Regression (1) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:46 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 Regression (2) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:44 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 White period standard errors & covariance (d.f. corrected) Variable LOG_GDPPC Coefficient -1.354828 0.235673 Std. Error 0.070919 0.008626 t-Statistic -19.10396 27.32173 Prob. 0.0000 0.0000 Variable LOG_GDPPC Coefficient -1.354828 0.235673 Std. Error 0.100138 0.011804 t-Statistic -13.52955 19.96613 Prob. 0.0000 0.0000 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.438465 Mean dependent var 0.437878 S.D. dependent var 0.271899 Akaike info criterion 70.67644 Schwarz criterion -110.7168 Hannan-Quinn criter. 746.4770 Durbin-Watson stat 0.000000 0.567871 0.362654 0.235317 0.245473 0.239185 0.660122 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.438465 Mean dependent var 0.437878 S.D. dependent var 0.271899 Akaike info criterion 70.67644 Schwarz criterion -110.7168 Hannan-Quinn criter. 746.4770 Durbin-Watson stat 0.000000 0.567871 0.362654 0.235317 0.245473 0.239185 0.660122 Regression (3) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:49 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 White period standard errors & covariance (d.f. corrected) WARNING: estimated coefficient covariance matrix is of reduced rank Regression (4) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:57 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 White period standard errors & covariance (d.f. corrected) WARNING: estimated coefficient covariance matrix is of reduced rank Variable LOG_GDPPC Coefficient Std. Error t-Statistic -0.115316 0.279148 -0.413100 0.083741 0.034216 2.447402 Prob. 0.6796 0.0146 Variable C LOG_GDPPC Coefficient Std. Error t-Statistic 0.130684 0.376010 0.347554 0.053588 0.046089 1.162698 Prob. 0.728 0.245 Effects Specification Effects Specification Cross-section fixed (dummy variables) Cross-section fixed (dummy variables) Period fixed (dummy variables) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.734448 Mean dependent var 0.685089 S.D. dependent var 0.203511 Akaike info criterion 33.42316 Schwarz criterion 247.9887 Hannan-Quinn criter. 14.87969 Durbin-Watson stat 0.000000 0.567871 0.362654 -0.202482 0.564316 0.089561 1.338914 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.761149 Mean dependent var 0.713916 S.D. dependent var 0.193972 Akaike info criterion 30.06256 Schwarz criterion 298.7476 Hannan-Quinn criter. 16.11503 Durbin-Watson stat 0.000000 0.56787 0.36265 -0.29174 0.51567 0.01576 1.38772 Use the regression results for the Income and Democracy dataset that are shown above. DEM_IND is a democracy index between 0 and 1, with a mean of 0.5. For answers using percents, use 2 decimal places, e.g., 7.12%). a) Briefly explain whether or not the Income and Democracy dataset is a balanced panel. b) Briefly describe how the results in Regression (1) are different from the results in Regression (2). c) Briefly explain why the results in Regression (1) are different from the results in Regression (2) d) Compare the statistical significance of the effect of GDP per capita on the democracy index in Regression (3) with the effect in Regression (4). e) Explain briefly the reason for the difference described in d). f) Using Regression (2), if per-capita income in a country increases by 15% by how much is the democracy index predicted to increase? Use 6 decimal places. Regression (1) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:46 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 Regression (2) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:44 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 White period standard errors & covariance (d.f. corrected) Variable LOG_GDPPC Coefficient -1.354828 0.235673 Std. Error 0.070919 0.008626 t-Statistic -19.10396 27.32173 Prob. 0.0000 0.0000 Variable LOG_GDPPC Coefficient -1.354828 0.235673 Std. Error 0.100138 0.011804 t-Statistic -13.52955 19.96613 Prob. 0.0000 0.0000 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.438465 Mean dependent var 0.437878 S.D. dependent var 0.271899 Akaike info criterion 70.67644 Schwarz criterion -110.7168 Hannan-Quinn criter. 746.4770 Durbin-Watson stat 0.000000 0.567871 0.362654 0.235317 0.245473 0.239185 0.660122 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.438465 Mean dependent var 0.437878 S.D. dependent var 0.271899 Akaike info criterion 70.67644 Schwarz criterion -110.7168 Hannan-Quinn criter. 746.4770 Durbin-Watson stat 0.000000 0.567871 0.362654 0.235317 0.245473 0.239185 0.660122 Regression (3) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:49 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 White period standard errors & covariance (d.f. corrected) WARNING: estimated coefficient covariance matrix is of reduced rank Regression (4) Dependent Variable: DEM_IND Method: Panel Least Squares Date: 01/01/20 Time: 10:57 Sample (adjusted): 1956 1996 Periods included: 9 Cross-sections included: 150 Total panel (unbalanced) observations: 958 White period standard errors & covariance (d.f. corrected) WARNING: estimated coefficient covariance matrix is of reduced rank Variable LOG_GDPPC Coefficient Std. Error t-Statistic -0.115316 0.279148 -0.413100 0.083741 0.034216 2.447402 Prob. 0.6796 0.0146 Variable C LOG_GDPPC Coefficient Std. Error t-Statistic 0.130684 0.376010 0.347554 0.053588 0.046089 1.162698 Prob. 0.728 0.245 Effects Specification Effects Specification Cross-section fixed (dummy variables) Cross-section fixed (dummy variables) Period fixed (dummy variables) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.734448 Mean dependent var 0.685089 S.D. dependent var 0.203511 Akaike info criterion 33.42316 Schwarz criterion 247.9887 Hannan-Quinn criter. 14.87969 Durbin-Watson stat 0.000000 0.567871 0.362654 -0.202482 0.564316 0.089561 1.338914 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.761149 Mean dependent var 0.713916 S.D. dependent var 0.193972 Akaike info criterion 30.06256 Schwarz criterion 298.7476 Hannan-Quinn criter. 16.11503 Durbin-Watson stat 0.000000 0.56787 0.36265 -0.29174 0.51567 0.01576 1.38772 Use the regression results for the Income and Democracy dataset that are shown above. DEM_IND is a democracy index between 0 and 1, with a mean of 0.5. For answers using percents, use 2 decimal places, e.g., 7.12%). a) Briefly explain whether or not the Income and Democracy dataset is a balanced panel. b) Briefly describe how the results in Regression (1) are different from the results in Regression (2). c) Briefly explain why the results in Regression (1) are different from the results in Regression (2) d) Compare the statistical significance of the effect of GDP per capita on the democracy index in Regression (3) with the effect in Regression (4). e) Explain briefly the reason for the difference described in d). f) Using Regression (2), if per-capita income in a country increases by 15% by how much is the democracy index predicted to increase? Use 6 decimal places