## Two-State Models with Exogenous Variables

We shall consider a two-state Markov model with exogenous variables, which accounts for the heterogeneity and nonstationarity of the data. This model is closely related to the models considered in Section 9.7.2. We shall also discuss an example of the model, attributed to Boskin and Nold (1975), to illustrate several important points.

This model is similar to a univariate binary QR model. To make the subsequent discussion comparable to the discussion of Chapter 9, assume that/ = 0 or 1 rather than 1 or 2. Let yu = 1 if the tth person is in state 1 at time t and ya = 0 otherwise. (Note that yu is the same as the y[(t) we wrote earlier.) The model then can be written as

P{yit= lyi. t-i) = F(Fxit + a’xttyUt-l), (11.1.34)

where Fisa certain distribution function. Note that (11.1...

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