This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Econ 103 UCLA, Fall 2010 Problem Set 3 Solutions by Anthony Keats and Sarolta Lacz Part 1: True or False and explain briefly why. 1. The assumption that E ( u i  X i = x i ) = 0 says that the expected value of u i changes depending on the value of X i . FALSE . This assumption says that the expected value of u i does not change depending on the value of X i , that is, X i and u i are uncorrelated. This is the first assumption of OLS. If E ( u i  X i = x i ) 6 = 0 , then X i and u i are correlated and the coefficient b associated with this regressor will be inconsistent. 2. If Cov ( X i ,u i ) > , then the OLS estimator 1 will tend to be higher than 1 . TRUE . To see this, refer to the formula for omitted variable bias: b 1 p 1 + X,u u X and to the forumula for the correlation coefficient : X,u = Cov ( X i ,u i ) X u Substituting into the first equation we have: b 1 p 1 + Cov ( X i ,u i ) 2 X Since the term in the denominator is just the variance of X i , it is always positive. Thus, if Cov ( X i ,u i ) > the direction of the bias will be positive as well. 3. Consider an omitted variable V i that is negatively correlated with X i . Also suppose that V i positively affects Y i . Then the OLS estimator 1 is negatively biased. TRUE . Since V i is omitted from the regression, it enters the error term u i . The formula given above (question 2) for the omitted variable bias tells us that when X,u < then the OLS estimator b 1 will be negatively biased. 4. Suppose you run a regression and obtain the estimate 1 = 3 . 4 . STATA tells you that the tstatistic for the null hypothesis that 1 = 0 is equal to 1.7. This implies that SE ( 1 ) is equal to 2. TRUE . The equation for the tstatistic is: t = b 1 1 , SE ( b 1 ) 1 Econ 103 UCLA, Fall 2010 where 1 , is the value under the null. In this case the null hypothesis is 1 , = 0 so the equation becomes: t = b 1 SE ( b 1 ) and rearranging this gives us: SE ( b 1 ) = b 1 t = 3 . 4 1 . 7 = 2 5. In the regression model Y i = + 1 Female i + 2 Education i + u i , 1 represents the intercept for females. FALSE . + 1 represents the intercept for females. The coefficient 1 on the dummy Female i represents the difference between the intercept for males and the intercept for females. 6. In the regression model Y i = + 1 Female i + 2 Education i + 3 Education i Female i + u i , 2 + 3 represents the return to education for females. TRUE . 2 + 3 represents the change in Y i associated with a marginal change in Education for females. 1 represents the associated change in Y i given a marginal change in Education for men. As with the intercept coefficients in the previous question, 3 represents the difference between men and women in the return to education 7. Under perfect multicollinearity, the OLS estimator cannot be computed....
View
Full
Document
This note was uploaded on 09/23/2011 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.
 Spring '07
 SandraBlack

Click to edit the document details