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Regressions for Partially Identified, Cointegrated Simultaneous Equations

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Abstract

This paper studies regressions for partially identified equations in simultaneous equations models (SEMs) where all the variables are I(l) and cointegrating relations are present. Asymptotic properties of OLS and 2SLS estimators under partial identification are derived. The results show that the identifiability condition is important for consistency of estimates in nonstationary SEMs as it is for stationary SEMS. Also, OLS and 2SLS estimators are shown to have different rates of convergence and divergence under partial identification, though they have the same rates of convergence and divergence for the two polar cases of full identification and total lack of identifiability. Even in the case of full identification. however, the OLS and 2SLS estimators have different distributions in the limit. Fully modified OLS regression and leads-and-lags regression methods are also studied. The results show that these two estimators have nuisance parameters in the limit under general assumptions on the regression errors and are not suitable for structural inference. The paper proposes 2SLS versions of these two nonstationary regression estimators that have mixture normal distributions in the limit under general assumptions on the regression errors, that are more efficient than the unmodified estimators, and that are suited to statistical inference using asymptotic chi-squared distributions. Some simulation results are also reported.

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  • In Choi & Peter C.B. Phillips, 1997. "Regressions for Partially Identified, Cointegrated Simultaneous Equations," Cowles Foundation Discussion Papers 1162, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1162
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    1. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    2. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
    3. Kydland, Finn E & Prescott, Edward C, 1991. " The Econometrics of the General Equilibrium Approach to Business Cycles," Scandinavian Journal of Economics, Wiley Blackwell, vol. 93(2), pages 161-178.
    4. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    5. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
    6. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    7. Shoven, John B & Whalley, John, 1984. "Applied General-Equilibrium Models of Taxation and International Trade: An Introduction and Survey," Journal of Economic Literature, American Economic Association, vol. 22(3), pages 1007-1051, September.
    8. Cheng Hsiao, 1997. "Cointegration and Dynamic Simultaneous Equations Model," Econometrica, Econometric Society, vol. 65(3), pages 647-670, May.
    9. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
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