Valuing Pain using the Subjective Well-being Method: The willingness to pay for pain relief is in the range of $56-145 per day, lower than previously reported

Valuing Pain using the Subjective Well-being Method. Thorhildur Ólafsdóttir, Tinna Laufey Ásgeirsdóttir, Edward C. Norton. Economics & Human Biology, November 16 2019, 100827. https://www.sciencedirect.com/science/article/pii/S1570677X19300656

Highlights
. Improved econometric methods provide new information on the value of pain
. We allow the trade-off between pain and income to vary across income ranges
. The willingness to pay for pain relief is in the range of 56-145 USD per day
. The monetary value of pain relief is lower than previously reported

Abstract: Chronic pain clearly lowers utility, but valuing the reduction in utility is empirically challenging. Here, we use improvements over prior applications of the subjective well-being method to estimate the implied trade-off between pain and income using four waves of the Health and Retirement Study (2008-2014), a nationally representative survey on individuals age 50 and older. We model income with a flexible functional form, allowing the trade-off between pain and income to vary across income groups. We control for individual fixed effects in the life-satisfaction equations and instrument for income in some models. We find values for avoiding pain ranging between 56 to 145 USD per day. These results are lower than previously reported and suggest that the higher previous estimates may be heavily affected by the highest income level and confounded by endogeneity in the income variable. As expected, we find that the value of pain relief increases with pain severity.

Discussion

By using improved econometric methods, we provide new information on the value of pain relief among people older than 50. Our results suggest a lower CV for pain than previously reported. More importantly, we contribute to the literature by using a PWL model as a more flexible method to express WTP across income ranges, instead of the traditional log transformation of income. Results from IV-models also yield CVs that are considerably lower than previous research suggests.

We compared our income coefficients to coefficients previously reported for lifesatisfaction equations from four different countries; Britain, Germany, Australia and USA (Clark et al., 2018) and found that our income coefficients correspond to the lower end of the range of coefficients. This is true after adjusting the income coefficients for different scaling of the life-satisfaction variable in the two studies (11/5), with our coefficients (times 2.2) closely reflecting those found using data from Britain (see Clark et al, Table 2.2). This comparison, although limited to model specifications where well-being is assumed to be linear in log income in OLS and FE models, is helpful to benchmark our income coefficients.

The two studies that use exogenous lottery wins to estimate the treatment effects of income on life-satisfaction . Lindqvist et al. (2018) and Apouey and Clark (2015) . have starkly different results. The treatment effect of $100K on life-satisfaction is estimated to be 0.037 SD units by Lindqvist et al. and 1.369 SD units by Apouey and Clark. We choose the former as an alternative for our income coefficient in Table 3 (column 1, OLS) because Lindqvist et al. use a larger sample size and have stronger internal validity. Lindqvist et al.  approximate a lifetime income effect on life-satisfaction using lottery prizes annuitized over 20 years at a 2% interest rate. To calculate a CIV for our linear income model in Table 3, we take the estimate 0.062 from Table A10 in Lindqvist et al., which, after adjustment to different scaling of the life-satisfaction variable (0.062/2.2=0.028) and to USD prices between 2011 and 2015, we can apply an estimate of 0.028/1.0537=0.027. Using the income coefficient of 0.027 and our pain coefficient of -0.0563 that is adjusted for individual heterogeneity (FE model in Table 3), the corresponding CIV is 57 USD per day.

We did two additional sensitivity tests. First, instead of using a pain coefficient from an experimental setting, we used the pain coefficient from our estimate of the effect of pain on life-satisfaction through transitions into and out of arthritis status (see Table A5). Using the pain coefficient of -0.0793 from Table A5 and the lifetime income effect estimate from Lindqvist et al. (0.027) generates a CIV of 80 USD per day. Second, we compared the CIV by income coefficients across the two studies for the case of ln(income). The corresponding Lindqvist estimate (adjusted) is 0.16 (0.377 in Table A10 in Lindqvist et al.) and applying the FE coefficient of -0.0561 the estimated CIV is 54 USD per day. Both CIV estimates, 57 and 80 USD per day, are within our estimated range of 56-145 USD per day. The CIV using lifetime log-income effect from Lindqvist et al. of 54 USD per day is lower.

Because there is some variability across countries in the income gradient for life satisfaction equations (Clark et al, 2018), an income effect estimate based on a sample of Swedish lottery players may not apply to US data. Furthermore, there is inherent uncertainty in the annuity-adjustment parameter used to rescale the lifetime income gradient. However, the comparison is helpful and will hopefully stimulate similar research in other countries. This sensitivity analysis points towards the lower part of our estimated range of 56-145 USD per day as the most credible CIV estimate. We note that using income estimates from lottery studies instrinsically produces willingness to accept (WTA), whereas by using variation in household income the estimated CIV is between WTA and WTP.

Our paper has several limitations. Pain can be a consequence of neurological diseases, diabetes, or of musculoskeletal origin, but we did not have controls for those conditions that we found validated by a doctor´s diagnosis. However, any possibility of omitted-variable bias should be mitigated by controlling for age because neurological disease and diabetes likelihood (Type 2) increases with age. Furthermore, the numerous other health controls included should capture the effect of musculoskeletal conditions on pain and life satisfaction, in particular psychiatric problems, lung disease, cancer and arthritis. External validity may be limited by the age range used, in particular if the marginal utility of income for those over 50 is lower than in the younger population, which would result in higher CV-estimates than in a sample with lower mean age. Responses to life-satisfaction questions may be liable to situational influences, such as the site of the interview, the weather, one´s mood and the interviewer, but those differences can be considered as random error (Veenhoven, 1993).  The value of pain is likely overestimated in previous research using the well-being valuation method, with our best approximation to a WTP estimate being in the range of 56- 145 USD per day. This range of estimates is derived from models where we take into account the effects of individual heterogeneity (by applying FE models), the leveraging effect of the highest income levels (by applying PWL models) and the endogeneity of the income variable with mother´s education as an instrument (by applying OLS-IV models). Those are issues that previous research and our analysis alike have highlighted as issues that should be taken into consideration when finding as reliable estimates as possible for the CIVs. Furthermore, the value of pain relief is positively related to severity of pain. Our research also has implications for the CV literature as a whole. We show the importance of controlling for the endogeneity of income and allowing the effect of income to vary flexibly across income levels. To this end, PWL models are promising because they perform well econometrically and allow for easier exploration of results across income groups than log transformations of income.