Errors of Truncation in Approximations to Expected Consumer Surplus
研究了从需求曲线计算消费者剩余时，使用二阶泰勒近似代替真实期望值所产生的截断误差，通过蒙特卡洛模拟发现忽略高阶项会导致显著偏差，尤其当分母方差大或均值小时。
Consumer surplus and other welfare measures calculated from demand curves are random variables. This is so because these measures are functions of estimated (as opposed to known) demand parameters, which, of course, are random variables. Increasingly, this realization has been incorporated into studies which assess such benefit measures. It is typical in these studies that the expected value of the benefit measure is employed, in keeping with the common practice of assuming that benefit-cost decision-makers are risk neutral.' Unfortunately, consumer surplus measures usually involve the ratio of random variables, and the expected value of a ratio of random variables is not equal to the ratio of the expected values. The use of the ratio of the expected values leads to a biased estimate of the true measure, although it is a consistent estimator. Indeed, in small samples the expectation of consumer surplus often does not have a closedform representation. In this case, one must resort to an approximation or a cumbersome Monte Carlo analysis. The former is the tack most often taken; for example, Bockstael and Strand (1987) and Kealy and Bishop (1986) have used a second-order Taylor series approximation to expected consumer surplus in their investigations. Use of a second-order approximation will improve the estimation of expected consumer surplus relative to the use of the ratio of expected values. However, this second-order approximation still may not be accurate, especially when the variance of the denominator of the ratio (typically an estimated demand parameter on a price variable) is relatively large and/or its mean is relatively small. This is because these statistics figure prominently in higher order terms of the approximation. We investigate this issue via a Monte Carlo analysis which (with a large enough number of trials) is able to give a direct estimate of the mean of the consumer surplus measure. Comparing this to the second-order approximation shows that the impact on estimated consumer surplus from omitting higher order terms can be substantial. In our example, the magnitude of the error due to truncation of the approximation varies markedly across functional forms for the demand