2.1 Valuation of risk to life in the context of crime

Calculating the benefits of reducing crime is challenging. It can be made from different perspectives: the government (the costs in anticipation of crime—as police—and in the consequences of crime—courts and prison systems) or the victim. And the issue is even wider, extending to the society as a whole over the nonvictims, as well as to varying mechanisms like undesired avoidance behavior, weakening community cohesiveness caused by fear, overdeterrence (i.e., activities avoided by innocent people for fear of being accused of criminal activity), the load imposed on the offenders and their families, and the undue cost of justice (i.e., punishing innocents and exonerating guilty). Monetizing the cost of crime (the benefits of reducing it) requires information on several types of costs involved (i.e., tangible costs that include direct costs as those incurred to repair material or health consequences of crime and indirect costs as productivity losses, as well as intangible costs such as pain and suffering). Atkinson et al. (Reference Atkinson, Healey and Mourato2005) estimate the intangibles at more than half of the value of crime.

Early valuations of crime were based on “bottom-up” calculations that added all possible direct and indirect costs in an accounting manner (analogous to the human capital approach), and measured intangibles by comparison to civil court compensation decisions (see McCollister et al., Reference McCollister, French and Fang2010). In particular, Cohen (Reference Cohen1988) studies the cost of crime from the standpoint of the victim, making an effort to measure the intangibles like subsequent suffering and loss of quality of life by examining jury awards from cases in which victims sued perpetrators.

The excessive burden of the bottom-up method and the difficulties estimating intangibles led the scientists to find another way (Cohen, Reference Cohen, Roman, Dunworth and Marsh2010). The “top-down” approach encompasses all these elements by acting on a single source, usually through hedonic pricing and CV.Footnote ⁵ Thaler (Reference Thaler1978) uses the hedonic price method to isolate the impact of the crime rate on property prices. Pope and Pope (Reference Pope and Pope2012) also relate decreases of violent crime rates to property value increases. In their work, violent crime rates include homicides and also other violent crimes because, as explained by the authors, “although homicides are a good national barometer of crime, they are rare enough at a localized level that it is difficult to use homicides as a crime indicator on its own.” Even if there were enough data by type of crime, different crimes are likely collinear (neighborhoods with a high murder rate are also high in all sorts of crimes) and it is not easy to control for all potential determinants of property prices. Beyond other empirical difficulties lying behind the hedonic pricing methodology (see Haab & McConnell, Reference Haab and McConnell2002; Freeman, Reference Freeman2003), data limitations substantially contribute to explain why direct methods began to be applied in crime valuation research studies.Footnote ⁶

Zarkin et al. (Reference Zarkin, Cates and Bala2000) utilize CV to assign a value to the use of drugs by making its drawbacks for society (one of which is crime) explicit. The change proposed is that a certain number of addicts undergo a recovery treatment. The cost is a voluntary contribution. Ludwig and Cook (Reference Ludwig and Cook2001) make a CV study of a weapon reduction program. The proposed change is a 30 % reduction in injuries produced by firearms, and the cost is a local tax. The valuation obtained is $1.2 million (US dollars as of 1998) per gun injury, not necessarily implying death. Cohen et al. (Reference Cohen, Rust, Steen and Tidd2004) value the risk of different types of crimes in the USA: burglary, assault, armed robbery, rape, and murder. The change proposed for the latter is a 10 % reduction. The valuation obtained for murder is $9.7 million (US dollars as of 2000), which is an order of magnitude higher than the bottom-up valuation.

Atkinson et al. (Reference Atkinson, Healey and Mourato2005) perform a CV of crime in the UK. They deal with three categories of crime: serious wounding, other wounding, and common assault (no injuries). The authors discover a large heterogeneity in the willingness to pay to reduce crime, depending on some personality traits, the belief of control of the situation, the fear of crime, security perception, etc. Nagin et al. (Reference Nagin, Piquero, Scott and Steinberg2006) address youth crime proposing two alternative programs: longer prison and rehabilitation. The value of the latter is somehow higher despite having a similar efficacy level. This study opens up the issue of policy: should the risk reduction or the policy be valued? On the one hand, it can be argued that the result is what counts. On the other hand, collateral effects of different policies may affect the valuation to the extent of a less effective policy being preferred by the society.Footnote ⁷

