The Increasing Marginal Returns of Better Institutions Felix Várdy Haas School of Business, UC Berkeley, and International Monetary Fund First draft: June, 2009 Abstract We study the interaction between the quality of a country’s institutions and the complexity of its economy. We show how bad institutions may condemn a country to the production of simple goods and services, produced by poorly skilled workers in vertically integrated …rms and product chains. In such an organizationally simple economy, the marginal bene…t of better institutions is lower than in more complex economies with good institutions. If institutional change is incremental and incentive-driven, as argued by the new institutional economics literature, then economic development becomes highly path-dependent, leading to poverty traps, threshold e¤ects, and divergence. Email: [email protected]. I would like to thank, without implicating, Laura Chioda, Burkhard Drees, John Nash, Roberto Rigobon, Emily Sinnott and, especially, Augusto de la Torre for their comments and suggestions. 1 1 Introduction How does the quality of a country’s institutions a¤ect its economic structure? And, conversely, how does a country’s economic structure a¤ect the development of its institutions? Building on insights from the new institutional economics literature, in this paper, we develop the idea that the quality of a country’s institutions and the organizational complexity of its economy are mutually reinforcing. On the one hand, this implies that countries with bad institutions may be condemned to the production of relatively simple goods and services by low-skilled workers in vertically integrated …rms and product chains. On the other hand, the complementarity between institutions and economic complexity also has implications for the dynamics of institutional change. If institutional change is overwhelmingly incremental and driven by incentives, as argued by, e.g., North (1990, 1991, 1994), then institutions are more likely to improve in economies where entrepreneurs and workers stand to gain a lot from marginal improvements in institutional quality than in economies where these gains are small. In the latter case, institutions are more likely to stagnate or even deteriorate over time.1 This raises the question whether the marginal bene…t of better institutions is higher in countries that already have good institutions, or in countries that still have to develop them. Clearly, the answer depends on whether institutional development exhibits increasing or decreasing returns. Under a standard decreasing-returns framework, the lower is a country’s “institutional capital,”the higher is the marginal bene…t of improvements, and vice versa. In that case, one would expect convergence of institutional quality and economic development across countries with di¤erent initial conditions. With increasing returns, by contrast, scarcity of institutional capital makes marginal institutional change not more but less valuable, and one would expect divergence: further improvements in advanced countries and stagnation and deterioration in the developing world. In our model, the complementarity between the quality of institutions and the organizational complexity of the economy makes returns increasing and, hence, divergence the more likely scenario. The intuition for our results is quite straightforward and, ultimately, based on Coase’s (1937) theory of the …rm. (See, also, Williamson, 1975, 1981, 1985.) When a …rm has to decide whether to produce an intermediate 1 In the words of North (1994): “The process of change is overwhelmingly incremental. The reason is that the economies of scope, the complementarities, and the network externalities that arise from a given institutional matrix of formal rules, informal constraints, and enforcement characteristics will typically bias costs and bene…ts in favor of choices consistent with the existing framework.” He goes on to say that: “Deliberate institutional change will come about (...) as a result of the demands of entrepreneurs in the context of the perceived costs of altering the institutional framework at various margins. The entrepreneur will assess the gains to be derived from recontracting within the existing institutional framework compared to the gains from devoting resources to altering that framework.” 