notably, this is not a strong assumption. The empirical literature indicates σ in the range of 2 to 5 (see for example, Head and Mayer, 2014), which implies reasonable fairness parameters of θ<0.5 to θ<0.8, respectively. Using the zero profit conditions for both sectors (10) and (11), I can specify the distance of informal to formal sector cutoff productivity level relative to the formal sector cutoff productivity level ϕf*−ϕi*ϕf*.   ϕf*−ϕi*ϕf*=1−(fiff−fi)1ξ((1−λ)−ξ−1)1ξ. (16) This allows the analysis of inter-firm productivity differences between the marginal informal and the marginal formal firm with regard to policy changes.9 Higher informal firm capital requirements fi or a higher share of enforceable contracts λ raises ϕi* relative to ϕf* and thereby diminishes the distance in relative productivity levels. It increases for a higher formal sector entry cost ff, because a higher ff reduces formal sector profitability. 2.6 Firm productivity distribution and free entry Firms are indexed by their productivity ϕ, hence firm size distribution, aggregate employment and aggregate output of the economy hinge on the productivity distribution. A commonly used distribution in Melitz-type models (2003) is the Pareto distribution. It is both tractable and fits empirical findings on firm size and the productivity distribution well (Axtell, 2001). The distribution is given by G(ϕ) with density g(ϕ) and shape parameter:   k>ξ.10 (17) The lower bound of productivities is normalized to 1:   G(ϕ)=1−ϕ−k and g(ϕ)=kϕ−(k+1). (18) There exists a mass Me of prospective entrants, all identical ex-ante, to the intermediate sector.1011 Entering entails a fixed cost of fe>0 and allows firms to draw a productivity ϕ from the distribution G(ϕ). Firms only start producing if the expected profit of production is non-negative. In equilibrium, the average profit of active firms, conditional on successful market entry, is equal to the sunk cost fe. This is described by the free entry condition:   ∫ϕi*ϕf*πi(ϕ)g(ϕ)dϕG(ϕf*)−G(ϕi*)+∫ϕf*∞πf(ϕ)g(ϕ)dϕ1−G(ϕf*)=fe. (19) Using the cutoff productivity levels and wage equations for both sectors, I can describe (7), the average wage income per worker in the economy, as:   Eiwi¯+Efwf¯=L−1[∫ϕi*ϕf*li(ϕ)wi(ϕ)g(ϕ)dϕ+∫ϕf*∞lf(ϕ)wf(ϕ)g(ϕ)dϕ]. (20) As firms price their goods with a constant markup 1/ρ over marginal costs, the wage income of employed workers is equal to a constant share of output (Eiwi¯+Efwf¯)L=ρY.12 Through (19), the expected profits of all firms equal their initial investment fe. Therefore, the workers’ income is the only disposable income for consumption and a natural utilitarian measure for welfare, as in Egger and Kreickemeier (2009), and can be written as:   YL=(Eiwi¯+Efwf¯)ρ. (21) 2.7 Employment The share of salaried employment in the economy consists of two parts: informal sector salaried employment share Ei and formal sector salaried employment share Ef. The salaried employment share can be written as:   E=Ei+Ef=L−1[∫ϕi*ϕf*li(ϕ)g(ϕ)dϕ+∫ϕf*∞lf(ϕ)g(ϕ)dϕ]. (22) Using this, I derive the relative salaried employment share (Ei/Ef) to determine the effect of policy changes:   EiEf=(1−λ)χ+k[(ϕi*ϕf*)χ−1], (23) where χ≡σ(1−θ)−k−1<0.13 The ratio of informal employment share to formal employment share EiEf is increasing in ff, and decreasing in fi and λ.14 This sheds light on the mechanics of the economy. A higher share of enforceable contracts λ leads to a relatively smaller informal sector, as found by Antunes and de V. Cavalcanti (2007) and Quintin (2007). A higher informal sector start-up cost fi similarly decreases the relative size of the informal sector. A decrease in formal sector profitability (i.e. increase in ff) increases relative informal sector salaried employment. Intuitively, reducing informal sector profitability or increasing formal sector profitability drives the least-productive informal sector firms out of the market. As a result, the informal sector sheds labour and informal sector average productivity increases. This extends Egger and Kreickemeier (2009) to a new adjustment margin. Informal and formal sector salaried employment are affected differently by changes in the economy. The employment effect of one sector can buffer the employment effect of the other one. 2.8 Wage inequality Prior to the hiring process workers are identical and subsequently can be employed in either the informal or formal sector. Additionally, wages in this model are firm-specific. Therefore, two types of wage inequality can be disentangled. First, given the productivity difference between the two sectors and the informal sector wage gap, I consider the wage inequality between informal and formal workers. Second, as all workers are identical in skill level, I analyse wage inequality among all employed workers similar in spirit to Egger and Kreickemeier (2012).15 The measure of between-group wage inequality is the ratio of the formal sector average wage relative to the informal sector average wage:   wf¯wi¯=(1−λ)−θ[1−(ϕi*ϕf*)χ][1−(ϕi*ϕf*)ξ−k]−1>1. (24) Given the informal sector wage gap and informal firms being low-productivity types, the average wage in the informal sector is lower than in the formal sector and the ratio is strictly greater than one. Second, I measure the wage inequality among all employed workers using the Gini-coefficient. Calculating the Gini-coefficient for the two-sector economy requires two steps. First, I calculate the Lorenz curve Q(γ) by relating the share of employment to the share of wage bill for firms with productivity below ϕ¯∈[ϕi*,∞]. Because employment and wages in the informal sector differ from the formal sector, the Lorenz curve consists of two segments and requires lengthy calculations that can be found in online Appendix B. Second, I derive the Gini-coefficient G(a), where subscript (a) stands for autarky, from the Lorenz curve through G(a)=1−2∫01Q(γ)dγ. G(a) is described by:   G(a)=Gf[1+2(ϕi*ϕf*)k−ξθΓΔ{χ[ϒ−Ξ(ϕi*ϕf*)θ+[Ξ−ϒ](ϕi*ϕf*)−χ]         +θϒ[1−(ϕi*ϕf*)−χ]}], (25) where Gf≡θθ−2(ξ−k),16 Γ≡1−[1−(1−λ)−ξ+θ](ϕi*ϕf*)−χ, Δ≡1−[1−(1−λ)−ξ](ϕi*ϕf*)k−ξ, ϒ≡1−(1−λ)−ξ and Ξ≡1−(1−λ)−ξ+θ. The Gini-coefficient in the two-sector economy G(a) depends on the ratio of the two cutoff productivity levels (ϕi*/ϕf*), which is a proxy for the relative sector size. For the extreme cases of (ϕi*/ϕf*)=1, i.e. all firms are formal, and (ϕi*/ϕf*)=0, i.e. all firms are informal, the specification collapses to the single-sector economy Gini-coefficient Gf.17 In the two-sector economy, that is (ϕi*/ϕf*)∈(0,1), G(a)>Gf holds and the wage distribution is more unequal than in the single-sector economy. Moreover, for θ∈(0,1), i.e. workers value firm-specific wages, the Gini-coefficient is strictly greater than 0.18 3. The open economy To explore how the presence of an informal sector may mediate the impact of trade liberalization, I extend the closed