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Bias assessment and reduction for the 2SLS estimator in general dynamic simultaneous equations models

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  • Phillips, Garry David Alan
  • Wang, Dandan

Abstract

We consider the bias of the 2SLS estimator in general dynamic simultaneousequation models with g endogenous regressors. By using asymptotic expansion techniques we approximate 2SLS coefficient estimation bias under innovation errors, p lagged-dependent variables and strongly-exogenous explanatory variables. Large-T approximations bias of the structural form is then used to construct corrected estimators for the parameters of interest in the general DSEM (C2SLS). Simulations show that the C2SLS gives almost unbiased estimators and low mean squared errors. Alternatively, the numerical bootstrap method results suggest that the non-parametric bootstrap could be used in 2SLS for improving estimation in general DSEM.

Suggested Citation

  • Phillips, Garry David Alan & Wang, Dandan, 2019. "Bias assessment and reduction for the 2SLS estimator in general dynamic simultaneous equations models," DES - Working Papers. Statistics and Econometrics. WS 28322, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:28322
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    References listed on IDEAS

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    1. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
    2. Phillips, Garry D.A. & Liu-Evans, Gareth, 2016. "Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 734-762.
    3. Peters, Thomas A., 1989. "The exact moments of ols in dynamic regression models with non-normal errors," Journal of Econometrics, Elsevier, vol. 40(2), pages 279-305, February.
    4. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
    5. Kiviet, Jan F. & Phillips, Garry D. A., 1994. "Bias assessment and reduction in linear error-correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 215-243, July.
    6. Grubb, David & Symons, James, 1987. "Bias in Regressions With a Lagged Dependent Variable," Econometric Theory, Cambridge University Press, vol. 3(3), pages 371-386, June.
    7. Kiviet, Jan F. & Phillips, Garry D.A., 1993. "Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable," Econometric Theory, Cambridge University Press, vol. 9(1), pages 62-80, January.
    8. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 505-520, June.
    9. Phillips, Garry D. A., 2000. "An alternative approach to obtaining Nagar-type moment approximations in simultaneous equation models," Journal of Econometrics, Elsevier, vol. 97(2), pages 345-364, August.
    10. Kiviet, Jan F. & Phillips, Garry D. A. & Schipp, Bernhard, 1999. "Alternative bias approximations in first-order dynamic reduced form models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(7), pages 909-928, June.
    11. Jan F. Kiviet & Garry D. A. Phillips, 2005. "Moment approximation for least-squares estimators in dynamic regression models with a unit root *," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 115-142, July.
    12. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-176, January.
    13. Bun, Maurice J.G. & Windmeijer, Frank, 2011. "A comparison of bias approximations for the two-stage least squares (2SLS) estimator," Economics Letters, Elsevier, vol. 113(1), pages 76-79, October.
    14. Liu-Evans Gareth D. & Phillips Garry D. A., 2012. "Bootstrap, Jackknife and COLS: Bias and Mean Squared Error in Estimation of Autoregressive Models," Journal of Time Series Econometrics, De Gruyter, vol. 4(2), pages 1-35, November.
    15. Sawa, Takamitsu, 1973. "Almost Unbiased Estimator in Simultaneous Equations Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(1), pages 97-106, February.
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    More about this item

    Keywords

    General Dynamic Simultaneous Equations Model;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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