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New results on asymptotic properties of likelihood estimators with persistent data for small and large T

Author

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  • Artūras Juodis

    (University of Amsterdam
    Tinbergen Institute)

  • Vasilis Sarafidis

    (Brunel University London
    BI Norwegian Business School)

Abstract

This paper revisits the panel autoregressive model, with a primary emphasis on the unit-root case. We study a class of misspecified Random effects Maximum Likelihood (mRML) estimators when T is either fixed or large, and N tends to infinity. We show that in the unit-root case, for any fixed value of T, the log-likelihood function of the mRML estimator has a single mode at unity as $$N\rightarrow \infty $$ N → ∞ . Furthermore, the Hessian matrix of the corresponding log-likelihood function is non-singular, unless the scaled variance of the initial condition is exactly zero. As a result, mRML is consistent and asymptotically normally distributed as N tends to infinity. In the large-T setup, it is shown that mRML is asymptotically equivalent to the bias-corrected FE estimator of Hahn and Kuersteiner (Econometrica 70(4):1639–1657, 2002). Moreover, under certain conditions, its Hessian matrix remains non-singular.

Suggested Citation

  • Artūras Juodis & Vasilis Sarafidis, 2023. "New results on asymptotic properties of likelihood estimators with persistent data for small and large T," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(3), pages 435-461, December.
    • Handle: RePEc:spr:series:v:14:y:2023:i:3:d:10.1007_s13209-023-00286-y
    DOI: 10.1007/s13209-023-00286-y
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    Keywords

    Dynamic panel data; Maximum likelihood; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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