2 good or service in-house or buy it from another …rm, it faces a trade-o¤ between the advantages of specialization and the costs of transacting in the market. Specialization favors buying from another …rm, while transaction costs favor in-house production. Bad (formal or informal) institutions raise transaction costs and, hence, make inhouse production relatively more attractive. As a result, the economic structure of a country with bad institutions is more likely to be characterized by vertically integrated product chains and …rms that transact little with each other. The paucity of inter-…rm transactions makes that, marginally, such an economy bene…ts relatively little from better institutions. In a country with good institutions, by contrast, …rms optimally choose to be highly specialized and transact a lot with other …rms. A further improvement of the country’s institutions positively a¤ects all of these many transactions. Hence, it is the country that already has good institutions— and, as a result, is organizationally complex— that bene…ts more from a marginal improvement of its institutions than the country with bad institutions. Finally, if institutional change is “demand-driven”and incremental, it is good institutions that are likely to get better and bad institutions that are likely get worse (up to a point). This analysis suggests that countries stuck in a trap of bad institutions and underdevelopment may not be able to rely on incremental change to lift themselves out of poverty. Instead, a more radical break with the past may be necessary to create the conditions for self-sustaining economic development. Obviously, our paper is closely related to the literature on poverty traps, which identi…es mechanisms that make poverty self-sustaining. (See Azariadis and Stachurski , 2005, for an overview.) Primary among those are various forms of market failures. These market failures originate in phenomena such as increasing returns technologies, coordination problems, asymmetric information, credit constraints, externalities, et cetera. Moreover, the di¤erent mechanisms can interact and reinforce each other. The poverty trap in this paper is of an institutional kind. The issue is that, unless the net gains from better institutions are su¢ ciently large, winners may not be able to adequately compensate the losers. And because the people in power are likely to be among the losers, the reforms will be blocked. In addition to the papers already mentioned, technically, this paper is closely related to Kremer’s (1993) “O-ring”theory of development. We build on the “O-ring” model by introducing a trade-o¤ between the bene…t of specialization and the cost of transacting. This introduces a natural measure of “organizational” complexity into the model, in addition to the already present measure of “technical” complexity. We show that higher levels of both organizational and technical complexity arise in response to an improvement in institutions. On the other hand, only organizational complexity, but not technical complexity, raises the marginal bene…t of better institutions. The remainder of the paper is organized as follows. The model is presented in Section 2 and analyzed in Section 3. Section 4 contains a discussion of the main 3 results, while Section 5 concludes. Finally, the Appendix studies some alternative replicator dynamics for institutional change. 2 Model The model consists of two parts. The …rst part describes how the structure of the economy— i.e., the organizational complexity of product chains, the technical complexity of products, and the skill levels and wages of workers— depends on the quality of institutions. The second part describes how economic structure a¤ects institutional change. The variables in the …rst part of the model are determined directly, and in a straightforward manner, by the individual choices of entrepreneurs and workers in the economy. Hence, we use a standard neoclassical optimization framework to describe them. Institutional change, on the other hand, is the result of a myriad of collective decisions, interacting in extremely complicated ways. Obviously, this is hard to model in detail, while maintaining necessary parsimony. To circumvent this problem, we take a rather “minimalist”approach and limit attention to the following question: If institutional change is incremental and incentive-driven, how conducive are di¤erent economic structures to institutional improvement? To answer this question, we determine the marginal bene…t of an improvement in institutional quality and feed this into a simple replicator dynamic. The replicator only assesses whether, on balance, the collective bene…ts of— and, by extension, pressure for— institutional change is large or small. If these bene…ts are su¢ ciently large, institutions improve over time; otherwise, they stagnate or deteriorate. 