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# ADDITIONAL PROBLEMS FOR FIRST EXAM ECON 8840

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This 3 page Study Guide was uploaded by Jamie Lee on Monday March 28, 2016. The Study Guide belongs to ECON 8840 at Georgia State University taught by BHATT in Spring 2016. Since its upload, it has received 17 views. For similar materials see APPLIED STAT & ECONOMETRICS II in Economcs at Georgia State University.

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Date Created: 03/28/16

Chapter 9 Additional Problems 6 7 9.1 There is functional form misspecification if , 0, where these are the estimated parameters on ceoten and comten , respectively. Therefore, we test the joint significance of these variables using the R-squared form of the F test: F = [(.375 .353)/(1 .375)][(177 – 8)/2] 2.97. With 2 and df, the 10% critical value is 2.30 awhile the 5% critical value is 3.00. If we choose alpha=10%, we conclude there is some slight evidence of functional form misspecification. 9.2 (i) The coefficient on voteA88 implies that if candidate A had one more percentage point of the vote in 1988, she/he is predicted to have only .067 more percentage points in 1990. Or, 10 more percentage points in 1988 implies .67 points, or less than one point, in 1990. The t statistic is only about 1.26, and so the variable is insignificant at the 10% level against the positive one-sided alternative. (The critical value is 1.282.) Therefore, what we are finding is that, controlling for being the incumbent, the percent of the vote received in 1988 does not have a strong effect on the percent of the vote in 1990. ii) Naturally, the coefficients change, but not in important ways, especially once statistical significance is taken into account. For example, while the coefficient on log(expendA) goes from .929 to .839, the coefficient is not statistically or practically significant anyway (and its sign is not what we expect). The magnitudes of the coefficients in both equations are quite similar, and there are no sign changes. This is not surprising given the insignificance of voteA88. Additional Problem: Make sure you review the proof of how is biased when there is classical measurement error in one of your dependent variables. Slide 24 from Chapter 9 lecture notes. Chapter 10 Additional Problems 2 R 10.4 We use the R-squared form of the F statistic (and ignore the information on ). The 10% critical value with 3 and 124 degrees of freedom is about 2.13 (using 120 denominator df in Table G.3a). The F statistic is F = [(.305 .281)/(1 .305)](124/3) 1.43, which is well below the 10% critical value. Therefore, the event indicators are jointly insignificant at the 10% level. 10.6 K (i) Given =j + 0 j + 1 j for2j = 0,1, ,4, we can write y = + z + ( + + )z + ( + 2 + 4 )z + ( + 3 + 9 )z t 0 0 t 0 1 2 t-1 0 1 2 t-2 0 1 2 t-3 + ( 0 4 + 11 )z 2 t-4+ u t = +0 (z 0 zt t-1+ z t-2+ z t-3+ z t-4 (z1 t-1+ 2z t-2+ 3z t-3 4z )t-4 + 2z t-1 4z t-2+ 9z t-3+ 16z ) t-4 . t (ii) Define three new variables: z = (z + zt0 t t-1 z t-2+ z t-3+ z t-4z =t1z t-1+ 2z t-2+ 3z t-3+ 4z )t-4nd z = (zt2 t-1+ 4z t-2+ 9z t-3+ 16z ).t-4en, , , 0 , 0nd1 are obt2ined from the OLS regression of y on z , zt, and t0, t1 t2 (iii) The unrestricted model is the original equation, which has six parameters ( 0 and the five ). The PDL model has four parameters. Therefore, there are two j restrictions imposed in moving from the general model to the PDL model. The df in the unrestricted model is n – 6. Therefore, we would obtain the unrestricted R- 2 Rur K squared, from the regression of y on z ,tz , t t-1 , zt-4and the restricted R-squared 2 R r from the regression in part (ii), . The F statistic is (R R ) (n6) F ur r . (1R )ur 2 Under H and0the CLM assumptions, F ~ F 2,n-6 10.8(part i only) (i) Strict exogeneity implies that the error at time t, u , is uncorrelattd with the regressors in every time period: current, past, and future. Sequential exogeneity states that u is utcorrelated with current and past regressors, so it is implied by E(u |...,x ,x ,x ,...) 0 t t1 t t1 strict exogeneity. More explicitly, strict exogeneity is , and (...,xt1 ,xt,.t1 (x tx t1.) so u conditional on any subset of , including , also has a t zero conditional mean.

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