Fully Modified Least Squares for Multicointegrated Systems

36 Pages Posted: 7 Dec 2019

See all articles by Igor Kheifets

Igor Kheifets

Instituto Tecnológico Autónomo de México (ITAM)

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Date Written: November 24, 2019

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.

Keywords: Cointegration, Multicointegration, Fully modified regression, Singular long run variance matrix, Degenerate Wald test, Fiscal sustainability

JEL Classification: C12, C13, C22

Suggested Citation

Kheifets, Igor and Phillips, Peter C. B., Fully Modified Least Squares for Multicointegrated Systems (November 24, 2019). Cowles Foundation Discussion Paper No. 2210, November 2019, Available at SSRN: https://ssrn.com/abstract=3499026 or http://dx.doi.org/10.2139/ssrn.3499026

Igor Kheifets

Instituto Tecnológico Autónomo de México (ITAM) ( email )

Av. Camino a Sta. Teresa 930
Col. Héroes de Padierna
Mexico City, D.F. 01000, Federal District 01080
Mexico

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

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Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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