2.1 From Institutions to Economic Structure We extend Kremer’s (1993) “O-ring” model of economic development to study the e¤ect of institutions on economic structure. The interested reader may want to consult the original paper for details. Let n 2 N denote the number of steps or tasks needed to produce some good or service, p. We interpret n as a measure of technical complexity. Each step 1; :::; n in the production process is executed by a worker of skill qi , i 2 f1; :::; ng, where qi is the probability that worker i does his job properly. If a worker screws up, the product is assumed to become worthless and the production e¤ort is wasted. If all steps are done in-house, i.e., within one vertically integrated …rm making up the whole product chain, then the expected value, y, of the …nished product is y= n a i=1 qi n B (n) Here, the parameter is an element of (0; 1] and B (n) is some factor valuing com~ (n) = na B (n) plexity. To ensure that our problem is well-behaved, we assume that B 00 ~ (n) < 0. To ensure that complexity is indeed valuable, we is concave in n, i.e., B ~ ^ (n) = B(n) is strictly increasing in n. also assume that B n 4 Specialized …rms focusing on fewer tasks are assumed to deliver a better product than vertically integrated …rms executing many di¤erent ones. Abstracting for the moment from transaction costs, we model this as follows. If p is produced through the collaboration of …rms 1; :::; m, m 1,2 where …rm 1 takes on the …rst n1 production steps, …rm 2 the next n2 steps, et cetera, such that n1 + ::: + nm = n, then the value y of the …nal product is y = > n i=1 qi ((n1 ) + n i=1 qi n B (n) ::: + (nm ) ) B (n) We interpret m, the number of …rms collaborating to produce p, as a measure of the organizational complexity of the economy. We interpret as a measure of the value of specialization: The closer is to 1, the smaller is the value of specialization. An entrepreneur managing the product chain optimally chooses m and n. Production chains do not consist of m = 1 …rms, each specialized in an in…nitesimal task, because transacting between …rms is costly. This cost is a¤ected by the quality of a country’s institutions.3 With good institutions, transaction costs are relatively low. If institutions are ine¤ective, transacting with other …rms is risky and expensive. On the basis of this observation, we take transaction costs to be a measure of institutional quality and use the two interchangeably. For analytical convenience, we assume that transaction costs are fractional in nature. This corresponds to a situation where, each time an intermediate product is shipped from one …rm to another, a fraction 1 g “melts.” (In international trade, these are known as “ice berg” costs.) Alternatively, there is a probability 1 g; g 2 (0; 1), that the good is expropriated, lost, stolen, or destroyed. Note that high g corresponds to good institutions, i.e., low transaction costs, and vice versa. The (expected) value of a …nal product of complexity n produced collaboratively by m …rms is4 y = ni=1 qi g m ((n1 ) + ::: + (nm ) ) B (n) Total production in the economy is f y, where f denotes the number of production chains. With a labor force of size L; we have f= L n As in Kremer (1993), …rms are wage-takers facing a wage schedule w (q). That is, w (q) is the cost of hiring a worker of skill q. Workers also take w (q) as given. They 2 Note that we allow m to be larger than n. That is, …rms can collaborate on a single task. For example, North (1990, p.66) writes: “the cost of transacting re‡ects the overall complex of institutions— formal and informal— that make up an economy or, on an even greater scale, a society.” 4 We write g m instead of g m 1 to assure that even completely integrated product chains (i.e., m = 1) are at least somewhat a¤ected by the quality of institutions, g: Even a fully integrated chain has to transact with …nal consumers. 3 5 acquire skill level q at a cost C (q), where C is some (su¢ ciently) convex function of q. 2.2 From Economic Structure to Institutions Following the new institutional economics literature, we assume that institutional change is incremental and incentive-driven. (See, e.g., North, 1990.) We take incrementality to mean that g is a continuous function of time. We take “incentive-driven” to mean that the drift of g is a (strictly) increasing function, h, of the bene…t of marginal improvements in g. Here, “bene…t”is interpreted as the percentage increase in the total production, f y, in the economy. The replicator dynamic for g is then characterized by the di¤erential equation5 dg =h dt d (ln (f y)) dg While total production is always at least somewhat increasing in g, the gains from a marginal increase in g may be large or small depending on the structure of the economy. When the gains are small, society may not be able to overcome or adequately compensate vested interests and solve the potentially sizable collectiveaction problems associated with institutional change. In that case, institutions will < 0 when stagnate or get worse over time. To operationalize this, we assume that dg dt the marginal bene…t of better institutions is at its global minimum. Formally, inf h g d (ln (f y)) dg <0 If, on the other hand, the collective bene…t of a marginal improvement in g is su¢ ciently large, presumably, vested interests and collective-action problems can be overcome one way or another. Hence, we assume that there exists an R > 0 such that for all R0 > R, h (R0 ) > 0. 