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Martin Salm and Ben Vollaard, Tilburg University Send correspondence to: Ben Vollaard, Department of Economics, Tilburg University, PO Box 90153, 5000 LE, Tilburg, Netherlands; E-mail: firstname.lastname@example.org We study how residents form beliefs about the prevalence of crime in their neigh- borhood. We document the process of learning about local crime for a uniquely long period of 10 years after taking up residence. Our analysis is based on four successive waves of a large crime survey in the Netherlands matched with administrative regis- ter data for the complete history of places of residence between 1995 and 2011. We ﬁnd that beliefs of residents are much more favorable shortly after their move into the neighborhood than they are longer after their move. The adjustments in beliefs only level off after many years. A large part of this adjustment in the years after a move can be explained by the accumulation of direct experiences with crime. Our ﬁndings show that victimization of crime is more than the outcome of a calculated risk; it is a costly form of learning about crime. (JEL: D81, K42) We would like to thank the editor J.J. Prescott, three anonymous referees, Padmaja Ayyagari, Philip Cook, Glenn Harrison, Jan Kabatek, Tobias Klein, Wieland Müller, Emily Owens, and Arthur van Soest for valuable comments and suggestions as well as participants of the 5th Transatlantic Workshop on the Economics of Crime in Frank- furt, the UCL-NHH Crime Workshop in London, the Health Economics Conference in Grindelwald, the 6th Annual Meeting on the Economics of Risky Behaviors in Medellin, the International Symposium on Environmental Criminology and Crime Analysis in Kerkrade, the Essen Health Conference, the SABE/IAREP conference in Wageningen, and seminar participants atAarhus University, CPB Netherlands Bureau of Economic Pol- icy Analysis, Erasmus University Rotterdam, Essen University, the Max-Planck Institute in Bonn, Ruhr University Bochum, and Tilburg University. The provision of individual- level survey and administrative data by Statistics Netherlands is gratefully acknowledged. The authors declare no conﬂict of interest. American Law and Economics Review doi:10.1093/aler/ahab012 © The Author 2021. Published by Oxford University Press on behalf of American Law and Eco- nomics Review. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial reproduction and distribution of the work, in any medium, provided the original work is not altered or transformed in any way, and that the work is properly cited. For commercial re-use, please email@example.com. The Dynamics of Crime Risk Perceptions 521 1. Introduction Beliefs about the likelihood of criminal victimization are an important driver of crime-preventive behavior, which in turn affects the level of crime in society (Ayres and Levitt, 1998; Vollaard and Van Ours, 2011; Gonzalez- Navarro, 2013; Tseloni et al., 2017). In most models of crime, the beliefs of potential victims are assumed to be given and to accurately reﬂect prevailing conditions. This existing work tends to focus on how victims interact with offenders given a set of correct beliefs, not how victims form their beliefs. Victims cannot make mistakes in these models. If people are victimized, then this does not come as a surprise, and it does not provide any new information. Yet, it is rather likely that potential victims make mistakes when forming their beliefs. Consider judgments about the frequency of crime incidents in an area, the topic of this article. When judging such frequencies, descrip- tions of crime incidents like stories or statistics may be misleading because of the large variation in risk across relatively small areas (Weisburd, 2015). Learning about crime risk by direct observation of offenders is also of lim- ited use because most crimes are rare, and offenders tend to take care not to be observed. Similarly, ﬁrst-hand experience with a crime is not useful due to the infrequent nature of victimization. In other words, it is quite a feat to form correct beliefs about local crime risk. If beliefs are not correct, then potential victims may not take the level of precaution that they would if they were fully informed. Thus, levels of crime in society could deviate from predictions of models with complete information. 1. In Ehrlich’s (1981), a canonical model of victim-offender interaction percep- tions of the expected harm from crime is assumed to be a correct estimate of actual harm. The same holds for related theoretical work by Mayhew et al. (1976), Clotfelter (1977, 1978), Cook (1986), Hui-Wen and Png (1994), Van Dijk (1994), Helsley and Strange (1999, 2005), Allen (2013), Vasquez (2021), Baumann et al. (2019), and Dominguez (2020). 2. As documented in Greenberg (1987) and Braakmann (2012), perceived crime risk—deﬁned as an assessment of the likelihood of victimization—is an input for crime preventive behavior. Though related, we do not address the fear of crime, the negative emotional response to this assessment (for a recent review, see Henson and Reyns, 2015). See Tyler (1981) and Jackson (2011) on beliefs about harm from crime and about the effectiveness of preventive behavior. 522 American Law and Economics Review V23 N2 2021 (520–561) We study the following questions: How do potential victims form beliefs about crime risk? How quickly do they adjust those beliefs? What does that tell us about the extent to which the common assumption of correct beliefs is violated? To answer these questions, we document and interpret the long- term dynamics of crime risk perceptions. We focus on beliefs about the prevalence of crime in one’s own neighborhood. We examine how perceptions of neighborhood crime risk evolve with increasing time of exposure starting from the moment of moving into a neighborhood. Moving into the neighborhood marks a distinct point in time: time of exposure is zero. Following the evolution of perceptions for multiple years is challenging given the paucity of longitudinal data. Typically, data on crime risk perceptions consist of repeated cross-sectional surveys. This also holds for the data in this article, but our empirical approach addresses this limitation. For each respondent in our repeated cross-sectional survey, we know their perception of crime risk in the neighborhood at the time of the survey interview, and we also know the date they moved into the neighborhood. Thus, for instance, for a cohort that moved in the Year 2005 we observe crime risk perceptions for all the years the survey was conducted, 2008, 2009, 2010, and 2011, which is 3, 4, 5, and 6 years after the move. Similarly, the 2006 cohort was observed 2, 3, 4, and 5 years after the move. This feature of our data enables us to examine changes in average crime risk perceptions at the level of cohorts of movers. We examine such changes for all neighborhoods in the Netherlands and for multiple cohorts of movers. A remaining challenge is to disentangle the effect of time of exposure, which is our effect of interest, and changes in crime risk over time. We account for changes in crime conditions by controlling for time trends in crime risk perceptions among incumbent residents who have lived in the 3. We stay away from perceptions of personal crime risk as these are affected by changes in (often unobserved) victim precaution, which in turn affect personal risk. The prevalence of crime in the locality is independent from an individual’s precautionary behavior. 4. The U.S. crime survey, the NCVS, has a rotating panel, but households only participate for at most 3 years. Occasionally, surveys are based on a true panel, but sample sizes tend to be very small and levels of attrition high. Robinson et al. (2003) is based on a panel of 305 residents running for 2 years; Brunton-Smith (2011) is based on a panel of about 1,500 adolescents running for 4 years; Russo et al. (2013) is based on a panel of 2,000 individuals surveyed four times over a period of almost 5 years, but with only 4% of the panel participating in all four waves. The Dynamics of Crime Risk Perceptions 523 neighborhood for more than 10 years. Thus, the remaining effect reﬂects the process of learning about local crime conditions and not how the crime rate varies over time. Our empirical strategy is similar to Borjas (1995), who examines how immigrant wages evolve with time since immigration. Once we have documented how beliefs evolve with increasing time of exposure to crime risk in the neighborhood, we explore the channels by which beliefs are adjusted. Based on a subset of individuals for which we have repeated survey responses, we analyze whether direct experience with a crime can explain the observed evolution of beliefs with increasing time of exposure. The longitudinal nature of these data allows us to control for any ﬁxed individual characteristics that are related to both victimization risk and risk perception. We thus estimate the effect of crime victimization on perceptions and use these results to simulate the process of upward and downward adjustments in perceptions that occurs once people have moved into the neighborhood. We then compare our simulations to the observed patterns in risk perceptions. An empirical analysis of risk perceptions that allows for updating beliefs by way of experiencing a fairly rare event like crime requires a very large sample size. We match extensive household-level administrative data for the complete population of the Netherlands (“Gemeentelijke Basisadmin- istratie”) with survey data on crime. The administrative records provide the history of all places of residence of every individual for the period between 1995 and 2011. We match the administrative data with four waves of the Netherlands Crime Survey (IVM, 2008–11), a cross-sectional survey that is repeated annually. The IVM is one of the largest crime surveys in the world relative to the size of the population, providing us with a sample of about half a million respondents, one out of 25 of the Dutch population aged 15 or over. We show that the elicited beliefs about crime in the neighborhood have face validity: the perceived prevalence of a crime is strongly related to its actual rate of occurrence. We ﬁnd that the process of learning about local crime risk at the level of cohorts of movers involves an extensive period of adjustment in beliefs. Risk perceptions are on average more favorable shortly after the move than they are longer after the move. The adjustments in perceptions only level off after many years. Relative to comparable residents who have lived in the same neighborhood for many years, recent movers perceive crime in the 524 