# Problem with simultaneous dynamic model

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Sergi
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Dear all,

I’m running a dynamic simultaneous equation model with the free statistical software aML. The first equation is a time-to-event model for the hazard of migration since the beginning of the observation window. The second equation models the probability of having intentions to move (yes or no), and intentions are recorded at 4 different points in time. Theoretically, the model should be sequential, but I decided to run it simultaneously in order to tackle selection issues. I performed different model specifications, where in the last specifications I inserted a variance component for the residual of each equation, drawn from a joint bivariate normal distribution. Then, I allowed for covariation among residual terms in order to control for unobserved heterogeneity (basically those thing that I cannot observe and commonly explain the propensity to move and to have intentions to move). As expected this correlation is positive. However, when I include the intentions to move as a covariate in the migration equation the residuals correlation turn to be negative.

I think that this might be unusual, but a possible explanation is that: once controlling for intentions in the migration equation, the unobserved heterogeneity is reduced to those unobserved aspects that make individuals migrate but we are not able to observe in their intentions to move. This might be due to individuals who are more likely to change suddenly their opinion about moving or not (for example) and measurement error in the intentions to move variable. Does it sound plausible my interpretation or do you think they could be a totally different thing going on?

A other information about the analyses is that I’m running Full information Maximum likelihood (as there is no possibility to do it with Limited information ML), but only one of the equations is structural (i.e. in the intentions equation I do not use as a covariate migration outcomes). As I only analyse one event per individual, I had problems to identify the variance of the residual term, so I set it constant. I tried different values for this variance, but the results kept robust. The survey design is stratified by intentions to move, for that reason I used sample weights in the analyses. However, I’m not pretty sure whether to use robust standard errors (Huber) in order to correct for potential heteroskedasticity for due to the usage of sampling weights.

Any help is appreciated 🙂

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