3 Analysis 3.1 E¤ect of Institutions on Economic Structure Recall that the production function is y= m n i=1 qi g ((n1 ) + ::: + (nm ) ) B (n) n and note that y is maximized only if n1 = n2 = ::: = nm = m . That is, all production n chains with ni 6= m , i 2 f1; :::; mg, are a priori ine¢ cient and will be competed out of 5 In the Appendix, we consider variants of this replicator dynamic. But the conclusions of the model do not change substantially. 6 the market. We may therefore restrict attention to “symmetric” production chains of the form n n m y = B (n) i=1 qi g m m n m 1 ~ (n) = B i=1 qi g m ~ (n) = na B (n) : where B The necessary …rst-order condition for m to be optimal is @y = @m n i=1 qi g m (1 )m + m1 ~ (n) g m ln g B which simpli…es to, m= 1 ln g For this m, we have to check the second-order condition gm m +1 2 + (m ln g + +1 2 ) m ln g < 0 The sign of the left-hand side (LHS) of this expression is determined by the second factor. Substituting for m, we get 2 = + (m ln g + 1 2 ) m ln g 1 1 ln g + 1 2 ln g + ln g ln g 1) 2 = ( < 0 Taking into account that m m = 1, the optimal m is if g e if g > e 1 1 ln g 1 1 Note that m is increasing in g. That is, the better are a country’s institutions, the more specialized are its …rms. Also, and for obvious reasons, m is decreasing in ; i.e., the smaller is the advantage of specialization, the less …rms specialize. Recall that …rms face a wage schedule w (q). Supermodularity of qi and qj , i 6= j, implies sorting. All …rms in the product chain choose workers with the same skill level qi = qj = q; for all i; j 2 f1; :::; ng. (See Kremer, 1993, for a detailed argument.) The …rst-order condition (FOC) for q to be optimal is n dw ~ (n) = nq n 1 g m m1 B dq dw ~ (n) = q n 1 g m m1 B dq 7 Integrating over q gives all wage schedules that satisfy the FOC for all q: Z q ~ (n) dr + c rn 1 g m m1 B w (q) = 0 qn m 1 = g m n ~ (n) + c B A zero-pro…t condition for …rms implies that w (0) = 0 and, hence, c = 0. Therefore, y w (q) = n Next, we determine the pro…t-maximizing technical complexity, n, of product p. The FOC for n to be optimal is q n g m m1 ~ 0 (n) + q n g m m1 B ~ (n) ln q = w (q) B Substituting for w (q) and simplifying, the FOC reduces to ~ B(n) n ln q = 0 ~ B(n) n ^0 B (n) ^ (n) B = The second-order condition (SOC) for n to be a maximum is ~ 00 (n) + B ~ 0 (n) ln q + q n ln (q) B ~ 0 (n) + B ~ (n) ln q < 0 qn B This reduces to ln2 q > ~ 00 (n) B ~ (n) B ~ 00 (n) < 0. which holds because B > 0. Note that Next, we verify that @n @q @ @n ^ 0 (n) B ^ (n) B ! = @n @q > 0 i¤ @ @n ^ 0 (n) B ^ B(n) < 0. Because ^ (n) B ^ 00 (n) B ^ 02 (n) B ^ 2 (n) B ^ 00 (n) < 0. Finally, it can be easily veri…ed a su¢ cient condition for @n > 0 is that B @q ^ 00 (n) < 0 is implied by B ~ 00 (n) < 0. that B 8 Workers choose their skill levels qi , i 2 f1; :::; ng, by optimally trading o¤ cost C (qi ) with reward w (qi ). The FOC for qi to be optimal is C 0 (q) = @w (qi ; q i ) jqi =q @qi @ = y(qi ;q n i =q i) dqi jqi =q i =q @ qi q n 1 g m m1 = ^ (n) B dqi In the unique symmetric equilibrium, C 0 (q) = q n 1 g m m1 y = nq ^ (n) B or qC 0 (q) = w (q) As long as C 0 (q) increases su¢ ciently fast, this equation always has a unique solution in q that satis…es the SOC. The optimal q is increasing in w and, hence, in g. We conclude: Proposition 1 Organizational complexity m, technical complexity n, skill level q; and wages w (q) are all increasing in the quality of institutions g. 3.2 E¤ect of Economic Structure on Institutions Recall that the marginal bene…t , M B, of better institutions is MB = d (ln (f y)) dg Substituting for y and simplifying we get MB = m g if g e 1 where m = 1 if g > e 1 ln g In the following …gure, mg is drawn as a function of g. 1 9 MB 20 10 0 0.0 0.2 0.4 0.6 0.8 1.0 g Marginal bene…t of better institutions Note that marginal bene…ts are U-shaped in g. The marginal bene…ts of better institutions are largest when institutions are either very bad, or when they are very good. In the middle they are substantially lower. The intuition is as follows. Good institutions support a complex economy in which highly specialized …rms transact a lot amongst each other to produce advanced goods and services. A marginal improvement of institutions, re‡ected in a marginal reduction in transaction costs, positively