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A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions

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  • Hugo Kruiniger

Abstract

In this paper we consider two generalizations of Lancaster's (Review of Economic Studies, 2002) Modified Maximum Likelihood estimator (MMLE) for the panel AR(1) model with fixed effects, arbitrary initial conditions, and strictly exogenous covariates when the time dimension of the panel, T, is fixed. When the autoregressive parameter rho=1, the limiting modified profile log-likelihood function for this model has a stationary point of inflection, and rho is first-order underidentified but second-order identified. We show that, unlike the Random Effects and Transformed MLEs for this type of model, the generalized MMLEs are uniquely defined in finite samples w.p.1. for any value of |rho|=

Suggested Citation

  • Hugo Kruiniger, 2025. "A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions," Papers 2508.20753, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2508.20753
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