Social Science Research 44 (2014) 114–125

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A non-stationary panel data investigation of the unemployment–crime relationship Johan Blomquist a,⇑, Joakim Westerlund b a b

Department of Economics, Lund University, P.O. Box 7082, 220 07 Lund, Sweden Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance, Australia

a r t i c l e

i n f o

Article history: Received 4 May 2012 Revised 4 July 2013 Accepted 23 November 2013 Available online 3 December 2013 Keywords: Crime Unemployment Panel data Unit roots Cointegration Cross-section dependence

a b s t r a c t Many empirical studies of the economics of crime focus solely on the determinants thereof, and do not consider the dynamic and cross-sectional properties of their data. As a response to this, the current paper offers an in-depth analysis of this issue using data covering 21 Swedish counties from 1975 to 2010. The results suggest that the crimes considered are non-stationary, and that this cannot be attributed to county-specific disparities alone, but that there are also a small number of common stochastic trends to which groups of counties tend to revert. In an attempt to explain these common stochastic trends, we look for a long-run cointegrated relationship between unemployment and crime. Overall, the results do not support cointegration, and suggest that previous findings of a significant unemployment–crime relationship might be spurious. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction 1.1. Some theories of unemployment and crime Crime rates usually exhibit substantial variation across time. Indeed, the total number of offences recorded by Swedish police per 100,000 of the population has gone from 9223 in 1975 to 14,613 in 2010, an increase of more than 50%. However, there is not only the variation across time, there is also cross-sectional variation, which is just as pronounced. For example, in 2001, the number of thefts and robberies per capita reported in the capital of Stockholm was 0.09, which is almost twice the crime rate in the rural southern county of Blekinge. The most northern county of Norrbotten has a similar low crime rate of 0.05, whereas in Skåne, which is a neighboring county of Blekinge, the crime rate is almost as high as in Stockholm. The large variation in crime rates over time and across areas has stimulated a large literature in economics, sociology, and criminology attempting to explain the determinants of crime. In economics, much of the literature has been influenced by the pioneering works of Becker (1968) and Ehrlich (1973), suggesting that the choice of the individual of whether or not to engage in crime may be viewed as a tradeoff between the expected costs and benefits of crime. While the theory does not rule out that criminals differ systematically in various aspects from those who abide laws, it predicts that individuals do respond to incentives. The works of Becker and Ehrlich have stimulated a voluminous empirical literature attempting to establish a link between crime and various measurable opportunities that can explain criminal motivation. A particularly well-researched area is the unemployment–crime relationship. The idea is that a depressed labor market, for example,

⇑ Corresponding author. Address: AgriFood Economics Center, Department of Economics, Swedish University of Agricultural Sciences, Scheelevägen 15D, 223 62 Lund, Sweden. Fax: +46 46 222 0791. E-mail address: [email protected] (J. Blomquist). 0049-089X/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.ssresearch.2013.11.007

