cointReg: Parameter Estimation and Inference in a Cointegrating Regression
Cointegration methods are widely used in empirical macroeconomics
and empirical finance. It is well known that in a cointegrating
regression the ordinary least squares (OLS) estimator of the
parameters is super-consistent, i.e. converges at rate equal to the
sample size T. When the regressors are endogenous, the limiting
distribution of the OLS estimator is contaminated by so-called second
order bias terms, see e.g. Phillips and Hansen (1990) <doi:10.2307/2297545>.
The presence of these bias terms renders inference difficult. Consequently,
several modifications to OLS that lead to zero mean Gaussian mixture
limiting distributions have been proposed, which in turn make
standard asymptotic inference feasible. These methods include
the fully modified OLS (FM-OLS) approach of Phillips and Hansen
(1990) <doi:10.2307/2297545>, the dynamic OLS (D-OLS) approach of Phillips
and Loretan (1991) <doi:10.2307/2298004>, Saikkonen (1991)
<doi:10.1017/S0266466600004217> and Stock and Watson (1993)
<doi:10.2307/2951763> and the new estimation approach called integrated
modified OLS (IM-OLS) of Vogelsang and Wagner (2014)
<doi:10.1016/j.jeconom.2013.10.015>. The latter is based on an augmented
partial sum (integration) transformation of the regression model. IM-OLS is
similar in spirit to the FM- and D-OLS approaches, with the key difference
that it does not require estimation of long run variance matrices and avoids
the need to choose tuning parameters (kernels, bandwidths, lags). However,
inference does require that a long run variance be scaled out.
This package provides functions for the parameter estimation and inference
with all three modified OLS approaches. That includes the automatic
bandwidth selection approaches of Andrews (1991) <doi:10.2307/2938229> and
of Newey and West (1994) <doi:10.2307/2297912> as well as the calculation of
the long run variance.
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