Scottish Journal OJ Politiml Economy, Vol. 39, No. 2. May 1992 0 1992 Scottish Economic Society

CRIME AND UNEMPLOYMENT IN SCOTLAND: AN ECONOMETRIC ANALYSIS USING

REGIONAL DATA

BARRY REILLY

University of Sussex

AND

ROBERT W ITT*

University of St Andrews

I

INTRODUCTION

Economists have devoted little effort to the economic analysis of crime. A notable exception, however, is provided by the seminal work of Becker (1968) who outlined a microeconomic model predicated on individual level expected utility maximization. Individuals are assumed to allocate their time between legal and illegal activities where the allocation is determined by the relative returns to these activities and the risks associated with detection if engaged in illegal activities.

The probability of detection and the level of punishment impacts negatively on expected utility assuming a positive marginal utility of income. Becker specified a crime function where crimes (or offences) were a function of the detection probability, the level of punishment and a portmanteau variable which was assumed to represent all other influences. For example, a rise in income available from legal activities would reduce the incentive to enter illegal activities. This particular effect would be captured in Becker’s portmanteau variable. Thus, the effect of unemployment (and a consequent low income) could induce individuals to engage in illegal activities since the opportunity cost of so doing is low.

The evident weakness of such a utility based theory is that not all individuals who could benefit from engaging in crime actually do so. The existence of social control prevents individuals from engaging in illegal activities. As Field (1990) points out, the breakdown of social control is a pre-condition for the economic determinants of crime to take effect. Economic conditions, like

The authors would like to thank an anonymous referee of this Journal for a number of constructive comments. The comments of Ron Smith and participants at a Staff Seminar in St Andrews and at the Scottish Economics Society conference in Edinburgh (April, 1991) are also acknowledged. Finally, the Scottish Office are thanked for providing some unpublished data uses in the analysis. However, in all cases the usual disclaimer applies.

Date of receipt of final manuscript: 13 June 1991

? l Y

214 BARRY REILLY AND ROB WITT

unemployment, may partly determine this breakdown thus giving rise to the relationship between unemployment and crime.

The existence of a causal link between unemployment and crime has been the subject of some investigation in the past. Indeed, references cited in Field (1990) and Timbrel1 (1990) confirm a tradition of such investigation, some of which dates back to the last century, The more recent empirical evidence remains equivocal about the relationship between unemployment and crime. Tarling (1982) examined a large number of empirical studies and concluded that a positive correlation did exist between the crime rate and the unemploy- ment rate but that, in general, the effect was attenuated when additional vari- ables were allowed to enter the analysis.

In a more recent study Field (1990) analyzed the effects of business cycle vari- ables like, for example, consumption growth on different categories of crime. Using data for England and Wales the author presented evidence in favour of a strong negative relationship between growth in consumption, in the post-war period, and most categories of crime. Field (1990) is sceptical about the exist- ence of a strong relationship between the unemployment rate and the crime rate and in presenting evidence, in our view, prematurely concludes that such a sim- plistic relationship is ‘disproved @. 7)’. Field’s conclusion relies on the fact that when the aggregate unemployment rate is included with the consumption growth rate in a crime rate equation, the unemployment effect is negligible at conventional levels of statistical significance. The observed insignificance of the unemployment term may be attributed to its high correlation with consumption growth. In modelling the relationship between the business cycle and crime, both variables can be viewed as proxying the same effect. It’s not clear that there is gain in including both.

The arguments for the inclusion of consumption growth as an important determinant of the crime rate are not more compelling than those in favour of including the unemployment rate. In fact the sign effect of the relationship is not unambiguous. For example. Field (1990) argues that consumption growth might effect crime in three distinct ways. Firstly, through an increase in the volume of goods available for theft (opportunity effect). Secondly, through an increase in the capacity for the lawful acquisition of goods, thus reducing the incentives for unlawful acquisition of goods (motivation effect). And thirdly, through an alteration in the pattern of crime opportunities (the life-style effect). The signs on the first and third effects are assumed positive and the sign on the second effect is assumed negative. In the context of property crime Field assumes the second effect dominates the other two effects. However, the observed positive relationship between personal crime and consumption growth is rationalized by assuming that, for this category of crime, the third effect dominates. There is, in our view, no a priori reason as to why the life-style effect should have a positive effect. The interpretation suggested by Field is that as consumer spending rises individuals spend more time outside the security of their home and are, therefore, more susceptible to criminal attentions. Of course, it’s easy to envisage the opposite effect. As consumer spending rises an individual may be able to afford more protection against crime and in venturing outside the home may prefer to use taxis rather than public transport.

