Protest treatment and its impact on the WTP and WTA estimates for theft and robbery in the UK

Protest treatment and its impact on the WTP and WTA estimates for theft and robbery in the UK Abstract We undertake a survey that estimates WTP and WTA measures for changes in the risk of being a victim of a robbery or theft in the UK. Respondents are less likely to protest when they are asked to reveal their WTP rather than WTA. Employing various protest-treatment techniques, we estimate the mean WTP for reducing current risks of theft and robbery by 50% to range between £38 and £220; for WTA, they are between £351 and £2,175. Higher values for robbery reflect people’s aversion to the violence implicit in this type of crime. The annual value of avoiding a statistical case of crime ranges between £7,011 for theft and £90,087 for robbery. WTP-WTA ratios range from 1:4.8 to 1:16.9 and are influenced by type of crime and elicitation method. In turn, these results support the economic sense of a pre-emptive crime policy that prevents, rather than compensates for, crime occurrence. 1. Introduction and literature review Crime imposes substantial costs on societies (Brand and Price, 2000; Mayhew, 2003; Skaperdas et al., 2009). For instance, according to Brand and Price (2000), in 2000, the total cost of crime was estimated to be around £60 billion for the UK. Mayhew (2003) estimated the cost of crime in Australia to be around 10% of GDP. Similarly, a more recent study in the USA found that the value of property loss to victims represents a social cost of $1.6 trillion, equivalent to 9.7% of annual GDP (Anderson, 2012). However, such measures are far from perfect, as noted by Soares (2015). How to properly measure the economic value of crime is still debated, and many different techniques have been proposed. To have a correct measure of the price tag of crime is of vital importance from a policy perspective. Better estimates mean that a stronger justification for allocation of resources spent in the criminal law system can be presented. Furthermore, better estimates should lead to improved targeting of groups within the population and allow fairer compensation for the victims of crime. The major distinction in crime-cost measures is between ‘bottom-up’ and ‘top-down’ approaches. The former is based on a standard accounting technique that sums up all the costs related to crime for each party affected (Cohen, 2009; Domínguez and Raphael, 2015). The approach includes the monetary loss caused by foregone earnings by individuals harmed by crime and the costs of policing and medical services. The bottom-up approach may also include the diminished levels of domestic business investment and incoming foreign direct investments (FDI) associated with crime-ridden areas. Moreover, this approach could also include intangible costs such as pain and suffering. However, doubts are casted on the reliability of these estimates because of issues such as double counting over these components (Soares, 2015). In contrast, ‘top-down’ approaches derive a total measure of the crime cost, including both tangible and non-tangible components, from a single data source. Among the top-down approaches, a survey-based contingent valuation method (CV) is potentially powerful, although rarely employed in formal impact assessment of policy initiatives and programmes.1 This stated preference method consists of asking survey respondents about their willingness to pay (WTP) and/or willingness to accept (WTA) for a change in the likelihood of a crime event. The CV method is very popular in other contexts, such as in the evaluation of environmental and health policies, where it is maturing as a practice and increasingly accepted as evidence in policy evaluations (Bateman et al., 2002; Hoyos, 2010). For crime, the CV literature is scarce and somewhat dated. Ludwig and Cook (2001) undertook the first published contingent valuation study undertaken in a crime context. US respondents were asked whether they would ‘vote’ for a specified dollar tax increase in return for a 30% reduction in gun injuries, using a dichotomous choice format. The results indicate that the mean (annual) WTP for a 30% reduction in gunshot wounds was estimated to lie between $203 and $239. This implies that the aggregate value of (statistical) gunshot wounds lies between $1,000,000 and $1,200,000.2Cohen et al. (2004) asked US respondents to value the benefits of US public programmes to reduce criminal offending associated with burglary, serious assaults, armed robbery, rape or sexual assault, and murder. The author found that the mean (annual) WTP to reduce incidents of these crimes by 10% was estimated to range between $111 for burglary to $147 for murder. The implied value of preventing a (statistical) crime case is then $30,000 for burglary and $9,700,000 for murder. In a subsequent paper, Cohen and Piquero (2009) updated such estimates. For example, murder was estimated at $11.8 million and burglary at $35,000.3 A further paper, Atkinson et al. (2005), considered the benefits of reducing by 50% the risk of suffering the health outcomes associated with common assault, wounding, and serious wounding in the UK, over the following 12 months. The payment was made through a one-off increase in local taxes for law enforcement. The parametric mean of WTP was in the range £106–£178 per person. The authors calculated the implied health cost of a crime case per family per year as being £913 for common assault, and £6,1964 for serious wounding.5 One of the biggest issues in CV is the treatment of protests. In general, a researcher would expect that individuals declare their true valuation of the good questioned. However, there may exist a proportion of respondents who declare that they are not willing to pay any amount of money, as a result of not accepting some aspect or other of the hypothetical market scenario. They therefore think that they should not pay for the provision of the good in consideration (Jorgensen et al., 1999). These are the so-called protesters, i.e. people who state a zero amount for other than economic reasons. Meyerhoff and Liebe (2006) have shown that even somebody who is willing to pay a value higher than zero—perhaps an extremely high bid—could be a protester. Nevertheless, the focus of the literature on protest has been on bids of value zero. The typical way to distinguish a true zero from a protest one is to ask some debriefing questions after a respondent answers that he/she is not willing to pay. According to the respondents’ answers, the researcher has to classify the nature of the zero. In the context of nonmarket valuation, there are two relevant issues about protests that should be considered. The first (ex ante) is to understand the factors that affect the probability of an individual protesting in the design of a hypothetical market scenario. The second (ex post) is to measure the mean and median WTP (WTA) employing different protest treatment techniques. Even though the issue of protests is not new in the CV literature, there are no systematic studies that specifically deal with them in the context of crime costs. Our paper fills this gap by a) specifically identifying the factors that jointly affect protesting behaviour for WTP and WTA, and b) considering how measures of WTA and WTP vary, when treatments are differentiated on the basis of treatment of protest values as well as on elicitation formats. We ask survey respondents about their WTP and WTA for two types of crime: theft from the person, and robbery. We asked respondents about the maximum amount they would pay for a reduction in crime level, and the amount they would need as compensation for an increase in crime. We chose these two crime types because they constitute a large portion of crime in the majority of countries. Whilst both crimes include loss of property, robbery also involves the use of violence, which makes it a violent crime.6 Thus, we can assess the value that people assign to the violent component. We evaluate individuals’ preferences by using two elicitation techniques: open-ended questions and payment cards. To our knowledge, this is the first attempt to value these types of crime using CV methods, and to calculate the WTA as a compensation for an increase in crime. Given the nature of the ‘good’ we are considering, we expect a high number of protests. Individuals are very sensitive to political and ethical considerations when it comes to their security. Many people believe that it should be the government that is responsible for such problems and are very sceptical of paying extra to reduce the level of crime. As we find in our study, the scepticism is even more acute when people are questioned about their willingness to accept compensation for an increase in the crime level. In the first instance, we proceed by studying the factors that affect the likelihood of protesting. One of the first papers on this topic is Halstead et al. (1992), which studied the socio-economic factors that explain protest behaviour, based on a survey regarding species conservation in New England. However, their analysis was unable to clearly identify the factors that affect the individuals’ decision to protest. Meyerhoff and Liebe (2006) tried to improve such analysis by using a CV relating to the biodiversity of woodland. Contrary to the strategy used by Halstead et al. (1992), Meyerhoff and Liebe (2006) constructed a protest index based on interviewees’ perceptions relating to six possible reasons for declaring a zero bid. Two recent papers, Meyerhoff and Liebe (2010) and Meyerhoff et al. (2013), studied the determinants of protests in further detail. In particular, Meyerhoff et al. (2013) is a meta-study that used a sample of 38 stated preferences papers. These authors analysed the respondent- and survey-specific variables that affect the probability of protesting. Among the former, they consider variables such as age, gender, marital status, and income. The latter include the type of goods in consideration, elicitation method, payment vehicle, or length of the scenario. Interestingly, they found that in the case of non-market goods such as crime reduction, the number of protests is higher compared to market goods that are valued using stated preference techniques. Moreover, the payment vehicle seems not to impact on the protest behaviour. Thus, there is no consensus on the factors that make a person more likely to be a protester and no papers on crime that study this issue. We contribute to the existing literature by identifying the explanatory factors of both the WTP and WTA in a crime context. Our survey form allows us to investigate the impact of crime type and elicitation methods. Our analysis of the determinants of protests (Section 3) shows that respondents are less likely to protest when they are asked to reveal their WTP than their WTA. Moreover, we find that the only variables that are statistically significant are the type of crime-elicitation method and age. We then proceed to calculate mean and median WTP/WTA. We make this estimation using three treatments. These are: considering all zero bids as true zeros, dropping identified protest bids from our estimates, and undertaking a Heckman two-step process that adjust the WTP estimates by selection bias.For WTP, the estimated means range between £38.56 and £127.27. These are similar to those of previous studies, although the risks and type of crimes are not identical. For WTA, the results are much higher, ranging between £348.36.22 and £2,152.97. The concepts of WTP and WTA are derived from the Hicksian welfare measures of the compensating variation (C) and equivalent variation (E). For an improvement in the current situation, both the C and E are positive, but the C represents the maximum WTP for accessing the change while the EV represent the minimum WTA to forego it. Conversely, if the change is negative both measures will be negative, the compensating variation will be the WTA to accept the change, while the equivalent variation will be the maximum WTP to avoid the change (Carson and Hanemann, 2006). Bergstrom and Randall (1987) noted that the estimates should differ only when the transacted good represents a large fraction of the household budget (income