An Extension of Neoclassical Growth Theory to Include Institutions 1

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1 An Extension of Neoclassical Growth Theory to Include Institutions 1 Theodore R. Breton* George Mason University March 27, 2002 Abstract Neoclassical theory can explain cross-country capital/labor ratios and levels of income/worker when institutional differences are taken into account. Very different cross-country rates of investment can be explained by differences in national economic efficiency, local investment costs, and the size of the underground economy. These national characteristics are themselves a function of the size and the integrity of government. A Solow model augmented with variables for government integrity and size can explain over 80 percent of cross-country variation in income, and in its reduced form shows that a country s institutional characteristics determine its relative level of income/worker. JEL Codes: A13, C51, E13, O41, O57, P17 Key Words: Governance, Corruption, Solow Model, Economic Growth, Institutions *9903 Rustic Rail Lane, Vienna, VA, 22181, USA, , tbreton@erols.com 1 N. Gregory Mankiw, Thomas Stratmann, Stephen Knack, Carlos Ramirez, G. Chris Rodrigo, and Roger Congleton provided useful comments on earlier drafts of this paper.

2 Commerce and manufactures can seldom flourish long in any state which does not enjoy a regular administration of justice, in which the people do not feel themselves secure in the possession of their property, in which the faith of contracts is not supported by law, and in which the authority of the state is not supposed to be regularly employed in enforcing the payment of debts from all those who are able to pay. Adam Smith (The Wealth of Nations, 1976/1776) Introduction Klenow and Clare-Rodriguez [1997] present evidence that differences in total factor productivity (TFP) across countries are as important as differences in physical and human capital levels in explaining cross-country income/worker, and they conclude that the basic neoclassical growth model, which has the same technology everywhere, has failed. Hall and Jones [1999] present evidence that cross-country differences in TFP are due to differences in social infrastructure, and they suggest that in the long run it is institutions and government policies that determine national economic performance. Although most empirical applications of the Solow model have assumed that the level and rate of growth of productivity are roughly the same across countries, there is nothing in neoclassical theory that requires this to be the case. If differing institutions and government policies affect the marginal product of capital and/or labor, then existing differences in cross-country income levels can be entirely consistent with neoclassical theory. If the basic neoclassical growth model has failed to explain the world distribution of income, it may be because the model has not been applied within a framework that takes institutional characteristics into account. This paper takes seriously Adam Smith s [1976/1776] view that just government is a precondition for economic success. It also takes seriously Mankiw, Romer, and Weil s [1992] contention that the Solow model, with its assumption of decreasing returns to capital, is a valuable tool for explaining economic growth. The conceptual framework and empirical results presented in this paper demonstrate that an augmented Solow model can combine country-specific government characteristics with 2

3 neoclassical theory to explain the world distribution of income. In the process the Solow model explains the cross-country rates of investment that previously were exogenous, and in its reduced form the model demonstrates Hall and Jones [1999] suggestion that in the long run it is institutions and government policies that determine economic performance. The empirical estimates of the model s coefficients meet the Cobb-Douglas criterion that the exponent on physical capital (α) be consistent with its actual factor share in national income. In addition, the explanatory variables pass standard tests for statistical significance, and the overall model explains over 80 percent of cross-country variation in living standards. The first section of the paper shows how country-specific variations in the size of the underground economy, in the level of national economic efficiency and in the local costs facing private investors affect reported income/worker in the context of a national production function. The second section shows how changes in government integrity and government size affect the level of economic efficiency, the local costs facing private investors, and the size of the underground economy. The third section presents cross-country empirical results for a Solow model augmented with indices for government integrity and government size. The fourth section presents some concluding remarks. I. National Economic Efficiency and Local Investment Costs The Solow growth model is a simple but rigorous application of neoclassical economic theory. Although it contains few variables, the model embodies certain key elements, including constant returns to scale, diminishing returns to capital and labor, technological growth, population growth, depreciation of capital, and constant factor shares of national income over time, that seem to characterize capitalist economies. In addition, while the Solow model is dynamic, under certain conditions income/worker converges to a steady-state equilibrium relationship with the capital stock, which may permit econometric estimation of the model s parameters. The basic model includes a total factor productivity (TFP) variable that increases over time. Although most cross-country empirical studies have assumed that this TFP variable has the same value 3

