연세대 계량경제학 족보 econo1 fall final exam

Final Exam for Econometrics(1)
Fall 2014
Prof. Tae-Hwan Kim

1. [33 points] Consider a simple regression given by where is the number of observations. Now, the unit of the explanatory variable () has changed so that the new explanatory variable (denoted by ) is related to as where is a constant between 0 and 1. Using the new explanatory variable, the same regression is re-run resulting in the following output: . Decide which of the following is changed and which is not; (i) the intercept OLS estimator, (ii) the slope OLS estimator. Explain your reasoning.

2. [33 points] Consider ; where and are vectors given by and we don’t know if is normally distributed. Suppose that all the asymptotic assumptions are true. We are interested in the following null hypothesis: . You have learned that the asymptotic Wald statistic (given by ) converges to in distribution. Prove or disprove that converges to zero in probability where is the R-square obtained from…