Growth of GDP per capita and Democracy. A Simultaneous Equation Generalized Probit Model

Master's Thesis, 2015

33 Pages, Grade: 1



1 Introduction

2 Framework for the Empirical Analysis
2.1 Methodology
2.1.1 Preliminaries
2.1.2 Procedure

3 Data
3.1 Endogenous Variable: Growth
3.2 Endogenous Variable: Non-Democratic
3.3 Exogenous Variables:

4 Empirical Findings
4.1 Direction of Effects
4.2 Squared per Capita Growth and the Policy Variable
4.3 Communism

5 Conclusion

A Mathematical Appendix

A.1 Reduced Form

A.2 Corrected Variances


List of Figures

1 military head

2 marginal effects - growth (baseline)

3 marginal effects - urban (baseline)

4 marginal effects of growth for 1986/2000 and comex

5 marginal effect of growth for 2000 and comex

List of Tables

1 1986 - Part I

2 1986 - Part II

3 2000 - Part I

4 2000 - Part II

5 Squared per Capita Growth

1 Introduction

A widespread preconception when it comes about democracy is that it has a positive effect on economic prosperity. Furthermore, without a detailed analysis, this notion seems to be in line with empirics. In depth analyses of the effect of democracy on growth are presented, among others, by Barro 1996 as well as Przeworski 2000. Przeworski 2000 finds that there is neither a positive nor a negative effect of democracy on economic development. Additionally, he finds that “In poor countries, regimes simply do not matter. In wealthier countries, their average growth rates are the same [independent of their political system], but the patterns of growth are different.” Also Barro 1996 does not find a clear pattern for the effect of democracy on economic growth. On the one hand he finds some indication for a quadratic relationship between democracy and economic growth, but on the other hand, if all other potential determinants of economic growth are held constant, the influence of democracy on growth is negative.

However, there could potentially also be a reversed effect, one from economic growth on the development and emergence of democratic systems, respectively. This effect is analyzed in Lipset 1959 and is identified empirically by Barro 1996. There, he finds some evidence for a positive effect of economic growth on democratization.

If both, the effect of democracy on growth and the effect in the opposite direction, are taken together, there is simultaneity problem caused by reverse causality. Democracy fosters growth and growth, via wealth, fosters democ- racy. Hence, I use a simultaneous equation system to examine the impact of democracy on economic growth per capita and the effect the other way round. Due to the discontinuous nature of the classification of different political sys- tems, I use a simultaneous equation system with a generalized probit model. The estimation system consists of two equations, one represents the impact of democracy on growth per capita, while the second equation, the probit equation, captures the impact of growth per capita on democracy. Given this framework, I run a cross-sectional estimation procedure for more than 107 countries and two different points in time, 1986 and 2000.

In the below analysis, although there is also a growth equation, the main focus is rather put on the effect of economic growth on a country’s political development. Under the assumption of a linear influence of per capita growth of GDP on the probability that a country has a democratic system, the main finding is that there is a positive but insignificant effect of per capita growth on a country’s probability to be a democracy. After introducing squared per capita growth as an additional variable to explain a country’s probability to be a democracy, I get a positive overall effect of growth on democracy for interme- diate growth rates. However, this effect becomes negative after a turning point, i.e., the relationship between growth and democracy is not only non-linear but also exhibits a change in its sign. Additionally, for the augmented model, both the linear as well as the quadratic coefficient corresponding to the impact of growth on democratization are significant.

Contrary, for the growth equation, the influence of the democracy variable is clearly positive and significant for the large majority of model specifications, i.e., the positive effect is robust.

Indeed, these estimation results support the thesis that democracy and growth mutually foster each other.

The rest of this master’s thesis is structured as follows: First, I explain the methods used for the estimation of the simultaneous effect of growth on democracy and vice versa, section (2). Section (3) gives a presentation of the data set and a description of the exogenous and endogenous variables of the model. Afterward, I present and discuss the estimation results and robustness checks, section (4). Section (5) concludes. - There is also a mathematical appendix at the end of this thesis, section (A).

