To What Extent is the Institutional Environment Responsible for Worldwide Differences in Economic Development

This study aims to assess to what extent the institutional environment is responsible for worldwide differences in economic development. To answer this question, a new concept of the institutions-augmented Solow model is constructed. The analysis covers 153 countries and the period 1994-2009. The empirical analysis confirms a large positive impact of the quality of the institutional environment on the level of economic development. This positive link has been evidenced for all six of the employed institutional indicators (although nonlinearities are present in some cases). Our own concept of the institutions-augmented Solow model fits the empirical data very well. It turns out that differences in physical capital, human capital and the institutional environment (which is measured by the governance indicator) explain approximately 75% of the differences in economic development among the countries of the world. According to the institutions-augmented Solow model, the production function that is consistent with the empirical data is Y = K0.372H0.315L0.313Q0.705, where K is the physical capital, H is the human capital, L is the labor and Q represents the institutional indicator.


Introduction
The economic growth and economic development of countries both depend on many factors. Using the most common classification, we can divide these factors into two groups: the demand-side determinants and the supply-side determinants. The first group encompasses the variables that create GDP according to the following equation: Y = C + I + G + NX, where C denotes consumption, I denotes investments, G denotes government spending on goods and services, and NX denotes the net exports. Except for consumption, which is not an autonomous factor because of its dependence on output, the remaining variables can be regarded as economic growth determinants, as confirmed by the Keynesian model. The second group of factors includes the supply-side determinants that are directly related to the macroeconomic production function. The most common production inter alia various types of investments or government spending or many more types of capital.
The above factors that influence economic growth and economic development can be called "direct" factors because they immediately transform inputs into outputs. These factors are analyzed in the theoretical models of economic growth that show what the determinants of long-run growth and the development level are.
However, the macroeconomic performances of countries do not depend exclusively on these direct determinants. There are also "deep" factors of production that have an impact on the "direct" factors, and in this way, the deep factors affect the process of economic growth and development. "Deep" determinants are institutions that provide the background for the interactions between measurable factor inputs and the level of output.
The aim of this paper is twofold. First, we would like to choose the best concept of the index that measures the institutional environment. Such an index should fit the empirical data very well and be useful in explaining the income differences of all of the countries in the world. We can select either one qualitative variable that is compiled by an international organization or a mix of such variables. Second, we would like to quantify the impact of institutions on countries' development levels.
Most theoretical models of economic growth do not explicitly include institutions as growth determinants.
Indeed, the macroeconomic production function includes only those quantitative variables that directly influence the level of output.
In this paper, we would like to answer the title question, which is the major research hypothesis: "To what extent the institutional environment is responsible for worldwide differences in economic development". We do not intend to analyze whether institutions have an impact on economic development because the answer is obvious; our goal is to quantify their impact, i.e., to measure what part of the variance in economic development can be attributed to a different institutional environment. We measure the level of economic development by GDP per capita at purchasing power parity (PPP). Our study covers 153 countries.
The analysis is based on our own concept of the institutions-augmented Solow model. The standard Solow model (1956) includes only one type of capi-tal according to the following production function: (K, L, A). Mankiw, Romer and Weil (1992) extended the Solow model by introducing another type of capital: human capital; to that end, they employed the following production function: Y = F(K, H, L, A). Nonneman and Vanhoudt (1996) further extended the Solow model by adding more types of capital. They analyzed the model with three types of capital: physical capital, human capital and technological know-how. In our opinion, the value added of introducing more and more types of capital is diminishing. This decrease is occurring because economic growth and economic development depend not only on "direct" factors but also on "deep" determinants that are related to the institutional environment. Thus, we propose the extension of the macroeconomic production function in the way similar to the method of Nonneman and Vanhoudt, but we argue that institutions should be included as new factors of production.
Thus, we use the following production function: F (K, H, Q, L, A), where Q is the qualitative index that measures the institutional environment of a country. Our aim is to choose the best concept of such an index and to estimate the impact of institutions on the level of economic development.
The paper consists of seven sections. In section 2, we present a literature review that describes some other empirical studies on the institutions-growth nexus.
Section 3 refers to the methodology that provides a concise description of the Mankiw-Romer-Weil model and the institutions-augmented Solow model.
Section 4 describes the data that were used. The results of the analysis are presented in sections 5 and 6. Section 7 concludes.

