Abstract
Averting behavior refers to actions taken to defend against environmental or other hazards, whether by reducing exposure to hazards or by mitigating adverse effects of exposure. This chapter examines how information on averting behavior can be used to improve nonmarket valuation. The chapter describes the history, theoretical foundation, and empirical application of averting behavior methods. These methods support estimation of economic benefits of public policies, especially those that reduce morbidity or mortality, in a way that is consistent with utility maximization and is based on observable behavior. The chapter: (1) shows how ignoring averting behavior may cause an invalid measurement of physical and economic damages of pollution or other hazards, and how controlling for averting behavior may improve welfare measurement; (2) explains several ways of using information on averting behavior to estimate the benefits of environmental improvement; (3) provides a simple empirical illustration; and (4) argues that the validity of welfare measurement using averting behavior methods depends on how the challenges of joint production, unknown prices of averting actions, and identification of the effects of pollution and averting behavior are met.
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Notes
- 1.
Although most research on averting behavior focuses on nonmarket valuation, economists also have investigated consequences of averting behavior for efficient control of externalities. Three key issues considered are (1) whether or not persons damaged by an externality who have opportunities for averting action should be taxed or compensated to achieve efficiency (Coase 1960; Baumol and Oates 1988); (2) how averting behavior affects the efficient quantity of an externality (Zeckhauser and Fisher 1976; Oates 1983) and/or complicates policy design and implementation by causing nonconvexity of the social marginal damage function (Shibata and Winrich 1983; McKitrick and Collinge 2002); and (3) whether providing information about environmental, health, or safety risks can reduce damages by promoting averting action (Smith et al. 1995; Shimshack et al. 2007; Graff Zivin and Neidell 2009).
- 2.
Against the same background, economists interested in improving methods for estimating benefits of reduced mortality also applied the contingent valuation method (Jones-Lee et al. 1985) and developed methods for inferring the value of reduced mortality from estimated trade-offs between wages and risks (Thaler and Rosen 1976).
- 3.
Early research provided evidence that (1) large proportions of survey respondents report that they change their behavior when pollution is high (Berger et al. 1987; Bresnahan et al. 1997); (2) many people take a variety of defensive actions in response to water contamination (Harrington et al. 1989; Abdalla 1990); (3) daily activities and demand for medical care respond to changes in ambient air pollution (Dickie and Gerking 1991b; Bresnahan et al. 1997); (4) mitigation increases with residential radon concentrations (Akerman et al. 1991; Doyle et al. 1991; Smith et al. 1995); and (5) individuals whose personal characteristics make them more susceptible to environmental hazards are more likely than others to engage in protective behavior (Bresnahan et al. 1997; Dickie and Gerking 1997, 2009). More recent work has examined behavioral responses to public information about air pollution hazards and/or has used quasi-experimental methods to identify causal effects of pollution, or information about pollution, on behavior and health. These studies support the inference that people act to reduce exposure to pollution hazards (Neidell 2009), implying that ignoring averting behavior causes understatement of the health effects of pollution and of the benefits of pollution reduction.
- 4.
For example, in the retrospective analysis of benefits and costs of the U.S. Clean Air Act, benefits of reduced mortality accounted for more than 80% of the total estimated benefits, and benefits of reduced morbidity made up most of the remainder (U.S. EPA 1997).
- 5.
Behavior is already held constant in the control group of children who experience no increase in pollution because these children play outdoors both days. The difference in probability of illness in this group is the same as measured originally: \(0/100 - 0/100 = 0.\)
- 6.
The “treatment” of averting behavior is self-selected. The difference-in-differences measure of the effect of averting behavior is valid because the children in the treated (indoors) and untreated (outdoors) groups are assumed to be identical but for the choice to avert. The difficulties arising in the more realistic situation in which the children are not identical and the differences between children are related both to health and to averting behavior are taken up in Sect. 8.2.3.
- 7.