CRIME AND UNEMPLOYMENT IN SCOTLAND 215

The inability to disentangle these relative effects is a disadvantage in using the consumption growth variable as a determinant of the crime rate. Use of the unemployment rate provides for less equivocation. This, however, is not to say that use of the unemployment rate is not itself subject to some criticism. Tarling (1982) outlines some drawbacks associated with the use of the unem- ployment rate. For example, many crimes are committed by people in employ- ment who, it is argued, have greater opportunities to commit crime. However, as Burden (1990) points out employee theft may sometimes be viewed as a pre- requisite of a particular job by employees and employers alike. Management may view such theft as simply ‘stock shrinkage’ and a way of allowing their employees to increase their income without paying higher wages. Thus most employee crime may go unreported.

A secondary problem with the use of the unemployment rate, also highlighted by Tarling (1982). is in fact that young people are more likely to participate in crime long before they participate in the labour market.

It could also be argued that unemployment is the conduit through which other factors influence the crime rate. For example, poor educational attain- ment may be highly correlated with the incidence of crime. However, this may also be a key determinant of unemployment. Indeed, Timbrel1 (l990), using cross-sectional data for 198 1 tentatively concluded that education was more important than unemployment in the determination of crime, although both registered insignificant effects when included in the same specification. The poorly determined nature of the education and unemployment coefficients in this case could again be linked to a high correlation between the unemployment variable and the education variable employed in the analysis.

Thus, certain caveats must be inserted concerning the use of unemployment. Its use in this study is inextricably linked to a data limitation problem. Given that this study employs regional data for Scotland no information exists on consumption to the regionally disaggregated level required for this analysis. In modelling the relationship between the business cycle and the crime rate at a regional level, it is not clear that any better variable than the regional unem- ployment rate exists for Scotland.

Most of the recent empirical evidence provided on this issue for the United Kingdom is based on the use of data for England and Wales. The purpose of this study is to investigate the existence of a relationship between the unemploy- ment rate and the crime rate using data for Scotland. However, unlike much of the empirical work for England and Wales attention in this paper focuses on regional disparities in the effects of unemployment on crime. For example, Table 1 provides summary statistics for crime and unemployment rates by region for selected years. Not surprisingly Strathclyde records the highest unemployment rates for the three years in question and the highest crime rates per 100 of the population. In contrast, Dumfries and Galloway reports relatively high unemployment rates but remarkably low crime rate figures. This casual observation suggests regional differences in the effect of unemployment on crime. This will be the subject of a more rigorous test subsequently. How- ever, the regional disparities observed in Table l suggest an interesting avenue of investigation.

216

TABLE 1 Regional crime and unemployment

BARRY REILLY A N D ROB WITT

1974 CR UR

Central 3.23 3-10 Dumfries & Galloway 1.81 3.60 Fife 2.64 3.10 Grampian 2.70 1-80 Strathclyde 4-15 4-40 Tayside 3.57 3.00

Rates for Scotland (selected years)

1981 CR UR

5.95 13.10 4.59 12-70 5.14 12.80 5.92 7-60 9-33 16.10 7.63 13.40

1988 CR UR

7-12 13.20 4-79 11-00 7.27 13.70 6.68 7.50

11.13 15.60 9.00 12-00

Nora: CR =Crime Rate per 100 of the population,

Source: Scorrish Absrmcr of Srorisrics (various issues). Sec Text for furthcz details. UR = Unemployment Rate

The objective of this paper is to add to a relatively small body of empirical evidence on the relationship between crime and unemployment and in so doing fill an empirical void in regard to Scotland. It should also be seen as the first study for the UK that has attempted to examine the regional dimension of this relationship within a time series framework.

The following section, Section 11, outlines the econometric methodology. In this section Feasible Generalized Least Squares (FGLS) estimators used in the empirical analysis are outlined. Section 111 details the data used in estimation and Section IV reports the empirical results. Section V concludes.

