# PanelDataMidterm2009-Answers - Department of Economics...

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Econometric Analysis of Panel Data Spring  2009 – Tuesday, Thursday:  1:00 – 2:20 Professor William Greene  Phone: 212.998.0876 Office: KMC   7-78                    Home page:www.stern.nyu.edu/~wgreene Office Hours: When the door is open Email: [email protected]       www.stern.nyu.edu/~wgreene/Econometrics/PanelDataEconometrics.htm Midterm Examination Solutions This examination has four parts. Weights applied to the four parts will be 15, 15, 20 and 50. 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. Fixed and random effects are two approaches to modeling unobserved heterogeneity in a model such as y it = β ′x it + c i + ε it . where c i is taken to be the time invariant, unobserved heterogeneity. The approaches are distinguished by their assumptions about the relationship between c i and x it . In particular, the “fixed effects” approach is a nonparametric treatment in which it is assumed that E[c i | x i1 ,...,x iT ] may be a function of at least one observation on x it . I.e., the conditional mean is not a constant. Under the random effects specification, it is assumed that E[c i | x i1 ,...,x iT ] = μ , a constant that does not vary with x it for any t. This is a semiparametric formulation in which the model typically goes on to assume that c i is a homoscedastic random variable with zero mean (assuming that x it now contains a constant term). The benefit of the fixed effects model is its semiparametric approach. No further assumptions about the distribution of c i is needed. The disadvantage is that in order to estimate the model as such, we require a new variable and a new parameter for each individual in the sample. When we turn to nonlinear models, this disadvantage will show up again in the form of the “incidental parameters problem,” which is a persistent bias in the conventional estimator of the parameters of the model. The fixed effects approach also precludes any other time invariant variables in the model. The advantage of the random effects model is its very tight formulation. The entire model is built around a single new parameter. The disadvantage is the need to assume that u i is uncorrelated with x it . This assumption is likely to be violated in models involving microeconomic data.

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