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No Country for Old Unit Root Tests: Bridge Estimators Differentiate between Nonstationary Versus Stationary Models and Select Optimal Lag

This paper introduces a novel way of differentiating a unit root from a stationary alternative. We write up the model consisting of zero and nonzero parameters. If the lagged dependent variable has a coefficient of zero, we know that the variable has a unit root. We exploit this property and treat this as a model selection problem. We show that Bridge estimators can select the correct model. They estimate zero parameter on the lagged dependent variable as zero (nonstationarity), if this is nonzero (stationary), estimate the coefficient with standard normal limit. In this sense, we extend the statistics literature as well, since that literature only deals with model selection among only stationary variables. The reason that our methodology can outperform the existing unit root tests with lag selection methods stems from the two-step nature of existing unit root tests. In our method, we select the optimal lag length and unit root simultaneously. We show that in simulations, this makes big difference in terms of size and power.