بی طرفانه می تواند سخت تر باشد؟ ارزیابی روش ها به کاهش تعصب واریانس تجارت کردن در برآورد WTP

This paper aims at verifying the claim, appeared in recent literature, that it is possible to control for response bias associated to the double bound elicitation method, while keeping gains in efficiency of the WTP estimates. Results from a Monte Carlo analysis lead, in general, to reject the claim; but when initial bids are not correctly chosen, the gains in efficiency are confirmed. An empirical application dealing with WTP estimation for drinking water quality improvements illustrates a case where a flexible modeling approach based on Copula distributions allows relevant gains with respect to the Single Bound estimator.

The informational and incentive properties of contingent valuation elicitation methods have long been debated in the last two decades. The Single Bound method, where individuals respond to a one-shot question, is recognized as a method which is capable, if some conditions hold, to induce a truthful revelation of preferences, as demonstrated by Carson and Groves (2007, henceforth CG). However, its statistical inefficiency can be a serious problem, especially for small sample sizes. Asking a second voting question, with a lower (higher) price than the first, conditional to a no (yes) answer, was suggested by Hanemann et al. (1991) as a way to add statistical efficiency to the estimations while keeping the survey costs under control. Unfortunately, this may cause a serious response bias, as early recognized by Cameron and Quiggin (1994): using a bivariate probit to model empirical double bound data, they showed that the values obtained from the two responses were not identical, and that assuming so, would definitely produce distorted estimates. Indeed, as argued by CG, even the hypothesis of perfect correlation implicit in the univariate double bound (interval data) model is hardly credible: “Any interpretation of the information signal provided by offering to make the same Q available at two different prices implies that less than a perfect correlation between the two responses should be observed (CG, p. 195). Yet, Herriges and Shogren (1996, henceforth HS), adopted a univariate model – which incorporates a Bayesian updating mechanism – to detect and correct a specific elicitation effect which they refer to as “anchoring bias”. Their approach was then generalized by Whitehead (2002), who modeled the anchoring mechanism using a random effect probit, which allows imperfect correlation between the two responses. Alberini et al. (1997) resorted to the more general bivariate probit approach proposed by Cameron and Quiggin (1994) to analyze several data sets. Their work supports the view that the bivariate approach is helpful to signal the possible existence of different elicitation effects. Based on a Monte Carlo analysis, Genius and Strazzera (2005) confirmed that the application of appropriate bivariate models to double bound data can help detection and correction of elicitation effects arising from the use of this elicitation format. In addition, they showed that more flexible distributions (i.e. bivariate Copulas) as an alternative to the standard bivariate probit model, can be useful to increase efficiency of the estimates of the coefficients of the WTP equation. However, their investigation did not include the assessment of the bias-efficiency trade-off for the central tendency measures estimates of WTP: the present paper aims at filling this gap. In their analysis of the anchoring behavioral model, HS (p. 129) argued that “even if the analysis corrects for this anchoring effect, the efficiency gains from follow-up questioning are likely to be reduced, since the effective information content of the follow-up questioning is diluted by the anchoring phenomenon”. McLeod and Bergland (1999, p. 122) concur with this view, and say that “the increased precision in the estimated WTP by asking a follow-up question is not as large, or even non-existent, when Bayesian updating is accounted for in the estimation”. As put forward by Carson et al. (2001), “the choice a CV researcher typically faces is between using an elicitation format that is unbiased but with a large confidence interval and using one that is potentially biased but with a much tighter confidence interval”. The same opinion was expressed by Whitehead (2002), who, based on empirical results, argued that the only case when gains in efficiency are still present after correction of elicitation effects is when the follow-up question allows for correction of a poor choice of initial bids. A completely different position was taken by Flachaire and Hollard (2006, FH hereafter), who claimed that if an appropriate modeling strategy is adopted, it is possible to circumvent the trade-off between efficiency and unbiasedness. If this were true, this would indeed be an important step forward for the CV discipline, in contrast with previous studies contending that when elicitation effects are present and are controlled for, the efficiency gains provided by the follow-up bid question are lost. In the present work, a Monte Carlo experiment is conducted to test the validity of the FH claim. The FH model tackles a mix of elicitation effects in a univariate setting, along the lines of the HS model. In this paper, further Monte Carlo exercises are conducted, simulating different elicitation effects, also drawing from recent works by Aprahamian et al., 2007 and Aprahamian et al., 2008. In accordance with the theoretical hypothesis expressed by CG, and reported above, in most experiments we will assume that the WTP is generated from a bivariate process. In addition, the paper contains an empirical application which gives an example where a bivariate model is used to detect elicitation effects. Alternative models are applied to the data and their performance in terms of efficiency of the estimates of the coefficients which are relevant for WTP measurement, is assessed. Another contribution of this paper is that it shows that the use of Copula distributions adds flexibility to the specification of bivariate models, and this can be useful to achieve efficiency gains. The article is organized as follows: in the next section it will be seen how different elicitation effects influence the shape of the WTP distribution. Section 3 presents the econometric models analyzed in the paper. Section 4 describes the experimental design for the Monte Carlo study and reports the main results, which are further illustrated in Section 5 by means of an empirical application related to the estimation of willingness to pay for quality improvements in drinking water; section 6 concludes the paper.

