By Marc Nerlove, Pietro Balestra (auth.), László Mátyás, Patrick Sevestre (eds.)
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Extra info for The Econometrics of Panel Data: A Handbook of the Theory with Applications
There are many different ways in which the observations for the full sample can be arranged. For instance, the NT values of Yit could be put in a (N x T) matrix. However, it is customary in panel data models to arrange these values in vector form, taking the individuals (with all their T observations) one after the other. • , X K and a non-observable random term u. Given the panel nature of the sample, for individual i at time t we write: Yit = f3lit X lit + ... it is the (K x 1) column vector of regression coefficients.
Deaton's cohorts and his proposed treatment of cohort averages is similar to the notion of a representative economic agent, introduced by Alfred Marshall in the last century, and in widespread theoretical use today. Kirman  has recently given a detailed critique of the concept and many of his points apply in the present context. Essentially, relationships among averages, or for representative individuals, are often not interpretable directly in terms of individual behaviour since the relationships among the aggregates is often a result of the aggregation.
This is a little more complicated than the usual minimization of the SS in the penultimate term because "I enters the final term as well. Then do a gradient search on p. 14 Formulation and Estimation of Econometric Models for Panel Data When (3 =F 0, things are more complicated still. Various alternative specifications considered in the literature are reported and analyzed in Chapter 7. 2 Considerable simplification, however, can be obtained if, following Nerlove [1971a], we are willing to assume that Xit follows a well-specified common stationary time series model for all individuals i.