Kruiniger, Hugo (2018): A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions.

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Abstract
In this paper we consider two kinds of generalizations of Lancaster's (Review of Economic Studies, 2002) Modified ML estimator (MMLE) for the panel AR(1) model with fixed effects and arbitrary initial conditions and possibly covariates when the time dimension, T, is fixed. When the autoregressive parameter ρ=1, the limiting modified profile loglikelihood function for this model has a stationary point of inflection and ρ is firstorder underidentified but secondorder identified. We show that the generalized MMLEs exist w.p.a.1 and are uniquely defined w.p.1. and consistent for any value of ρ≥1. When ρ=1, the rate of convergence of the MMLEs is N^{1/4}, where N is the crosssectional dimension of the panel. We then develop an asymptotic theory for GMM estimators when one of the parameters is only secondorder identified and use this to derive the limiting distributions of the MMLEs. They are generally asymmetric when ρ=1. One kind of generalized MMLE depends on a weight matrix W_{N} and we show that a suitable choice of W_{N} yields an asymptotically unbiased MMLE. We also show that Quasi LM tests that are based on the modified profile loglikelihood and use its expected rather than observed Hessian, with an additional modification for ρ=1, and confidence regions that are based on inverting these tests have correct asymptotic size in a uniform sense when ρ≤1. Finally, we investigate the finite sample properties of the MMLEs and the QLM test in a Monte Carlo study.
Item Type:  MPRA Paper 

Original Title:  A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions. 
Language:  English 
Keywords:  dynamic panel data, expected Hessian, fixed effects, Generalized Method of Moments (GMM), inflection point, Modified Maximum Likelihood, Quasi LM test, secondorder identification, singular information matrix, weak moment conditions. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C23  Panel Data Models ; Spatiotemporal Models 
Item ID:  88623 
Depositing User:  Dr Hugo Kruiniger 
Date Deposited:  30 Aug 2018 02:24 
Last Modified:  29 Sep 2019 11:19 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/88623 