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Unformatted text preview: 1 Econometrics Karen Macours Fall 2005 Midterm: Answer Key A) Firms and Bribes in Transition Countries 1) Older firms are predicted to pay a smaller share of their revenue in informal payments. Specifically, an increase of a firms age with 1 year is predicted to decrease the (reported) share of revenue payments to public officials with 0.028 percentage points, ceteris paribus. The coefficient is significantly different from 0 at the 1% significance level (t-value = - 0.028/0.009 = 3.11 which is bigger than 2.576, the critical value at 1% (with more than 120 degrees of freedom). Since we can reject the null-hypothesis at the 1%, we can automatically reject at the 5 and 10%. 2) 99% confidence interval for coefficient of firm size: [-0.005-2.576*0.001, -0.005+2.576*0.001] = [-0.00758, -0.00242] 3) Since column (1) and (2) show 2 non-nested models, we would use the adjusted R-squared to choose between the 2 specifications in this case because (1) and (2) dont have a different number of variables, the R-squared gives you the same result. Given that the 2 models were estimated with practically the same variables, only a different functional form, there is no need to worry about introducing bias or the like (a priori it is not clear that the linearity assumption in the specification in column (1) is more reasonable than the one in column (2). 4) To evaluate whether the regressions are BLUE we want to consider whether the 5 Gauss- Markov assumptions are reasonable for this regression: Linearity assumption: While we could potentially hypothesize that there might be decreasing effects of age and size, linearity can be argued to be reasonable as a first approximation. Moreover, the second regression allows for decreasing returns in size. Random sampling assumption: Although the survey was conducted on a random sample of 4000 firms, the regression only shows 1921 observations (1915 in second column). This makes us suspicious, as it is highly likely that the reason for this drop in observations, is the unwillingness of many firms to answer the question about informal payments. Given that those that dont want to answer is probably not a random sample, the remaining sample is probably not random. Zero Conditional Mean Assumption: One can imagine many variables that might affect both the independent and the dependent variables. E.g. informal payments to officials might be more common in some sectors/countries than in other, and these sectors/countries might also happen to have bigger firms, or more firms with foreign capital, etc No Perfect Collinearity Assumption: None of the independent variables is a linear combination of the other. Indeeed, given that an estimation of the model was obtained, we know there cant have been perfect collinearity. 2 Homoscedasticity assumption: One might doubt whether the variance of the error terms is constant for different levels of age. It is not impossible to imagine that all young firms might report rather similar shares of informal payment, but there is more variation for older...
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