In Panel B of Table 8.1, none of the 100 children facing low pollution on both days is sick on either day. In contrast, of the 100 children facing increased pollution on Day 2, 24 are sick when pollution is high, compared to none when pollution is low. Thus, the total effect of pollution on probability of illness is \((24/100 - 0/100) - (0/100 - 0/100) = 0.24.\) To compute the causal effect, hold behavior constant. Among the 20 children who face increased pollution but continue to play outdoors, the increased probability of illness is \((8/20 - 0/20) = 0.4,\) whereas the change in probability of illness among the children who do not face increased pollution but continue to play outdoors is \((0/100 - 0/100) = 0.\) Holding behavior constant, the causal effect of pollution is \(0.4 - 0 = 0.4.\) The effect of pollution on the probability of averting behavior may be computed by comparing the increased probability of staying indoors between those facing increased pollution \((80/100 - 0/100)\) and those facing no increased in pollution \((0/100 - 0/100)\) to obtain \(0.8 - 0 = 0.8.\) Finally, among those who face increased pollution, the probability of illness increases by \((16/80 - 0/80) = 0.2\) for those who engage in averting behavior by staying indoors and by \((8/20 - 0/20) = 0.4\) among those who do not engage in averting behavior. Averting behavior changes the probability of illness by \(0.2 - 0.4 = - 0.2.\)
- 8.
In the model by Gerking and Stanley (1986), for example, h = “health capital,” I = use of medical care, and \(q =\) ambient air quality.
- 9.
In Jakus (1994), for example, the home-produced output (h) is the quality of trees on an individual’s property, the environmental input (q) is pest infestation, and the defensive behavior (I) is effort to control pests, such as spraying pesticide.
- 10.
For example, Richardson et al. (2012) estimated models in which h = symptoms of illness. Neidell (2004, 2009) and Moretti and Neidell (2011) considered situations where h represents emergency rooms visits or hospital admissions. Joyce et al. (1989) estimated health production functions where the outputs include h = probability of infant mortality. In all of these papers, the environmental inputs are measures of air pollution.
- 11.
If there is more than one averting input (e.g., \(I_{1}\) and \(I_{2}\) with relative prices \(p_{1}\) and \(p_{2}\)), one finds the quantities of inputs that minimize the cost of producing a given output level at a given level of environmental quality. The cost-minimizing demands are \(I_{j} (p_{1} ,p_{2} ,q,h),\;j = 1,2.\) The defensive expenditure function is the minimum cost function \(D(p_{1} ,p_{2} ,q,h) = p_{1} I_{2} (p_{1} ,p_{2} ,q,h) + p_{2} I_{2} (p_{1} ,p_{2} ,q,h).\).
- 12.
Even the compensated, or utility constant, effect of environmental quality on the demand for a defensive input is indeterminate in sign. The Marshallian effect will be negative if the defensive input is more productive when environmental quality is low, the marginal utility of market consumption is greater when home-produced output is higher, and there is diminishing marginal utility in home-produced output.
- 13.
With a Cobb–Douglas production function, \(I^{D} (h,q) = \left( {G^{ - 1} hq^{{ - \gamma_{q} }} } \right)^{{1/\gamma_{I} }} ,\) and the change in defensive expenditure that holds health constant when environmental quality improves is \(\partial D/\partial q = - \left( {D\gamma_{q} /q\gamma_{I} } \right) = - p\left( {\gamma_{q} /\gamma_{I} } \right)(I/q) < 0.\) With a quasi-linear utility function, the utility-maximizing change in defensive expenditure is \(p\left( {\partial I^{*} /\partial q} \right) = \left( {\beta_{q} /(1 - \beta_{I} )} \right)\left( {D/q} \right) > 0.\) Thus, the chosen change in defensive expenditure does not even take the same sign as the change that holds output constant. As another example, if both the production function and the utility function take the Cobb–Douglas form, the utility-maximizing change in defensive expenditures is zero, whereas the change that holds output constant remains negative and takes the same form as in the example considered in the text.
- 14.
