Approximating a Truncated Normal Regression with the Method of Moments
展示了一种70多年前提出的矩方法，可替代复杂的最大似然或工具变量法来近似截断正态回归，只需计算器和文中表格即可生成最小二乘近似，并给出了与多种估计量的比较示例。
A NUMBER OF ARTICLES have been written in recent as well as more distant times on the subject of limited dependent variables. This broad classification includes two particular special cases. First, the dependent variable has finite probability mass concentrated at some limit point-the so called Tobit model. This case is referred to as the censored model in the statistical literature. The second case is when the dependent variable simply has a limited range and follows a continuous density on this support-the truncated case. In this note we show that a fairly powerful technique for truncated normal distributions, first suggested over 70 years ago by Karl Pearson and Alice Lee [9], can be used in the place of more sophisticated iterative maximum likelihood or instrumental variables techniques. Approximations based upon least squares regressions can be generated which require only a calculator and the table produced here. The censored or limited variable case can also be treated in much the same way. Although the estimator is inconsistent, a consistent estimator based upon this general approach could probably be constructed. An example is given comparing this approximation with the results produced by least squares, maximum likelihood, and Amemiya's consistent estimator. The estimator suggested here compares very favorably with Amemiya's. In a more literary vein, Pearson and Lee should be given substantial credit for their work without detracting in any way from those who independently advanced the area without the benefit of reference to the rather obscure article by Pearson and Lee.2