4 everywhere, neoclassical theory does not require that this assumption be made. An alternative set of assumptions, consistent with the evidence provided by Hall and Jones [1999], is that there is a world class level of TFP in the most advanced countries, each country has its own efficiency factor that determines its capability to utilize resources relative to this world class level, and the magnitude of this efficiency factor is determined by each country s institutions and policies. In addition, the Solow model can be transformed into a model of reported rather than actual income by including explicitly the size of the unreported underground economy. This change is required if the model is to be estimated using national data, since Schneider and Enste [2000] provide evidence that the underground economy is large, particularly in poor countries. With these changes, the Solow model has the following components: (1) RY it = (1+u it ) -1 Y it = (1+u it ) -1 P it Q it = (1+u it ) -1 α P it K it [At E it L it ] 1-α where RY it is reported national income, Y it is actual national income, P it is the price of national output, Q it is national output, K it is the national capital stock, A t is the world level of total factor productivity, E it is the country-specific efficiency with which the world s technology can be combined with capital and labor to produce goods and services, L it is the number of (homogeneous) workers, α is the share of reported national income accruing to capital, and u it is the size of the underground economy as a share of reported national income. 2 3 If P it is normalized, so that it is equal to 1 across countries and over time, then the Solow model can be rewritten on a per effective worker basis as follows: 2 In this model there is presumed to be no unreported labor or capital in the underground economy. Implicitly only some fraction of income accruing to reported capital or labor (e.g., workers wages) is unreported. 3 Note that when Klenow and Clare-Rodriguez [1997] calculated TFP, in the context of this model they were actually calculating A it = A t E it /(1+u it ) 4

5 (2) ry it = (1+u it ) -1 (E it ) 1-α (k) it α where ry it = RY it /A t L it and k it = K it /A t L it. Implicitly an effective worker in this model is one whose labor productivity is on the world s maximum production possibility frontier. A country whose workers are effective in this sense has the maximum national efficiency, E it = 1. E it may increase (up to a maximum of E it =1) or decrease, as changes in country-specific institutional characteristics affect the ability of managers to convert resources into economic output. For example, growing civil instability or an increase in rent-seeking activity reduces E it, while improving resource management practices (in a country with E it < 1) at a rate greater than g implicitly increases E it. If E it does not change, a country s TFP (A t E it ) will rise based solely on improvements in the world level of TFP. In the model presented here, world technology and a world-class level of resource conversion efficiency are available to all countries if they adopt the institutional structure required. 4 At steady-state a constant fraction of reported output s i = I it /RY it is invested, u it is constant, E it is constant, A t is growing at rate g, and L it is growing at rate n i. K it is growing at rate n i +g on a net basis and at rate n i +g+d on a gross basis, where d is a presumed uniform depreciation rate for capital in all countries. The rates n i, g, and d are all constant. As shown by Mankiw, Romer, and Weil [1992], under these conditions k it changes over time as follows: (3) d k it /dt = sry it (n i +g+d) k it = ((s i (1+u it ) -1 E i 1-α kit α ) ((n i +g+d) k it ) At steady state d k it /dt = 0, so k it converges to k i * and (3) can be solved as follows: 4 In growth models that do not include institutional characteristics, an increase in E it in the less efficient countries would be viewed as an increase in the rate of technology diffusion from the more efficient countries. 5

6 (4) k i * = E i [s i /((1+u it ) (n i + g + d))] 1/(1-α) Substituting (4) into (1) yields: (5) RY/L it = A t E it (1+u it ) 1/α-1 [s i /(n i + g + d)] α /(1-α) In addition, while in a world capital market there should be a single (net) market return on investment, there are also country-specific investment costs that will affect the rate of investment in each country. As a result, for those countries characterized by capitalist economic systems with competitive markets, in equilibrium the following conditions will hold: (5) Π it = Y it r t (1+lc it )K it w it L it = 0 (7) Y it / K it = α (Y it /K it ) = r t (1+ lc it ) (8) Y it / L it = (1-α) (Y it /L it ) = w it where Π it is economic profit, r t is the international private return on capital net of country-specific costs, lc it is the ratio of the local costs to r t, and w it is the wage paid to labor. Solving the Solow model in the context of a world capital market for the capital/worker ratio at the steady-state yields: (9) K it /L it = A t E it [α /(r t (1+lc it ))] 1/1- α This formulation makes evident the dependence of a country s capital/worker ratio on national economic efficiency and the level of country-specific costs that must be paid by the private investor. As national efficiency declines and local costs of investment increase, a country s ratio of capital/worker declines relative to other countries. This relationship outlines clearly neoclassical theory s answer as to why the capital/worker ratio is so low in poor countries. This ratio is low either because national economic efficiency is low and/or the country-specific local costs facing private investors (as a share of the net international private return on capital) are high relative to other countries. 6