ECONOMETRIC METHODOLOGY

The pooling of time series data and regional cross-sectional data allows for the specification of a more general structure for the error variance of the model. Cross-sectional observations may exhibit heteroscedasticity while time-series observations have a tendency to be autoregressive. However, with the data employed in this study cross-sectional correlation (or spatial effects) must also be considered. The six cross-sectional units used in this analysis are geographi- cal regions and a number of these regions are contiguous. The possibility that there exists some form of correlation in unobservables across the regional boundaries cannot be ruled out. Ultimately, it’s an empirical question whether such cross-sectional correlations exist. If they do, then the specification of the error variance must become even more general allowing, as it must, for the potential presence of heteroscedasticity, autocorrelation and cross-sectional dependence.

This section outlines how a set of Generalized Least Squares (GLS) regression models can be specified to deal with the problems posed by hetero- scedasticity, autocorrelation and cross-sectional correlation.

Following Greene (1 W), the pooled cross-sectional and time-series model may be written as

CRIME AND UNEMPLOYMENT IN SCOTLAND 217

(1)

where i = 1, ..., n (Regions, in this case six Scottish regions) and t = 1, ..., T (Time periods, in this case fifteen years). If the six sets of time periods are col-

Yit = B ’ x i t + &it,

lected and stacked by region, (1) could then be re-written as:

yi = B ’ x i + Ei,

The stacked vectors and matrices would then be given by:

In the classical regression model the following assumptions are made

E ( c i t ) = 0, E(&) = u2,

E(&itEjs) = 0 if t # s or i # j .

(11) assumes homoscedastic errors and (111) cross-sectional independence.

written (in matrix form) as If we assume cross-sectional correlation, the variance term may now be

E(&i&j) = U i j I

where I is the identity matrix. This may be written, in more general terms, as:

~ 1 1 1 a121 ... ulnI v = [ i i

0.11 an11 . . .annI

The uij terms are estimated from the least square residuals as

8ij = 2$j/T, (3)-

where i and j are different regions. GLS is only implementable if the uij terms are known. Since they are

unknown and require estimation by (3) the appropriate estimator is a Feasible Generalized Least Squares (FGLS) estimator and this is defined as

6 = [x ’V- ’x ] - l x ’ V - ’ y . (4)

Var@ = [ x ’ V - ’ X ] - ’ . ( 5 )

The asymptotic variance co-variance matrix, in this case, is given by

In terms of the data set employed in this study we have 6 geographical regions (details of which are outlined in the subsequent section) and 15 years of data for each region. The total number of observations in the pooled model is 90. Thus, the dimensions of the V matrix is 90 x 90. The inversion of this is not trivial computationally. A short-cut, however, is to note that

V = € x I

where f; is, in our case, a 6 x 6 matrix of regional error variances and

218 BARRY REILLY AND ROB WITT

covariances. Thus v - I = E-I x I.

Thus, the most that's required for inversion in this study is a 6 x 6 matrix and the 9-l matrix may now be written as:

6"I 6I2I ... +'"I

;"'I iY21 ... ;""I

where 6u is the 0th element of 2-l. Then

and X'V-'y= c c i%XiYj

i i (7)

The FGLS estimator is obtained by inverting (6) and multiplying by (7). Equation (6) has k x k dimensions, where k is the number of parameters to be estimated.

A Lagrange multiplier test based on Breusch and Pagan (1980) provides a test for cross-sectional independence. It can be calculated as

M i - 1 L M I = ~ zi)t

i - I j - I

where Pv is the correlation coefficient between the residuals in the different regions and they are calculated from the OLS residuals. In the case of this study there are fifteen pair-wise regional correlations and thus the number of restrictions under test is fifteen.

The foregoing FGLS estimator can be modified to allow for the prescnce of serial correlation. The simplest form to assume is the AR(1) process. The struc- ture of the AR( 1) process in terms of the pooled time-serieslcross-sectional model is given by

(8)

This implicitly assumes that the AR( 1) process is the same across regions. Given that there are just fifteen observations per region, estimation of individual p values may lead to small sample bias in the p estimates with obvious conse- quences for the FGLS estimates.

