Instrumental variable estimation of large-T panel data models with common factors

We introduce the xtivdfreg command in Stata, which implements a general instrumental variables (IV) approach for estimating panel data models with a large number of time series observations, T, and unobserved common factors or interactive effects, as developed by Norkute, Sarafidis, Yamagata, and Cui (2021, Journal of Econometrics) and Cui, Norkute, Sarafidis, and Yamagata (2020, ISER Discussion Paper). The underlying idea of this approach is to project out the common factors from exogenous covariates using principal components analysis, and to run IV regression in both of two stages, using defactored covariates as instruments. The resulting two-stage IV (2SIV) estimator is valid for models with homogeneous or heterogeneous slope coefficients, and has several advantages relative to existing popular approaches. In addition, the xtivdfreg command extends the 2SIV approach in two major ways. Firstly, the algorithm accommodates estimation of unbalanced panels. Secondly, the algorithm permits a flexible specification of instruments. It is shown that when one imposes zero factors, the xtivdfreg command can replicate the results of the popular ivregress Stata command. Notably, unlike ivregress, xtivdfreg permits estimation of the two-way error components panel data model with heterogeneous slope coefficients.