How Much Should We Pay for Mental Health Deterioration? The Subjective Monetary Value of Mental Health After the 27F Chilean Earthquake

Abstract

In this article we use the life satisfaction approach to assess the non-pecuniary costs of Mental health impacts after the 2010 Chile earthquake. By linking both subjective well-being valuation literature with studies that describe psychological impacts after natural disasters, we are able to quantify how big a compensation should be to leave individuals as well as they were before the event. Our results suggest that people who experience stress should be compensated by approximately 80–90% of the average monthly income if the shock was strong enough to cause significant damages. These estimates are robust to different empirical specifications, endogeneity, shock intensity measures, and mental health definitions. We estimate that the total costs of mental health deterioration are about 7% of the total reported damages, a significant amount that policymakers should not ignore in post-earthquake reconstruction stages.

Appendices

Appendix 1: Additional Tables and Figures

See Tables 9, 10, 11 and 12 and Figs. 6 and 7.

Fig. 6

Correlation across PGA, PGV and MMI. Notes: Own elaboration based on USGS shakemaps

Fig. 7

Source: Own elaboration

Compensating variation across models (one standard deviation increase). Notes: Compensating variation were computed using Eq. (5). SE computed using Delta Method and clustered standard errors

Table 9 Sensitivity analysis for earthquake-intensity measures (OLS)

Table 10 Compensating variation for being affected by earthquake (MMI)

Table 11 Instrumental variable estimation (PGA)

Table 12 Instrumental variable estimation (tsunami)

Appendix 2: Derivation of Welfare Measures

Equation (2) can be obtained in the following way. Total differentiation of Eq. (1) gives:

$$\begin{aligned} d\upsilon = \frac{\partial h}{\partial r}dr + \frac{\partial h}{\partial y}dy + \frac{\partial h}{\partial x}dx + \frac{\partial h}{\partial \epsilon }d\epsilon , \end{aligned}$$

Setting $d \upsilon = 0$ and holding x and $\epsilon$ constant yields:

$$\begin{aligned} \frac{\partial h}{\partial r}dr + \frac{\partial h}{\partial y}dy = 0. \end{aligned}$$

Solving for $\frac{d y}{d r}$ gives Eq. (2). Note that in our model income is in logarithm, thus using the fact that $d \ln (y)= dy/ y$ yields Eq. (5).

Equation (6) is derived as follows. Considering Eqs. (3) and (4), we get:

$$\begin{aligned} \begin{aligned} h(y_{i0};\,r_{i0};\,{\mathbf{x}}_{i0})&= h(y_{i0} - CV;\, r_{i1}, {\mathbf{x}}_{i0}) \\ \alpha + \beta \ln (y_{i0}) + \gamma r_{i0}&= \alpha + \beta \ln (y_{i0} - CV) + \gamma r_{i1} \\ \gamma (r_{i0} - r_{i1})&= \beta \left[ \ln (y_{i0} - CV) - \ln (y_{i0})\right] \\ \frac{\gamma (r_{i0} - r_{i1}) }{\beta } + \ln (y_{i0})&= \ln (y_{i0} - CV) \\ \exp \left[ \frac{\gamma (r_{i0} - r_{i1}) }{\beta } + \ln (y_{i0}) \right]&= y_{i0} - CV \\ CV&= y_{i0} - \exp \left[ \frac{\gamma (r_{i0} - r_{i1}) }{\beta } + \ln (y_{i0}) \right] \\ CV&= y_{i0} - \exp \left[ \ln (y_{i0})\right] \exp \left[ \frac{\gamma (r_{i0} - r_{i1}) }{\beta } \right] \\ CV&= y_{i0} - y_{i0}\exp \left[ \frac{\gamma (r_{i0} - r_{i1}) }{\beta } \right] \\ CV&= y_{i0}\left[ 1 - \exp \left[ \frac{\gamma (r_{i0} - r_{i1}) }{\beta } \right] \right] \end{aligned} \end{aligned}$$