American Law and Economics Review V23 N2 2021 (520–561) neighborhood to be less prevalent on average. The observed pattern at the level of cohorts of movers holds for both high-crime areas and low-crime areas and across all crime types that we consider. Taken over the 10-year period, changes in risk perceptions are large and statistically signiﬁcant. For example, the observed decrease in the percep- tion that burglary is rare in the neighborhood over 10 years is 13 percentage points, relative to a baseline of 43%. This is equivalent to 1.1 standard deviation of the distribution of the average perceived burglary risk across municipalities. Our assertion that the survey reveals the beliefs that respondents truly hold is validated by the ﬁnding that changes in elicited beliefs with time since the move date is in line with changes in avoidance behavior. In other words, we not only ﬁnd particular patterns in the beliefs that people report in the survey, but also that people act on those beliefs. The pattern that we observe at the cohort level is the summation of different personal histories within the same risk environment. We provide evidence that direct experience with crime at the individual level can explain a large part of the observed adjustment in risk perceptions at the cohort level. Based on the subsample of individuals for whom we have repeated observations, we ﬁnd that the belief that crime is rare in the neighborhood is sharply adjusted downwards upon victimization—and slowly adjusted upwards as time since victimization increases. Simulations based on these effects estimated at the individual level demonstrate how the rare incidence of crime victimization generates patterns in perceived crime risk at the level of cohorts of movers that are similar to those observed in the data. Appar- ently, victimization of crime is an important determinant of how people form perceptions of crime risk in their locality. It can explain up to 40% of the observed adjustment in risk perceptions with increased time of exposure, but the conﬁdence bounds around the estimates are such that this percentage may well be higher or lower. 5. Properties of the study population are not unlike those in other countries. The frequency at which people move house, for instance, is similar between the Netherlands and Britain (Ofﬁce for National Statistics, 2014). Based on British data, Hellmuth (2017) ﬁnds dynamics in crime risk perceptions after a move that is similar to what we report for the Netherlands. The Dynamics of Crime Risk Perceptions 525 Our ﬁndings are consistent with experience-based learning: residents learn about a phenomenon in their living environment by way of personal experience. We discuss two alternative explanations for what we ﬁnd. First, individuals with overoptimistic beliefs about the neighborhood crime risk may be overrepresented among movers to a neighborhood. If selection of households is the driving force, then the observed pattern should not hold for people with little say over where to move—those in rent-controlled public housing. We ﬁnd that they adjust their beliefs similarly to homeowners who are free to move wherever they like, suggesting that selection is not the driving force. Second, movers may cast characteristics of the neighborhood of their choice, including the crime risk, in too positive a light out of a tendency to justify their decision to move to that speciﬁc location. Again, households with highly restricted choice on where to move should be less affected by this tendency than those who do not face such restrictions, but that is not what we ﬁnd. Our study contributes to a growing body of evidence in contexts other than crime that beliefs are adjusted strongly after personal experience of adverse events such as ﬂoods, hurricanes, and unfavorable investment out- comes. We contribute to the study of how personal experience affects 6. Homeowners are more likely to buy ﬂood insurance after they have experienced a ﬂood in their area (Kunreuther, 1995; Gallagher, 2014). This applies even when the actual risk of ﬂooding remains unchanged and accurate descriptions of the risk are readily available. Likewise, individuals are more likely to take precautions against hurricanes in response to recent experiences with hurricanes (Meyer, 2012); investors are less likely to own stocks if they have experienced periods of poor stock market returns such as the great depression (Malmendier and Nagel, 2011); young fund managers are more likely to shift their investments towards stocks that presently show high returns than old fund managers (Greenwood and Nagel, 2009); consumers become penny-pinching individuals once they have lived through times with great unemployment (Malmendier and Nagel, 2016); portfolio managers take less risks if they have personally experienced adverse investment outcomes (Chernenko et al., 2016); residents are much more likely to drink bottled water once they have experienced illness as a result of drinking contaminated tap water (Viscusi and Zeckhauser, 2014); individuals are more likely to buy long-term care insurance when their parents or in-laws become institutionalized in a nursing home, i.e., when they gain ﬁrst-hand experience with long-term care (Coeetal, 2015); individuals “learn from suffering” in the sense that they are more likely to take a ﬂu shot after having had the ﬂu—unless they got the ﬂu in spite of the vaccine (Jin and Koch, 2018). Agan and Prescott (2014) ﬁnd that experiencing a bad event in the form of becoming aware of living close to a convicted sex offender by way of offender registries and community notiﬁcations has a heterogeneous impact on future victimization of sex offenses. 526 American Law and Economics Review V23 N2 2021 (520–561) beliefs and risk-taking behavior by taking the empirical study of this topic to a new area: perceptions of crime, an important determinant of the public’s response to crime. Recent work into the role of beliefs within the context of crime has been largely limited to offenders. We shift the focus to potential victims. We show that potential victims’ beliefs about the local prevalence of crime are dynamic and at least sometimes incorrect. Risk perceptions are dynamic because they change in response to exposure to local condi- tions. Risk perceptions are at least sometimes incorrect because they change with increasing time since the move date while the local crime risk is held constant. Our ﬁndings have important policy implications. Victim-focused crime prevention policies such as regulatory mandates prescribing the use of preventive measures and burglary prevention advice are not uncommon (Grabosky, 2010), albeit often limited in scale and scope relative to offender- focused policies (Felson and Clarke, 2010), but the rationale for such policies is often left implicit. The underlying question is why potential victims cannot fend for themselves. First of all, they may well have incor- rect beliefs, given our ﬁnding that potential victims exposed to the same risk environment can have very different crime risk perceptions depending on how long they have been exposed to the risk environment. Second, when we look at how beliefs are formed, evidence suggests that potential victims learn the hard way. Beliefs are updated in response to rather than in antic- ipation of crime (cf. Van Dijk and Vollaard, 2012). As such, victimization 7. See Hjalmarsson (2009), for instance, and see Pickett and Roche (2016) and Apel and Nagin (2017) for reviews of the literature on perceptual deterrence. 8. Within criminology, there is an extensive literature on fear of crime and its measurement, which is primarily focused on fear as an outcome rather than as an input into crime preventive behavior (for an exception see Jackson and Gray, 2010). See also Dustmann and Fasani (2016) for a study into the effect of local crime rates on residents’ mental health and for a review of related studies in the economics literature. Similar to economics, the interest in precautionary behavior in criminology waxed in the 1970s and 1980s (e.g., Skogan and Maxﬁeld, 1981) and waned afterwards, with Van Dijk (1994) as a rare exception. This also holds for work by psychologists in this area (e.g., Tyler, 1980). The Dynamics of Crime Risk Perceptions 527 of crime is not simply the outcome of a calculated risk; it is a costly form of learning about the appropriate way of addressing the threat of crime. If policy is not successful in altering the level of victim precaution— either because the intervention does not have the desired effect on victim precaution or because the intervention only displaces crime—then the alter- native is to increase public expenditures on crime control (for a discussion of public vs. private crime control, see Philipson and Posner, 1996). Thus, public intervention in crime control may not only be grounded in its pub- lic good character but also in the inability of citizens to take appropriate precautions. The remainder of the article is structured as follows. In the next section, we introduce a conceptual framework for the analysis of the dynamics of risk perceptions. In Section 3, we present the empirical strategy. Section 4 describes the data. In Section 5, we present our estimation results. In Section 6, we discuss how well experience-based learning can explain these ﬁndings. Section 7 discusses alternative interpretations of our ﬁndings. Section 8 concludes with a discussion of our ﬁndings. 2. Conceptual Framework In this section, we present the conceptual framework for our analysis of the dynamics of individual beliefs about the prevalence of crime in the neighborhood of residence. Our analysis starts at the moment of moving into a new neighborhood. At this moment, the individual has formed an initial belief, a prior. Someone’s prior is primarily based on descriptions of the local crime risk, for example, information from conversations with real estate agents and new neighbors, media reports, and ofﬁcial crime statistics. Initial beliefs are likely to bear some resemblance to actual conditions. Perceptions of the prevalence of theft from car, for instance, are likely to be less favorable when the assessment involves a neighborhood in an urban area rather than a neighborhood in a rural town. The initial belief may also 9. This ﬁnding also helps to explain why the level of victim precaution is often found to be exceedingly low, with a sizeable share of all burglaries occurring in homes with windows or doors left open, for instance (Budd, 1999). 