PanelDataProblemSet4 - Department of Economics Econometric...

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Econometric Analysis of Panel Data Professor William Greene Phone: 212.998.0876 Office: KMC 7-78 Home Office Hours: TR, 3:00 - 5:00 Email: [email protected] URL for course web page: Assignment 4 Parameter Heterogeneity in Linear Models: RPM and HLM The estimation parts of this assignment will be based on the Baltagi and Griffin gasoline market and the Cornwell and Rupert labor market data sets that are posted on the course website. We will begin with the gasoline market.The basic linear regression model in use will be y it = β 1 + β 2 x it ,1 + β 3 x it ,2 + β 4 x it ,3 + w it where and i = 1,…,18 OECD countries t = 1,…,19 years (1960 to 1978). y it = lgaspcar = log of per capita gasoline use x it ,1 = lincomep = log of per capita income x it ,2 = lrpmg = log of gasoline price index x it ,3 = lcarpcap = log of cars per capita w it = a disturbance that may have have both permanent (time invariant) components and time varying components, and may, under some circumstances, be correlated with x it . Denote x it = (1, x it ,1 , x it ,2 , x it ,3 ) and X i = the 19 × 4 matrix containing all the data on x it for country i . Department of Economics
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Part I. Parameter Variation in the Gasoline Market A. Homogeneous parameters : To begin, we assume that all parameters, including the constant term, are homogeneous across countries and through time and that w it = ε it , a classical zero mean, homoscedastic disturbances. 1. Under these assumptions, what are the properties of the pooled OLS estimator? 2. Estimate the parameters of the model using OLS and report your results. 3. As a first cut at assessing whether the assumptions are correct, compute the robust, cluster (country) corrected standard errors for the least squares estimator. Do they appear to be the same, or close to the same, as the uncorrected OLS standard errors? What do you conclude about the disturbances in the equation? B. Heterogeneous Constant Terms : Now, consider fixed and random effects formulations of the model. We write the model as y it = β 1 i + β 2 x it ,1 + β 3 x it ,2 + β 4 x it ,3 + ε it where β 1 i = β 1 + u i and E[ u i ] = 0. Thus, this is a model with a random constant term. By substituting the second equation into the first, you can see that it is the “effects” model we have discussed in class.
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PanelDataProblemSet4 - Department of Economics Econometric...

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