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Fully Modified Least Squares for Multicointegrated Systems

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Abstract

Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The semiparametric framework has the advantage that short run dynamics do not need to be modeled and estimation by standard techniques such as fully modified least squares (FM-OLS) on the original I(1) system is straightforward. The paper derives FM-OLS limit theory in the multicointegrated setting, showing how faster rates of convergence are achieved in the direction of singularity and that the limit distribution depends on the distribution of the conditional one-sided long run covariance estimator used in FM-OLS estimation. Wald tests of restrictions on the regression coefficients have nonstandard limit theory which depends on nuisance parameters in general. The usual tests are shown to be conservative when the restrictions are isolated to the directions of singularity and, under certain conditions, are invariant to singularity otherwise. Simulations show that approximations derived in the paper work well in finite samples. We illustrate our findings by analyzing fiscal sustainability of the US government over the post-war period.

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  • Igor Kheifets & Peter C.B. Phillips, 2019. "Fully Modified Least Squares for Multicointegrated Systems," Cowles Foundation Discussion Papers 2210, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:2210
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d22/d2210.pdf
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    1. Hamilton, James D & Flavin, Marjorie A, 1986. "On the Limitations of Government Borrowing: A Framework for EmpiricalTesting," American Economic Review, American Economic Association, vol. 76(4), pages 808-819, September.
    2. Hakkio, Craig S & Rush, Mark, 1991. "Is the Budget Deficit "Too Large?"," Economic Inquiry, Western Economic Association International, vol. 29(3), pages 429-445, July.
    3. Haug, Alfred A, 1991. "Cointegration and Government Borrowing Constraints: Evidence for the United States," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 97-101, January.
    4. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    5. 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.
    6. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    7. Peter C. B. Phillips & Mico Loretan, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 407-436.
    8. D’Erasmo, P. & Mendoza, E.G. & Zhang, J., 2016. "What is a Sustainable Public Debt?," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.),Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 2493-2597, Elsevier.
    9. Vanessa Berenguer‐Rico & Josep Lluís Carrion‐i‐Silvestre, 2011. "Regime shifts in stock–flow I(2)–I(1) systems: the case of US fiscal sustainability," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 298-321, March.
    10. Phillips, Peter C.B., 2014. "Optimal estimation of cointegrated systems with irrelevant instruments," Journal of Econometrics, Elsevier, vol. 178(P2), pages 210-224.
    11. Trehan, Bharat & Walsh, Carl E, 1991. "Testing Intertemporal Budget Constraints: Theory and Applications to U.S. Federal Budget and Current Account Deficits," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 206-223, May.
    12. Quintos, Carmela E, 1995. "Sustainability of the Deficit Process with Structural Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 409-417, October.
    13. Bohn, Henning, 2007. "Are stationarity and cointegration restrictions really necessary for the intertemporal budget constraint?," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 1837-1847, October.
    14. Johansen, Søren, 1992. "A Representation of Vector Autoregressive Processes Integrated of Order 2," Econometric Theory, Cambridge University Press, vol. 8(2), pages 188-202, June.
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    More about this item

    Keywords

    Cointegration; Multicointegration; Fully modified regression; Singular long run variance matrix; Degenerate Wald test; Fiscal sustainability;

    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
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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