ARCHIVED: In Stata, how do I estimate the coefficients of time-invariant variables in the Panel FE model, using the xthtaylor command?

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When a fixed effect (FE) model is assumed in panel data, the FE or FD (First Difference) methods provide consistent estimates only for time-varying regressors, not for time-invariant regressors.

Since Stata automatically deletes the time-invariant regressors, they can't be estimated by ordinal methods like FE. In that case, we can use the Hausman-Taylor estimator, xthtaylor, a transformed Random Effect (RE) model with instrument variables (IV). This method should distinguish basically between time-varying and time-invariant regressors as follows:

  . webuse psidextract, clear 
  . xthtaylor lwage wks south smsa ms exp exp2 occ ind union fem blk ed, /// 
endog(exp exp2 wks ms union ed) constant(fem blk ed)

The above example model expects log(wage) using several regressors, where occ, south, smsa, and ind are exogenous time-varying regressors; exp, exp2, wks, ms, and union are endogenous time-varying regressors; fem and blk are exogenous time-invariant regressors; and ed is an endogenous time-invariant regressor.

Thus, the time-invariant variables such as female (fem), black (blk), and education level (ed) can be consistently estimated in the xthtaylor method, which is otherwise impossible in the estimation. In particular, when determining the impact of education (ed) on log(wage) (lwage), the Hausman-Taylor method consistently estimates the coefficient of ed, the time-invariant endogenous variable.

To use the drop-down menu, from the Statistics menu, select Endogenous Covariates, then panel data, and then Hausman-Taylor regression (RE).

Notes:

  • This method needs a stronger assumption that a specified subset of the regressors (IVs) is uncorrelated with the fixed effect or individual effect terms (ai), in addition to all regressors uncorrelated with the idiosyncratic error terms (eit).
  • The above stronger assumption can be tested by xtoverid post-estimation command.
  • In order to do xtoverid test, the statistic must have ranktest and xtoverid ado files installed.

For more, see Stata help on xtoverid or ranktest.

If you have questions about using statistical and mathematical software at Indiana University, contact the UITS Research Applications and Deep Learning team.

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Last modified on 2023-05-09 14:38:57.