Nonlinear Panel Data Models Slides

Nonlinear Panel Data Models Slides - WNE 7/30/07 #4 Whats...

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What’s New in Econometrics? Lecture 4 Nonlinear Panel Data Models Jeff Wooldridge NBER Summer Institute, 2007 1. Basic Issues and Quantities of Interest 2. Exogeneity Assumptions 3. Conditional Independence 4. Assumptions about the Unobserved Heterogeneity 5. Nonparametric Identification of Average Partial Effects 6. Dynamic Models 7. Applications to Specific Models 8. Estimating the Fixed Effects 1
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1 . Basic Issues and Quantities of Interest Let  x it , y it : t 1,. .., T be a random draw from the cross section. Typically interested in D y it | x it , c i (1) or some feature of this distribution, such as E y it | x it , c i , or a conditional median. In the case of a mean, how do we summarize the partial effects? If x tj is continuous, then j x t , c m t x t , c x tj , (2) or discrete changes. How do we account for unobserved c i ? If we know enough about the distribution of c i we can insert meaningful values for c . For example, if c E c i , then we can compute the partial effect at the average (PEA) , 2
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PEA j x t j x t , c . (3) Of course, we need to estimate the function m t and c . We might be able to insert different quantiles, or a certain number of standard deviations from the mean. Alternatively, we can average the partial effects across the distribution of c i : APE x t E c i j x t , c i  . (4) The difference between (3) and (4) can be nontrivial. In some leading cases, (4) is identified while (3) is not. (4) is closely related to the notion of the average structural function (ASF) (Blundell and Powell (2003)). The ASF is defined as ASF x t E c i m t x t , c i  . (5) Passing the derivative through the expectation in 3
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(5) gives the APE. How do APEs relate to parameters? Suppose m t x t , c G x t c , (6) where, say, G  is strictly increasing and continuously differentiable. Then j x t , c j g x t c , (7) where g  is the derivative of G  . Then estimating j means we can sign of the partial effect, and the relative effects of any two continuous variables. Even if G  is specified, the magnitude of effects cannot be estimated without making assumptions about the distribution of c i Altonji and Matzkin (2005) define the local average response (LAR) as opposed to the APE or PAE. The LAR at x t for a continuous variable x tj is 4
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LAR j x t m t x t , c x tj d H t c | x t , (8) where H t c | x t denotes the cdf of D c i | x it x t . “Local” because it averages out the heterogeneity
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Nonlinear Panel Data Models Slides - WNE 7/30/07 #4 Whats...

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