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Inference on trending panel data

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  • Robinson, Peter M.
  • Velasco, Carlos
Abstract
Semiparametric panel data modelling and statistical inference with fractional stochastic trends, nonparametrically time-trending individual effects, and general cross-sectional correlation and heteroscedasticity in innovations are developed. The fractional stochastic trends allow for a wide range of nonstationarity, indexed by a memory parameter, nesting the familiar I(1) case and allowing for parametric short-memory. The individual effects can nonparametrically vary simultaneously across time and across units. The cross-sectional covariance matrix is also nonparametric. The main focus is on estimation of the time series parameters. Two methods are considered, both of which entail an only approximate differencing out of the individual effects, leaving an error which has to be taken account of in our theory. In both cases we obtain standard asymptotics, with a central limit theorem, over a wide range of possible parameter values, unlike the nonstandard asymptotics for autoregressive parameter estimates at a unit root. For statistical inference, consistent estimation of the limiting covariance matrix of the parameter estimates requires consistent estimation of a functional of the cross-sectional covariance matrix. We examine efficiency loss due to cross-sectional correlation in a spatial model example. A Monte Carlo study of finite-sample performance is included.

Suggested Citation

  • Robinson, Peter M. & Velasco, Carlos, 2018. "Inference on trending panel data," Journal of Econometrics, Elsevier, vol. 206(2), pages 282-304.
    • Handle: RePEc:eee:econom:v:206:y:2018:i:2:p:282-304
    DOI: 10.1016/j.jeconom.2018.06.003
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    1. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(6), pages 927-997, December.
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    6. Ergemen, Yunus Emre & Velasco, Carlos, 2017. "Estimation of fractionally integrated panels with fixed effects and cross-section dependence," Journal of Econometrics, Elsevier, vol. 196(2), pages 248-258.
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    More about this item

    Keywords

    Semiparametric panel data modelling; Nonparametrically time-trending individual effects; Nonparametric cross-sectional correlation and heteroscedasticity; Spatial model; Parametric fractional dependence; Consistency; Asymptotic normality;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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