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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.

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Fig. 1

Source: USGS shakemaps

Fig. 2

Source: Own elaboration

Fig. 3

Source: Own elaboration based on USGS shakemaps

Fig. 4

Source: Own elaboration

Fig. 5

Source: Own elaboration

Notes

  1. 8.8\(^{\circ }\) in the Moment magnitude scale (MMS).

  2. Similar evidence has been found for other environmental disasters such as floods (Luechinger and Raschky 2009; Sekulova et al. 2016), droughts (Carroll et al. 2009), extreme weather events (von Möllendorff and Hirschfeld 2016), and hurricanes (Berlemann 2016).

  3. The Life Satisfaction Approach has also been used to value intangibles as diverse as airport noise (Van Praag and Baarsma 2005) and terrorism (Frey et al. 2009).

  4. For a further review of welfare measures in economics see Bockstael and Freeman (2005). Van Praag and Baarsma (2005), Welsch and Kühling (2009) and Frey et al. (2009) provide good examples of how these measures can be used under the LSA to compute the monetized value of intangible goods.

  5. Another approach to compute the non-pecuniary costs of an earthquake would be to compute a Quality of Life Index using hedonic price models as in Naoi et al. (2007).

  6. Appendix 2: Derivation of Welfare Measures” section presents the derivation of Eq. (2).

  7. Good controls are those likely to have an effect on mental health and income, but that are not themselves affected by mental health, income or the earthquake/tsunami intensity (Angrist and Pischke 2008). Thus, we refrain to include any variables measured after the earthquake took place as controls.

  8. See “Appendix 2: Derivation of Welfare Measures” section.

  9. Even though the immediate shock was unexpected, the whole country is known for frequent earthquake activity that could have affected past firm and household decisions. Fortunately, since every region in Chile has had major earthquakes in the past, there is no credible possibility of self-sorting into “earthquake-free zones”, therefore we have a strong case to claim exogeneity at least for our earthquake/tsunami measures.

  10. The sample can be downloaded at http://observatorio.ministeriodesarrollosocial.gob.cl/enc_post.php.

  11. The regions affected by 27-F earthquake are Valparaiso, Metropolitana, Libertador Bernando O’Higgins, Maule, Biobio and Araucania. See Fig. 1.

  12. They correspond to the 6.1% of the raw sample.

  13. One of the reviewers raised the concern of the potential relationship between the attrition and the negative experiences related to the 2010 earthquake. We regress the non-response dummy variable on some earthquake intensities controlling for several factors using a Probit Model. The results, available upon request, show no significant association between the non-response and the exposure to the earthquake.

  14. Although the total sample of the CASEN-PT survey corresponds to 62,194 individuals, only the individuals present in the interview (21,603) answered the questions related to PTSD.

  15. The question was: “In the last 30 days have you have a health problem?”.

  16. PGA is often a good predictor of both fatal and nonfatal injuries (Peek-Asa et al. 2003; Mahue-Giangreco et al. 2001).

  17. The affected area corresponds to 150 municipalities, which range from entirely rural areas to big cities containing both urban and rural areas.

  18. We choose to use the inverse of the DTS to maintain the same interpretation as in our theoretical model presented in Sect. 3.

  19. To take into account of a potential correlation of residuals when individuals are taken from the same city, cluster standard errors at the city level are used in all specifications.

  20. We also test whether income has a diminishing marginal effect on mental health. Table 9 in “Appendix 1: Additional Tables and Figures” section show that, at least for this sample, the relationship between income and mental health is linear.

  21. An important control is whether the individuals are religious-minded and have social capital (Ali et al. 2012). However, our survey data does not provide detailed information about these dimensions.

  22. This contrasts with the results for the earthquake in Pakistan found by Ali et al. (2012), which show that being the head of the family is one of the strongest predictors of PTSD.

  23. Note that this contradicts the hypothesis that individuals with better social networks are more resilient.

  24. Standard errors were clustered at the city level in the Probit Model. Partial effects were computed at the mean of the variables, whereas standard errors were computed using Delta method. The marginal impact for dummy variables is the discrete change from the reference level.

  25. For the models estimated by the Maximum Likelihood procedure, such as the IV-Probit and IV-Ordered Probit model, the weak-instrument test is carried out by testing whether the instrument is significant in the reduced equation which is estimated jointly with the mental health equation. Since our model is just identified, the \(\chi ^2\)-squared statistic is approximately similar to the F-statistic.

  26. Here we run the following model:

    $$\begin{aligned} h_{i1}^* = \alpha + \beta \ln (y_{i0})+ \gamma r_i + {\mathbf{x}}_{i0}'{\varvec{\delta }}+ \lambda z_i + \epsilon _{i0}, \end{aligned}$$

    and test whether \(\lambda = 0\). This test has been used to test the validity of the exclusion restriction, i.e., \({\text {Cov}}(z_{i0}\cdot \epsilon _{i0}) = 0\). See for example Kan (2007).

  27. For the 2SLS, the exogeneity of income is tested using Wooldridge (1995)’s robust score test. For the IV-Probit and IV-Ordered Probit model the exogeneity test corresponds to \(H_0:\rho = 0\), where \(\rho\) is the correlation between the error terms of the mental health’s and income’s equation.

  28. Table 10 shows that the estimates of the compensatory variations are not sensitive if we consider that the individuals affected by the earthquake were those who experienced an intensity equal to or greater than 6.5 on the MMI scale.

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Appendices

Appendix 1: Additional Tables and Figures

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

Fig. 6
figure 6

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

Fig. 7
figure 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:

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

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Sarrias, M., Jara, B. How Much Should We Pay for Mental Health Deterioration? The Subjective Monetary Value of Mental Health After the 27F Chilean Earthquake. J Happiness Stud 21, 843–875 (2020). https://doi.org/10.1007/s10902-019-00112-y

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Keywords

  • Mental health
  • Subjective well-being
  • Life satisfaction approach
  • Economic valuation
  • Natural disasters
  • Monetary compensation
  • PTSD