a¤ects all of these many transactions. Hence, the more complex is the economy, the larger is the bene…t of a marginal improvement of institutions. This explains the upward-sloping part of the marginal bene…t curve to the right. When institutions deteriorate, …rms respond by becoming more vertically integrated and less specialized in order to be less a¤ected by the higher transaction costs. At some point, however, m reaches its lowest point, i.e., m = 1, and cannot fall any further. (This happens when g e 1 , which corresponds to g = 0:61 in the …gure.) At this point, the product chain is fully integrated. As long as even a fully integrated product chain is at least somewhat a¤ected by bad institutions— because it has to transact with …nal consumers, for instance— having run out of mitigation options, it will be hit harder and harder by further deteriorations in institutions. This explains the downward sloping part of the marginal bene…t curve to the left. What does the U-shape of the M B curve imply for institutional change? Recall that the replicator dynamic for g is characterized by dg = h dt = h d (ln (f y)) dg m g 10 Because h is a strictly increasing function, dg is also U-shaped. The following dt dg …gure depicts (a generic representation of) dt as a function of g. dg/dt g dg dt as a function of g In this …gure, the y-axis cuts through points at which the forces for and against institutional improvement exactly cancel each other, i.e., dg = 0. Above the y-axis, dt dg dg > 0 and institutions improve, below, dt < 0 and they deteriorate. By assumption, dt the curve lies below the y-axis at its minimum. Moreover, for g # 0 and g " 1, M B goes to in…nity. Hence, there are always two interior equilibria, 0 < glow < ghigh < 1, the …rst of which is stable. looks as follows: The phase diagram for dg dt 0 ¤ glow ¤ ghigh 1 Phase diagram Countries starting out anywhere below ghigh converge to glow . Countries starting out above ghigh keep improving and move towards g = 1. 11 4 Discussion Convergence / Divergence. The decreasing-returns assumptions of standard neoclassical growth models such as Solow (1956), Cass (1965), and Koopmans (1965) imply economic convergence of countries that start out at di¤erent initial conditions. In our model, returns to institutional development are initially decreasing, but become increasing thereafter. As we have seen, this implies that countries fall into two categories depending on their initial conditions of institutional development. Countries starting out below some threshold converge to a stable equilibrium characterized by an economy of low organizational and technical complexity. These countries are caught in a poverty trap. Countries starting out above the threshold, on the other hand, are in a state of continuous, self-perpetuating growth. Their levels of institutional development support an economy that is so complex that the bene…ts of a further reduction in transaction costs is su¢ ciently lucrative to overcome inherent obstacles to further institutional development. This puts these countries in a virtuous cycle of economic and institutional growth that feed on each other. Institutions and the returns to education. Our model suggests that the quality of institutions a¤ects the returns to education: The better are a country’s institutions, the higher is the skill premium. More generally, the model predicts a positive relationship between economic development (in terms of organizational and technical complexity) and the steepness of the wage schedule in terms of skills. While better institutions raise the returns to education, within our model, a better-skilled workforce does not raise the marginal bene…ts of better institutions. The reason is that q only a¤ects technical complexity n, but has no direct e¤ect on organizational complexity m. Size versus specialization. The …nding in Rajan, Zingales and Kumsar (1999) that …rms tend to be larger in countries with better institutions might seem to contradict our model’s prediction that better institutions lead to more specialized …rms. However, a highly specialized …rm focussing on single task in a long product chain and replicating that same task many times may very well be larger than a less specialized …rm executing many di¤erent tasks. Hence, …rm size cannot be taken as a proxy for vertical integration and Rajan, Zingales and Kumsar (1999) does not contradict our model. Enclave industries. Enclave industries are highly vertically-integrated, exportoriented operations that have very little connections with the rest of the economy. They tend to have a bad reputation, associated as they are in people’s minds with the resource curse. (Auty, 1993, Sachs and Warner, 2001.) Famous examples from the past and