economy specification by adding international trade with n symmetric countries. The symmetry assumption allows me to focus on firm-level effects and renders country indices obsolete. Moreover, a world in which every country is characterized by sector dualism is sensible, since informality is a global phenomenon (Schneider et al., 2010). Two types of costs are distinguished for firms participating in international trade. As has been empirically shown by Roberts and Tybout (1997), sunk costs of exporting critically determine export participation. Firms have to cover a fixed exporting cost fx > ff, in addition to the domestic entry cost, to participate in trade. The fixed cost fx can be interpreted as a one-time expense for knowledge or infrastructure needed to engage in international trade and allows firms to access all n markets. Subscript x is used henceforth to describe variables related to export activities. In addition, firms face a variable trade cost that is modelled in the form of an iceberg trade cost τ>1, i.e. for one unit to arrive at the destination market, τ units have to be shipped. 3.1 The firm’s decision to export Given the previous constraint on informal firms being characterized by lower productivities than formal firms, it is never profitable for informal firms to export.19 Intuitively, informal firms decide against formality out of profitability considerations arising from the formal sector fixed cost ff. Exporting induces an even higher fixed cost fx than the formal sector participation already does. Hence, the same profitability considerations will lead informal sector firms to not be able to profitably export. The complete exclusion of informal sector firms from exporting is stylized. Yet, this model result is supported by the empirical literature that finds that informal firms rarely export (Batra et al., 2003; Bigsten et al., 2004; La Porta and Shleifer, 2008). Notably, the exclusion of informal firms from international trade arises as a model result in this setup, opposed to being an assumption as in the related work by Davies and Paz (2011). Lemma 1 Informal sector firms do not find it profitable to export. In regards to the formal sector, empirical studies find a clear correlation between export participation and firm productivity, i.e. the highest-productivity firms in an economy self-select into exporting (Bernard and Jensen, 1995; Roberts and Tybout, 1997). Hence, I focus on parameters that satisfy ϕx*>ϕf*, where ϕx* stands for the cutoff productivity level at which exporting becomes profitable. That is, I assume that exporters are characterized by a higher productivity level than non-exporters. Upon drawing a productivity ϕ, a firm in the open economy therefore decides on its formality status and export participation according to max⁡{πi(ϕ),πf(ϕ),πf(ϕ)+πx(ϕ),0}. The number of firms operating in the domestic market then consists of informal sector firms and formal sector firms, which are domestic, as well as foreign exporters, i.e. M=Mi+Mf+(1+n)Mx. The sorting ϕx*>ϕf*, is ensured if:   fxτξ1−θn(1−λ)−ξ>ff−fi(1−λ)−ξ−1, (26) which I assume henceforth holds.20 The sorting depends on the entry costs to the informal and formal sector (fi and ff), the share of enforceable contacts (λ) and the variables determining the costs and benefits of trade (fx, τ and n). Intuitively, the inequality compares two cost–benefit ratios. If the cost–benefit ratio of exporting fxτξ1−θn(1−λ)−ξ is higher than the cost–benefit ratio of domestic production ff−fi(1−λ)−ξ−1, then a higher productivity is required to be able to profit from exporting. Given the variable and fixed cost, the formal sector firm revenue function is:   r(ϕ)={rf(ϕ) if the firm sells domestically ,rf(ϕ)+nτ1−σrf(ϕ) if the firm exports.  (27) A firm’s profit from exporting is described by:   πx(ϕ)=rf(ϕ)nτ1−σσ−fx. (28) In addition to (10) and (11), there is a new condition to determine the export participation productivity cutoff level ϕx*:   πx(ϕx*)=0. (29) In summary, to achieve the productivity sorting of firms in the open economy according to the empirical literature, the model builds on (9) and (26). If they hold, informal sector firms are assumed to be the lowest-productivity firms followed by domestic formal firms. Lastly, formal firms that export are the highest-productivity firms and there are no informal sector exporters. 3.2 Firm-specific variables I can express the relationship between formal firms and formal exporting firms as ratios solely in terms of their productivity levels, variable trade costs τ and the number of countries n, independent of assumptions on the distribution of firm productivity. Notably, the price and quantity with subscript x refer solely to the export markets, but the revenue and labour demand below refer to both domestic and export markets. Exporters pay the same wage as formal sector producers conditional on productivity, i.e. wf(ϕ). However, if (26) holds, exporters are more productive than non-exporting formal firms, wf(ϕx*)>wf(ϕf*) and the model captures the empirical observation that exporting firms pay higher wages than non-exporting firms (Bernard and Jensen, 1995):   pf(ϕf)px(ϕx)=(ϕfϕx)θ−1τ−1<1 and qf(ϕf)qx(ϕx)=(ϕfϕx)σ(1−θ)τσ>1. (30) Given the same productivity, firms charge a higher price and sell a lower quantity abroad than at home:   rf(ϕf)rx(ϕx)=(ϕfϕx)ξ11+nτ1−σ<1 and lf(ϕf)lx(ϕx)=(ϕfϕx)σ(1−θ)−111+nτ1−σ<1. (31) With regard to revenue and labour demand, both are increasing in the number of countries n and decreasing in the variable trade cost τ for exporters relative to formal non-exporters. These model results are in line with the commonly stated firm-level evidence on exporters being characterized by higher employment and higher revenues than their non-exporting counterparts (Bernard and Jensen, 1995). Equation (32) allows me to analyse the distance between formal sector productivity cutoff ϕf* and exporting cutoff productivity level ϕx* relative to the exporting cutoff productivity level ϕx*:   ϕx*−ϕf*ϕx*=1−((ff−fi)nτ1−σ)fx)1ξ((1−λ)−ξ−1)−1ξ(1−λ)−1. (32) The results can be separated into two groups.21 First, variables increasing the attractiveness of international trade (increase in n or decrease in fx or τ) close the relative distance between the productivities, as trade liberalization increases the profitability of exporting firms and decreases the required productivity level for participation. For non-exporting formal sector firms, an increased number of foreign competitors in the domestic market drives down profitability and increases productivity requirements. Second, factors increasing the profitability of formal relative to informal sector participation (increase in fi and λ, decrease in ff) lower the productivity threshold of becoming formal, but affect export participation only indirectly. Lastly, comparing ϕx*=(fx/fi)1ξ(nτ1−σ)−1ξ(1−λ)ϕi*, i.e. the