The Local to Unity Dynamic Tobit Model

This paper extends local to unity asymptotics to the non-linear setting of the dynamic Tobit model, motivated by the application of this model to highly persistent censored time series. We show that the standardised process converges weakly to a non-standard limiting process that is constrained (regulated) to be positive, and derive the limiting distributions of the OLS estimates of the model parameters. This allows inferences to be drawn on the overall persistence of a process (as measured by the sum of the autoregressive coefficients), and for the null of a unit root to be tested in the presence of censoring. Our simulations illustrate that the conventional ADF test substantially over-rejects when the data is generated by a dynamic Tobit with a unit root.