ABSTRACT: Pesaran, Shin, and Smith (2001) (PSS) proposed a bounds procedure for testing for the existence of long run relationships between a unit root ependent variable (y_t) and a set of weakly exogenous regressors x_t when the analyst does not know whether the independent variables are stationary, unit root, or mutually cointegrated processes. This procedure recognizes the analyst's uncertainty over the nature of the regressors but not the dependent variable. We extend their analysis to the case where the analyst is uncertain whether y_t is a stationary or unit root process. In this case, the test statistics proposed by PSS are uninformative for inference on the existence of a long run relationship between y_t and x_t. We propose the LRM test statistic as an alternative. Using stochastic simulations, we demonstrate the behavior of the test statistic given uncertainty about the univariate dynamics of both y_t and x_t, 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 specifications. We demonstrate the utility of the bounds procedure by re-examining the relationship between economic conditions and domestic policy mood.

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