Dynamic unobserved effects model: Difference between revisions

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P(y<sub>it</sub> = 1│y<sub>i,t-1</sub>, … , y<sub>i,0</sub> , z<sub>i</sub> , c<sub>i</sub> ) = G (z<sub>it</sub> δ + ρ y<sub>i,t-1</sub> + c<sub>i</sub>)
 
where c<sub>i</sub> is aan unobservable explanatory variable, z<sub>it</sub> is explanatory variables which are exogenous conditional on the c<sub>i</sub>, 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, ''y<sub>i,t</sub>'' can be a woman’s choice whether work or not, ''z<sub>it</sub>'' includes the ''i''-th individual’s age, education level, numbers of kids and so on. ''c<sub>i</sub>'' can be some individual specific characteristic which cannot be observed by economists.<ref>James J. Heckman (1981): Studies in Labor Markets, University of Chicago Press, Chapter Heterogeneity and State Dependence</ref> It is a reasonable conjecture that one’s labor choice in period ''t'' should depend on his or her choice in period ''t''&nbsp;&minus;&nbsp;1 due to habit formation or other reasons. This is dependence is characterized by parameter ''ρ''.