TSLS and LIML Estimators in Panels with Unobserved Shocks

Giovanni Forchini, Bin Jiang and Bin Peng
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Bin Jiang: Department of Econometrics and Business Statistics, Monash University, Clayton VIC 3800, Australia
Bin Peng: Department of Economics, University of Bath, Bath BA2 7AY, UK

Econometrics, 2018, vol. 6, issue 2, 1-12

Abstract: The properties of the two stage least squares (TSLS) and limited information maximum likelihood (LIML) estimators in panel data models where the observables are affected by common shocks, modelled through unobservable factors, are studied for the case where the time series dimension is fixed. We show that the key assumption in determining the consistency of the panel TSLS and LIML estimators, as the cross section dimension tends to infinity, is the lack of correlation between the factor loadings in the errors and in the exogenous variables—including the instruments—conditional on the common shocks. If this condition fails, both estimators have degenerate distributions. When the panel TSLS and LIML estimators are consistent, they have covariance-matrix mixed-normal distributions asymptotically. Tests on the coefficients can be constructed in the usual way and have standard distributions under the null hypothesis.

Keywords: two-stage least squares; limited information maximum likelihood; common shocks (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2018
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