In linear-in-income logit, a case with no income effect, the expectation ofthe compensating variation and the expectation of the equivalent variation are identical and provided by the logsum formula. The statistical properties of the estimator of this measure of welfare change are investigated. Under regularity conditions, the estimator of the measure obtained from maximum likelihood estimators of the utility coefficients is consistent, asymptotically normal and asymptotically efficient. Estimates are provided of the variance of the estimator of the measure, useful to derive large sample confidence bounds, and of the covariance of estimators of the measure in distinct scenarios, useful for large sample hypothesis testing.

在收入线性对数中，没有收入影响的情况下，补偿变量的期望值和等效变量的期望值相同，并由对数公式提供。研究了这种福利变化测度的估计量的统计性质。在规则性条件下，从效用系数的最大似然估计器获得的度量估计是一致的，渐近正态的和渐近有效的。提供了估计值的估计方差的估计值（可用于得出大的样本置信范围），以及估计值的估计值在不同场景下的协方差的估计值（可用于大样本假设检验）。