By Arnold Zellner
This can be a classical reprint variation of the unique 1971 variation of An advent to Bayesian Inference in Economics. This old quantity is an early creation to Bayesian inference and method which nonetheless has lasting price for modern day statistician and scholar. The assurance levels from the basic options and operations of Bayesian inference to research of purposes in particular econometric difficulties and the trying out of hypotheses and versions.
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Pietro Balestra 3 FIXED EFFECT MODELS AND FIXED COEFFICIENT MODELS As noted in the introductory chapter, the simplest and most intuitive way to account for individual and/or time differences in behaviour, in the context of a panel data regression problem, is to assume that some of the regression coefficients are allowed to vary across individuals and/or through time. The regression coefficients are unknown, but fixed parameters. When these are allowed to vary in one or two dimensions, we speak of a fixed effect model (or fixed coefficient model).
Second, also pointed out, even in the case in which all the explanatory variables . are truly exogenous, failure to take account of heterogeneity may result in bias, not merely inefficiency, in nonlinear cases, whereas no bias results in the linear case. The solution in principle is to formulate a model in terms of the probability of individual observations and then to "integrate out" the heterogeneity factors if these can be parametrically specified. In practice, of course, this is rarely possible analytically and may even be extremely difficult computationally.
D. random variables, it is unlikely that past history and past experience will play no latent role in the determination of current expectations, not fully taken into account by Xi',t-l' Thus, write (1-19) where the individual specific effects are likely to be correlated with past Xit'S and also, presumptively, with past Uit'S and xit's. 3Ui,t-l . (1-20) 18 Formulation and Estimation of Econometric Models for Panel Data Not only do the usual difficulties, discussed above, arise because of the correlation between Yi,t-1 and JLi, but the third term of the disturbance is serially correlated.
An introduction to Bayesian inference in econometrics by Arnold Zellner