A review of the literature on the institutions-growth nexus
There is no unique method for measuring institutions. nexus. This review of the empirical evidence will also justify our selection of variables.
There are many empirical studies that analyze the relationship between economic freedom and economic growth, and most of them confirm the positive impact of economic freedom on macroeconomic performance. For example, de Haan and Sturm (2000) analyze 80 Rapacki, 2009;Rapacki & Próchniak, 2009;.
Empirical studies also focus on other measures of the institutional environment. There are many studies that include the variables that are related to political factors (inter alia, the level of democracy and political stability). The general conclusion of these studies is that a stable and democratic environment is conducive to macroeconomic development. However, there are some deviations among particular studies from this general rule. The most comprehensive cross-sectional study was conducted by Barro and Sala-i-Martin (2003). These authors analyze almost 100 countries during 1965-1995, and their results suggest that the democracy indicator (which is measured by the electoral rights and taken from the Freedom House) reveals a nonlinear relationship with the growth rate of the GDP. Nonlinearities are also present in the case of another indicator provided by this institution, i.e., civil liberties. In contrast, the quality of bureaucracy reveals a positive linear impact on the economic development.
In addition, these authors test dummy variables that represent various institutions on a 0-1 scale, such as: colony dummies (British, French, Spanish/Portuguese and other), a landlocked dummy, and legal-structure dummies (British and French). Plümper and Martin (2003)   , confirms that the quality of governance positively and significantly affects the economic growth, whereas democracy only stimulates economic growth when it is related with improved governance. Leblang (1997) analyzes the democracy index according to Gurr for 91 countries during 1960-1989, and the results confirm that the initial level of democracy positively and significantly influences the GDP dynamics. Feng (1997) uses several institutional variables, such as the democracy level according to Gurr, the democracy level according to Bollen and the probabilities of government changes. This analysis covers 96 countries in the years 1960-1980, and the results suggest that democracy has a twofold impact on economic growth: the direct impact is negative, whereas an indirect impact is positive because of influence on the probability of government changes.
Moreover, important regular government changes favorably affect macroeconomic performance, whereas irregular changes have the opposite effect. Thus, democracy indirectly influences the GDP growth because it increases the probability of important regular government changes and lowers the probability of irregular changes. Barro (1996) focuses on the political rights index compiled by Gastil and Bollen as well as on the rule-of-law index. The data for approximately 100 countries and the period 1960-1994 indicate that political freedom is nonlinearly related with economic growth: given a low level of political rights, extending political rights stimulates economic growth; however, when a specified level of democracy has been achieved, any further extension of political rights negatively affects the growth of output. In contrast, the rule-of-law index is positively and significantly correlated with the economic growth. Próchniak and Witkowski (2012a;2012b;2013) analyze the impact of economic freedom and the level of democracy on GDP growth using an innovative method of Bayesian model averaging; they find that economic freedom is one of the main growth drivers in the EU.
In addition, there are several studies that verify the relationship between political stability and economic growth. For example, Asteriou and Siriopoulos (2000) analyze data for Greece during 1960Greece during -1995Asteriou and Price (2001) focus on the UK in the years 1961-1997and Fosu (2002) examines 31 Sub-Saharan African countries in the period 1960-1986. All of these studies confirm the existence of the negative relationship between political instability and economic development. Although the studies differ in terms of the variables used (inter alia, terrorist attacks, political strikes, coups d' états, political assassinations, the Falkland war and the Persian Gulf War), the results clearly indicate that political stability is conducive to economic development. Similarly, Chen and Feng (1996) analyze the probability of changing the regime (which is calculated based on the logit model), economic freedom and the number of political assassinations using a sample of 88 countries during 1974-1990. According to their work, a higher probability of changing the regime, a greater number of political assassinations and a lower scope of economic freedom are factors that hamper economic growth. However, Wu and Davis (1999) achieve opposite findings: they analyze the political stability index (compiled based on political rights and civil liberties from the work of Gastil) and apply it to approximately 100 countries during 1975-1992. They conclude that for a given level of economic freedom, the rate of economic growth does not depend on the level of political freedom. In an analysis that covers 105 countries in the period 1960-1989, Durham (1999 finds that the number of political parties in the government is not correlated with economic growth. Some institutions are very hard to measure, and they require descriptive analysis rather than quantitative (formal) models. For example, Hunt (2012a) analyzes the relationship between trust within a society and economic growth and shows that trust-promoting, societal-level moral codes promote productivity and economic growth (see also Foss (2012) and Hunt (2012b) for further discussion).
In summation, the empirical evidence confirms an enormous impact of institutions on economic growth.
Thus, when analyzing the sources of income-level differences between countries from different parts of the world, we have to include institutional measures. This requirement is why we extend the Solow model to account for institutions.

