> I want to analyze an ordinal dependent variable using cross sectional
> time series data, and I want to include the lagged dependent variable on
> the right hand side.
>
> Is there a command that can do this?
>
> First I thought that perhaps -reoprob- could work, but now I am inclined
> to believe that this random effects command is unsuitable for a lagged
> dependent variable.
First, about estimation of the ordered logit / probit in the panel
context. This indeed can be done with -reoprob-, but a more appropriate
way would probably be -gllamm- as it has been reworked somewhat by Stata
Corp. to run somewhat faster. Quadrature integration is not much fun,
computationally. So yes, ordinal panel random effect estimation is
possible in Stata. I doubt that fixed effect estimation is possible...
well let's put it this way -- I don't see an immediate way to go around
it. The fixed effect logit (= McFadden's conditional logit) just happens
to work nicely be conditioning on the fixed effects, and I don't think
such conditioning is possible for the ordinal context. I know that
economists tend not to like RE as those give biased estimates, but I
personally don't see that much fault with biased estimates (Stein's
admissibility of a multivariate mean and all that stuff, you know :)),
especially when there is no better solution available.
Now, the second question is, what exactly is the model you want to
estimate? How do you want to see your lagged variable incorporated?
Usually people tend to think of the ordinal models as if there is an
underlying index that is chopped into ordered categories. (You can also
view this as a measurement error that makes this index discrete, together
with some nonlinear transformation of scale.) So the question is, if you
want to incorporate this index as your lagged variable (and that is going
to be a very messy computation), or you want to include the observed
ordinal variable from the previous period (and then it is subject to the
measurement error that leads to biased estimates), or finally you can just
create category indicators, a dummy variable equal to 1 for each
particular category of your lagged dependent varaible (that's probably the
most reasonable way to go; you might need to think of testing whether the
coefficients of those dummy variables follow a monotone pattern, and that
is far from trivial). Of course you would also need to make all sorts of
exogeneity assumptions for all of that to be trustworthy. Was this
the issue that turned you away from the random effect model?
--- Stas Kolenikov
-- Ph.D. student in Statistics at UNC-Chapel Hill
- http://www.komkon.org/~tacik/ -- [email protected]
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