cutoff productivity level of the marginal exporting and informal sector firms highlights what drives their difference. The ratio of sector entry costs, trade variables and the share of enforceable contracts lead to a higher productivity requirement for exporting firms relative to informal sector producers. To derive the new free entry condition in the open economy, I extend (19) to include potential exporting profit:   ∫ϕi*ϕf*πi(ϕ)g(ϕ)dϕG(ϕf*)−G(ϕi*)+∫ϕf*ϕx*πf(ϕ)g(ϕ)dϕG(ϕx*)−G(ϕf*)+∫ϕx*∞[πf(ϕ)+πx(ϕ)]g(ϕ)dϕ1−G(ϕx*)=fe. (33) 3.3 Employment Salaried employment at multi-worker firms in the open economy consists of three segments: informal, formal and formal exporter employment. The employment share in the economy is:   E=L−1[∫ϕi*ϕf*li(ϕ)g(ϕ)dϕ+∫ϕf*ϕx*lf(ϕ)g(ϕ)dϕ+∫ϕx*∞lx(ϕ)g(ϕ)dϕ]. (34) In analysing the impact of trade liberalization on salaried employment, I first separately study the impact on the formal and informal sectors. Formal sector employment adjusts along two margins. The high-productivity formal firms become exporters and hire additional workers to be able to serve the foreign demand. After trade liberalization, foreign competitors enter the domestic market and more varieties of the intermediate good are sold domestically (increase in M). As competitive pressure rises, the demand for each variety decreases and the profitability of all firms is reduced. Low-productivity formal firms informalize to remain profitable. As a result, formal sector employment is affected negatively, dampening total salaried employment. Informal sector firms do not experience the productivity bonus λ due to enforceable contracts and thus hire fewer workers than formal sector firms at the same productivity level. This is obvious when comparing the labour demand ratio li(ϕ1)/lf(ϕ2)=(ϕ1/ϕ2)σ(1−θ)−1(1−λ)σ(1−θ)−1. Whether the hiring effect of exporting firms or the labour shedding of informalized firms dominates depends on the key characteristics of the economy. Thus, the effect of trade liberalization on formal sector employment is ambiguous. Informal sector employment is also affected along two margins. With falling demand for each input variety, the lowest-productivity informal producers are forced out of the market and release labour. Along the other margin, the least-productive formal sector firms become informal and thereby increase informal sector employment. Given the Pareto productivity distribution, the labour releasing effect is stronger than the labour hiring and therefore informal sector salaried employment unambiguously decreases upon trade liberalization.22 This result provides theoretical support for decreasing informal sector employment upon trade liberalization (Fiess and Fugazza, 2012; McCaig and Pavcnik, 2014) amidst conflicting empirical evidence with a wide range of definitions of informality and data sets in use. Alternatively, Goldberg and Pavcnik (2003) and Attanasio et al. (2004) find an increase in informal employment upon trade liberalization. However, they define workers as informal if no social security contributions for them are made. Accordingly, firms can hire both informal and formal workers by evading social security contributions for only some of their workers, whereas in this model all workers at a firm that evades regulations are considered informal. Within their framework, formal firms can substitute formal for informal workers, while remaining formal at the firm-level. Accordingly, workers would be considered formal from the firm-level perspective of this work, but informal from their labour market perspective, which can explain the diverging results on informal employment upon trade liberalization. Lastly, I analyse the total salaried employment in the economy as a combination of the employment adjustments of both sectors. As illustrated in Fig. 2, liberalizing trade changes the position of both sectors along the productivity distribution. Three forces determine the change in total salaried employment: an employment gain as a result of exporter hiring, an employment loss caused by the informalization of the least-productive formal sector firms and an employment loss that occurs as the least-productive informal sector firms exit the market. While there are unambiguously fewer informal salaried workers in the economy, the effect of trade liberalization on formal sector employment is ambiguous, thus rendering the total salaried employment effect ambiguous. Given that informal self-employment is a last resort and residual to salaried employment, also informal self-employment is impacted ambiguously by trade liberalization. The magnitude of each sectoral adjustment and accordingly the direction of total salaried employment adjustment is determined by the economy’s characteristics, such as entry costs to both sectors. The move from autarky to full integration is stylized. However, the aforementioned results hold also for gradual trade integration, as measured by a reduction in τ or fx.23 Fig. 2 View largeDownload slide Sector sorting along the productivity distribution in autarky and the open economy Fig. 2 View largeDownload slide Sector sorting along the productivity distribution in autarky and the open economy This highlights a key contribution of this model. In Egger and Kreickemeier (2009) there are only two forces at work. The highest-productivity firms become exporters and hire additional workers; the lowest-productivity firms exit the market and shed labour. In sum, Egger and Kreickemeier (2009) find an unambiguous decrease in salaried employment. The existence of an informal sector gives rise to a third force, i.e. the informalization of low-productivity formal firms, which dampens the reallocation of labour towards more productive firms. The economy’s characteristics affect the three forces and accordingly the magnitude of each. This result, as summarized in Proposition 1, bridges the gap between the original model of Egger and Kreickemeier (2009) and the mixed empirical evidence on the relationship between trade liberalization and formal salaried employment (Davidson and Matusz, 2009; Dutt et al., 2009; Felbermayr et al., 2011ba; Menezes-Filho and Muendler, 2011). Moreover, the finding that trade liberalization reduces informal employment, complements the related work by Davies and Paz (2011), who show a reduction of both the number of informal firms, and accordingly informal employment, as well as informal output through the same pro-competitive effect of trade liberalization, albeit in a setup without labour market frictions. Proposition 1 Trade liberalization reduces informal salaried employment unambiguously and can either reduce or increase formal salaried employment. In combination, the effect of trade liberalization on total salaried employment and informal self-employment in the economy is ambiguous. Proof See online Appendix D. □ To gain further insight into the mechanics of the model, analogously to the closed economy case, I can describe the informal salaried employment share relative to the formal salaried employment share:   (EiEf)(t)=η(EiEf)(a), (35) where η≡[1+nτ1−σ(ϕf*ϕx*)−χ]−1<1. Subscript (a) and (t) stand for autarky and trade. The intuition follows from the earlier result. Informal salaried employment unambiguously decreases, while formal sector employment may either increase or decrease. In combination, trade liberalization unambiguously reduces the informal salaried employment share relative to the formal salaried share. 