Among direct methods, the CV technique is the most frequent approach for assessing the VSL (Freeman, Reference Freeman2003), and the only one used to date within the context of crime. However, CV presents the respondent with an improved scenario having a cost for the individual to choose versus the status quo, whereas CE consists of several scenarios characterized by a number of attributes, including the aspects of risk (for instance fatality, permanent injury, or temporary injury), the cost, and even policies. Both allow observation of decisions in hypothetical scenarios presented in controlled experiments, but CE permits overcoming the package effect (Saelensminde, Reference Saelensminde2003) present in CV.Footnote ⁸ This means that when the proposed improvement covers a singular risk, e.g., a reduction in the rate of death, the respondent attaches to it an improvement in all sorts of related risks and policies. Hence, CE can avoid the package effect by presenting several dimensions, including simultaneously different risks and policies. The use of CE for valuing policing policies was proposed in Carson and Louviere (Reference Carson and Louviere2017). To our knowledge, Picasso and Cohen (Reference Picasso and Cohen2019) is the only academic publication that values policies to fight against crime, and this is the only article that employs the CE method to value VSL in the context of crime. It is worth mentioning that direct methods go beyond active value (lower risk for the individual or her friends and family) as they are capable of measuring the passive value (altruistic idea of a better society regardless of a personal impact).

In summary, the valuation of crime is generally restricted to a few developed countries,Footnote ⁹ and the efforts in top-down valuation done to date employ the CV method and, with the exception of Cohen et al. (Reference Cohen, Rust, Steen and Tidd2004), they cover a variety of crimes, whereas the value of life is not directly addressed. The objective of the present study is to measure the VSL in the crime context via a CE in a developing country (Argentina). CE has not been used in the crime context before, to the best of our knowledge. The crime context is not only relevant by itself, but it also expands the scope of validity of existing estimates of the VSL since the labor context limits the scope to the population of workers, and the traffic context to the population of drivers, whereas the crime context addresses the whole population of adults.

2.2 Demographic determinants of the value of the risk to life

As it is recognized in the literature (Hammitt, Reference Hammitt2017), the VSL depends on the mortality risk involved in terms of both the type and the amount of the risk (Hoffmann et al., Reference Hoffmann, Krupnick and Qin2017), income levels, the context of death, risk aversion, cultural and religious beliefs, life expectancies and health, family network, etc. Hence, the value of a statistical life is not a universal constant to be determined, but a value depending on the individual and the context.

The demographic determinants of the VSL have been empirically explored mainly in the labor and transportation context.Footnote ¹⁰ Viscusi (Reference Viscusi1978) shows that safety is a normal good, i.e., it has positive income elasticity; and continued developing this same idea in Kniesner et al. (Reference Kniesner, Viscusi and Ziliak2010), by estimating the income elasticity of the VSL between 1.23 and 2.24, with a median of 1.44, using a quantile regression.Footnote ¹¹

The context of death also adds or deducts utility. As shown in Cameron and De Shazo (Reference Cameron and De Shazo2013), the value of health risk reductions depends on their attributes. This explains why people may tend to dismiss the high probability risk caused by unhealthy food, whereas they are horrified by extremely rare diseases when they are long and painful. That could explain why Alberini and Scasny (Reference Alberini and Scasny2013) find that the VSL is different for cancer and traffic accidents.

The demographic determinants of the VSL have been empirically explored mainly in the labor context; however, Viscusi and Aldy (Reference Viscusi and Aldy2003) find that risk takers (as identified by the habits of smoking or not using the safety belt) tend to have a lower VSL, suggesting that risk aversion can be a fundamental characteristic showing up in different contexts. In the same line, Hoffmann et al. (Reference Hoffmann, Krupnick and Qin2017) show that people who buy commercial insurance (a proxy for their risk aversion) have lower VSL.

Another factor that might mitigate the VSL is the perception of control. Rizzi and Ortuzar (Reference Rizzi and Ortuzar2003) find evidence supporting that the VSL is lower when the individual thinks he can control the situation. The individual perceives that the probability of death is lower for him despite the general risk prevalence reported. This could explain a higher perceived risk for flying compared with road travel. Family composition is another factor to take into account. Hojman et al. (Reference Hojman, Ortúzar and Rizzi2005) find that having small children correlates with higher VSL.Footnote ¹²

As a result of the review of the literature, we organize the exploration of the demographic factors in several hypotheses. First, we expect VSL to increase with income. Second, impatience is hypothesized to erode the VSL, as predicted by the life cycle theory, through increased subjective discount rate affecting the future benefits derived from life. General risk aversion is expected to induce higher VSL, as found empirically. The subjective perception of the probability of death is hypothesized to influence the VSL. The belief of control of the crime situation is expected to decrease the VSL. The VSL is hypothesized to increase with family size, as a projection of the own life onto dependents. Individualism (the personality trait) is expected to negatively influence VSL. The rationale behind this, not established in the literature yet, is that an individualistic person would disregard the passive valueFootnote ¹³ , focusing mainly on the active value, and then tolerate more risk to avoid funding collective efforts.