In the example with Cobb–Douglas production and quasi-linear utility, \(\partial I^{*} /\partial q > 0\), as discussed above in connection with the change in defensive expenditures. Thus the total effect exceeds the partial effect, \(\partial h^{*} /\partial q = \left( {\partial f/\partial q} \right)/\left( {1 - \beta_{I} } \right) > \left( {\partial f/\partial q} \right) > 0.\) Alternatively, if both the production function and the utility function take the Cobb–Douglas form, \(\partial I^{*} /\partial q = 0\) and the partial and total effects coincide. Available empirical evidence suggests, in contrast to these two examples, that in most cases considered, \(\partial I^{*} /\partial q < 0\) and the total effect of changes in environmental quality will be less than the partial effect. In any case, the two effects are not identical, and it is the partial effect that is needed to estimate marginal willingness to pay in Eq. (8.17).
- 15.
The relationship between estimates of damage costs and willingness to pay, however, is less clear cut when considering a change in environmental quality rather than a change in health or other home-produced output. This occurs because damage cost estimates normally rely on the total effect of environmental quality \({\text{d}}h/{\text{d}}q\) rather than the partial effect used to estimate marginal willingness to pay in Eq. (8.17). The relative magnitude of partial and total effects is theoretically ambiguous, but prior empirical evidence suggests that defensive behavior increases when environmental quality diminishes, causing the partial effect to exceed the total effect in absolute value. This outcome leads to the presumption that willingness to pay for improved environmental quality exceeds the savings in damage costs associated with improved environmental quality.
- 16.
The Bockstael–McConnell model is more general than the one considered here in that it allows q to enter the utility function directly (as opposed to being only an input into a household production function), and allows for multiple home-produced goods.
- 17.
The change in expenditures equals
$$\begin{aligned} {\text{d}}e\left( {p^{c} ,q,U^{0} } \right)/{\text{d}}q = & \left( {\partial e\left( {p^{c} ,q,U^{0} } \right)/\partial p} \right)\left( {\partial p^{c} /\partial q} \right) - \left( {\partial e\left( {p^{c} ,q,U^{0} } \right)/\partial q} \right) \\ = & I^{h} \left( {p^{c} ,q,U^{0} } \right)\left( {\partial p^{c} /\partial q} \right) - \left( {\mu \partial U/\partial h} \right)\left( {\partial f/\partial q} \right) - \mu \left( {\partial U/\partial q} \right) \\ = & 0\left( {\partial p^{c} /\partial q} \right) - \left( {\mu \partial U/\partial h} \right)\left( {\partial f/\partial q} \right) - \mu \left( {\partial U/\partial q} \right) \\ \end{aligned}$$.
- 18.
Bockstael and McConnell (1983) explained how these two conditions generalize to the case in which there are multiple home-produced outputs and discussed approximating the compensating surplus using the ordinary (Marshallian) demand curve for a defensive input.
- 19.
The compensated and ordinary demand functions are identical because of the quasi-linear form of the utility function.
- 20.
Recall that \(\beta_{I} = \alpha \gamma_{I} > 0\) because h is a good \((\alpha > 0)\) and q is a good \((\gamma_{I} > 0)\). Also, \(\beta_{I} < 1\) to meet second-order sufficient conditions.
- 21.
In the example model, \(D\left( {p,q^{0} ,h^{0} } \right) - D\left( {p,q^{1} ,h^{0} } \right) = \left[ {\beta_{I} G^{\alpha } p^{{ - \beta_{I} }} \left( {q^{0} } \right)^{{\gamma_{q} /\gamma_{I} }} u} \right]^{{1/1 - \beta_{I} }} \left[ {\left( {q^{0} } \right)^{{ - \gamma_{q} /\gamma_{I} }} - \left( {q^{1} } \right)^{{ - \gamma_{q} /\gamma_{I} }} } \right].\) The observed change in defensive expenditures is \(pI\left( {p,q^{0} ,y} \right) - pI\left( {p,q^{1} ,y} \right) = \left[ {\beta_{I} G^{\alpha } p^{{ - \beta_{I} }} u} \right]^{{1/1 - \beta_{I} }} \left[ {\left( {q^{0} } \right)^{{\beta_{q} /1 - \beta_{I} }} - \left( {q^{1} } \right)^{{\beta_{q} /1 - \beta_{I} }} } \right]\).
