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Unformatted text preview: Imbens, Lecture Notes 16, ARE213 Spring ’06 1 ARE213 Econometrics Spring 2006 UC Berkeley Department of Agricultural and Resource Economics Discrete Response Models VI: Random-Effects Logit Models: Berry-Levinsohn-Pakes (BLP) I. Set Up Here we consider again random effects logit models. Such models have recently found much application in Industrial Organization, where they are used to model demand for differentiated products, often in settings with a large number of products. The first and very influential application of these methods by Berry, Levinsohn and Pakes (1995) looked at the market for automobiles. Compared to the earlier examples we have looked at there is an emphasis in this study and those that followed it on the large number of goods and the potential endogeneity of some of the product characteristics. (Typically one of the regressors is the price of the good.) In addition the procedure only requires market level data. We do not need individual level purchase data, just market shares and estimates of the distribution of individual characteris- tics by market. In practice we need a fair amount of variation in these things, but in principle this is less demanding in terms of data required. On the other hand, we do need data by market, where before we just needed individual purchases in a single market (although to identify price effects we would need variation in prices by individuals in that case). The data have three dimensions: products, indexed by j = 0 , . . . , J , markets, t = 1 , . . . , T , and individuals, i = 1 , . . . , N t . We only observe one purchase per individual. The large sample approximations are based on large N and T , and fixed J . Let us go back to the random coefficients model, now with each utility indexed by indi- vidual, product and market: U ijt = β i X jt + ζ jt + ijt . Imbens, Lecture Notes 16, ARE213 Spring ’06 2 The ζ jt is a unobserved product characteristic. This can include product and market dum- mies (for example, we can have ζ jt = ζ j + ζ t ). Unlike the observed product characteristics this unobserved characteristic does not have a individual-specific coefficient. The observedthis unobserved characteristic does not have a individual-specific coefficient....
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- Spring '06
- Logit, XJT, β Xjt, Zi Γ