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makes crime relatively more attractive than work. Thus, we may expect a positive unemployment–crime relationship for crimes that give direct financial payoff such as burglary, theft and auto theft. The theory advanced by Becker (1968) and Ehrlich (1973) has been generalized by Sah (1991), who develops the first of a new class of dynamic deterrence models. In contrast to the original theory, Sah advances a model where individuals’ perceptions concerning their probability of punishment are determined endogenously in the economy. Also, by letting the perceived probability of arrest differ from the actual probability, and therefore has to be learned from experience, crime is expected to be persistent over time. An important implication of this is that the effects of policy may take time to materialize, and hence that any static approach to modeling is likely to be inadequate.1 In another influential study, Cantor and Land (1985) point out that the unemployment–crime relationship is not only affected by changes in motivation of unemployed individuals, the so-called ‘‘direct effect’’, but also by employed individuals’ motivation to commit crime, the so-called ‘‘contextual effect’’, both of which are driven by economic conditions. Since the rate of unemployment may be viewed as a measure of economic activity, the total effect of unemployment on crime is given by the sum of the direct and contextual effects. The authors also highlight a potential countervailing effect of economic activity, the criminal ‘‘opportunity effect’’. Fluctuations in economic activity affect the availability of criminal targets and therefore the number of criminal opportunities. If the unemployment rate is high, for example, more individuals are at home rather than at work, leading to increased guardianship and fewer crime targets. Conversely, due to the increased income, a booming economy increases both the number and attractiveness of crime targets. An alternative perspective on the unemployment–crime relationship is offered by sociological theories, such as strain and social control theory (see, for example, Agnew, 1992). Strain theory emphasizes that the anxiety of unemployment impacts individuals’ aspirations and expectations, which in turn affect their motivation to commit crime. If such mechanisms are in action, we expect a positive unemployment–crime relationship. Social control theory suggests that individuals’ commitments, relationships and beliefs encourage them to abide laws. According to this view, the process of socialization and social learning builds self-control and reduces criminal involvement by increasing the costs associated with deviant acts. The theory predicts that as individuals invest time and energy in their work, criminal behavior is avoided in order not to jeopardize these investments. Thus, as with strain theory, social control theory suggests a positive unemployment–crime relationship. The above theories are, of course, not the only factors affecting the unemployment–crime relationship. Alcohol consumption, for example, usually varies pro-cyclically leading to a negative relationship between unemployment and crime (Ruhm, 1995). However, while the exact impact of unemployment is ambiguous, these theories and factors all predict that crime should have a strong common component, and that this component should be driven mainly by unemployment. There are other theories, not directly related to unemployment, which also predict that local-level crime rates should tend to co-move. LaFree (1998), for example, argues that crime is affected by the legitimacy that individuals grant to key social institutions, who act to suppress crime. According to this view, crime rates are expected to increase in periods of diminishing trust in political institutions and decreasing family stability. While perceptions of institutional legitimacy may vary somewhat between regions within a country, it is likely that they are driven by a general pattern that operate across the nation as a whole. Similarly, routine activity theory (Cohen and Felson, 1979) emphasizes the role country-wide factors, such as female labor force participation, that influence criminal opportunities. 1.2. The empirics of unemployment and crime The discussion above makes clear that the hypothesized unemployment–crime relationship may be either positive or negative, and over the past decades a large empirical literature has attempted to estimate this relationship. In is section we offer a brief discussion of this literature with a focus on recent panel data studies. The point is not to make a complete review, but to point to two issues that we believe have not been appropriately addressed in the literature; (i) the persistence, or trending behavior, of crime and (ii) the co-movement of local-level crime rates. Chiricos (1987) provides an early overview of the large empirical literature on the unemployment–crime relationship. The results of the 63 articles considered (published in journals in economics, sociology and criminology) are mixed, at best. He therefore concludes that ‘‘this paper underscores how little we really know about this issue’’ (page 202). More recent reviews are provided by Piehl (1998), Levitt (2001) and Mustard (2010). While the first author declares that there is surprisingly little evidence that economic conditions influence crime rates, the latter two find supportive evidence of a positive unemployment–crime relationship. One reason for this, it is argued, is the increased availability and use of data at local levels, such as cities, counties, and metropolitan areas, which are more likely to document a relationship between labor markets and crime than research that uses aggregated country data. This is because national data might disguise cross-sectional variation in crime that is needed to identify the relationship. Indeed, as Forni and Lippi (1997) show, aggregation across heterogenous units is likely to lead to misleading results. The issue of aggregation is discussed to some extent by McDowall and Loftin (2009), who try to assess the degree to which the crime rates of US cities follow a national trend. Clearly, if the observed nationwide trend is just due to chance aggregation of factors that varies within local areas, then national conditions are unlikely to be successful in explaining 1 Lochner (2004) provides empirical evidence of such belief updating and concludes that the full impact of crime reduction policies may not be realized for many years. Imai and Krishna (2004) and Sickles and Williams (2008) provide further evidence in favor of a dynamic deterrence theory based on an individual’s perceived probability of arrest.

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local-level fluctuations in crime. On the other hand, if local rates display similar behaviors, it is natural to search for national factors to help explain the common crime trends. Using data between 1960 and 2004 the authors find evidence that a national pattern underlies city-level crime trends. Unfortunately, panel data studies of this kind are rare, especially when trying to model crime trends. Indeed, trends of this type are almost always modeled using time series methods applied to aggregate data, which means that the cross-sectional variation is effectively ignored (see, for example, Witt and Witte, 2000; Shoesmith, 2010). A notable exception is Spelman (2008), who conducts a comprehensive study of the persistence of US state-level crime rates. However, while the data have the panel structure, the econometric approach is still a time series one, and approaches of this kind are known to suffer from poor precision unless the number of time periods is very large, a condition that is rarely fulfilled in studies of crime. As a response to the poor precision of time series methods when applied to samples with a short time span, some studies have resorted to methods designed specifically for panel data. Unfortunately, most panel studies use static panel regressions that ignore the dynamics. This is problematic because unattended dynamics may compromise inference, and in the extreme case in which crime is unit root non-stationary, results may even be spurious. Take, for example, the study of Edmark (2005), who uses Swedish county-level data covering the 1988–1999 period to infer the unemployment–crime relationship. Although many of her panel regressions have R2 statistics that are very close to unity, a well-known sign of spuriousness, the unit root hypothesis is never tested. Other studies use static regressions augmented with a linear time trend to account for the fact that crime is usually trending (see, for example, Gould et al., 2002; Raphael and Winter-Ebmer, 2001). The main problem here is that the slope of the crime trend is assumed to be constant through time, which is not very realistic. In other words, while recognizing the presence of a trend, these studies do not allow for the possibility that the slope might be changing. Also, by assuming that the trend is deterministic, this means that the long-run movement of the data, which arguably the most important one, is left unexplained. Another important but often neglected feature of panel data is cross-section dependence, that is, co-movement among the cross-sectional units. A common source such dependence is country-wide shocks affecting all regions within the country. Indeed, as pointed out by McDowell and Loftin (2009), and as alluded in Section 1.1, many theories of crime actually predict that local-level crime rates should tend to co-move. A limited form of such cross-section dependence can be permitted through the use of common time-specific fixed effects. However, unless the pair-wise cross-correlations are identical, this approach is not expected to work, leading to deceptive inference.

