The Effect of Financial Development on Convergence: Theory and Evidence*

Philippe Aghion; Peter Howitt; David Mayer-Foulkes

doi:10.1162/qjec.2005.120.1.173

Aghion, Philippe;Howitt, Peter;Mayer-Foulkes, David;

2005-02-01 00:00:00

The Effect of Financial Development on Convergence: Theory and Evidence Citation Aghion, Philippe, Peter Howitt, and David Mayer-Foulkes. 2005. The effect of financial development on convergence: Theory and evidence. Quarterly Journal of Economics 120, no. 1: 173-222. Published Version http://dx.doi.org/10.1162/qjec.2005.120.1.173 Permanent link http://nrs.harvard.edu/urn-3:HUL.InstRepos:4481509 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Share Your Story The Harvard community has made this article openly available. Please share how this access benefits you. Submit a story . Accessibility THE EFFECT OF FINANCIAL DEVELOPMENT ON CONVERGENCE: THEORY AND EVIDENCE* PHILIPPE AGHION PETER HOWITT DAVID MAYER-FOULKES We introduce imperfect creditor protection in a multicountry Schumpeterian growth model. The theory predicts that any country with more than some critical level of ﬁnancial development will converge to the growth rate of the world technology frontier, and that all other countries will have a strictly lower long-run growth rate. We present evidence supporting these and other implications, in the form of a cross-country growth regression with a signiﬁcant and sizable negative coefﬁcient on initial per-capita GDP (relative to the United States) interacted with ﬁnancial intermediation. In addition, we ﬁnd that other variables representing schooling, geography, health, policy, politics, and institutions do not affect the signiﬁcance of the interaction between ﬁnancial intermediation and initial per capita GDP, and do not show any independent effect on convergence in the regressions. Our ﬁndings are robust to removal of outliers and to alternative conditioning sets, estimation procedures, and measures of ﬁnancial development. I. INTRODUCTION Most current theories of the cross-country distribution of per-capita income imply that all countries share the same long- run growth rate (of TFP or per-capita GDP). Yet the historical record shows that growth rates can differ substantially across countries for long periods of time. For example, Pritchett [1997] estimates that the proportional gap in per-capita GDP between the richest and poorest countries grew more than ﬁvefold from 1870 to 1990, and according to the tables in Maddison [2001] the proportional gap between the richest group of countries and the poorest grew from 3 in 1820 to 19 in 1998. The “great divergence” between rich and poor countries con- tinued through the end of the twentieth century. Although many * With the usual caveat we thank Daron Acemoglu, Alberto Alesina, Jess Benhabib, Sean Campbell, Sebnem Kalemli-Ozcan, Ross Levine, Andrei Shleifer, David Weil, three anonymous referees, and participants at the 2003 NBER Sum- mer Institute, McMaster University, the 2003 Canadian Macroeconomics Study Group, the Federal Reserve Board, Brigham Young University, New York Uni- versity, and Harvard University for helpful comments. Cristina Santos and Stylianos Michalopoulos provided excellent research assistance. 1. The richest group was Western Europe in 1820 and the “European Off- shoots” (Australia, Canada, New Zealand, and the United States) in 1998. The poorest group was Africa in both years. © 2005 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. The Quarterly Journal of Economics, February 2005 173 174 QUARTERLY JOURNAL OF ECONOMICS studies show that a large group of rich and middle-income coun- tries have been converging to parallel growth paths over the past 50 years or so, the gap between these countries as a whole and the very poorest countries as a whole has continued to widen. For example, the proportional gap in per-capita GDP between Mayer- Foulkes’s [2002] richest and poorest convergence groups grew by a factor of 2.6 between 1960 and 1995, and the proportional gap between Maddison’s richest and poorest groups grew by a factor of 1.75 between 1950 and 1998. Technology appears to be the central factor underlying diver- gence. Easterly and Levine [2001] estimate that about 60 percent of the cross-country variation in growth rates of per-capita GDP is attributable to differences in productivity growth, while Kle- now and Rodrı´guez-Clare [1997] estimate that in their sample about 90 percent of the variation is attributable to differences in productivity growth. Although the level of productivity can be affected by many factors other than technology, such as geogra- phy and institutions that affect the efﬁciency of resource alloca- tion, it is hard to see how substantial differences in the growth rate of productivity persisting for such long periods of time can be accounted for by these nontechnological factors, which are them- selves highly persistent over time. Instead, it seems more likely that divergence reﬂects long-lasting cross-country differences in rates of technological progress. These facts are especially puzzling when one takes into account the possibility of international technology transfer and the “advantage of backwardness” [Gerschenkron 1952] that it confers on technological laggards. That is, the further a coun- try falls behind the world’s technology leaders, the easier it is for that country to progress technologically simply by imple- menting new technologies that have been discovered else- where. Eventually this advantage should be enough to stabilize the proportional gap that separates it from the leaders. This is what happens in neoclassical models where technology trans- fer is instantaneous [Mankiw, Romer, and Weil 1992], where technologies developed on the frontier are not “appropriate” for poorer countries [Basu and Weil 1998; Acemoglu and Zilibotti 2001], where technology transfer can be blocked by special 2. For example, Barro and Sala-i-Martin [1992], Mankiw, Romer, and Weil [1992], and Evans [1996]. FINANCIAL DEVELOPMENT AND CONVERGENCE 175 interests [Parente and Prescott 1994, 1999] and where a coun- try adopts institutions that impede technology transfer [Ace- moglu, Aghion, and Zilibotti 2002]. This paper explores the hypothesis that ﬁnancial constraints prevent poor countries from taking full advantage of technology transfer and that this is what causes some of them to diverge from the growth rate of the world frontier. It introduces credit constraints into a multicountry version of Schumpeterian growth theory with technology transfer, and shows that the model im- plies a form of club convergence consistent with the broad facts outlined above. In the theory, countries above some threshold level of ﬁnancial development will all converge to the same long- run growth rate, and all other countries will have strictly lower long-run growth rates. There are three key components to the theory. The ﬁrst is that because technological knowledge is often tacit and circum- stantially speciﬁc, technology transfer requires the receiving country to invest resources in order to master foreign technol- ogies and adapt them to the local environment. Although these investments may not ﬁt the conventional deﬁnition of R&D, they play the same role as R&D in an innovation-based growth model; that is, they generate new technological possibilities where they are conducted, building on previous knowledge. Accordingly, our theory assigns to R&D the role that Nelson and Phelps [1966] assumed was played by human capital, namely that of determining a country’s “absorptive capacity.” The second key component is the assumption that as the global technology frontier advances, the size of investment required in order to keep innovating at the same pace as before 3. See Aghion and Howitt [1998], Howitt [2000], Acemoglu, Aghion, and Zilibotti [2002], and Howitt and Mayer-Foulkes [2002]. The last of these papers implies three convergence groups, analogous to the three groups of the present paper, but the disadvantage of backwardness that prevents some countries from converging in that paper arises from low levels of human capital rather than from credit-market imperfections. 4. See Arrow [1969] and Evenson and Westphal [1995]. 5. Cohen and Levinthal [1989] and Grifﬁth, Redding, and Van Reenen [2001] have also argued that R&D by the receiving country is a necessary input to technology transfer. 6. Grossman and Helpman [1991] and Barro and Sala-i-Martin [1997] also model technology transfer as taking place through a costly investment process, which they portray as imitation; but in these models technology transfer always leads to convergence in growth rates except in special cases studied by Grossman and Helpman where technology transfer is inactive in the long run. 176 QUARTERLY JOURNAL OF ECONOMICS rises in proportion. This assumption recognizes the force of increasing complexity, which makes technologies increasingly difﬁcult to master and to adapt to local circumstances. The third key component is an agency problem that limits an innovator’s access to external ﬁnance. Speciﬁcally, we assume that an innovator can defraud her creditors by hiding the results of a successful innovation, at a cost that depends positively on the level of ﬁnancial development. Because of this, in equilibrium the innovator’s access to external ﬁnance will be limited to some multiple of her own wage income. Since wages are limited by domestic productivity, therefore a technological laggard can face a disadvantage of backwardness that counteracts Gerschenkron’s advantage; that is, the further behind the frontier it falls the less its innovators will be able to invest relative to what is required in order to keep innovating at a given rate. The lower the level of ﬁnancial development in the country the greater will be this disadvantage. Our paper relates to several important strands of theory relating growth, convergence, and ﬁnancial-market development. There is ﬁrst the literature on poverty traps and interpersonal convergence or divergence in economies with credit market im- perfections, in particular Banerjee and Newman [1993], Galor and Zeira [1993], Aghion and Bolton [1997], and Piketty [1997]. In these models, all agents face the same production technology and, unlike in our model, the same (productivity-adjusted) invest- ment costs, and what generates poverty traps are either noncon- vexities in production or monitoring, or pecuniary externalities working through factor prices. However, there is no technical progress and therefore no positive long-run growth in these mod- els, which therefore cannot analyze the issue of long-term con- vergence in growth rates. Another literature analyzes the effects of ﬁnancial con- straints or ﬁnancial intermediation on long-term growth. Thus, 7. A similar assumption has been shown elsewhere to be helpful in account- ing for the fact that productivity growth rates have remained stable in OECD countries over the second half of the twentieth century despite a steady increase in R&D expenditures. See Jones [1995] and Howitt [1999]. 8. See Banerjee [2003] for a comprehensive survey of this literature. 