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Homework 3 Solutions

# Homework 3 Solutions - Mehmet Soytas Wednesday Applied...

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Mehmet Soytas Applied Econometrics I, Summer, 2009 Wednesday, May 27, 2009 (due: Wednesday, June 03, 2009) Homework Assignment 3 1. State whether the following statements are TRUE or FALSE (Provide an explanation in either case). a. When there are omitted variables in the regression, which are determinants of the dependent variable, then the OLS estimator is biased if the omitted variable is correlated with the included variable. TRUE. Remember the two conditions for omitted variable bias to be present in the OLS estimates. If omitted variable is both a determinant of the dependent variable and is correlated with the other variables in the regression. b. Imagine you regressed earnings of individuals on a constant, a binary variable (°Male±) which takes on the value 1 for males and is 0 otherwise, and another binary variable (°Female±) which takes on the value 1 for females and is 0 otherwise. Because females typically earn less than males, you would expect the coe¢ cient for Male to have a positive sign, and for Female a negative sign. FALSE. You can not include the binary variable (°Male±) and binary variable (°Fe- male±) in the same regression if you include a constant. Since in this case you will not be able to estimate the OLS estimates due to Perfect Multicollinearity. c. When you have an omitted variable problem, the assumption that E ( u i j X i ) = 0 is violated. This implies that the OLS estimator is no longer consistent. TRUE. Omitted variable problem arises because omitted variables are correlated with the independent variables already in the regression. When you estimate OLS without adding the omitted variables, you actually assume that they are in the error term u i . Since in this case because of the correlation between omitted variable and the independent variables, the error term and the independent variables become correlated which implies E ( u i j X i ) 6 = 0 . d. You have to worry about perfect multicollinearity in the multiple regression model because OLS estimates will be always upward biased. FALSE. First of all, it is true that you have to worry about perfect multicollinearity in the OLS Regression, but due to a completely di/erent reason than upward biased estimates. The 4 th assumption of the Multiple Regression is that there is no perfect multicollinearity. If it exists, then you can not estimate OLS. e. In the multiple regression model, the least squares estimator is derived by minimizing the sum of squared errors. TRUE. That is the de²nition of least squares estimation and it does not depend on how many independent variables you have. f. One of the least squares assumptions in the multiple regression model is that you have random variables which are °i.i.d.±This stands for independently and identically distributed.

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