1.3. The main results of this study As the above discussion makes clear, most of the earlier panel data approaches have ignored the problems associated with the co-movement and/or trending behavior of the data, and this paper therefore proposes an alternative approach. We argue that to provide any reliable evidence concerning the behavior of crime, and to minimize the risk of deceptive inference, one needs to consider the time series and cross-section properties of the data not separately but simultaneously. To the best of our knowledge Witt et al. (1998) is the only other crime study that uses an approach that is capable of dealing with both co-movement and/or trending behavior of the data. The motivation for their paper is that if regional crime rates are non-stationary, so that they are trending stochastically, then there is a possibility that they might be long-run cointegrated, or ‘‘co-trended’’, a situation closely related to what is commonly referred to in the growth literature as ‘‘club convergence’’. That is, there might be clubs of regions whose crime rates are driven by a common stochastic trend, making them long-run related. Using data covering four English regions between 1975 and 1996, the authors find evidence of such a trend, suggesting the existence of a long-run relationship between the four regions. The problem is that the econometric approach is a multivariate one that cannot handle panels unless the cross-sectional dimension, N, is very small. In fact, for this approach to work properly, not only must N be small enough, but the time-series dimension, T, must be substantial, a condition rarely fulfilled in practice. Thus, what is really needed here is a panel approach applicable even in situations in which N is large, and the current chapter can be seen as an attempt in this direction. Another shortcoming with the Witt et al. (1998) study is that it provides no insight into the forces underlying the common crime trends. Our starting point is the panel analysis of non-stationary idiosyncratic and common components (PANIC) method of Bai and Ng (2004). The idea is to first decompose the observed data into two components, one that is common to all cross-section units and one that is idiosyncratic, or unit-specific. The objective of PANIC is then to infer the order of integration of the data by testing for unit roots (stochastic trends) in each component separately, making it possible to disentangle the source of the trending behavior. If unit roots are found, one may then proceed to analyze the determinants thereof. The main advantage of this approach over that used by Witt et al. (1998) is twofold; first, N does not have to be small (in relation to T), and, second, the determinants of the trends can be studied using panel cointegration techniques.2 2 There are, of course, other panel unit root tests around that allow for cross-section dependence in a large-N environment (see Breitung and Pesaran, 2008). However, PANIC has a number of distinct features that makes it more suitable for our purposes. Its main advantage is that, unlike most other available tests, PANIC does not restrict the common and idiosyncratic components to have the same order of integration. PANIC is also very simple to implement and has been demonstrated to perform well in samples as small as ours (see Gutierrez, 2006).

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We consider three crime categories; burglary, theft, and vehicle theft. The PANIC results, based on data that cover 21 Swedish counties between 1975 and 2010, suggest that all three crime categories are non-stationary, and that this is not attributable to county-specific disparities alone, but that there is also a small number of common stochastic trends present. The next step is therefore to study the determinants of these trends. One of the most natural candidates is unemployment, and in this paper we therefore focus on this variable. Since the data are non-stationarity, we cannot rely on standard panel data techniques, which may lead to spurious results, but have to use special tools. Specifically, the common correlated effects (CCE) approach of Pesaran (2006) and Kapetanios et al. (2011) is applied. Contrary to what might be expected, cointegration is not supported, suggesting that in the long-run there is no unemployment–crime relationship. Moreover, once the non-stationarity of the data has been appropriately accounted for, the estimated unemployment elasticities are close to zero and insignificant for all crime categories. This last finding is very different from the results obtained when using the otherwise so common fixed effects (FE) estimator, suggesting that the existing evidence based on this estimator needs to be revisited, as the possibility remains that it is spurious.

2. Preliminary evidence Our study uses crime data obtained from the Swedish National Council for Crime Prevention covering the 21 Swedish counties between 1975 and 2010, which means that 756 observations are available for each of the three crime categories considered; burglary, theft, and vehicle theft. As these are crime categories for which economic incentives may play an important role, they have attracted considerable attention in the economics of crime literature. Burglary is defined as illicit entry into a building for the purposes of committing an offense (usually theft). It includes burglary and attempted burglary of residences and commercial buildings. Theft includes shoplifting and pickpocketing (which together constitute approximately 50% of all thefts), theft from schools, libraries, hotels, restaurants, and so on, but not burglaries or vehicle thefts. In 2010 the number of reported theft offences constituted approximately 17% of all reported crimes in Sweden, making it the largest crime category considered here. Vehicle theft includes both thefts and attempted thefts of cars, motorcycles, bicycles, etc. The crime rates are defined as the number of offences reported to the police per 100,000 of the population. While we would like to use data on crimes actually committed, there are good reasons why the number of offences reported to the police is a good proxy of this. For burglary and vehicle theft the error incurred when replacing actual offences with reported offences is likely small, as reporting a crime is necessary for receiving insurance compensation. This is what studies based on comparisons between the number of reported crimes and the number of victims have found (Swedish National Council for Crime Prevention, 2008). When it comes to other thefts, the problem of underreporting is likely to be more pronounced. In the case of shoplifting, for example, there is often no economic incentive for the individual salesperson to report the theft; the official statistics are therefore likely to understate the true rate of such theft (Swedish National Council for Crime Prevention, 2002). However, as long as the magnitude of this problem remains roughly constant over time, it should not affect our conclusions.3 To get a feeling for the persistence and cross-correlation of the three crime categories, we begin by graphically inspecting the data. Fig. 1 plots the cross-county mean, range, and normal 90% confidence bands for each of the three crime categories. Looking first at burglary, which is plotted in Fig. 1(a), it is evident that the mean reversion is weak at best, suggesting that burglary crime rates may be non-stationary. We also see that the mean can explain much of the overall variation in the data, suggesting that the common component of burglary is fairly strong. Another interesting observation is that both the range and confidence bands become narrower over time, suggesting that county crime rates may be converging towards a common crime trend. Looking next at theft in Fig. 1(b) we see a clear upward trend. As with burglary, there is a strong common component. However, in this case, nothing suggests that county crime rates are converging. In fact, both the range and confidence bands seem to become wider over time, suggesting that the crime rates could actually be diverging. As in Fig. 1(a), the confidence bands of vehicle theft in Fig. 1(c) become narrower over time, which we again take as evidence of convergence. To infer the statistical significance of the cross-correlations, we compute the pair-wise cross-county correlation coefficients of each of the first differenced crime variables. The simple averages of these correlation coefficients across all 210 county pairs, together with the associated CD test discussed in Pesaran et al. (2008), are given in the top panel of Table 1. The average correlation coefficients are quite high and the CD statistics are highly significant, which obviously strengthens the case against independence.