3.1 The choice experiment

The measurement instrument, distributed online, has four sections. The first one contains a filter to select the relevant population. Students living with their parents are considered mostly economically dependent and excluded from the sample. It also includes a preliminary measure of the socioeconomic level via the value of the main car in the household, which is used to determine the cost level for the valuation question. The second section holds the CE itself, to be described below. The third one contains a series of questions related to beliefs and perceptions about security issues, experience as a crime victim, impatience and risk aversion, as well as credibility (to assess the validity of the responses to the CE). The last (fourth) section is devoted to demographics, including gender, place of residence, education, and socioeconomic level.Footnote ¹⁶

The CE consists of 10 tasks (as well as 2 previous practice tasks) like the example in figure 1. Each choice task presents two alternative security programs, characterized by risk, policy, and cost. The individual was able to choose one of the programs or a third alternative representing the status quo. The choice tasks differ in the values of the variables following a predesigned experimental plan. Choice tasks seem random to the individual; nevertheless, they are carefully planned with the objective of maximizing the data richness by presenting alternatives forcing trade-off among the variables, as explained below.

Figure 1 Example of choice task.

The security programs are characterized by five variables. The first two variables are homicide and other violent crime risk.Footnote ¹⁷ Our approach, like in Cohen et al. (Reference Cohen, Rust, Steen and Tidd2004), is to learn the value the public assigns to perceived risks. In order to work with current perceptions, we avoided exposing the respondents to descriptions of the process or the consequences of different kinds of crime. We assume the urban population is sufficiently informed about victimization given the high local relevance of crime and the enhanced intensity of social communication prevailing in modern societies. Both risks are varied independently in the experiment, enabling specific valuation and avoiding the package effect.

The metrics for the risk variables deserve consideration. As shown by Kahneman and Tversky (Reference Kahneman and Tversky1979) and Tversky and Kahneman (Reference Tversky and Kahneman1986), people find it difficult to make sense of very low probabilities like the one of being murdered. We avoid this problem by defining the metric as the absolute number of homicides per year in the area. On the other hand, the probability of being a victim of a violent crime is rather high in Argentina. Then the metric was defined as the number of households out of 100 where any of the members faces a violent crime (not death) during one year.

Two policies entered the experiment: extended police presence and the strict fulfillment of court sentences. The former was characterized by frequent police surveillance in the streets, video surveillance cameras in all dangerous places, and empowering the police with pre-emptive rights to arrest suspects. The latter was defined by strict respect for the prison term,Footnote ¹⁸ criminal responsibility since 16 years of age instead of 18, housing dangerous convicted persons far from urban centers,Footnote ¹⁹ and prison improvement to ensure dignity. Respondents were exposed to a detailed description of the policies before starting the experiment, and it was kept available throughout the process in a help screen.

The CE requires creating a hypothetical market where the “trade” of risks and policies is performed by means of a monetary vehicle. In this case, we have created a hypothetical local tax to serve as payment. This tax would be earmarked to fund a local police force, operating at a district level. As is well known, the monetary vehicle is a critical element in the design of experiments. Given the failure of crime control policies implemented in the past, the population has become fairly skeptical about the ability of the government to control crime. This leads some people to reject additional taxes collected by the discredited high-level institutions like the national or provincial government, surrounded by a cloud of corruption (Moreno & Salvia, Reference Moreno and Salvia2012). People rely on private security, but this would be an imperfect vehicle with limited reach to the proposed policies. The payment vehicle was designed to resemble private security in terms of closeness to the local people, but having a wider reach: A tax to create, equip, and instruct a local police force dependent on the district authority. Despite the careful design, we anticipated that a certain number of extreme skeptical individuals would persist. The metric defined for the cost is Ar$Footnote ²⁰ per household-month, so that people can easily relate it to their income and expenditures.

