The Tobit model with a non‐zero threshold
标准Tobit模型在删失阈值非零且未知时估计有偏，本文提出新估计量解决该问题，蒙特卡洛模拟显示偏差可能很大，新估计量超一致且渐近分布不受阈值估计影响。
The standard Tobit maximum likelihood estimator under zero censoring threshold produces inconsistent parameter estimates, when the constant censoring threshold γ is non‐zero and unknown. Unfortunately, the recording of a zero rather than the actual censoring threshold value is typical of economic data. Non‐trivial minimum purchase prices for most goods, fixed cost for doing business or trading, social customs such as those involving charitable donations, and informal administrative recording practices represent common examples of non‐zero constant censoring threshold where the constant threshold is not readily available to the econometrician. Monte Carlo results show that this bias can be extremely large in practice. A new estimator is proposed to estimate the unknown censoring threshold. It is shown that the estimator is superconsistent and follows an exponential distribution in large samples. Due to the superconsistency, the asymptotic distribution of the maximum likelihood estimator of other parameters is not affected by the estimation uncertainty of the censoring threshold.