Asymptotic and finite-sample properties of a new simple estimator of cointegrating regressions under near cointegration

Resumen

Asymptotically efficient estimation of a static cointegrating regression represents a critical requirement for later development of valid inferential procedures. Existing methods, such as fully-modified ordinary least-squares (FM-OLS), canonical cointegrating regression (CCR), or dynamic OLS (DOLS), that are asymptotically equivalent, require the choice of several tuning parameters to perform parametric or nonparametric correction of the two sources of bias that contaminate the limiting distribution of the OLS estimates and residuals. The so-called Integrated Modified OLS (IM-OLS) estimation method, recently proposed by Vogelsang and Wagner (2011), avoids these inconveniencies through a simple transformation (integration) of the system variables in the cointegrating regression equation, so that it represents a very appealing alternative estimation procedure that produces asymptotically almost efficient estimates of the model parameter. In this paper we study the performance of this estimator, both asymptotically and in finite samples, in the case of near cointegration when mechanism generating the error term of the cointegrating regression equation represents a certain generalization of the I(0) assumption in the standard case. Particularly, we consider three different specifications for the error term that generate a stationary sequence with finite variance in large samples, but are nonstationary for small sample sizes, and a fourth specification known as a stochastically trendless process that represents an intermediate situation between ordinary stationarity and nonstationarity and that determines what has been termed as stochastic cointegration. With this, we characterize the limiting distribution of the IM-OLS estimator, determining the main differences with respect the reference case of stationary cointegration, and evaluate its performance in finite samples as measured by bias and root mean squared error through a small simulation experiment.