The CE involves setting each variable at specific points to describe each security program. These points are defined in relation to base values. The decisions are grounded on the differences in the values of the variables between alternative programs, so the base values do not enter the model directly. However, realistic values contribute to the external validity of the experiment. The base values for the security risks were set at the actual levels: 1100 homicides per year,Footnote ²¹ and 20 % of households having been a victim of violent crime per year.Footnote ²² The points used in the experiment were set downward, reflecting improvements to the current situation. Five points were set for the rate of homicides: 1100, 900, 700, 500, and 300. Four points were set for violent crime: 20, 15, 10, and 5 households affected out of each 100. The zero level was not included in either case in order to avoid the certainty effect identified by Kahneman and Tversky (Reference Kahneman and Tversky1979) and Tversky and Kahneman (Reference Tversky and Kahneman1986). The base value for the policies is the current situation, as perceived by the individual. The base value for the cost was set at a level compatible with the resources required to implement the policies. Specifically, the cost of the local police organization of the Federal District as stated in the Budget of the Government of the City, was extrapolated to the whole metropolitan area, representing 544 Ar$/household/month. Given the heterogeneity of income, this level could be irrelevant to a large part of the population. Then, we used the preliminary socioeconomic level assessment to classify the respondents into three levels, and dynamically assigned different base values for the cost: 300, 500, and 1000 Ar$/month. Five points were set around the base value: BV − 60 %, BV − 30 %, BV, BV + 30 %, and BV+60 % (Table 2).

Table 2 Experimental plan.

^a BV is the base value, which is determined by an approximation of each individual’s income.

A set of 5 × 4 × 5 × 2 × 2 = 400 combinations is available for each security program, making a total of 400² possible choice tasks. In order to bring this number down to a manageable level for each respondent we performed an optimal experimental plan. An experimental design having 200 tasks was created out of the full factorial, by means of the Federov (Reference Federov, Studden and Eugene1972) algorithm. The tasks were arranged into blocks of 10 by means of the Meyer and Nachtsheim (Reference Meyer and Nachtsheim1995) algorithm.Footnote ²³ In this way, we created blocks of 10 tasks for 20 respondents, planned to maximize the information content. Two practice tasks were added at the beginning of each block to account for learning effects. These 20 blocks of 12 tasks were assigned at random to respondents, repeating as necessary to complete the sample.

Several demographic variables were measured in the survey. Standard questions were used for gender, age, residence, education, and family composition. Income was measured by the socioeconomic level methodology developed by the local society of market research (SAIMO, 2015), primarily based on education and job position.Footnote ²⁴ The habits of smoking and safety belt usage were measured to represent risk aversion. A trade-off instrument was created to measure impatience via subjective discount rate: the respondent was prompted to choose between receiving a certain amount in two weeks or 20 % more 8 weeks later, followed up with another question to determine the point of indifference. The perception of the crime risk exposure was captured by a specific question besides victimization experience. The perception of control was assessed with the question: “How do you think you would behave in a violent assault situation? Drive the criminal away/negotiate to neutralize the risk/don’t know/ask for help/follow the criminal instructions/be paralyzed”. Individualism, as a personality trait, was measured with a stylized version of Triandis and Gelfand (Reference Triandis and Gelfand1998) scale.Footnote ^{25 .} Footnote ²⁶

The instrument was programmed in Lime Survey language, combined with an ad hoc application for the CE. A pilot test was implemented with supervised respondents, and understanding issues were solved before actual fieldwork.

3.2 The discrete choice model

CEs are appropriately represented by DCM based on random utility theory (Mc Fadden, Reference Mc Fadden1975). The DCM represents the decision patterns of the individuals via utility functions. Each alternative is assumed to generate a certain utility level to the individual depicted by a deterministic term (U), and an idiosyncratic random term (ε):

(1) $$ \left\{\begin{array}{l}{\tilde{U}}_{1 it}={U}_{1 it}\left({H}_{1 it},{V}_{1 it},{S}_{1 it},{P}_{1 it},{C}_{1 it}\right)+{\varepsilon}_{1 it}\\ {}{\tilde{U}}_{2 it}={U}_{2 it}\left({H}_{2 it},{V}_{2 it},{S}_{2 it},{P}_{2 it},{C}_{2 it}\right)+{\varepsilon}_{2 it}\\ {}{\tilde{U}}_{3 it}={U}_{3 it}\left({H}_{3 it},{V}_{3 it}\right)+{\varepsilon}_{3 it}\end{array}\right. $$

The following explanatory variables enter the utility functions of the main model: H is the rate of homicides (thousands/year), V is the rate of violent crimes (% of households victimized/year), S is the strictness of the execution of court sentences (0 for current, 1 for strict), P is the police force presence (0 for current, 1 for extended), and C is the cost (Ar$/Month). The random term accounts for model limitations and deviations from pure rationality that may occur in human behavior. The characteristics of the alternatives vary for different tasks and different individuals, being the reason for the subscripts t and i, respectively. Note that the third alternative, the status quo, does not have strict execution of sentences nor extended police presence nor cost, but only prevailing risks.

