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First Difference MLE and Dynamic Panel Estimation

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Abstract

First difference maximum likelihood (FDML) seems an attractive estimation methodology in dynamic panel data modeling because differencing eliminates fixed effects and, in the case of a unit root, differencing transforms the data to stationarity, thereby addressing both incidental parameter problems and the possible effects of nonstationarity. This paper draws attention to certain pathologies that arise in the use of FDML that have gone unnoticed in the literature and that affect both finite sample peformance and asymptotics. FDML uses the Gaussian likelihood function for first differenced data and parameter estimation is based on the whole domain over which the log-likelihood is defined. However, extending the domain of the likelihood beyond the stationary region has certain consequences that have a major effect on finite sample and asymptotic performance. First, the extended likelihood is not the true likelihood even in the Gaussian case and it has a finite upper bound of definition. Second, it is often bimodal, and one of its peaks can be so peculiar that numerical maximization of the extended likelihood frequently fails to locate the global maximum. As a result of these pathologies, the FDML estimator is a restricted estimator, numerical implementation is not straightforward and asymptotics are hard to derive in cases where the peculiarity occurs with non-negligible probabilities. We investigate these problems, provide a convenient new expression for the likelihood and a new algorithm to maximize it. The peculiarities in the likelihood are found to be particularly marked in time series with a unit root. In this case, the asymptotic distribution of the FDMLE has bounded support and its density is infinite at the upper bound when the time series sample size T approaching infinity. As the panel width n approaching infinity the pathology is removed and the limit theory is normal. This result applies even for T fixed and we present an expression for the asymptotic distribution which does not depend on the time dimension. When n,T approaching infinity, the FDMLE has smaller asymptotic variance than that of the bias corrected MLE, an outcome that is explained by the restricted nature of the FDMLE.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1780.

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Length: 32 pages
Date of creation: Jan 2011
Date of revision:
Publication status: Published in Journal of Econometrics (July 2013), 175(1): 35-45
Handle: RePEc:cwl:cwldpp:1780

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Asymptote; Bounded support; Dynamic panel; Efficiency; First difference MLE; Likelihood; Quartic equation; Restricted extremum estimator;

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Cited by:
  1. Santiago Carbo-Valverde & Edward J. Kane & Francisco Rodriquez-Fernandez, 2011. "Safety-net benefits conferred on difficulty-to-fail-and-unwind banks in the U.S. and EU before and during the Great Recession," Proceedings 1132, Federal Reserve Bank of Chicago.
  2. Switek, Malgorzata, 2012. "Internal Migration and Life Satisfaction: Well-Being Effects of Moving as a Young Adult," IZA Discussion Papers 7016, Institute for the Study of Labor (IZA).

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