7 The relationship for the capital/worker ratio in (9) can be substituted into (1) and solved for reported income/worker to obtain the following reduced form model: (9) RY it /L it = [A t E it /(1+u it )] [α /(r t (1+lc it ))] α /1- α In this formulation of the Solow model, a country s relative income/worker is entirely dependent on its national economic efficiency, the size of its underground economy as a share of the reported economy, and the magnitude of local costs facing private investors compared to other countries. 5 This model can be augmented to include various types of capital, various determinants of economic efficiency, and various types of local investment costs, but disaggregation of the variables does not change the nature of their effect on cross-country relative income/worker. The model clearly indicates that if poor countries did not have low economic efficiency and high local investment costs, international capital would flow from rich to poor countries, and over time income/worker would tend to converge in an absolute sense. This convergence process could be slow, however, since during the transition an above-normal private return on investment in poor countries would flow to the rich countries, raising the income of capital owners in these countries. During the transition the relative decline in investment in rich countries would slow the growth in worker s wages in the rich countries. The overall effect of an improvement in national economic efficiency in poor countries would be faster than steady-state growth in average income/worker in both rich and poor 5 If the national production function varies across countries, then α would also vary, but different levels of national economic efficiency and different levels of local investment costs do not in themselves imply that the structure of the production function itself must be different. If available technologies for producing goods are similar across countries, local institutional characteristics may only change the mix of factors on the same production function. 7

8 countries, but an increase in the dispersion of income between capital owners and workers within countries. 6 II. Causes of Low Economic Efficiency and High Local Investment Costs Working in the context of neoclassical theory, Olson [1996] and Hall and Jones [1999] surmised that there must be a set of institutional characteristics and policies in poor countries that seriously limit the rate of investment. The internal logic of neoclassical theory indicates that these institutional characteristics and policies must either reduce economic efficiency and/or raise the local costs facing private investors. Evidently though, the important country-specific characteristics could be almost anything, including domestic capability to use technology, formal laws, the structure of economic and political institutions, economic policies, social and political stability, and worker differences related to attitudes, education, or health. Researchers have examined the effect of all of these factors and more within the context of economic growth regressions. Observing that different studies have identified over 50 variables that are significantly correlated with economic growth, Levine and Renelt [1992] tested the sensitivity of the statistical results for a particular variable to the conditioning variable set included in a growth model. They found that physical capital is the only variable that is robustly and positively correlated with economic growth. They also found that investment s share of (reported) GDP (s = I/RY) is robustly and positively correlated with the ratio of international trade to (reported) GDP and that the government s share of (reported) consumption is negatively, but not always significantly, correlated with economic growth. Statistical significance in growth regressions cannot indicate causality because the dependent and independent variables are endogenous, but Levine and Renelt s statistical results for physical capital and 6 Care must be taken to avoid confusing average national income/worker with the income accruing to workers, which is their share of national income (wl). National income/worker is the income received by capital owners and workers divided by the number of workers. 8

9 trade are consistent with the structure of the Solow model in (1). The positive correlation between economic growth and physical capital is, of course, the fundamental relationship in the basic Solow model. But in addition, since higher levels of international trade are likely to be associated with increased competition and increased competition is likely to be associated with higher economic efficiency, and since higher investment is associated with higher income, Levine and Renelt s positive correlation between trade and investment is consistent with (8). Similarly, their identification of government size as a variable negatively correlated with growth is consistent with the weak incentives for economic efficiency in most government enterprises. Since the structure of the Solow model is quite rigid, it is not a convenient framework for the creation of a multi-variable model that might fully capture the country-specific causes of differences in national economic efficiency and local investment costs. But the model s limited capability to include numerous explanatory variables is a potential strength. Any successful specification of the Solow model requires the identification of the few key variables that really matter. And the production function structure of the model indicates that the important variables must be capable of substantially affecting relative (measured) national productivity and the national choice of factors of production. These criteria provide a clear focus to the search for these variables. A low education level clearly could reduce national economic efficiency and is an obvious candidate to be one of the key variables. Mankiw, Romer, and Weil (MRW) [1992] suggested that education was the key variable other than physical capital that determines a country s level of income/worker. Numerous other researchers, however, including Benhabib and Siegel [1994], Islam [1995], and Klenow and Clare-Rodriguez [1997], have since provided evidence that education cannot explain much, if any, of the cross-country differences in income. Data measurement problems could explain the lack of statistical correlation between changes in income/worker and changes in the level of education of the work force in cross-country studies. Nevertheless, Klenow and Clare-Rodriguez [1997] and Hall and Jones [1999] provide evidence using micro data that education is at most a minor contributor to cross-country differences in national income/worker. 9

