Midterm2007Answers

Midterm2007Answers - Department of Economics Econometric...

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1 Econometric Analysis of Panel Data Spring 2007 – Tuesday, Thursday: 1:00 – 2:20 Professor William Greene Midterm Examination This examination has four parts. Weights applied to the four parts will be 15, 15, 30 and 40. This is an open book exam. You may use any source of information that you have with you. You may not phone or text message or email or Bluetooth (is that a verb?) to “a friend,” however. Part I. Fixed and Random Effects Define the two basic approaches to modeling unobserved effects in panel data. What are the different assumptions that are made in the two settings? What is the benefit of the fixed effects assumption? What is the cost? Same for the random effects specification. Now, extend your definitions to a model in which all parameters, not just the constant term, are heterogeneous. For the random parameters case, describe the estimators that one would use under the two assumptions. Two approaches are fixed effects and random effects. In the “effects model,” y it = x it β + c i + ε it , x it is exogenous with respect to ε it . FE: c i may be correlated with x it . Benefits: General approach, Robust – estimator of β is consistent even if RE is the right model. Cost: Many parameters, inefficient if RE is correct. Precludes time invariant variables. RE: c i is uncorrelated with x it Benefits: Tight parameterization – only one new parameter Efficient estimation – use GLS Allows time invariant parameters Cost Unreasonable orthogonality assumption Inconsistent if RE is the right model. Random parameters case. Replace the model statement with y it = x it β i + ε it , β i = β + w i . C a s e 1 : w i may be correlated with x it . This is the counterpart to FE. In this case, it is necessary to fit the equations one at a time. Requires that there be enough observations to do so, so T > K. The efficient estimator is equation by equation OLS. Same benefits (robustness) and costs (inefficiency) as FE C a s e 2 ; w i is uncorrelated with x it . This RP model can be fit An efficient estimator will be the matrix weighted FGLS estimator. (Swamy et al.) This would be a two step estimator, just like FGLS for the RE model. This model can also be fit by simulation – we mentioned this briefly in class, and Department of Economics
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2 will return to it later this semester. Part II. Minimum Distance Estimation I have data on 10 firms for 25 years of production. Variables are y it = log of value added, and x it = (log K it , log L it , log E it ) where K , L and E are capital, labor and energy. I also have a variable d it which equals 1 if the firm is in a service industry and 0 if the firm is a manufacturing firm. Note that d it is time invariant. The model I propose is y it = α i + x it β + δ d it + ε it where E[ ε it | x js , d js ] = 0 for all i , t and j,s .
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Midterm2007Answers - Department of Economics Econometric...

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