High-dimensional IV cointegration estimation and inference

A semiparametric triangular systems approach shows how multicointegrating linkages occur naturally in an  cointegrated regression model when the long run error variance matrix in the system is singular. Under such singularity, cointegrated  systems embody a multicointegrated structure that makes them useful in many empirical settings. Earlier work shows that such systems may be analyzed and estimated without appealing to the associated  system but with suboptimal convergence rates and potential asymptotic bias. The present paper develops a robust approach to estimation and inference of such systems using high dimensional IV methods that have appealing asymptotic properties like those known to apply in the optimal estimation of cointegrated systems (Phillips, 1991). The approach uses an extended version of high-dimensional trend IV (Phillips, 2006, 2014) estimation with deterministic orthonormal instruments. The methods and derivations involve new results on high-dimensional IV techniques and matrix normalization in the limit theory that are of independent interest. Wald tests of general linear restrictions are constructed using a fixed- long run variance estimator that leads to robust pivotal HAR inference in both cointegrated and multicointegrated cases. Simulations show good properties of the estimation and inferential procedures in finite samples. An empirical illustration to housing stocks, starts and completions is provided.