Estimation and Inference of Nonlinear Autoregressive Distributed Lag Models With Time Trend by Ordinary Least Squares

This study examines the large-sample behavior of an ordinary least squares (OLS) estimator within a correctly specified nonlinear autoregressive distributed lag (NARDL) model for nonstationary data. Although the OLS estimator suffers from an asymptotically singular matrix problem, it remains consistent for unknown model parameters and asymptotically follows a mixed normal distribution. Additionally, we examine the large-sample behavior of the standard Wald test, as defined by the OLS estimator, for asymmetries in long- and short-run NARDL parameters, and enhance this analysis with a super-consistent long-run parameter estimator. We then confirm the theory on the Wald test using Monte Carlo simulations. Finally, using U.S. GDP and exogenous fiscal shock data, we demonstrate the use of the OLS estimator and show statistical evidence of long- and short-run symmetries between the effects of tax increases and decreases on U.S. GDP.