present are the banana enclaves of the United Fruit Company in Central 12 America and the Caribbean, mining enclaves in Chile and Peru, and oil enclaves in Ecuador, Mexico and Venezuela. (Lindsay-Poland, 2003). Recently, however, the resource curse hypothesis has come under critical scrutiny. (See, e.g., Wright and Czelusta, 2004, Brunnschweiler, 2008, Brunnschweiler and Bulte, 2008, and Lederman and Maloney, 2006, 2008). The critique has focused on the fact that there is often no way of telling whether countries have not grown because they are dependent on commodities, or whether they are dependent on commodities because they have not been able to grow. In other words, commodity dependence and enclave industries may not be the cause but the consequence of underdevelopment. Indeed, our model provides a rationale why, in countries with bad institutions, enclave industries may be— and can continue to be over long periods of time— “the only game in town.” When institutions are bad, only highly vertically integrated product chains can be pro…tably operated. These operations will make an active e¤ort to be self-su¢ cient and transact as little as possible with the rest of the economy. Once they have achieved that goal, the operators of these enclaves bene…t little from broad improvements in the host county’s institutions. Hence, they will not push for them and things will stay pretty much as they were. 5 Conclusion In this paper we have studied how the quality of a country’s institutions— as proxied by the cost of market transactions— a¤ects the structure of the economy. Conversely, we have analyzed how economic structure a¤ects the marginal bene…ts of improving institutions. The main insight derived from the model is that, beyond some threshold, there are increasing returns to institutional development. Hence, it is not countries with bad institutions but those that already have decent institutions that bene…t most from further improvements. Put di¤erently, scarcity of institutional capital makes institutions not more, but less valuable in marginal terms. If institutional change is incremental and determined by incentives, as proposed by the new institutional economics literature, then good institutions will get better and bad institutions will get worse. As a result, “convergence”remains elusive. In a possible extension of the model with two types of goods and two countries, one could compare the marginal bene…t of institutional development under autarky and free trade. Under autarky, the model proceeds roughly along the lines set out above and both countries produce both goods. Under free trade, the country with the worse institutions would specialize in the simpler good, “out-sourcing”the production of the more complex good to the country with the better institutions. Initially, trade liberalization makes both countries better o¤. However, in the country with worse institutions, the marginal bene…t of improving institutions would drop considerably. In the long run, this could cost the country dearly, since institutional development could go into reverse. 13 A Alternative Replicator Dynamics In the main text, we analyzed the replicator dynamic characterized by dg = h dt = h d ln (f y) dg m g While this replicator does indeed express the idea that dg is monotone in the mardt ginal bene…t of an improvement in g, it is clearly not the only way this idea can be expressed. Two obvious alternatives are dg =h dt and d (f y) dg d ln (f y) d ln g dg =h dt In the …rst case, dg is assumed to be monotone in the absolute— as opposed to dt relative— increase in total production that a marginal improvement in g generates. is monotone in the relative increase in total production caused In the second case, dg dt by a relative marginal improvement in g. The replicator dg = h d(fdgy) reduces to dt dg =h dt while the replicator dg dt =h d ln(f y) d ln g my L g n reduces to dg = h (m) dt In both cases, the phase diagram looks as follows g¤ 0 Phase diagram of alternative replicator dynamics 14 1 Countries starting out below g converge to 0. Countries starting out above ghigh converge to 1. References [1] Auty, Richard. 1993.“Sustaining Development in Mineral Economies: The Resource Curse Thesis,”Taylor and Francis, New York, NY. [2] Azariadis, Costas, and John Stachurski. 2005. “Poverty Traps”in: Handbook of Economic Growth, Volume 1A. Philippe Aghion and Steven N. Durlauf (eds.), Elsevier, Amsterdam. [3] Brunnschweiler, Christa N.and Erwin H. Bulte. 2008. “The resource curse revisited and revised: A tale of paradoxes and red herrings,”Journal of Environmental Economics and Management 55: 248-264. [4] Brunnschweiler, Christa N. 2008. “Cursing the Blessings? 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