A random sample drawn from a population would appear to offer an ideal opportunity to use the bootstrap in order to perform accurate inference, since the observations of the sample are IID. In this paper, Monte Carlo results suggest that bootstrapping a commonly used index of inequality leads to inference that is not accurate even in very large samples. Bootstrapping a poverty measure, on the other hand, gives accurate inference in small samples. We investigate the reasons for the poor performance of the bootstrap, and find that the major cause is the extreme sensitivity of many inequality indices to the exact nature of the upper tail of the income distribution. Consequently, a bootstrap sample in which nothing is resampled from the tail can have properties very different from those of the population. This leads us to study two non-standard bootstraps, the m out of n bootstrap, which is valid in some situations where the standard bootstrap fails, and a bootstrap in which the upper tail is modelled parametrically. Monte Carlo results suggest that accurate inference can be achieved with this last method in moderately large samples.

We examine the statistical performance of inequality indices in the presence of extreme values in the data and show that these indices are very sensitive to the properties of the income distribution. Estimation and inference can be dramatically affected, especially when the tail of the income distribution is heavy, even when standard bootstrap methods are employed. However, use of appropriate semiparametric methods for modelling the upper tail can greatly improve the performance of even those inequality indices that are normally considered particularly sensitive to extreme values.

This article addresses the important issue of anchoring in contingent valuation surveys that use the double-bounded elicitation format. Anchoring occurs when responses to the follow-up dichotomous choice valuation question are influenced by the bid presented in the initial dichotomous choice question. Specifically, we adapt a theory from psychology to characterize respondents as those who are likely to anchor and those who are not. Using a model developed by Herriges and Shogren (1996), our method appears successful in discriminating between those who anchor and those who did not. An important result is that when controlling for anchoring ? and allowing the degree of anchoring to differ between respondent groups ? the efficiency of the double-bounded welfare estimate is greater than for the initial dichotomous choice question. This contrasts with earlier research that finds that the potential efficiency gain from the double-bounded questions is lost when anchoring is controlled for and that we are better off not asking follow-up questions. JEL Classification: Q26, C81, D71.

In this paper, we study starting-point bias in double-bounded contingent valuation surveys. This phenomenon arises in applications that use multiple valuation questions. Indeed, response to follow-up valuation questions may be influenced by the bid proposed in the initial valuation question. Previous researches have been conducted in order to control for such an effect. However, they find that efficiency gains are lost when we control for undesirable response effects, relative to a single dichotomous choice question. Contrary to these results, we propose a way to control for starting-point bias in double-bounded questions with gains in efficiency.