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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) t...

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 fr…(투비컨티뉴드 ) om the regression of on .

3. [34 points] Consider the following DGP where all the asymptotic assumptions hold. Suppose that without knowing the true DGP, we run the following regression:
.
That is, the 2nd explanatory variable ( ) was omitted. Suppose that it is known that Are the OLS estimators consistent for respectively Say ‘Yes’ or ‘No’ first and then try to justify your answers.










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