The alternative with the highest utility is selected in each choice task. A number of parameters govern the sensitivity of the utility to each of the variables. Hence, the calibration of the model consists of finding the value of the parameters that best reproduce the decisions made via utility calculation. The basic DCM, the Multinomial Logit, assumes that the random terms follow independent Gumbel Maximum laws (Train, Reference Train2009). This assumption produces a simple expression for the probability of choice of each alternative that can be used for calibration purposes. The alternatives of our CE are not all alike. The two security programs are hypothetical, whereas the status quo is a well-known situation. Following Adamowicz et al. (Reference Adamowicz, Louviere and Swait1998), we employ a Nested Logit DCM to take this into account. The decision is represented in two stages. The individual decides first to engage in a security program or to stay in the status quo, and then, if the former is chosen, s/he selects among the security programs. A multinomial logit model is employed at each level, producing a higher correlation among the programs compared to the status quo. That correlation is empirically tested by the so-called inclusive value (IV) coefficient. The calibration of the model is done via maximum likelihood by means of the “mlogit” package in the R software.

The utility functions in (1) are usually established as linear. However, they could well take alternative forms. Hence, we performed a quadratic Box and Cox (Reference Box and Cox1964) estimation that includes the linear specification as a special case. Quadratic Box-Cox implies to include level, square and cross terms for each of the independent variables. A second model was built to explore the influence of the demographic factors, by including these variables in the utility functions. Demographic variables (D) enter the model in a specific way: by interacting with the risk of homicides (H´), the cost (C´), and their interaction (H´C´).Footnote ²⁷ Several demographics are included in the model simultaneously, provided they are not collinear. Then, models are compared via Akaike’s Information Criteria (AIC) and likelihood-ratio (LR) tests.

Finally, the VSL is calculated according to the definition:

(2) $$ VSL=-\frac{\partial U/\partial H}{\partial U/\partial C} $$

The VSL is the ratio of the utility gain from avoiding a life-risk as is a homicide and the reduction in utility that the cost of this less risky alternative implies.

4.1 Results

As expected, a significant part of the sample (41 %) showed signs of skepticism about the effectiveness of the government to fight crime. It was necessary to remove this part of the sample, not for lack of interest in their preferences, but for the impossibility to elicit them. In order to project the results of the study to the whole population we compared the profile of the skeptical with the rest of the sample across 30 variables. No statistically significant demographic differences were found for age, gender, family size, or socioeconomic levels.Footnote ²⁸ The skeptical prefer a higher police presence in the streets and longer sentences for criminals, whereas they show lower interest in their reintegration to the society. Among attitudes and behavior, only a higher fear for death was detected. This analysis shows that, if there is any difference between skeptical people and believers, this is the fear for crime. This means that the valuation based on the believers is conservative. The remaining sample size, after removing the skeptical and a few lexicographic responses, 1475 data units, is adequate for DCM calibration according to Hensher (Reference Hensher2004, Reference Hensher2006) and Caussade et al. (Reference Caussade, Ortúzar, Rizzi and Hensher2005).

Several modeling alternatives were considered for robustness checks. The results shown in Table 3 are for the main model and the general quadratic Box-Cox estimation as well as simpler versions of it. All DCM considered have the nested logit structure to properly represent the status quo alternative. First, we have considered a model with linear utility functions in the main explanatory variables (homicide risk, violent crime risk, extended police presence, strictness of sentences, and cost). Its performance is very good (all parameters have the expected sign and are statistically significant); however, it was surpassed by other more elaborate models. Specifically, AIC is 2696.6 compared with 2688.4 for the main model, and the likelihood ratio test shows supremacy at p < 1 %. We also explore curvature by means of quadratic and rectangular terms for all variables. The quadratic terms were not significant, and the significant rectangular terms are the interactions retained in the main model: homicide risk with cost, and severity of sentences with cost. The likelihood ratio test proves the advantage of this model compared to the linear one (p = 2 %), whereas it is below the main model, with AIC at 2696.4. We have also explored the Box-Cox transformation on the three metric variables: the two risks (homicides and violent crimes) and cost. The model shows all statistically significant parameters having the expected sign. Then a Box-Cox model with all quadratic and rectangular terms was calibrated. The large number of parameters, many of them nonsignificant, cause deterioration in the AIC indicator. By retaining the significant parameters, we find the best structure for the main model (“Box-Cox Simplified” in Table 3). The parameters eliminated are not globally significant according to the Likelihood ratio test (p = 66 %).