3.4 Wage inequality Trade liberalization affects wage inequality indirectly by adjusting the number of workers employed in the informal and formal sector.24 Thus, the model introduces a novel impact of trade liberalization in the presence of informality that is not featured in the related work, such as Davies and Paz (2011), without labour market frictions. Between-group wage inequality in the open economy is higher than under autarky:   (wf¯wi¯)(t)=ω(wf¯wi¯)(a), (36) where ω≡[1+nτ1−σ(ϕx*ϕf*)ξ−k][1+nτ1−σ(ϕx*ϕf*)χ]−1>1. Intuitively, trade liberalization raises the competitive pressure in the economy and forces the least-productive informal firms to exit and the lowest-productivity formal firms to informalize. The informal firms paying the lowest wages exit and higher-wage formal firms start informal production. This raises the informal sector average wage. With regard to the formal sector, the highest-wage exporters hire more workers and the lowest-wage formal firms informalize. The average wage of the formal sector increases and does so at a greater magnitude than the informal sector average wage. Hence, the average wages diverge and between-group inequality increases. This corresponds to the empirical work of Attanasio et al. (2004), who document an increase in the average wage of formal relative to informal workers in the years following Colombia’s tariff reductions in 1990–1991. Similarly, wage inequality among all employed workers measured by the Gini-coefficient hinges on the share of employment in both sectors. The derivation of the Gini-coefficient is analogous to the closed economy, albeit more complicated.25 The Lorenz curve consists of not just informal and formal workers, but also workers employed by exporting firms.26 Trade liberalization affects wage inequality indirectly through the employment shares and can either increase or decrease wage inequality. The intuition for this result derives from section 3.3. Both a purely-formal and a purely-informal economy feature the same Gini-coefficient, which is strictly lower than that of an economy featuring both sectors.27 Trade liberalization increases the formal sector employment share relative to informal sector employment share. If initially formal sector employment is large relative to informal sector employment, a relative increase in the formal labour share pushes the economy closer to a purely formal economy. Hence, wage inequality decreases. The opposite holds true if the formal sector is relatively small before trade trade liberalization. Due to the relative formalization of labour through trade, the economy diverges from a purely-informal economy. Trade then increases wage inequality.28 Proposition 2 Trade liberalization increases between-group wage inequality and has an ambiguous effect on wage inequality among all employed workers. Proof See online Appendix D. □ 3.5 Welfare The average wage income per worker (Eiwi¯+Efwf¯) in the open economy is described by all three cutoff productivities and, in combination with (21), determines the aggregate output in the open economy:   (Eiwi¯+Efwf¯)=L−1[∫ϕi*ϕf*li(ϕ)wi(ϕ)g(ϕ)dϕ+∫ϕf*ϕx*lf(ϕ)wf(ϕ)g(ϕ)dϕ+∫ϕx*∞lx(ϕ)wf(ϕ)g(ϕ)dϕ]. (37) The effect of trade liberalization on welfare, as measured by the aggregate output of the economy per capita, is similar to the employment effect. The intuition is as follows. Trade liberalization allows the highest-productivity firms to become exporters and shifts resources towards the most-productive firms in the economy. Thereby aggregate formal sector output is increased. The lowest-productivity formal firms, however, switch to informal sector production. The result is a reduction in aggregate formal sector output through the loss of the formal sector productivity bonus. In sum, the effect of trade on the aggregate formal sector output is ambiguous. The informal sector is affected along two margins, as well. The lowest-productivity informal sector firms cease production and decrease aggregate informal sector output, while the informalization of the lowest-productivity formal firms increases the aggregate output of the informal sector. Depending on the economy’s characteristics the former may or may not compensate for the latter, rendering the effect on aggregate informal sector output ambiguous. As before, depending on the key parameters of the economy, the net effect of trade liberalization on the aggregate output of the whole economy can be positive or negative. This result also holds for gradual trade liberalization (decrease in τ or fx).29 The effect of trade on aggregate output in this model is more nuanced than in Egger and Kreickemeier (2009), who find an unambiguous increase in aggregate output through trade liberalization. The ambiguous result highlights the effect of the informal sector on resource allocation, as suggested by Hsieh and Klenow (2009) and Bruhn (2013), that can either lead to an increase in aggregate output (McCaig and Pavcnik, 2013), and hence welfare, or decrease in aggregate output upon trade liberalization. Moreover, this result underlines the ambiguous welfare effect of trade liberalization in the presence of informality shown by Davies and Paz (2011), which in this model also arises without the shift from tariffs to VAT.30 Proposition 3 Trade liberalization in the presence of informality has an ambiguous effect on the aggregate output of the informal sector, the formal sector and in sum on the welfare of the economy. Proof See online Appendix D. □ 3.6 Numerical Simulation To substantiate the policy relevance of the model, I proceed with a numerical simulation to: (i) compare the effectiveness of different policy instruments on welfare; and (ii) size the impact of trade liberalization on informal employment. Table 1 lays out the baseline scenario with parameters that either stem from empirical literature or follow from model conditions.31 The respective constraints and equations to derive these results, as well as additional scenarios to highlight the ambiguity of the effect of trade on welfare and total salaried employment, can be found in online Appendix D. First, I compare the impact of liberalizing trade (decreasing τ), improving access to the formal sector (decreasing ff) and improving contract enforcement in the formal sector (increasing λ) in their impact on welfare captured by Y(t). More specifically, I estimate the required change in each of the parameters to increase welfare by 5%. The results listed in table 2 indicate that increasing contract enforceability in the formal sector is the most effective in achieving this goal, closely followed by decreasing trade costs with implied welfare elasticities of 1.2 and –1.1, respectively. Additionally, both have a similar impact on informal employment with informal salaried employment elasticities of –0.7 for λ and 0.6 for τ. To achieve the same welfare gain, the formal sector entry costs needs to be decreased to a larger extent (11.7%) implying lower welfare and informal salaried employment elasticities. Table 1 Parameter values for the baseline scenario     Baseline  Source  Elasticity of substitution  σ  5.0  Head and Mayer (2014)  Pareto distribution parameter  k  3.0    Formal fixed cost  ff  1.4  Ulyssea (2010)  Informal fixed cost  fi  0.3  Ulyssea (2010)  Exporting fixed cost  fx  2.0    Fairness parameter  θ  0.7    Share of enforceable contracts  λ  0.47  World Bank (2016)  Iceberg transportation cost  τ  1.1    Number of foreign countries  n  1        Baseline  Source  Elasticity of substitution  σ  5.0  Head and Mayer (2014)  Pareto distribution parameter  k  3.0    Formal fixed cost  ff  1.4  Ulyssea (2010)  Informal fixed cost  fi  0.3  Ulyssea (2010)  Exporting fixed cost  fx  2.0    Fairness parameter  θ  0.7    Share of enforceable contracts  λ  0.47  World Bank (2016)  Iceberg transportation cost  τ  1.1    Number of foreign countries  n  1    Table 2 Simulation results.   λ  ff  τ  Change in parameter  4.1%  –11.7%  –4.6%  Change in Y(t)  5.0%  5.0%  5.0%  Implied elasticity  1.2  –0.4  –1.1  Change in Ei  –2.9%  –4.6%  –2.8%  Implied elasticity  –0.7  0.4  0.6    λ  ff  τ  Change in parameter  4.1%  –11.7%  –4.6%  Change in Y(t)  5.0%  5.0%  5.0%  Implied elasticity  1.2  –0.4  –1.1  Change in Ei  –2.9%  –4.6%  –2.8%  Implied elasticity  –0.7  0.4  0.6  Lastly, I size the reduction of informal employment upon trade liberalization, as shown in Fig. 3. For the baseline value of τ=1.1, moving from autarky to trade reduces informal salaried employment by –1.9%. Abolishing all tariffs and going from autarky to τ = 1, leads to a –4.7% reduction in informal employment. In sum, the numerical simulation substantiates trade liberalization as an effective policy instrument in both increasing welfare and curbing informality at a level comparable to improving contract enforcement, and more effective than alleviating barriers to formality. Fig. 3 View largeDownload slide The effect of moving from autarky to trade on informal employment Ei Fig. 3 View largeDownload slide The effect of moving from autarky to trade on informal employment Ei 4. Conclusion Previous trade models did not reconcile heterogeneous firms, labour market frictions and informality in the form of registration non-compliance. By introducing informality into heterogeneous firm trade models with labour market frictions, this paper shows analytically how informality distorts resource allocation in an economy and trade can affect total salaried employment, wage inequality and welfare ambiguously. A numerical simulation corroborates trade liberalization as an effective tool in curbing informality and potentially raising welfare in the process. Therefore, the implication of this framework for policymakers is clear. While trade liberalization achieves the often-targeted reduction in informal employment, the economic conditions in a country ultimately determine whether trade is beneficial or detrimental in regard to employment, welfare and wage inequality in the presence of informality. Hence, this setup emphasizes the need to consider the existence of an informal sector and the economic environment jointly in policy decisions on trade. However, using reasonable parameters, a numerical simulation demonstrates that informal employment can be reduced, while increasing welfare, through trade liberalization and that liberalizing trade is a more effective tool than reducing entry costs to the formal sector. Several extensions of this work would provide for interesting future research endeavours. First, replacing the productivity sharing motif of the fair wage specification with revenue sharing would lead to a wage premium for exporters from foreign sales conditional on firm productivity, and can possibly entail different distributional consequences than the present work. Second, including heterogeneous workers and allowing firms to hire both informal and formal workers is a useful extension to capture the empirical findings of works with labour market-specific definitions of informality. Lastly, introducing informality with a broader definition as tax evasion and registration non-compliance and in a public finance framework would inform optimal taxation and enforcement decisions in the presence of an informal sector. Supplementary material Supplementary data are available at OEP online. Funding This work was supported by the Cornell Population Center. Footnotes 1 Several empirical studies find wage curves, that is the negative relationship between regional unemployment and wages, for informal and formal salaried workers (Bucheli and González, 2007; Ramos et al., 2010; Baltagi et al., 2013), which is consistent with my model setup of the labour market frictions arising from fair wage preferences in both sectors (Blanchflower and Oswald, 1995). 2 This CES-specification ensures that the unemployment rate is independent of the size of the economy, as there is no evidence on the correlation between the two, and prevents an increase in aggregate output due to an increase in the number of input varieties. If, for example, equal amounts of every input q(v)=qM were to be used in the final good production process, the production function would imply Y = q. External scale effects are well understood from previous literature, e.g. Ethier (1982), and through this specification the focus lies purely on the selection effect of trade liberalization. 3 Recent empirical work that examines the effect of formality on firm performance, controlling for firm characteristics and self-selection into the formal sector, finds a significant effect of formality, particularly of increasing firm profits (Fajnzylber et al., 2011; McKenzie and Sakho, 2010; Rand and Torm, 2012). λ can be seen to capture this effect of formality on firm performance. 4 If an outsider were to be hired for a lower wage, she would adjust her reference wage w^ and, given the wage below reference level, decrease her effort level accordingly. Therefore, in equilibrium wage underbidding is not attractive to firms. 