Econometrics Lab exercises-Chapter 4 Exercises on...
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Econometrics Lab exercises-Chapter 4 Exercises on Heteroskedasticity 2.1) (Ex. 8.6 Wooldridge). Use the data in SLEEP75.RAW to estimate the following sleep equation: sleep = β 0 + β 1 totwrk + β 2 educ + β 3 age + β 4 age 2 + β 5 yngkid + β 6 male + u. (i) Write down a model that allows the variance of u to differ between men and women. The variance should not depend on other factors. (ii) Estimate the parameters of the model for heteroskedasticty. (You have to estimate the sleep equation by OLS, first, to obtain the OLS residuals.) Is the estimated variance of u higher for men or for women? (iii) Is the variance of u statistically different for men and for women? 2.2) (Ex. 8.7 Wooldridge). (i) Use the data in HPRICE1.RAW to obtain the heteroskedasticity-robust standard errors for equation: price = β 0 + β 1 lotsize + β 2 sqrft + β 3 bdrms + u (1) (ii) What does this example suggest about heteroskedasticity and the transformation used for the dependent variable? 2.3) (Ex. 8.9 Wooldridge). Use VOTE1.RAW for this exercise. (i) Estimate a model with voteA as the dependent variable and prtystrA, democA, log (expendA), and log (expendB) as independent variables. Obtain the OLS residuals, ˆ u i , and regress these on all of the independent variables. Explain why you obtain R 2 = 0. (ii) Now compute the Breusch-Pagan test for heteroskedasticity. Use the F statistic version and report the p-value. (iii) Compute the special case of the White test for heteroskedasticity, again using the F statistic form. How strong is the evidence for heteroskedasticity now? 2.4) (Ex. 8.11 Wooldridge). With the data CRIME1.RAW we have estimated a linear probability model (LPM) whose dependent variable is arr86. It takes the value 1 if a young was arrested in 1986 and 0 otherwise: arr86 = β 0 + β 1 pcnv + β 2 avgsen + β 3 tottime + β 4 ptime86 + β 5 qemp86 + u. (2) (i) Estimate this model by OLS and verify that all fitted values are strictly between zero and one. What are the smallest and largest fitted values? (ii) Estimate the equation by weighted least squares. (iii) Use the WLS estimates to determine whether avgsen and tottime are jointly significant at the 5 % level. 1
Transcript of Econometrics Lab exercises-Chapter 4 Exercises on...
Econometrics
Lab exercises-Chapter 4
Exercises on Heteroskedasticity
2.1) (Ex. 8.6 Wooldridge). Use the data in SLEEP75.RAW to estimate the following sleepequation:
sleep = β0 + β1totwrk + β2educ + β3age
+ β4age2 + β5yngkid + β6male + u.
(i) Write down a model that allows the variance of u to differ between men and women. Thevariance should not depend on other factors.
(ii) Estimate the parameters of the model for heteroskedasticty. (You have to estimate the sleepequation by OLS, first, to obtain the OLS residuals.) Is the estimated variance of u higherfor men or for women?
(iii) Is the variance of u statistically different for men and for women?
2.2) (Ex. 8.7 Wooldridge).
(i) Use the data in HPRICE1.RAW to obtain the heteroskedasticity-robust standard errors forequation:
price = β0 + β1lotsize + β2sqrft + β3bdrms + u (1)
(ii) What does this example suggest about heteroskedasticity and the transformation used for thedependent variable?
2.3) (Ex. 8.9 Wooldridge). Use VOTE1.RAW for this exercise.
(i) Estimate a model with voteA as the dependent variable and prtystrA, democA, log(expendA),and log(expendB) as independent variables. Obtain the OLS residuals, ui, and regress theseon all of the independent variables. Explain why you obtain R2 = 0.
(ii) Now compute the Breusch-Pagan test for heteroskedasticity. Use the F statistic version andreport the p-value.
(iii) Compute the special case of the White test for heteroskedasticity, again using the F statisticform. How strong is the evidence for heteroskedasticity now?
2.4) (Ex. 8.11 Wooldridge). With the data CRIME1.RAW we have estimated a linear probabilitymodel (LPM) whose dependent variable is arr86. It takes the value 1 if a young was arrested in1986 and 0 otherwise:
arr86 = β0 + β1pcnv + β2avgsen + β3tottime + β4ptime86 + β5qemp86 + u. (2)
(i) Estimate this model by OLS and verify that all fitted values are strictly between zero andone. What are the smallest and largest fitted values?
(ii) Estimate the equation by weighted least squares.
(iii) Use the WLS estimates to determine whether avgsen and tottime are jointly significant atthe 5 % level.
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