Two FGLS estimators are common in time series for the correction of serial correlation. One is the Cochrane-Orcutt procedure while the other is the Prais-Winsten procedure. These two procedures differ in their treatment of the first observation. In the former case it is deleted as the data is subjected to a quasi-differencing procedure. Thus, only T - 1 of the time series observations are used in estimation. In the latter case all T observations are used in estima- tion with the first observation transformed to ensure homoscedasticity in the transformed errors.

Eir = pei,r- I + Uir.

CRIME AND UNEMPLOYMENT IN SCOTLAND 219

To implement the FGLS model a value of p is necessary and in this study this value is calculated as a simple correlation coefficient using the OLS residuals for time period T and time period T - 1. This values is defined as f i .

The transformed X and y matrices can now be written as X* and y* where:

The Prais-Winsten procedure uses all of the observations in the y* vector and the X* matrix. The Cochrane-Orcutt procedure uses the observations from the second row down. In small samples there is a strong efficiency argu- ment in favour of the Prais-Winsten procedure and it has been shown in time series applications that it produces more efficient estimates than the Cochrane-Orcutt procedure.

The above transformations just correct for the presence of autocorrelation. The residuals generated from this procedure can be used to re-specify the V matrix in order to implement an autocorrelated/cross-sectionally correlated FGLS estimator. Define the residuals from employing either of the above trans- formations as G: (where there are now i sets of transformed residuals). The variances and covariances of the E error terms can now be estimated by

where 4" = C ii:ii$/T.

The 3ij terms replace the &j in the 8 matrix and the FGLS formulae of (4) and ( 5 ) again apply but with the transformed data. The coefficient and asymp- totic variance covariance matrix is given by (9) and (10) respectively.

p* = [x*'v*-lx*l - I x * ' v * - l y * ~

Var(p*) = [X*'V*-'X*]-'

where V* is the V matrix with $0 replacing the &j terms. Estimates based on equations (9) and (10) for the auto-correlated/cross-sectionally correlated model are reported in the empirical section. It should be noted that in estimat- ing (9) and (10) for the Cochrane-Orcutt procedure and the Prais-Winsten procedure heteroscedasticity is also being corrected for in the V* matrix.

In all cases, the estimates are two-step in the sense that no attempt is made to iterate to the maximum likelihood estimates. Johnston (1984, p. 326) pro- vides evidence for the superiority of the two-step variants of the Cochrane-Orcutt and the Prais-Winsten procedures over their iterative ver- sions. Furthermore, no RZ values are reported for the FGLS estimators since these are not defined over the [0,1] interval.

Estimates for two other models are also reported. The first is the Least Squares Dummy Variable (LSDV) model or the fixed effects model. The second is the random effects model.

220 BARRY REILLY A N D ROB WITT

The LSDV model assumes that differences across regions can be captured by differences in the constant term. This model is implemented by augmenting equation (2) with six regional dummies. No intercept term is thus required and since the LSDV is a classical regression model OLS is valid. And F-test can then be employed to test whether the effects are the same across regions. The LSDV model assumes that the individual specific characteristic of a region is a parameter. The disadvantage in estimating the LSDV model is the reduction in the degrees of freedom.

It is because of this latter problem that attention has turned to the random effects model where the individual specific characteristic of a region is assumed to be a normal randomly distributed variable. The random effects can be expressed in a number of different ways. For the purposes of this study we assume that the error now has two components and equation (1) can be re- formulated as:

where E(&) = a: and E ( u f ) = at. Thus there are two components to the error term. The Ui is the individual specific effect that, in this case, is assumed ran- domly distributed across regions. If d is equal to zero then the use of OLS is valid. An LM test based on the OLS residuals and due to Breusch and Pagan (1980) provides the statistical test for this hypothesis. The LM test is defined as

LM2 = (nT)/(2(T- 1)) C (C air)’ C C f i f , - 1 [ [ i t / i f ] 1’

and the null under test is at = 0. Thus, the test statistic has just one degree of freedom.