528 American Law and Economics Review V23 N2 2021 (520–561) be dependent on conditions in the previous place of residence, something we return to in Section 5. After taking up residence, an individual collects additional information about neighborhood conditions, which may lead to adjustment of his or her prior. Our aim is to uncover this process of adjustment in beliefs. Factors that mediate the relationship between time of exposure and perception can be grouped into two main categories. Beliefs may be adjusted in response to experiences with crime—personal victimization, victimization of direct peers such as members of the household, observation of criminal events— and in response to taking in further descriptions of local crimes. We should note that beliefs may also be adjusted in response to the absence of these experiences and impressions. In a formal framework, we assume that, at the time of moving, individuals form an initial perception of local crime risk in the new neighborhood denoted as p . In each period after the move, individuals receive a signal about local crime risk that we denote as s , s , .., s for periods 1...T after 1 2 T the move. Individuals’ perception of crime risk in period T is determined as a weighted average of initial perceptions and the signals the individuals has received after the move. y = w p + w s + w s + ··· + w s , (1) i 0 0 1 1 2 2 T T where w is the weight given to p and w ...w are the weights given to 0 0 1 T s , s , .., s . The weights w ...w sum up to one. We assume that p is a 1 2 T 0 T 0 random variable with mean μ , and s , s , .., s are random variables with p 1 2 T mean μ . Then, the expected value of an individual’s perception of crime risk is given by E(y ) = w μ + (1 − w )μ . We further assume that the i 0 p 0 s weight given to initial perceptions w is a strictly decreasing function in time since move T with w = 1 for T = 0 and w → 0as T →∞. Thus 0 0 E(y ) = μ for T = 0 and E(y ) → μ as T →∞. In Section 6, we present i p i s a more restrictive version of the framework above, in which signals about local crime risk depend exclusively on whether or not an individual was recently victimized. There are reasons to believe that μ = μ , i.e., that an individual’s p s mean of the prior is different form the mean of the signals. For instance, information from descriptions of the local crime rate before a move may be less salient and emotionally loaded than information obtained from having The Dynamics of Crime Risk Perceptions 529 lived through these crime conditions, leading to an downward adjustment in the belief that crime is rare in the neighborhood (we discuss alternative explanations for why μ = μ in Section 7). If the mean value of initial p s perceptions is indeed lower than the mean value of signals, then average perceptions of local crime risk will increase during the years after a move. 3. Empirical Strategy Our empirical strategy is based on linear regression models of the following type: y = timehere β + incumbent γ + X λ + I μ + α + ε , (2) i i i n,t i i c where outcome variable y measures perceptions of crime in the neigh- borhood (or avoidance behavior); i indexes individuals; timehere measures time since the move date to the current address for up to 10 years, Parameter of interest β denotes how perceptions are adjusted in response to time since move. incumbent is a binary indicator for individuals who have lived at their current address for more than 10 years. X is a vector of individual character- istics, including age, age squared, female, household size, education, labor force participation, home ownership, having moved more than once over the last 10 years, and type of residence. I is a vector of binary indicators for annual cohorts of movers, e.g., for persons who have moved to the current address in the year c. α is a vector of interaction terms of neighborhoods n,t and survey years, i.e. for individuals who lived in neighborhood n in survey year t ε is an individual-speciﬁc error term. We use heteroskedasticity- robust White–Eicken standard errors, and we cluster them at the level of the neighborhood. In Equation (2), parameter of interest β represents a linear trend of how perceptions of crime change with time since the date of moving to the cur- rent neighborhood. The variable timehere is measured in years and ranges from 1 for residents who have moved to the current neighborhood less than 1 year ago to 10 for residents who moved to the current neighborhood between 9 and 10 years ago. In the baseline speciﬁcation, we assume that the effect of time since move is linear for the ﬁrst 10 years after the move. In an alternative speciﬁcation that we discuss in Section 5, we allow for a 530 American Law and Economics Review V23 N2 2021 (520–561) nonlinear relationship, and ﬁnd that the effect of time since move indeed follows a linear pattern. In our data, we are not able to observe places of residence before the year 1995. Thus, we cannot observe the exact time since the move date for all persons in our sample, and we assume that the adjustment process ends after 10 years. The variable incumbent accounts for persons who have moved to the current neighborhood more than 10 years ago. With this variable, we group together persons who have moved to the current neighborhood 11 years ago, 12 years ago, or more years ago. For incumbent residents who have moved to the neighborhood more than 10 years ago the variable timehere is set to zero, and the binary variable incumbent is set to one. In addition to controlling for observed characteristics included in X ,we control for the year of having moved into the neighborhood by including the vector of cohort ﬁxed-effects I . Our data consist of four repeated cross- sections, which were collected in the Years 2008, 2009, 2010, and 2011. Thus, for the cohort that moved in the Year 2005, for instance, we observe crime risk perception 3, 4, 5, and 6 years after the move. Similarly, the 2006 cohort was observed 2, 3, 4, and 5 years after the move. While the repeated cross-sections include (mostly) different persons in different years, they are all based on random samples drawn from the same underlying populations. That is, we draw four random samples from individuals who have moved to their current neighborhood in the Year 2005, four random samples from individuals who have moved to their current neighborhood in the Year 2006, and so on. Thus, by controlling for the cohort vector I , we can essentially follow the average risk perceptions of cohorts of movers over time. Average risk perceptions can differ between cohorts of movers for two main reasons. First, moving cohorts might have been different already at the time of move. For example, persons who move during a recession might be different from persons who move during times of fast growth. Second, moving cohorts might differ due to selective attrition. By the time we ﬁrst observe movers in the Year 2008, there was more time for selective attrition 10. In our data, we can observe the complete history of residence between the years 1995 and 2011 for all individuals in our sample based on administrative records, but we cannot observe places of residence before the year 1995. Thus, we can observe whether a person lived in the current neighborhood already in 1995, but we cannot observe whether she moved there in 1994, 1993, or in an earlier year. The Dynamics of Crime Risk Perceptions 531 into moving out of the neighborhood for example for the moving cohort of 2005 than for the moving cohort of 2006. Cohort ﬁxed-effects allow us to control for both initial differences between moving cohorts and for selective attrition, which has taken place between the time of the move and the ﬁrst survey wave in the Year 2008. To make sure that the samples we use for theYears 2008, 2009, 2010, and 2011 are indeed drawn from the same population, we exclude all respondents from our sample who moved away to a different neighborhood between the date of the survey interview and the end of the Year 2011. In this way, we make sure that, for instance, for the moving cohort of 2005 the persons we observe 3 years after the move in the Year 2008 and the persons we observe 6 years after the move in 2011 are comparable. A further challenge is to disentangle the effect of timehere , the effect of interest in our study, and changes in crime risk over calendar time. For this reason, we include the vector α in our estimation equation. This allows for n,t neighborhood and survey-year speciﬁc ﬁxed-effects. In this way, we control for ﬂexible and neighborhood-speciﬁc time trends in risk perceptions. We can identify the vector α given the presence of incumbent residents in n,t our estimation sample. Since we assume that the adjustment process to the new neighborhood ends after 10 years, we can use changes in incumbent residents’ risk perceptions between survey years to estimate neighborhood- speciﬁc time trends. Equation (2) is based on the assumption that time trends are the same for incumbent residents and for different cohorts of movers in the same neighborhood. Formally, we assume: α = α = α = ··· = α . (3) n,t,incumbents n,t,cohort1998 n,t,cohort1999 n,t,cohort2011 This assumption is similar to the assumption that for example Borjas (1995) uses in a study on immigrant wages. In his study, underlying trends for immigrant wages are assumed to be the same to underlying trends for the wages of natives. Our question on risk perception refers to the perceived frequency of crime in the neighborhood. Thus, we assume that changes in 11. Thus, selective attrition of persons who move away from the neighborhood for example as a result of victimization does not bias our estimation results. Previous studies have shown that people are more likely to move after they have been victimized (Dugan, 1999; Bindler and Ketel, 2019). 532 American Law and Economics Review V23 N2 2021 (520–561) crime risk at the neighborhood level do not systematically affect incumbent residents and different cohorts of movers in different ways. One main requirement for our estimation coefﬁcients to be unbiased and consistent is that the following exogeneity assumption holds: E[ε |time here , incumbent , X , I , α ]= 0. (4) i i i i c n,t Thus, unobserved determinants of risk perception in ε must be uncorrelated with explanatory variables. In Section 5.3, we discuss possible violations of this assumption, and how we can address these violations. 