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Econometrics 2018, 6(2), 19; doi:10.3390/econometrics6020019

TSLS and LIML Estimators in Panels with Unobserved Shocks

1
Department of Economics, Umeå University, 901 87 Umeå, Sweden
2
Department of Econometrics and Business Statistics, Monash University, Clayton VIC 3800, Australia
3
Department of Economics, University of Bath, Bath BA2 7AY, UK
*
Author to whom correspondence should be addressed.
Received: 17 August 2017 / Revised: 13 March 2018 / Accepted: 27 March 2018 / Published: 9 April 2018
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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. View Full-Text
Keywords: two-stage least squares; limited information maximum likelihood; common shocks two-stage least squares; limited information maximum likelihood; common shocks
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Forchini, G.; Jiang, B.; Peng, B. TSLS and LIML Estimators in Panels with Unobserved Shocks. Econometrics 2018, 6, 19.

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