On the validity of the estimates of the VSL from contingent valuation: Evidence from the Czech Republic

Abstract

We assess the reliability and validity of estimates of the Value per Statistical Life (VSL) from contingent valuation by administering the same contingent valuation (CV) questionnaire on samples drawn from the population of the Czech Republic five years apart. We use a novel approach in eliciting the WTP for cancer mortality risk reduction, in that we present respondents with two probabilities—that of getting cancer, and that of surviving it. We find that the cancer VSL is somewhat different across the two samples, but this difference is completely explained by income and cancer dread. The WTP is proportional to the size of the cancer mortality risk reduction, and increases with income and with cancer dread. The income elasticity of the VSL is 0.5 to 0.7, and is thus in line with the findings in Masterman and Viscusi (2018). Our estimates of the VSL (approximately €3–4 mill. May 2019 PPP euro) are close to Viscusi and Masterman’s prediction (2017) based on compensating wage studies, less than the estimates from compensating wage studies conducted in the Czech Republic, and similar to estimates from other stated preference studies in the Czech Republic. We conclude that the CV questionnaire and administration procedures produce reliable and stable results, and that construct and criterion validity are likewise good. We interpret these findings as providing support for an approach that expresses very small mortality risks and risk reductions as the product of two probabilities.

Appendices

APPENDIX 1: Derivation of cancer and non-cancer VSL, and VSCC

The expected utility of the individual is:

$$ EU=\left(1-\theta \right)\left(1-p\right)U(y)+\left(1-\theta \right)p\left(1-q\right)V(y)+\left(1-\theta \right) pqW(y)+\theta G(y), $$

(9)

where θ is the chance of dying from any cause other than cancer, p is the chance of getting cancer, and q is the chance of dying from cancer, if one gets cancer. The unconditional cancer mortality risk is thus m = p·q.

We define the non-cancer VSL as the WTP for a marginal reduction in θ, the cancer VSL as the WTP for a marginal reduction in m, and the Value per Statistical Case of Cancer (VSCC) as the WTP for a marginal reduction in the risk of getting cancer p. It is also possible to obtain the WTP for a marginal improvement in the conditional chance of surviving cancer, namely q.

We first derive expressions for these metrics assuming that the utility of income when dead is always zero (i.e., W(y) = G(y) = 0). Under this simplifying assumption, it is straightforward to show that the non-cancer VSL is

$$ {VSL}_N=\frac{d y}{d\theta}=\frac{1}{1-\theta}\cdotp \frac{\left(1-p\right)U(y)+p\left(1-q\right)V(y)}{\left(1-p\right){U}^{\prime }(y)+p\left(1-q\right){V}^{\prime }(y)}, $$

(10)

where the numerator is the expected utility when alive, and the denominator is the marginal expected utility of income when alive, further multiplied by the chance of being alive (in the sense of not dying from cancer).

We arrive at the cancer VSL by replacing p in Eq. (9) with m/q, taking the total differential of the expected utility with respect to m and y, and setting that equal to zero:

$$ {VSL}_C=\frac{dy}{dm}=\frac{1}{q}\cdotp \frac{U(y)-\left(1-q\right)V(y)}{\left(1-p\right){U}^{\prime }(y)+p\left(1-q\right){V}^{\prime }(y)} $$

(11)

The VSCC is.

$$ \mathrm{VSCC}=\frac{dy}{dp}=\frac{U(y)-\left(1-q\right)V(y)}{\left(1-p\right){U}^{\prime }(y)+p\left(1-q\right){V}^{\prime }(y)}. $$

(12)

In other words, the cancer VSL is equal to the VSCC, divided by q. The WTP for an improvement in conditional survival is $\frac{dy}{dq}=\frac{pV(y)}{\left(1-p\right){U}^{\prime }(y)+p\left(1-q\right){V}^{\prime }(y)}$.

If we further assume that V(y) = (1-h)U(y), where h (0 ≤ h ≤ 1) is the reduction in utility with respect to the healthy state, expressions (10) and (11) further simplify to

$$ {VSL}_N=\frac{1}{1-\theta}\cdotp \frac{U(y)}{U^{\prime }(y)}, $$

(13)

$$ {VSL}_C=\frac{dy}{dm}=\frac{U(y)}{U^{\prime }(y)}\cdotp \frac{\left[\frac{1+\left(1-h\right)\left(q-1\right)}{q}\right]}{\left[\left(1-p\right)+p\left(1-q\right)\left(1-h\right)\right]}, $$

(14)

respectively.

Expressions (13) and (14) show that the baseline odds of getting cancer, the chance of dying from it, and the loss of utility h when in the sick state enter in both the numerator and the denominator of the expression for the cancer VSL (Alberini & Ščasný 2018), but do not affect the non-cancer VSL, which depends exclusively on the utility in the healthy state and the chance of dying from all causes other than cancer.

