Fully modified least squares cointegrating parameter estimation in multicointegrated systems

Igor L. Kheifets and Peter Phillips

Journal of Econometrics, 2023, vol. 232, issue 2, 300-319

Abstract: Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional cointegrating 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 I1 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. The findings are illustrated empirically in an analysis of 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 (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations: View citations in EconPapers (2)

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Working Paper: Fully Modified Least Squares Cointegrating Parameter Estimation in Multicointegrated Systems (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:232:y:2023:i:2:p:300-319

DOI: 10.1016/j.jeconom.2021.07.002

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