10 So what is more important in the determination of economic output institutions or economic policies? Since a country s level of economic output is the end result of the conditions affecting investment for a century or more, transitory policies cannot explain vastly different absolute levels of income. So the focus in this paper is on the relatively permanent institutional factors that affect crosscountry levels of income. What institutional conditions could have a major impact on the efficiency of resource utilization and the local costs associated with investment in physical capital? A useful starting point for this search is to consider the theoretical process that enables resources to be used in a manner that maximizes output. As summarized in (6) and (7) above, neoclassical theory indicates that when capital is privately owned, income is maximized when all factors of production are allocated in perfectly competitive markets to those processes where their marginal revenue product equals the factor price. Any deviation from this ideal leads to a sub-optimal use of resources that lowers the overall efficiency of resource conversion and prevents the national economy from operating on its maximum production possibility frontier. A. Government Corruption and Rent-Seeking Olson [1996] suggests that the main obstacles to the optimal use of physical capital are the lack of protection (from theft or expropriation) for private property and the high level of rent-seeking associated with ineffective and/or corrupt government institutions. In this suggestion he follows Adam Smith [1976/1776], who observed long ago that manufactures cannot flourish in the absence of just government. Levine and Renelt [1992] did not include any government integrity/rule of law variables in their tests of specific institutional variables, but Mauro [1995] and Barro [1997] performed some limited tests and found that indices for government integrity and the rule of law are highly correlated with cross-country economic growth. Government corruption and lack of protection for property clearly could affect both economic efficiency and the local costs facing private investors. Government corruption can lower efficiency in a direct fashion. Government officials manage the creation of public infrastructure, such as roads. If 10

11 officials are corrupt, they may distort the allocation of public resources to favor special interests. For example, roads may be constructed to provide jobs in districts of powerful officials rather than where they will best serve the public interest. Alternatively, in countries where the public sector provides goods and services (e.g., via a national oil company), inappropriate technologies may be purchased for government use if bribery and kickbacks distort government resource allocation decisions. Any distortion of (optimal) public sector technology selection for private gain will lower technological efficiency. 7 Yet another reduction in efficiency can occur if government corruption leads to a less competitive economy through laws and regulations supporting monopolistic market conditions or restrictions on free trade. Such regulations are often presumed to reduce economic efficiency, but the absence of competitive pressure delays the implementation of new technologies and administrative practices, which ends up reducing technical efficiency as well. Figure 1 shows the traditional static equilibrium deadweight loss from monopoly as well as an additional dynamic deadweight loss due to delay in adopting the most efficient technology available. Government corruption also can lower efficiency in an indirect manner. Firms that must pay bribes to obtain permission to import capital equipment or make local investments may alter their mix of factor inputs to avoid paying the bribes. Any change from the optimal mix that does not constitute a movement along the maximum production possibility frontier will reduce national economic efficiency. These various distortions determine the magnitude of one component of a country s overall level of national economic efficiency the component related to the level of government integrity: (11) Egi it = f 1 (gd, pm, tr, pd) = f 1 (GInt it ) Where Egi it is the efficiency associated with the level of government integrity, gd is the loss in efficiency due to distorted government investment decisions, pm is the level of private sector monopolization, tr is 7 Principal-agent problems in public corporations have the same negative effect on efficiency as bribery in the public sector. Any distortion of resource allocation lowers national efficiency. 11

12 the level of trade restrictions obtained by the private sector, pd is the level of distorted private investment decisions caused by inappropriate regulation and bribery requirements, and GInt it is an index of government integrity. The country s level of efficiency is positively related to the level of government integrity. A second important effect of government corruption and failure to protect private property may be its impact on the cost of investment. If there is any uncertainty about the security of an investor s property, whether it be the capital stock or the expected income stream, the expected return on investment declines. Uncertainty over property rights implicitly raises the unit cost of capital. In addition, if bribes are required to obtain necessary permits for operation or to import capital equipment, this further raises the unit cost of capital. Just the uncertainty about whether bribes will be required to remain in business raises the perceived investment cost. As the unit cost of capital rises, the return on investment falls, which requires reductions in the capital stock until the marginal product of capital rises to the world rate. Clearly then, in a capitalist system a decline in government integrity causes a decline in national economic efficiency and in the capital/worker ratio, which, as shown above in equation (8), together reduce national income/worker. The local costs related to government corruption can be written as a function of the various components of these costs, whose magnitude is, in turn, a function of government integrity: (12) lcgc it = f 2 (b it, rc it ) = f 2 (GInt it ) Where lcgc it are the local costs arising from government corruption, b is the level of bribes that must be paid to government and rc is the regulatory costs imposed on private firms due to the imposition of unnecessary regulations (e.g., excessive numbers of permits) to induce them to pay bribes. The country s level of local investment costs is negatively related to the level of government integrity. 8 8 Fisman and Svensson [2000] present evidence that bribery in Uganda has a much larger negative effect on firm growth than similar levels of taxation. 12

