A Bounds Approach to Inference Using the Long Run Multiplier

Pesaran, Shin, and Smith 2001 (PSS) proposed a bounds procedure for testing for the existence of long run cointegrating relationships between a unit root dependent variable (yt) and a set of weakly exogenous regressors xt when the analyst does not know whether the independent variables are stationary, unit root, or mutually cointegrated processes. This procedure recognizes the analysts uncertainty over the nature of the regressors but not the dependent variable. When the analyst is uncertain whether yt is a stationary or unit root process, the test statistics proposed by PSS are uninformative for inference on the existence of a long run relationship between yt and xt. We propose the LRM test statistic as a means of testing for long run relationships without knowing whether the series are stationary or unit roots. Using stochastic simulations, we demonstrate the behavior of the test statistic given uncertainty about the univariate dynamics of both yt and xt, illustrate the bounds of the test statistic, and generate small sample and approximate asymptotic critical values for the upper and lower bounds for a range of sample sizes and model speci cations. We demonstrate the utility of the bounds framework for testing for long run relationships in models of public policy mood and presidential success.

Originally Published at 10.1017/pan.2019.3