5 Breaking even at a lower productivity requires that ϕi*<ϕf* for ϕi* from πi(ϕi*)=0 & ϕf* from πf(ϕf*)=0. From eq. (6): ϕi*=[fiσMY]1ξ(Eiwi¯+Efwf¯)ρ1θ−1 and ϕf*=[ffσMY]1ξ(Eiwi¯+Efwf¯)ρ1θ−1(1−λ). Hence, (1−λ)−ξ<fffi. 6 Mathematically, [rf(ϕi)/ri(ϕf)]=(ϕf/ϕi)ξ(1−λ)−ξ and ∂[rf(ϕi)/ri(ϕf)]/∂(ϕf/ϕi)=ξ(ϕf/ϕi)ξ−1(1−λ)−ξ>0. 7 Verhoogen (2008) models product quality explicitly, albeit by using heterogeneous workers. 8 An interpretation of the condition comes from rewriting it as 1/ρ<1/θ, that is the love of variety 1/ρ needs to be greater than the inverse of the fairness consideration parameter θ. Intuitively, for a lower love of variety 1/ρ, the cheaper varieties are demanded relatively more, which are produced by higher-productivity firms. Hence, higher-productivity firms hire more workers. On the other hand, a higher fairness preference θ raises the wages paid by high-productivity firms and accordingly a decrease in those firms’ hiring. 9 See online Appendix A.1. 10 A Pareto distributions has a finite mean only if its shape parameter k > 1. Productivity is Pareto distributed and labour as well as revenue are power functions of productivity. Therefore, also firm size and revenue are Pareto distributed. For the distributions of firm size and revenue to have a finite mean: kξ−θ>1 and kξ>1, respectively, have to hold. Thus, as in Egger and Kreickemeier (2009), k>ξ is assumed. 11 Me is exogenously given and without loss of generality normalized to 1. 12 The aggregate revenue in the economy is described by Y, because P = 1. It consists of both the firms’ and the workers’ share of the aggregate revenue. Due to the monopolistic competition assumption and resulting prices characterized by a constant markup 1/ρ over marginal costs, the shares are constant proportions. A constant fraction 1/σ of the firm revenue accrues to the firm and (σ−1)/σ=ρ accrues to the workers of the firm. Hence, the wage income of all employed workers (Eiwi¯+Efwf¯)L has to equal their constant share of the aggregate revenue ρY. 13 k>ξ is assumed. This implies σ(1−θ)−k−1+θ<0 and thus σ(1−θ)−k−1<0. 14 For proof see online Appendix A.2. 15 The analysis in this model differs to the one in Egger and Kreickemeier (2012) in two ways. First, Egger and Kreickemeier (2012) consider heterogeneous individuals and examine wage inequality between self-selected entrepreneurs and salaried workers. Second, workers consider firm revenue in their fair wage preference, which leads to an exporter wage premium. Opposed to that, I examine wage inequality among identical workers that can be employed in the informal or formal sector and workers consider firm productivity in their fair wage preference. 16 Gf is the Gini-coefficient of a purely-formal or purely-informal economy. This result is derived in online Appendix B. 17 Wage inequality being exactly the same in a purely informal and a purely formal economy is a stylized result. However, some support for this result comes from Saavedra (2001), who finds that the coefficient of variation for the hourly wage of salaried informal workers is comparable to the one of salaried formal workers. 18 For the extreme case of θ = 0, i.e. all workers receive the same wage, Gf = 0 and the economy would be perfectly equal. 19 What is required for informal exporting to be profitable at a lower productivity level than formal exporting, i.e. ϕi<ϕf from: πix(ϕi)=nYσM{ϕiθ−1(Eiwi¯+Efwf¯)1−θρ−1τ}1−σ−fx=0 & πfx(ϕf)=nYσM{(ϕf1−λ)θ−1(Eiwi¯+Efwf¯)1−θρ−1τ}1−σ−fx=0. The resulting requirement is 1>(1−λ)−1, which is a contradiction given that λ∈(0,1). 20 Ensuring ϕx*>ϕf* for ϕf* from πi(ϕf*)=πf(ϕf*) and ϕx* from πx(ϕx*)=0 is sufficient to sort domestic productivity levels below export productivity levels. This results in: ϕf*=[(ff−fi)MσY((1−λ)−ξ−1)]1ξ(Eiwi¯+Efwf¯)ρ1θ−1 and: ϕx*=[fxnσMY]1ξ(Eiwi¯+Efwf¯)(ρτ)1θ−1(1−λ). In combination, fxτξ1−θn(1−λ)−ξ>ff−fi(1−λ)−ξ−1. 21 See online Appendix A.3. 22 Ei(t)Ei(a)=[1+n(fxfinτ1−σ)−kξ(1−λ)−k]−θξ[1+(1−λ)−k(nτ1−σ)kξ(fxfi)ξ−kξ((1−λ)−ξ−1)kξ(fiff−fi)k−ξξ+1]θξ−1, where the subscript (a) and (t) stand for autarky and trade. (Ei(t)Ei(a))<1 because −θξ<0 and θξ−1<0. Hence, informal sector employment unambiguously decreases upon trade liberalization. 23 Proof available on request. 24 The model focuses on the interaction between the informal and formal sector and accordingly ignores an exporter wage premium conditional on firm productivity. The model can be extended to include a fair wage constraint that uses firm revenue and not firm productivity as firm-internal reference point. This would lead to an exporter wage premium and could provide another source for wage inequality, even among formal workers. 25 Given its complicated nature, the Gini-coefficient for the open economy is derived in online Appendix C. 26 For the extreme case of (ϕi*/ϕx*)=0, i.e. no firm exports, the open economy Gini-coefficient collapses to the autarky specification. If in addition to that, (ϕi*/ϕf*)=0 or (ϕi*/ϕf*)=1 are imposed, the coefficient further collapses to the formal-sector-only specification. 27 For a derivation of this result, see online Appendix B. As shown by Helpman et al. (2010), the Gini-coefficient depends only on the shape parameter of the wage distribution, but not its lower limit. Both informal and formal sector wage distribution feature the same shape parameter and thus the same inequality. 28 The intuition here is similar to the effect of a conditional exporter wage premium on wage inequality, as shown empirically by Akerman et al. (2013) and theoretically by Helpman et al. (2010). The findings suggest that a major share of overall wage inequality arises from the wage differences between firms in the same industry paid to workers with similar characteristics, i.e. within-industry wage inequality. Moreover, wage inequality is driven by the employment adjustments of these firms upon trade liberalization. 29 Proof for this is available from the author upon request. 30 Recent work by Dhingra and Morrow (2014) shows that the pro-competitive effect of trade can decrease welfare when market allocations or firm entry are not inefficient, as is the case here in the presence of informality. 31 For the share of enforceable contacts I employ quality of judicial processes index for Latin American & Caribbean, which is 8.4/16=0.47. Acknowledgements I am grateful to Nancy Chau, Ravi Kanbur, Ankita Patnaik, Joel Landry, the 2013 NEUDC, 2013 ISI conference, 2014 Midwest International Trade and 2014 ThReD participants, as well as two anonymous referees for helpful comments and suggestions. References Acosta P., Montes-Rojas G. ( 2014) Informal jobs and trade liberalisation in Argentina, Journal of Development Studies , 50, 1104– 18. Google Scholar CrossRef Search ADS   Akerlof G.A., Yellen J.L. ( 1990) The fair wage-effort hypothesis and unemployment, Quarterly Journal of Economics , 105, 255– 83. Google Scholar CrossRef Search ADS   Akerman A., Helpman E., Itskhoki O., Muendler M.