effect) or if the transaction costs are very high. However, neo-classical economic theory suggests that for the majority of goods the two estimates should be very close if not identical. Despite these theoretical predictions, the empirical literature has shown that this is not the case and that the WTA are generally much higher than WTP. For example, a meta study by Horowitz and McConnell (2002) found a median ratio of average WTA/WTP to be 2.6, with a mean of 7.17. As a consequence of such evidence, the literature has started investigating the determinants of the WTP/WTA gap (Brown and Gregory, 1999). In recent years, many meta studies on the topic have been conducted, such as that by Horowitz and McConnell (2002). A recent study, by Tunçel and Hammitt (2014), accounted for various economical and psychological explanations of such disparity in a regression framework. Among them, prospect theory (Kahneman and Tversky, 1979) posits that people are risk adverse and value possible losses more than gains. Therefore, people need to receive a larger amount of money for a decrease of utility than they would pay for an increase of the same magnitude. In a seminal paper, Hanemann (1991) ascribed such a discrepancy to (the absence of) substitutes. Plott and Zeiler (2005) affirmed that the elicitation techniques might also be a determining factor. In their meta study, Tunçel and Hammitt (2014) considered 76 papers7 and regressed the log of the WTA-WTP ratio on many variables that capture these various competing explanations. The results show that this ratio is smaller for private goods than for public and non-market goods. Moreover, real market scenarios do not have a significant difference effect on the disparity compared with hypothetical scenarios. Following Hanemann (1991), the authors also found that goods with substitutes have smaller ratios. Payment methods also affect the disparity. For example, double-bound dichotomous choice surveys have larger ratios compared to open-ended and single-bounded survey questions. Interestingly, there is no statistically significant difference between the results where payment cards are used and the open-ended format—the two methods we use in our survey. Our estimates of WTA and WTP allow us to calculate such a ratio, a novelty in the crime literature. We find that on average the ratio is about 10 to 1 higher than those calculated from surveys that focus on environmental and ‘health and safety’ goods. The paper is organized in the following way. In the next section, we outline the survey and the data used. Section 3 explores the determinants of protests using various estimation techniques. Section 4 then presents estimates of the WTP and WTA using various protest treatment techniques. Section 5 shows the estimation of the WTP/WTA ratio, whilst Section 6 concludes. 2. Description of survey and crime variables Respondents, 1,398 in total, were questioned through an internet survey administered by an online company.8 We considered two types of crimes: theft from the person and robbery.9 The two crimes are almost identical except for the use of violence in the latter. If violence is not involved or it has been used against property, but not directly toward a person, this would classify as theft from the person rather than robbery.10 The main reason for choosing these two crimes is that, by comparing the respective willingness to pay and accept, we can also have an idea of the value that people assign to the violence component. According to the crime survey for England and Wales (CSEW), formerly known as the British crime survey, the percentage of households who have been victims once or more of theft from a person was 1.1% and of robbery 0.3% in 2013. To make things clear for respondents, we presented them with a brief definition of each crime, a table that summarize the main consequences that victim suffer along with a clarifying picture.11 We considered two elicitation methods: open-ended and payment cards. These are among the most frequently used methods in contingent valuation studies. Therefore, the possible combinations of crime-payment methods were four: Theft–Open Ended (Theft-OE), Theft–Payment Cards (Theft-PC), Robbery–Open Ended (Robbery-OE) and Robbery–Payment cards (Robbery-PC). The survey company randomly assigned respondents to one of these four options. The final number of respondents for each survey is quite similar, well above 350 individuals. However, for Robbery-OE the number is lower, 261, due to technical reasons.12 The data show (Table 1) that there are no significant differences in terms of socio-economic characteristics between the respondents of the four types of surveys.13 Table 1 Mean (Std. Dev) or percentage for socio-economic characteristics by type of survey. Variable / Type of Crime  Theft   Robbery   Elicitation format  PC  OE  PC  OE  Victimized  16.2%  21.3%  17.6%  16.5%  Feeling very unsafe  1.8%  1.7%  1.8%  0.4%  Household crime  8.1%  12.6%  11.1%  12.3%  Household members  2.65  2.69  2.8  2.76  (1.329)  (1.299)  (1.308)  (1.297)  Married  61.5%  57.9%  64.8%  61.3%  Male  33.2  33.4%  40.2%  34.9%  Very good health  36.2%  32.3%  31.1%  38.7%  Age  46.53  45.15  47.74  43.06  (13.00)  (13.20)  (12.21)  (13.61)  College  68.9%  70.5%  66.8%  70.9%  Income  31776.65  32247.19  32564.77  32279.69  (20823.16)  (20969.61)  (21057.18)  (19510.21)  Variable / Type of Crime  Theft   Robbery   Elicitation format  PC  OE  PC  OE  Victimized  16.2%  21.3%  17.6%  16.5%  Feeling very unsafe  1.8%  1.7%  1.8%  0.4%  Household crime  8.1%  12.6%  11.1%  12.3%  Household members  2.65  2.69  2.8  2.76  (1.329)  (1.299)  (1.308)  (1.297)  Married  61.5%  57.9%  64.8%  61.3%  Male  33.2  33.4%  40.2%  34.9%  Very good health  36.2%  32.3%  31.1%  38.7%  Age  46.53  45.15  47.74  43.06  (13.00)  (13.20)  (12.21)  (13.61)  College  68.9%  70.5%  66.8%  70.9%  Income  31776.65  32247.19  32564.77  32279.69  (20823.16)  (20969.61)  (21057.18)  (19510.21)  In each survey, we asked individuals to state their willingness to pay for a decrease in the risk of being victimized of 50%, from baseline annual probabilities. The size of decrease makes our results comparable with those of Atkinson et al. (2005), whilst being close to the largest change judged to be realistic given current policing policy options. Moreover, given that the baseline probability of risk is relatively low, such an increase/reduction is not considered particularly high. Finally, from a graphical presentation point of view, it helps respondents imagine such a change more easily. We presented a hypothetical situation where police would implement a range of crime-reducing measures. However, the survey explained that the budget of the Home Office (British Ministry of the Interior) would not cover the cost of such measures and that private citizens would have to make an additional payment for it. In order to help individuals picture the change in risk before and after the implementation of these measures, we showed it graphically (Figure A1). For Theft-OE and Theft-PC, we asked for the willingness to pay for a reduction of the probability of being victimized from 1.1% (11 in 1,000 chance) to 0.55% (5.5 in 1,000 chance). In the case of robbery, the reduction is from 0.3% (3 in 1,000 chance) to 0.15% (1.5 in 1,000 chance). For the open-ended elicitation technique, we left a blank space for the respondents to insert his/her stated value. For payment cards, we presented the respondents with a series of possible bids starting from 0 and then progressively going up until £5,000. Respondents also had the option to choose ‘more’ and specify a higher value. The payment vehicle was a one-off annual increase in taxes. Moreover, we made it clear that the money would go directly to a special public fund, earmarked for the purpose of crime reduction. In addition, we reminded respondents that the money used to reduce crime must either come from their savings or from what they would have spent on other things. We then asked respondents the reasons for choosing an amount equal to, or above, zero (see Fig. 1). Protesters were those people who answered that they were not willing to pay anything for the following reasons: ‘The question about paying is too difficult to answer’, ‘I already pay enough charges and taxes’, ‘The crime reducing measures cannot reduce crime levels’, and ‘Government should pay’. On the other hand, we considered as true zeros the options ‘I cannot afford to pay’, ‘I have not been affected, disturbed or annoyed by crime levels’, and ‘it is more important to invest in other social issues’. Respondents also had the option to select ‘Other’. According to their reasons, in some cases, we also classified these as protesters. Fig. 1. View largeDownload slide Reasons for answering zero in the WTP question. Fig. 1. View largeDownload slide Reasons for answering zero in the WTP question. For the same four combinations of surveys, we questioned people on their willingness to accept compensation for an increase in the probability of being victimized (Fig. 2). We presented a hypothetical situation where, due to certain budget restrictions, the government could not enforce the law as before, so that consequently the annual probability of being victimized would increase by 50%. However, the government would compensate people for such an increase; the survey asked what level of compensation would be acceptable. In this case, we considered protest answers to be the following: ‘It is impossible to make an evaluation of such costs’, ‘It is not ethical to receive money from the state for these issues’, ‘The question is too difficult to answer’, and ‘This programme is of no value to my household’. In all these cases, the respondents did not provide any value for the WTA. Fig. 2. View largeDownload slide Reasons for protesting in the WTA question. Fig. 2. View largeDownload slide Reasons for protesting in the WTA question. Among those who declare a WTP equal to zero, the majority thinks that they already pay enough taxes. In addition, many justified their decision not to pay by saying that the government should pay for such a service. On the other hand, the majority of those that did not want to accept any payment stated, ‘It is impossible to make an evaluation of such costs’ and ‘It is not ethical to receive money from the state for these issues’. This demonstrates a clear difference depending on the hypothetic market situation we presented to the respondents. Figure 3 summarizes protest rates for WTP and WTA, disaggregated by crime type and elicitation format. Whilst there is a clear difference in proportion of protest bids for WTP compared with WTA for the same ‘good’, the proportions do not hold constant; Theft-Open is the most obvious outlier. Fig. 3. View largeDownload slide Protest rates by crime type and elicitation format. Fig. 3. View largeDownload slide Protest rates by crime type and elicitation format. 3. Determinants of protests In analysing our response data, we first identify the factors that affect the likelihood of protesting. In order to do so, we pooled all the observations and considered a panel data-type of model that can exploit the features of our data. Our dependent variable Pi takes the value of one if the individual declared a positive WTP or WTA, and zero otherwise, such that:   Pi={1, if WTP>0 or WTA>00, protest  (1) In other words, Pi = 0 if an individual protests while Pi = 1 if she/he does not. As regressors, we included the standard socio-economic and perception variables. We also included a dummy representing the randomization of the type of crime-elicitation method. We estimated the panel data model using a probit random effects specification (Table 2). The type of crime-elicitation technique impacts negatively on the probability of participating (not protesting) relative to Robbery-OE, which is the reference category. Moreover, age of the respondent is found to be negative and significant. On the other hand, male, marital status, and declaring themselves to have very good health are not significant. The dummy for the WTP data is significant and positive, reflecting the fact that people are less likely to protest when asked about their WTP. The correlation parameter ( ρ) is significantly different from zero.14 Finally, σμ2, representing the degree of heterogeneity across individuals, is significant. Table 2 Determinants of participation (not protesting), random effect regressions.   