13 A measure of the level of taxes, bribes, and diversion of public funds for private gain in local investment costs is the price of capital goods in a particular country relative to the international price. Summers and Heston [1991] found that the local price of capital goods in 1980 in the poorest countries was 55 percent higher than in rich countries. 9 B. Government Size While lack of protection for private property and government corruption are likely to be the biggest obstacles to the efficient use of capital, a poorly functioning labor market is likely to be the biggest obstacle to the efficient use of labor. And the most obvious institutional obstacle to a wellfunctioning labor market is public sector control of a large share of the resource allocation decisions in an economy. Government is a necessary institution for any society, and government potentially provides enormous benefits to an economy by eliminating anarchy, creating and enforcing the rule of law, and providing necessary public infrastructure. While government services are critical for a productive economy, they can be provided by a relatively small government. When the government grows larger, it inevitably becomes more involved in regulating the private sector and in producing goods and services that could be provided more efficiently by the private sector. In both cases the overall economic efficiency of the national economy is likely to suffer. 10 The competitive model assumes that resources are allocated to maximize consumer and producer surplus and in the process to maximize national income. While the private sector has the incentives that may lead to this outcome, the public sector generally does not have these incentives, at least not to the same degree. In the absence of competition and a profit incentive, the government is likely to be less 9 A government official in Mexico, Carlos Hank Gonzalez, reportedly became a billionaire through the diversion of government funds via the purchase of equipment at inflated prices [Sullivan, 2001: A21]. 10 In theory government regulation can correct for market failures, but beneficial regulation requires a level of sophistication in governance that normally is beyond the capability of poor countries. 13

14 efficient than the private sector in selecting and implementing new technology and less efficient in its use of labor. Personnel in government bureaucracies typically are selected based on patronage or in conjunction with civil service regulations. In patronage systems the criterion for decision-making is likely to be highly political, which will lead to choices in both physical investment and staffing that are inefficient from an economic standpoint. In governments with a greater reliance on civil servants, the selection of technology and staff is likely to be more economically efficient than in a patronage system, but risk-averse bureaucrats and the politically-driven, government budgeting process are likely to delay and distort the investment process. The net effect is likely to be lower technical and economic efficiency in public sector than in private sector operations. 11 Public sector labor productivity is likely to be low for numerous reasons. If salaries are not competitive with the private sector and unions or civil service regulations prevent dismissal, inept and unproductive civil servants may be hired and employed for life. While labor productivity will be low under these conditions, the negative effect on national economic efficiency may far exceed the direct productivity effect, since services critical for the efficient operation of the private sector (e.g., the provision of telephones or an efficient court system) may not be available at any price. Recognition of this reality is the rationale behind the worldwide tendency toward privatization of public sector enterprises. These various distortions determine the magnitude of one component of a country s overall level of national economic efficiency the component related to the level of government size: (13) Egs it = f 3 (gm, gd, gi, gl) = f 3 (Gsize it ) 11 Majumdar [1998] examined government-owned, mixed sector, and private sector enterprises in India for the period and found that the government-owned enterprises were much less efficient than the mixed or completely private enterprises. 14

15 Where Egs it is the efficiency associated with the level of government size, gm is the loss of efficiency due to government monopoly, gd is the loss of efficiency due to political choices or delay in an honest government s implementation of new technology, gi is the loss in national efficiency when critical infrastructure is not provided by government due to incompetence, gl is the loss in labor productivity from a larger share of the labor force in the government sector, and Gsize it is an index of government size. All of the measures of inefficiency are positive when institutional characteristics are sub-optimal, or zero when resources are allocated optimally, as they are in theory in a perfectly competitive market. The government size efficiency factor is negatively related to government size. The higher local investment costs resulting from government corruption and excessive government size can also be represented as a sum of individual components that raise the total local cost of investment above the (net) cost of capital in the international market. (14) lcgs it = f 4 (t+ge+gr) = f 4 (Gsize it ) where t is legitimate taxation, ge is the increased cost to cover official government expropriation, and gr is the increased cost from excessive (honest) government regulation. The local costs are positively related to the size of government. C. Size of the Underground Economy In addition to their real effects on efficiency, government corruption and size also have a nominal effect on measured efficiency by encouraging or allowing an increase in the size of the underground economy. As the underground economy increases in size, reported income becomes a smaller share of actual income. Since the unreported share of national income is likely to be larger than the unreported share of capital and labor, the underground economy causes measured total factor productivity (TFP) to be less than actual TFP. In the context of the proposed model in this paper, government corruption and size cause measured national efficiency to fall even more than actual efficiency. The underground 15

