Fully Modified Least Squares Cointegrating Parameter Estimation in Multicointegrated Systems

TL;DR

This paper develops a semiparametric FM-OLS approach for estimating multicointegrating relationships, revealing the impact of covariance matrix singularity on convergence and distribution, with applications to US fiscal data.

Contribution

It introduces a semiparametric FM-OLS framework for multicointegration, accounting for covariance singularity, and derives new limit theories and test properties.

Findings

Faster convergence rates in singular directions.

Limit distribution depends on long run covariance estimator.

Standard Wald tests are conservative or invariant under certain conditions.

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 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. The findings are illustrated empirically in an analysis of fiscal sustainability of the US government over the post-war period.