3. Econometric methodology The preliminary results reported so far indicate that the crime rates considered may be non-stationary and possibly cointegrated across counties. To investigate this issue more formally, we now proceed to discuss the econometric methodology. 3 Although data are scarce, there seems to be a stable relationship between the number of actual and reported crimes for the three crime categories considered here (Swedish National Council for Crime Prevention, 2008; von Hofer, 2011).

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Fig. 1. Cross-county mean, range, and 90% confidence bands.

Table 1 Cross-county correlations of crime. Statistic

Burglary

Theft

Vehicle theft

Raw data Correlation CD p-Value

0:22 19:05 0:00

0:22 18:80 0:00

0:40 44:93 0:00

Idiosyncratic component Correlation CD p-Value

0:03 2:58 0:01

0:02 1:50 0:13

0:04 3:78 0:00

Note: The results are for the first-differenced series. The CD statistic tests the null of no cross-correlation. ‘‘Correlation’’ refers to the average of the estimated pair-wise correlations.

Consider the crime rate, yi;t , observable for i ¼ 1; . . . ; N counties and t ¼ 1; . . . ; T years. We assume that the data-generating process of yi;t is given by

yi;t ¼ l0i dt þ bxi;t þ /0i F t þ i;t ;

ð1Þ

xi;t ¼ P0i dt þ K0i F t þ ei;t ;

ð2Þ

where dt is the deterministic component, i;t and ei;t represent idiosyncratic error terms, and xi;t is a variable commonly believed to explain yi;t . In our case, xi;t is the unemployment rate.4 The r-dimensional vector F t contain the common factors, or common shocks, which may represent, for example, common crime-fighting policies, changes in law, national wealth variations generated by business cycle fluctuations, and common attitudes towards crime. As pointed out in Section 1, several criminological theories predict that nationwide factors will be important determinants of regional crime dynamics. The common factor specification in (1) is therefore implied by theory. County unemployment rates may also be subject to common shocks. Indeed, one of the most notable features of the recent economic downturn and of the deep recession in the early 1990s is the 4 Of course, more explanatory variables can be included. To make the exposition clear, however, we focus solely on the unemployment rate. In Section 4 we demonstrate how the empirical results are affected by the inclusion of additional variables.

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widespread increase in unemployment across Swedish counties. This effect is captured by the presence of F t in (2). Note also how some of the elements of F t may affect both yi;t and xi;t . This is important, since some factors, such as changes in demographic composition and social insurance, may affect both crime and unemployment. By substituting for xi;t using (2), Eq. (1) can be written as

yi;t ¼ a0i dt þ k0i F t þ ei;t ;

