PanelDataProblemSet7

PanelDataProblemSet7 - 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 page:www.stern.nyu.edu/~wgreene Office Hours: TR, 3:00 - 5:00 Email: wgreene@stern.nyu.edu URL for course web page: www.stern.nyu.edu/~wgreene/Econometrics/PanelDataEconometrics.htm Assignment 7 Under Construction This assignment uses the German health care data that we have used in class. You can download the data set from the course website in the form of an Excel spreadsheet, at http://www.stern.nyu.edu/~wgreene/Econometrics/healthcare.xls You should be able to import this into Stata, SAS, etc. If you are using LIMDEP or NLOGIT, you can download the files in project format that you can load directly, at http://www.stern.nyu.edu/~wgreene/Econometrics/healthcare.lpj Department of Economics
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Part I. Random Effects Poisson Model The Poisson model for a panel of data may be formulated Prob[Y it = y it ] = exp(- λ it ) λ it yit / y it ! Note, it’s usually convenient to write the factorial as Γ (y it +1) where Γ is the gamma function. We’ll use the usual loglinear specification λ it = exp( β′ x it ). Consider now a random effects model, λ it = exp( β′ x it + w i ) Rather than using a normal distribution, we will suppose that w i is distributed as ‘log-gamma.’ That is, exp(w i ) has a gamma density. Denote exp(w i ) as u i . Note that λ it = exp(w i ) exp( β′ x it ) = u i φ it We will assume u i has mean 1 – this is the same as assuming the mean of u i in more familiar cases equals zero. We then have u i ~ Gamma( θ , θ ) (That is gamma with parameters θ and θ , so the mean is θ / θ = 1.) Thus, f ( u i ) = [ θ θ / Γ ( θ )]u i θ -1 exp(- θ u i ), u i > 0 With this in place, then P ( y it |u i ) = exp(- u i φ it )(u i φ it ) yit / y it ! What is the marginal distribution of y
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This note was uploaded on 01/05/2012 for the course B 55.9912 taught by Professor Willamgreene during the Fall '11 term at NYU.

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PanelDataProblemSet7 - Department of Economics Econometric...

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