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The “dynamic” here means the dependence of the dependent variable on its past history, this is usually used to model the “state dependence” in economics. For instance, a person who cannot find a job this year, it will be hard for her to find a job next year because the fact that she doesn’t have a job this year will be a very negative signal for the potential employers. The “unobserved effects” means that one or some of the explanatory variables are unobservable. For example, one’s preference affects quite a lot her consumption choice of the ice cream with a certain taste, but preference is unobservable. A typical dynamic unobserved effects model is represented 〔 Wooldridge, J. (2002): Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, Mass, pp 495.〕 as: P(yit = 1│yi,t-1, … , yi,0 , zi , ci ) = G (zit δ + ρ yi,t-1 + ci) where ci is a unobservable explanatory variable, zit is explanatory variables which are exogenous conditional on the ci, and G(∙) is a cumulative distribution function. In this type of model, economists have a special interest in ρ, which is used to characterize the state dependence. For example, ''yi,t'' can be a woman’s choice whether work or not, ''zit'' includes the ''i''-th individual’s age, education level, numbers of kids and so on. ''ci'' can be some individual specific characteristic which cannot be observed by economists 〔James J. Heckman (1981): Studies in Labor Markets, University of Chicago Press, Chapter Heterogeneity and State Dependence〕. It is a reasonable conjecture that one’s labor choice in period ''t'' should depend on his or her choice in period ''t'' - 1 due to habit formation or other reasons. This is dependence is characterized by parameter ''ρ''. There are several MLE-based approaches to estimate ''δ'' and ''ρ'' consistently. The simplest way is to treat ''yi,0'' as non-stochastic and assume ''ci'' is independent with ''zi''. Then integrate ''P(yi,t , yi,t-1 , … , yi,1 | yi,0 , zi , ci)'' against the density of ''ci'', we can obtain the conditional density P(yi,t , yi,t-1 , … , yi,1 |yi,0 , zi). The objective function for the conditional MLE can be represented as: '' log (P (yi,t , yi,t-1, … , yi,1 | yi,0 , zi)).'' Treating ''yi,0'' as non-stochastic implicitly assumes the independence of ''yi,0'' on ''zi''. But in most of the cases in reality, ''yi,0'' depends on ''ci'' and ''ci'' also depends on ''zi''. An improvement on the approach above is to assume a density of ''yi,0'' conditional on (''ci, zi'') and conditional likelihood ''P(yi,t) , yi,t-1 , … , yt,1,yi,0 | ci, zi)'' can be obtained. Integrate this likelihood against the density of ''ci'' conditional on ''zi'' and we can obtain the conditional density ''P(yi,t , yi,t-1 , … , yi,1 , yi,0 | zi)''. The objective function for the conditional MLE 〔 Greene, W. H. (2003), Econometric Analysis , Prentice Hall , Upper Saddle River, NJ .〕 is '' log (P (yi,t , yi,t-1, … , yi,1 | yi,0 , zi)).'' Based on the estimates for (''δ, ρ'') and the corresponding variance, test about the coefficients can be implemented 〔 Whitney K. Newey, Daniel McFadden, Chapter 36 Large sample estimation and hypothesis testing, In: Robert F. Engle and Daniel L. McFadden, Editor(s), Handbook of Econometrics, Elsevier, 1994, Volume 4, Pages 2111-2245, ISSN 1573-4412, ISBN 9780444887665,〕 and the average partial effect can be calculated. 〔Chamberlain, G. (1980), “Analysis of Covariance with Qualitative Data,” Journal of Econometrics 18, 5-46〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dynamic unobserved effects model」の詳細全文を読む スポンサード リンク
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