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# ps5 - Problem Set 5 Introduction to Econometrics Fall 2006...

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Problem Set 5 Introduction to Econometrics - Fall 2006 Due Date: Thursday, November 30th, BEFORE CLASS. Each student is responsible for handing one handwritten solution. If working in groups, indicate the members of the group (to facilitate grading). PLEASE SHOW YOUR WORK . 1. The following multiple regression function was estimated from a random sample of 2000 observations: b Y i = 10 . 9 (2 . 3) + 2 . 35 (0 . 99) X 1 i + 1 . 07 (0 . 61) X 2 1 i + 1 . 32 (0 . 44) X 2 i R 2 = 0 . 26 This function is quadratic in X 1 , and linear in X 2 . Assume that all the least squares assumptions hold. a. What is the predicted change in Y i when X 1 i increases by 1 unit and X 2 i is constant? Does it depend on the value of X 1 i ? Does it depend on the value of X 2 i ? b. Is the coef fi cient on the squared term ( X 2 1 i ) statistically signi fi cant at the 5% signi fi cance level? Can we say that this nonlinear model improves upon a linear model? Explain. c. From the same random sample, you estimate the following multiple regression function: b Y i = 11 . 5 (1 . 9) + 2 . 21 (0 . 89) X 1 i + 1 . 17 (0 . 41) X 2 i + 1 . 23 (0 . 47) X 1 i X 2 i R 2 = 0 . 32 which includes an interaction term between the regressors. What is the predicted change in Y i when X 1 i increases by 1 unit and X 2 i is constant in this case? Does it depend on the value of X 1 i ? Does it depend on the value of X 2 i ? d. Is the coef fi cient on the interaction term ( X 1 i X 2 i ) statistically signi fi cant at the 5% signi fi cance level? Can we say that the nonlinear model improves upon a linear model in this case? Explain. 2. From a random sample of 5000 observations you estimated the following quadratic regression function: b Y i = 2 . 52 (0 . 96) + 1 . 47 (0 . 54) X i + 1 . 01 (0 . 38) X 2 i R 2 = 0 . 51 Assume that the least squares assumptions hold. a. Use hypothesis testing to check whether the quadratic model improves upon the linear model. Use a 1% signi fi cance level. Is the quadratic speci fi cation appropriate? (Recall that the critical value for a 1% signi fi cance level test is 2 . 58 ) b. From the same random sample used to estimate the quadratic regression function, you estimate the following log-linear regression function: \ ln ( Y i ) = 1 . 28 (0 . 51) + 0 . 39 (0 . 11) X i R 2 = 0 . 43

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