16 economy function in (1) is positively related to the level of government integrity and negatively related to government size: (15) 1/(1+u it ) = f 5 (GInt it, Gsize it ) III. Empirical Estimates for an Augmented Solow Model The next step is to convert these theoretical relationships into a testable proposition. A. Models As shown in (11), (13), and (15), the level of national efficiency, the size of the local investment costs, and the size of the underground economy are all functions of the level of government integrity and government size. Given the many components that determine these functions, however, and the somewhat subjective nature of indices measuring government characteristics, it is not a priori evident what mathematical form the functions would take. In the case of government size, experience indicates that government is necessary, but that the private sector is more efficient at providing goods and services. Accordingly, it seems likely that the government s marginal contribution to GDP rises until government size reaches its optimal level and then declines, suggesting a complex functional form. 12 But if all existing governments are at least as large as the optimal size, then over the range of existing government shares of national consumption, the marginal contribution of government to GDP is likely to be negative. Governments in poor countries often do not provide critical government services very well, but it is not for lack of size. Figure 2 illustrates the hypothesized true relationship between the government s share of consumption and national economic output and an exponential function s potential fit to this relationship. Over the range of government shares of consumption in the data, the exponential function should be a good substitute for the actual function. The effect of greater government integrity on national economic 12 Government may provide other useful services that do not lead to a maximization of economic output. Only economic output is examined here. 16

17 output can also be represented by an exponential function. Since it is not known a priori whether the effect of government integrity and size is increasing or decreasing with the magnitude of the indices for these variables, both possibilities can be investigated by also testing the effect of inverted indices; i.e, indices of government corruption and private sector size. The initial efficiency and local cost models are defined based on government integrity and government size, since this is the form of the available crosscountry indices: γ δ (16) E it /(1+u it ) = c 1 GInt it GSizeit (17) (1 + lc it ) = c 2 GInt it θ GSizeit ε The sign on government integrity is expected to be positive for the efficiency model (γ) and negative for the cost model (θ). The sign on government size is expected to be negative for the efficiency model (δ) and positive for the cost model (ε). Equations (7) and (16) can be substituted into (1) to yield the following structural version of the Solow model in log form: (18) ln[(ry/l) i ] = c + γ ln[gint i ] + δ ln[gsize i ] + α/(1- α) ln [s i /(n i+g+d)] One note of clarification relates to the interpretation of the coefficients of the model in (18). In this model the capital and labor components are presumed to be the inputs to the Cobb-Douglas structure with constant returns to scale, while the government integrity and government size variables are indices controlling for the country-specific level of efficiency and the size of the underground economy. Given the manner in which they were derived above, it should be evident that the GInt it and GSize it variables are not inputs into the Cobb-Douglas structure, even though they have a similar mathematical form. This model also can be written in the reduced form version by substituting (16) and (17) into (9), which makes income/worker solely a function of government integrity and government size: (19) ln[(ry/l) i ] = C + (γ θ (α /1-α)) ln[gint i ] + (δ ε (α /1-α)) ln[gsize i ] 17

18 It is noteworthy that this version of the neoclassical model predicts that the institutional characteristics of the country determine its steady-state level of income/worker relative to other countries. B. Data MRW s [1992] data were used for income/adult in 1985 and for average investment rates for physical capital, average growth in the labor force, and average investment rates for human capital (in a comparison test only) over the period. The average investment rate for physical capital is calculated based on international prices, so these rates exclude any country-specific local investment costs. 13 Summers and Heston s [1991] Penn World Tables data were used to estimate the average government share of consumption over the period. The assumed rate for depreciation and world technological growth (d+g) was 0.05 for all countries. The cross-country measure of government integrity is Mauro s [1995] bureaucratic efficiency index, which measures the integrity with which a country s public institutions create and enforce rules and regulations that are necessary for efficient business operations. This index is the average of three Business International indices for types of corruption-related risk affecting foreign business operations in : Legal System, Judiciary Efficiency and integrity of the legal environment as it affects business, particularly foreign firms. Bureaucracy and Red Tape The regulatory environment foreign firms must face when seeking approvals and permits. The degree to which it represents an obstacle to business. Corruption The degree to which business transactions involve corruption or questionable payments. Although the indices for these three factors are correlated, the three combined are a better overall measure of the integrity of a country s government institutions, or quality of governance, from an economic 13 The use of unadjusted data could bias the estimated coefficients on the production function. 18

