Problem3

# Problem3 - Department of Economics ECONOMETRICS I...

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ECONOMETRICS I Assignment 3: Asymptotics Professor William Greene Phone: 212.998.0876 Office: KMC 7-90 Home page:ww.stern.nyu.edu/~wgreene Office Hours: Open Email: [email protected] URL for course web page: www.stern.nyu.edu/~wgreene/Econometrics/Econometrics.htm Part I. Econometric Theory 1. We have examined in great detail the least squares estimator of the parameter vector β in the linear regression model, E[ y | x ] = x ′β . We have also encountered the least absolute deviations estimator, which is an estimator of the parameter vector β in the model Med( y | x ) = x ′β . Rather than use least squares, we use linear programming methods to compute the estimator of β . Suppose the model is changed to a “quantile regression” which states Q ( y | x , α ) = x ′β ( α ), where α is a specific quantile. For example, the case of α = .5 is the median regression just noted. The quantile regression estimator can be computed for any α ; it is done by linear programming methods. Discuss how the researcher will obtain an estimator of the asymptotic covariance matrix for this estimator. 2. Suppose b is an estimator of a regression coefficient vector. The asymptotic covariance matrix for b is V. Now, we are going to compute a function of b , g ( b ). The delta method and Krinsky and Robb are two methods of estimating the asymptotic variance of g ( b ). Describe these two methods in detail, and distinguish between them. 3. Prove that the least squares estimator of β in the linear regression model is consistent. What assumptiona are needed to complete your proof? Department of Economics

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Part II. Applications The following exercises use the gasoline data which we have used at various points before. The data are posted on the course web page in the file gasoline.csv. All variables in all regressions discussed below are assumed to be logarithms.
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## This note was uploaded on 01/05/2012 for the course B 30.3351 taught by Professor Williamgreene during the Fall '11 term at NYU.

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Problem3 - Department of Economics ECONOMETRICS I...

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