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Unformatted text preview: 73-261 Econometrics November 4, 2009 Midterm 2
50 minutes. 50 points. Write answers in the Blue Book. Do not forget to write your name on it. 1. [8 points] The following regression has been run in an attempt to explain savings decisions of people in various socioeconomic groups: savings = β0 + β1income + β2married + β3income*married + u Dataset also included series black, female and ParentEduc. The distribution of variables in the dataset is representative of the general US population. What is a potential issue with this regression? How would it affect the estimates? How would you fix that issue? How would you check whether the issue is present? 2. [5 points] A friend of yours is trying to predict daily stock price movements from previousday movements. Stock price st is a positive real number, and ∆st+1 = st+1 − st. Your friend wants to find the best predictor, and plans to run the following regression: ∆st+1 = β0 + β1∆st + β2(st / st−1) + β3[log(st) − log(st−1)] + β4log(st/st−1) + u Can you anticipate a problem with this regression? What is it? How can it be avoided? 3. [7 points] You have run a regression over 10,000 observations, and the histogram of the fitted ˆ residuals ( U i 's) looks more like Uniform distribution rather than Normal. Your teammate comments that since distribution of residuals is definitely not Normal, you cannot use t-test to check significance of coefficients. Would you agree? If not, what is the property that allows you to use t-test in this situation, what are the necessary assumptions, and what exactly follows from them? 4. [10 points] Recall that cov(f,g) = E[(f−Ef)(g−Eg)], so cov(f,f) = V(f), cov(αf,g) = αcov(f,g) and cov(f,g+h) = cov(f,g) + cov(f,h). 4.a Imagine that y = β0 + β1x + u, (*) and cov(u,x) = 0. Take covariance of x with either side of (*), and solve for β1. Report your result. Call it b1 (Hint: it will be a ratio, and it should look familiar) 4.b Now imagine that cov(u,x) = 1.23. Again, take covariance of x with either side of (*). Solve for b1 ratio that you found in part 4.a. (Hint: you need to divide by something) 4.c Consider turning b1 into in estimator by replacing population moments with sample moments, Would this lead to a biased estimate of β1 under the assumptions of 4.b? Can you say whether bias is positive or negative? Whether is it toward zero or away from zero? 5.[20 points] Yet another attempt to estimate the effect of education on wage has lead to a number of regressions that are presented on the next page, along with commands that generated them. Same set of controls is omitted from each output to save space. Examine these regressions and answer the questions below. Support your answers with values of test statistics as well as p-values or critical values. p-values for t- and F-statistics are reported in the output; critical values for χ2 can be obtained from the table below. Significance level of all tests is 5%. 5.a[5 points] What are the OLS and the IV estimates of the effect of education on wage? Are they significant? 5.b[5 points] What are instruments used for educ? Which of them are relevant? 5.c [5 points] Does the endogeneity test tell us that IV correction was necessary? 5.d [5 points] Does the exogeneity test tell us that instruments are uncorrelated with residual? Note: there was a typo in lecture notes, test statistic for this test is computed as NR2, not just R2. 5% critical values for χq2 q c 1 3.84 2 5.99 3 7.81 4 9.49 5 11.07 6 12.59 7 14.07 8 15.51 9 16.92 10 18.31 ls lwage c educ exper … genr resid01=resid Dependent Variable: LWAGE Included observations: 2220 Variable Coefficient Std. Error C 4.570002 0.087359 EDUC 0.077009 0.004071 EXPER 0.089850 0.007904 R-squared F-statistic Prob(F-stat) 0.272222 54.95971 0.000000 t-Statistic Prob. 52.31293 0.0000 18.91439 0.0000 11.36827 0.0000 ls lwage c resid02 educ exper … Dependent Variable: LWAGE Included observations: 2220 after adjustments Variable Coefficient Std. Error t-Statistic C 4.152228 0.217435 19.09643 RESID02 -0.027685 0.013197 -2.097859 EDUC 0.101750 0.012475 8.155970 EXPER 0.100483 0.009384 10.70785 R-squared F-statistic Prob(F-stat) 0.273673 51.87930 0.000000 Prob. 0.0000 0.0360 0.0000 0.0000 ls educ c nearc4 nearc2 fatheduc motheduc exper … genr resid02=resid forecast educf Dependent Variable: EDUC Included observations: 2220 after adjustments Variable Coefficient Std. Error t-Statistic C 13.64333 0.335418 40.67566 NEARC4 0.260473 0.098390 2.647367 NEARC2 0.018045 0.087154 0.207043 fatheduc 0.111180 0.014597 7.616722 motheduc 0.132483 0.017068 7.762189 EXPER -0.380537 0.038297 -9.936412 R-squared F-statistic Prob(F-stat) 0.486034 115.6326 0.000000 ls resid03 c nearc4 nearc2 fatheduc motheduc exper … Dependent Variable: RESID03 Included observations: 2220 after adjustments Prob. 0.0000 0.0082 0.8360 0.0000 0.0000 0.0000 Variable C NEARC4 NEARC2 fatheduc motheduc EXPER R-squared F-statistic Prob(F-stat) Coefficient Std. Error t-Statistic -0.008334 -0.006502 0.037292 -0.004016 0.004230 -0.000525 0.002652 0.325131 0.996711 0.072067 0.021140 0.018726 0.003136 0.003667 0.008228 -0.115637 -0.307592 1.991473 -1.280567 1.153444 -0.063823 Prob. 0.9080 0.7584 0.0466 0.2005 0.2489 0.9491 ls lwage c educf exper … genr resid03=resid Dependent Variable: LWAGE Included observations: 2220 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 4.152228 0.231538 17.93323 0.0000 EDUCF 0.101750 0.013285 7.659175 0.0000 EXPER 0.100483 0.009993 10.05562 0.0000 R-squared F-statistic Prob(F-stat) 0.176020 31.38819 0.000000 ls resid01^2 c educ exper … Dependent Variable: RESID01^2 Included observations: 2220 Variable Coefficient Std. Error C 0.079842 0.058443 EDUC 0.002981 0.002724 EXPER 0.004811 0.005287 R-squared F-statistic Prob(F-stat) 0.010240 1.520192 0.089537 t-Statistic Prob. 1.366160 0.1720 1.094519 0.2738 0.909915 0.3630 ...
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This note was uploaded on 01/21/2011 for the course ECON 73261 taught by Professor Kyrkv during the Spring '10 term at Carnegie Mellon.
- Spring '10