The estimator employed to estimate the above model is again an FGLS esti- mator. Greene (1990, pp. 486-487) outlines the appropriate estimator. The assumption of a random effect (rather than a fixed effect) is a more realistic assumption if the cross-sectional units are drawn at random from a larger population. Whether the fixed effects model or the random effects model is the appropriate model for a particular application is an empirical question. The clear advantage of employing the random effects model is that it involves the estimation of only one additional parameter, i.e. an estimate of at. This con- serves degrees of freedom and renders the estimates more efficient. However, the disadvantage lies in the fact that if the cross-sectional characteristic is corre- lated with the included independent variables, the estimated regression coeffi- cients are biased. Hausman (1978) provides the appropriate framework for testing whether the random effects are orthogonal to the regressors. The Hausman test can be employed to test the null of orthogonal random effects against the alternative of correlated effects. If the null is rejected, the argu- ments in favour of retaining the random effects model are diminished. A Hausman test statistic based on this null is reported in the empirical section.

C R I M E A N D U N E M P L O Y M E N T IN S C O T L A N D

111

DATA

22 1

The data used in this study are obtained exclusively from the Scottish Absfruct of Sfatistics (various issues). The six Scottish regions used in the analysis were chosen on the basis of available and compatible crime and unemployment data. The six regions that form the basis for the analysis are

(i) Central (ii) Dumfries and Galloway

(iii) Fife (iv) Grampian (v) Tayside

(vi) Strathclyde

The dependent variable in the analysis is the crime rate per 100 of the popu- lation in the region in question. Offences are excluded from the definition since there is no u priori reason for why offences should be linked to cyclical move- ments in the economy. Observations on this series range from 1974 to 1988. The major problem with this variable is the fact that the crime rate is based on crimes reported to the police. As Field (1990) points out for the United States, there exists a strong positive correlation between actual crimes (as measured by the Victim Survey) and reported crimes. Thus, trends in actual crime are strongly correlated with trends in reported crime. This evidence pro- vides the basis for some confidence in the use of the reported crime rate vari- able. Nevertheless many types of crime go unreported. See Burden (1990) for further evidence.

The business cycle variable, and the key independent variable in the analysis, is the regional unemployment rate. The observations on this series also range from 1974 to 1988. It might be more appropriate to use the male unemploy- ment rate or even the youth male unemployment rate given the presumed relationship between young males and crime. However, a long enough series on either of these categories is not readily available. A second problem that is posed by use of the unemployment data is the changes in definitions that have occurred, in particular during the 1980s. This is a problem that confronts most applied econometricians who use unemployment rates and one can do nothing more than assume that the definitional changes don’t alter the nature of the relationship under consideration.

Another independent variable used in the analysis is designed to capture the regional influence of government or local authority. Government expenditure figures by region are not available for Scotland on a calender year basis. Thus as a proxy for government/local authority influence in a region we use the number of completed public authority houses per head of population. This is thus a flow variable. It should be stressed that the variable may be proxying many things and thus may be regarded as relatively weak. However, given the limitations of the Scottish data in regard to government/local authority expen- diture it is deemed to be the most appropriate variable available from published

222 BARRY REILLY AND ROB WITT

sources. In this particular study it plays the role of an indicator of social pri- vation. We would expect a priori a negative relationship between this variable and the regional crime rate i.e. as the flow of public authority housing increases the lower is the crime rate.

In other studies that examine the determinants of the crime rate, demo- graphic variables like the age structure of the population have been seen to play a role. The younger the population the greater the crime rate. However, data limitations prevented the construction of a consistent age structure variable for the Scottish regions employed in this analysis.

IV

EMPIRICAL RESULTS

Prior to examining the estimates reported in Table 2, Figure 1 plots the aggre- gate crime and unemployment rates for Scotland between 1974 and 1988. As

TABLE 2 Regional crime and unemployment

Coefficient estimates ( 5 ) (6) - 2.7239'

(0.6939) (0.0643). (2.2765) (1.5240). - (0-781 1) Unemployment 0.3349. 0.1546 0,1775. 0.2633 0.3466. 0-3464* Rate (0.0455) (0.0408) (0.1042) (0- 1047) (0.0208) (0.0208) Public -0.2050 -0.0541 -0.0681 -0.0768 -0.1945* -0.1954. Housing (0.1290) (0.0572) (0-09oO) (0.0924) (0.0565) (0.0565)

(1) (2) (3) (4) Constant 2.8661' 0.2243. 4.8206. 3.7878.

Central

Dumfries & Galloway

2*1040* (0.3378) 0.9136.