ð3Þ

where ai ¼ li þ bPi ; ki ¼ /i þ bKi and ei;t ¼ i;t þ bei;t , suggesting that crime may be decomposed into a common component, k0i F t , and an idiosyncratic component, ei;t . This is the model we have in mind when testing for unit roots in crime. In response to the poor precision and power of conventional time-series tests, Moody and Marvell (2005), Phillips (2006), and Phillips and Land (2012) apply a battery of so-called ‘‘first-generation’’ panel unit root tests to US state-level crime rates. Their results suggest that the unit root hypothesis can be safely rejected. Unfortunately, these tests are only appropriate if the states are uncorrelated. In terms of the model in (3), the first-generation tests assume that there is no common component, and hence that yi;t is completely idiosyncratic. This also implies that ei;t is the only source of potential non-stationarity. This problem is recognized by Spelman (2008), who apply the unit root test of Pesaran (2007). However, while cross-section dependence is permitted, this test assumes that there is only one common factor, and that the dynamics of the common and idiosyncratic components are the same. The model presented in (3) is more general, and allows for multiple factors, whose dynamics may differ from that of ei;t . Whether or not F t and ei;t are actually stationary is an empirical question. Since both variables are unobserved, the first step in PANIC is to obtain estimates of these, which can be done using the principal components method. However, since this method requires stationary data, we work with the first-differences, Dyi;t , which are mean zero and stationary as long as dt P does not contain a trend.5 If a trend is present, we work with Dyi;t  Dyi , where Dyi ¼ Tt¼2 Dyi;t =ðT  1Þ. By applying the principal components method to either Dyi;t or Dyi;t  Dyi , we obtain estimates of the components in first differences, which can then be accumulated to obtain the corresponding level estimates. The final step in PANIC is to test the two components for unit roots, making it possible to disentangle the sources of potential non-stationarity in yi;t . If the non-stationary is due to F t , crime is diverging along a common stochastic trend, while, if the non-stationary is due to ei;t , the divergence is due to county-specific sources. If F t is non-stationary, while ei;t is stationary, crime is cointegrated across counties, allowing for convergence across counties. Finally, if F t and ei;t are both non-stationary, the divergence has two sources, one that is common and one that is idiosyncratic. To determine the order of integration of F t , we can apply any conventional time-series unit root test to the estimated factor. Similarly, when testing for unit roots in the estimated idiosyncratic component, since this estimator is consistent for ei;t , which is in turn independent across i, any first-generation panel unit root test will do. However, note that rejecting the unit root null using such a test does not mean that each series is stationary, but rather that there is at least one stationary series. To determine which of the series that are in fact stationary, one might be tempted to apply a conventional time series unit root test to each series. However, this means ignoring the multiplicity of the testing problem, which is likely to result in too many rejections. In response to this, Smeekes (2011) proposes a bootstrap sequential quantile test (BSQT), that can deal with the multiplicity problem and consistently estimate the proportion of stationary units. Having determined the order of integration of the data the next step is to investigate the unemployment–crime relationship. We begin by estimating b in (1) using the CCE estimator of Pesaran (2006), which is consistent despite the potential cross-sectional dependence and non-stationarity, as long as i;t and ei;t are stationary (Kapetanios et al., 2011). The idea is to replace F t with an estimator, and then to estimate the resulting model by least squares. While one could use estimated principal components factors, in the present study we follow Pesaran’s (2006) recommendation and use the cross-sectional averages of yi;t and xi;t . Two CCE estimators are considered. The first, the CCE mean group estimator, is defined as the average of the individual CCE estimators applied to each county, while the second, the CCE pooled estimator, which is simply the pooled panel CCE estimator. As mentioned in Section 1, theory is ambiguous as to the sign of b. Cantor and Land (1985) argue that it is possible to use the difference in time frame to identify the motivational and opportunity effects. In particular, they argue that while the opportunity effect is immediate (guardianship matters in the short-run), the motivational effect brought about by changing economic conditions is more long-run. This prediction is relevant, as it has implications for modeling. In particular, as noted by, for example, Hale and Sabbagh (1991), while the long-run effect can be inferred from a regression in the level variables, in order to infer the short-run effect the variables need to be transformed by taking first-differences. In this paper, we focus on the trending behavior of crime, which means that we are interested in the long-run. The motivational effect should therefore dominate, suggesting that b should be positive. Moreover, yi;t and xi;t should be cointegrated. In order test this later condition we follow Holly et al. (2010), and subject the CCE residuals to the BSQT approach. A necessary condition for cointegration is that the residuals are stationary. Interestingly, while several time series studies have tested for cointegration (see, for example, Hale and Sabbagh, 1991; Scorcu and Cellini, 1998; Spelman, 2008), as far as we are aware, the present study is the first to consider the issue of cointegration within a panel-analytic framework. 5

Note that since F t and ei;t are assumed to be integrated of at most order one, Dyi;t must be stationary.

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J. Blomquist, J. Westerlund / Social Science Research 44 (2014) 114–125 Table 2 Tests for the presence of a trend. Crime

Slope

t-Test

p-Value

Burglary Theft Vehicle theft

0:01 0:02 0:02

1:17 1:83 1:06

0:24 0:07 0:29

Note: The ‘‘slope’’ refers to the estimated average trend slope.