Random effects  Theft-PC  –0.432**  (0.149)  Theft-OE  –0.370*  (0.157)  Robbery-PC  –0.195  (0.152)  Victimized  0.0150  (0.131)  Feeling very unsafe  –0.211  (0.405)  Household crime  –0.138  (0.159)  Household size  0.0748  (0.417)  Married  −0.193  (0.113)  Male  0.129  (0.105)  Very good health  0.153  (0.107)  Age  –1.576***  (0.410)  College  –0.151  (0.113)  Income  0.0190  (0.0245)  WTP  0.991***  (0.0790)  Constant  1.627***  (0.295)  Heterog(ln⁡σμ2)  0.482**  (0.154)  N  2788      ρ  0.618    Log-likelihood  –1436.7      χ2  172.9    P-value  0      Random effects  Theft-PC  –0.432**  (0.149)  Theft-OE  –0.370*  (0.157)  Robbery-PC  –0.195  (0.152)  Victimized  0.0150  (0.131)  Feeling very unsafe  –0.211  (0.405)  Household crime  –0.138  (0.159)  Household size  0.0748  (0.417)  Married  −0.193  (0.113)  Male  0.129  (0.105)  Very good health  0.153  (0.107)  Age  –1.576***  (0.410)  College  –0.151  (0.113)  Income  0.0190  (0.0245)  WTP  0.991***  (0.0790)  Constant  1.627***  (0.295)  Heterog(ln⁡σμ2)  0.482**  (0.154)  N  2788      ρ  0.618    Log-likelihood  –1436.7      χ2  172.9    P-value  0    Note: This table shows the results for a probit random effects model. The dependent variable is a dummy equal to one if the respondent does not protest (participate) and zero if he/she protest. Each individual represents two observations: one with his/her WTP value and the other with his/her WTA value. A description of the variables can be found in Table A1. The model includes a dummy equal to one if the observation refers to WTP and zero for WTA. The standard probit random effect uses a random distribution for individual heterogeneity. 4. Protest treatment in a crime study If there is no consensus in the literature on the determinants of protests, the same applies to the treatment of protests to measure WTP and WTA. The most common, and easiest, way to deal with the protests is simply remove them from the sample (Halstead et al., 1992). This strategy should not yield any effect on the mean WTP if the number of protests is low, the sample is relatively large, or if protesters are similar to non-protesters. Otherwise, by simply eliminating them, a selection bias would be introduced which could invalidate the estimations (Calia and Strazzera, 1999). Another technique is to consider protests as true zeros. Again, this would be an error if the zeros are really protests. An obvious consequence of such a strategy is that the WTP and WTA would be underestimated. This is particularly true if the number of protests treated in this way is high. These two methods of dealing with protests have been used by the existing literature on crime valuation. For example, Atkinson et al. (2005) found that about 279 out of 802 individuals, about 34%, were protesters.15 The authors checked whether there were significant differences, in terms of the distribution of the variables, between the protesters and the non-protesters and found none. Therefore, they proceeded to remove the protesters from the sample and generated the results on the basis of the non-protesters. In contrast, Ludwig and Cook (2001) included all the protests as zeros in the calculation of the WTP. However, as a separate exercise they also excluded the 24% that strongly agree that ‘taxes are too high’. Consequently, they found a WTP 13% higher than the one previously calculated16 (Cohen et al., 2004). However, none of these papers has specifically addressed the issue of protests on crime as we do here. In our baseline estimation, we consider a simple OLS model and assume that the protests are legitimate, true zeros. Moreover, as suggested by Halstead et al. (1992), we also remove all the protests from the sample, retaining an OLS specification. Our third method is an adaptation of the one used by Strazzera et al. (2003a).17 Following these authors, we suppose that the variable Y1i represents the stated amount, and Y2i is a dummy variable equal to one if the individual i participates and zero if he/she protests. The valuation of the ‘crime’ good takes the following form:   ln⁡(Y1i)=xi′β+σui, (2) where Y1i is observed only if Y2i=1. xi is a matrix of independent variables which explains WTP or WTA, β is a vector of unknown parameters, σ is a scale parameter, and μi is a measurement error. Thus,   Y2i={1, if zi′γ+ɛi≥0,0, if zi′γ+ɛi<0. (3) where zi is a matrix of independent variables which explains the participation decision, γ is a vector of unknown parameters, and ɛi is measurement error. This equation is already estimated in Table 2. In other words, the equation that explains protest bids is the participation equation needed in the Heckman approach. The stated amount depends on the decision to participate and not protest—the ‘participation Decision’.18 The expected value of the logarithm of the bid, given that a person wishes to participate, is:   E[ln⁡(Y1i)|ɛi>−zi′γ]=xi′β+σρ(φ(zi′γ)Φ(zi′γ))=xi′β+σρλ(zi′γ), (4) where φ(·) and Φ(·) are the standard normal probability density function and cumulative distribution function, respectively, and λ(zi′γ) is the inverse Mills ratio. This equation can be generalized to other elicitation models such as payment cards with intervals (see Atkinson et al., 2005). We follow the two-step approach shown in Heckman (1979), using estimates of Table 2 to obtain a prediction for λ(ziγ). These predicted values are incorporated on each valuation equation to estimate the second-step equation using OLS. We corrected the variance-covariance matrix of the estimated final parameters, following Cameron and Trivedi (2005). Given the log-normal distribution, we assume that the unconditional median and mean for the WTP are respectively:   median(WTPi)=exp(xi′β), (5)  mean(WTPi)=exp(xi′β)*exp(σ2/2). (6) For the Heckman equations, the conditional expected value of Y1i is equal to19:   E(Y1i|Y2i=1)=exp(xi′β+σ22)*(1−Φ(−zi′δ−ρ2σ2))(1−Φ(−zi′δ)), (7) where the median is:   Median(Y1i|Y2i=1)=exp⁡(xi′β)*(1−Φ(−zi′δ−ρ2σ2))(1−Φ(−zi′δ)). (8) The unconditional expected value of Y1 is equal to:   E(Y1i)=exp⁡(xi′β+σ22)*(1−Φ(−zi′δ−ρ2σ2)), (9) and the median is:   Median(Y1i)=exp(xi′β)*(1−Φ(−zi′δ−ρ2σ2)). (10)Table 3 presents the mean and median WTP results. The mean value estimated in the study can be aggregated for the total population affected and used in cost-benefit analysis of crime policies, while the median has a voting interpretation, which is that 50% of the population is willing to pay that amount of money or would support the project if they have to pay that amount (Carson and Hanemann, 2006). We focus our discussion on the mean values since we are more interested in cost-benefit policy contexts. Table 3 Mean WTP (median in parentheses). WTP/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £38.56 (8.02)  £63.94 (12.19)  £59.95 (8.99)  £127.27 (18.95)  Drop protests  £48.74 (12.74)  £73.38 (18.92)  £83.23 (16.63)  £135.13 (28.80)  Heckman  £45.78 (12.78)  £70.37 (18.93)  £70.47 (18.79)  £125.80 (28.77)  WTP/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £38.56 (8.02)  £63.94 (12.19)  £59.95 (8.99)  £127.27 (18.95)  Drop protests  £48.74 (12.74)  £73.38 (18.92)  £83.23 (16.63)  £135.13 (28.80)  Heckman  £45.78 (12.78)  £70.37 (18.93)  £70.47 (18.79)  £125.80 (28.77)  Note: The table presents the mean and median estimates of the WTP using three different protest-treatment techniques. Zeros kept and Drop protests are calculated through OLS. Heckman estimated parameters through a two-step Heckman model. In general, the mean is lower if we consider all protest bids as legitimate zeros. WTP for theft ranges between £38.56 and £83.23, whereas for robbery WTP is between £63.94 and £135.13. The results clearly show that people are willing to pay more to avoid the risk of violence. By dropping the protests, we generate higher means than when we correct for sample selection. The median values are much smaller than the mean values, reflecting the fact that the data are skewed to the right. However, the ranking of the medians follows the same pattern as the means. Directly comparing such results with other studies is not an easy task because the type of crime and the baseline risk changes are not always comparable. For example, Ludwig and Cook (2001) found a parametric mean WTP of $239 (about £155 at current exchange rates) for a decrease of 30% in gun violence. However, their change in risk was lower and gun violence is a more serious crime than robbery. Cohen et al. (2004) estimated the WTP for a reduction of crime by 10%. This included armed robbery value, which had a value of $110 (£71), whereas our estimates for robbery are £63.94 with payment cards and £127.27 for open ended—a less serious crime but a larger reduction. Atkinson et al. (2005) considered violent crime with no material loss. However, among the three violent crimes they considered, the closest to robbery in terms of psychological and physical harm is common assault. As the authors removed the protests from the analysis, we compare these to our analogous estimates. Their central estimate was £105.63—higher than all our estimates apart from those for Robbery-OE, presumably reflecting the more violent nature of the crime that Atkinson et al. (2005) considered. Such results allow us to calculate the implied cost of ‘statistical’ crimes, estimated as the amount that the average person would pay to reduce with certainty the risk of crime. It is derived by multiplying the mean (or median) by the percentage reduction in the risk of being victimized multiplied by 100 (see Table A3 in the appendix). Table 4 shows the estimated mean, and median, WTA, which have a similar pattern to those for WTP.20 The WTA for theft ranges between £348.36 and £559.36, whereas for robbery it ranges between £902.22 and £2152.97. A direct comparison of these values with previous estimates is not possible since no other crime survey has investigated the WTA for an increase in crime rates. However, these WTA values may be compared with those offered by the UK government to crime victims by way of compensation (Ministry of Justice, 2012) in order to assess whether these compensation levels accurately reflect social preferences. Table 4 Mean WTA (median in parentheses). WTA/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £348.36 (13.06)  £945.47 (20.73)  £364.21 (15.66)  £2152.97 (67.41)  Protests dropped  £559.36 (66.46)  £1131.79 (108.09)  398.97 (69.59)  £995.54 (171.49)  Heckman  £508.74 (67.11)  £1026.75 (108.10)  £371.05 (71.31)  £902.22 (172.07)  WTA/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £348.36 (13.06)  £945.47 (20.73)  £364.21 (15.66)  £2152.97 (67.41)  Protests dropped  £559.36 (66.46)  £1131.79 (108.09)  398.97 (69.59)  £995.54 (171.49)  Heckman  £508.74 (67.11)  £1026.75 (108.10)  £371.05 (71.31)  £902.22 (172.07)  Note: The table presents the mean and median estimates of the WTP using three different protest-treatment techniques. Zeros kept and Drop protests are calculated through OLS. Heckman estimated parameters through a two-step Heckman model. Finally, we calculate the WTP for those who gave a protest response to the WTA question and vice versa. Table 4A in the Appendix shows those results. For the WTP we found no differences in order of magnitude for the sample as a whole. The WTA values are significantly higher, though these values are less robust since the sample size is rather small for regression analysis. 