hw02_answer_econ120b_su06 - Economics 120B Professor Yongil...

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Economics 120B Name: _________________________ Professor Yongil Jeon Summer 2006 Student ID#: _________________________ Answer to Homework #2, Summer 2006 (Exam 2, Summer 2005) 1-a. (5 points) A nonlinear function a. makes little sense, because variables in the real world are related linearly. b. can be adequately described by a straight line between the dependent variable and one of the explanatory variables. c. is a concept that only applies to the case of a single or two explanatory variables since you cannot draw a line in four dimensions. d. is a function with a slope that is not constant. Answer : d 1-b. (5 points) An example of a quadratic regression model is a. 2 01 2 ii YX Y u ββ β =+ + + . b. ln( ) u + . c. 2 2 X u + + . d. 2 u + . Answer : c 1-c. (5 points) In the case of the simple regression model Y i = 0 + 1 X i + u i , i = 1,…, n , when X and u are correlated, then a. the OLS estimator is biased in small samples only. b. OLS and 2SLS produce the same estimate. c. X is exogenous. d. the OLS estimator is inconsistent. Answer : d 1-d. (5 points) Having more relevant instruments a. is a problem because instead of being just identified, the regression now becomes overidentified. b. is like having a larger sample size in that more information is available for use in the IV regressions. c. typically results in larger standard errors for the 2SLS estimator. d. is not as important for inference as having the same number of endogenous variables as instruments. Answer : b

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2 Answer to HW #2, ECON 120B, Summer 2006 2 2. (25 points) Based on data from sixty-three countries, the following model was estimated by least squares: ) 042 . 0 ( ) 019 . 0 ( 17 . 0 , 005 . 0 052 . 0 058 . 0 2 2 1 = = R X X Y i where Y = Growth rate in real gross domestic product 1 X = Real income per capita 2 X = Average tax rate, as a proportional of gross national product Note that 66 . 2 005 . 0 , 60 = t , 296 . 1 1 . 0 , 60 = t , and . 98 . 4 ) 01 . 0 , 60 , 2 ( = F (a) (5 points) Test against a two-sided alternative the null hypothesis that 1 β is 0.
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hw02_answer_econ120b_su06 - Economics 120B Professor Yongil...

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