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Statistical inference in a random coefficient panel model

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  • Horváth, Lajos
  • Trapani, Lorenzo

Abstract

This paper studies the asymptotics of the Weighted Least Squares (WLS) estimator of the autoregressive root in a panel Random Coefficient Autoregression (RCA). We show that, in an RCA context, there is no “unit root problem” : the WLS estimator is always asymptotically normal, irrespective of the average value of the autoregressive root, of whether the autoregressive coefficient is random or not, and of the presence and degree of cross dependence. Our simulations indicate that the estimator has good properties, and that confidence intervals have the correct coverage even for sample sizes as small as (N,T)=(10,25). We illustrate our findings through two applications to macroeconomic and financial variables.

Suggested Citation

  • Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    • Handle: RePEc:eee:econom:v:193:y:2016:i:1:p:54-75
    DOI: 10.1016/j.jeconom.2016.01.006
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    Cited by:

    1. Chi Yao & Wei Yu & Xuejun Wang, 2023. "Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-21, March.
    2. Stavros Degiannakis & George Filis & Grigorios Siourounis & Lorenzo Trapani, 2023. "Superkurtosis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 55(8), pages 2061-2091, December.
      • Degiannakis, Stavros & Filis, George & Siourounis, Grigorios & Trapani, Lorenzo, 2019. "Superkurtosis," MPRA Paper 94473, University Library of Munich, Germany.
      • Stavros Degiannakis & George Filis & Grigorios Siourounis & Lorenzo Trapani, 2023. "Superkurtosis," Working Papers 318, Bank of Greece.
      • Degiannakis, Stavros & Filis, George & Siourounis, Grigorios & Trapani, Lorenzo, 2019. "Superkurtosis," MPRA Paper 96563, University Library of Munich, Germany.
    3. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    4. Lajos Horvath & Lorenzo Trapani, 2021. "Changepoint detection in random coefficient autoregressive models," Papers 2104.13440, arXiv.org.
    5. Hwang, Eunju, 2021. "Weighted least squares estimation in a binary random coefficient panel model with infinite variance," Statistics & Probability Letters, Elsevier, vol. 168(C).
    6. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    7. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    8. Abonazel, Mohamed R., 2016. "Generalized Random Coefficient Estimators of Panel Data Models: Asymptotic and Small Sample Properties," MPRA Paper 72586, University Library of Munich, Germany.
    9. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Economics and Statistics Working Papers 18-2017, Singapore Management University, School of Economics.
    10. Yu Bai & Massimiliano Marcellino & George Kapetanios, 2023. "Mean Group Instrumental Variable Estimation of Time-Varying Large Heterogeneous Panels with Endogenous Regressors," Monash Econometrics and Business Statistics Working Papers 13/23, Monash University, Department of Econometrics and Business Statistics.
    11. Yuxin Pang & Dehui Wang, 2024. "A New Random Coefficient Autoregressive Model Driven by an Unobservable State Variable," Mathematics, MDPI, vol. 12(24), pages 1-16, December.
    12. Breitung, Jörg & Salish, Nazarii, 2021. "Estimation of heterogeneous panels with systematic slope variations," Journal of Econometrics, Elsevier, vol. 220(2), pages 399-415.
    13. Marie Badreau & Frédéric Proïa, 2023. "Consistency and asymptotic normality in a class of nearly unstable processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 619-641, October.
    14. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    15. Zheqi Wang & Dehui Wang & Jianhua Cheng, 2023. "A new autoregressive process driven by explanatory variables and past observations: an application to PM 2.5," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 619-658, June.
    16. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.

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    More about this item

    Keywords

    Random Coefficient Autoregression; Panel data; WLS estimator; Common factors;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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