5. WTP/WTA ratio As previously mentioned, there are no previous studies that estimated the WTA in a crime scenario, so we cannot directly compare the WTA/WTP ratio. Nevertheless, our research allows us to evaluate such a ratio in various ways. We can check the disparity in the ratio for two different types of crimes. In addition, we can see whether the elicitation technique plays any role in determining the ratio. Table 5 shows these ratios. The first thing to note is that these are sizeable, ranging from 4.79 (Theft-OE, protests dropped) to 16.91 (Robbery-OE, zeros kept). The average among all the combinations of crime-elicitation technique is 10.33. Moreover, with the exception of the 16.91 result, the values are lower for open-ended format than for payment cards. Table 5 WTA to WTP ratio. WTA-WTP treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  9.03  14.78  6.08  16.91  Protests dropped  11.47  15.42  4.79  7.37  Heckman  11.11  14.59  5.27  7.17  WTA-WTP treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  9.03  14.78  6.08  16.91  Protests dropped  11.47  15.42  4.79  7.37  Heckman  11.11  14.59  5.27  7.17  We would generally expect a high ratio for a variety of reasons. We consider a public good, and our scenario is hypothetical compared to the market of an ordinary private good. Moreover, people do not generally have a direct experience of victimization, which makes difficult for them to ‘quantify’ the costs. As Tunçel and Hammitt (2014) report in their work, ‘environmental’ and ‘health and safety’ goods are the ones that on average have the WTA:WTP highest ratio, 6.23 and 5.09, respectively. It seems possible—though we have no proof—that the lower ratios for the OE elicitation format reflect the fact that whilst respondents are known not to be so influenced by income constraints when facing WTP questions that use OE (Mitchell and Carson, 1989), they see the bid levels presented to them in payment cards in the WTA questions as legitimizing potential values not suggested in the OE format. The lower OE bids in the WTA questions therefore reflect a conservatism in the respondents’ preferences in this elicitation context. 6. Conclusions The treatment of protests in applications of the contingent valuation method is a controversial issue. If protests are not treated properly, this can introduce estimation bias and affect the final results, reducing their value to the policymaker. This is even more relevant in a survey like ours, on crime, because people may be expected to disagree about aspects of the hypothetical market scenario. Despite this, there is no research that studies protests in crime-contingent valuation scenarios. In particular, the literature has neglected to identify the factors that are more likely to affect protesting behaviour and how sensitive the estimates of the mean and median WTP and WTA are to various protest treatment techniques. This paper aims at filling such a gap by disaggregating these factors. In order to do so, we run a survey that derives the willingness to pay for, and willingness to accept, a change in the probability of being a victim of theft and robbery. Moreover, we consider two elicitation techniques: open-ended and payment cards. We structure our analysis around two main themes. The first focuses on the individual determinants of protesting behaviour using a random effects panel data model. The results show that the type of crime-elicitation technique, Theft-PC and Theft-OE, affects the probability of protesting, as does age. Interestingly, we find that the appropriate model needs to take into account the correlation between the decision to protest in a WTP and the decision to protest in a WTA question. In the case of age, the finding that the probability of protest falls with age suggests that those who are old are likely to be more willing to devote resources to crime deterrence than younger people. This may reflect the fact that older people own more of their material goods and so are more concerned with protecting them, and/or that they are more aware of their own physical and mental vulnerabilities in relation to their being victims of crime. An implication of this result for policy is that localities with high proportions of older populations should have more crime deterrence resources devoted to them relative to other localities. We employ three protest treatment strategies to estimate the WTP and WTA. The results show that the WTA is much higher than the WTP for the same crime and elicitation method. Moreover, we find that WTP and WTA are lower when we consider protests as legitimate zeros. WTP for theft ranges between £38.56 and £83.23, depending on treatment and elicitation method, whereas for robbery the range is between £63.94 and £135.13; unsurprisingly, the involvement of violence significantly increases the willingness to pay. The WTA for theft is in the range £348.36–£559.36 and for robbery £902.22–£2,152.97, depending on treatment. These results allow us to calculate, for the first time, the WTA:WTP ratio in a crime study. The average ratio across all combinations of crime-elicitation technique is 10.33, whilst the individual ratios are lower for the open-ended question format than for the payment card format, probably reflecting the fact that we consider a public good with a relatively hypothetical scenario. Such a big difference between the WTP and WTA results has two policy implications. First, a forward-looking public authority is likely to find it cheaper and easier to implement policies aimed at decreasing crime levels, rather than compensating citizens to tolerate a higher level of crime risk. Second, people tend to refuse compensation for an increase in crime for reasons that are not easily justified on the basis of economic rationality; rather, reflecting a rejection of the notion that increased risks can be traded off against money. This leads to a higher number of protests for WTA than for WTP. Our findings therefore also support the idea that it is impossible to fully compensate a victim of a crime, i.e., make a crime victim ‘whole’ (Mulder, 2009; Ludwig, 2010).21 Supplementary material Supplementary material is available online at the OUP website. Footnotes 1 Another one is the value of a statistical life (Soares, 2015). 2 The cost of statistical crime is given by multiplying the mean or median WTP for a certain percentage reduction in the risk of being victimized by the relevant (at-risk) population denominator, which is 100. As Atkinson et al. (2005, p. 577) said: ‘this transformation gives the implied amount that the average individual would be willing to pay to avoid a violent crime happening with certainty’. 3 Interestingly, the authors used the WTP estimates to calculate the value of a criminal career. One of the most important results is that society would save $3 million and $5 million if a 14-year-old could be saved from a life of crime. As Cohen et al. (2010, p. 282) said: ‘Saving a group of high-risk (chronic) youth should result in substantial cost-savings for the would-be offender, the potential victim(s), the criminal justice system, and for society as a whole’. The estimates on the cost of crime by Cohen et al. (2004) and Cohen and Piquero (2009) were used by Heaton (2010) to calculate the expected benefits of hiring extra police officers in several large police departments in the USA. 4 Other notable work on crime costs includes that by Nagin et al. (2006), who found that the total willingness to pay for a 30% reduction in youth crime in all households from Pennsylvania is between $387 million and $468 million. 5 For a detailed history of the use of stated preference approaches in crime contexts, see Cohen (2009). In this work, Cohen also outlined best practices for running a CV survey. 6 As defined by the FBI for the purposes of the Uniform Crime Reports. 7 The majority of the studies considered in such meta-analysis refer to ordinary private goods, health and safety, environmental, or public goods (but not on law enforcement). 8 We used the popular surveygizmo website: http://www.surveygizmo.com/. 9 A person is accused of the former if ‘there is theft of property while it is being carried by, or on the person of, the victim (for example pick-pocketing)’ (British Office of National Statistics, 2015). On the other side, a person is accused of robbery ‘if he steals, and immediately before or at the time of doing so, and in order to do so, he uses force on any person or puts or seeks to put any person in fear of being then and there subjected to force’ (British Office of National Statistics, 2015). 10 For example, if ‘a bag is taken cleanly from the shoulder of a victim or a phone is taken cleanly from the hand) the allegation should be classified as theft from the person and not a robbery’ (British Office of National Statistics, 2015). 11 We included a figure because Corso et al. (2001) showed that respondents are more sensitive to risk changes when showed it graphically. 12 By mistake, the online survey company sent away more questionnaires to Theft-OE, Theft-PC, and Robbery-PC compared to Robbery-OE. Due to budget limitations, we could not increase the number of the last type of survey to balance its number with the other ones. 13 An exception seems to be the share of people that state they ‘feel very unsafe’, which is lower than the other three categories. Although we cannot fully substantiate it, we think that it might depend on the slightly younger age of this group compared to the others. 14 Along with these panel data models, we also run two separate probit regressions and a bivariate probit. Results are very similar to the ones presented in the paper, and are available upon request. 15 Interestingly, as we have seen in Fig. 1, we find a lower number of protests for our WTP question. 16 In a seminal study in this area, Cohen et al. (2004) did not talk explicitly about protests, nor did they discuss their treatment. 17 Of course, there are other ways of dealing with protests, for example by including all the protests and assigning a value of WTP/WTA for each protest depending on how non-protests with similar socio-economic characteristics have answered. This is similar to the treatment of missing data presented in Cameron and Trivedi (2005). Another way to treat protests is the one proposed by Strazzera et al. (2003b), which combines the double dichotomous model and a Spike model (Kriström, 1997), and which is used to deal with protests in a double-bounded dichotomous choice format. Nevertheless, it is not possible to apply such a method with the open-ended or payment card formats used in our study. 18 We thank the editor for noticing this estimation possibility, which allows us to link the explanation of protest with the value equations. 19 This formulation is derived from Cameron and Trivedi (2010). 20 Results in Tables A7 and A8 show that respondents who feel very unsafe have significantly lower WTP/WTA. Though this appears counterintuitive, we speculate that this finding results from an inability on the respondents’ part to imagine such an improvement in crime rates to be possible—perhaps because of a chronic crime epidemic in the neighborhood or because previous initiatives have failed. 21 We thank an anonymous referee for highlighting this principle. Acknowledgments We would like to thank participants at seminars at the Catholic University of the North, Chile. Funding This work was supported by the Alumni Fund at University of Bath, UK; CONICYT, Programa POSTDOCTORADO [under grant number 3160521 to M.P.]; and the Institute for Research in Market Imperfections and Public Policy, ICM IS130002, Ministerio de Economía, Fomento y Turismo de Chile [to M.P.]. References Anderson D. A. ( 2012) The cost of crime, Foundations and Trends in Microeconomics , 7, 209– 65. Google Scholar CrossRef Search ADS   Atkinson G., Healey A., Mourato S. ( 2005) Valuing the costs of violent crime: a stated preference approach, Oxford Economic Papers , 57, 559– 85. Google Scholar CrossRef Search ADS   Bateman I. J., Carson R. T., Day B., Hanemann M., Hanley N., Hett T., Jones-Lee M., Loomes G., Mourato S., Özdemiroglu E. ( 2002) Economic Valuation with Stated Preference Techniques: A Manual , Edward Elgar Publishing, Cheltenham. Google Scholar CrossRef Search ADS   Bergstrom J. C., Randall A. ( 1987) Resource Economics: An Economic Approach to Natural Resource and Environmental Policy , Edward Elgar Publishing, Cheltenham. Brand S., Price R. ( 2000) The Economic and Social Costs of Crime , Home Office, London. British Office for National Statistics ( 2015) Focus on property crime: 2014 to 2015 report, British Office for National Statistics, London. Brown T. C., Gregory R. ( 1999) Why the WTA–WTP disparity matters, Ecological Economics , 28, 323– 35. Google Scholar CrossRef Search ADS   Calia P., Strazzera E. ( 1999) Sample selection model for protest votes in contingent valuation analyses, FEEM Working Paper 55.99, Fondazione Eni Enrico Mattei, Milan. Cameron A. C., Trivedi P. K. ( 2005) Microeconometrics: Methods and Applications , Cambridge University Press, Cambridge. Google Scholar CrossRef Search ADS   Cameron A. C., Trivedi P. K. ( 2010) Microeconometrics using Stata , Stata Press, College Station, TX. Carson R. T., Hanemann W. M. 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Google Scholar CrossRef Search ADS   © Oxford University Press 2017 All rights reserved This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Oxford Economic Papers Oxford University Press