4. Data The source of data on perceptions of crime risk is the Netherlands Crime Survey (IVM). The IVM is an annual survey among some 200,000 ran- domly selected respondents in odd years and about 50,000 respondents in even years. Respondents are 15 years of age or older. The interviews are conducted from September 15 to December 31. Respondents are invited to participate in a letter. They can choose to complete the survey online or on paper. If they do not respond, they are asked to complete the survey in a telephone interview or, if that does not work out, in a face-to-face interview. Overall, the response rate is about 40%. The survey is based on a repeated cross-section design. Relative to the size of the population (16 million), the IVM is one of the largest, if not the largest, crime survey in the world. We pool the four waves of the survey for the Years 2008, 2009, 2010, 2011. Constructing the history of places of residence of respondents is facil- itated by the fact that the sampling frame of the survey is the population register (Gemeentelijke Basisregistratie). In the population register, which is administered by municipalities, demographic details for each individual resident of the Netherlands are recorded, including the history of places of residence, going back to 1995. We merge these records from the popula- tion register with the survey data. We examine movers who moved to a 12. Both the survey and the population register contain a unique person identiﬁ- cation number (an encrypted version of the “burgerservicenummer”). The match rate is close to 100%. The Dynamics of Crime Risk Perceptions 533 different neighborhood during the last 10 years before the survey. Individ- uals who move within the same neighborhood are not considered as movers according to our deﬁnition. The earliest cohort moved in 1998, 10 years before the ﬁrst survey in 2008; the latest cohort moved in 2011. Part of the survey relates to “neighborhood problems.” Respondents are asked about their perception of the prevalence of crimes in the neighbor- hood of residence based on a verbal assessment of likelihood. The exact question is: “Can you indicate whether in your view [crime type] occurs frequently, occasionally, or almost never in your neighborhood?” We select the following crime types: bicycle theft, burglary, theft from car, and vio- lent crime. The answer category “frequently” is rarely chosen. For our main speciﬁcation, the outcome variable is a binary indicator which is one if a respondent answers “almost never” and zero otherwise. As a sensitiv- ity analysis, we show that using all three answer categories (using ordered logit) produces qualitatively similar results. In the baseline speciﬁcation, we treat the answer “don’t know” as missing. As a sensitivity analysis, we show that our results are robust if we control for “don’t know” answers with a Heckman selection model. Respondents may not answer questions about the neighborhood crime risk accurately and thoughtfully if the questions are not incentivized (Loughran et al. 2014)—even though untruthful reporting has been found to be less important for well-deﬁned events that are relevant to respondents’ lives (Manski, 2004), such as crime. As we show in Figure 1, the responses have face validity: the perceived prevalence of a crime is related to its rate of occurrence. If the prevalence of victimization of crime is higher in a municipality, then fewer people think that it is rare, and vice versa. This 13. In Section 5.2, we also examine perceptions of movers within the same neighborhood. 14. We focus on the survey questions on neighborhood problems that have a direct relationship with common crime, to the exclusion of, among others, nuisance from youth and nuisance from homeless people. We also exclude behaviors that do not occur at a clear frequency, including grafﬁti, littering, and dog fouling. 15. Figure A1 in the Supplementary Appendix shows that the slope in the rela- tionship between perceptions and rate of occurrence of crime in the neighborhood is similar for the full sample, for recent movers who moved less than 3 years ago, and for movers who moved more than 3 years ago. Compared to the full sample, conditional on the actual victimization rate in the municipality, a much larger share of recent movers think that burglary is rare in the municipality. This difference largely disappears for those 534 American Law and Economics Review V23 N2 2021 (520–561) holds for each of the four crime types. Although the time period we consider is too short to examine whether this also holds across time, this relationship has been shown elsewhere for similar data (Innes, 2011). As a further check on the accuracy of the elicited beliefs, we also analyze avoidance behavior. Respondents are asked whether they avoid unsafe places in their neighbor- hood and whether they do not allow their children to go to some places in the neighborhood because of crime concerns. The outcome variable is a binary indicator which is one if a respondent answers ‘yes, frequently’ and zero otherwise. Another challenge is the interpersonal comparability of the elicited beliefs. Different respondents may not interpret the verbal assessment of likelihood in the same way. In our analysis, we compare average crime per- ceptions of cohorts of movers across time. Since we keep the composition of (the randomly selected samples of) the cohorts the same, it is as if we follow a representative individual over time. In this sense, our analysis does not rest on interpersonal comparisons of beliefs. That leaves the assertion that the responses are intrapersonally comparable. A potential concern is a shift in reference point from the previous to the current place of residence. The survey questions do not provide an explicit reference point for the risk assessment. If a shift in reference point occurs, then its effect depends on how the crime rate in the previous place of residence compares to the current place of residence. In the empirical analysis, we test whether the change in perceptions varies between moves from relatively low-crime areas to rela- tively high-crime areas and vice versa. We also analyze avoidance behavior, which is likely to be at least partly driven by beliefs. If a change in avoidance behavior corresponds with the observed change in beliefs, then this makes it less likely that the change in beliefs is simply the result of a change in reference point. who moved longer ago. We show the results for domestic burglary. The ﬁgures for other crime types show very similar patterns. 16. We focus on avoidance behavior in the neighborhood. We do not consider preventive behaviors related to the individual’s own home, such as leaving lights on when not at home, since changes in perceptions of the local crime risk are likely to differ from changes in perceptions of the individual risk (Tyler, 1980). Moreover, people who have just moved may be more careful about their own home simply because it was recently acquired. The Dynamics of Crime Risk Perceptions 535 Figure 1. Actual Victimization of Crime vs. Perceived Prevalence of Crime, by Municipality and Crime Type. Note. Victimization and perception of crime are based on the Netherlands Crime Survey (IVM, 2008–11). In line with the survey questions about the perception of the crime risk, the analysis is conducted at the level of the neighborhood. We use the def- inition of a neighborhood provided by Netherlands Statistics. In 2011, the Netherlands had 2,572 neighborhoods. The average population of a neigh- borhood was 6,475. A small municipality like Ten Boer (population of 7,400) has two neighborhoods; a provincial capital like Groningen (popula- tion of 200,000) has 10 neighborhoods; a large city in the densely populated western part of the country like The Hague (population of 500,000) has 44 neighborhoods. Our data include 550,760 respondents. In the sample used for the base- line estimation (column (1) in Table 2) we exclude 106,637 respondents because they respond “don’t know” on the question about perceived neigh- borhood risk; 1,688 respondents were excluded because they refuse to answer this question. We exclude 15,414 respondents who moved after the 536 American Law and Economics Review V23 N2 2021 (520–561) interview date and 908 respondents for whom the neighborhood of residence is unknown. This leaves an estimation sample of 425,593 respondents. As stated before, we test how robust our ﬁndings are to excluding the answer category “don’t know” as a sensitivity analysis. Table 1 presents summary statistics. The ﬁrst two columns relate to the full sample of 425,593 respondents in the baseline speciﬁcation. The next columns relate to the subsample of respondents who moved at least once in the last 10 years before the survey interview, and the subsample of those who moved to their current neighborhood of residence more than 10 years ago, respectively. Movers are on average more likely than nonmovers to be young, well- educated, to have paid work, and to live in an apartment. On average, those who moved within the last 10 years have been living in their current neighborhood of residence for about 5 years (58 months). Some 40–50% of respondents believe that burglary, bicycle theft, and theft from car occur rarely in their neighborhood. For violent crime, about 80% hold this belief. 5. Estimation Results 5.1. Baseline Results In Table 2, we show our baseline estimation results. The ﬁrst row shows estimation coefﬁcients on the effect of time since the move date based on linear regression models (parameter β in Equation 2). In the ﬁrst column, the outcome variable is a binary indicator for “bicycle theft occurs almost never in this neighborhood,” The estimated coefﬁcient in the ﬁrst row of column 1 is −0.753, which is statistically highly signiﬁcant. Thus, we ﬁnd a negative effect of time since the move date on the perception that bicycle theft is rare in the neighborhood. Dividing the estimated coefﬁcients by 1,000, multiplying by 12 (months to years) and by 9 (number of years), 17. If “don’t know” answers are correlated with time since the move date, then omitting “don’t know” answers from the estimation sample can bias our estimation results. In Section 5.3, we show that our results are robust to controlling for “don’t know” answers based on a Heckman selection model. 