﻿਍ഀ ਍ഀ ਍ഀ ਍ഀ ਍ഀ Heteroscedasticiy਍ഀ ਍ഀ ਍ഀ ਍ഀ ਍ഀ ਍ഀ ਍ഀ
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## Heteroscedasticity Homework

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Practice

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For this problem set use the dataset਍ഀ on home characteristics and prices. The data description can also be਍ഀ downloaded.

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1. Local government and public schools are largely financed by property਍ഀ taxes. One's property tax bill is based on the tax rate and the assessed value਍ഀ of the house. From time to time the local tax authority must revise the਍ഀ assessed values of houses in the jurisdiction. To bring some regularity to the਍ഀ re-assessment process the authority often uses regression models. The dataset਍ഀ hprice1.wf1 has data on assessed value and house attributes. It is your job to਍ഀ help with the modeling of home attributes and assessed value.

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a. Estimate by OLS the regression coefficients of and report your results.

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b. For the same model as that in part a, use EVIEWS to find the਍ഀ heteroscedasticity robust standard errors for the coefficients and report your਍ഀ findings.

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c.Compare and contrast your results for parts a and b.

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d. Use EVIEWS to conduct a Breusch-Pagan test for heteroscedasticity at the਍ഀ 5% level and report your results.

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e. Revise the model to by taking logs of assess, lotsize and sqrft,਍ഀ but not bdrms. Conduct a Breusch-Pagan test for heteroscedasticity at਍ഀ the 5% level.

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f. In reviewing your resutls for aprts d and e, did transforming the data਍ഀ mitigate the heteroscedasticity problem in any way?

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Theory

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2. Consider the linear regression model where the number of observations, n,਍ഀ is equal to 3m.  The first three rows of the X matrix are ,

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and every subsequent group of਍ഀ three rows is identical to this first group.  The error covariance matrix Ω is਍ഀ diagonal, with typical diagonal element equal to , where ω > 0 and x2t਍ഀ is the tth element of the second column of X.

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a. What is the variance of , the OLS estimator of

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b. What is the probability limit, as n →∞, of the ratio of the conventional਍ഀ estimate of this variance, which assumes homoscedasticity, to a਍ഀ heteroscedasticity consistent estimate based on ?

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