4. Empirical results 4.1. Unit root tests of crime As a first test of potential non-stationarity, the BSQT approach is applied to the raw crime rates. To make our results comparable to those of previous studies, all variables are transformed into natural logs. In applying the BSQT approach, we have to decide whether or not to include a deterministic trend in the model. One way of dealing with this uncertainty is to consider the union of rejections approach of Harvey et al. (2009, 2012), which takes as the test statistic the minimum of the chosen constant-only, and constant and trend unit root tests. This leads to the simple decision rule: ‘‘reject the unit root null if either of the two test statistics rejects when the significance level is a’’. That is, we look at the union of rejections of the two tests. The particular unit root test used is the conventional augmented Dickey–Fuller (ADF) test where the order of lag augmentation is determined using the Schwarz Bayesian information criterion (BIC). The quantiles to be tested are given by 0, 0.25, 0.5 and 0.75, and the number of bootstrap replications is set to 1999 with the block length set to 1:75T 1=3 (see Palm et al., 2011). The results (not reported) do not lead to a single rejection at the 10% level, suggesting that when accounting for the uncertainty over the deterministic trend and the multiplicity of the testing problem, all series can be regarded as unit root nonstationary. 4.2. Unit root tests of the estimated components of crime We now proceed to discuss the results of the PANIC procedure when applied to (3). As described in Section 3, the first step is to use the principal components method to estimate F t and ei;t . Unfortunately, PANIC is not equipped to handle cases when there is uncertainty concerning the presence of the deterministic time trend. Therefore, in response to this, we apply the trend test of Westerlund and Blomquist (2013), which is valid even if the presence of the trend is unknown. The test statistic is very simple and can be viewed as a t-test of the average trend slope, which is zero under the no trend null hypothesis. The results obtained from applying the trend test are reported in Table 2. We see that the test statistic for theft is significant at the 10% level, suggesting that for this crime we should keep the trend in the model. For burglary and vehicle theft, however, the trend is insignificant and can therefore be removed. Since the extent of the trend is now ‘‘known’’, we can proceed to estimate the components of the data. For theft, the principal components method is applied to Dyi;t  Dyi , whereas for burglary and vehicle theft, it is applied to Dyi;t . Following the recommendation of Bai and Ng (2002), the number of factors to use is determined using the IC 2 information criterion, with the maximum number of factors set to five. The results suggest that while the common component of theft is made up of two factors, for burglary and vehicle theft we end up with one factor. Table 3 reports the ADF test results for each estimated factor, where the order of the lag augmentation has again been determined using the BIC. Since none of the tests is significant at the 10% level, we conclude that all factors are nonstationary. The non-stationarity of the factors suggests that the common component is an important source of variation, which corroborates the preliminary evidence reported in Section 2. It is also consistent with some of the more recent US studies (see, for example, McDowall and Loftin, 2009; McCall et al., 2011). To further quantify the importance of the common variation, we computed the fraction of the total variation in the data explainable by the estimated common component. The results (not reported) suggest that while initially quite volatile, in recent years the fraction of common variation has stabilized around 30% for burglary and around 50% for theft and vehicle theft.6 The next step is to test for unit roots in the estimated idiosyncratic component, which can be done using any first-generation panel unit root test. However, this presupposes that the sample is large enough to ensure that ei;t can be treated as known, which may not be the case. Indeed, given the finiteness of our sample, one might expect some remaining cross-sectional dependence, even after extracting the estimated common component. Therefore, to test the appropriateness of the independence assumption, we again apply the CD test. The results are reported in the lower panel of Table 1. As can be seen, the average correlation is close to zero, suggesting most of the cross-sectional dependence has indeed been accounted for. However, while smaller than for the raw crime data, for burglary and vehicle theft the CD test is still significant, suggesting 6

To guard against spurious effects, the variance is calculated from first-differenced data.

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J. Blomquist, J. Westerlund / Social Science Research 44 (2014) 114–125 Table 3 Unit root tests of the estimated factors of crime. Crime

Factor

AR slope

ADF

Burglary Theft

1 1 2 1

1.01 0.85 0.87 1.04

0.27 2.17 1.39 1.07

Vehicle theft

Notes: ‘‘AR slope’’ and ‘‘ADF’’ refer to the estimated first-order autoregressive coefficient and the ADF unit root test, respectively. An asterisk indicates significance at the 10% level.

Table 4 p-Value results for the Palm et al. (2011) panel bootstrap unit root test for crime. Variable

Burglary

Theft

Vehicle theft

Raw data Idiosyncratic

0.40 0.00

0.61 0.00

0.94 0.00

Notes: ‘‘Idiosyncratic’’ refers to the estimated idiosyncratic component of the data. The numbers in the table are the p-values.

that the accuracy of the estimated idiosyncratic component is not perfect. Therefore, instead of applying a first-generation test, we look for a test that is valid even if there is some cross-section dependence remaining. In particular, the panel unit root test of Palm et al. (2011) is applied, which is a block bootstrap version of the well-known Im et al. (2003) test. As before, the number of bootstraps is set to 1999 and the block length is set to 1:75T 1=3 . The test results are reported in Table 4. As we can see, the evidence is uniformly against the unit root null. We also apply the test to the raw crime data. In agreement with the results obtained when applying the BSQT approach to these data, there is no evidence against the unit root null. The presence of non-stationary factors and stationary idiosyncratic components implies that crime is cointegrated across counties. However, as already mentioned, the fact that the panel test rejects the unit root null does not mean that the idiosyncratic component of each county is stationary. This can be seen in Table 5, which summarizes the results of applying the BSQT to the estimated idiosyncratic component. The evidence suggests that 50% of the series are stationary, and that this is true for all three crime categories. Thus, while both the idiosyncratic and common components are non-stationary for half of the counties, there is evidence of cross-county cointegration for the other half. 4.3. The unemployment–crime relationship Since all three crime rates appear to be unit root non-stationary, any attempt to explain these crimes must be based on variables exhibiting similar unit root behaviors. This knowledge helps narrowing the search for possible determinants of crime. The fact that the non-stationarity of crime seem to be driven by a small number of common stochastic trends further suggests that the long-run behavior of county crime rates is, at least in part, driven by nationwide conditions. Motivated by these findings, in this section we analyze to what extent crime can be explained by labor market conditions, as measured by the unemployment rate. We begin by investigating the dynamic and cross-sectional properties of unemployment, using the same methodology as for crime. The unemployment data are from Statistics Sweden and cover the same 21 counties over the 1976–2007 period. This is shorter than the original 1975–2010 period used for crime, but is the longest time period for which consistent data are available at the county level.7 As with crime, the unemployment rate is transformed into natural logs. The result of the trend test indicates no deterministic trends, and the IC 2 criterion suggests two common factors, both found to be non-stationary using the constant-only ADF test. The rest of the test results are summarized in Table 6. In agreement with the crime results, the evidence strongly suggests both cross-sectional dependence and cross-unit cointegration. The next step is to estimate the unemployment–crime relationship in (1). A key assumption underlying the CCE approach is that the idiosyncratic component of both crime and unemployment are stationary. While for unemployment, this assumption seems to be satisfied, this is not the case for crime, for which the idiosyncratic component is non-stationary in 50% of the counties. Therefore, to guard against possible bias, the CCE approach is applied to both the full sample and the subsample corresponding to those counties for which the idiosyncratic component was found to be stationary. We also consider the FE estimator, which has been very popular in previous studies. Following the usual convention in the literature, the regressions are fitted with individual-specific time trends. The CCE results are reported in columns 2–4 of Table 7, in which, for purposes of comparison, the right-most column also includes the FE results reported by Edmark (2005, Table A1).8 7