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To What Extent Is the Institutional Environment Responsible for Worldwide Differences in Economic Development

Theoretical background and the methodology
In this part of the paper, we describe the determinants of economic development by referring to the family of Solow models. We begin with the Solow model that is The production function exhibits constant returns to all three of the inputs (i.e., physical capital, human capital and effective labor) and the diminishing marginal product of both physical and human capital. One of the functions that satisfy these properties is the Cobb-Douglas production function: where α > 0, β > 0, α + β < 1. The output may be devoted to consumption, the accumulation of physical capital, or the accumulation of human capital. The level of technology and the size of the population both grow at constant exogenous rates that are equal to a and n, respectively: The analysis of the economy is carried out for the capital and the output per unit of effective labor, which are denoted by k(t), h(t) and f(k(t),h(t)): To find equations that describe the behavior of the economy, we differentiate the definitions of k and h (given by (6)) with respect to time. Then, we apply formulas (3) -(6). Assuming that the production func- Because in the steady-state both physical and human capital per unit of effective labor are constant, by setting (7) and (8) Because the output per unit of effective labor (y) is equal to the per capita GDP (Y/L) divided by the level of technology (A), from (9) we can calculate the steady-state level of per capita output: Equation ( Figure 1. The transition period and the steady-state in the Mankiw-Romer-Weil model

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To What Extent Is the Institutional Environment Responsible for Worldwide Differences in Economic Development The above formula indicates that in the basic Solow model, the GDP per capita in the steady-state depends inter alia on the savings rate (with which it has a positive relationship) and the growth rate of the population (with which it has a negative relationship). Equation (12) can also be estimated as a linear regression model, which allows us to find the production function's parameters.

(b) The institutions-augmented Solow model
Nonneman and Vanhoudt further extended the Solow model. They analyze the model with many inputs, each of which is a specified type of capital. The production function has the form ( ) However, as we argued in the introduction, the value that is added by introducing more types of capital is diminishing. This decreasing return is because economic growth and economic development depend not only on "direct" factors but also on "deep" determinants that are related to the institutional environment. Thus, we propose an extension of the macroeconomic production function in a way that is similar to the extension of Nonneman and Vanhoudt, but we argue that institutions should be included as new factors of production and not as different types of capital. Thus, we propose the following production function: where Q is the qualitative index that measures the institutional environments of countries. One difference between our proposition (14) and the neoclassical production function is that our production function Returning to the mathematical analysis of the model, the production function per unit of effective labor is The time paths for the physical and human capital are derived in the same way as equations (7) and (8), which yields the following: Using a similar analysis as before, the respective stocks of physical capital, human capital and output per unit of effective labor in the steady-state are as follows: Equation (20) The above formula can be estimated as a linear regres- The estimation of equations (11), (12) and (21) is presented in section 6.

