Question

Question 1: Jason and Vincent are two economists who work on questions of economic history. They are interested in knowing if there were statistically significant differences in wages between anglophones and francophones male workers aged between 15 and 50 (relative to anglophones) in Quebec between 1901 and 1921. No other groups are included. To make their tests, they collected samples from the censuses of 1901, 1911 and 1921. Their variable for education is whether or not a person was able to read and write. They also argue that age would be a factor in determining wages as it is well-known that younger workers earn less than prime-age workers but earn roughly the same as older workers. They are four different linguistic groups: i) Unilingual Native French Speaker; ii) Bilingual Native French Speaker; iii) Unilingual Native English Speaker; iv) Bilingual Native English speaker. They coded a dummy variable for each of these four linguistic groups. Their regressions take the following form: In(wages) = b + b, Age, + b, Age? + b2ReadWrite + b MonthsSpentAtCurrentJob + b UnilingualFrench + beBilingualFrench + b UnilingualEnglish + b BilingualEnglish + e Below is a partial print out of what the data looked like. 1 Wages Age 2 11.11 16.24 Age2 ReadWrite MonthsSpentatCurrentJob UnilingualFrench BilingualFrench Unilingual English Bilingual English 28784 In writing that regression, they made a blatant violation of Gauss-Markov assumptions. Which of the following is it? (The partial look at the data above and the equation will tell all that you need to know). A) Non-zero conditional mean B) Non-constant variance of errors C) Serially correlated errors D) Mean of errors is non-zero E) Perfect multicollinearity F) None of the above

Answer 1

The assumption regarding multicollinearity is violated in the above regression. There are four linguistic groups as explained. To captur the impact of linguistic groups 3 indicator variables would be sufficient in the presence of the intercept. If they consider all four indicator variables, then the intercept needs to be dropped from the regression. Because of inclusion of all four indicator variables, the linear combination of these indicator variables is equal to the intercept. As a result of shich there would be dummy variable trap. In such a case, they will not be able to estimate all four coefficients corresponding to the linguistic indicator variables along with the intercept. Hence, option E is the correct answer.