9. In contrast, in our model countries face a productivity-adjusted cost of innovation which increases with its distance to the technological frontier. It is the interplay between credit constraints and this technological heterogeneity which generates the possibility of long-term divergence. FINANCIAL DEVELOPMENT AND CONVERGENCE 177 Greenwood and Jovanovic [1990], Levine [1991], Bencivenga and Smith [1991, 1993], Saint-Paul [1992], Sussman [1993], Harri- son, Sussman, and Zeira [1999], and Kahn [2001] analyze the effects of ﬁnancial intermediation on growth in an AK-style model with no distinction being made between investing in technology and investing in physical or human capital. King and Levine [1993b], de la Fuente and Marin [1996], Galetovic [1996], Black- burn and Hung [1998], and Morales [2003] consider the relation- ship between ﬁnance and growth in the context of innovation- based growth models. De Gregorio [1996] studies the effects on growth of ﬁnancial constraints that inhibit human capital accu- mulation. Krebs [2003] shows how imperfect sharing of individ- ual human-capital risk can depress long-run growth. However, none of these models analyzes the process of technology transfer that we are focusing on, and therefore none of them is capable of addressing the question of why technology transfer is not sufﬁ- cient to put all countries on parallel long-run growth paths. The paper also produces evidence to support its main impli- cations. There is already a substantial body of evidence to the effect that ﬁnancial development is an important determinant of a country’s short-run growth rate, almost all of which is predi- cated on the assumption of long-run convergence in growth rates. We extend this analysis to allow for the possibility of different long-run growth rates, using a cross section of 71 countries over the period 1960–1995. Speciﬁcally, we use the same data, condi- tioning sets, instruments, and robustness checks as Levine, Loayza, and Beck [2000], who found a strong and robust effect of the level of ﬁnancial development in a standard cross-country growth regression. We add to their regression an interaction term between the log of initial per-capita GDP (relative to the United States) and ﬁnancial development, and interpret a negative coef- ﬁcient as evidence that low ﬁnancial development makes conver- gence less likely. We ﬁnd that the coefﬁcient is indeed negative, and is large both statistically and economically. Our empirical methodology is similar to that of Benhabib and Spiegel [2005], who found a negative interaction term between ini- tial TFP and schooling and concluded that schooling was a key determinant of whether or not a country will converge to the frontier 10. See the surveys by Levine [1997, 2005] and the book by Demirgu¨c¸-Kunt and Levine [2001]. 178 QUARTERLY JOURNAL OF ECONOMICS growth rate. We test the robustness of our results by including both schooling and an interaction term between the initial GDP gap and schooling as additional regressors in our equation. In addition, we repeat this robustness test using instead of schooling a large number of different variables suggested by other growth theories. In all cases the main implications of our theory pass the test. We also present evidence to the effect that the main channel through which ﬁnancial development affects convergence is productivity growth, as implied by the theory, rather than capital accumulation, and show that our results are robust to elimination of outliers, to alternative condition- ing sets, to alternative estimation procedures and to alternative measures of ﬁnancial development. II. THEORETICAL FRAMEWORK We follow Acemoglu, Aghion, and Zilibotti [2002] in casting Schumpeterian growth theory in a simple discrete-time frame- work. There are m countries, who do not exchange goods or factors, but do make use of each others’ technological ideas. There is a continuum of individuals in each country. Each country has a ﬁxed population P, which for notational convenience we nor- malize to unity. Thus, aggregate and per-capita quantities are identical. Everyone lives for two periods, being endowed with two units of labor services in the ﬁrst period and none in the second, with a utility function linear in consumption: U c c , 1 2 where 0 1. Within each country the growth path is deter- mined as follows. II.A. The General Sector There is one multipurpose “general” good, produced by labor and a continuum of specialized intermediate goods according to the production function, 11. Linear utility implies that people are indifferent between investing in any country, whether technologically or ﬁnancially developed or not. We assume that all investment is locally ﬁnanced, but if were the same across all countries, we could allow perfect capital mobility with no change in the analysis. Extending our analysis to the case of strictly concave utility would allow us to analyze the possibility and implications of capital ﬂowing from less to more ﬁnancially devel- oped economies in accordance with Lucas’ [1990] oft-cited observation that capital ﬂows from poor to rich countries rather than the reverse. FINANCIAL DEVELOPMENT AND CONVERGENCE 179 1 1 (1) Z P A i x i di,0 1, t t t where x (i) is the input of the latest version of intermediate good i and A (i) is the productivity parameter associated with it. The general good is used for consumption, as an input to R&D and also as an input to the production of intermediate goods. The general good is produced under perfect competition, so the price of each intermediate good equals its marginal product: x i (2) p i . A i (We use the general good as nume´raire, and P 1.) II.B. Intermediate Sectors For each intermediate good i there is one person born each period t 1 who is capable of producing an innovation for the next period. This person is called the ith innovator in t 1, and if she succeeds (innovates), then she will be the ith incumbent in t. Let (i) be the probability that she succeeds. Then A with probability i t t A i , A i with probability 1 i t1 t where A is the world technology frontier, which grows at the constant rate g 0, taken as given for now. The fact that a successful innovator gets to implement A is a manifestation of technology transfer, of the kind that Keller [2002] calls “active”; that is, domestic R&D makes use of ideas developed elsewhere in the world. 12. In Aghion, Howitt, and Mayer-Foulkes [2004] we extend our analysis and results to the more general case in which innovations do not result in an imme- diate jump to the frontier, so that bA 1 b A with probability i t t1 A i , A i with probability 1 i t1 t where A A i di t t is the average domestic productivity at date t and b is a real number between 0 and 1. 180 QUARTERLY JOURNAL OF ECONOMICS In each intermediate sector where an innovation has just occurred, the incumbent is able to produce any amount of the intermediate good using as the sole input one unit of the general good per unit of intermediate good. In addition, in every interme- diate sector there are an unlimited number of people capable of producing copies of the latest generation of that intermediate good at a unit cost of So in sectors where an innovation has just occurred, the incumbent will be the sole producer, at a price equal to the unit cost of the competitive fringe, whereas in noninnovating sectors where the most recent incumbent is dead, production will take place under perfect competition with a price equal to the unit cost of each producer. In either event the price will be , and according to the demand function (2) the quantity demanded will be 1/1 (3) x i A i. t t It follows that an unsuccessful innovator will earn zero prof- its next period, whereas the proﬁt of an incumbent will be (i) 1/(1) A , where ( 1)(/) . II.C. Aggregate Behavior Deﬁne the country’s “average productivity” A as A A i di. t t Substituting (3) into (1), we see that gross output of the general good will be Z A , t t /(1) where (/) . In equilibrium the probability of innovation will be the same in each sector: (i) for all i; therefore, average productivity t t evolves according to 13. Thus, imitation of a successful innovation is costless within a country, whereas we shall assume below that, because of the well-documented fact that technologies work differently in different countries, moving a domestic sector up to the world technology frontier is costly and requires a positive R&D investment. 14. This requires the further assumption that , which we now make. FINANCIAL DEVELOPMENT AND CONVERGENCE 181 A A 1 A . t t t t t1 That is, the productivity parameter will equal A in the fraction of sectors that innovated at t 1, but will remain equal to A (i) in the 1 sectors that did not innovate at t 1, and t1 t since innovations are distributed randomly across sectors the average value of A (i) among noninnovating sectors will equal t1 the economywide average A . t1 Deﬁne the country’s normalized productivity as a A /A . t t t Normalized productivity is an inverse measure of the country’s distance to the technological frontier, or its “technology gap.” It follows that the gap evolves according to (4) a a . t t t1 1 g Since the general sector is perfectly competitive, the wage rate w will be the marginal product of labor in producing the general good: w 1 Z 1 A . t t t The fact that w is proportional to domestic productivity A plays t t an important role in what follows. For as we shall see, it implies that technology investment in a country that is credit-constrained will be strictly proportional to A . Value added in the general sector is wage income, whereas value added in the intermediate sectors is proﬁt income. Per- capita GDP is the sum of value added in all sectors: Y w 1 A A . t t t t t t t II.D. Innovations In each sector the R&D investment needed to innovate at any given rate is governed by the cost function, N n ˜ A /2A , 0, t1 t t t t t where N is the quantity of general good that must be invested. t1 We multiply n ˜ by A to recognize the “ﬁshing-out” effect; the further ahead the frontier moves, the more difﬁcult it is to inno- vate. This effect is crucial in what follows. 182 QUARTERLY JOURNAL OF ECONOMICS In our analysis below, we make extensive use of the inverse of the R&D cost function n ˜ . Namely, an intermediate producer who invests the amount nA in R&D will innovate next period with probability 1 2 (5) ˜ n n ˜ n 2n /. Finally, we assume that This condition guarantees that the equilibrium probability will always lie strictly between 0 and 1. In equilibrium will be chosen so as to maximize the ex- pected net payoff (6) A n ˜ A t t t t in each sector, subject to credit constraints. II.E. Equilibrium Innovation under Perfect Credit Markets In this subsection we show that if innovators had unlimited access to outside ﬁnance all economies would converge to the same growth rate. The level of each country’s growth path might be different because of country-speciﬁc differences in parameters such as and , but their long-run growth rates would all be the same. Suppose accordingly that each innovator can borrow (from other young people) unlimited quantities at the going rate r 1 subject to a binding commitment to repay if the project succeeds. Then will be chosen so as to maximize (6) with no constraint. This implies that *, where * /, with corresponding equilibrium R&D expenditure N n ˜ *A n*A . t1 t t It follows from this and equation (4) that the country’s tech- nology gap evolves according to 1 * (7) a * a H a , t1 t 1 t 1 g 15. Note that ˜ (0) 0, ˜ (n) 0 and ˜ (n) 0. FINANCIAL DEVELOPMENT AND CONVERGENCE 183 which converges in the long run to the steady-state value 1 g * a* 0,1. g * Per-capita GDP in the steady state is (8) Y 1 a* * A , t t which grows at the same rate g as the technology frontier A ,as claimed. II.F. Credit Constraints Now suppose that credit markets are imperfect. Each entre- preneur at the end of period t is a young person with access to the wage income w . Thus, to invest N in an R&D project, she must t t borrow N w . Assume that if she pays a cost cN she can t t t defraud her creditors by hiding the proceeds in the event that the project is successful. This implies that in equilibrium the entre- preneur cannot borrow more than a ﬁnite multiple of her accu- mulated wealth w , as in Bernanke and Gertler [1989], and therefore she cannot invest more than in innovation, where [1, ) depends positively on the hiding cost c. This credit constraint will be binding if the unconstrained optimal investment n*A is strictly greater than the innova- t1 tor’s investment capacity w , or equivalently, after dividing through by A ,if t1 (9) n* a , where 1 g 16. The result that a* is strictly less than one reﬂects the fact that no country, even the most technologically advanced in terms of its average produc- tivity, will ever be the world leader in all intermediate sectors simultaneously, because of the randomness of the innovation process. Thus, the model is consis- tent with the evidence of Baily and Solow [2001] to the effect that different countries are technology leaders in different industries. 17. See Appendix 1. 