Protest treatment and its impact on the WTP and WTA estimates for theft and robbery in the UK

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Abstract

Abstract We undertake a survey that estimates WTP and WTA measures for changes in the risk of being a victim of a robbery or theft in the UK. Respondents are less likely to protest when they are asked to reveal their WTP rather than WTA. Employing various protest-treatment techniques, we estimate the mean WTP for reducing current risks of theft and robbery by 50% to range between £38 and £220; for WTA, they are between £351 and £2,175. Higher values for robbery reflect people’s aversion to the violence implicit in this type of crime. The annual value of avoiding a statistical case of crime ranges between £7,011 for theft and £90,087 for robbery. WTP-WTA ratios range from 1:4.8 to 1:16.9 and are influenced by type of crime and elicitation method. In turn, these results support the economic sense of a pre-emptive crime policy that prevents, rather than compensates for, crime occurrence. 1. Introduction and literature review Crime imposes substantial costs on societies (Brand and Price, 2000; Mayhew, 2003; Skaperdas et al., 2009). For instance, according to Brand and Price (2000), in 2000, the total cost of crime was estimated to be around £60 billion for the UK. Mayhew (2003) estimated the cost of crime in Australia to be around 10% of GDP. Similarly, a more recent study in the USA found that the value of property loss to victims represents a social cost of $1.6 trillion, equivalent to 9.7% of annual GDP (Anderson, 2012). However, such measures are far from perfect, as noted by Soares (2015). How to properly measure the economic value of crime is still debated, and many different techniques have been proposed. To have a correct measure of the price tag of crime is of vital importance from a policy perspective. Better estimates mean that a stronger justification for allocation of resources spent in the criminal law system can be presented. Furthermore, better estimates should lead to improved targeting of groups within the population and allow fairer compensation for the victims of crime. The major distinction in crime-cost measures is between ‘bottom-up’ and ‘top-down’ approaches. The former is based on a standard accounting technique that sums up all the costs related to crime for each party affected (Cohen, 2009; Domínguez and Raphael, 2015). The approach includes the monetary loss caused by foregone earnings by individuals harmed by crime and the costs of policing and medical services. The bottom-up approach may also include the diminished levels of domestic business investment and incoming foreign direct investments (FDI) associated with crime-ridden areas. Moreover, this approach could also include intangible costs such as pain and suffering. However, doubts are casted on the reliability of these estimates because of issues such as double counting over these components (Soares, 2015). In contrast, ‘top-down’ approaches derive a total measure of the crime cost, including both tangible and non-tangible components, from a single data source. Among the top-down approaches, a survey-based contingent valuation method (CV) is potentially powerful, although rarely employed in formal impact assessment of policy initiatives and programmes.1 This stated preference method consists of asking survey respondents about their willingness to pay (WTP) and/or willingness to accept (WTA) for a change in the likelihood of a crime event. The CV method is very popular in other contexts, such as in the evaluation of environmental and health policies, where it is maturing as a practice and increasingly accepted as evidence in policy evaluations (Bateman et al., 2002; Hoyos, 2010). For crime, the CV literature is scarce and somewhat dated. Ludwig and Cook (2001) undertook the first published contingent valuation study undertaken in a crime context. US respondents were asked whether they would ‘vote’ for a specified dollar tax increase in return for a 30% reduction in gun injuries, using a dichotomous choice format. The results indicate that the mean (annual) WTP for a 30% reduction in gunshot wounds was estimated to lie between $203 and $239. This implies that the aggregate value of (statistical) gunshot wounds lies between $1,000,000 and $1,200,000.2Cohen et al. (2004) asked US respondents to value the benefits of US public programmes to reduce criminal offending associated with burglary, serious assaults, armed robbery, rape or sexual assault, and murder. The author found that the mean (annual) WTP to reduce incidents of these crimes by 10% was estimated to range between $111 for burglary to $147 for murder. The implied value of preventing a (statistical) crime case is then $30,000 for burglary and $9,700,000 for murder. In a subsequent paper, Cohen and Piquero (2009) updated such estimates. For example, murder was estimated at $11.8 million and burglary at $35,000.3 A further paper, Atkinson et al. (2005), considered the benefits of reducing by 50% the risk of suffering the health outcomes associated with common assault, wounding, and serious wounding in the UK, over the following 12 months. The payment was made through a one-off increase in local taxes for law enforcement. The parametric mean of WTP was in the range £106–£178 per person. The authors calculated the implied health cost of a crime case per family per year as being £913 for common assault, and £6,1964 for serious wounding.5 One of the biggest issues in CV is the treatment of protests. In general, a researcher would expect that individuals declare their true valuation of the good questioned. However, there may exist a proportion of respondents who declare that they are not willing to pay any amount of money, as a result of not accepting some aspect or other of the hypothetical market scenario. They therefore think that they should not pay for the provision of the good in consideration (Jorgensen et al., 1999). These are the so-called protesters, i.e. people who state a zero amount for other than economic reasons. Meyerhoff and Liebe (2006) have shown that even somebody who is willing to pay a value higher than zero—perhaps an extremely high bid—could be a protester. Nevertheless, the focus of the literature on protest has been on bids of value zero. The typical way to distinguish a true zero from a protest one is to ask some debriefing questions after a respondent answers that he/she is not willing to pay. According to the respondents’ answers, the researcher has to classify the nature of the zero. In the context of nonmarket valuation, there are two relevant issues about protests that should be considered. The first (ex ante) is to understand the factors that affect the probability of an individual protesting in the design of a hypothetical market scenario. The second (ex post) is to measure the mean and median WTP (WTA) employing different protest treatment techniques. Even though the issue of protests is not new in the CV literature, there are no systematic studies that specifically deal with them in the context of crime costs. Our paper fills this gap by a) specifically identifying the factors that jointly affect protesting behaviour for WTP and WTA, and b) considering how measures of WTA and WTP vary, when treatments are differentiated on the basis of treatment of protest values as well as on elicitation formats. We ask survey respondents about their WTP and WTA for two types of crime: theft from the person, and robbery. We asked respondents about the maximum amount they would pay for a reduction in crime level, and the amount they would need as compensation for an increase in crime. We chose these two crime types because they constitute a large portion of crime in the majority of countries. Whilst both crimes include loss of property, robbery also involves the use of violence, which makes it a violent crime.6 Thus, we can assess the value that people assign to the violent component. We evaluate individuals’ preferences by using two elicitation techniques: open-ended questions and payment cards. To our knowledge, this is the first attempt to value these types of crime using CV methods, and to calculate the WTA as a compensation for an increase in crime. Given the nature of the ‘good’ we are considering, we expect a high number of protests. Individuals are very sensitive to political and ethical considerations when it comes to their security. Many people believe that it should be the government that is responsible for such problems and are very sceptical of paying extra to reduce the level of crime. As we find in our study, the scepticism is even more acute when people are questioned about their willingness to accept compensation for an increase in the crime level. In the first instance, we proceed by studying the factors that affect the likelihood of protesting. One of the first papers on this topic is Halstead et al. (1992), which studied the socio-economic factors that explain protest behaviour, based on a survey regarding species conservation in New England. However, their analysis was unable to clearly identify the factors that affect the individuals’ decision to protest. Meyerhoff and Liebe (2006) tried to improve such analysis by using a CV relating to the biodiversity of woodland. Contrary to the strategy used by Halstead et al. (1992), Meyerhoff and Liebe (2006) constructed a protest index based on interviewees’ perceptions relating to six possible reasons for declaring a zero bid. Two recent papers, Meyerhoff and Liebe (2010) and Meyerhoff et al. (2013), studied the determinants of protests in further detail. In particular, Meyerhoff et al. (2013) is a meta-study that used a sample of 38 stated preferences papers. These authors analysed the respondent- and survey-specific variables that affect the probability of protesting. Among the former, they consider variables such as age, gender, marital status, and income. The latter include the type of goods in consideration, elicitation method, payment vehicle, or length of the scenario. Interestingly, they found that in the case of non-market goods such as crime reduction, the number of protests is higher compared to market goods that are valued using stated preference techniques. Moreover, the payment vehicle seems not to impact on the protest behaviour. Thus, there is no consensus on the factors that make a person more likely to be a protester and no papers on crime that study this issue. We contribute to the existing literature by identifying the explanatory factors of both the WTP and WTA in a crime context. Our survey form allows us to investigate the impact of crime type and elicitation methods. Our analysis of the determinants of protests (Section 3) shows that respondents are less likely to protest when they are asked to reveal their WTP than their WTA. Moreover, we find that the only variables that are statistically significant are the type of crime-elicitation method and age. We then proceed to calculate mean and median WTP/WTA. We make this estimation using three treatments. These are: considering all zero bids as true zeros, dropping identified protest bids from our estimates, and undertaking a Heckman two-step process that adjust the WTP estimates by selection bias.For WTP, the estimated means range between £38.56 and £127.27. These are similar to those of previous studies, although the risks and type of crimes are not identical. For WTA, the results are much higher, ranging between £348.36.22 and £2,152.97. The concepts of WTP and WTA are derived from the Hicksian welfare measures of the compensating variation (C) and equivalent variation (E). For an improvement in the current situation, both the C and E are positive, but