A threshold model of real US GDP and the problem of constructing confidence intervals in TAR models

We estimate real US GDP growth as a threshold autoregressive process, and construct confidence intervals for the parameter estimates. However, there are various approaches that can be used in constructing the confidence intervals. We construct confidence intervals for the slope coefficients and the threshold using asymptotic results and bootstrap methods, finding that the results for the different methods have very different economic implications. We perform a Monte Carlo experiment to evaluate the various methods. Surprisingly, the confidence intervals are wide enough to cast doubt on the assertion that the time-series responses of GDP to negative growth rates are different than the responses to positive growth rates.