184 QUARTERLY JOURNAL OF ECONOMICS We represent ﬁnancial development by the cost parameter c,or equivalently by the credit multiplier (or by ), on the grounds that a highly developed ﬁnancial system protects creditors by making it hard to defraud them. We see from (9) that (i) for a given level of technological development a of the country, domestic ﬁrms are more likely to be credit-constrained if ﬁnancial development is lower; (ii) for a given level of ﬁnancial development ﬁrms are more likely to be credit-constrained the further the country is behind the techno- logical frontier (i.e., the smaller is a ). This is the “disadvantage of backwardness” induced by the existence of credit constraints. Thus, ﬁrms in more advanced countries with a n*/ a will invest the unconstrained amount n*A in innovation and t1 therefore will innovate with probability *, whereas ﬁrms in less advanced countries with a n*/ a cannot invest more than w a A and therefore will inno- t t t1 vate with probability ˜ a *, where the innovation technology ˜ is given by (5). In that case a will be determined according to t1 1 ˜ a (10) a ˜ a a H a . t1 t t 2 t 1 g 18. Our model implies that, holding the credit multiplier (or ) constant, among those countries that are ﬁnancially constrained external ﬁnancing (equal to ( 1)w ) is bigger in those that are closer to the technological frontier. However, the opposite is true among those countries that are not constrained, as the amount of external ﬁnancing is then entirely determined by the gap between the R&D cost n*A , which is proportional to the frontier productivity A , and the t t amount of internal ﬁnance which is proportional to current domestic productivity. 19. This raises the question of why a constrained entrepreneur at t 1 would not instead target a lower technology level B A , which would be less t t expensive given the assumption that the cost of innovating at a given rate is proportional to the targeted technology level. In Aghion, Howitt, and Mayer- Foulkes [2004] we answer the question by showing that this alternative would be dominated, from the entrepreneur’s point of view, by the strategy of always targeting the frontier. This relies on the fact that the innovation function ˜ (n) has an elasticity less than one, which in turn follows from the fact that the innovation cost function n ˜ ( ) is strictly convex with n ˜ (0) 0. FINANCIAL DEVELOPMENT AND CONVERGENCE 185 II.G. The World Growth Rate As in other Schumpeterian models, we suppose that the growth rate g of the global technology frontier is determined by the pace of innovations in the leading countries, none of which are assumed to be credit-constrained. For simplicity, assume that there is just one leader, labeled country 1. Then 1 1 1 g , where 0 is a spillover coefﬁcient and the subscript 1 indicates a parameter value in country 1. III. THEORETICAL IMPLICATIONS III.A. Three Dynamic Patterns In general, the country’s technology gap a will evolve accord- ing to the unconstrained dynamical system (7) when a a () and according to the constrained system (10) when a a (). Thus, a Ha minH a , H a . tt t 1 t 2 t Note that H is a linear function with positive vertical intercept and a slope between 0 and 1. Also, H is an increasing concave function when a min{a (), 1}, with H (0) 0 and t 2 (11) H0 . 1 g Countries will fall into three groups, deﬁned by the level of ﬁnancial development . The evolution of the technology gap is illustrated for each case in Figures I–III below. 1. Convergence in growth rate, no marginal effect of ﬁnancial development. When ﬁnancial development is sufﬁciently high that n*/a* , so that a* a (), then as shown in Figure I, a will converge asymptotically to the unconstrained steady state a* 0. Per-capita GDP will be given by equation 20. See footnote 15 above. 186 QUARTERLY JOURNAL OF ECONOMICS FIGURE I A Country with the Highest Level of Financial Development (8) in the long run, which implies that the country will grow at the same rate g as the global technology frontier in the long run. Increases in ﬁnancial development will have no marginal effect on either the steady-state growth rate or the steady-state technology gap; these converge, respectively, to the values g and a* which are independent of . 2. Convergence in growth rate with a level-effect of ﬁnancial development. When the level of ﬁnancial development is neither too high nor too low, so that g n* 1 g a* 21. That differences in the credit multiplier within this high ﬁnancial- development range do not affect the long-run technological gap results from the fact that the incentive constraint underlying (see Appendix 1) only places an upper bound on the amount borrowed by the entrepreneur. As soon as this constraint ceases to bind, then becomes irrelevant in determining the dynamics of productivity. A different model of credit constraints, e.g., one that would rely on ex ante moral-hazard considerations and a continuous effort choice, might gen- erate the possibility that differences in ﬁnancial development always affect long- run productivity. 22. Note that g n* 1 g a* because g/1 g g * * * n*/a* n* g * n* * * /2 FINANCIAL DEVELOPMENT AND CONVERGENCE 187 FIGURE II A Country with a Medium Level of Financial Development then H(a*) H (a*), so a cannot converge to the uncon- 1 t strained steady state a*. From (11) we have 1 g 1 H0 1. 1 g 1 g 1 g Therefore, as shown in Figure II, a will converge to a limit a ˆ that is strictly positive (except in the borderline case where g/(1 g) and a ˆ 0) but less than a*. In the long run, per-capita GDP will be (12) Y 1 a ˆ ˜ a ˆ A Y . t t t This country will also grow at the rate g in the long run, because Y is strictly proportional to A ,asis Y . Increases in t t t ﬁnancial development will have no marginal effect on the steady-state growth rate, but they will have a positive mar- ginal effect on the steady-state technology gap a ˆ, because they shift the curve H (a ) up in Figure II. According to 2 t (12), increases in ﬁnancial development will also have a positive effect on the country’s steady-state per-capita GDP because of both the direct effect on ˜ and the indirect effect working through a ˆ. 23. Formally, from (10), a a t1 t a ˜ a 1 0. t t 1 g 188 QUARTERLY JOURNAL OF ECONOMICS 3. Divergence in growth rate, with a growth-effect of ﬁnancial development. When the level of ﬁnancial development is sufﬁciently low that g/1 g, then H(a*) H (a*) and H(0) 1, so a will converge to 1 t zero, as shown in Figure III. The following argument shows that in this case the rate of productivity growth, deﬁned as G A /A 1, will approach a limiting t t1 t value that is strictly between 0 and g. By l’Hoˆpital’s rule a 1 t1 lim lim Ha 0,1. a 1 g t3 a30 Therefore, t1 lim G 1 g lim 1 1 g 0,g. t3 t3 Thus, the steady-state growth rate will be strictly less than the frontier growth rate g and will be strictly increasing in the country’s level of ﬁnancial development. III.B. Summary In summary, the two main implications of our theory are that 1. The likelihood that a country will converge to the frontier growth rate increases with its level of ﬁnancial develop- ment, and 2. in a country that converges to the frontier growth rate, ﬁnancial development has a positive but eventually van- ishing effect, ceteris paribus, on the steady-state level of per-capita GDP relative to the frontier. IV. CREDIT AND CONVERGENCE:EVIDENCE In this section we confront our theoretical predictions with evidence. After describing our data, we test implications 1 and 2 above with a cross-country growth regression involving an inter- action term between the log of initial GDP per capita and ﬁnan- 24. Aghion, Howitt, and Mayer-Foulkes [2004] show that per-capita GDP grows at the same asymptotic rate as productivity in this case. FINANCIAL DEVELOPMENT AND CONVERGENCE 189 FIGURE III A Country with the Lowest Level of Financial Development cial development. This test provides strong evidence for our model and for the general proposition that whether or not a country converges to the frontier growth rate depends on its level of ﬁnancial development. IV.A. Data We do not have a direct empirical measure of the parameter or which our theory takes as an indicator of ﬁnancial devel- opment. Instead, we follow the usual practice of using a measure of ﬁnancial intermediation to proxy for ﬁnancial development. We analyze cross-sectional data on 71 countries over the period 1960–1995, taken from Levine, Loayza, and Beck [2000] (LLB) who found a strongly positive and robust effect of ﬁnancial inter- mediation on short-run growth in a regression with initial GDP on the right-hand side. We follow LLB in using private credit as our preferred measure of ﬁnancial development. This is the value of credits by ﬁnancial intermediaries to the private sector, divided by GDP. It is LLB’s preferred measure because it excludes credit granted to the public sector and credit granted by the central 25. We do not pursue a panel-data approach because we believe that ﬁnancial development is imperfectly measured and persistent, which means that its growth effects are likely to be underestimated by a panel-data approach relative to a cross-section approach [Hauk and Wacziarg 2004]. This may explain why Ben- habib and Spiegel [1997, 2000] found no signiﬁcant interaction between initial GDP and ﬁnancial development using panel data on 92 countries from 1960 to 26. See Appendix 2 for a detailed description and sources of data. 190 QUARTERLY JOURNAL OF ECONOMICS FIGURE IV Average Financial Development and Growth Rate of Per-Capita GDP, 1960–1995 bank and development banks. We also report results below using alternative measures. Figures IV and V show that the raw data are roughly con- sistent with implications 1 and 2. Figure IV plots the average growth rate of per-capita GDP over the sample period against the average level of ﬁnancial development over the period. Except for the countries with the three highest growth rates, which are clearly above their steady-state values, the scatter diagram ap- pears consistent with a positive effect of ﬁnancial development on growth that vanishes at approximately Greece’s level of ﬁnancial development (39 percent), as predicted by the implication 1. Fig- ure V plots the average log of per-capita GDP on the vertical axis. It appears consistent with a positive effect of ﬁnancial develop- ment on the level of GDP which vanishes once ﬁnancial develop- ment has reached approximately Canada’s level (61 percent), as predicted by implication 2. FINANCIAL DEVELOPMENT AND CONVERGENCE 191 FIGURE V Average Financial Development and Log of Per-Capita GDP, 1960–1995 These ﬁgures do not control for the effects of initial GDP or any other possible inﬂuences on a country’s growth path. Nor do they deal with the problem of possible endogeneity of ﬁnancial development. For these we turn to the following regression results. IV.B. Growth Regression with an Interaction Term Our theoretical model can be approximated by the following growth regression: (13) g g F y y i 1 0 f i y i 1 F y y X ε , fy i i 1 x i i where g denotes the average growth rate of per-capita GDP, F the average level of ﬁnancial development, y the initial (1960) log of per-capita GDP, X a set of other regressors and ε a disturbance 27. See Appendix C of our [2004] working paper for the details of the approximation. 