Data for 2008 and onwards are not comparable with earlier data due to changes in the definition of the official unemployment rate. Edmark (2005) uses data on the same counties as we do, but covering a shorter time span, 1988–1999. Moreover, her definitions of theft and vehicle theft include only shoplifting and car theft, respectively. However, since shoplifting and car theft are the two major sub-categories of theft and vehicle theft, the results should be somewhat comparable. 8

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J. Blomquist, J. Westerlund / Social Science Research 44 (2014) 114–125 Table 5 BSQT results for the idiosyncratic component of crime. County Blekinge län Dalarnas län Gotlands län Gävleborgs län Hallands län Jämtlands län Jönköpings län Kalmar län Kronobergs län Norrbottens län Skåne län Stockholms län Södermanlands län Uppsala län Värmlands län Västerbottens län Västernorrlands län Västmanlands län Västra Götalands län Örebro län Östergötlands län Proportion of stationary units

Burglary

Theft

Vehicle theft

⁄ ⁄ ⁄ ⁄

⁄ ⁄ ⁄ ⁄

⁄ ⁄ ⁄ ⁄ ⁄

⁄ ⁄ ⁄ ⁄

⁄ ⁄ ⁄

⁄

⁄

⁄

⁄

⁄ ⁄

⁄

⁄

⁄

⁄

⁄ 0.5

0.5

⁄ ⁄ 0.5

Note: An asterisk indicates significance at the 10% level.

Table 6 Test statistics for unemployment. Statistic

Raw data

Idiosyncratic

Cross-county correlations Correlation CD p-Value

0.70 57.15 0.00

0.05 3.87 0.00

0.00 0.27

1.00 0.00

Unit root tests BSQT proportion Unit root p-value

Notes: ‘‘BSQT proportion’’ refers to the estimated proportion of stationary units. The p-value is for the Palm et al. (2011) panel bootstrap unit root test. See Table 1 for an explanation of the remaining features.

The first thing to notice is the difference between the FE and CCE estimates. According to the former, the unemployment elasticity of burglary and vehicle theft ranges between 0.1% and 0.16%, and is highly significant, a result in line with Edmark (2005) and others (see, for example, Entorf and Spengler, 2000; Papps and Winkelmann, 2000; Öster and Agell, 2007). The problem is that the FE estimator presumes that the data are cross-correlation free, which we have shown not to be the case. The FE results are therefore likely to be misleading (Urbain and Westerlund, 2011). The results from the CCE approach are quite suggestive of this. Indeed, controlling for the cross-sectional dependence, we see that the coefficient of unemployment drops and becomes close to zero and insignificant for all three crime categories. We also see that this result holds regardless of the sample used. The seemingly spurious relationship between crime and unemployment gains support from the cointegration test results (not reported). In fact, according to the BQST approach, the CCE residuals are non-stationary for all 21 counties, and this is true for all three crime categories. Note how the presence of the common factors in (1) can be seen as common omitted variables. The CCE approach is very general in that it is valid even if these omitted variables happen to be non-stationary. However, if relevant county-specific variables are omitted, the CCE approach may be biased. Therefore, to check the robustness of our results, we experimented with several control variables chosen on their relevance and popularity in previous studies (see Entorf and Spengler, 2000; Raphael and Winter-Ebmer, 2001; Edmark, 2005). The following control variables were included: the proportion of divorced persons, population density, proportion of foreign citizens, proportion of young men (aged 15–24 years), and clear-up rate. All data, except for the clear-up rate, are measured at the county level and are from Statistics Sweden; for the clear-up rate, country level data were obtained from the Swedish National Council for Crime Prevention. The results are reported in columns 5–7 of Table 7. Looking first at burglary and vehicle theft, we see that while the estimated unemployment elasticities obtained from the FE estimator are lower than before, they are still significantly positive. This result is consistent with those of Edmark (2005), but not with the results obtained from the CCE estimators, which are again mostly insignificant. The results for theft are also similar to those obtained without the controls. The most notable

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J. Blomquist, J. Westerlund / Social Science Research 44 (2014) 114–125 Table 7 Estimation results. Crime

