Imprecision in the Estimation of Willingness to Pay Using Subjective Well-Being Data

The subjective well-being (SWB) method has become a popular tool to estimate the willingness to pay (WTP) for non-market goods using widely available well-being data. In this method, the WTP measure contains the ratio of two coefficients (of the non-market good and consumption), which are both estimated in a regression on SWB. Computing confidence intervals for such ratios turns out to be error-prone, in particular when the consumption coefficient is imprecisely estimated. Even though this problem is known, many studies either do not report imprecision in the final estimate, or use inadequate methods. This paper compares five different methods to compute confidence intervals for normal ratio distributions: the delta, Fieller, parametric bootstrapping, and bootstrapping method, and a numerical integration of Hinkley’s formula. In a simulation, a large number of emulated SWB data sets are generated to calculate confidence intervals for WTP and the corresponding coverage rates with each method. The findings suggest that the delta method is the least accurate and not robust to lowering the statistical power or changing correlations between the estimators. All other methods are fairly accurate, robust, and can be recommended for use.