The above expressions for the cancer and non-cancer VSLs change somewhat when one allows the utility of income when dead to be different from zero. Assume for the sake of simplicity that W(y) = G(y) at all values of y, i.e., the utility from leaving a bequest does not depend on the cause of the death. Under this assumption, Eq. (9) becomes

$$ EU=\left(1-\theta \right)\left(1-p\right)U(y)+\left(1-\theta \right)p\left(1-q\right)V(y)+\left[\left(1-\theta \right) pq+\theta \right]W(y). $$

(15)

The non-cancer VSL is now

$$ {VSL}_N=\frac{d y}{d\theta}=\frac{1}{1-\theta}\cdotp \frac{\left(1-p\right)U(y)+p\left(1-q\right)V(y)-\left(1-m\right)W(y)}{\left(1-p\right){U}^{\prime }(y)+p\left(1-q\right){V}^{\prime }(y)+\left(m+\frac{\theta }{1-\theta}\right){W}^{\prime }(y)} $$

(16)

The numerator in the second term in the right-hand side of (16) is the utility differential between being alive and dead from non-cancer causes, while the denominator is the expected marginal utility of income.

The cancer VSL and the VSCC are now

$$ {VSL}_C=\frac{dy}{dm}=\frac{1}{q}\cdotp \frac{U(y)-\left(1-q\right)V(y)- qW(y)}{\left(1-p\right){U}^{\prime }(y)+p\left(1-q\right){V}^{\prime }(y)+\left(m+\frac{\theta }{1-\theta}\right){W}^{\prime }(y)} $$

(17)

$$ VSCC=\frac{dy}{dp}=\frac{U(y)-\left(1-q\right)V(y)- qW(y)}{\left(1-p\right){U}^{\prime }(y)+p\left(1-q\right){V}^{\prime }(y)+\left(m+\frac{\theta }{1-\theta}\right){W}^{\prime }(y)}, $$

(18)

showing once again that the cancer VSL is equal to the VSCC divided by q.

If we assume that V(y) = (1-h)U(y) and W(y) = (1-λ)U(y), with λ > h, then (16), (17) and (18) are simplified to

$$ {VSL}_N=\frac{d y}{d\theta}=\frac{1}{1-\theta}\cdotp \frac{U(y)\cdotp \left[\left(1-p\right)+p\left(1-q\right)\left(1-h\right)-\left(1-m\right)\left(1-\lambda \right)\right]}{U^{\prime }(y)\left[\left(1-p\right)+p\left(1-q\right)\left(1-h\right)+\left(m+\frac{\theta }{1-\theta}\right)\left(1-\lambda \right)\right]}. $$

(19)

$$ {VSL}_C=\frac{dy}{dm}=\frac{1}{q}\cdotp \frac{U(y)\cdotp \left[1-\left(1-q\right)\left(1-h\right)-q\left(1-\lambda \right)\right]}{U^{\prime }(y)\left[\left(1-p\right)+p\left(1-q\right)\left(1-h\right)+\left(m+\frac{\theta }{1-\theta}\right)\left(1-\lambda \right)\right]} $$

(20)

$$ VSCC=\frac{dy}{dp}=\frac{U(y)\cdotp \left[1-\left(1-q\right)\left(1-h\right)-q\left(1-\lambda \right)\right]}{U^{\prime }(y)\left[\left(1-p\right)+p\left(1-q\right)\left(1-h\right)+\left(m+\frac{\theta }{1-\theta}\right)\left(1-\lambda \right)\right]} $$

(21)

Compared to the simpler expected utility presented in Section 2 of this paper, this broader model results in p, q, h, λ and θ entering in the expressions for the cancer and non-cancer VSLs, and the VSCC.

APPENDIX 2. Wording of the Dread Question

C1. In the table below we list illnesses, health problems or situations that can be hazardous to one’s health or even fatal.

Which of these situations are those that you dread the most for the physical, psychological and social suffering they bring? Try to rate each of them on a scale from 1 to 5, where 1=low dread and 5=high dread.

Please keep in mind that for “dread” we do not mean how likely this situation is. Instead, we want you to think of how much this situation scares you for the physical, psychological and social suffering it may bring.

Programmer: Keep the order, but rotate the start at random, for ex. 1 to 8, then 2..8 followed by 1, etc.

Aspect or consequences	Low dread			High dread
Dying in a car or road traffic accident.	1	2	3	4	5
Dying in a domestic accident.	1	2	3	4	5
Surgery on an emergency basis.	1	2	3	4	5
Developing chronic respiratory illnesses (asthma, chronic bronchitis, emphysema).	1	2	3	4	5
Getting cancer.	1	2	3	4	5
Becoming paralyzed.	1	2	3	4	5
Having a heart attack.	1	2	3	4	5
Developing an illness that makes me completely dependent on being taken care of by someone else.	1	2	3	4	5

1. Note: the order of these statements was randomized to the respondent. The “high dread” dummy we use in our analyses is equal to one when the respondent selects “5” as the level of dread associated with getting cancer

APPENDIX 3: Alternative Calculation of the VSL for different risk reductions levels from the 2014 wave

Fig. 4

The VSL is calculated as median WTP for a specified cancer mortality risk reduction as per the model in Table 6, col. (A), divided by the mortality risk reduction