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The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators

Author

Listed:
  • Alvarez, J.
  • Arellano, M.

Abstract

In this paper we derive the asymptotic properties of within groups (WG), GMM and LIML estimators for an autoregressive model with random effects when both T and N tend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. When T/N->0 the fixed T results for GMM and LIML remain valid, but WG although consistent has an asymptotic bias in its asymptotic distribution. When T/N tends to a positive constant, the WG, GMM and LIML estimators exhibit negative asymptotic biases of order T,N and (2N-T), respectively. In addition, the crude GMM estimator that neglects the autocorrelation in first differenced errors is inconsistent as T/N->c>0, despite being consistent for fixed T. Finally, we discuss the properties of a random effects MLE with unrestricted initial conditions when both T and N tend to infinity.

Suggested Citation

  • Alvarez, J. & Arellano, M., 1998. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Papers 9808, Centro de Estudios Monetarios Y Financieros-.
  • Handle: RePEc:fth:cemfdt:9808
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    Keywords

    ECONOMETRIC MODELS ; ESTIMATION OF PARAMETERS ; TIME SERIES;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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