2 Framework for the Empirical Analysis

2.1 Methodology

There are many different empirical approaches to investigate the relationship between democracy and economic growth. Two of them appear to be especially relevant with respect to the endogeneity problem as potentially present for the relationship between democracy and economic growth per capita (cf. section 1). One approach is presented in Amemiya 1978 and the other in Vreeland 2003. The method developed by Amemiya 1978 explicitly takes into account the reverse causality issue. To account for this issue, he developed an estima- tion method for a simultaneous equation system with two mutually dependent equations in which at least one endogenous variable can take on binary values only. In my case the policy variable is binary, and indicates whether a country is a democracy or not. The estimation procedure of Amemiya 1978 is picked up and described in Maddala 1983. There, the author estimates the two endoge- nous variables one after another. Therefore, he first regresses the continuous endogenous variable (in my model per capita growth of GDP) on several exoge- nous variables by OLS while at this point ignoring the endogenous explanatory variable. Then, he estimates the other endogenous variable on the same set of exogenous variables as used in the first-step OLS estimation by means of probit Maximum Likelihood. In my probit model policy (democracy) is the endoge- nous variable to be explained. Afterward, he uses the estimated coefficients and the set of explanatory variables to calculate the associated z-values. These predicted z-values are then used as a continuous measure of how well developed a democracy is. This continuous measure can take on values from minus to plus infinity. For the evaluation of the estimation results it will turn out con- venient to interpret the z-values in terms of their corresponding probabilities. The final step is to use the new, continuous measure of democracy and the predicted values obtained from the first-stage OLS model to estimate the two original structural equations. In my case this final step consists of the simple regressions of growth on the continuous measure of democracy and several ex- planatory variables on the one hand and the estimation of the probit model of democracy on growth and several exogenous variables on the other hand. In the probit model the endogenous variable is the discrete variable for the politi- cal system and the exogenous variables are the predicted values of growth and several other variables.

This explicit tackling of reverse causality is the main difference between the approaches of Amemiya 1978 and Vreeland 2003. Unlike Amemiya 1978, Vreeland 2003 does not account for reverse causality. In a first step, contrary to Amemiya 1978, Vreeland 2003 estimates only one equation, without consid- eration of the reverse causality issue. He, first, estimates democracy on several explanatory variables using a probit procedure, and then takes a random sample from the distribution of estimated coefficients. For example, he draws from the distribution, say, 10 times. So he gets 10 different combinations of coefficient vectors. Then, for each of these coefficient vectors, he calculates predictions.

These predictions are probabilities between zero and one. Finally, he uses the different predictions for the probability of democracy in the equation of interest. In the case of Vreeland2003, in the final stage, there is only one equation to be estimated. Because of the 10 random draws of the coefficient vector, this estimation has to be conducted for 10 different sets of predicted values. In the end, he averages the 10 different results for the estimated coefficients of the final stage to obtain the coefficients expected values.

I chose the model of Amemiya1978 because he takes into account the issue of reverse causality, and thus it is more appropriate for the research question of this master’s thesis.

2.1.1 Preliminaries

The structural system of equations is assumed to be as follows:1

Abbildung in dieser Leseprobe nicht enthalten

The endogenous variables y1 and y2 capture (1) economic dynamics, mea- sured by per capita growth of GDP, and (2) a country’s degree of democrati- zation, respectively. The vectors y1 andy 2 bothareofdimension N × 1where N is equal to the number of countries observed. Xi is a N × k i (k = k 1 + k 2 ) matrix which contains the k i exogenous explanatory variables and β i is a k i × 1 vector of coefficients. The subscripts indicate to which equation a vector or a matrix belongs. The vector ui contains the error terms which, by assumption, are jointly normally distributed with mean zero. Finally, γ i measures the quan- titative impact of one endogenous variable on the other endogenous variable.

The variable y ∗ 2 n isnotdirectlyobservable.Fortheestimationof γ 1 , y 2 n is assumed to take on the value 0 if y ∗ 2 n ≤ 0 and 1 otherwise.

Abbildung in dieser Leseprobe nicht enthalten

With respect to the structural model one has to keep in mind that y ∗ 2 hasto be divided by σ 2 in order to obtain a proper distribution in the probit model, i.e, one where the densities ‘sum up’ to one. This results in the following modified system of structural equations:

1Amemiya 1978 describes how to alternatively estimate the following model by Maximum Likelihood. He shows that the Maximum Likelihood estimator is more efficient than the method which is used in this master’s thesis. However, the computation cost for the Maximum Likelihood estimation are much higher. Hence, I use the two stage procedure for the estimation of my model.

For the next steps I use the reduces forms of (1) and (2). According to Maddala1983, they are:2

Therefore, without some additional assumption, some of the parameters could only be identified up to a scalar multiple. Hence, σ 2 (the variance of the errors in the reduced form probit model) is normalized to one.3 Then, equations (8) and (9) reduce to:

2.1.2 Procedure

In the first step, equation (6) is estimated by Ordinary Least Squares and equa- tion (7) is estimated by probit Maximum Likelihood. Keep in mind that X includes all exogenous variables of the system of equations. From this first estimation of the reduced form equations, the following predicted values are obtained:

Abbildung in dieser Leseprobe nicht enthalten

At the second stage, the predicted values, as obtained from equations (12) and (13), are used to estimates the original structural equations (4) and (5). This is, the following two equations are estimated:4

2For a detailed derivation I refer to the appendix.