18. See Table A1 in the Supplementary Appendix for summary statistics separately by time since move for movers who moved up to 3 years ago, 4–6 years ago, and 7–10 years ago. The Dynamics of Crime Risk Perceptions 537 Table 1. Summary Statistics Full Sample Movers Nonmovers Mean (st.dev.) Mean (st.dev.) Mean (st.dev.) Risk perception: crime type is rare in neighborhood Bicycle theft 0.481 (0.500) 0.472 (0.499) 0.485 (0.500) Burglary 0.393 (0.488) 0.431 (0.495) 0.380 (0.485) Theft from car 0.542 (0.498) 0.544 (0.498) 0.541 (0.498) Violent crime 0.796 (0.403) 0.762 (0.426) 0.808 (0.394) Avoidance behavior: frequently engages in behavior Avoid unsafe places 0.053 (0.215) 0.059 (0.235) 0.052 (0.222) Restrict children’s movement out 0.096 (0.207) 0.119 (0.324) 0.087 (0.282) of concern for crime Personal characteristics Months since the move date 58.20 (35.61) Moved at least twice in last 10 0.467 (0.499) years Age 48.88 (17.17) 42.34 (15.15) 51.35 (16.24) Female 0.529 (0.499) 0.521 (0.500) 0.531 (0.499) Household size 2.712 (1.240) 2.651 (1.256) 2.735 (1.233) Secondary education 0.370 (0.483) 0.362 (0.481) 0.373 (0.484) Tertiary education 0.303 (0.460) 0.411 (0.492) 0.263 (0.440) Paid work for more than 12 h per 0.553 (0.497) 0.676 (0.468) 0.507 (0.500) week Homeowner 0.704 (0.457) 0.688 (0.463) 0.709 (0.454) Resides in detached house 0.186 (0.389) 0.139 (0.346) 0.204 (0.403) Resides in townhouse 0.548 (0.498) 0.497 (0.500) 0.567 (0.495) Resides in apartment 0.258 (0.438) 0.358 (0.479) 0.220 (0.415) Type of move by crime risk From safe to safe neighborhood 0.261 (0.439) From risky to safe neighborhood 0.193 (0.395) From safe to risky neighborhood 0.170 (0.376) From risky to risky neighborhood 0.376 (0.484) Type of move by distance To different neighborhood in same 0.484 (0.500) municipality To different municipality in same 0.339 (0.473) province To different province 0.177 (0.382) Victimization in last 12 months Any crime 0.304 (0.460) 0.367 (0.482) 0.280 (0.449) Bicycle theft 0.086 (0.281) 0.065 (0.248) 0.058 (0.234) Burglary 0.025 (0.157) 0.020 (0.143) 0.019 (0.137) Theft from car 0.031 (0.174) 0.023 (0.151) 0.020 (0.141) Violent crime 0.087 (0.282) 0.065 (0.247) 0.057 (0.232) Number of observations 425,593 116,699 308,894 Notes. Sample of movers is restricted to respondents who have moved to a different neighborhood at least once in the last 10 years. Sample statistics are for baseline estimation in Column 1 of Table 2. Relates to own neighborhood. 538 American Law and Economics Review V23 N2 2021 (520–561) we obtain a decrease of about 8 percentage points between the ﬁrst year and the 10th year after the move, which comes down to a drop of 17%. The standard deviation of the perceived prevalence of bicycle theft in the neighborhood across municipalities is 12.4. This means that the adjustment amounts to 0.6 standard deviations. We also ﬁnd statistically signiﬁcant effects of time since the move date on the perception of the risk of burglary, theft from car, and violent crime (columns 2–4). When taking the estimated coefﬁcients and calculating the overall change between the ﬁrst year after the move and the tenth year after the move, as we did for bicycle theft above, we ﬁnd that risk perception for burglary changed by 13 percentage points (31% or 1.1 standard deviations); risk perception for theft from care changed by 12 percentage points (23% or 1.0 standard deviations); and risk perception for violent crime changed by 11 percentage points (15% or 1.6 standard deviations). Since these four variables for crime risk perceptions are related, the likelihood of incorrectly rejecting the null hypothesis of no effect increases. If we test each individ- ual hypothesis at a signiﬁcance level that is four times smaller (0.05/4 = 0.0125), following the Bonferroni correction, then we ﬁnd that our results remain statistically signiﬁcant at the 5% level. Columns 5 and 6 of Table 2 show the effect of time since the move date on avoidance behavior. The estimation coefﬁcients are positive and statistically highly signiﬁcant. The estimation coefﬁcients in the ﬁrst row of Columns 5 and 6 are 0.222 for frequently avoiding unsafe places in the neighborhood and 0.678 for not allowing children to some places in the neighborhood because of crime concerns. Thus, adjustment in avoidance behavior is in line with the observed changes in beliefs. The longer people live in a neighborhood, the more careful they become. The adjustments are large, around 41% for avoiding unsafe places in the neighborhood and around 61% for not allowing children to some places in the neighborhood 19. Given an average of 0.47 (see Table 1), a change of 8 percentage points is equal to a 17% change. 20. The standard deviation of the percent of respondents who think that burglary is rare in their neighborhood across municipalities is 12; it is also 12 for the perceived prevalence of theft from car; it is 7 for the perceived prevalence of violence. The differ- ences in the size of the adjustment should be interpreted with caution, as the verbal risk assessment may have been interpreted differently across crime types. 539 Table 2. Effect of Time Since Move on Risk Perception and Avoidance Behavior Risk Perceptions: “Crime type is rare in neighbor- Avoidance Behavior: “Frequently hood” avoid/do not allow the following in neighborhood” Bicycle Burglary Theft from Violent Visit unsafe Children visiting theft car crime places unsafe places Panel A: average effect ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ Months since move −0.7526 −1.2861 −1.1463 −1.0398 0.2222 0.6778 (0.156)(0.149)(0.160)(0.141)(0.084)(0.148) Panel B: effect by level of crime in current and previous place of residence ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ Months since move × −0.7311 −1.3738 −1.2206 −1.0049 0.2865 0.7415 move from safe to safe neighborhood (0.1754)(0.1692)(0.1688)(0.1514)(0.093)(0.1595) ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗ ∗∗∗ Months since move × −0.8083 −1.3921 −1.2311 −0.9647 0.2421 0.6618 move from risky to safe neighborhood (0.1722)(0.1713)(0.1937)(0.1692)(0.0951)(0.1670) ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗∗ ∗∗∗ Months since move × −0.7072 −1.2714 −1.1439 −1.1116 0.2469 0.8754 move from safe to risky neighborhood (0.1747)(0.1823)(0.1890)(0.1722)(0.0974)(0.1876) ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∗ ∗∗∗ Months since move × −0.7077 −1.1449 −0.9980 −1.0643 0.1554 0.5399 move from risky to risky neighborhood (0.1572)(0.1583)(0.1596)(0.1470)(0.0889)(0.1620) P-value cohort-FE = 0.1059 0.0065 0.1104 0.0038 0.0878 0.1029 N 425,593 447,487 428,190 410,675 338,664 192,678 Notes. Results show estimation results based on Equation (2) (Panel A) and Equation (5) (Panel B). Coefﬁcients are multiplied by a factor of 1,000. N is the number of observations. A neighborhood is denoted as safe if the crime rate is below average and as risky if the crime rate is above average. Not shown are coefﬁcients for age, age squared, female, household size, education, labor force participation, home ownership, two or more moves during last 10 years, type of residence, for moves from a risky to a safe municipality, for moves from a safe to a risky municipality, for moves from a risky to a risky municipality, survey mode, cohort ﬁxed-effects, and ﬁxed-effects for neighborhood and year interactions. Robust standard errors clustered at the level of the neighborhood between parentheses. Statistical signiﬁcance at the *** 1%, ** 5%, * 10% level. 540 American Law and Economics Review V23 N2 2021 (520–561) because of crime concerns. This suggests that the changes in beliefs that we ﬁnd are real in the sense that they go together with behavioral changes. In Rows 2–5 of Table 2, we allow the effect of time since the move date to vary by the nature of the change in the neighborhood crime risk resulting from a move. We distinguish four types of moves, depending on the level of crime in the previous and in the current neighborhood of residence: from safe to safe, from safe to risky, from risky to safe, and from risky to risky. We deﬁne neighborhoods as safe if they have a rate of victimization of crime below the national average; we deﬁne neighborhoods as risky if they have a rate of victimization of crime above the national average. We estimate the following equation: y = timehere × I β + incumbent γ + X λ + I μ + α + ε . (5) i i typemove i n,t i i c This estimation equation is similar to Equation (2) but estimates the effect of time since the last move separately by type of move. timehere × I i typemove is an interaction variable between a linear variable for time since the last move and indicator variables for the type of move. β is a vector of four parameters. The estimation coefﬁcients in Rows 2–5 of Table 2 show that the adjust- ment is similar for the four types of moves, and this holds for each crime type. In other words, the risk adjustment is found to be independent of the crime rate in the previous place of residence relative to the new place of residence. This suggests that the reference point that respondents use to answer questions about the neighborhood crime risk does not gradually shift from the previous to the current place of residence after having moved (see the discussion in Section 4). Such a shift would have been apparent in a different adjustment for different types of moves. Finally, the results in Columns 5 and 6 of Table 2 show that avoid- ance behavior also increases with time since the move date for all types 21. Individuals are aware that crime risk is higher in risky than in safe neighbor- hoods. This holds both for the full sample (see Figure 1) and for recent movers (see Figure A1 in the Supplementary Appendix). Yet, the adjustment in risk perceptions between the ﬁrst and the tenth year after the move is similar for all types of moves. The Dynamics of Crime Risk Perceptions 541 of moves. However, for moves from risky to risky neighborhoods the esti- mation coefﬁcient in Column 5 is statistically signiﬁcant at the 10% level only. 5.2. Heterogeneity Next, we go beyond the average effect of time since the move date on perceived risk and heterogeneity by type of move, and also allow the effect to vary between different groups of movers. Motives for moving can differ across groups in the population. For example, young persons often move for work or study, while older persons might move in order to be closer to family. The motive for moving could be related to the adjustment pro- cess in risk perceptions after the move. While exploring heterogeneity, we also relax the assumption that risk perceptions and avoidance behaviors evolve linearly with time since the move date. We estimate the following equation: y = I I β + incumbent γ + X λ + I μ + α + ε . (6) i timehere typemove i n,t i i c I I is an interaction of indicators for annual time since move timehere typemove categories and indicators for the type of move. The estimation equation is similar to Equation (5), but we substitute the linear term for time since the move date with a vector of binary indicators for annual time since move categories that are estimated separately for each type of move. Thus, β represents a set of binary indicators rather than one coefﬁcient for each type of move. We take those who moved less than 12 months ago as the reference group (in the graphs referred to as “recent movers”). Figure 2 shows the estimation results based on