Table 3 Main discrete choice model.

Note: *, ** and *** denotes significance at 10, 5 and 1 %, respectively. The VSL is in 2014 million US dollars.

Hence, the main model specification is as follows:Footnote ²⁹

(3) $$ \left\{\begin{array}{l}{\tilde{U}}_1={\beta}_H{H}_1^{\prime }+{\beta}_V{V}_1^{\prime }+{\beta}_S{S}_1+{\beta}_P{P}_1+{\beta}_C{C}_1^{\prime }+{\beta}_{HC}{H}_1^{\prime }{C}_1^{\prime }+{\beta}_{SC}{S}_1{C}_1^{\prime }+{\varepsilon}_1\\ {}{\tilde{U}}_2={\beta}_2+{\beta}_H{H}_2^{\prime }+{\beta}_V{V}_2^{\prime }+{\beta}_S{S}_2+{\beta}_P{P}_2+{\beta}_C{C}_2^{\prime }+{\beta}_{HC}{H}_2^{\prime }{C}_2^{\prime }+{\beta}_{SC}{S}_2{C}_2^{\prime }+{\varepsilon}_2\\ {}{\tilde{U}}_3={\beta}_3+{\beta}_H{H}_3^{\prime }+{\beta}_V{V}_3^{\prime }+{\varepsilon}_3\end{array}\right. $$

The parameters measure the change in utility due to each characteristic of the alternatives: β_H to the rate of homicides, β_V to the rate of violent crime, etc. The parameters for the main effects are highly statistically significant (p < 0.01) and have the expected sign. Both risks (homicide and violent crimes) have negative influence on utility, corresponding to rational behavior. The security policies (police in the streets and strictness of punishment) have positive effect on utility, meaning they are appreciated by the people. The cost effect on utility is negative, as expected according to economic theory.

There are two interactions showing statistical significance in most models. The intense interaction between the homicide risk and the cost (HC) means that the effects of these variables on utility are non-additive, but rather reinforce each other. The rationale for this is that the burden of the cost is psychologically more intense when it is ineffective, as shown by a concurrent high homicide risk. There is also a negative sign on the interaction between the strict execution of court sentences and the cost. This may reflect the lower interest for such a policy among the more affluent individuals, measured in an independent question, whose results are shown in Table 4. The difference between mid-high class and mid-low class is statistically significant. As the former faced higher costs in the experiment, this difference explains the interaction.

Table 4 Interest for security policies by socioeconomic level.

Note: The socioeconomic levels A and B represent the high income class and they are numerically minimal, adding to less than 1 % of the population. The middle class covers about half of the population and it is divided into C1 (mid-high), C2, and C3 (mid-low). The D level forms practically the other half of the population, the low income class. *, ** and *** denotes significance at 10, 5 and 1 %, respectively.

The second program constant (β ₂) measures its preference beyond its characteristics. As it is not statistically significant we conclude that respondents do not exhibit any stimulus position bias. The status quo constant (β ₃) has a similar role. Rational behavior does not require it to be null because the status quo may have perceived characteristics beyond the ones explicit in the experiment. However, being not statistically significant adds notable strength to the results of the experiment, meaning that reality has been fully represented by the selected variables.

The inclusive value (IV) coefficient measures the complement of the correlation between programs. It validates for all our results the hierarchical decision making process represented in the Nested Logit model because the correlation between both programs is approximately 0.4 (1–0.6).

The coefficient of the Box-Cox transformation (not shown in the tables for length reasons) for homicides is λ_H  = 1.2, slightly departing from linearity. The coefficient for violent crime, λ_V  = 2.0, implies that its marginal disutility grows with the risk. This pattern might be related to the high risk prevalence in Argentina (UNDP, 2013, p. 57). The coefficient for the cost, λ_C  = 0.4, implies declining marginal dis-utility. This is consistent with the Prospect Theory proposed by Kahneman and Tversky (Reference Kahneman and Tversky1979) and Tversky and Kahneman (Reference Tversky and Kahneman1986), considering that the contribution represents a loss with respect of the status quo frame.

