Fully modified least squares cointegrating parameter estimation in multicointegrated systems

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