Equation (6). The upper left ﬁgure shows heterogeneity by the level of crime risk in the previous and current neighborhood, as in Rows 2–5 of Table 2, but with a ﬂexible functional form. Perceptions are estimated relative to people who moved less than 1 year ago (“recent movers”). The adjustment process is similar for the four types of moves, and it follows a roughly linear pattern. Between the ﬁrst year after the move and the 10th year after the move, the percentage of movers who think that bicycle theft is rare has declined by about 8 percentage points. This is similar in size to the overall adjustment that we 542 American Law and Economics Review V23 N2 2021 (520–561) Safe to risky Risky to risky Safe to safe Risky to safe Figure 2. Perception of Risk of Bicycle Theft in the Neighborhood Since Move Relative to Those Who Moved Less Than 1 Year Ago, by Type of Move, Home Owner/Renter, Age at Time of Move, Educational Attainment, Gender, Number of Moves in Last 10 Years. Notes. A neighborhood is denoted as safe if the crime rate is below average and as risky if the crime rate is above average. Estimation coefﬁcients shown in the ﬁgure are based on Equation (6). computed earlier based on the estimation coefﬁcient shown in the linear speciﬁcation in Column 1 of Table 2. In the other ﬁgures, we compare treatment effects for home owners and renters, young and old, high and low levels of education, males and females, The Dynamics of Crime Risk Perceptions 543 and infrequent and more frequent movers. In all cases, we ﬁnd a change in perceived risk with time since the move date that is similar to what we reported earlier. These ﬁndings suggest that the adjustment process between the ﬁrst and tenth year after the move is similar for all groups in the popula- tion even when their motives for moving are very different. We only report estimates for the perceived risk of bicycle theft; the results for the three other crime types are similar. In Figure 3, we allow the effect to differ by the distance of the move. We distinguish four types of moves: moves within the same neighbor- hood, moves to another neighborhood but within the same municipality, moves to another municipality but within the same province, and moves to a different province (in 2001, the Netherlands had 12 provinces and 418 municipalities). For all types of moves, we ﬁnd that risk perceptions become less favor- able. This also holds for moves within the same neighborhood. This suggests that at least part of locally gained experiences with a crime are very local in nature, that is, attached to a smaller geographical unit than the neighbor- hood as deﬁned in our study. We also ﬁnd the adjustment in risk perceptions to be somewhat lower for moves within the same neighborhood compared to moves to a different neighborhood, whether in a different municipality or province. The difference in adjustment after 10 years for moves within the same neighborhood versus moves to a different province is statistically signiﬁcant at the 1% level for all four crime types. This suggests that the local experiences that were gained prior to the move can be partially trans- ferred to moves in the same neighborhood, but less so for moves in the same municipality, and even less for moves to a different municipality or province. 5.3. Sensitivity Analysis We conduct a number of tests to analyze the sensitivity of our results to alternative assumptions and alternative empirical speciﬁcations. In our baseline speciﬁcation, we use a linear probability model. One reason for 22. Results for risk perceptions for all types of crime by type of move based on the level of crime risk in the previous and current neighborhood are shown in Figure A2 in the Supplementary Appendix. 544 American Law and Economics Review V23 N2 2021 (520–561) Figure 3. Perception of Crime Risk Since Move Relative to Those Who Moved Less Than 1 Year Ago, by Distance of Move and Crime Type. Notes. Estimation coefﬁcients shown in the ﬁgure are based on regressions similar to Equation (6). our choice is that some of the parameters of interest refer to interaction terms. Estimation coefﬁcients for interaction terms are hard to interpret in nonlinear models such as a logit model, and even the sign of the estimation coefﬁcient can be different from the sign of the marginal effect (Ai and Norton, 2003). In contrast, results from a linear probability can be directly interpreted as marginal effects. In order to account for heteroscedasticity, which is inherent to linear probability models, we use heteroskedasticity- robust White–Eicken standard errors throughout our paper. In Table A2 in the Supplementary Appendix, we show estimation coefﬁcients for logit The Dynamics of Crime Risk Perceptions 545 models. Estimation coefﬁcients from a logit model are not directly com- parable to our baseline estimation results shown in Table 2. Still, results are qualitatively similar when using a logit rather than a linear probability model. 5.3.1. Heckman selection model for “don’t know” answers A substantial fraction of respondents answer “don’t know” to questions about the per- ceived crime risk in the neighborhood (see Section 4). So far, we excluded this response category. It could be that the share of respondents in this cate- gory is related to time since the move date, and should this be so, those who switch to (or from) an answer in another category may be different from those who have always remained in the “don’t know” response category. In that case, our results may be biased. As a robustness check, we re-estimate our baseline speciﬁcation includ- ing a Heckman selection model that takes sample selection caused by “don’t know” answers into account. In the ﬁrst stage, we estimate the probability of giving an answer other than “don’t know.” As an instrumental variable for giving a valid answer about crime risk perception, we use a binary indicator for responding “don’t know” on a different question in the survey: whether playgrounds are sufﬁciently available in the neighborhood. We are not able to estimate Heckman selection models with a complete set of neighborhood by year interaction variables due to an incidental parameter problem (Lan- caster, 2000). This means that the optimization did not converge because we tried to include more ﬁxed effects than the model could handle. Instead, we estimate a model with national time trends. Estimation results for Heckman selection models are shown in Table A3 in the Supplementary Appendix. We ﬁnd that “don’t know” answers about crime risk perception in the neigh- borhood strongly and signiﬁcantly decrease with increasing time since the move date. Still, estimation results for crime risk perceptions are very simi- lar to the baseline speciﬁcation in Table 2. Perceptions that crime is rare in the neighborhood strongly and signiﬁcantly decrease with increasing time since the move date. 23. Estimation results are also similar to results based on a national rather than a neighborhood time trend reported in Table A5 in the Supplementary Appendix. 546 American Law and Economics Review V23 N2 2021 (520–561) 5.3.2. Ordered logit model with three categories of crime perceptions In our baseline model, we reduce the responses to questions about crime per- ceptions from the three presented in the survey (frequently, occasionally, or almost never) to a binary indicator of whether a crime occurs almost never in the neighborhood. We use the binary indicator as an outcome variable in linear probability models. As a robustness check, we also estimate ordered logit models for all three outcome categories. The ordered logit models can only be estimated with national time trends. Including a full set of neighbor- hood and year interactions would lead to an incidental parameter problem. Estimation results for ordered logit models are shown in Table A4 in the Supplementary Appendix. Coefﬁcients from ordered logit models are not directly comparable with coefﬁcients from linear regressions, given the use of three rather than two answer categories. Still, the estimation results from ordered logit models and from linear probability models point in the same direction. Crime risk perceptions decrease with increasing time since the move date, and this relationship is statistically signiﬁcant. 5.3.3. Alternative speciﬁcations of time trends As discussed in Section 3, our empirical models rely on the assumption that time trends in the crime rate are the same for incumbent residents of a neighborhood and for those who moved into that neighborhood. A formal deﬁnition of this assumption is given in Equation (3). As a sensitivity test, we control for time trends in crime risk perceptions at geographical levels other than the neighborhood: the national level and the municipality level. The results for these two alter- native speciﬁcations are shown in Table A5 and A6 in the Supplementary Appendix. Results in both tables are very similar to the results based on the baseline speciﬁcation in Table 2. Risk perceptions become strongly and statistically signiﬁcantly more negative with increasing time since the move date, while avoidance behavior goes up. These results suggest that our results are robust to alternative speciﬁcations of time trends. 5.3.4. Alternative speciﬁcation of covariates In Table A7 in the Supplementary Appendix, we show a speciﬁcation without individual- speciﬁc covariates such as age, age squared, female, household size, education, labor force participation, home ownership, two or more moves The Dynamics of Crime Risk Perceptions 547 during the last 10 years, and type of residence. Estimation results are very similar to the baseline results shown in Table 2. Thus, omitting individual- speciﬁc covariates does not alter our results. This is as expected since in our empirical approach we compare average crime perceptions of cohorts of movers across time and the composition of moving cohorts is comparable across survey waves. 5.3.5. Graphical evidence for adjustments in crime perceptions for different cohorts of movers In Figure A3 in the Supplementary Appendix, we show trends in risk perception and avoidance behavior for individual cohorts of movers. In line with our earlier ﬁndings, the ﬁgure shows that for most cohorts of movers with increasing time since move fewer residents belief that crime is rare in the neighborhood, while more residents engage in avoidance behaviors. 