Problem2

Problem2 - Department of Economics ECONOMETRICS I...

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ECONOMETRICS I Assignment 2 Professor William Greene Phone: 212.998.0876 Office: KMC 7-90 Home page: www.stern.nyu.edu/~wgreene Email: wgreene@stern.nyu.edu Course web page: www.stern.nyu.edu/~wgreene/Econometrics/Econometrics.htm Part I. Econometric Theory 1. Prove e e increases when a restriction, R β = q , is imposed on the regression coefficients 2. Show how to do constrained least squares regression entirely using matrix algebra, not your software's built-in regression procedures. That is, what computations would you do to compute a constrained least squares estimator. Part II. Applications of Hypothesis Testing The data sets for these applications are posted on the course home page, in the Problems page, as .csv files. 1. This part of the exercise is based on the gasoline data, which you can download from the Problem Sets page of the course website. Using nlogit, you can get started by reading the data with IMPORT;file=…$ a. Estimate by least squares a version of the regression model of which looks as follows: logG = β 1 + β 2 (log GasP up to 1973, 0 else) + β 3 (log GasP after 1973, 0 else) + β 4 log PCIncome + β 5 ( YEAR - 1952) + ε . b. Now, use least squares to fit the coefficients of the model logG = β 1 + β 2 log GasP + β 3 (log GasP after 1973, 0 else) + β 4 log PCIncome + β 5 ( YEAR - 1952) + ε Report the least squares coefficients for both cases. Could you have computed the second least squares regression from the first one? If so, show how, algebraically. If not, why not? Describe this "model" in terms of the relationship between price and quantity that it implies. c. We now examine whether the three aggregate price indexes, PD = durables price, PN = nondurbles price, PS = services price, are significant explanatory variables in the equation. Add logPD, logPN and logPS to your regression in part b. Report the results. Now, test the hypothesis that the coefficients on the three variables are all zero. Use an F test and a Wald test. Department of Economics
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2. Using the health care data, carry out a chow test for whether different regressions apply for men and women, using this model for log of income, log(hhninc) = β 1 + β 2 Age + β 3 Educ + β 4 Married + β 5 Hhkids + ε . Carry out the chow test using the standard F test. Now, add at least one variable to the model and carry out the test again with your expanded model. Report all relevant results. 3.
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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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Problem2 - Department of Economics ECONOMETRICS I...

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