In this paper we have explored the conditions under which the trade-off between efficiency and unbiasedness can be reduced. We have used Monte Carlo simulations to assess the accuracy and precision of the estimates obtained from alternative models, including recent proposals by DeShazo (2002), Flachaire and Hollard (2006), and Aprahamian et al., 2007 and Aprahamian et al., 2008, under different elicitation effects scenarios. The simulations results show that when the initial bid design is flawed, use of appropriate econometric techniques can effectively reduce the trade-off between efficiency and unbiasedness in a substantial way. In contrast to the FH's claims, we find that in other circumstances, however, the efficiency gains are negligible, confirming previous empirical findings by Whitehead (2002). The practical relevance of these results rests upon the fact that, especially when budget constraints do not allow extensive pre-tests, the possibility that the bid design is incorrect is quite concrete. It should be recalled that application of optimal bid design techniques requires prior knowledge of the underlying WTP distribution which is rarely a possibility for applied researchers. Improved bid designs based on empirical data such as the ones proposed in Scarpa and Bateman (2000), might still be “not good enough” if they rely heavily on the median estimates of pre-test data and on an initial assumption about WTP distribution. In fact, the final distribution used in a contingent valuation study could differ from the one assumed to derive the initial bids.8 Unfortunately, in many cases the practitioner realizes that the bid design is poor when it is too late already to make any improvement. If a possible solution might be to use many bids to avoid the risk of leaving some part of the WTP distribution uncovered, this would have the effect of increasing the variance of the estimates: as shown by Kanninen (1995), an optimal bid design should use only few (as many as four) bids, concentrated around the median of the WTP distribution. Alberini (1995b) upholds this view, suggesting that no more than six bids should be employed. But with just a few bids, the possibility of ending up with a wrong bid design becomes more serious: in applied work, especially with small sample sizes, it is far from remote. Hence, especially when the sample size is not large, we would recommend gathering of double bound data: the application of a bivariate model (as simple as a bivariate probit) will suffice to test for the existence of elicitation effects. If the two equations are not significantly different, then elicitation effects are not significant, and the Double Bound model will provide efficient and accurate estimates. If elicitation effects are present, we have seen that the Double Bound model most often leads to WTP estimates which are seriously biased, although very efficient. In this case, if the initial bids are well chosen, alternative models do not provide significant improvements with respect to the Single Bound model. However, if the choice of initial bids is imperfect, a case not uncommon in practice when small budgets preclude extensive pre-test studies, the application of an appropriate bivariate model will help to provide significant gains in the efficiency of the estimates.