6. Learning from Personal Experience One explanation for what we ﬁnd is that learning about the frequency of a rare, adverse event is based on personal experience with local crime condi- tions. For most people, it is likely to hold that they only start to accumulate personal experience after their move. Learning based on personal experi- ence can lead to a downward adjustment in the belief that crime is rare in the neighborhood at the population level if downward shocks in beliefs for persons who experience crime dominate the upward adjustment through discounting of past information. Then, the stock of crime-related experi- ences grows with increasing time of exposure, resulting in a progressively greater perceived risk. Beliefs are likely to be particularly shaped by one element of personal experience, victimization of crime, given the evidence discussed in the 24. This interpretation also ﬁts well with results from evolutionary biology (see Baumeister et al., 2001: 344–348): a bad event has a longer lasting and more intense consequence for impression formation than a good event. In our case, the good event is the realization that crime did not occur. 548 American Law and Economics Review V23 N2 2021 (520–561) introduction (see footnote 6 for references). Information based on per- sonal experience with the adverse event is likely to be more salient and emotionally loaded than information based on descriptions or observations. The data allow us to explore how well victimization of crime explains the observed adjustment in beliefs. While our data are based on a repeated cross- section of the Dutch adult population, a number of individuals have been included in the sample repeatedly—by chance rather than by design. We can identify repeat observations based on their unique identiﬁcation num- ber. The sample size of repeat observations differs depending on the number of responses per crime type. The number of individuals with repeated obser- vations varies from 2,285 for risk perception of bicycle theft to 2,681 for risk perception of burglary. The total number of observations varies from 4,479 for bicycle theft to 5,371 for burglary. While this sample is much smaller than the sample in our baseline estimation, it is still sizable. This sample includes both incumbent residents and movers. The empirical approach is based on a framework in which perceptions about local crime risk depend exclusively on whether or not an individual was recently victimized. We assume that individuals have not yet been victimized in the new neighborhood at the time of the move. Thus, the initial perception at the time of the move is y = 0. In each period t = 1…T i,0 after the move individuals receive a signal which takes on the value β if the individual is victimized in the respective period, and 0 otherwise. In the periods after victimization, individuals discount their victimization experience. The degree to which past events are discounted is determined by parameter γ. Perceptions of local crime risk y of individual i at time t i,t are determined by: y = max(0, victimized β – timevict γ). (7) i,t i,t i,t Where victimized is a binary indicator for individuals who have been i,t victimized in the current place of residence, and timevict is a variable i,t 25. Table A8 in the Supplementary Appendix shows summary statistics for the sample with repeated observations. 26. For movers, only observations with a survey date after moving to the current neighborhood are included in the estimation sample. The Dynamics of Crime Risk Perceptions 549 for the length of time since the most recent victimization experience. In this framework, risk perceptions depend on the stock of victimization experiences. In order to estimate the parameters β and γ of the framework above, we use linear models with individual ﬁxed-effects. Speciﬁcally, we estimate the following regression model: y = victimized β + timevict γ + Z λ + I μ + α + ε . (8) i,t i,t i,t i i,t i,t t Where Z is a vector of time-varying individual characteristics, I is a vector i,t t of indicators for years t, α are individual-speciﬁc ﬁxed-effects, and ε are i i,t time varying error terms. β, γ, λ, and μ are (vectors of) parameters. Varia- tion in victimized comes from respondents who were victimized between i,t waves. time vict changes with the time passed between surveys, as well i,t as for respondents who have been victimized between survey waves. Estimation results are shown in Table 3. The results show that risk per- ceptions strongly respond to victimization. As a response to becoming a victim of bicycle theft, the belief that bicycle theft is rare in the neighbor- hood drops by 15.2 percentage points. The corresponding decreases are 7.7 percentage points for burglary, 11.9 percentage points for theft from car, and 6.4 percentage points for violence. With the exception of burglary, all coefﬁcients are statistically signiﬁcant at the 5% level. The coefﬁcients for time since victimization are all positive, which indicates that the effect of victimization diminishes over time. These coefﬁcients are small compared to the effect of victimization and they are not statistically signiﬁcant at the 27. Our data include information on, ﬁrst, whether individuals have been victim- ized during the last 5 years, and, second, the year and month when the last victimization happened. This allows us to compute the variables victimized and time vict . We clean i,t i,t the data such that victimized is set to one if it is one at an earlier interview, and we i,t correct some inconsistencies in time vict . Victimizations that took place at a time before i,t moving to the current neighborhood are excluded. 28. This vector of time-varying individual characteristics includes age, age squared, household size, and labor force participation. In Table A8 of the Supplementary Appendix, we show that average household size and rate of labor force participation barely change between the ﬁrst time and the later times that respondents are observed. As a consequence, the effects of these time-varying covariates are estimated imprecisely. Estimation results remain similar when we omit covariates for household size and labor force participation (results available upon request). 550 American Law and Economics Review V23 N2 2021 (520–561) Table 3. Effect of own victimization on risk perceptions (ﬁxed-effect estima- tion) “Bicycle theft “Burglary is “Theft from “Violent crime is rare in neigh- rare in car is rare in is rare in borhood” neighborhood” neighborhood” neighborhood” ∗∗∗ ∗ ∗∗∗ ∗∗ Victimization in −0.1517 −0.0765 −0.1186 −0.0643 last ﬁve years (0.027)(0.042)(0.028)(0.026) Years since last 0.0221 0.0012 0.0030 0.0050 victimization (0.012)(0.019)(0.013)(0.013) Number of 4,479 5,371 4,607 4,691 observations Number of 2,285 2,681 2,295 2,341 individuals Notes. Results show coefﬁcients for linear regressions with individual-speciﬁc ﬁxed-effects as in Equation (8). Not shown are coefﬁcients for age, age squared, household size, labor force participation, and survey year indicators. Robust standard errors clustered at the level of the individual between parentheses. Statistical signiﬁcance at the ***1%, **5%, *10% level. 5% level. For example, the coefﬁcient for time since bicycle theft is equiva- lent to 2.2 percentage points. This implies that it would take around 7 years to offset the impact of a stolen bike on risk perceptions. The corresponding time for other crime types is even longer. Figure 4 shows simulations results for how risk perceptions evolve after a move, and when taking personal victimization as the only reason for updating beliefs. We simulate risk perceptions for a group of 2,000 movers over a 10-year period. We assume that perceptions of local crime are zero at the time of move, and that they evolve according to Equation (7) in the periods thereafter, when individuals are randomly hit by victimization. The simulations are based on the estimation coefﬁcients shown in Table 3—the response to victimization and absence of victimization—and victimization rates shown in Table 1—the frequency at which the bad event occurs. The pattern that emerges from these simulations is very similar to the pattern in the actual adjustment process shown in Figure 3. Perceptions of local crime risk gradually become less favorable with increasing time since move. The simulation results suggest that time since move at least in part captures an 29. The panel data contain only a small number of movers. Therefore, we do not conduct additional analyses such as following movers over time and see how their crime risk perceptions change at the time of move, or looking at risk perceptions of movers who were never victimized. The Dynamics of Crime Risk Perceptions 551 Figure 4. Simulations of Changes in Perceptions of Crime Risk in Reaction to Own Victimization. Notes. Perceptions evolve according to Equation (7). The simulations are based on coefﬁcients shown in Tables 1 and 3. Simulations involve 2,000 draws. important element of experience-based learning, namely gaining personal experience with local crime conditions by way of victimization. 7. Other Explanations In the previous section, we discussed how the process of accumulat- ing experiences with crime in the neighborhood can explain the observed dynamics in crime risk perceptions. From this perspective, the initial risk assessment is relatively low because the stock of local experiences is small shortly after a move. Within the context of our paper, however, the initial risk assessment may also be relatively low for reasons other than a lack of experience. We discuss two alternative reasons below. 30. An adjustment in beliefs after a move can also occur when people follow the anchoring and adjustment heuristic (Tversky and Kahneman, 1974). The anchoring and adjustment heuristic posits that an individual’s prior beliefs are determined by an 552 American Law and Economics Review V23 N2 2021 (520–561) 7.1. Winner’s Curse Individuals with overoptimistic beliefs about the neighborhood crime risk may be overrepresented among movers to that neighborhood. This idea is similar to the winner’s curse in auctions: those who win an auction are likely to overpay. Movers may be attracted by house prices that to them seem relatively low, but in the views of incumbent residents of the neighborhood simply reﬂect broadly shared perceptions of the neighborhood crime rate. Over time, these movers come to realize that they had too positive a picture of the neighborhood crime risk. The initial misperception and following adjustment result in a positive relation between time since the move date and perceived risk. It should be noted that even when the winner’s curse adds to the relatively low risk assessment at the time of move, then this does not go against the idea that the adjustment in beliefs over time is driven by experience-based learning. After all, we still need to explain why perceptions become less favorable with increasing time since move. Our ﬁnding that the observed adjustment takes many years is in line with directly or indirectly experi- encing a low frequency-event like crime, and we also ﬁnd that it is at least partly driven by actual direct experience with crime. But this leaves the possibility that the winner’s curse may be an important explanation of the initial low-risk assessment, casting our ﬁndings in a very context-speciﬁc light. Results reported in Section 5.2 allow us to gauge how important the winner’s curse is. If the winners’ curse is at work, then it should have less of an effect for people who have limited choice of where to live. After all, they do not have the luxury to move to a speciﬁc neighborhood because of its supposedly favorable characteristics, including beliefs about the local crime rate. In the Netherlands, this holds for most renters. The reason is that the great majority of renters live in rent-controlled public housing (almost anchor. In our case, that could be the level of crime in the previous neighborhood. This explanation does not ﬁt our results: in Section 5, we found that changes in beliefs after the move date are independent from the crime level in the previous neighborhood. 