Example Of First Analysis: Political Instability (Pol2) Essay

Assignment 8: Types of Regression

This assignment will use the Barro Growth Data, which is a dataset used in Koenker and Machado (1999) consisting of 161 observations with 13 determinants of cross country GDP growth rates. According to my class number, I will use a subset consisting of 90 observations from years 1985-87. In this assignment, Annual Change Per Capita GDP (y.net) will be the dependent variable and according to my student number, Political Instability (pol2) and Public Consumption/GDP (gcony2) will be my first and second independent variables, respectively.

The results from the OLS and robust regressions are presented in Table 1. In this case, political instability exerts an inverse and significant effect on annual change per capita GDP (estimate for pol2: -0.020106, p-value: 0.0388). Also, political instability explains about 3.68% of the variance (adjusted R-squared 0.0368). Diagnostic plots are shown in Figure 1. These diagnostic plots suggest that Cyprus, Guyana, and Zambia have either high leverage or high residuals. Cook’s distance was manually calculated using 4/n as a cut-off point (where n in this case equals 90). According to this calculation apparently Zaire, Zambia, Nicaragua, Guyana, Indonesia, Jordan and Cyprus have high leverage. From this group of countries, those which also have high residuals are all except Zaire. In order to adjust for these potential influences, a robust model is suggested. OLS models weight all observations equally, while robust models penalize those with larger residuals, so robust regression weights observations differently based on how they behave. The results from the robust regression are also shown in Table 1, and the estimates do not change too much most probably because more than two thirds of the observations have a weight value of 1 (look into the R script for this values), so the models is not that different from the OLS model in this case. This is further observed in Figure 2, where the OLS and robust regression lines are plotted together.
Figure 1. Diagnostic plots for annual change per capita GDP according to political instability.
Figure 2. Regression plot of annual change per capita GDP according to political instability, showing OLS, robust and non-parametric regression lines.
The non-parametric regression line on Figure 2 suggests that perhaps a non-linear model might be more suitable in this case (e.g. a polynomial model).

Second analysis: Public Consumption/GDP (gcony2)

The results of the second regression analyses are presented in Table 2, where it is observed that public consumption/GDP also exerts a significant and inverse effect on annual change per capita GDP (estimate for gcony2: -0.143106, p-value: 0.000624), and the model explains 11.52% of the variance in y.net. The diagnostic plots (Figure 3) show that Congo, Cyprus, Nicaragua, Guyana and Zambia have either high leverage or high residuals. The manual calculation of Cook’s distance shows that the high leverage problem is only with Congo, Zambia and Guyana. However, Zambia does not appear within the top 10 of countries with higher residuals, according to this data, but only Congo and Guyana. The results of the robust model are then also shown in Table 2, which provide a better estimate, but still do not differ that much from the OLS model, for the same reasons as with the first analysis: more than two thirds of the observations have a weight value of 1. Figure 4 shows the OLS, robust and non-parametric lines for these regressions.
Figure 3. Diagnostic plots for annual change per capita GDP according to public consumption/GDP.
Figure 4. Regression plot of annual change per capita GDP according to public consumption/GDP, showing OLS, robust and non-parametric regression lines.
The non-parametric regression line on Figure 4 also suggests that perhaps a non-linear model might be more suitable in this case (e.g. a polynomial model), although there is still some linearity conserved.

Works Cited

Koenker, R. and J.A.F. Machado (1999) Goodness of Fit and Related Inference Processes for Quantile Regression, JASA, 1296-1310.