Valuation is performed according to the definition:

(4) $$ \mathrm{VSL}=-\frac{\partial U/\partial H}{\partial U/\partial C}=\frac{\left[{\beta}_H+{\beta}_{HC}\frac{C^{\lambda_C}-1}{\lambda_C}\right]{H}^{\lambda_H-1}}{\left[{\beta}_C+{\beta}_{HC}\frac{H^{\lambda_H}-1}{\lambda_H}+{\beta}_{SC}S\right]{C}^{\lambda_C-1}} $$

The VSL calculated results in $3.2 million (US dollars). This figure is adjusted to reflect the population income in Argentina. The average income of the sample indexes 1.66 versus the population, and the income elasticity estimated by Kniesner, Viscusi et al. (Reference Kniesner, Viscusi and Ziliak2010) is 1.44. The income adjusted VSL is then $1.5 million per statistical life.Footnote ³⁰

This estimate is consistent with results obtained in the literatureFootnote ³¹ . Viscusi and Masterman (Reference Viscusi and Masterman2017) recommend to consider the VSL estimates for the US as the basis of transference for all other countries. For that purpose, they select the VSL figure determined by the US CFOI: $9.6 million. The US value transferred to Argentina is between $1.5 and $2.8 million. Robinson (Reference Robinson2017) estimates the average VSL for OECD countries at $4.0 million. The OEDC value transferred to Argentina is between $1.1 and $1.7 million. Then, we conclude that our results are in the same order of magnitude as the values determined for other regions.

The VSL is sensitive to respondent income, consistently with economic theory. Another model sensitivity, also described more thoroughly below, shows that respondents having recent victimization experience have higher VSL. These two elements, as well as other demographic exploration performed below, contribute to demonstrate the sensitivity of scope of the model. Our model also shows adequate sensitive to scope. This validation is not as critical as for CV, as CE involve comparative evaluation that is more accurate than monadic evaluation (Carson, Reference Carson, Kopp, Pommerehne and Schwarz1997), however it can be considered relevant to stated preference methods in general. Choice experiments have a built-in scope sensitivity test as they involve different levels of the risks (Hanley et al. Reference Hanley, Wright and Adamowicz1998). This test has been considered internal, but it is also external in this case as respondents face different starting risk levels. The Cochran-Mantel-Haenzel test was performed on raw experimental data revealing statistically significant decay of security program choice with homicide risk (p < 0.01), stratified by income level and cost. Desvousgues et al. (Reference Desvousgues, Mathews and Train2012) go beyond this standard validation pointing out that the difference should also be economically adequate in magnitude to achieve sensitivity to scope. Our model satisfies this more stringent criterion as demonstrated by the elasticity of VSL to risk amounting to 0.75.

The model is also employed to measure the value of violent crime risk reduction in a similar way, resulting $4.1 thousand (US dollars) per statistical crime. Violence implies the victim being forced against her will, whereas injuries may occur only occasionally, and homicide is excluded. The value is significantly lower as expected. (The reader is referred to Picasso and Cohen (Reference Picasso and Cohen2019) for criminology discussion.)

The main model is then expanded for demographic exploration. Demographics enter the model by interacting with alternative specific variables,Footnote ³² specifically with the risk of homicides, the cost, and their interaction, by adding the following terms to the utility of each alternative j:

(5) $$ +{\beta}_{HD}D\;{H}_j+{\beta}_{CD}D\;{C}_j+{\beta}_{HCD}D\;{H}_j{C}_j $$

The service level variables do not contribute to collinearity by constructionFootnote ³³ , however the demographics should be evaluated in this aspect. Most of the correlations among demographics are low, except between variables measuring the same concept, like family size and number of children under 18 years old. These substitutes do not enter the model simultaneously. Setting redundancy aside, the determinant of the demographics correlation matrix is 0.18, dismissing any serious collinearity problem.

Table 5 shows the results of the model including demographic variables. The valuation expression (4) is modified appropriately by taking into account the new terms in expression (5) for the derivatives. We do not reproduce here the entire formula for length reasons.

Table 5 Model with demographic variables.

Note: The asterisks correspond to individual parameter significance (Wald test). The two parameters related to the Indiv variable are collectively significant (Likelihood ratio test) in spite of the fact that they are individually not significant.

There are several sociodemographic variables, which have the expected sign and are significant. First, the VSL is positively and significantly associated with Income, confirming the results in Viscusi and Aldy (Reference Viscusi and Aldy2003) and Kniesner et al. (Reference Kniesner, Viscusi and Ziliak2010). The model was also estimated on subsamples of high (low) income individuals producing +63 % (−41 %) variation in the VSL.