(0.3463)

Fife 1 *5633* (0.3433)

Grampian 3.9700. (0- 3250)

Strathclyde 4.2025. (0.3702)

Tayside 3.5619* (0.3255)

1?= 0.6256 0.1423 0.9308 Std.Error 1 4 3 7 0.6034 0-1907 0. 0-7580

Notes: ( I ) = Ordinary Least Squares. (2) = First Differences. (3) = Cross-sectional correlation with Cochrane-Orcutt procedure. (4) = Cross-sectional correlation with Prais-Winsten procedure. (5) = Least Squares Dummy Variable model (Fixed Regional Effects). (6) = Random Effects Model.

'denotes significance at the 5% level or better using a two-tailed test. (9, (4) and (6) are Feasible Generalized Least Squares Estimators (FGLS) and the standard errors in these

columns are asymptotic.

CRIME AND UNEMPLOYMENT IN SCOTLAND

Aggregate crime and unemployment rates for Scotland (1974-1988)

223

14

13

12

11

10

E 9

a ! 8

7

6

5

4

3 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988

-m- Aggregate unemployment rate 4 Aggregate crime rate

Figure 1. Aggregate crime and unemployment.

is evident both series move in trend together. Both could be interpreted as inte- grated of order one (denoted I(1)) and thus require first differencing to induce stationarity. Use of non-stationary variables has implications for the OLS stan- dard errors though the estimated coefficients remain consistent. Given the fact that we have only fifteen time series observations, use of Dickey-Fuller type tests to establish orders of integration is clearly inappropriate. However, to address the issue of potential non-stationarity a model in first differences is esti- mated. Thus if the series are 1(1) the estimated first difference model will be based on the use of variables that are stationary. ' Furthermore, the first differ- ence model also provides an indication of the robustness of the relationship given the possibility that the levels relationship could be a spurious one.

Initially attention will focus on the OLS estimates of column one in Table 2. A robust and positive coefficient is attached to the unemployment rate variable. The public housing variable has the correct negative u priori sign but only possesses a t-value in absolute terms of 1 *6. The reported adjusted R2 is 0.6256 suggesting that a good deal of the variation in the crime rate is

'Testing for orders of integration is a pre-requisite for testing whether series are co- integrated or not. Again, given the short time series available, examining the co-integrating properties of the specified relationship is not regarded as sensible.

224 BARRY REILLY A N D ROB WITT

explained by variation in the unemployment rate and the flow of public housing. 2*3.

The estimates reported in column two are based on OLS estimation of the first difference model. An intercept term is included in this specification and this should be interpreted as the trend coefficient. A strong positive relationship is found between crime and unemployment. The effect of the flow of public housing on the crime rate is lessened somewhat in comparison to the levels' specification. Though the R2 drops significantly, this result provides an import- ant test of the robustness of the relationship between crime and unemployment.

The contiguous nature of some of the cross-sectional units used in this study raises the question of correlation across regions in the error terms. Central and Strathclyde, Strathclyde and Dumfries and Galloway, Central and Fife, Fife and Tayside, Tayside and Grampian, Tayside and Central and Tayside and Strathclyde are all contiguous combinations. The LM test of Breusch and Pagan (1980) outlined in Section I1 provides an appropriate test for the exist- ence of correlations in the errors across regions. The LM statistic in this case is a xz variate with 15 degrees of freedom and the test value is 34-561. The rel- evant critical value is 24.996 at the 5% level. Thus the null of cross-sectional (or regional) independence in the error terms is rejected by the data.

Columns three and four in Table 2 provide FGLS estimates that correct for cross-sectional correlation and an AR( 1) process. The construction of these estimators was described in Section 11. The p value used to transform the vari- ables was calculated on the basis of a correlation coefficient between the residuals in the current period and the previous period. The residuals were obtained from the OLS regression equation of column one. The calculated p value was 0.8912.- A common AR(1) process was therefore assumed to exist across regions. Reilly and Witt (1990) report estimates based on separate p values for the different regions. Given that the time series employed only uses fifteen years of observations, the estimation of individual p values may be subject to the problems associated with small sample bias. The use of a single p value is thus viewed as more appropriate.