- 22.
Utility in death is often considered “bequest utility.” The key assumption is that \(U_{a} (x) > U_{d} (x)\).
- 23.
To see this, differentiate the identity (8.37) with respect to W and S to obtain \(\left( {U_{a} - U_{d} } \right){\text{d}}s - \left( {sU_{a}^{\prime } + (1 - s)U_{d}^{\prime } } \right){\text{d}}W.\) Set the differential equal to zero to hold expected utility constant and solve for \({\text{d}}W/{\text{d}}s\).
- 24.
The value of statistical life is determined from Eq. (8.32) by applying the change in survival probability to a population sufficiently large to be expected to save one life and computing the amount the population would be willing to pay. For example, suppose the small change in survival probability evaluated in Eq. (8.31) is \({\text{d}}s = 10^{ - 5} .\) If a population of 10,000 persons each experienced this change in survival probability, one would expect the number of deaths in the population to decline by one. Thus, multiplying the value of reduced risk in Eq. (8.32) by 10,000 would yield the value of statistical life.
- 25.
The sufficient condition \(- \left( {\partial^{2} s/\partial I^{2} } \right)\left( {U_{a} - U_{d} } \right) + 2p\left( {\partial s/\partial I} \right)\left( {U_{a}^{{\prime }} - U_{d}^{{\prime }} } \right) + p^{2} \left( {{\text{d}}E[MUC]/{\text{d}}x} \right) < 0\) holds if there is (1) diminishing marginal productivity of defensive action, (2) a higher marginal utility of consumption when alive than when dead, and (3) financial risk loving in neither state of the world \(\left( {U_{a}^{{\prime \prime }} (x),U_{d}^{{\prime \prime }} (x) \le 0} \right)\).
- 26.
Blomquist (2004) reviewed pertinent conceptual and empirical issues involved in applying averting behavior models to estimate the value of reduced risk of death and provides citations to the literature. Results for models more complex than the two-state model were considered by Shogren and Crocker (1991), Quiggin (1992), and Bresnahan and Dickie (1995).
- 27.
Alternative approaches include the following: Blomquist (1979) applied a clever empirical strategy to attack joint production; Hori (1975) derived theoretical conditions, implemented empirically by Dickie and Gerking (1991a), that allow the problem to be overcome; Dardis (1980) simulated willingness to pay under varying assumptions about the relative magnitudes of the values of the joint benefits of an averting good.
- 28.
Mansfield et al. (2006) addressed this problem using a stated preference survey to estimate the value of adjustments in time use.
- 29.
Another way to estimate the household production technology is to transform the production function to obtain the function giving the amount of averting input required to produce a given level of home-produced output at a specified level of environmental quality \(I^{D} = I^{D} (h,q).\) Estimated parameters of this function are used to compute marginal willingness to pay based on Eq. (8.18). Gerking and Stanley (1986) implicitly solved the production relationship to express medical care use (I) as a function of measures of health (h) and ambient air pollution (q). They estimated the effect of ambient ozone on use of medical care and multiplied by the full price of medical care to estimate marginal willingness to pay to reduce ozone concentrations, as suggested by Eq. (8.18).
- 30.
Similar problems hinder identification of parameters of the required defensive input function \(I^{D} (h,q)\) and of the defensive expenditure function \(D(h,p,q)\) because these functions are transformations of the household production function.
- 31.
Many applications use medical care as an averting input. The price of medical care depends on health insurance coverage, and insurance coverage is probably related to unobserved determinants of health (the disturbance in Eq. (8.37)). Also, many averting behaviors involve use of time and the full price of the averting input depends on the value of time. But the value of time is probably correlated with human capital and with unobserved determinants of health.