Second, general risk aversion is positively associated with VSL. We have used smoking habit as a measure of (lack of) risk aversion, as in previous research (“Smokes” in Table 5). The VSL results $0.1 million lower among smokers. Considering the strong official communication campaign on the negative consequences of smoking, could assume that the population knows about its risk to life. This result is in agreement with other research reviewed in Viscusi and Aldy (Reference Viscusi and Aldy2003) across various life risk contexts.

Third, the VSL we estimate is associated with victimization experience since it is higher by $0.7 million for recent victims compared to non-victims (“Victim” in Table 5). This suggests that more involved people can perceive the probability in a different way. On the other hand, the individuals perceiving higher crime risk exposure in their environment show lower VSL (“Perc.Risk” in Table 5). The perception of risk exposure is probably built through long term experience, providing the time to take protective measures, like private security. This may explain why people perceiving higher risk show lower VSL. On the other hand, recent victimization, volatile by definition, would not provide the time for defensive actions.

The VSL increases with the family size by $0.2 million per child (“Child” in Table 5). The VSL is negatively associated with individualism. The corresponding parameters (“Indiv” in Table 5), despite lacking individual significance (Wald tests), are collectively statistically significant (likelihood ratio test).

On the other side, the impact of other demographic variables is not statistically significant. The VSL is negatively associated with Impatience, measured by the inter-temporal discount rate, as predicted by the life cycle theory. Individuals demanding 1 % higher rate appear to have $21 thousand lower VSL. This result is directional as the specific coefficients involved in the valuation (“Impatience” in Table 5) are not statistically significant. The VSL is also found negatively correlated with the belief of control of the crime situation (“Perc.Ctrl” in Table 5). Such belief was measured by means of a direct question. The result is also directional as the corresponding coefficients are not statistically significant.

4.2 Discussion

This study shows that risk to life in the context of crime is severely undervalued if foregone earnings techniques are employed. In Argentina, and likely in most developing countries where subjective individual willingness-to-pay measures are unavailable, the VSL is over 10 times higher than the human capital estimate.Footnote ³⁴ This finding has wide implications. As the VSL represents the amount the population is willing to pay to reduce the risk, it provides the right figure for ex-ante economic evaluation. New and more effective crime control policies would be viable in benefit-cost terms by employing the subjective value of risk to life in the analysis. This type of valuation could also be used for ex-post compensation. As the VSL is subjective it properly represents the damage caused to the victim. This value would be useful in case of a crime derived from negligence of public or private authority.

There are implications beyond crime control policy as well. Assuming that our crime related VSL determination could be used as a proxy for other contexts, at least in the absence of specific research, it should be employed in the economic evaluation of local projects having risk to life implications. Many environmental improvement programs would encounter economic validation by using the VSL rather than the human capital value. For instance, the project for improving a 100 km route on the basis of traffic accidents would only be economically validated over 33 fatalities per year under the latter, whereas 2 fatalities per year would suffice under the VSL criterion. On the other hand, noisy social discussions about environmentally concerning projects may find an objective decision criterion in the VSL determined in this study.

Our experiment seems to corroborate the erosion in VSL produced by impatience proposed by the life cycle theory, albeit only directionally. The argument that an impatient individual would recklessly take higher risks paying less attention to the value of the asset at risk is intuitively appealing. However, we must admit that further research is required in this matter. Firstly, we have measured financial impatience whereas other dimensions might exist. The measurement instrument should be further refined and tested for concurrent validity with other approaches. Secondly, we are focusing on the context of crime risk, and impatience might have different influence vis-a-vis other assets. A refined instrument would probably be more conclusive about this hypothesis.

Our work seems to confirm the fundamental nature of risk aversion, linking smoking habit, a well-known indicator of low risk aversion, with the VSL determined in the context of crime. This correlation was also observed across other contexts like labor and traffic risks. These findings support the universality of risk aversion, which is itself a very interesting psychological subject for further research.

Our results support the idea that recent victimization impacts the way people perceive crime risk. This is aligned with the theory of availability bias, and provides an explanation to the empirical observation that the willingness-to-pay for risk reduction is higher wherever the risk is higher and more readily available, as explained above.

The result showing a higher VSL for larger families seems to confirm that children provide value to their parents’ life. One potential rationale is that the children create a sense of responsibility in their parents. Another explanation is the intergenerational altruistic effect proposed by Birchenall and Soares (Reference Birchenall and Soares2009).

The result about a lower VSL for individualistic persons is not established in the literature yet, to our knowledge. We think that the individualistic would disregard the passive value, focusing mainly on the active value, and then tolerate more risk to avoid funding collective efforts. The model corroborates this hypothesis.