Data
Our analysis is entirely based on the family of Solow models. Thus, we empirically verify only those equations that can be derived from the theoretical analysis of the model, which is presented in section 3.
To analyze the determinants of economic development, we use equations (12), (11) and (21) However, this equality will hold in the restricted version of the equation, where the explanatory variables ln s i and ln(n + a + δ) are interrelated. The restricted model is obtained by subtracting ln(n + a + δ) from each of the ln s i variables.
The details are presented in Table 1. Table 1 is composed of three parts that represent the basic Solow model, the Mankiw-Romer-Weil model and the institutions-augmented Solow model in that order. The first two rows specify the number of inputs and the production function, and the next two rows present the regression equations that are estimated using the ordinary least squares (OLS) method for the unrestricted and restricted model. In addition, the next row relates the regression coefficients with the production function parameters according to equations (11), (12) and (21).
Finally, the last row shows the way in which we estimate the production function parameters.
Before conducting our calculations, we have to impose one additional assumption. Equations (11), (12) and (21) include (inter alia) the technical progress and the depreciation rate. However, it is impossible to obtain real values for these parameters in our sample of countries. Hence, we assume that the sum of the rate of technical progress and the depreciation rate equals 0.05 (i.e., 5%), which is a common assumption in such analyses and should not lower the reliability of the results with respect to the aim of our study (see, e.g., Mankiw, Romer, Weil, 1992;Murthy, Chien, 1997;Murthy, Upkolo, 1999;Nonneman, Vanhoudt, 1996).
The variable denoted by y in Table 1    Regression coefficients: Estimation of the parameters physical capital's share in income:  The investment rate in human capital is not so easy to find, as there is no unique and commonly accepted measure of human capital. In empirical studies, many indices are used depending on the research methodology and data availability. For the purposes of our analysis, we estimate the variable s H by various methods to choose the best variant. The investment rate in human capital has been calculated in eight distinct variants: • public spending on education (% of GDP) -edu; • secondary school enrollment (% gross) -enrol_sec; • tertiary school enrollment (% gross) -enrol_ter; • average years of tertiary schooling (age 25+) -years_ter; • average years of total schooling (age 25+) -years_tot; • percentage of the population (age 25+) that has completed a tertiary education -pop_ter; • duration of compulsory education (years) -dur_comp; • labor force with a tertiary education (% of total) -lab_ter.

Some empirics on human capital accumulation and the quality of institutions
In this section, we verify the relationships among the variables that are tested in our study using a number of econometric techniques. First, we analyze the mutual correlation of some explanatory variables. Then, we test the relationship between the quality of the institutional environment and the level of economic development. That is why we decided to ignore the edu variable in our analysis. Moreover, the correlation matrix indicates that although edu is statistically significant, it is not strongly correlated with the remaining variables (due to low values of the coefficients).
The second criterion of our selection is the statistical significance. All the variables except edu are highly mutually correlated (the correlation coefficients even approach 0.8-0.9). However, because lab_ter is only available for a relatively small number of countries, it should be excluded. From the rest of the variables, we select enrol_ter (the tertiary school enrolment ratio) for further analysis, and we take into account a slightly arbitrary choice but also a high number of observations (153 is the maximum possible number of observations).
Now, let us analyze the results for the second group of variables, that is, the institutional indicators. Table 3 presents the respective correlation matrix.
It turns out that all of the selected institutional measures are strongly and significantly correlated with
To What Extent Is the Institutional Environment Responsible for Worldwide Differences in Economic Development each other. The data in Table 3 indicate that all the correlations are statistically significant at the 1% level.
Although the coefficients range between 0.2764 and 0.8763, most of them are in the range 0.6-0.8, which confirms that there is a very strong relationship between these variables.
Hence, we reach two conclusions. First, all of the qualitative indicators are very good proxies for the institutional environment. It is unlikely that such a good correlation for a large sample of countries is spurious.
Second, various types of institutions are of a comparable quality in the same country. Thus, there are only a few countries that perform extraordinarily well in terms of, e.g., economic freedom, but reveal poor governance and/or have unfriendly business regulations.
The typical country has institutions that have developed similarly. For example, if a given country exhibits a large scope of economic freedom, it is very likely that it will also be characterized by a high quality of governance, business-friendly regulations and a high level of democracy. Of course, from the statistical point of view, these results are partly biased because the qualitative institutional indicators are composed of the category indices that can be the same across a number of aggregate institutional measures (for example, corruption is included in both the index of economic freedom and the governance indicator).
As we know that all the institutional indicators are strongly mutually correlated, let us switch to the title topic of the analysis. We must verify the relationship between the institutional environment and the level of economic development. We assess this link using the regression analysis, which allows us to quantify to what extent differences in institutions can explain differences in income levels between the various countries in the world.
The existing literature (e.g., Barro & Sala-i-Martin, 2003, p. 529) suggests that the relationship between some institutional variables and economic growth can be nonlinear. Hence, to check for eventual nonlinearities, we estimate both linear and nonlinear regression models of the following form:

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To What Extent Is the Institutional Environment Responsible for Worldwide Differences in Economic Development       To enrich a country, its policy makers should focus on those institutional reforms that affect the GDP via supply-side and demand-side determinants.