192 QUARTERLY JOURNAL OF ECONOMICS term with mean zero. Country 1 is the technology leader, which we take to be the United States. This is a standard growth regression except for the interaction term F ( y y ). i i 1 Deﬁne y ˆ y y , country i’s initial relative per-capita GDP. i i 1 Under the assumption that F 0, we can rewrite (13) as y fy i g g y ˆ y ˆ , i 1 i i i where the steady-state value y ˆ is deﬁned by setting the right- hand side of (13) to zero: F X ε 0 f i x i i (14) y ˆ y fy i and is a country-speciﬁc convergence parameter: (15) F i y fy i that depends on ﬁnancial development. A country can converge to the frontier growth rate if and only if the growth rate of its relative per-capita GDP depends nega- tively on the initial value y ˆ ; that is, if and only if the convergence parameter is negative. Thus, the likelihood of convergence will increase with ﬁnancial development (implication 1 above) if and only if (16) 0. fy Since this implication constitutes the central proposition of our theoretical model, our main objective in estimating (13) will be to see whether or not the estimated interaction coefﬁcient is indeed signiﬁcantly negative. It follows from (14) that the long-run effect of ﬁnancial de- velopment on relative output is * * y ˆ y ˆ i f fy i (17) . F F i y fy i Assume that all countries lag the United States in steady state: y ˆ 0. Then if (16) holds, ﬁnancial development will have a positive long-run effect on per-capita GDP of each (nonleader) country that converges if and only if 0. For then the numer- ator of (17) will be positive. Moreover, this effect will eventually vanish (when F reaches the leader’s level) if and only if the direct effect is equal to zero: (18) 0. f FINANCIAL DEVELOPMENT AND CONVERGENCE 193 So if we were to ﬁnd that (18) held in addition to our main prediction (16), this would corroborate implication 2. If instead we were to ﬁnd that 0, then the estimated effect of ﬁnancial development on y ˆ would never vanish, even for the leader, whereas 0 would imply a negative effect for countries close to the leader. IV.C. Regression Results The ﬁnancial development variable F in (13) may be endoge- nous because of feedback from growth to ﬁnance, or because of the common effects of omitted variables on both growth and ﬁnance. Moreover, endogeneity of F is likely to entail endogeneity of the interaction variable F ( y y ). To deal with this problem, we estimated (13) using instrumental variables, instrumenting for F and F ( y y ) using legal origins (L) and legal origins inter- acted with initial relative output (L ( y y )). Legal origins is a set of three zero-one variables, used ﬁrst in the economics literature by La Porta et al. [1997, 1998] and further extended to all 71 countries by LLB, indicating whether the country’s legal system is based on French, English, or Ger- man traditions (the omitted case is Scandinavian). La Porta et al. argue that the main effect of L is on the rights of investors and creditors. LLB conclude that L constitutes a good set of instru- ments for ﬁnancial development because they were established too long ago to suffer from reverse causation, they have a strong effect on ﬁnancial development and their main effects on growth should be through ﬁnancial channels. We used the interacted variables L ( y y ) as additional instruments to model the interaction term F ( y y ), because using L without L ( y y ) resulted in too much collinearity between the ﬁtted values of F and F ( y y ) to identify the crucial coefﬁcients and . 1 f fy We defer further discussion of the instruments until the next section. Our main results are presented in the ﬁrst column of Table I, which reports the slope-coefﬁcient estimates for the case where there are no other regressors X. These results show that ﬁnancial development interacted with initial relative output has a signiﬁ- cantly negative effect ( 0.061 0), bearing out the main fy implication of the theory to the effect that convergence depends positively on ﬁnancial development. They also fail to reject the hypothesis that the direct effect of ﬁnancial development is f 194 QUARTERLY JOURNAL OF ECONOMICS TABLE I GROWTH,FINANCIAL DEVELOPMENT, AND INITIAL GDP GAP Estimation of equation: g g F ( y y ) F ( y y ) X 1 0 f y 1 fy 1 x Private credit Liquid liabilities Conditioning a b a b set (X) Empty Policy Full Empty Policy Full Coefﬁcient estimates 0.015 0.013 0.016 0.029 0.030 0.027 (0.93) (0.68) (0.78) (1.04) (0.99) (0.90) 1.507*** 1.193* 1.131 2.648*** 2.388** 2.384** (3.14) (1.86) (1.49) (3.12) (2.39) (2.11) 0.061*** 0.063*** 0.063*** 0.076*** 0.077*** 0.073*** fy (5.35) (5.10) (4.62) (3.68) (3.81) (3.55) Instrument test p-values 1st-stage F-test: F 0.0000 0.0014 0.0024 0.0044 0.0032 0.0042 1st-stage F-test: F(y y ) 0.0000 0.0000 0.0000 0.0690 0.0078 0.0088 1st-stage F-test: L(y y ) 0.0000 0.0000 0.0001 0.0003 0.0002 0.0022 Sargan test 0.5372 0.7255 0.5573 0.2217 0.3952 0.3627 C-test for L(y y ) 0.3773 0.7013 0.4654 0.2700 0.3549 0.2799 C-test for (y y ) 0.6475 0.7790 0.7781 0.6240 0.6341 0.6226 Sample size 71 63 63 71 63 63 zero, thus bearing out our theoretical implication of a positive but vanishing steady-state effect. These ﬁndings are signiﬁcant quantitatively as well as sta- tistically, because they imply that countries will indeed belong to 28. The wide conﬁdence intervals for are also consistent with a quantita- tively large direct effect of ﬁnancial development, although as pointed out below the point estimate of indicates that for most converging countries the effect will be quantitatively quite small. FINANCIAL DEVELOPMENT AND CONVERGENCE 195 TABLE I (CONTINUED) 7 8 9 10 11 12 Bank assets Commercial-central bank a b a b Empty Policy Full Empty Policy Full 0.019 0.020 0.022 0.000 0.031 0.013 (1.07) (1.03) (1.12) (0.00) (0.17) (0.07) 1.891*** 1.335* 1.365 7.166 5.279 5.645 (3.57) (1.93) (1.66) (1.04) (0.73) (0.72) 0.081*** 0.081*** 0.081*** 0.110 0.100 0.102 (5.07) (4.85) (4.46) (1.29) (1.18) (1.14) 0.0000 0.0000 0.0000 0.2654 0.2180 0.1704 0.0010 0.0003 0.0011 0.5160 0.2743 0.2962 0.0000 0.0000 0.0000 0.2329 0.2315 0.4516 0.8486 0.8816 0.8279 0.9661 0.8861 0.9223 0.9940 0.9642 0.8424 0.9482 0.7680 0.8240 0.7699 0.9944 0.9784 0.9700 0.9818 0.9320 71 63 63 71 63 63 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is the average Financial Development 1960–1995 using four alternative measures, and y y is the log of per-capita GDP in 1960 relative to the United States. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L( y y ) as instruments for F and F( y y ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, respectively. a. The Policy conditioning set includes average years of schooling in 1960 (school), government size (gov), inﬂation (pi), black market premium (bmp), and openness to trade (trade). b. The Full conditioning set includes the Policy set plus indicators of revolutions and coups (revc), political assassinations (assass), and ethnic diversity (avelf). different convergence clubs. Speciﬁcally, a country can converge to the frontier growth rate if and only if its convergence parame- ter (15) is negative; that is, if and only if its level of private credit exceeds the critical value F / , y fy which according to our estimates equals 25 percent. Just over half the countries in our sample (37 of 71) exceed this critical value. 196 QUARTERLY JOURNAL OF ECONOMICS FIGURE VI Estimated Convergence Parameter over the Observed Range of Private Credit (Positive values imply nonconvergence.) Figure VI shows the estimated convergence parameter as a func- tion of private credit, over the observed range of F, with two- standard-deviation bands. As indicated in Table II, the estimated parameter is at least two standard deviations below zero for 30 countries, the group most likely to converge in growth rate, and two standard deviations above zero for 7 countries, those most likely to diverge. The average estimated convergence parameter in the sample is 0.82, which implies an annual convergence rate of almost 5 percent. Another measure of the economic signiﬁcance of our parame- ter estimates is the size of the implied effect of ﬁnancial develop- ment on a converging country’s steady-state relative output. As predicted by implication 2 of our theoretical analysis, this effect is a diminishing function of ﬁnancial development. Speciﬁcally, a one-standard-deviation increase in private credit (28 percentage points) would raise steady-state GDP by 21 percent in Belgium, the (estimated) converging country with the smallest level of private credit. But the effect would be less than 8 percent in every other converging country, and less than 1 percent for each of the 30 “most likely to converge” countries. The next two columns of Table I show that our results are robust to the inclusion of other regressors. Speciﬁcally, column 2 FINANCIAL DEVELOPMENT AND CONVERGENCE 197 TABLE II CONVERGENCE CLUB MEMBERSHIP 12 3 Countries most Countries most likely to Countries uncertain likely to converge in to converge in diverge in growth rate growth rate growth rate Switzerland Iceland Liberia Japan Venezuela Syrian Arab Republic United States Trinidad & Tobago Nepal Sweden Chile Haiti Netherlands Senegal Ghana Norway Philippines Sierra Leone Germany Belgium* Zaire France Jamaica South Africa Mauritius Korea Honduras Austria Fiji Spain Zimbabwe Cyprus Mexico Canada El Salvador Italy Kenya Taiwan Colombia Portugal Togo Australia Costa Rica Finland Brazil Ireland Uruguay Thailand Papua New Guinea Malaysia Pakistan United Kingdom Guyana Malta India Denmark Dominican Republic Barbados Ecuador Panama Sri Lanka New Zealand Argentina Israel Paraguay Greece Bangladesh Peru Guatemala Bolivia Niger Financial development decreases, and hence the estimated convergence parameter increases, as you move down each list and then to the right. * The estimated convergence parameter is negative (indicating convergence) in countries above (and including) Belgium and positive (indicating divergence) in countries below Belgium. 198 QUARTERLY JOURNAL OF ECONOMICS uses LLB’s policy conditioning set, which includes average years of schooling in 1960, government size, inﬂation, the black market exchange-rate premium, and openness to trade. Column 3 uses their full conditioning set, which includes the policy conditioning set plus measures of political stability and ethnic diversity. As these two columns indicate, the sign, size, and signiﬁcance of the crucial coefﬁcients and remain virtually unchanged across f fy alternative conditioning sets. The remaining columns report the results when three alter- native measures of ﬁnancial development are used. The ﬁrst is liquid liabilities, which is currency plus demand and interest- bearing liabilities of banks and nonbank ﬁnancial intermediaries, divided by GDP. This is a commonly used measure of ﬁnancial development, although it includes liabilities backed by credits to the public sector and may involve double counting. The second alternative measure is bank assets, the ratio of all credits by banks (but not other ﬁnancial intermediaries) to GDP. The third is commercial-central bank, the ratio of commercial bank assets to the sum of commercial plus central bank assets, which has been used by others although it is not so much a measure of ﬁnancial development as a measure of what fraction of credit is issued by private intermediaries. Our main results ( 0 and fy 0) are robust to all three alternative measures, although in the case of commercial-central bank (our least preferred measure ex ante) the coefﬁcient estimates all lose their statistical signiﬁ- cance. As in the case of private credit, in all three cases the sign, size, and signiﬁcance of the crucial coefﬁcients and remain f fy virtually unchanged across alternative conditioning sets. We checked the robustness of our results against outliers by removing all countries with a residual more than three standard deviations from zero and then reestimating. We also did this using two standard deviations instead of three. We did this for each of the ﬁrst nine cases in Table I. The coefﬁcient never fy changed sign, and its statistical signiﬁcance was always even larger than reported in Table I, while was never signiﬁcantly different from zero. Thus, it seems that the results reported in Table I are not driven by outliers. 