19 perspective than any single factor. The bureaucracy and red tape index is included in the overall corruption index because extensive amounts of red tape are often used as a vehicle to extract bribes. 14 While the original MRW non-oil data set included 98 countries, Mauro s index was only available for 68 countries, and only 63 countries had data available from both data sets. In addition, the OPEC members Venezuela, Algeria, and Nigeria were removed for consistency with the non-oil concept of the data set. The net result was a reduction in the number of countries available for the empirical analysis from 98 in the MRW non-oil country data set to 60 in this study. A summary description of the data is shown in Table 1. The data set for these 60 countries is provided in the Appendix. An important issue is whether the 60-country data set is a reasonable sample for estimating a cross-country national production function. Figure 3 shows the distribution of income in 1985 for the countries included in the sample. There are 17 low-income countries with income/adult under 3000 USD, 20 medium-income countries with income/adult between 3,000 and 8,000 USD, and 23 high-income countries with income/adult between 8,000 and 20,000 USD (1985 dollars). The distribution also includes 22 OECD countries and 38 non-oecd countries, of which ten are Latin American, nine are sub- Saharan African, three are Asian tigers, and six are Islamic states. Although a larger sample would be better, the sample covers a wide range of countries and has a balanced distribution of countries by income level. C. Statistical Issues The ordinary least squares (OLS) statistical technique estimates unbiased and consistent coefficients for the models in (18) and (19) only under certain conditions. First, there must not be any omitted variables that are correlated with the explanatory variables. Second, the data for the variables must not suffer from data measurement error. Third, the independent variables must not be endogenous. 14 Using World Bank data from 75 countries, Djankov, et.al. [2002] found that greater regulation is strongly and significantly related to higher levels of corruption. 19

20 Finally, y it must be equal to y i *, or any deviations from y i * must be random. Fortunately, it appears that these conditions can be met for empirical estimates of the determinants of income/adult in Arguably the omitted variables problem in the basic Solow model is largely solved by adding the government integrity and government size variables. While the augmented models do not include any variables for transitory policies, the effect of these policies is small relative to absolute levels of income at a given point in time and potentially random in their effects across countries. In addition, regional dummy variables can be added to control for unspecified geographic and cultural variables. Despite these controls the coefficient on government integrity may be biased upward if it captures the effects of both government and private integrity on national income, since these characteristics are likely to be correlated. In a country where corruption is rife in the bureaucracy and the courts, armslength business relationships between anonymous private individuals may be rare, since doing business with anyone other than trusted colleagues (e.g., within the family or the mafia) may be too risky. Further, it is possible that the government integrity variable may be a general proxy in the model for the efficiency gains that occur when markets replace personal relationships as the norm for business transactions. Nevertheless, the estimated coefficient on government integrity arguably is unbiased as a measure of this larger effect. Schneider and Enste s [2000] estimates of the size of the underground economy indicate that there is substantial, non-random measurement error in the reported cross-country income data. This measurement error affects the income/adult, investment ratio, and government share of consumption data used to estimate the models. Fortunately, as shown above, the government integrity and size variables in the models control for this measurement error. Since the available cross-country income data are for reported income, not actual income, the regression model estimates the coefficients that explain reported income/worker. The coefficients on the government integrity and size variables capture the real and the measured effect of government corruption on reported income, including the effect from changes in the size of the underground economy. 20

21 Although endogeneity problems have plagued growth model regressions, estimation of the static version of the Solow model arguably is free of these problems since all of the independent variables in (18) and (19) may be exogenous. The rate of investment in physical capital, the rate of labor growth, and the government share of consumption are all calculated based on the average of their values over the period, which are exogenous relative to the level of income/worker in The observed distribution of government size across countries in 1985 appears to be more a function of domestic political beliefs about the desirability of socialism than a function of the absolute level of income. Since the developed country experience is that the government share of consumption has increased, not decreased, as income/capita has increased over time, the larger government share in the poor countries does not seem to be an endogenous function of the level of income. The issue of whether government integrity is endogenous to the growth process (i.e., improving with income levels) is more controversial, but some evidence suggests that government integrity is correlated with civic values and levels of social trust, which are relatively stable cultural traits. 15 Treisman [2000] has shown that perceived corruption is negatively associated with high income, the share of a population that is Protestant, a history of British rule, and a long tradition of democracy. Some of these factors are clearly exogenous. If economies reach high levels of income/worker due to low corruption, as proposed in this paper, then Treisman s findings are consistent with the assumption that government integrity is exogenous relative to income. A potential problem with estimating the static version of the Solow model is that the coefficients will be biased if income/worker is not at the steady-state level, or if deviations from this level are not random across countries in the data set. Fortunately, a review of the trends in levels of income, rates of investment, and the government share of consumption over the period indicates that steady-state conditions prevailed to a remarkable degree. And even if there are mild trends in the exogenous 15 Feldman and Rice find strong correlations between the civic values of various ethnic groups in the U.S. and the values prevailing in their countries of origin, even after two or three generations [Inglehart, 2000]. 21

