JinSeo.Cho - Estimating and Inferring the Nonlinear Autoregressive Distributed Lag Model by Ordinary Least Squares

<Abstract> This study examines the large sample behavior of an ordinary least squares (OLS) estimator when a nonlinear autoregressive distributed lag (NARDL) model is correctly specified for nonstationary data. Although the OLS estimator suffers from an asymptotically singular matrix problem, it is consistent for unknown model parameters, and follows a mixed normal distribution asymptotically. We also examine the large sample behavior of the standard Wald test defined by the OLS estimator for asymmetries in long- and short-run NARDL parameters, and further supplement it by noting that the long-run parameter estimator is not super-consistent. Using Monte Carlo simulations, we then affirm the theory on the Wald test. Finally, using the U.S. GDP and exogenous fiscal shock data provided by Romer and Romer (2010), we find statistical evidence for long-and short-run symmetries between tax increase and decrease in relation to the U.S. GDP.