29. Although our theory does not rule out nonﬁnancial determinants of steady-state output and growth, the fact that our estimated effects of ﬁnancial development are independent of other conditioning variables suggests that we can safely treat the inﬂuence of those other determinants as part of the error term in the equations with empty conditioning sets. FINANCIAL DEVELOPMENT AND CONVERGENCE 199 IV.D. Instruments We tested the strength of our instruments with the usual F-tests of joint signiﬁcance in the ﬁrst-stage regressions of F and F ( y y ). The p-values reported in the ﬁrst two rows of the lower panel of Table I indicate that the instruments passed this test at the 1 percent level in all three equations involving private credit, our preferred measure of ﬁnancial development, in all equations involving bank assets and in all but one involving liquid liabilities. The instruments passed at the 10 percent sig- niﬁcance level in all equations not involving commercial-central bank. Because of our a priori doubts as to the suitability of the commercial-central bank measure, we believe that the other three measures are telling us the right message. These results conﬁrm and extend similar ﬁndings by LLB. However, we have added to their analysis the three interacted instruments L ( y y ), and it is important that they have additional explanatory power. Accordingly, the third row of the lower panel of Table I reports the p-value of an F-test of the hypothesis that all three interacted instruments are insigniﬁcant in both ﬁrst-stage regressions. The hypothesis is rejected at the 1 percent level in all equations except those using the suspect commercial-central bank measure. Thus, our addition of the in- teracted instruments does not appear to have created a “many- instruments” problem. From here on we omit the commercial-central bank measure from our analysis, on the grounds that for our purposes it is a priori inferior to the other measures and behaves empirically very differently from the others. To be valid, our legal-origins instruments must not affect growth through any channel other than ﬁnance, since otherwise the effects we are attributing to ﬁnance might actually be effects of these nonﬁnancial channels. This restriction might appear questionable because, for example, different legal systems could result in different regulatory environments that affect barriers to entry as argued by Djankov et al. [2000]. Therefore, we tested the restriction using the standard Sargan test, whose null hypothesis is that the instruments are uncorrelated with the IV residuals. If our instruments were affecting growth through an omitted non- ﬁnancial variable, then the Sargan test should reject the null. However, the large p-values reported in the fourth row of the 200 QUARTERLY JOURNAL OF ECONOMICS lower panel of Table I show that the instruments pass the test in all cases. Again, these results conﬁrm and extend the ﬁndings of LLB with respect to the three main instruments L. We tested the speciﬁc validity of our interacted instruments L ( y y ) with a C-test. The large p-values in the ﬁfth row of the lower panel of Table I indicate that the instruments pass this test in all cases. The large p-values in the sixth row indicated that we also cannot reject the exogeneity of initial relative income. Another way to test for instrument validity is to include in the equation those variables that represent the alternative non- ﬁnancial channels through which the instruments might affect growth. If these nonﬁnancial channels are at work, then the new regressors should rob our ﬁnancial variables of explanatory power. To some extent, the results of Table I already constitute such a test, but the conditioning sets there do not include any interaction terms between the extra regressors and initial rela- tive output. So they leave open the possibility that our main result, the strong negative effect on growth of the interaction between ﬁnancial development and initial relative output, is com- ing from the explanatory power of the interacted instruments L ( y y ) and that this explanatory power derives from correlation between the interacted instruments and some omitted interacted variable. Table V provides strong evidence that this theoretical possi- bility is not what is driving our results. As we explain in more detail below, Table V reports the estimates that result from including each of a long list of alternative regressors, including one that measures regulatory entry barriers, both directly and interacted with initial relative output. But in no case does the inclusion affect our main results, and in no case does the alter- native regressor or its interaction have signiﬁcant explanatory power. If our legal-origins instruments are working through some nonﬁnancial channel, then it must be one that cannot be mea- sured or has not been brought to our attention. Our ﬁnal check on instrument validity was to reestimate Table I using alternative instruments. Speciﬁcally, we used the log of settler mortality, which Acemoglu, Johnson, and Robinson [2001] have argued is a good instrument for modern institutions in formerly colonized countries. To model the interacted ﬁnancial development variable, we also used the log of settler mortality FINANCIAL DEVELOPMENT AND CONVERGENCE 201 interacted with initial relative output as a second instrument. The results are displayed in Table III. This reestimation produces support for our main hypotheses ( 0 and 0), because the estimated is always fy f fy negative and the estimate of is always statistically indistin- guishable from zero. The statistical signiﬁcance of is generally fy much lower than in Table I, but we attribute this largely to the smaller sample size. Data on settler mortality are available only for 41 ex-colonies in our 71-country data set. We prefer to work mainly with our legal-origins instruments rather than settler mortality because we do not want to throw 30 countries out of our data set and because in this data set the settler mortality instruments have relatively little explanatory power for the two ﬁnancial development variables, as indicated by the large p-values of the ﬁrst-stage F-tests in the lower panel of Table III, especially when there is a nonempty set of condition- ing variables. In summary, we believe that the effects of ﬁnancial develop- ment on convergence that we ﬁnd empirically are not artifacts of our use of legal-origins instruments, because the instruments pass standard statistical tests, the effects are robust to control- ling for alternative channels through which legal origins might inﬂuence growth, and to the extent that data limitations permit, we have reproduced our main results using alternative instruments. IV.E. Productivity As a further test of our theory, we examined whether the effects of F and F ( y y ) on per-capita GDP growth were work through productivity growth, as implied by the theory, instead of working just through capital accumulation. Speciﬁcally, we re- estimated the basic growth equation (13) using productivity 30. Beck, Demirgu¨c¸-Kunt, and Levine [2003] and Acemoglu and Johnson [2003] ﬁnd that settler mortality is a stronger instrument than legal origins for ﬁnancial development. This may be partly because they do not include in their equations initial GDP, which in our analysis robs settler mortality of much of its explanatory power. 31. We found the same results using as instruments the initial (1960) value F of ﬁnancial development and F ( y y ). The only exception was the case 0 0 1 using liquid liabilities with the full conditioning set, where the p-value of the interaction coefﬁcient rose to 0.12. 32. Our procedure follows closely that of King and Levine [1993a] and Beck, Levine, and Loayza [2000], who used a similar framework without the interaction terms. 202 QUARTERLY JOURNAL OF ECONOMICS TABLE III ESTIMATION USING LOG SETTLER MORTALITY AS INSTRUMENT Estimation of equation: g g F ( y y ) F( y y ) X 1 0 f y 1 fy 1 x 1 2 34 5678 9 Financial development (F) Private credit Liquid liabilities Bank assets a b a b a b Conditioning set (X) Empty Policy Full Empty Policy Full Empty Policy Full Coefﬁcient estimates 0.006 0.015 0.056 0.039 0.121 0.127 0.010 0.052 0.043 (0.16) (0.15) (0.32) (0.80) (1.31) (1.01) (0.16) (0.41) (0.19) 1.666* 0.560 0.670 2.313** 3.337* 3.745 1.980* 0.947 0.139 (1.85) (0.34) (0.26) (2.17) (1.76) (1.52) (1.80) (0.59) (0.06) 0.091*** 0.096* 0.080 0.062** 0.116** 0.126* 0.093** 0.107* 0.083 fy (3.03) (1.76) (1.33) (2.34) (2.18) (1.91) (2.48) (1.72) (1.06) Instrument test p-values 1st-stage F-test: F 0.0020 0.2471 0.5589 0.0007 0.1538 0.2915 0.0017 0.1033 0.3283 1st-stage F-test: F(y y ) 0.0043 0.0750 0.0717 0.0012 0.2249 0.3093 0.0025 0.0412 0.0477 Sample size 41 38 38 41 38 38 41 38 38 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is average Financial Development 1960–1995 using three alternative measures, and y y is the log of per-capita GDP in 1960 relative to the United States. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using the log of settler mortality and the log of settler mortality times ( y y ) as instruments for F and F( y y ). The numbers in parentheses are t-statistics. 1 1 Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, respectively. a. The Policy conditioning set includes average years of schooling in 1960 (school), government size (gov), inﬂation (pi), black market premium (bmp), and openness to trade (trade). b. The Full conditioning set includes the Policy set plus indicators of revolutions and coups (revc), political assassinations (assass), and ethnic diversity (avelf). c. Only two of the four instrument tests of Table I can be performed because there are only as many settler-mortality instruments as endogenous variables, namely 2. FINANCIAL DEVELOPMENT AND CONVERGENCE 203 growth as the dependent variable instead of growth in per-capita GDP, and interpreting y as the log of aggregate productivity in 1960 instead of the log of per-capita GDP. We took our produc- tivity variable from Benhabib and Spiegel [2005]. The results are presented in Table IV. These results are similar to what we obtained using per- capita GDP. Speciﬁcally, the crucial interaction coefﬁcient is fa still negative and signiﬁcant at the 1 percent level in all equa- tions, with magnitudes similar to Table I. Also the coefﬁcient of F remains not signiﬁcantly different from zero, except in the case of speciﬁcation 4, where it is signiﬁcant at the 10 percent level. As before, the results are stable across conditioning sets, and our legal-origins instruments continue to pass the tests for strength and validity. IV.F. Alternative Explanations of Divergence Perhaps what prevents poor countries from converging in growth rate is not lack of ﬁnancial development but lack of education, or perhaps ﬁnancial development matters for growth only because it facilitates investment in schooling, as in Galor and Zeira [1993]. Or maybe divergence is explained by some other variable that is associated with a low initial level of GDP, or with a low level of private credit. Table V addresses these questions by checking whether the effect of ﬁnance on convergence is robust to including a possible effect of initial relative output, schooling, or a host of other variables on convergence. Speciﬁcally, we included as an additional regressor the square of initial relative output, ( y y ) . If this term were to have a signiﬁcant negative coefﬁcient , it might indicate that yy what keeps poor countries from joining the convergence club is just being poor to start with, or something other than ﬁnance that is correlated with being poor to start with. Next we included as additional regressors not ( y y ) but the variable school— average years of schooling in 1960—and also the interaction term school ( y y ). If the latter were to have a signiﬁcant negative coefﬁcient, it might indicate that lack of education is what keeps 33. Another interpretation of our ﬁnding of a negative interaction coefﬁcient is that entrepreneurs in poor countries have relatively few alternatives to fy borrowing from ﬁnancial intermediaries because of weak or nonexistent equity and bond markets. To the extent that weak equity and bond markets are a by-product of weak investor protection, the same factor that our theory is focusing on, this alternative interpretation is complementary with ours. 204 QUARTERLY JOURNAL OF ECONOMICS TABLE IV PRODUCTIVITY GROWTH,FINANCIAL DEVELOPMENT, AND INITIAL PRODUCTIVITY GAP Estimation of equation: g g F (lna lna ) F (lna lna ) X 1 0 f a 1 fa 1 x Financial development (F) Private credit Liquid liabilities Bank assets a b a b a b Conditioning set (X) Empty Policy Full Empty Policy Full Empty Policy Full Coefﬁcient estimates 0.004 0.008 0.009 0.028* 0.025 0.026 0.014 0.016 0.019 (0.43) (0.75) (0.78) (1.82) (1.61) (1.50) (1.33) (1.50) (1.51) 0.844 0.633 0.496 3.402*** 2.499** 2.662* 1.792*** 1.278 1.426 (1.66) (0.91) (0.57) (3.31) (2.19) (1.79) (2.95) (1.63) (1.35) 0.051*** 0.057*** 0.057*** 0.100*** 0.090*** 0.091*** 0.081*** 0.080*** 0.083*** fa (4.19) (4.15) (3.46) (4.06) (3.88) (3.26) (4.63) (4.37) (3.60) Instrument test p-values 1st-stage F-test: F 0.0000 0.0003 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1st-stage F-test: F (lna lna ) 0.0000 0.0000 0.0004 0.0045 0.0029 0.0111 0.0008 0.0007 0.0043 1st-stage F-test: L (lna lna ) 0.0001 0.0002 0.0017 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Sargan test 0.2803 0.3616 0.4555 0.8986 0.9081 0.9596 0.6381 0.6746 0.6873 C-test for L (lna lna ) 0.1741 0.2604 0.6936 0.8427 0.8579 0.9111 0.6358 0.5075 0.8082 C-test for (lna lna ) 0.8681 0.9888 0.9793 0.9306 0.7976 0.8103 0.8117 0.8080 0.7876 Sample size 65 59 59 65 59 59 65 59 59 The dependent variable g g is the average growth rate of multifactor productivity relative to the United States, 1960–1995. F is average Financial Development 1960–1995 using three alternative measures, and lna lna is the log of productivity in 1960 relative to the United States. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L (lna lna ) as instruments for F and F (lna lna ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 1 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, respectively. a. The Policy conditioning set includes average years of schooling in 1960 (school), government size (gov), inﬂation (pi), black market premium (bmp), and openness to trade (trade). b. The Full conditioning set includes the Policy set plus indicators of revolutions and coups (revc), political assassinations (assass), and ethnic diversity (avelf). FINANCIAL DEVELOPMENT AND CONVERGENCE 205 poor countries from joining the convergence club, for the same reason that a negative interaction effect with ﬁnancial develop- ment indicates that lack of ﬁnance is what keeps them from converging. We repeated the same procedure with 31 other vari- ables that have been suggested in the literature. These include alternative schooling variables, geographical variables, variables measuring population health, policy variables, variables indexing the degree of sociopolitical stability, and a list of eleven institu- tional variables. If our results were fragile, if the main determinant of con- vergence were not ﬁnancial development but something else that was just correlated with ﬁnancial development, or if our legal instruments were working on growth and convergence primarily through some channel other than ﬁnancial development, then the addition of at least some of these variables and their interaction with initial relative output should destroy the explanatory power of F ( y y ) in our growth regression, or make the coefﬁcient on F signiﬁcantly different from zero. But the results of Table V show otherwise. The estimated sign of the coefﬁcient re- fy mains negative in all cases, and statistically signiﬁcant in all cases except when the alternative variable is settler mortality, a case in which, as mentioned above, the number of observations is very small. According to Table V, in all cases the coefﬁcient of F remains not signiﬁcantly different from zero when these alterna- tive variables are included in the regression. Moreover, in no case was the interaction between an alternative variable and initial relative output statistically signiﬁcant. The lower panel of Table V indicates that our instruments remained strong and that they continued to pass the Sargan test. To guard against the possibility that these results are an artifact of some powerful but unexplained effect of the interacted legal-origins instruments on growth, we redid all the estimations of Table V using OLS. This reestimation again conﬁrmed our 34. We explored this single exception further by pooling the 41 ex-colonies with the others. We set settler mortality equal to the New Zealand value (the lowest in the data) for all non-ex-colonies and included in the regression a dummy for non-ex-colony and an interaction between this dummy and initial relative output. This formulation assumes that being an ex-colony has an effect on growth and convergence but not on the growth effects of having more ﬁnancial develop- ment. The results are displayed in the last column of Table V. They conﬁrm our main predictions, and suggest that the only exception in Table V to the ﬁnding of a signiﬁcantly negative interaction coefﬁcient may indeed be attributable to a small sample size. 206 QUARTERLY JOURNAL OF ECONOMICS TABLE V TEST FOR OTHER INTERACTIONS Estimation of equation: g g ( y y ) F F( y y ) X X( y y ) 1 0 y 1 f fy 1 x xy 1 Category Schooling Geography Other variable (X) nothing y y school sec hy gschool ghy afr eq. dist. pop100cr tropop Coefﬁcient estimates 0.015 0.015 0.017 0.019 0.001 0.015 0.005 0.008 0.120 0.015 0.012 (0.93) (0.71) (0.86) (1.01) (0.07) (0.88) (0.40) (0.48) (0.70) (0.89) (0.70) 0.061*** 0.061*** 0.061*** 0.057*** 0.041*** 0.061*** 0.043*** 0.053*** 0.046*** 0.063*** 0.053*** fy (5.35) (4.05) (3.70) (3.71) (3.36) (4.90) (3.65) (4.34) (2.98) (4.62) (4.05) 1.711 0.158 0.442 0.910 0.229 0.328 0.973 1.270 0.849 0.470 (0.97) (0.96) (0.96) (0.44) (0.55) (0.46) (0.55) (0.58) (0.56) (0.40) 0.063 0.027 0.211 1.836 0.036 0.464 0.229 1.105 0.265 0.271 xy (0.15) (0.19) (0.61) (1.30) (0.22) (1.18) (0.29) (0.66) (0.38) (0.43) Instrument test p-values 1st-stage F-test: F 0.0000 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0001 0.0004 1st-stage F-test: F(y y ) 0.0000 0.0000 0.0000 0.0003 0.0002 0.0000 0.0005 0.0000 0.0024 0.0002 0.0005 1st-stage F-test: L(y y ) 0.0000 0.0001 0.0002 0.0005 0.0000 0.0000 0.0000 0.0001 0.0054 0.0002 0.0010 Sargan test 0.5372 0.5303 0.4037 0.5468 0.1140 0.5624 0.8624 0.3411 0.5456 0.6136 0.7448 C-test for L(y y ) 0.3773 0.3784 0.2598 0.4821 0.0849 0.6097 0.9093 0.4498 0.7742 0.5165 0.9116 C-test for (y y ) 0.6475 0.6338 0.4270 0.4556 0.3299 0.6833 0.7071 0.5767 0.7645 0.6664 0.6422 Sample size 71 71 71 69 70 71 70 71 70 67 67 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is average Private Credit 1960–1995, y y is 1 1 the log of per-capita GDP in 1960 relative to the United States, school is average years of schooling in 1960, sec is average years of secondary education 1960–1995, hy is the Klenow-Rodriguez-Clare ratio of human capital to output, gschool is average growth rate of years of schooling 1960–1995, ghy is the average growth rate of the human capital ratio 1960–1985, afr is an African dummy, eq. dist is distance from the equator, pop100cr is measure of access to ocean-navigable waterways, and tropop is the fraction of population living in the tropics. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L( y y ) as instruments for F and F( y y ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, respectively. . a. When the other variable X is ( y y ), the estimated equation is g g F F( y y ) ( y y ) ( y y ) . 1 1 0 f fy 1 x 1 xy 1 FINANCIAL DEVELOPMENT AND CONVERGENCE 207 TABLE V TEST FOR OTHER INTERACTIONS (CONTINUED) Estimation of equation: g g ( y y ) F F( y y ) X X( y y ) 1 0 y 1 f fy 1 x xy 1 Category Health Policy Sociopolitical stability Other variable (X) avgmort avgexpect me trade bus. reg. gov bmp pi soe avelf revc assass Coefﬁcient estimates 0.011 0.010 0.006 0.013 0.010 0.020 0.018 0.016 0.014 0.011 0.020 0.019 (0.61) (0.51) (0.38) (0.83) (0.64) (1.19) (0.94) (0.83) (0.76) (0.63) (1.15) (1.21) 0.046*** 0.047*** 0.046*** 0.062*** 0.052*** 0.067*** 0.065*** 0.060*** 0.056*** 0.056*** 0.063*** 0.062*** fy (3.09) (3.10) (3.83) (5.27) (3.71) (5.34) (4.97) (4.68) (4.05) (4.21) (5.22) (5.47) 0.006 0.090 0.048 0.007 0.300 0.124 0.017 0.007 0.080 1.013 2.836 0.700 (1.62) (1.15) (0.31) (0.38) (0.50) (1.48) (1.00) (0.26) (0.32) (0.52) (1.12) (0.73) 0.001 0.005 0.049 0.001 0.247 0.067 0.008 0.003 0.068 0.952 1.539 0.169 xy (0.26) (0.13) (0.83) (0.09) (0.68) (1.27) (1.00) (0.17) (0.47) (0.97) (1.13) (0.28) Instrument test p- values 1st-stage F-test: F 0.0004 0.0009 0.0002 0.0001 0.0001 0.0002 0.0001 0.0003 0.0002 0.0000 0.0001 0.0001 1st-stage F-test: F(y y ) 0.0003 0.0003 0.0002 0.0000 0.0003 0.0000 0.0000 0.0000 0.0002 0.0001 0.0000 0.0000 1st-stage F-test: L(y y ) 0.0024 0.0016 0.0003 0.0000 0.0001 0.0000 0.0000 0.0001 0.0002 0.0003 0.0000 0.0000 Sargan test 0.3559 0.3499 0.5337 0.6917 0.3331 0.5287 0.7317 0.5057 0.3224 0.2865 0.5368 0.6461 C-test for L(y y ) 0.2871 0.2503 0.6657 0.5326 0.3676 0.3809 0.8368 0.3516 0.5490 0.1890 0.5732 0.4823 C-test for (y y ) 0.7671 0.7533 0.5061 0.6348 0.6343 0.2411 0.8726 0.6331 0.6344 0.6637 0.6744 0.6895 Sample size 64 64 67 66 66 64 67 71 66 71 71 71 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is average Private Credit 1960–1995, y y is 1 1 the log of per-capita GDP in 1960 relative to the United States, avgmort is average child mortality 1970–1990, avgexpect is average life expectancy at birth 1960–1990, me is malaria ecology, trade is openness to trade, bus. reg is an (inverse) index of the regulatory problems involved in opening a business, gov is government size, bmp is the black market premium, pi is the average inﬂation rate 1960–1995, soe is an index of state-owned enterprises, avelf is an index of ethnolinguistic fractionalization, revc is an indicator of revolutions and coups, and assass is a measure of political assassinations. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L( y y ) as instruments for F and F( y y ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, 1 1 respectively. 208 QUARTERLY JOURNAL OF ECONOMICS TABLE V TEST FOR OTHER INTERACTIONS (CONTINUED) Estimation of equation: g g ( y y ) F F( y y ) X X( y y ) 1 0 y 1 f fy 1 x xy 1 Category Institutions Other variable (X) bureau corrupt rulelaw pr.rights exprisk civil kkz infra statehist socap setmortal setmortal Coefﬁcient estimates 0.022 0.025 0.020 0.016 0.018 0.014 0.024 0.028 0.015 0.066 1.078 0.019 (0.98) (1.12) (0.92) (0.77) (0.85) (0.69) (1.02) (1.08) (0.82) (1.50) (0.04) (1.02) 0.060*** 0.067*** 0.056*** 0.055*** 0.046** 0.057*** 0.061*** 0.062*** 0.055*** 0.079** 1.914 0.057*** fy (3.15) (3.79) (3.12) (2.68) (2.29) (3.58) (2.91) (2.85) (4.51) (2.53) (0.04) (4.42) 0.349 0.399 0.431 0.452 0.441 0.212 1.012 3.880 0.058 0.695 10.130 0.421 (0.82) (0.98) (0.99) (0.68) (1.10) (0.63) (1.30) (1.33) (0.04) (0.53) (0.04) (0.77) 0.114 0.220 0.011 0.230 0.061 0.043 0.321 0.895 0.812 0.095 13.058 0.066 xy (0.39) (0.84) (0.04) (0.50) (0.24) (0.25) (0.60) (0.46) (1.05) (0.19) (0.04) (0.27) Instrument test p-values a b 1st-stage F-test: F 0.0028 0.0004 0.0016 0.0015 0.0043 0.0009 0.0016 0.0010 0.0007 0.0000 0.1017 0.0008 1st-stage F-test: a b F(y y ) 0.0041 0.0002 0.0016 0.0060 0.0231 0.0014 0.0034 0.0020 0.0001 0.0000 0.6995 0.0002 1st-stage F-test: a b L(y y ) 0.0036 0.0010 0.0015 0.0071 0.0080 0.0009 0.0082 0.0098 0.0001 0.0000 0.2271 0.0002 Sargan test 0.6577 0.7170 0.7723 0.3069 0.8770 0.8161 0.6674 0.7221 0.8497 0.3660 — 0.8655 C-test for L(y y ) 0.7069 0.6951 0.8032 0.1914 0.8888 0.8066 0.5488 0.7543 0.9538 0.3660 — 0.8641 C-test for (y y ) 0.6185 0.6806 0.7897 0.6539 0.8316 0.6860 0.6547 0.8011 0.6075 0.6849 — 0.7269 Sample size 67 67 67 66 67 70 70 69 67 40 41 71 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is average Private Credit 1960–1995, y y is 1 1 the log of per-capita GDP in 1960 relative to the United States, bureau is an index of bureaucratic efﬁciency, corrupt is a measure of corruption, rulelaw is an index of the country’s tradition of law and order, pr. rights is an index of strength of property rights, exprisk is an index of expropriation risk, civil is an index of civil liberties, kkz is a measure of the quality of governance, infra is a measure of social infrastructure, statehist is a measure of the antiquity of a state, socap is an index of social capability, and setmortal is the log of settler mortality. