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.
Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces additional coin-tegrating 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 multicointe-grated 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.
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.
We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models involving conditional volatility, conditional higher moments, conditional quantiles, asymmetry, Value at Risk models, duration models, diffusion models, etc. Compared to other tests, the new test properly controls the nonlinear dynamic behavior in conditional distribution and does not rely on smoothing techniques which require a choice of several tuning parameters. The test is based on a new kind of multivariate empirical process of contemporaneous and lagged probability integral transforms. We establish weak convergence of the process under parameter uncertainty and local alternatives. We justify a parametric bootstrap approximation that accounts for parameter estimation effects often ignored in practice. Monte Carlo experiments show that the test has good finite-sample size and power properties. Using the new test and graphical tools we check the adequacy of various popular heteroscedastic models for stock exchange index data.
This paper proposes new specification tests for conditional models with discrete responses. In particular, we can test the static and dynamic ordered choice model specifications, which is key to apply efficient maximum likelihood methods, to obtain consistent estimates of partial effects and to get appropriate predictions of the probability of future events. The traditional approach is based on probability integral transforms of a jittered discrete data which leads to continuous uniform iid series under the true conditional distribution. We investigate in this paper an alternative transformation based only on original discrete data. We show analytically and in simulations that our approach dominates the traditional approach in terms of power. We apply the new tests to models of the monetary policy conducted by the Federal Reserve.