31. One possible reason why movers may be over-optimistic is when their crime perceptions are based on historical data from before the Great Recession, back when some types of crime such as domestic burglary were less frequent. In contrast, incumbent residents can rely on their experience of the current state of affairs. The Dynamics of Crime Risk Perceptions 553 70%, see VanDijk, 2019). Due to the highly restricted supply of this type of housing, prospective tenants need to compromise many of their wishes, including their preferred neighborhood of residence. Our survey data include whether the respondent owns or rents their home. We ﬁnd similar patterns for the evolution of risk perceptions for owners and renters. Figure 2 provides graphical evidence; we provide a statistical test on whether the effect of time since the move date is the same for homeowners and renters in Table A9 in the Supplementary Appendix. The evidence is not in line with the winner’s curse explanation. 7.2. Cognitive Dissonance Cognitive dissonance may result in a tendency to justify the deci- sion to choose the new neighborhood by casting characteristics of this neighborhood—including the neighborhood crime risk—in too positive a light (see Akerlof and Dickens, 1982; this tendency is also known as choice- supportive bias). If this tendency diminishes over time, then this may also explain the positive relation between time since the move date and perceived neighborhood crime risk. Whether cognitive dissonance leads to a downwards adjustment in the belief that crime is rare in the neighborhood with time of exposure is not clear: the belief that the neighborhood someone lives in is special or bet- ter than other neighborhoods can be enduring or even grow with time of exposure (the “mere exposure”-hypothesis, see Harrison, 1977). Even if we believe that cognitive dissonance fades over the years, then this source of the initial underestimation relative to later years does not contradict that people adjust their beliefs in response to experience. But it is of concern, because it would make our ﬁndings very context-speciﬁc. The similar ﬁndings for owners and renters discussed above also suggest that cognitive dissonance is not an important explanation for what we ﬁnd. If someone has limited inﬂuence over the neighborhood of residence, then cognitive dissonance 32. Allocation of public housing is based on a waiting list. It can take many years before a person ends up at the top of the list, on average from four years in rural areas to 9 years in urban areas. Once ranked ﬁrst, households still have to wait for a home to become available that matches their reported income and household size. Consequently, households are under great pressure to accept pretty much any offered home once they are at the top of the list. 554 American Law and Economics Review V23 N2 2021 (520–561) is likely to be less important. The absence of any heterogeneity between owners and renters is not in line with this alternative explanation. 8. Discussion We ﬁnd that beliefs about local crime risk are strongly related to time of exposure to local conditions. Perceptions become on average consider- ably less favorable in the years after taking up residence in a locality, a process that can easily take 10 years before leveling off. In other words, for a prolonged period, the priors of movers are on average always adjusted in the direction that crime is more prevalent, not less prevalent. This result is independent of the speciﬁc motive to move , from differences in the capa- bility of dealing with risk , from gender differences and, perhaps most surprisingly, from being in the position to learn from previous moves. The size of the adjustment in beliefs differs by distance of move. It is smaller for moves within the same neighborhood, and it is larger for moves to a different province. The accumulation of direct experiences with crime explains in large part the dynamics in average beliefs of movers. Based on the subset of individuals that we observe in multiple years, we estimate how individ- ual beliefs change upon and after the victimization of crime. Using these individual-level estimates, we simulate how victimization affects the evo- lution of average beliefs with increasing time of exposure. We ﬁnd that the temporal patterns in our simulations are very similar to those we observe in our data. For many years after taking up residence, the downward shocks in beliefs in response to victimization dominate the more gradual upward adjustment through discounting of past information. Our ﬁndings ﬁt with theories of experience-based learning and with recently uncovered evidence in other areas such as investment behavior and natural hazard mitigation. In short, the stock of crime-related experiences 33. Given the evidence for heterogeneity by age: people younger than 30 often move for work or study; older people often out of a preference for a better home or neighborhood (WoON survey, 2012). 34. Given the evidence for heterogeneity by educational attainment, which is related to cognitive ability (Dohmen etal., 2010). The Dynamics of Crime Risk Perceptions 555 of households increases over time, resulting in a progressively greater per- ceived risk of crime on average, until the infrequent downward adjustments are balanced with the gradual upward adjustments from all those who were victimized over the last years. If this is how potential victims’ beliefs evolve, then perceptions of crime risk are primarily based on recent or particularly disturbing experiences with crime in their neighborhood rather than sta- tistical information such as ofﬁcial crime statistics. The exceedingly long duration of the adjustment process is related to the infrequent occurrence of victimization of crime: the stock of direct experiences with crime expands only slowly. This interpretation of the observed dynamics in crime risk perceptions is consistent with two other ﬁndings. First, we ﬁnd that the crime rate in the previous place of residence is unrelated to how residents adjust their beliefs in the years after moving. Apparently, residents start with a clean slate, and then adjust their beliefs in response to experiences. Availability, not anchoring explains how crime risk perception evolve. Second, adjustment in risk perceptions is lower for moves within the same neighborhood than for moves to a different neighborhood. This makes sense from the perspective of experience-based learning: the stock of experiences built up in the previous place of residence is relevant for moves within the same neighborhood but less so for moves further away. Our results suggest that beliefs about local crime risks are at least some- times incorrect. The belief that crime is rare is adjusted downwards with increasing time since the move date, even when we adjust for any trends in local crime risk. As a consequence, people exposed to the same risk envi- ronment can have very different perceptions of the risk. This has important implications for our understanding of the causes of crime. For a crime to occur, a potential victim needs to offer an opportunity. We show that one key element in precautionary decision making, assessment of the crime risk, can be off for an extensive period of time. Our ﬁndings do not contradict the popular belief that the public tends to overestimate the crime risk, and the ﬁnding that subjective probabilities are generally higher than objective probabilities within the context of crime risk (Dominitz and Manski, 1997; Quillian and Pager, 2010). We focus on how perceptions of crime risk evolve over time, not on the levels of perceived 556 American Law and Economics Review V23 N2 2021 (520–561) risk at a particular moment. Our qualitative measures of risk perception— based on statements that a type of crime occurs “almost never”—would not allow us to do so. This leaves the question whether risk perceptions become less distorted with greater time of exposure to the new environment. If we believe that the ability to draw upon a greater stock of experiences of crime makes people better informed about what goes on in their neighborhood, then movers’ perceptions better reﬂect the true risk the longer they live in a neighborhood. We should note that under the above assumption about the value of gained experiences with crime, a convergence of beliefs towards those of long- time residents only suggests less distortion, not that crime risk perceptions converge to the correct value. As stated above, beliefs of the incumbent residents may well be off—even though we ﬁnd differences in crime risk perceptions to correspond with differences in actual victimization rates. Beliefs that do not accurately reﬂect the actual situation may be com- mon in many domains of life, but they may be particularly costly within the context of crime. Think about having to experience a robbery ﬁrst before taking proper precautions. That is a behavioral strategy that defeats the pur- pose of limiting harm from a low probability, high consequence event like crime. Such systematic mistakes in dealing with rare events are a commonly debated rationale for government intervention in areas such as natural haz- ard mitigation and public health; a similar line of reasoning can be followed when it comes to crime prevention. Our paper opens avenues for an alternative way of lowering the cost of crime: targeting victim behavior rather than offender behavior. 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