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Homework 2 1. Finish this problem from before: [From Wool C5.3] Suppose you are interested in the effect of parental education on child birthweights. a. Conduct an F test for whether or not parental education (both mother and father) are jointly significant. What is the test statistic? How is it distributed? What do you conclude and why? b. Now construct an LM test of whether motheduc and fatheduc are jointly significant. [NOTE: In obtaining the residuals for the restricted model, be sure that the restricted model is estimated using only those observations for which all the variables in the unrestricted model are available.] 2. Finish the Fundamental Econometrics Concepts review and make any edits to your previous answers as requested. (See Homework 1.) 3. [Based on Wool C8.4] Use the data in VOTE1.RAW to estimate the following equation: voteA = βo + β1prtystrA+ β2democA+ β3log(expendA) + β4log(expendB) + u (a) First estimate the equation by OLS. Please include your log file in your homework so I can correct mistakes in your commands. (b) Obtain the predicted OLS residuals. Regress these on all of the independent variables. Explain why you obtain R2 = 0 (c) Now estimate the model with heteroskedasticity-robust standard errors. Discuss any differences with (a). (d) Compute the Breusch-Pagan test for heteroskedasticity. You can calculate either the F or the LM statistic version. Please calculate this using the steps described in class—do not just use the STATA command to conduct this test. How do you interpret the results of this test? (e) Compute the special case of the White test for heteroskedasticity. How strong is the evidence for heteroskedasticity now? 4. Show that the estimated coefficient and estimated errors in this 2 variable regression model: (𝑦𝑖 ) = 𝛽̂0 + 𝛽̂1 (𝑥𝑖 ) + 𝑢̂𝑖 are equivalent to those in this model: (𝑦𝑖 − 𝑦̅) = 𝛽̂1 (𝑥𝑖 − 𝑥̅ ) + 𝑢̂𝑖 If you need to draw on other assumptions/properties of the OLS estimator in your derivation, state these.