3Additionally, it is assumed that the errors (v 2 t = v 1 t σ 12 + e t) are correlated within time, where e t and v 2 t are independent. This correlation can be traced back to the joint normality of v 1 t and v 2 t with mean zero.

4Note that the predicted values of a country’s degree of democratization are not binary but continuous.

Abbildung in dieser Leseprobe nicht enthalten

Rewriting equation (4) gives:

y1 = γ 1XΠ 2 +X1 β 1 +v1 − γ 1X(Π2 Π2)=XĤ α 1 +w1 (16) where Ĥ is defined as (Π 2 : J1) . Furthermore, J1 is a matrix consisting only of zeros and ones arranged in a way such that XJ1 results in X1 . Furthermore w1=v1 − γ 1X(Π 2 Π2)

Equation (16) is then estimated by OLS. The estimator for α 1is:

Abbildung in dieser Leseprobe nicht enthalten

The second equation, equation (15), is estimated by probit Maximum Likelihood. Therefore, I insert the predictions from the first-stage estimation, equation(12), into the target equation, equation (5), and get:

Abbildung in dieser Leseprobe nicht enthalten

where Ĝ= (Π1 : J2) with XJ2 = X2 .

I estimate equation (18) by Maximum Likelihood with the following LogLikelihood-Function.

Abbildung in dieser Leseprobe nicht enthalten

where F is the standard normal distribution function. Maximizing with respect to α 2 gives the following F.O.C.:

Abbildung in dieser Leseprobe nicht enthalten

From this F.O.C. one can obtain the estimated coefficient for α 2, i.e., α 2.

Corrected Variances and Standard Errors5

It is easy to see that for each model the calculated standard errors at the second stage are based on the estimated values of y1 and y2 ∗∗ (cf. equations (16) and

(18)). Hence, a correction of the variances and standard errors is necessary. The corrected variances of α 1 and α 2 are:

Abbildung in dieser Leseprobe nicht enthalten

5For a detailed derivation of the corrected variances and standard errors I refer to the appendix at the end of this master’s thesis.

Abbildung in dieser Leseprobe nicht enthalten

6Remember, the variance of the errors of a probit model is one, i.e., σ 2 = 1 .

3 Data

As discussed in the introduction and in the section on methodology, per capita growth and democracy are likely to be mutually dependent. Generally, there are many potential explanations why economic growth fosters the development of democratic institutions. For example, increasing economic wealth makes it easier to earn a living and therefore allows the population to invest time and resources into a change of the current political system towards their favor.7 Al- ternatively, one could argue that economic growth goes hand in hand with an increase in international trade which then, following a “best-practice”-principle, leads to an adoption of democratic structures. It is not the focus of this mas- ter’s thesis to present a detailed analysis of the various channels through which economic development might influence the democratization process, yet, the general idea behind most channels is that “economic wealth awakens the de- sire for participation.” (Lipset 1959 ), and therefore economic growth promotes democratization.

The other way round, democracy also has a positive effect on growth. Peo- ple are heterogenous and so are their interests. Furthermore, democratic struc- tures create an environment in which it is relatively easy to engage in economic activity targeted at the fulfillment of one’s individual needs. This creates a high incentive to participate in economic development and eventually results in growth. Furthermore, democracies are less prone than non-democratic systems to accumulate capital at the political elite. Intuitively, people can keep a larger proportion of their earnings which increases the incentive to participation even further. Further arguments pick up the issue of distribution and the negative effect of inequality on efficiency and the outcome of decision making processes.

3.1 Endogenous Variable: Growth

In Keynesian and Neoclassical models of growth, Harrod-neutral technical progress is a necessary requirement for the existence of an balanced growth path (BGP). A general production function with Harrod-neutral technical progress can be written as:

Abbildung in dieser Leseprobe nicht enthalten

The variables K, L and A represents the input factors capital, labor and the level of technology, respectively. Y denotes Output.

Harrod-neutrality means that technological progress is labor augmenting, i.e., it increases the marginal product of labor but not that of capital. With Harrod-neutral technological progress, the interest rate on capital remains con- stant along the BGP (however, the amount of capital per worker increases) whereas the real wage rate per worker increases. Therefore, one can say that technological progress increases the cost of labor relative to capital. Further- more, technological progress increases the capital intensity of production, K Y 7This as well as the following explanations are based on the assumption that democracy is the socially preferred system for an given level of economic wealth.


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Growth of GDP per capita and Democracy. A Simultaneous Equation Generalized Probit Model
Vienna University of Economics and Business  (Institut für Makroökonomie)
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Democracy, GDP per Capita, Simultaneous Probit Model, Probit Model, Democratic, Amemiya, Economic, political stability, Barro, Growth
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Katharina Böhm-Klamt (Author), 2015, Growth of GDP per capita and Democracy. A Simultaneous Equation Generalized Probit Model, Munich, GRIN Verlag,


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