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st: obtaining varying fixed effects coefficients for a panel data hierarchical model

 From JOSE A ALEMAN To statalist@hsphsun2.harvard.edu Subject st: obtaining varying fixed effects coefficients for a panel data hierarchical model Date 27-Aug-2010 13:06:41 EDT

```Dear Stata listserver participants,

I'm trying to estimate a hierarchical model using panel data where the
model has a random intercept for the country and a random slope for a dummy
variable that returns a 1 if the country is democratic and 0 if its
authoritarian.

I'm trying to implement a maximum likelihood version of Western's (1998)
Bayesian hierarchical model for panel data ("Causal Heterogeneity in
Comparative Research: A Bayesian Hierarchical Modeling Approach"). Whereas
his model is Bayesian, I'm trying to estimate mine with maximum likelihood.
If you take a look at equations 12 and 13 in the paper, one of the
variables (in my case 'democracy') enters the coefficients for every other
independent variable in a unique way for every country. This is why it has
a random slope. In Stata, I would estimate the model the following way:

xtmixed Y x1 x2 x3 x4 x5 || country: democracy

Stata returns the country specific random effects for country and democracy
using the command 'predict' with option 'reffects':

predict u*, reffects

But the coefficients for the fixed effects (x1 x2 x3 x4 x5) provided are
one per variable, meaning they must be the same for each country. Yet in
this model they are supposed to differ by country. My questions are the
following: 1) how can I obtain the country specific betas for the fixed
part of the model (that is, for x1 x2 x3 x4 and x5)? 2) As Western (1998)
points out in equation 11 of his paper, this model is nothing more than a
set of interactions between the variable with the random slope
('democracy') and every other independent variable. In the Stata output
provided, are the coefficients with the fixed effects already interacted
with the random slope of 'democracy', or do I have to do that myself?

Thank you,

Jose A. Aleman
http://faculty.fordham.edu/aleman

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