the C represents the maximum WTP for accessing the change while the EV represent the minimum WTA to forego it. Conversely, if the change is negative both measures will be negative, the compensating variation will be the WTA to accept the change, while the equivalent variation will be the maximum WTP to avoid the change (Carson and Hanemann, 2006). Bergstrom and Randall (1987) noted that the estimates should differ only when the transacted good represents a large fraction of the household budget (income effect) or if the transaction costs are very high. However, neo-classical economic theory suggests that for the majority of goods the two estimates should be very close if not identical. Despite these theoretical predictions, the empirical literature has shown that this is not the case and that the WTA are generally much higher than WTP. For example, a meta study by Horowitz and McConnell (2002) found a median ratio of average WTA/WTP to be 2.6, with a mean of 7.17. As a consequence of such evidence, the literature has started investigating the determinants of the WTP/WTA gap (Brown and Gregory, 1999). In recent years, many meta studies on the topic have been conducted, such as that by Horowitz and McConnell (2002). A recent study, by Tunçel and Hammitt (2014), accounted for various economical and psychological explanations of such disparity in a regression framework. Among them, prospect theory (Kahneman and Tversky, 1979) posits that people are risk adverse and value possible losses more than gains. Therefore, people need to receive a larger amount of money for a decrease of utility than they would pay for an increase of the same magnitude. In a seminal paper, Hanemann (1991) ascribed such a discrepancy to (the absence of) substitutes. Plott and Zeiler (2005) affirmed that the elicitation techniques might also be a determining factor. In their meta study, Tunçel and Hammitt (2014) considered 76 papers7 and regressed the log of the WTA-WTP ratio on many variables that capture these various competing explanations. The results show that this ratio is smaller for private goods than for public and non-market goods. Moreover, real market scenarios do not have a significant difference effect on the disparity compared with hypothetical scenarios. Following Hanemann (1991), the authors also found that goods with substitutes have smaller ratios. Payment methods also affect the disparity. For example, double-bound dichotomous choice surveys have larger ratios compared to open-ended and single-bounded survey questions. Interestingly, there is no statistically significant difference between the results where payment cards are used and the open-ended format—the two methods we use in our survey. Our estimates of WTA and WTP allow us to calculate such a ratio, a novelty in the crime literature. We find that on average the ratio is about 10 to 1 higher than those calculated from surveys that focus on environmental and ‘health and safety’ goods. The paper is organized in the following way. In the next section, we outline the survey and the data used. Section 3 explores the determinants of protests using various estimation techniques. Section 4 then presents estimates of the WTP and WTA using various protest treatment techniques. Section 5 shows the estimation of the WTP/WTA ratio, whilst Section 6 concludes. 2. Description of survey and crime variables Respondents, 1,398 in total, were questioned through an internet survey administered by an online company.8 We considered two types of crimes: theft from the person and robbery.9 The two crimes are almost identical except for the use of violence in the latter. If violence is not involved or it has been used against property, but not directly toward a person, this would classify as theft from the person rather than robbery.10 The main reason for choosing these two crimes is that, by comparing the respective willingness to pay and accept, we can also have an idea of the value that people assign to the violence component. According to the crime survey for England and Wales (CSEW), formerly known as the British crime survey, the percentage of households who have been victims once or more of theft from a person was 1.1% and of robbery 0.3% in 2013. To make things clear for respondents, we presented them with a brief definition of each crime, a table that summarize the main consequences that victim suffer along with a clarifying picture.11 We considered two elicitation methods: open-ended and payment cards. These are among the most frequently used methods in contingent valuation studies. Therefore, the possible combinations of crime-payment methods were four: Theft–Open Ended (Theft-OE), Theft–Payment Cards (Theft-PC), Robbery–Open Ended (Robbery-OE) and Robbery–Payment cards (Robbery-PC). The survey company randomly assigned respondents to one of these four options. The final number of respondents for each survey is quite similar, well above 350 individuals. However, for Robbery-OE the number is lower, 261, due to technical reasons.12 The data show (Table 1) that there are no significant differences in terms of socio-economic characteristics between the respondents of the four types of surveys.13 Table 1 Mean (Std. Dev) or percentage for socio-economic characteristics by type of survey. Variable / Type of Crime  Theft   Robbery   Elicitation format  PC  OE  PC  OE  Victimized  16.2%  21.3%  17.6%  16.5%  Feeling very unsafe  1.8%  1.7%  1.8%  0.4%  Household crime  8.1%  12.6%  11.1%  12.3%  Household members  2.65  2.69  2.8  2.76  (1.329)  (1.299)  (1.308)  (1.297)  Married  61.5%  57.9%  64.8%  61.3%  Male  33.2  33.4%  40.2%  34.9%  Very good health  36.2%  32.3%  31.1%  38.7%  Age  46.53  45.15  47.74  43.06  (13.00)  (13.20)  (12.21)  (13.61)  College  68.9%  70.5%  66.8%  70.9%  Income  31776.65  32247.19  32564.77  32279.69  (20823.16)  (20969.61)  (21057.18)  (19510.21)  Variable / Type of Crime  Theft   Robbery   Elicitation format  PC  OE  PC  OE  Victimized  16.2%  21.3%  17.6%  16.5%  Feeling very unsafe  1.8%  1.7%  1.8%  0.4%  Household crime  8.1%  12.6%  11.1%  12.3%  Household members  2.65  2.69  2.8  2.76  (1.329)  (1.299)  (1.308)  (1.297)  Married  61.5%  57.9%  64.8%  61.3%  Male  33.2  33.4%  40.2%  34.9%  Very good health  36.2%  32.3%  31.1%  38.7%  Age  46.53  45.15  47.74  43.06  (13.00)  (13.20)  (12.21)  (13.61)  College  68.9%  70.5%  66.8%  70.9%  Income  31776.65  32247.19  32564.77  32279.69  (20823.16)  (20969.61)  (21057.18)  (19510.21)  In each survey, we asked individuals to state their willingness to pay for a decrease in the risk of being victimized of 50%, from baseline annual probabilities. The size of decrease makes our results comparable with those of Atkinson et al. (2005), whilst being close to the largest change judged to be realistic given current policing policy options. Moreover, given that the baseline probability of risk is relatively low, such an increase/reduction is not considered particularly high. Finally, from a graphical presentation point of view, it helps respondents imagine such a change more easily. We presented a hypothetical situation where police would implement a range of crime-reducing measures. However, the survey explained that the budget of the Home Office (British Ministry of the Interior) would not cover the cost of such measures and that private citizens would have to make an additional payment for it. In order to help individuals picture the change in risk before and after the implementation of these measures, we showed it graphically (Figure A1). For Theft-OE and Theft-PC, we asked for the willingness to pay for a reduction of the probability of being victimized from 1.1% (11 in 1,000 chance) to 0.55% (5.5 in 1,000 chance). In the case of robbery, the reduction is from 0.3% (3 in 1,000 chance) to 0.15% (1.5 in 1,000 chance). For the open-ended elicitation technique, we left a blank space for the respondents to insert his/her stated value. For payment cards, we presented the respondents with a series of possible bids starting from 0 and then progressively going up until £5,000. Respondents also had the option to choose ‘more’ and specify a higher value. The payment vehicle was a one-off annual increase in taxes. Moreover, we made it clear that the money would go directly to a special public fund, earmarked for the purpose of crime reduction. In addition, we reminded respondents that the money used to reduce crime must either come from their savings or from what they would have spent on other things. We then asked respondents the reasons for choosing an amount equal to, or above, zero (see Fig. 1). Protesters were those people who answered that they were not willing to pay anything for the following reasons: ‘The question about paying is too difficult to answer’, ‘I already pay enough charges and taxes’, ‘The crime reducing measures cannot reduce crime levels’, and ‘Government should pay’. On the other hand, we considered as true zeros the options ‘I cannot afford to pay’, ‘I have not been affected, disturbed or annoyed by crime levels’, and ‘it is more important to invest in other social issues’. Respondents also had the option to select ‘Other’. According to their reasons, in some cases, we also classified these as protesters. Fig. 1. View largeDownload slide Reasons for answering zero in the WTP question. Fig. 1. View largeDownload slide Reasons for answering zero in the WTP question. For the same four combinations of surveys, we questioned people on their willingness to accept compensation for an increase in the probability of being victimized (Fig. 2). We presented a hypothetical situation where, due to certain budget restrictions, the government could not enforce the law as before, so that consequently the annual probability of being victimized would increase by 50%. However, the government would compensate people for such an increase; the survey asked what level of compensation would be acceptable. In this case, we considered protest answers to be the following: ‘It is impossible to make an evaluation of such costs’, ‘It is not ethical to receive money from the state for these issues’, ‘The question is too difficult to answer’, and ‘This programme is of no value to my household’. In all these cases, the respondents did not provide any value for the WTA. Fig. 2. View largeDownload slide Reasons for protesting in the WTA question. Fig. 2. View largeDownload slide Reasons for protesting in the WTA question. Among those who declare a WTP equal to zero, the majority thinks that they already pay enough taxes. In addition, many justified their decision not to pay by saying that the government should pay for such a service. On the other hand, the majority of those that did not want to accept any payment stated, ‘It is impossible to make an evaluation of such costs’ and ‘It is not ethical to receive money from the state for these issues’. This demonstrates a clear difference depending on the hypothetic market situation we presented to the respondents. Figure 3 summarizes protest rates for WTP and WTA, disaggregated by crime type and elicitation format. Whilst there is a clear difference in proportion of protest bids for WTP compared with WTA for the same ‘good’, the proportions do not hold constant; Theft-Open is the most obvious outlier. Fig. 3. View largeDownload slide Protest rates by crime type and elicitation format. Fig. 3. View largeDownload slide Protest rates by crime type and elicitation format. 3. Determinants of protests In analysing our response data, we first identify the factors that affect the likelihood of protesting. In order to do so, we pooled all the observations and considered a panel data-type of model that can exploit the features of our data. Our dependent variable Pi takes the value of one if the individual declared a positive WTP or WTA, and zero otherwise, such that:   Pi={1, if WTP>0 or WTA>00, protest  (1) In other words, Pi = 0 if an individual protests while Pi = 1 if she/he does not. As regressors, we included the standard socio-economic and perception variables. We also included a dummy representing the randomization of the type of crime-elicitation method. We estimated the panel data model using a probit random effects specification (Table 2). The type of crime-elicitation technique impacts negatively on the probability of participating (not protesting) relative to Robbery-OE, which is the reference category. Moreover, age of the respondent is found to be negative and significant. On the other hand, male, marital status, and declaring themselves to have very good health are not significant. The dummy for the WTP data is significant and positive, reflecting the fact that people are less likely to protest when asked about their WTP. The correlation parameter ( ρ) is significantly different from zero.14 Finally, σμ2, representing the degree of heterogeneity across individuals, is significant. Table 2 Determinants of participation (not protesting), random effect regressions.   