Theorem 2 is a generalization to the asymptotic results of Hansen (2000)’s constant threshold model.4 Theorem 2 shows that the convergence rate of (γˆ0, γˆ1, γˆ2) is T1−2α, which is decreasing in α. This convergence rate of γˆ0 is equal to the rate found for the constant threshold model in Hansen (2000).