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Heterogeneous Autoregressions in Short T Panel Data Models

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  • M. Hashem Pesaran
  • Liying Yang

Abstract

This paper considers a first-order autoregressive panel data model with individual-specific effects and heterogeneous autoregressive coefficients defined on the interval (-1,1], thus allowing for some of the individual processes to have unit roots. It proposes estimators for the moments of the cross-sectional distribution of the autoregressive (AR) coefficients, assuming a random coefficient model for the autoregressive coefficients without imposing any restrictions on the fixed effects. It is shown the standard generalized method of moments estimators obtained under homogeneous slopes are biased. Small sample properties of the proposed estimators are investigated by Monte Carlo experiments and compared with a number of alternatives, both under homogeneous and heterogeneous slopes. It is found that a simple moment estimator of the mean of heterogeneous AR coefficients performs very well even for moderate sample sizes, but to reliably estimate the variance of AR coefficients much larger samples are required. It is also required that the true value of this variance is not too close to zero. The utility of the heterogeneous approach is illustrated in the case of earnings dynamics.

Suggested Citation

  • M. Hashem Pesaran & Liying Yang, 2023. "Heterogeneous Autoregressions in Short T Panel Data Models," Papers 2306.05299, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2306.05299
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    References listed on IDEAS

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    1. Han, Chirok & Phillips, Peter C. B., 2010. "Gmm Estimation For Dynamic Panels With Fixed Effects And Strong Instruments At Unity," Econometric Theory, Cambridge University Press, vol. 26(1), pages 119-151, February.
    2. Mavroeidis, Sophocles & Sasaki, Yuya & Welch, Ivo, 2015. "Estimation of heterogeneous autoregressive parameters with short panel data," Journal of Econometrics, Elsevier, vol. 188(1), pages 219-235.
    3. Costas Meghir & Luigi Pistaferri, 2004. "Income Variance Dynamics and Heterogeneity," Econometrica, Econometric Society, vol. 72(1), pages 1-32, January.
    4. Anderson, T. W. & Hsiao, Cheng, 1982. "Formulation and estimation of dynamic models using panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 47-82, January.
    5. Blundell, Richard & Bond, Stephen, 1998. "Initial conditions and moment restrictions in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 87(1), pages 115-143, August.
    6. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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