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L( y y ) as instruments for F and F( y y ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, respectively. a. No Scandinavian legal origins in this sample. b. No Scandinavian or German legal origins in this sample. c. See footnote 34 in the text. FINANCIAL DEVELOPMENT AND CONVERGENCE 209 main theoretical results; the coefﬁcient on F was never signiﬁ- cantly different from zero, and the interaction coefﬁcient in all fy cases was negative and statistically signiﬁcant except when the alternative variable was settler mortality. To the same end, and also to take into account the possibility that some of the alternative regressors X are endogenous to the growth regression, we followed the suggestion of an anonymous referee to reestimate Table V instrumenting for the X’s and the interacted X ( y y ) variables instead of for private credit and private credit interacted. If the interaction coefﬁcient were to fy lose its signiﬁcance and the coefﬁcient of some X ( y y ) were to show up as signiﬁcant in this “switched” IV regression, this would suggest that the effects we have been attributing to the interaction between ﬁnance and the initial GDP gap were really attributable to the effect of our legal origins instruments working through some channel other than ﬁnance. The results shown in Table VI indicate that our earlier ﬁnd- ings pass this test. In only one case (state history) is the coefﬁ- cient of the interaction variable X ( y y ) signiﬁcant at the 10 percent level in the switched IV regression, and in that case the critical interaction coefﬁcient retained its signiﬁcance at the 1 fy percent level. Although in several other cases lost its statis- fy tical signiﬁcance, this only happened when our legal origins in- struments turned out to have little explanatory power in the ﬁrst-stage regressions for X ( y y ), being jointly insigniﬁcant at the 10 percent level; since weak instruments are known to produce unreliable and imprecise IV estimates we do not inter- pret this loss of signiﬁcance as casting doubt on our theoretical predictions. However, it does perhaps provide a clue for under- standing our otherwise surprisingly robust results. More speciﬁcally, most of the loss in signiﬁcance of in fy Table VI occurs when X represents an institutional variable. This is probably because the interacted forms of these variables, and especially their ﬁtted values from the ﬁrst-stage regression, are highly correlated with the interacted private credit variable (see columns 2 and 3, Table VII), which makes it hard econometri- cally to identify their effects on growth separately from those of 35. See, for example, Davidson and MacKinnon [2004, p. 329]. 36. Speciﬁcally, our main predictions (insigniﬁcant and signiﬁcantly nega- tive ) were conﬁrmed in the case of 18 of the 22 noninstitutional variables but fy only in 3 of the 11 institutional variables. 210 QUARTERLY JOURNAL OF ECONOMICS TABLE VI TEST FOR OTHER INTERACTIONS—SWITCHED IV REGRESSIONS Estimation of equation: g g ( y y ) F F( y y ) X X( y y ) 1 0 y 1 f fy 1 x xy 1 Category Schooling Geography Other variable (X) y y school sec hy gschool ghy afr eq.dist. pop100cr tropop Coefﬁcient estimates 0.025 0.064 0.026 0.004 0.033 0.005 0.004 0.005 0.009 0.023 (1.22) (1.24) (0.62) (0.31) (1.52) (0.50) (0.19) (0.36) (0.48) (0.91) 0.059*** 0.113* 0.060 0.038*** 0.069*** 0.035*** 0.040** 0.030* 0.045** 0.035** fy (3.65) (1.82) (1.19) (3.14) (3.67) (3.90) (2.34) (1.96) (2.03) (2.43) 3.325 0.123 0.452 0.939 0.520 0.251 2.532 0.257 1.373 4.073 (1.15) (0.29) (0.37) (0.35) (0.46) (0.21) (0.37) (0.07) (0.25) (0.79) 0.542 0.941 0.798 2.865 0.212 0.785 1.483 4.330 0.602 0.175 xy (0.70) (1.07) (0.33) (1.02) (0.41) (1.21) (0.63) (1.06) (0.21) (0.08) Instrument test p-values 1st-stage F-test: X 0.0000 0.0011 0.3534 0.0000 0.4245 0.0154 0.9886 0.0068 0.9529 0.6872 1st-stage F-test: X(y y ) 0.0000 0.9012 0.9910 0.0975 0.6667 0.0262 0.9659 0.4229 0.9701 0.3553 1st-stage F-test: L(y y ) 0.0000 0.0006 0.7720 0.0000 0.0234 0.0050 0.5736 0.5607 0.8867 0.2045 Sargan test 0.2456 0.9450 0.3894 0.1628 0.8966 0.8465 0.1186 0.6450 0.0926 0.9813 C-test for L(y y ) 0.1500 0.8692 0.3056 0.1030 0.8187 0.7308 0.3148 0.9382 0.0679 0.9396 C-test for (y y ) 0.7819 0.4441 0.5001 0.8770 0.8214 0.4640 0.8929 0.4460 0.9360 Sample size 71 71 69 70 71 70 71 70 67 67 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is average Private Credit 1960–1995, y y is 1 1 the log of per-capita GDP in 1960 relative to the United States, school is average years of schooling in 1960, sec is average years of secondary education 1960–1995, hy is the Klenow-Rodriguez-Clare ratio of human capital to output, gschool is average growth rate of years of schooling 1960–1995, ghy is the average growth rate of the human capital ratio 1960–1985, afr is an African dummy, eq. dist. is distance from the equator, pop100cr is measure of access to ocean-navigable waterways, and tropop is the fraction of population living in the tropics. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L( y y ) as instruments for X and X( y y ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, respectively. a. When the other variable X is ( y y ), the estimated equation is g g F F( y y ) ( y y ) ( y y ) . 1 1 0 f fy 1 x 1 xy 1 FINANCIAL DEVELOPMENT AND CONVERGENCE 211 TABLE VI TEST FOR OTHER INTERACTIONS—SWITCHED IV REGRESSIONS (CONTINUED) Estimation of equation: g g ( y y ) F F( y y ) X X( y y ) 1 0 y 1 f fy 1 x xy 1 Category Health Policy Sociopolitical stability Other variable (X) avgmort avgexpect me trade bus. reg. gov bmp pi soe avelf revc assass Coefﬁcient estimates 0.050 0.020 0.017 0.007 0.019 0.010 0.034 0.007 0.017 0.020 0.020 0.020 (0.68) (0.55) (0.55) (0.60) (0.87) (0.78) (0.88) (0.33) (0.73) (1.15) (1.09) (1.33) 0.114 0.070 0.06 0.046*** 0.061* 0.042*** 0.072*** 0.040*** 0.053*** 0.056*** 0.048*** 0.050*** fy (1.04) (1.81) (1.60) (5.49) (1.96) (3.50) (3.34) (2.95) (3.10) (3.51) (3.94) (5.02) 0.017 0.260 0.865 0.030 0.259 0.074 0.068 0.036 0.042 2.698 3.643 2.696 (0.500) (0.51) (0.85) (0.56) (0.17) (0.43) (0.59) (0.39) (0.06) (0.43) (0.41) (0.51) 0.016 0.004 0.246 0.010 0.693 0.159 0.042 0.035 0.308 1.894 0.477 3.326 xy (0.56) (0.02) (0.96) (0.34) (0.48) (0.93) (0.80) (0.64) (0.70) (0.55) (0.08) (0.76) Instrument test p-values 1st-stage F-test: X 0.8767 0.9228 0.9818 0.2564 0.4947 0.0088 0.3855 0.4555 0.4498 0.3267 0.5113 0.2514 1st-stage F-test: X(y y ) 0.9699 0.6186 0.8794 0.2004 0.9306 0.4145 0.3205 0.4696 0.5912 0.5190 0.6848 0.6244 1st-stage F-test: L(y y ) 0.4225 0.7282 0.1008 0.6826 0.2659 0.0066 0.8513 0.6072 0.6977 0.9894 0.9154 0.8191 Sargan test 0.9972 0.8964 0.8837 0.2192 0.4000 0.5373 0.9980 0.2269 0.7874 0.2857 0.2832 0.7290 C-test for L(y y ) 0.9852 0.8341 0.8447 0.2187 0.3601 0.5134 0.9981 0.1522 0.7729 0.3671 0.3485 0.6081 C-test for (y y ) 0.8887 0.7972 0.6222 0.4499 0.6383 0.6521 0.8826 0.5472 0.6234 0.5004 0.6357 0.8105 Sample size 64 64 67 66 66 64 67 71 66 71 71 71 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is average Private Credit 1960–1995, y y is 1 1 the log of per-capita GDP in 1960 relative to the United States, avgmort is average child mortality 1970–1990, avgexpect is average life expectancy at birth 1960–1990, me is malaria ecology, trade is openness to trade, bus. reg. is an (inverse) index of the regulatory problems involved in opening a business, gov is government size, bmp is the black market premium, pi is the average inﬂation rate 1960–1995, soe is an index of state-owned enterprises, avelf is an index of ethnolinguistic fractionalization, revc is an indicator of revolutions and coups, and assass is a measure of political assassinations. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L( y y ) as instruments for X and X( y y ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, 1 1 respectively. 212 QUARTERLY JOURNAL OF ECONOMICS TABLE VI TEST FOR OTHER INTERACTIONS—SWITCHED IV REGRESSIONS (CONTINUED) Estimation of equation: g g ( y y ) F F( y y ) X X( y y ) 1 0 y 1 f fy 1 x xy 1 Category Institutions Other variable (X) bureau corrupt rulelaw pr.rights exprisk civil kkz infra statehist socap setmortal Coefﬁcient estimates 0.011 0.028 0.014 0.007 0.006 0.010 0.013 0.008 0.010 0.077 0.003 (0.58) (1.25) (0.71) (0.29) (0.27) (0.64) (0.31) (0.22) (0.82) (0.96) (0.10) 0.028 0.068** 0.026 0.003 0.004 0.042*** 0.034 0.006 0.034*** 0.068 0.004 fy (1.40) (2.17) (0.95) (0.07) (0.13) (3.37) (0.43) (0.12) (4.04) (1.19) (0.14) 0.185 0.489 0.703 0.154 0.657 0.272 1.113 4.267 1.008 9.324 0.636 (0.28) (0.80) (1.03) (0.11) (0.91) (0.42) (0.93) (0.78) (0.48) (1.30) (0.41) 0.433 0.479 0.408 1.275 0.511 0.039 0.170 3.394 2.788* 2.862 0.569 xy (0.88) (0.72) (0.63) (0.98) (0.97) (0.13) (0.07) (0.63) (1.74) (1.12) (1.11) Instrument test p-values a b 1st-stage F-test: X 0.0464 0.1069 0.3626 0.2421 0.3503 0.0526 0.3877 0.8066 0.0057 0.2398 0.3003 a b 1st-stage F-test: X(y y ) 0.1863 0.8286 0.8301 0.7969 0.7018 0.0228 0.9985 0.9794 0.0659 0.1998 0.1124 a b 1st-stage F-test: L(y y ) 0.0913 0.3981 0.2105 0.0217 0.2981 0.0358 0.5840 0.6971 0.0010 0.1755 0.0006 Sargan test 0.7333 0.3533 0.5419 0.9734 0.8857 0.2924 0.1703 0.3948 0.1380 0.5528 — C-test for L(y y ) 0.7410 0.2995 0.6666 0.9189 0.8931 0.2515 0.1687 0.5869 0.1380 0.5528 — C-test for (y y ) 0.8211 0.4787 0.9251 0.9487 0.8791 0.5191 0.4656 0.9679 0.1955 0.4021 — Sample size 67 67 67 66 67 70 70 69 67 40 41 The dependent variable g g is the average growth rate of per-capita real GDP relative to the United States, 1960–1995. F is average Private Credit 1960–1995, y y is 1 1 the log of per-capita GDP in 1960 relative to the United States, bureau is an index of bureaucratic efﬁciency, corrupt is a measure of corruption, rulelaw is an index of the country’s tradition of law and order, pr. rights is an index of strength of property rights, exprisk is an index of expropriation risk, civil is an index of civil liberties, kkz is a measure of the quality of governance, infra is a measure of social infrastructure, statehist is a measure of the antiquity of a state, socap is an index of social capability, and setmortal is the log of settler mortality. Appendix 2 gives a detailed description of all variables and indicates sources. Estimation is by IV using L (legal origins) and L( y y ) as instruments for X and X( y y ). The numbers in parentheses are t-statistics. Signiﬁcance at the 1 percent, 5 percent, and 10 percent level is denoted by ***, **, and *, respectively. a. No Scandinavian legal origins in this sample. b. No Scandinavian or German legal origins in this sample. FINANCIAL DEVELOPMENT AND CONVERGENCE 213 TABLE VII PRIVATE CREDIT AND OTHER INSTITUTIONAL VARIABLES Correlation P-value of F-test between for joint Correlation ﬁtted X(y signiﬁcance of between y ) and X(y y ) and 1 1 Correlation X(y y ) F(y y ) F(y y )in 1 1 1 between X and F(y in switched switched Variable and F y ) regression regression 12 3 4 bureau 0.7325 0.6752 0.7872 0.0000 corrupt 0.7053 0.6663 0.8303 0.0000 rulelaw 0.7138 0.6656 0.7996 0.0000 pr.rights 0.6273 0.5786 0.6491 0.0434 exprisk 0.7552 0.6032 0.6140 0.0272 civil 0.5701 0.1233 0.1819 0.0000 kkz 0.7251 0.3185 0.4051 0.0014 infra 0.7318 0.7130 0.9025 0.0165 statehist 0.4924 0.4716 0.6091 0.0000 socap 0.4399 0.3055 0.1831 0.3581 setmortal 0.6375 0.2052 0.0782 0.3111 the interacted private credit variable. This interpretation is supported by the fact that in all but two cases with a relatively small sample size we can reject the hypothesis that both inter- acted variables have a zero effect at the 5 percent signiﬁcance level using the switched regression results (see column 4, Table VII). But it leaves open the possibility that what really matters for convergence is some unspeciﬁed combination of ﬁnancial de- velopment and other institutions, and that the effects of other institutions have not shown up in the above results because of our inability to ﬁnd appropriate instruments to correct for their endogeneity. Overall, we interpret the results of this section as further evidence to the effect that lack of ﬁnancial development accounts 37. This is not independent of the weak instrument problem. When the legal origins instruments have little explanatory power, the ﬁtted value of X ( y y ) is just a noisy linear combination of the other “exogenous” regressors in the growth equation, including F ( y y ). 38. For example, perhaps what matters most for convergence is well- functioning markets, for which many institutional variables are a good indicator but none better than ﬁnancial development. We have tried exploring the issue further by instrumenting in the same equation for X, X ( y y ), F and F ( y y ) but our inability to ﬁnd strong instruments for X and X ( y y ) has 1 1 prevented us from shedding any further light on the question. 