-A., Redding S. ( 2013) Sources of wage inequality, American Economic Review , 103, 214– 19. Google Scholar CrossRef Search ADS   Aleman-Castilla B. ( 2006) The effect of trade liberalization on informality and wages: evidence from Mexico. CEP Discussion Paper 763, Centre for Economic Performance, London School of Economics, London. Amiti M., Davis D.R. ( 2012) Trade, firms, and wages: theory and evidence, Review of Economic Studies , 79, 1– 36. Google Scholar CrossRef Search ADS   Antunes A.R., de V., Cavalcanti T.V. ( 2007) Start up costs, limited enforcement, and the hidden economy, European Economic Review , 51, 203– 24. Google Scholar CrossRef Search ADS   Arias J., Artuc E., Lederman D., Rojas D. ( 2013) Trade, informal employment and labor adjustment costs. Policy Research Working Paper 6614, World Bank, Washington, DC. Google Scholar CrossRef Search ADS   Attanasio O., Goldberg P.K., Pavcnik N. ( 2004) Trade reforms and wage inequality in Colombia, Journal of Development Economics , 74, 331– 66. Google Scholar CrossRef Search ADS   Auriol E., Warlters M. ( 2005) Taxation base in developing countries, Journal of Public Economics , 89, 625– 46. Google Scholar CrossRef Search ADS   Axtell R.L. ( 2001) Zipf distribution of U.S. firm sizes, Science , 293, 1818– 20. Google Scholar CrossRef Search ADS PubMed  Baltagi B.H., Baskaya Y.S., Hulagu T. ( 2013) How different are the wage curves for formal and informal workers? Evidence from Turkey, Papers in Regional Science , 92, 271– 83. Google Scholar CrossRef Search ADS   Bargain O., Kwenda P. ( 2011) Earnings structures, informal employment, and self-employment: new evidence from Brazil, Mexico, and South Africa, Review of Income and Wealth , 57, 100– 22. Google Scholar CrossRef Search ADS   Basu A.K., Chau N.H., Kanbur R. ( 2011) Contractual dualism, market power and informality. IZA Discussion Papers 5845, Institute for the Study of Labor (IZA), Bonn. Google Scholar CrossRef Search ADS   Batra G., Kaufmann D., Stone A.H.W. ( 2003) Investment climate around the world: Voices of the firms from the world business environment survey . The World Bank, Washington, DC. Google Scholar CrossRef Search ADS   Bernard A.B., Jensen J.B. ( 1995) Exporters, jobs, and wages in U.S. manufacturing: 1976–1987. Brookings Papers on Economic Activity. Microeconomics , 1995: 67– 112. Google Scholar CrossRef Search ADS   Bewley T. ( 2005) Fairness, reciprocity, and wage rigidity, in Gintis H., Bowles S., Boyd R., Fehr E. (eds) Moral Sentiments and Material Interests: The Foundations of Cooperation in Economic Life , MIT Press, Cambridge, MA, 303– 8. Google Scholar CrossRef Search ADS   Bigsten A., Kimuyu P., Lundvall K. ( 2004) What to do with the informal sector?, Development Policy Review , 22, 701– 15. Google Scholar CrossRef Search ADS   Blanchard O., Giavazzi F. ( 2003) Macroeconomic effects of regulation and deregulation in goods and labor markets, Quarterly Journal of Economics , 118, 879– 907. Google Scholar CrossRef Search ADS   Blanchflower D.G., Oswald A.J. ( 1995) An introduction to the wage curve, Journal of Economic Perspectives , 9, 153– 67. Google Scholar CrossRef Search ADS   Brown C., Medoff J. ( 1989) The employer size-wage effect, Journal of Political Economy , 97, 1027– 59. Google Scholar CrossRef Search ADS   Bruhn M. ( 2013) A tale of two species: revisiting the effect of registration reform on informal business owners in Mexico, Journal of Development Economics , 103, 275– 83. Google Scholar CrossRef Search ADS   Bucheli M., González C. ( 2007) An estimation of the wage curve for Uruguay. Documentos de Trabajo 11/07, Departamento de Economía, Facultad de Ciencias Sociales. Universidad de la República, Montevideo. Bustos P. ( 2011) Trade liberalization, exports, and technology upgrading: evidence on the impact of MERCOSUR on Argentinian firms, American Economic Review , 101, 304– 40. Google Scholar CrossRef Search ADS   Dabla-Norris E., Gradstein M., Inchauste G. ( 2008) What causes firms to hide output? The determinants of informality, Journal of Development Economics , 85, 1– 27. Google Scholar CrossRef Search ADS   Danthine J.-P., Kurmann A. ( 2007) The macroeconomic consequences of reciprocity in labor relations, Scandinavian Journal of Economics , 109, 857– 81. Google Scholar CrossRef Search ADS   Davidson C., Matusz S.J. ( 2009) International Trade with Equilibrium Unemployment , Princeton University Press, Princeton, NJ. Google Scholar CrossRef Search ADS   Davies R.B., Paz L.S. ( 2011) Tariffs versus vat in the presence of heterogeneous firms and an informal sector, International Tax and Public Finance , 18, 533– 54. Google Scholar CrossRef Search ADS   Davis D.R., Harrigan J. ( 2011) Good jobs, bad jobs, and trade liberalization, Journal of International Economics , 84, 26– 36. Google Scholar CrossRef Search ADS   de Paula A., Scheinkman J.A. ( 2011) The informal sector: an equilibrium model and some empirical evidence from Brazil, Review of Income and Wealth , 57, 8– 26. Google Scholar CrossRef Search ADS   de Soto H. ( 1989) The Other Path , Harper and Row, New York, NY. Dhingra S., Morrow J. ( 2014) Monopolistic competition and optimum product diversity under firm heterogeneity. Mimeo, London School of Economics, London. Djankov S., La Porta R., Lopez-De-Silanes F., Shleifer A. ( 2002) The regulation of entry, Quarterly Journal of Economics , 117, 1– 37. Google Scholar CrossRef Search ADS   Dutt P., Mitra D., Ranjan P. ( 2009) International trade and unemployment: theory and cross-national evidence, Journal of International Economics , 78, 32– 44. Google Scholar CrossRef Search ADS   Egger H., Kreickemeier U. ( 2009) Firm heterogeneity and the labor market effects of trade liberalization, International Economic Review , 50, 187– 216. Google Scholar CrossRef Search ADS   Egger H., Kreickemeier U. ( 2012) Fairness, trade, and inequality, Journal of International Economics , 86, 184– 96. Google Scholar CrossRef Search ADS   El Badaoui E., Strobl E., Walsh F. ( 2010) The formal sector wage premium and firm size, Journal of Development Economics , 91, 37– 47. Google Scholar CrossRef Search ADS   Ethier W.J. ( 1982) National and international returns to scale in the modern theory of international trade, American Economic Review , 72, 389– 405. Fajnzylber P., Maloney W.F., Montes-Rojas G.V. ( 2011) Does formality improve micro-firm performance? Evidence from the Brazilian SIMPLES program, Journal of Development Economics , 94, 262– 76. Google Scholar CrossRef Search ADS   Fehr E., Falk A. ( 1999) Wage rigidity in a competitive incomplete contract market, Journal of Political Economy , 107, 106– 34. Google Scholar CrossRef Search ADS   Felbermayr G., Prat J., Schmerer H.-J. ( 2011a) Trade and unemployment: what do the data say?, European Economic Review , 55, 741– 58. Google Scholar CrossRef Search ADS   Felbermayr G., Prat J., Schmerer H.