22 variables, the log form of the equation prevents bias as long as the relative levels of the variables across countries are stable. Figure 4 shows the annual growth rates for reported income over the period from MRW [1992] for the 60 countries in the data set. Although the dispersion in growth rates is much higher for the low-income countries, excluding a few high-growth outliers, the mean rate of annual growth is remarkably consistent over the range of national income levels in the sample. Figure 5 shows the average investment ratios (I/RY) i /(n i+g+d) for countries in the same three income categories over the 25-year time period. The investment ratios are high in the high-income countries and low in the low-income countries, as predicted by the Solow model. And importantly for the validity of the OLS estimation process, the investment ratios are relatively stable for each group of countries. Figure 6 shows the government share of consumption for the three income categories over the period. Although the trends appear to be rising, the relative size of government across the three income categories appears to be stationary. Overall the assumption that income/adult in 1985 is a reasonable estimate of steady-state income/adult, or that any country-specific deviations are random, seems consistent with the historic data. D. Empirical Results A series of OLS regressions were performed to estimate the coefficients on the models shown in equations (18) and (19). As discussed earlier, one test of the validity of the augmented Solow model is whether it provides a statistical estimate of physical capital s share of national income (α) that is consistent with actual estimates. As shown in Table 2, Kendrick and Vaccara s [1980] estimates of the average share of income accruing to capital for nine countries in 1973 was The empirical results for the various regression models are shown in Table 3. The first column presents the results with the basic Solow model, which are similar to those obtained by MRW [1992]. The basic model has an implied value of α =.62, which is too high. The second column presents the 22

23 results obtained when the government integrity and government size variables are added to the basic Solow model. The explained variance rises from 69 to 83 percent, and all of the variables are statistically significant at the five percent level. In this model the implied value of α is 0.47, which is an improvement over the basic model, but still too high. The third column presents the results when regional/cultural dummy variables are added for the OECD countries, the Asian tigers, Islamic countries, Latin American countries, and the sub-saharan African countries. In this regression the explanatory variables maintain statistical significance at the five percent level, and the coefficients on the OECD and sub-saharan African country dummies are also significant. In this regression α = 0.35, which is consistent with the average share of national income accruing to capital shown in Table 2. These results provide strong support for the Solow model and the importance of government integrity and size in the determination of cross-country national income. The results also indicate that some additional unspecified factors raise income levels in the OECD countries and reduce income levels in the sub-saharan African countries. Columns 4-6 present the results of some tests of the model shown in column 3. Column 4 shows the results when the variables for government integrity and government share of consumption are replaced with variables for government corruption and the private sector share of consumption. The results are not strictly comparable since four data points for GovIntegrity = 1.0 were dropped in the test. The government corruption and private sector share variables are less statistically significant than the government integrity and government share variables in column 3, and the overall explained variance is lower, suggesting that the model in column 3 is superior. Column 5 presents the results for the model in column 3 when the coefficients on the explanatory variables ln(i/ry) i and ln(n i+g+d) are not restricted to be identical. The statistical results indicate that the hypothesis that the coefficients on these two variables are different is rejected, which provides additional support for the validity of the Solow model. 23

24 Column 6 presents a test in which MRW s [1992] variable for human capital (SCHOOL) is included in the model from column 3. The results indicate that SCHOOL has no explanatory capability when the institutional variables and the regional dummy variables are included in the model. These results are consistent with the criticisms cited earlier that MRW s positive statistical support for the importance of education was due to omitted variables bias. The fact that SCHOOL has no effect on the magnitude or the statistical significance of the explanatory variables supports the validity of the proposed model. Column 7 presents the results for the reduced form augmented Solow model. Using the estimated coefficients in column 3 for α, γ, and δ, the implied value of θ is 0.43 and the implied value of ε is This result provides further support for the validity of the proposed Solow model and indicates that local investment costs, such as bribes, theft, the danger of expropriation, high taxes to support big government, and costs due to excessive regulations have a substantial deterrence effect on the level of private investment. The extremely high statistical significance for the government integrity variable in the reduced form model (t = 7.7) indicates strongly that it is capturing a real effect. IV. Concluding Remarks The empirical results for the augmented Solow model indicate that government integrity and government size are critical characteristics in the determination of capital/worker ratios and income/worker levels in capitalist economies. Since the income variable is reported income/adult, not actual income/adult, the effect of government corruption and government size on real economic output cannot be determined from these results. Nevertheless, the magnitude of the coefficients is so large that the real effect is likely to be very substantial: (20) Reported (Y/L) it = c A t GInt it GSizeit These results indicate that a decrease in government s share of reported consumption from 20 percent to 15 percent (a transfer of less than five percent of the labor force) would increase average reported income/adult by 15 percent. Actual income probably would not increase as much, since the measured 24