We correct the limit theory presented in an earlier paper by Hu and Phillips (Journal of Econometrics, 2004) for nonstationary time series discrete choice models with multiple choices and thresholds. The new limit theory shows that, in contrast to the binary choice model with nonstationary regressors and a zero threshold where there are dual rates of convergence ( n 1 /4 and n 3 /4 ), all parameters including the thresholds converge at the rate n 3 /4 . The presence of non-zero thresholds therefore materially aﬀects rates of convergence. Dual rates of convergence reappear when stationary variables are present in the system. Some simulation evidence is provided, showing how the magnitude of the thresholds aﬀects ﬁnite sample performance. A new ﬁnding is that predicted probabilities and marginal eﬀect estimates have ﬁnite sample distributions that manifest a pile-up, or increasing density, towards the limits of the domain of deﬁnition.
Phillips, Peter C.B.; Jin, Sainan; and Hu, Ling, "Nonstationary Discrete Choice: A Corrigendum and Addendum" (2005). Cowles Foundation Discussion Papers. 1800.