-J. ( 2011b) Globalization and labor market outcomes: wage bargaining, search frictions, and firm heterogeneity, Journal of Economic Theory , 146, 39– 73. Google Scholar CrossRef Search ADS   Fields G.S. ( 1975) Rural-urban migration, urban unemployment and underemployment, and job-search activity in LDCs, Journal of Development Economics , 2, 165– 87. Google Scholar CrossRef Search ADS PubMed  Fiess N.M., Fugazza M. ( 2012) Informality and openness to trade: insights from cross-sectional and panel analyses, Margin: The Journal of Applied Economic Research , 6, 235– 75. Google Scholar CrossRef Search ADS   Fiess N.M., Fugazza M., Maloney W.F. ( 2010) Informal self-employment and macroeconomic fluctuations, Journal of Development Economics , 91, 211– 26. Google Scholar CrossRef Search ADS   Foster L., Haltiwanger J., Syverson C. ( 2008) Reallocation, firm turnover, and efficiency: selection on productivity or profitability?, American Economic Review , 98, 394– 425. Google Scholar CrossRef Search ADS   Goldberg P.K., Pavcnik N. ( 2003) The response of the informal sector to trade liberalization, Journal of Development Economics , 72, 463– 96. Google Scholar CrossRef Search ADS   Günther I., Launov A. ( 2012) Informal employment in developing countries: opportunity or last resort?, Journal of Development Economics , 97, 88– 98. Google Scholar CrossRef Search ADS   Head K., Mayer T. ( 2014) Chapter 3 – gravity equations: workhorse, toolkit, and cookbook, in Gita Gopinath E.H., Rogoff K. (eds) Handbook of International Economics , vol. 4, Elsevier, Amsterdam, 131– 95. Heid B. ( 2015) Regional trade agreements, unemployment, and the informal sector. Working paper, CESifo Area Conference on Global Economy Working Paper, Munich. Heid B., Larch M., Riaño A. ( 2013) The rise of the maquiladoras: a mixed blessing, Review of Development Economics , 17, 252– 67. Google Scholar CrossRef Search ADS   Helpman E., Itskhoki O. ( 2010) Labour market rigidities, trade and unemployment, Review of Economic Studies , 77, 1100– 37. Google Scholar CrossRef Search ADS   Helpman E., Itskhoki O., Redding S.J. ( 2010) Inequality and unemployment in a global economy, Econometrica , 78, 1239– 83. Google Scholar CrossRef Search ADS   Howitt P. ( 2002) Looking inside the labor market: a review article, Journal of Economic Literature , 40, 125– 38. Hsieh C.-T., Klenow P.J. ( 2009) Misallocation and manufacturing TFP in China and India, Quarterly Journal of Economics , 124, 1403– 48. Google Scholar CrossRef Search ADS   Kreickemeier U., Nelson D. ( 2006) Fair wages, unemployment and technological change in a global economy, Journal of International Economics , 70, 451– 69. Google Scholar CrossRef Search ADS   La Porta R., Shleifer A. ( 2008) The unofficial economy and economic development, Brookings Papers on Economic Activity , 2008, 275– 352. Google Scholar CrossRef Search ADS   La Porta R., Shleifer A. ( 2011) The unofficial economy in Africa. Working Paper 16821, National Bureau of Economic Research, Cambridge, MA. Loayza N.V. ( 1996) The economics of the informal sector: a simple model and some empirical evidence from Latin America, Carnegie-Rochester Conference Series on Public Policy , 45, 129– 62. Google Scholar CrossRef Search ADS   Maloney W.F. ( 2004) Informality revisited, World Development , 32, 1159– 78. Google Scholar CrossRef Search ADS   Marjit S., Ghosh S., Biswas A. ( 2007) Informality, corruption and trade reform, European Journal of Political Economy , 23, 777– 89. Google Scholar CrossRef Search ADS   McCaig B., Pavcnik N. ( 2013) Moving out of agriculture: structural change in Vietnam. Working Paper 19616, National Bureau of Economic Research, Cambridge, MA. McCaig B., Pavcnik N. ( 2014) Export markets and labor allocation in a low-income country. Working Paper 20455, National Bureau of Economic Research, Cambridge, MA. McKenzie D., Sakho Y.S. ( 2010) Does it pay firms to register for taxes? The impact of formality on firm profitability, Journal of Development Economics , 91, 15– 24. Google Scholar CrossRef Search ADS   Melitz M.J. ( 2003) The impact of trade on intra-industry reallocations and aggregate industry productivity, Econometrica , 71, 1695– 725. Google Scholar CrossRef Search ADS   Menezes-Filho N.A., Muendler M.-A. ( 2011) Labor reallocation in response to trade reform. Working Paper 17372, National Bureau of Economic Research, Cambridge, MA. Paz L.S. ( 2014) The impacts of trade liberalization on informal labor markets: a theoretical and empirical evaluation of the Brazilian case, Journal of International Economics , 92, 330– 48. Google Scholar CrossRef Search ADS   Prado M. ( 2011) Government policy in the formal and informal sectors, European Economic Review , 55, 1120– 36. Google Scholar CrossRef Search ADS   Quintin E. ( 2007) Contract enforcement and the size of the informal economy, Economic Theory , 37, 395– 416. Google Scholar CrossRef Search ADS   Radchenko N. ( 2014) Heterogeneity in informal salaried employment: evidence from the Egyptian labor market survey, World Development , 62, 169– 88. Google Scholar CrossRef Search ADS   Ramos R., Duque J.C., Surinach J. ( 2010) Is the wage curve formal or informal? Evidence for Colombia, Economics Letters , 109, 63– 65. Google Scholar CrossRef Search ADS   Rand J., Torm N. ( 2012) The benefits of formalization: evidence from Vietnamese manufacturing SMEs, World Development , 40, 983– 98. Google Scholar CrossRef Search ADS   Rauch J.E. ( 1991) Modelling the informal sector formally, Journal of Development Economics , 35, 33– 47. Google Scholar CrossRef Search ADS   Roberts M.J., Tybout J.R. ( 1997) The decision to export in Colombia: an empirical model of entry with sunk costs, American Economic Review , 87, 545– 64. Saavedra L.A. ( 2001) Female wage inequality in Latin American labor markets. Policy Research Working Paper 2741, World Bank, Washington, DC. Google Scholar CrossRef Search ADS   Schneider F., Buehn A., Montenegro C.E. ( 2010) New estimates for the shadow economies all over the world, International Economic Journal , 24, 443– 61. Google Scholar CrossRef Search ADS   Ulyssea G. ( 2010) Regulation of entry, labor market institutions and the informal sector. Journal of Development Economics , 91, 87– 99. Google Scholar CrossRef Search ADS   Verhoogen E.A. ( 2008) Trade, quality upgrading, and wage inequality in the Mexican manufacturing sector, Quarterly Journal of Economics , 123, 489– 530. Google Scholar CrossRef Search ADS   World Bank ( 2016) Doing Business 2016: Measuring Regulatory Quality and Efficiency. The World Bank, Washington, DC. © Oxford University Press 2017 All rights reserved

Journal

Oxford Economic PapersOxford University Press

Published: Jan 1, 2018

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off