No controls

Non-economic controls

Edmark

CCEMG

CCEP

FE

CCEMG

CCEP

FE

0:01 ð0:237Þ 0:010 ð0:273Þ 0:048 ð0:910Þ

0:01 ð0:256Þ 0:021 ð0:850Þ 0:002 ð0:053Þ

0:102⁄⁄⁄ ð6:725Þ 0:005 ð0:330Þ 0:157⁄⁄⁄ ð6:578Þ

0:046 ð0:994Þ 0:003 ð0:064Þ 0:029 ð0:975Þ

0:046 ð1:105Þ 0:006 ð0:231Þ 0:049⁄⁄ ð2:130Þ

0:069⁄⁄⁄ ð5:116Þ 0:063⁄⁄⁄ ð4:063Þ 0:127⁄⁄⁄ ð10:622Þ

0:123⁄ ð1:732Þ 0:093 ð0:894Þ 0:153⁄⁄ ð2:068Þ

Subsample with stationary idiosyncratic component Burglary 0:03 0:067 ð0:609Þ ð1:392Þ Theft 0:009 0:050 ð0:150Þ ð1:395Þ Vehicle theft 0:018 0:017 ð0:288Þ ð0:359Þ

0:097⁄⁄⁄ ð4:831Þ 0:019 ð1:003Þ 0:109⁄⁄⁄ ð5:352Þ

0:049 ð0:853Þ 0:018 ð0:378Þ 0:048 ð1:086Þ

0:033 ð0:487Þ 0:063⁄ ð1:817Þ 0:040 ð0:969Þ

0:071⁄⁄⁄ ð3:620Þ 0:083⁄⁄⁄ ð3:545Þ 0:042⁄⁄ ð2:024Þ

     

Full sample Burglary Theft Vehicle theft

Notes: ‘‘CCEMG’’ and ‘‘CCEP’’ refers to the CCE mean group and pooled estimators, respectively. ‘‘FE’’ refers to the fixed effects estimator. The results reported in the ‘‘Edmark’’ column are taken from Edmark (2005). The number within parentheses are the absolute value of the t-statistics. Significance at the 10% level. ⁄⁄ Significance at the 5% level. ⁄⁄⁄ Significance at the 1% level. ⁄

difference is that the FE estimator of the unemployment elasticity is now significantly negative, which is consistent with the pooled CCE estimate. The insignificant CCE results for burglary and vehicle theft may be surprising in light of the most recent empirical evidence based on panel data, suggesting that unemployment and crime are significantly and positively related (Mustard, 2010). However, these studies assume that the data are stationary and/or cross-correlation free, which is clearly not the case. To check the extent of the cross-correlation in the estimated regressions, we computed the average of the pair-wise correlation coefficients of the residuals from the FE and CCE regressions. As expected, while the correlations for the FE residuals are quite large, varying between 0.19 (for burglary) and 0.47 (for theft), the correlations for the CCE residuals are much lower, hovering around 0:03. Thus, conditioning on county-specific variables alone is insufficient to remove the cross-correlation in crime. How can we explain the insignificant unemployment effect? Parker and Horwitz (1986) argue that since habitual criminals are often chronically unemployed, changes in unemployment should have little motivational effect on individuals likely to engage in crime. Moreover, as discussed in the Introduction, because of increased guardianship of homes, vehicles, and other potential targets, an economic downturn may actually reduce the opportunity of committing crime, which would not only weaken the hypothesized positive unemployment–crime relationship but could even make it negative. Such an inverse relationship has been documented by D’Alessio et al. (2012), who use US state-level data to examine the relationship between unemployment and the weekday residential burglary rate. Furthermore, the average unemployment duration in Sweden is fairly short. In 2010, the average duration of unemployment was 31 weeks, and since unemployment benefits typically last twice as long, most unemployed have already found a new job long before they run into economic difficulties. Hence, it seems likely that the motivational effect of unemployment is most relevant to the relatively small number of unemployed people experiencing long-term unemployment. Some preliminary evidence favoring this hypothesis is provided by Almén and Nordin (2011). 5. Conclusions In this study, we try to shed some light on the persistence and interregional dependency of crime, an often neglected feature of empirical studies of the economics of crime. For this purpose, we take advantage of recent developments in non-stationary panel data econometrics. In particular, the PANIC methodology of Bai and Ng (2004) is employed, which enables us first to estimate and then to test for unit roots in both the idiosyncratic and common components of the data. This decomposition is appropriate, because crime rates usually exhibit both high variability within each region over time and strong comovement across regions, features consistent with recent theoretical models of crime. Using a panel that covers 21 Swedish counties between 1975 and 2010, we can reject the presence of a unit root in the estimated idiosyncratic component for 50% of the counties and for all three crime categories considered, but not in the estimated common component. This leads us to conclude that the crimes are cointegrated across counties. The fact that the common components are also relatively important suggests that most crime shocks are common. Our results therefore support the view that a national pattern underlies Swedish county-level crime trends. They also imply that the standard approach of employing conventional regression techniques designed for stationary panels may be hazardous, and that conclusions from

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prior research need to be reevaluated, as they may have been spuriously induced by the presence of common stochastic trends. This is a potentially very serious issue, as all of the leading panel data studies in the field assume that their data are stationary and cross-section independent. With the above results in mind, the unemployment–crime relationship is estimated using the recently advanced CCE methodology, which is robust to both the non-stationarity and cross-section dependence of the data. Our results are very strong in that there is no evidence of the hypothesized positive unemployment–crime relationship. Indeed, if anything, the relationship appears to be negative. This finding is in sharp contrast to the significantly positive effect obtained when applying the common FE estimator. Hence, again, much of the existing evidence of a positive unemployment effect can be due to unattended non-stationarity and/or cross-correlation. 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