Geometric mean of population from 1991 to 2010
Average government consumption from 1991 to 2010
Average score of index “Rule of Law” from 1991 to 2010
List of countries in sample
Egypt, Arab Rep.
Trinidad and Tobago
The data set for this article comes from the World Bank Database. It includes 89 observations (countries). Table 1 contains descriptive statistics of the examined model. The list of countries is presented in Table 2.
Table 1 contains the mean, median, min and max observations for separate variables. As we can notice the mean and median of Population are considerably different. That is due to two outliers with abnormal population that are included into the data – India and China.
GDP_GR will be the subject of the article. In order to understand the distribution of the variable better please refer to the figure 1
Figure 1. GDP growth rate
The distribution of GDP growth rate looks normally distributed
The correlation matrix (Table 3) reviles potential multicolleniarity between GDP_PC (initial GDP per capita) and R&L (Rule of law index). That result is expectable because countries with established institutes of property rights tend to have higher initial GDP per capita as a result of previous growth. Fertility rate and GDP_PC are also significantly correlated due to the similar reasons. One of the solutions is to omit the regressor Fertility. It is also possible to ignore multicolleniarity as the model overall is viable and coefficients are having appropriate signs.
Table 3. Correlation matrix
There is notable correlation between R&L and GDP_PC and Fertility and GDP_PC
Estimation of the full model
Estimation of the model
S.E. of regression
Sum squared resid
The F statistic of the model (please refer to Table 4) equals to 11.41 with corresponding p-value of 0.00. Therefore the hypotheses that all coefficients except intercept are equal to 0 should be rejected. The explanatory power of the model denoted by the r-squared and adjusted R-squared totals to 0.41 and 0.37 accordingly. That is acceptable result for that kind of models. Sum of squares residuals totals to 122
As expected the coefficient before variable GDP_PC is negative. According to the specification of the model the coefficient is -0.09 with standard error 0.02. That means that every increase of initial per capita GDP on 1 thousand USD leads to reduction of 0.09% of the growth rate of GDP. The coefficient is distinguishable from 0 with t-Statistic -4.06 and P-value 0.00.
GDP growth rate inversely depends on the fertility rate. As theory suggests the higher the economic growth rate the less time individuals devote to rising children. This is due to increased opportunity costs of having children. The coefficient equals to -0.16 with standard error 0.11. That means that an increase of growth rate of GDP of 0.16% leads to a decrease in fertility rate of 1 child per woman. T-statistic equals to -1.46 with corresponding p-value of 0.23. Therefore, the hypothesis that fertility rate is not connected with growth rate of GDP cannot be rejected. Please see the specification of the model with omitted Fertility (Table 5).
Geometric mean of the country’s population is positively correlated to the GDP growth rate. As expected larger countries tend to have higher GDP growth rates as a result of having larger labour market. The coefficient amounts to 0.003 means that an increase of population on one million people leads to increase in GDP growth rate of 0.003%. 14
As expected, government consumption is negatively related to GDP growth rate with coefficient -0.06 with standard error – 0.02. Therefore, an increase of government consumption as percentage of GDP to 1% leads to decrease of GDP growth rate of 0.06%. T-statistics totals to -2.31 with corresponding P-value of 0.02. Therefore the hypotheses that government consumption does not decrease GDP growth rate may be rejected at 5% significance level.
Not surprisingly, the model shows the importance of stable property rights (represented by rule of law index). The coefficient is 0.02 with standard error amounting to 0.008. Therefore, every additional point in the index adds 0.02 per cent of GDP growth rate. T-statistic and corresponding p-value totals to 3.37 and 0.00 accordingly. Therefore the hypotheses that property rights do not affect growth rate of GDP should be rejected.
Estimation of corrected model
Corrected model with omitted variable (Fertility)
S.E. of regression
Sum squared resid
As we may see R-squared dropped from 0.41 to 0.39 while the adjusted R-squared insignificantly decreased from 0.37 to 0.36. Therefore we should use the corrected model with omitted variable Fertility as this variable is unlikely influence GDP growth rate.
CLRM assumptions testing
This assumption holds because the intersect is included into the model.
I have conducted White’s test of heteroskedasticity. F statistics totals to 2.61 with corresponding p-value amounting to 0.0018. Therefore, there are signs of heteroscedastisity problem in the model. Thus, in order to estimate the regression with heteroscedasticity-robast standard errors, HAC standard errors should be used. Heteroskedasticity consistent coefficient covariance in White’s modification are presented in table 2.
Plain Standard error and HAC standard error
HAC standard error
HAC standard errors do not differ significantly from standard errors previously obtained.
To deal with the problem of heteroskedasticity I apply heterscedasticity-consistent standard error estimates. The OLS estimators will still give unbiased coefficient estimates but they are no longer BLUE.
1. Cov()=0 for ij
To check this assumption I conducted Dorbin-Watson test. To conduct the test, three assumptions must be met: equation includes constant term, repressors are not stochastic, there is no lags of dependant variable. All of that assumptions are met. DW statistics equals to 2.30. The critical values are: DL= 1.55 DU=1.74.We decide whether there is autocorrelation from the test because the statistic is between 4-DU= 2.26 and 4-DL=2.45.
The Breusch-Godfrey statistics with 1 lag is equal to 2.31 with corresponding p-value of 0.12. Therefore we cannot reject the hypothesis that there is no autocorrelation.
1. Disturbances are uncorrelated with regressors.
The disturbance of the regression is the variance that is not explained by the model. There may be another regressors that are important for the model and explain the disturbances. In that case estimated coefficients are biased and inconsistent. However I am not awere of an economic theory that could add additional explanation to the possible correlation. Therefore I neglect this problem further.
1. The disturbances are normally distributed.
In order to test that assumption I have conducted Jarque-Bera test. Jarque-Bera statistics amounts to 1.23 with corresponding p-value of 0.53. Therefore the hypotheses that the distribution of disturbances is normal should not be rejected.
Test for the joint hypothesis
To check the hypotheses that two coefficients GConsumption and R&L are equal to 0 we should use F test. The null hypothesis is GConsumption = R&L = 0, alternative hypotheses is that GConsumption 0 or R&L 0. F statistics totals to 5.23 with corresponding p-value amounting to 0.007. Therefore, we may reject the null hypothesis at 1% significance level.
The aim of this article is to understand what influences the GDP growth rate. I have considered the model and found that starting level of GDP per capita, population of the country, government consumption and stability of property rights influence GDP growth rate. Also I found out that fertility rate has no effect on GPD growth rate.