Random effects  Theft-PC  –0.432**  (0.149)  Theft-OE  –0.370*  (0.157)  Robbery-PC  –0.195  (0.152)  Victimized  0.0150  (0.131)  Feeling very unsafe  –0.211  (0.405)  Household crime  –0.138  (0.159)  Household size  0.0748  (0.417)  Married  −0.193  (0.113)  Male  0.129  (0.105)  Very good health  0.153  (0.107)  Age  –1.576***  (0.410)  College  –0.151  (0.113)  Income  0.0190  (0.0245)  WTP  0.991***  (0.0790)  Constant  1.627***  (0.295)  Heterog(ln⁡σμ2)  0.482**  (0.154)  N  2788      ρ  0.618    Log-likelihood  –1436.7      χ2  172.9    P-value  0      Random effects  Theft-PC  –0.432**  (0.149)  Theft-OE  –0.370*  (0.157)  Robbery-PC  –0.195  (0.152)  Victimized  0.0150  (0.131)  Feeling very unsafe  –0.211  (0.405)  Household crime  –0.138  (0.159)  Household size  0.0748  (0.417)  Married  −0.193  (0.113)  Male  0.129  (0.105)  Very good health  0.153  (0.107)  Age  –1.576***  (0.410)  College  –0.151  (0.113)  Income  0.0190  (0.0245)  WTP  0.991***  (0.0790)  Constant  1.627***  (0.295)  Heterog(ln⁡σμ2)  0.482**  (0.154)  N  2788      ρ  0.618    Log-likelihood  –1436.7      χ2  172.9    P-value  0    Note: This table shows the results for a probit random effects model. The dependent variable is a dummy equal to one if the respondent does not protest (participate) and zero if he/she protest. Each individual represents two observations: one with his/her WTP value and the other with his/her WTA value. A description of the variables can be found in Table A1. The model includes a dummy equal to one if the observation refers to WTP and zero for WTA. The standard probit random effect uses a random distribution for individual heterogeneity. 4. Protest treatment in a crime study If there is no consensus in the literature on the determinants of protests, the same applies to the treatment of protests to measure WTP and WTA. The most common, and easiest, way to deal with the protests is simply remove them from the sample (Halstead et al., 1992). This strategy should not yield any effect on the mean WTP if the number of protests is low, the sample is relatively large, or if protesters are similar to non-protesters. Otherwise, by simply eliminating them, a selection bias would be introduced which could invalidate the estimations (Calia and Strazzera, 1999). Another technique is to consider protests as true zeros. Again, this would be an error if the zeros are really protests. An obvious consequence of such a strategy is that the WTP and WTA would be underestimated. This is particularly true if the number of protests treated in this way is high. These two methods of dealing with protests have been used by the existing literature on crime valuation. For example, Atkinson et al. (2005) found that about 279 out of 802 individuals, about 34%, were protesters.15 The authors checked whether there were significant differences, in terms of the distribution of the variables, between the protesters and the non-protesters and found none. Therefore, they proceeded to remove the protesters from the sample and generated the results on the basis of the non-protesters. In contrast, Ludwig and Cook (2001) included all the protests as zeros in the calculation of the WTP. However, as a separate exercise they also excluded the 24% that strongly agree that ‘taxes are too high’. Consequently, they found a WTP 13% higher than the one previously calculated16 (Cohen et al., 2004). However, none of these papers has specifically addressed the issue of protests on crime as we do here. In our baseline estimation, we consider a simple OLS model and assume that the protests are legitimate, true zeros. Moreover, as suggested by Halstead et al. (1992), we also remove all the protests from the sample, retaining an OLS specification. Our third method is an adaptation of the one used by Strazzera et al. (2003a).17 Following these authors, we suppose that the variable Y1i represents the stated amount, and Y2i is a dummy variable equal to one if the individual i participates and zero if he/she protests. The valuation of the ‘crime’ good takes the following form:   ln⁡(Y1i)=xi′β+σui, (2) where Y1i is observed only if Y2i=1. xi is a matrix of independent variables which explains WTP or WTA, β is a vector of unknown parameters, σ is a scale parameter, and μi is a measurement error. Thus,   Y2i={1, if zi′γ+ɛi≥0,0, if zi′γ+ɛi<0. (3) where zi is a matrix of independent variables which explains the participation decision, γ is a vector of unknown parameters, and ɛi is measurement error. This equation is already estimated in Table 2. In other words, the equation that explains protest bids is the participation equation needed in the Heckman approach. The stated amount depends on the decision to participate and not protest—the ‘participation Decision’.18 The expected value of the logarithm of the bid, given that a person wishes to participate, is:   E[ln⁡(Y1i)|ɛi>−zi′γ]=xi′β+σρ(φ(zi′γ)Φ(zi′γ))=xi′β+σρλ(zi′γ), (4) where φ(·) and Φ(·) are the standard normal probability density function and cumulative distribution function, respectively, and λ(zi′γ) is the inverse Mills ratio. This equation can be generalized to other elicitation models such as payment cards with intervals (see Atkinson et al., 2005). We follow the two-step approach shown in Heckman (1979), using estimates of Table 2 to obtain a prediction for λ(ziγ). These predicted values are incorporated on each valuation equation to estimate the second-step equation using OLS. We corrected the variance-covariance matrix of the estimated final parameters, following Cameron and Trivedi (2005). Given the log-normal distribution, we assume that the unconditional median and mean for the WTP are respectively:   median(WTPi)=exp(xi′β), (5)  mean(WTPi)=exp(xi′β)*exp(σ2/2). (6) For the Heckman equations, the conditional expected value of Y1i is equal to19:   E(Y1i|Y2i=1)=exp(xi′β+σ22)*(1−Φ(−zi′δ−ρ2σ2))(1−Φ(−zi′δ)), (7) where the median is:   Median(Y1i|Y2i=1)=exp⁡(xi′β)*(1−Φ(−zi′δ−ρ2σ2))(1−Φ(−zi′δ)). (8) The unconditional expected value of Y1 is equal to:   E(Y1i)=exp⁡(xi′β+σ22)*(1−Φ(−zi′δ−ρ2σ2)), (9) and the median is:   Median(Y1i)=exp(xi′β)*(1−Φ(−zi′δ−ρ2σ2)). (10)Table 3 presents the mean and median WTP results. The mean value estimated in the study can be aggregated for the total population affected and used in cost-benefit analysis of crime policies, while the median has a voting interpretation, which is that 50% of the population is willing to pay that amount of money or would support the project if they have to pay that amount (Carson and Hanemann, 2006). We focus our discussion on the mean values since we are more interested in cost-benefit policy contexts. Table 3 Mean WTP (median in parentheses). WTP/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £38.56 (8.02)  £63.94 (12.19)  £59.95 (8.99)  £127.27 (18.95)  Drop protests  £48.74 (12.74)  £73.38 (18.92)  £83.23 (16.63)  £135.13 (28.80)  Heckman  £45.78 (12.78)  £70.37 (18.93)  £70.47 (18.79)  £125.80 (28.77)  WTP/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £38.56 (8.02)  £63.94 (12.19)  £59.95 (8.99)  £127.27 (18.95)  Drop protests  £48.74 (12.74)  £73.38 (18.92)  £83.23 (16.63)  £135.13 (28.80)  Heckman  £45.78 (12.78)  £70.37 (18.93)  £70.47 (18.79)  £125.80 (28.77)  Note: The table presents the mean and median estimates of the WTP using three different protest-treatment techniques. Zeros kept and Drop protests are calculated through OLS. Heckman estimated parameters through a two-step Heckman model. In general, the mean is lower if we consider all protest bids as legitimate zeros. WTP for theft ranges between £38.56 and £83.23, whereas for robbery WTP is between £63.94 and £135.13. The results clearly show that people are willing to pay more to avoid the risk of violence. By dropping the protests, we generate higher means than when we correct for sample selection. The median values are much smaller than the mean values, reflecting the fact that the data are skewed to the right. However, the ranking of the medians follows the same pattern as the means. Directly comparing such results with other studies is not an easy task because the type of crime and the baseline risk changes are not always comparable. For example, Ludwig and Cook (2001) found a parametric mean WTP of $239 (about £155 at current exchange rates) for a decrease of 30% in gun violence. However, their change in risk was lower and gun violence is a more serious crime than robbery. Cohen et al. (2004) estimated the WTP for a reduction of crime by 10%. This included armed robbery value, which had a value of $110 (£71), whereas our estimates for robbery are £63.94 with payment cards and £127.27 for open ended—a less serious crime but a larger reduction. Atkinson et al. (2005) considered violent crime with no material loss. However, among the three violent crimes they considered, the closest to robbery in terms of psychological and physical harm is common assault. As the authors removed the protests from the analysis, we compare these to our analogous estimates. Their central estimate was £105.63—higher than all our estimates apart from those for Robbery-OE, presumably reflecting the more violent nature of the crime that Atkinson et al. (2005) considered. Such results allow us to calculate the implied cost of ‘statistical’ crimes, estimated as the amount that the average person would pay to reduce with certainty the risk of crime. It is derived by multiplying the mean (or median) by the percentage reduction in the risk of being victimized multiplied by 100 (see Table A3 in the appendix). Table 4 shows the estimated mean, and median, WTA, which have a similar pattern to those for WTP.20 The WTA for theft ranges between £348.36 and £559.36, whereas for robbery it ranges between £902.22 and £2152.97. A direct comparison of these values with previous estimates is not possible since no other crime survey has investigated the WTA for an increase in crime rates. However, these WTA values may be compared with those offered by the UK government to crime victims by way of compensation (Ministry of Justice, 2012) in order to assess whether these compensation levels accurately reflect social preferences. Table 4 Mean WTA (median in parentheses). WTA/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £348.36 (13.06)  £945.47 (20.73)  £364.21 (15.66)  £2152.97 (67.41)  Protests dropped  £559.36 (66.46)  £1131.79 (108.09)  398.97 (69.59)  £995.54 (171.49)  Heckman  £508.74 (67.11)  £1026.75 (108.10)  £371.05 (71.31)  £902.22 (172.07)  WTA/Treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  £348.36 (13.06)  £945.47 (20.73)  £364.21 (15.66)  £2152.97 (67.41)  Protests dropped  £559.36 (66.46)  £1131.79 (108.09)  398.97 (69.59)  £995.54 (171.49)  Heckman  £508.74 (67.11)  £1026.75 (108.10)  £371.05 (71.31)  £902.22 (172.07)  Note: The table presents the mean and median estimates of the WTP using three different protest-treatment techniques. Zeros kept and Drop protests are calculated through OLS. Heckman estimated parameters through a two-step Heckman model. Finally, we calculate the WTP for those who gave a protest response to the WTA question and vice versa. Table 4A in the Appendix shows those results. For the WTP we found no differences in order of magnitude for the sample as a whole. The WTA values are significantly higher, though these values are less robust since the sample size is rather small for regression analysis. 