Fixed effects: LSDV estimation leads to different point estimates than within-estimation

[Jonas Wereld]

I'd like to run a simple LSDV vs. within-estimator logit regression, comparing the results. (In content: Testing the effect of GDP on a country's participation in a intergovernmental conference)

I've run the following:

logit participation gdp i.country
clogit participation gdp, group(country)

From all I've read so far, the first (LSDV) should give me the same coefficients than the second (which provides the same coefficients as xtlogit, but is preferred because it accepts clustered standard errors in a further model specificaition). However, that is not true (also tried with more variables). Coefficients and the p-value differ moderately.

Why is this the case?

[daniel klein]

You did not run a LSDV (least squares dummy variable) model, but used an maximum likelihood estimator in both regressions. What is more important is that the within-estimator in non-linear models, such as logistic regression, is not based on a transformation of the data to deviations from the panel-unit means, but on a conditional likelihood function where the fixed effects are conditioned out (hence the name conditional logit). You can read more on the non-equivalence of this model to the estimates from a model including indicators for each panel-unit searching for the term: incidental parameter problem.

Best
Daniel

[Jonas Wereld]

Thanks a lot, Daniel!