Across State Modeling Time-series Data

[Ben Fields]

Hello Stata List,

I am working on a modeling strategy for college enrollment data during the decade from 2009-2018. I am trying to create a model in which I can compare between states. For instance, I would like to be able to say if a state's tuition changes more than it has a greater decline in enrollment over the period. I have run fixed effects models with fixed effects for both State and Year with clustered standard errors, but these seem to only give me within-state estimates as opposed to between state estimates. I am looking at Random Effects as well using clustered standard errors, but don't know if I can include years in these models or if they will show me what I am looking for. I have also looked into using hierarchical linear models, but am not sure if that is the right thing given that I only have my data grouped by State.
I am hoping to figure out a good modeling strategy to allow me to look across and between states rather than just within. We are really interested in seeing the differences between states during this time period rather than just what happens within the states.

[Clyde Schechter]

I have run fixed effects models with fixed effects for both State and Year with clustered standard errors, but these seem to only give me within-state estimates as opposed to between state estimates.

Yes, that is precisely what fixed-effects models do. You cannot estimate cross-panel effects in a fixed-effects model.

If you use a random effects model, the estimated effects are a mixture (weighted mean) of within- and across-panel effects. The validity of such models in this situation is predicated on the assumption that the within and between effects are, in fact, the same, so the estimates are understood as an estimate of this common effect.

If you cannot justify the assumption that the within- and between- effects are the same, then I would recommend looking at -xthybrid-, which gives you separate estimates of each. -xthybrid- is written by Francisco Perales and Reinhard Schunck, and is available from SSC. Another possible approach, if you are running linear regressions, is to use -xtreg, be-, which gives pure estimates of between effects.

As for using multi-level models, they are conceptually the same as random-effects models. In fact, a random effects model is just a multi-level model with only 2 levels. You can use -xtreg, re- or you can use -mixed- and you should get the same results (with perhaps tiny differences due to different numerical estimation algorithms)--they fit the same model, but use different calculations to fit the parameters.

And, yes, you can include year variables in all of these models.

[Ben Fields]

Thank you so much Clyde,

What is the best way to deal with autocorrelation and heteroskadisticity when using the xthybrid command? It seems to work very well for the basic model but does not allow for year to be in the model.

I used the following code:
xthybrid enrollment gpd unemployment, cluster(State) vce(robust)

when I tried to add i.year to the model it wouldn't allow me to run it.