First difference maximum likelihood and dynamic panel estimation

Chirok Han, Peter C B Phillips

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 performance 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. 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→∞. As the panel width n→∞ 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. We also show how this limit theory depends on the form of the extended likelihood.

Original languageEnglish
Pages (from-to)35-45
Number of pages11
JournalJournal of Econometrics
Volume175
Issue number1
DOIs
Publication statusPublished - 2013 Jul 1

Fingerprint

Maximum likelihood
Maximum Likelihood
Likelihood
Pathology
Time series
Unit Root
Asymptotic distribution
Parameter estimation
Data structures
Upper bound
Nonstationarity
Gaussian Function
Fixed Effects
Data Modeling
Panel Data
Bimodal
Stationarity
Likelihood Function
Dynamic panel estimation
Dynamic Panel

Keywords

  • Asymptote
  • Bounded support
  • Dynamic panel
  • Efficiency
  • First difference MLE
  • Likelihood
  • Quartic equation
  • Restricted extremum estimator

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics
  • History and Philosophy of Science

Cite this

First difference maximum likelihood and dynamic panel estimation. / Han, Chirok; Phillips, Peter C B.

In: Journal of Econometrics, Vol. 175, No. 1, 01.07.2013, p. 35-45.

Research output: Contribution to journalArticle

Han, Chirok ; Phillips, Peter C B. / First difference maximum likelihood and dynamic panel estimation. In: Journal of Econometrics. 2013 ; Vol. 175, No. 1. pp. 35-45.
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