214 QUARTERLY JOURNAL OF ECONOMICS for the failure of some countries to converge to the growth rate of the global technology frontier, a further corroboration of our theory, and a further indication of the validity of our legal-origins instruments for ﬁnancial development. But we cannot rule out the possibility that at least some of the failure to converge is also attributable to institutional factors other than ﬁnance, or to some other variable that is also endogenous to the growth process. V. CONCLUSION The paper has developed and tested a Schumpeterian model of cross-country convergence with ﬁnancial constraints. The model is consistent with the broad facts of convergence and di- vergence since the early nineteenth century. It implies that all countries above some critical level of ﬁnancial development should converge in growth rate, and that in such countries ﬁnan- cial development has a positive but eventually vanishing effect on steady-state GDP. These implications were tested by estimating a cross-country growth regression with an interaction term be- tween ﬁnancial development and the country’s initial relative output. As predicted, the coefﬁcient of this interaction term is negative and highly signiﬁcant, and the direct effect of ﬁnancial development is not signiﬁcantly different from zero. Why some countries fail to converge in growth rates despite the possibility of technology transfer has been a puzzle. In com- bination with the contributions of Howitt [2000], Acemoglu, Aghion, and Zilibotti [2002], and Howitt and Mayer-Foulkes [2002] our theoretical results show that Schumpeterian growth theory provides a framework for analyzing a variety of forces that contribute to nonconvergence. Our empirical results suggest that ﬁnancial development is among the most powerful of these forces, especially considering that educational attainment, initial relative output, and a large number of other candidate variables do not have an analogous effect when included in the same regression with ﬁnancial development. 39. See Galor and Weil [2000], Gollin, Parente, and Rogerson [2002], and Hansen and Prescott [2002] for alternative theories of convergence and divergence based on the transition from agricultural to industrial technologies. 40. Our results also suggest that a country might escape divergence by using foreign direct investment as a substitute for lending to local entrepreneurs. However, the results of Alfaro et al. [2003] indicate that foreign direct investment and local ﬁnance are complements. Speciﬁcally, they ﬁnd that foreign direct investment has a signiﬁcant effect on growth only when interacted with ﬁnance. FINANCIAL DEVELOPMENT AND CONVERGENCE 215 APPENDIX 1: ENDOGENIZING THE CREDIT MULTIPLIER This Appendix closely follows Aghion, Banerjee, and Piketty [1999] in deriving a constant credit multiplier from ex post en- forcement considerations. More precisely, suppose that at a non- monetary cost cN an entrepreneur can hide the result of a successful innovation and thereby avoid repaying her creditors, where 0 c 1. This cost is an indicator of the degree of creditor protection. In countries where laws and institutions make fraud a costly option, creditors are better protected, and therefore, as we shall see, credit is more readily available to entrepreneurs. The entrepreneur must pay the hiding cost at the beginning of the period, when she decides whether or not to be dishonest. She will do so when it is in her self-interest, namely when the following incentive-compatibility constraint is violated: (19) A cN A R N w , t1 t t1 t t where R is the interest factor on the loan, N w is the size of t t the loan, and ˜ N /A t t1 is the innovation probability. The left-hand side of (19) is the expected payoff from deciding to be dishonest when investing at the rate N , whereas the right-hand side is the expected payoff from deciding to be honest. (If she does not successfully innovate, her payoff is zero, because having invested all her wealth in the unsuccessful project she cannot be made to repay anything.) The only potential lenders in this OLG model are other young people, who will lend only if offered an expected rate of return equal to r 1. Thus, the interest factor on the loan in equilibrium must satisfy not only the incentive-compatibility con- dition (19) but also the arbitrage condition R 1 r, so that the incentive-compatibility condition boils down to an upper limit on the entrepreneur’s investment: This is consistent with the view that foreign direct investment results in technol- ogy transfer only when complemented by the local entrepreneurial investments at the heart of our theory, which investments are impeded by lack of ﬁnancial development. 216 QUARTERLY JOURNAL OF ECONOMICS 1 r N w w , t t t 1 r c where 1 . APPENDIX 2: SOURCES AND DESCRIPTION OF DATA setmortal: Log of European settler mortality, Acemoglu, John- son, and Robinson [2001]. statehist: Measure of the antiquity of a state (1 to 1950 CE) regarding the existence of native foreign government and the extent of the territory ruled by this government. The measure used corresponds to statehist5 of the database in Bockstette, Chanda, and Putterman [2002]. avgexpect: Average life expectancy at birth for the years 1960– 1990, Children Data Bank for International. socap: Measure of social capability derived by Adelman and Morris [1967] using assessment of each country’s development as of 1957–1962 in a variety of respects such as extent of urbaniza- tion, extent of dualism, extent of social mobility, extent of liter- acy, crude fertility rate, degree of modernization of outlook, char- acter of basic social organization, extent of mass communication, size of traditional agricultural sector and importance of indige- nous middle class, Temple and Johnson [1998]. infra: Measure of social infrastructure (1986–1995) computed as the average of the GADP and an openness measures. GADP is an index of government antidiversion policies including law and order, bureaucratic quality, corruption, risk of expropriation, and government repudiation of contracts, Hall and Jones [1999]. avgmort: Average under-5 mortality rate for the years 1970– 1990, Children Data Bank for International. pop100cr: Percentage of population within 100 km of ice- free coast, CID at Harvard University. General Measures of Geography. tropop: Percentage of population in geographical tropics, CID at Harvard University. General Measures of Geography. kkz: Composite index of six dimensions of governance: voice and accountability, political stability and absence of violence, govern- ment effectiveness, regulatory quality, rule of law, control of corruption, Kaufmann, Kraay, and Zoido-Lobato´n [1999a, 1999b]. FINANCIAL DEVELOPMENT AND CONVERGENCE 217 me: Malaria Ecology. An ecologically based variable that is pre- dictive of the extent of malaria transmission [Kiszewski et al. 2004]. Malaria is intrinsically a disease of warm environments because a key part of the life-cycle of the parasite (sporogony) depends on a high ambient temperature. Malaria also depends on adequate conditions of mosquito breeding, mainly pools of clean water, usually due to rainfall ending up in puddles, cisterns, discarded tires, and the like. Additionally, the intensity of ma- laria transmission depends on the speciﬁc mosquito species that are present. The basic formula for Malaria Ecology combines temperature, mosquito abundance, and mosquito vector type. The underlying index is measured on a highly disaggregated subna- tional level, and then averaged for the entire country and weighted by population, The Earth Institute at Columbia University. bureau: An index of the efﬁciency of the bureaucracy, ranging from 1 (least efﬁcient) to 6 (most efﬁcient). The data are averaged over the period 1992–1997. International Country Risk Guide (ICRG) at http://www.countrydata/datasets/. exprisk: Expropriation risk. Assessment of risk of “outright con- ﬁscation” or “forced nationalization.” It ranges from 0 to 10, with lower scores indicating a higher risk. The data are averaged over the period 1992–1997. ICRG. lat_abst: Distance from the equator scaled between 0 and 1, La Porta, Lopez-de-Silanes, Shleifer, and Vishny [1998]—henceforth LLSV. pr. rights: Property rights. Rating of property rights on a scale from 0 to 5. The more protection private property receives, the higher the score, LLSV. soe: Index of state-owned enterprises (SOE). Measures the role of SOEs in the economy, ranging from 0 to 10. Higher scores denote countries with fewer government-owned enterprises, which are estimated to produce less of the country’s output, LLSV. corruption: Measure of corruption, with the scale ranging from 1 (high level of corruption) to 6 (low level). The data are averaged over the period 1992–1997. ICRG. assass: Number of assassinations per 1000 inhabitants, averaged over 1960–1990, Banks [1994]. revc: Revolutions and coups. A revolution is deﬁned as any illegal or forced change in the top of the governmental elite, any attempt at such a change, or any successful or unsuccessful armed rebel- lion whose aim is independence from central government. Coup 218 QUARTERLY JOURNAL OF ECONOMICS d’Etat is deﬁned as an extraconstitutional or forced change in the top of the governmental elite or its effective control of the nation’s power structure in a given year or both. Unsuccessful coups are not counted. Data are averaged over 1960–1990, Banks [1994]. avelf: Ethnic fractionalization. Average value of ﬁve indices of ethnolinguistic fractionalization, with values ranging from 0 to 1, where higher values denote higher levels of fractionalization, Easterly and Levine [1998]. rulelaw: Measure of the law and order tradition in a country. It ranges from 10, strong law and order tradition, to 1, weak law and order tradition. The data are averaged over the period 1992– 1997. ICRG. bus. reg: Business regulation. Rating of regulation policies re- lated to opening and keeping open a business. The scale is from 0 to 5, with higher scores meaning that regulations are straight- forward and applied uniformly to all businesses and that regula- tions are less of a burden to business, LLSV. civil: Index of civil liberties, Freedom House 1994. legal origins: Dummy variables for British (Eng), French (Fre), German (Ger) and Scandinavian legal origins, LLSV. private credit: {(0.5)*[F(t)/Pe(t) F(t 1)/Pe(t 1)]}/ [GDP(t)/Pa(t)], where F is credit by deposit money bank and other ﬁnancial institutions to the private sectors (lines 22d 42d), GDP is line 99b, Pe is end- of period CPI (line 64) and Pa is the average CPI for the year, IFS. bank assets: {(0.5)*[F(t)/Pe(t) F(t 1)/Pe(t 1)]}/[GDP(t)/ Pa(t)], where F is domestic assets of deposit money banks (lines 22a–d), GDP is line 99b, Pe is end-of-period CPI (line 64), and Pa is the average CPI for the year, IFS. liquid liabilities: {(0.5)*[F(t)/Pe(t) F(t 1)/Pe(t 1)]}/ [GDP(t)/Pa(t)], where F is liquid liabilities (line 55), GDP is line 99b, Pe is end-of-period CPI (line 64), and Pa is the average CPI for the year, IFS. commercial-central bank: DBA(t)/(DBA(t) CBA(t)), where DBA is assets of deposit money banks (lines 22a–d) and CBA is central bank assets (lines 12a–d), IFS. bmp: Black market premium: Ratio of black market exchange rate and ofﬁcial exchange rate minus one, Picks’ Currency Year- book through 1989 and the World Currency Yearbook. sec: Average years of secondary schooling in the population over ﬁfteen from 1960–1995, Barro and Lee [1996]. FINANCIAL DEVELOPMENT AND CONVERGENCE 219 school: Average years of schooling in the population over 25 in 1960, Barro and Lee [1996]. pi: Inﬂation rate. Log difference of consumer price index average from 1960–1995, IFS (line 64). trade: Openness to trade. Sum of real exports and imports as a share of real GDP, average 1960–1995, Levine, Loayza, and Beck [2000], henceforth LLB. gov: Government expenditure as a share of GDP, average 1960– 1995, LLB. africa: Dummy for countries in the African continent. y y : Difference between log per-capita real GDP 1960 in each country and the United States, LLB. gschool: Average annual growth rate of schooling from 1960 to 1995, LLB. hy: 1985 human-capital to output ratio, Klenow and Rodrı´guez- Clare [1997]. ghy: 1960–1985 annual growth rate of human capital to output ratio, Klenow and Rodrı´guez-Clare [1997]. lna lna : The log of productivity in 1960 relative to the United States, Benhabib and Spiegel [2005]. 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