Item nonresponse in contingent valuation: should CV researchers impute values for missing independent variables?

INTRODUCTIONResearchers who use the contingent valuation (CV) method have as a goal the measurement of valid and reliable estimates of economic values, or willingness to pay (WTP), for environmental goods (Mitchell & Carson, 1989). The contingent values should be free of sample-related bias, such as unit nonresponse (Loomis 1987, Edwards & Anderson, 1987, Dalecki, Whitehead, & Blomquist, 1993), sample selection (Whitehead, Groothuis, & Blomquist, 1993), or item nonresponse on the CV question (Mitchell & Carson, 1989).Item nonresponse is a common problem in survey-based research (Madow, Olkin, & Rubin, 1983; Connelly & Brown, 1992). CV researchers have overlooked, however, the potential bias associated with item nonresponse on variables other than WTP. This may be due to a preoccupation with other important CV issues such as market design and appropriate econometric methods. Item nonresponse bias can be a critical problem in contingent valuation research, especially when estimating aggregate benefits.THE POTENTIAL PROBLEMSConsider a mail, telephone, or in-person survey that collects data on a random sample of a general population. Suppose a large proportion of respondents fail to report their income due to embarrassment or for privacy reasons. Several strategies are available when dealing with item nonresponse on income (Little & Rubin, 1989). The simplest strategy, and the one most often observed in CV research, is complete case analysis which is the default in most statistical software packages. That is, the researcher discards the cases with item nonresponse and analyzes only the complete cases. There are two problems with this strategy.First, when incomplete cases are discarded because of item nonresponse on an independent variable, information on other independent variables is lost. This type of item nonresponse creates problems similar to unit nonresponse. Throwing out incomplete cases will result in a biased sample unless the discarded cases are a random subsample. For example, if low income households are less likely to report income and these cases are discarded the remaining sample overly represents high income households. Further, sample sizes can decrease substantially when cases with missing income data are discarded.Second, when incomplete cases are discarded information on the dependent variable, WTP, is lost. The sample bias is intensified when the variable with item nonresponse is a determinant of WTP. Extending the previous example, if incomplete cases are discarded a form of selection bias results. Respondents select themselves out of the analysis by failing to report income. For normal goods, income should be positively related with measures of WTP. If the sample under-represents low income households, WTP will be biased upward if incomplete cases are discarded.POTENTIAL SOLUTIONSTwo strategies that can be used to correct for item nonresponse bias are weighting or data imputation. The weighting approach analyzes only complete cases but corrects for the sample bias by explicitly recognizing the proportion of the population represented by the sample. Weighting reduces the bias from analyzing only the complete cases but information from the incomplete cases, which may be different from information reported in the complete cases, is lost. Weighting reduces the effects of item nonresponse but does not alter the effects of item selection.(1)Imputation requires replacing missing data with estimates of the missing values. Such a strategy allows analysis of the entire sample which reduces the effects of item nonresponse. If the estimate of the missing value is unbiased, data imputation also reduces the effects of item selection. The least costly imputation methods are unconditional mean imputation and conditional mean imputation (Little & Rubin, 1987, 1989).(2)To employ the unconditional mean imputation method, calculate the univariate mean of the variable with problematic item nonresponse and replace missing values with the mean value. …