Empirical verification of the institutions-augmented Solow model
We verify the institutions-augmented Solow model using the equations presented in Table 1    The data in Table 4 indicate that all the types of the Referring to the unrestricted regressions, which give more reliable results in our opinion, the investment rate in physical capital positively affects the creation of GDP. In all the regression equations, this variable is highly significant with a p-value less than 0.01. The countries that devote large parts of their income to investments are on average richer than those countries that have low investment rates.
Similarly, human capital accumulation also plays an important role in enhancing economic development.
In both considered models, the human capital variable is extraordinarily significant (with t-statistics exceeding 10 and p-values of 0.000). Such an outcome is not spurious and emphasizes the enormous impact of human capital formation on economic development. As a result, countries that want to be rich should invest in education (in both qualitative and quantitative terms); of course, they should invest not only in tertiary education, which is included in the regression equations, but also in secondary and primary education. Our study shows that human capital is the most important variable that is responsible for economic development.
Indeed, without a sufficient stock of human capital, it is very hard for a society to develop institutions that are favorable for economic development. It is worth comparing the R 2 coefficients of the respective models, and the results are very interesting.
We focus on adjusted R-squares. According to the basic Solow model, the differences in the investment rate (as well as the population growth) explain 20% of the differences in the worldwide income levels, which is not particularly revealing. However, if we introduce human capital, this figure increases to 65%. In other words, approximately 2 / 3 of the worldwide variety in GDP per capita can be explained by physical and human capital accumulation. This number rises further when we consider the institutions-augmented Solow model. Based on this model, the differences in physical capital, human capital and the quality of the institutional environment explain approximately 75% of the income differentiation among the world's countries.
The last figure is extremely high. Almost all of the worldwide development differences can be explained by three variables: physical capital accumulation, human capital accumulation and the quality of institutions. Hence, the institutions-augmented Solow model works very well; indeed, it is clearly superior to the basic Solow model, which only includes physical capital.
The above results imply that rich countries usually invest more in physical and human capital and have more developed institutions than poor countries. In other words, if a given country exhibits large investment rates, popular and high-quality education and a favorable institutional environment, then it is very likely that this country will be rich.
Of course, in interpreting these results we assume that the theoretical causal relationship between the explanatory variables and the level of economic development is as follows: the past values of the explanatory

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To What Extent Is the Institutional Environment Responsible for Worldwide Differences in Economic Development variables affect the current state of development. In reality, many macroeconomic relationships have mutual causality. Hence, it is worth noticing that rich countries also have greater opportunities to save, to invest in human capital and to have friendly regulations and institutions just because they are rich.
As we mentioned earlier, our main findings are based on unrestricted regression equations. However, it is worth adding that restricted models yield similar results to the unrestricted ones, with one exception. In The exponent for L is calculated as 1 -α -β (in line with the assumption of constant returns to K, H and L).
The above formula seems to be reliable. The physical capital, human capital and labor shares in income are approximately 1 / 3 each, which is consistent with the empirical data for many countries. The institutions are more important in forming the GDP: the institutional elasticity of the output equals 0.705.
The production function for restricted regressions can be derived in an analogous way. It has the following form: The powers of the measurable inputs (K, H and L) are at comparable levels to formula (24) (any discrepancies that appear are statistical). The only significant change concerns the institutional share. In production function (25), the institutional elasticity of output is significantly higher (1.133), which means that institutions play an even more important role in forming the GDP, as suggested by equation (24).
Overall, our study gives some valuable recommendations for politicians and policy makers. Governments should focus on improving the institutional environment, investing in education and stimulating investments. The empirical analysis clearly confirms that these factors are necessary for rapid economic development.

Summary
This study aims to assess to what extent the institutional environment is responsible for the worldwide differences in economic development. To answer this question, we build our own concept of the institutions-