- 32.
Another exclusion restriction suggests income as an instrument for averting action. Were it not for the quasi-linear form of the utility function, individual income would appear in the Marshallian demand for the defensive input in Eq. (8.38), but income is not an input in the household production function. However, income is almost certainly correlated with unobserved determinants of health and thus would not satisfy instrument exogeneity.
- 33.
- 34.
Additionally, there can be substantial measurement error in the measures of pollution concentrations because of imperfect matching of individuals to pollution monitors and variations in the amounts of time spent indoors and outdoors. Measurement error would be expected to attenuate the estimated effect of pollution on health.
- 35.
On the basis of evidence that boat traffic is unrelated to participation in outdoor activities, they argued that the instrument isolates variation in ozone that is independent of averting behavior and therefore that the instrumental variables’ estimator identifies the partial effect of ozone on health. Their instrumental variables’ estimates of the effect of ozone are about four times larger than their least-squares estimates.
- 36.
For example, the reduced-form behavioral and demand functions in Eqs. (8.38) and (8.39) are determined as solutions to the illustrative model of Sect. 8.3 in which the utility function is quasi-linear, the household production function is Cobb–Douglas, and the budget constraint is linear (see Eq. (8.16)).
- 37.
External validity concerns whether inferences can be generalized from the population and setting studied to other populations and settings.
- 38.
- 39.
Bresnahan et al. (1997) discussed other averting inputs.
- 40.
Day and month indicators are used for time fixed effects because sample members were contacted on different dates. Air pollution varies by day and season, as do unobserved determinants of behavior and symptoms.
- 41.
Ozone is not emitted directly by sources but is formed from interactions involving other pollutants, sunlight, and heat. Thus ozone is correlated with weather, and because weather also affects symptoms and outdoor activities, exclusion of weather variables would lead to omitted variables bias in estimated ozone coefficients.
- 42.
At concentrations above 20 pphm, the estimated effect of a 1-pphm increase equals 0.153 − 0.7867 = 0.63, with a standard error of 0.30. The estimated slope change occurring at 20 pphm should not be taken literally as indicating a discrete change in behavior because the choice of 20 pphm for the knot is arbitrary. Using a variety of piecewise linear and quadratic specifications, Bresnahan et al. (1997) found that outdoor time declines when ambient ozone rises above 12 to 14 pphm. The knot at 20 pphm is used for a comparison to results of Neidell (2009), who found that outdoor activities decline when the forecast ozone concentration exceeds 20 pphm, triggering an air quality alert.
- 43.
The coefficient of ozone in the medical care equation is not significant at 10% in the full sample.
- 44.
The conditional mean number of symptoms and the probability of obtaining medical care are nonlinear functions of the inner products of co-variates and coefficients in the Poisson and logit models; coefficients therefore do not measure marginal effects of co-variates on the expected number of symptoms or probability of medical care use. See Greene (2012, Chapters 17-18) regarding the computation of marginal effects in these models. In the present analysis, marginal effects are computed at the mean of all co-variates.
- 45.
The value of avoiding a symptom is computed as the average of values obtained by Dickie and Messman (2004) and Richardson et al. (2012) after inflating these values to 2014 dollars. The full price of medical care, computed as the out-of-pocket expense of a visit to one’s regular physician plus the product of the wage and the time usually required for the doctor visit, was measured in the initial interview, averaged over the sample, and inflated to 2014 dollars. See Dickie and Gerking (1991b).
- 46.
An initial list of suspected sources of omitted variables bias might include lagged values of pollution and weather variables, additional measures of weather conditions, measures of allergens, and uncontrolled adjustments in behavior, such as changing the time of day of outdoor activities to avoid exposure to the peak daily concentrations of air pollution.
- 47.
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Dickie, M. (2017). Averting Behavior Methods. In: Champ, P., Boyle, K., Brown, T. (eds) A Primer on Nonmarket Valuation. The Economics of Non-Market Goods and Resources, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7104-8_8
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