5. WTP/WTA ratio As previously mentioned, there are no previous studies that estimated the WTA in a crime scenario, so we cannot directly compare the WTA/WTP ratio. Nevertheless, our research allows us to evaluate such a ratio in various ways. We can check the disparity in the ratio for two different types of crimes. In addition, we can see whether the elicitation technique plays any role in determining the ratio. Table 5 shows these ratios. The first thing to note is that these are sizeable, ranging from 4.79 (Theft-OE, protests dropped) to 16.91 (Robbery-OE, zeros kept). The average among all the combinations of crime-elicitation technique is 10.33. Moreover, with the exception of the 16.91 result, the values are lower for open-ended format than for payment cards. Table 5 WTA to WTP ratio. WTA-WTP treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  9.03  14.78  6.08  16.91  Protests dropped  11.47  15.42  4.79  7.37  Heckman  11.11  14.59  5.27  7.17  WTA-WTP treatment  Theft-PC  Robbery-PC  Theft-OE  Robbery-OE  Zeros kept  9.03  14.78  6.08  16.91  Protests dropped  11.47  15.42  4.79  7.37  Heckman  11.11  14.59  5.27  7.17  We would generally expect a high ratio for a variety of reasons. We consider a public good, and our scenario is hypothetical compared to the market of an ordinary private good. Moreover, people do not generally have a direct experience of victimization, which makes difficult for them to ‘quantify’ the costs. As Tunçel and Hammitt (2014) report in their work, ‘environmental’ and ‘health and safety’ goods are the ones that on average have the WTA:WTP highest ratio, 6.23 and 5.09, respectively. It seems possible—though we have no proof—that the lower ratios for the OE elicitation format reflect the fact that whilst respondents are known not to be so influenced by income constraints when facing WTP questions that use OE (Mitchell and Carson, 1989), they see the bid levels presented to them in payment cards in the WTA questions as legitimizing potential values not suggested in the OE format. The lower OE bids in the WTA questions therefore reflect a conservatism in the respondents’ preferences in this elicitation context. 6. Conclusions The treatment of protests in applications of the contingent valuation method is a controversial issue. If protests are not treated properly, this can introduce estimation bias and affect the final results, reducing their value to the policymaker. This is even more relevant in a survey like ours, on crime, because people may be expected to disagree about aspects of the hypothetical market scenario. Despite this, there is no research that studies protests in crime-contingent valuation scenarios. In particular, the literature has neglected to identify the factors that are more likely to affect protesting behaviour and how sensitive the estimates of the mean and median WTP and WTA are to various protest treatment techniques. This paper aims at filling such a gap by disaggregating these factors. In order to do so, we run a survey that derives the willingness to pay for, and willingness to accept, a change in the probability of being a victim of theft and robbery. Moreover, we consider two elicitation techniques: open-ended and payment cards. We structure our analysis around two main themes. The first focuses on the individual determinants of protesting behaviour using a random effects panel data model. The results show that the type of crime-elicitation technique, Theft-PC and Theft-OE, affects the probability of protesting, as does age. Interestingly, we find that the appropriate model needs to take into account the correlation between the decision to protest in a WTP and the decision to protest in a WTA question. In the case of age, the finding that the probability of protest falls with age suggests that those who are old are likely to be more willing to devote resources to crime deterrence than younger people. This may reflect the fact that older people own more of their material goods and so are more concerned with protecting them, and/or that they are more aware of their own physical and mental vulnerabilities in relation to their being victims of crime. An implication of this result for policy is that localities with high proportions of older populations should have more crime deterrence resources devoted to them relative to other localities. We employ three protest treatment strategies to estimate the WTP and WTA. The results show that the WTA is much higher than the WTP for the same crime and elicitation method. Moreover, we find that WTP and WTA are lower when we consider protests as legitimate zeros. WTP for theft ranges between £38.56 and £83.23, depending on treatment and elicitation method, whereas for robbery the range is between £63.94 and £135.13; unsurprisingly, the involvement of violence significantly increases the willingness to pay. The WTA for theft is in the range £348.36–£559.36 and for robbery £902.22–£2,152.97, depending on treatment. These results allow us to calculate, for the first time, the WTA:WTP ratio in a crime study. The average ratio across all combinations of crime-elicitation technique is 10.33, whilst the individual ratios are lower for the open-ended question format than for the payment card format, probably reflecting the fact that we consider a public good with a relatively hypothetical scenario. Such a big difference between the WTP and WTA results has two policy implications. First, a forward-looking public authority is likely to find it cheaper and easier to implement policies aimed at decreasing crime levels, rather than compensating citizens to tolerate a higher level of crime risk. Second, people tend to refuse compensation for an increase in crime for reasons that are not easily justified on the basis of economic rationality; rather, reflecting a rejection of the notion that increased risks can be traded off against money. This leads to a higher number of protests for WTA than for WTP. Our findings therefore also support the idea that it is impossible to fully compensate a victim of a crime, i.e., make a crime victim ‘whole’ (Mulder, 2009; Ludwig, 2010).21 Supplementary material Supplementary material is available online at the OUP website. Footnotes 1 Another one is the value of a statistical life (Soares, 2015). 2 The cost of statistical crime is given by multiplying the mean or median WTP for a certain percentage reduction in the risk of being victimized by the relevant (at-risk) population denominator, which is 100. As Atkinson et al. (2005, p. 577) said: ‘this transformation gives the implied amount that the average individual would be willing to pay to avoid a violent crime happening with certainty’. 3 Interestingly, the authors used the WTP estimates to calculate the value of a criminal career. One of the most important results is that society would save $3 million and $5 million if a 14-year-old could be saved from a life of crime. As Cohen et al. (2010, p. 282) said: ‘Saving a group of high-risk (chronic) youth should result in substantial cost-savings for the would-be offender, the potential victim(s), the criminal justice system, and for society as a whole’. The estimates on the cost of crime by Cohen et al. (2004) and Cohen and Piquero (2009) were used by Heaton (2010) to calculate the expected benefits of hiring extra police officers in several large police departments in the USA. 4 Other notable work on crime costs includes that by Nagin et al. (2006), who found that the total willingness to pay for a 30% reduction in youth crime in all households from Pennsylvania is between $387 million and $468 million. 5 For a detailed history of the use of stated preference approaches in crime contexts, see Cohen (2009). In this work, Cohen also outlined best practices for running a CV survey. 6 As defined by the FBI for the purposes of the Uniform Crime Reports. 7 The majority of the studies considered in such meta-analysis refer to ordinary private goods, health and safety, environmental, or public goods (but not on law enforcement). 8 We used the popular surveygizmo website: http://www.surveygizmo.com/. 9 A person is accused of the former if ‘there is theft of property while it is being carried by, or on the person of, the victim (for example pick-pocketing)’ (British Office of National Statistics, 2015). On the other side, a person is accused of robbery ‘if he steals, and immediately before or at the time of doing so, and in order to do so, he uses force on any person or puts or seeks to put any person in fear of being then and there subjected to force’ (British Office of National Statistics, 2015). 10 For example, if ‘a bag is taken cleanly from the shoulder of a victim or a phone is taken cleanly from the hand) the allegation should be classified as theft from the person and not a robbery’ (British Office of National Statistics, 2015). 11 We included a figure because Corso et al. (2001) showed that respondents are more sensitive to risk changes when showed it graphically. 12 By mistake, the online survey company sent away more questionnaires to Theft-OE, Theft-PC, and Robbery-PC compared to Robbery-OE. Due to budget limitations, we could not increase the number of the last type of survey to balance its number with the other ones. 13 An exception seems to be the share of people that state they ‘feel very unsafe’, which is lower than the other three categories. Although we cannot fully substantiate it, we think that it might depend on the slightly younger age of this group compared to the others. 14 Along with these panel data models, we also run two separate probit regressions and a bivariate probit. Results are very similar to the ones presented in the paper, and are available upon request. 15 Interestingly, as we have seen in Fig. 1, we find a lower number of protests for our WTP question. 16 In a seminal study in this area, Cohen et al. (2004) did not talk explicitly about protests, nor did they discuss their treatment. 17 Of course, there are other ways of dealing with protests, for example by including all the protests and assigning a value of WTP/WTA for each protest depending on how non-protests with similar socio-economic characteristics have answered. This is similar to the treatment of missing data presented in Cameron and Trivedi (2005). Another way to treat protests is the one proposed by Strazzera et al. (2003b), which combines the double dichotomous model and a Spike model (Kriström, 1997), and which is used to deal with protests in a double-bounded dichotomous choice format. Nevertheless, it is not possible to apply such a method with the open-ended or payment card formats used in our study. 18 We thank the editor for noticing this estimation possibility, which allows us to link the explanation of protest with the value equations. 19 This formulation is derived from Cameron and Trivedi (2010). 20 Results in Tables A7 and A8 show that respondents who feel very unsafe have significantly lower WTP/WTA. Though this appears counterintuitive, we speculate that this finding results from an inability on the respondents’ part to imagine such an improvement in crime rates to be possible—perhaps because of a chronic crime epidemic in the neighborhood or because previous initiatives have failed. 21 We thank an anonymous referee for highlighting this principle. Acknowledgments We would like to thank participants at seminars at the Catholic University of the North, Chile. Funding This work was supported by the Alumni Fund at University of Bath, UK; CONICYT, Programa POSTDOCTORADO [under grant number 3160521 to M.P.]; and the Institute for Research in Market Imperfections and Public Policy, ICM IS130002, Ministerio de Economía, Fomento y Turismo de Chile [to M.P.]. References Anderson D. A. ( 2012) The cost of crime, Foundations and Trends in Microeconomics , 7, 209– 65. Google Scholar CrossRef Search ADS   Atkinson G., Healey A., Mourato S. ( 2005) Valuing the costs of violent crime: a stated preference approach, Oxford Economic Papers , 57, 559– 85. Google Scholar CrossRef Search ADS   Bateman I. J., Carson R. T., Day B., Hanemann M., Hanley N., Hett T., Jones-Lee M., Loomes G., Mourato S., Özdemiroglu E. ( 2002) Economic Valuation with Stated Preference Techniques: A Manual , Edward Elgar Publishing, Cheltenham. Google Scholar CrossRef Search ADS   Bergstrom J. C., Randall A. 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Published: Apr 1, 2018

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