Tarun Singh

Worked with: Alexander Marcus, Alex Sloan

Economics 1123, Problem Set 2

Table 2Growth Regression ResultsDependent variable: Growth

Regressor (1) (2) (3)

tradeshare 1.898

( .8655 )

1.819

(.8259)

1.243

(.7515)

school60 .243

(.0758)

.501

(.1426)

.392

(.1295)

capstock60 __ -.137

(.0592)

-.187

(.0521)

revc __ __ -1.507

(.8746)

civil __ __ -.3358

(.1730)

Intercept -.122

(.6911)

-.328

(.6716)

1.921

(.8516)

F-statistics testing the hypothesis that the population coefficients on the indicated regressors are all zero:

tradeshare, school60 6.4

(.0030)

7.96

(.0009)

5.18

(.0086)

tradeshare, school60, capstock60 __ 5.56

(.0020)

5.07

(.0035)

revc, civil __ __ 8.88

(.0004)

Regression summary statistics

.133 .184 .303

R2 .161 .223 .359

Regression RMSE 1.691 1.641 1.420

n 64 64 63

Notes: Heteroskedasticity-robust standard errors are given in parentheses under estimated coefficients, and p-values are given in parentheses under F- statistics. The F-statistics are heteroskedasticity-robust. The regression results exclude data on Malta.

2. Oil has been dropped from the regression because it is a dummy variable because all the observations are 0. Therefore, it can reveal no information, and STATA has removed it from the regression.

3. a) growth = -.1222 + 1.8978 tradeshr + .2430 school60

                        (.6911)  (.8655)                 (.0758)

b) The coefficient on school60 (.2430) is the estimated increase in per capita GDP growth due to a one year increase in the average years of schooling in the total population in 1960. So if the average years of schooling in the total population in 1960 increases by 1, the per capita GDP will increase by .2430 units.

c) Since the t statistic is 2.19, and the p-value is .032 the hypothesis that the coefficient on tradeshr is zero is rejected at the 5 percent level. In other words, we are testing the hypothesis that there is no statistically significant effect on growth due to a country’s average share of trade in the economy. Our test shows us that there is a statistically significant effect on growth due to a country’s average share of trade in the economy.

d) Yes. The coefficients on tradeshr are very similar in regressions 1 and 2, but the coefficient in regression 3 is smaller by about .6. This is very large - .6 points of real per capita GDP growth is extraordinarily significant. I think this is because there was some omitted variable bias, in other words, adding two variables, revc and civil, explained some aspect of growth that was previously

explained by tradeshr. This could be true, since both have negative coefficients, if there is a strong negative correlation between either revc and tradeshr or between civil and tradeshr. Testing this possibility, we see that corr(civil, tradeshr)= -.0504, and corr(revc, tradeshr)= -.2046. This is the relationship we perdicted. We see that corr(revc, civil)= .4534. Since revc and civil move in the same direction, I think that even if I removed one of them from the regression, the coefficient on tradeshr would still be lower, but not as low.

e) We reject the null hypothesis that all the coefficients are zero because the p-value we got from the F-test was .0020 which is small enough to reject the null hypothesis at the 5% level

f) The coefficient on revc is -1.507 which is both large and negative. This makes sense because revc is the average number of annual revolutions. During a revolution, it would make sense for economic growth to decrease because investment in a country is encouraged by a stable government. This means that for every increase in the number of annual revolutions there is a change of -1.507 points in GDP growth due to the relationship between a stable government and investment in an economy as just mentioned.

g) The coefficient of civil is -.3558. Civil is an index of civil liberties where the higher the score the fewer the civil liberties in that country. So we see that the more civil liberties a country has, the better the economic growth of that country. The magnitude makes sense because the scale measuring civil liberties is large enough that there shouldn’t be a huge difference in economic growth for a one point difference on the civil liberties scale. The negativity also makes sense because if a country has fewer civil liberties, the country is less likely to have an open government which lowers confidence amongst investors.

h) The p-value for revc is .09 so revc is not statistically significant at the 5% level. The p-value for civil is .057 so civil is not statistically significant at the 5% level.

i) Running the regression we get an F-statistic of 8.88 and a p-value of .0004 which means that at the 1% level we reject the null hypothesis meaning not both revc and civil are 0. This is different from part h) because in part h) we included variables such as capstock60 and school60 which have large correlations with civil. This means that in part i) we are getting a lot of omitted variable bias.

j) The coefficient is .3916, since this is a positive value that is significant, that means that there is a positive effect of human capital in growth. However, it is possible that countries that have higher growth rates have more money to spend on education, and thus the relationship could be causal from the opposite direction. Although we don’t know what variable is causing what, we do know that the data supports the possibility of the neoclassical theory of human capital.

k) Due to omitted variable bias, we see that school60 and capstock60 have a very strong positive correlation, in regression 2 we see school60 has a positive coefficient and capstock60 has a negative coefficient, therefore we say that the coefficient on school60 in regression 1 was artificially low because it was showing the negative effect of the omitted capstock60 variable.

l) The difference in growth rates between a country with 4 years of schooling and a country with 8 years of schooling in 1960 could be estimated as 4(.3915698)= 1.5662792, where .3915698 is the coefficient for school60 and 4 is the difference in years between the two groups. The confidence interval for the difference in groups is just a linear transformation of the confidence interval for the coefficient. We multiply the CI by 4 since there are 4 years of difference between the two groups. Thus we get, 4(.1322655 to .6508742) = .529062 to 2.6034968.