A distribution theory is developed for least-squares estimates of the
threshold in Threshold Autoregressive (TAR) models. We find that if we
let the threshold effect (the difference in slopes between the two re
gimes) become small as the sample sire increases, then the asymptotic
distribution of the threshold estimator is free of nuisance parameters
(up to scale). Similarly, the likelihood ratio statistic for testing
hypotheses concerning the unknown threshold is asymptotically free of
nuisance parameters. These asymptotic distributions are nonstandard, b
ut are available in closed form, so critical values are readily availa
ble. To illustrate this theory, toe report an application to the U.S.
unemployment rate. We find statistically significant threshold effects
.