In using the Cochrane-Orcutt procedure, the unemployment coefficient is now only significant at the loolo level of significance using a two-tailed test. The magnitude of the coefficient is also reduced somewhat but the effect is still posi- tive. A negative coefficient is still reported on the flow of housing variable

'In order to capture dynamic effects, the model in column one was augmented by the inclusion of lagged values of the unemployment rate and crime rate. The estimated coefficients suggested poorly determined long-run effect which is not surprising, given the short time series available. A test for common factors was also carried out on the dynamic equation using a Wald statistic with one degree of freedom (see Kmenta, 1986, pp. 491-494). The estimated statistic was 0.7488 suggesting the existence of common factors. This finding provides some justification for using the Cochrane-Orcutt and Prais-Winsten procedures.

' A possible source of bias in the standard errors may be attributable to the presence of heteroscedasticity. White (1980) provides the appropriate test and in terms of the estimates reported in column 1, this is calculated as 11.24 which is a x' with five degrees of freedom. Since the critical value at the 5% level is 11.07, the null of homoscedasticity is just about rejected. The FGLS models of columns three and four provide a correction, among other things, for heteroscedasticity.

CRIME A N D UNEMPLOYMENT IN SCOTLAND 225

although it still remains insignificant at conventional levels of significance. The Prais-Winsten procedure, which uses all the sample points in estimation, reports a noticeably higher unemployment coefficient in column four. The effect is statistically significant at the 5% level using a two-tailed test. Both FGLS estimators produce unemployment coefficient estimates that are con- siderably smaller than those obtained when differing p values were assumed for each region. On the face of it, they are dimensionally sensible and in comport with most of the estimates reported in Table 2.

Estimates based on the LSDV (or fixed effects) model are reported in column 5. These estimates provide an opportunity to assess regional differences in terms of crime. The smallest effect is recorded for the Dumfries and Galloway region with the largest fixed effect reserved for, not surprisingly, the Strathclyde region. Hypothetically, if the unemployment rate. was zero and public housing completions per lo00 of the population were zero, the crime rate per 100 of the population in Strathclyde would be 4.2. A similar exercise for Dumfries and Galloway suggests a crime rate of only 0.914 per 100 of the population.

Though the above hypothetical exercise is a crude one it does, nevertheless, suggest that policies designed to reduce unemployment are not in themselves sufficient to reduce the crime rate. Other regional specific factors which may be less easy to quantify in economic terms are also playing a role. Numbered among these other factors are the lack of social facilities, lack of recreational facilities and poor housing facilities. Differences in the social infrastructure of a region can lead to differing degrees of anomy across regions. The fixed effects may be picking up these omitted factors.

Nevertheless, controlling for the fixed effects enhances the coefficient on the public housing variable which is now not only negative but also very well deter- mined. The coefficient on the unemployment variable retains its positive and robust character. The adjusted R2 rises to a respectable 0.9308.

An F-test can be employed to test whether the fixed effects are constant across regions, The F-test based on this exercise is distributed with 5 and 82 degrees of freedom. The test value is 77.7 and the hypothesis that the regional effects are the same is decisively rejected by the data. Thus, it can be concluded that there exists strong regional differences in terms of the fixed effects.

A casual examination of Table 1 appeared to suggest that the effect of unem- ployment on crime varied across regions. An F-test was used to test this hypothesis. Regional dummies were interacted with unemployment for five of the regions under consideration and added to the fixed effects model. The omitted interactive category was the Strathclyde region. The F-test value obtained was 5.283 and with 5 and 77 degrees of freedom, the null of constant unemployment effects is rejected by the data. Due to space limitations, these estimates are not reported here. However, the major regional differences appeared to be between Central and Strathclyde, and Grampian and Strathclyde.

Finally, column 6 reports estimates based on the random effects model. The estimation of this model is justified on the basis of the calculation of the LM2

226 BARRY REILLY AND ROB WITT

test. The calculated value for this statistic is 416.02. This suggests a decisive rejection of the null of no random effects. The coefficients associated with the random effects model are comparable to those of the LSDV model. The sign on the unemployment rate is positive and again robust. A negative and well determined sign is reported for the flow of public housing variable. As pointed out above, the Hausman test4 provides a test for the null of the

independence of the random effects from the unemployment and public housing regressors. The Hausman value is a x2 variate with two degrees of freedom (the two slope coefficients). The resultant value is O-OOOl which clearly fails to reject the null of independence. The random effects model can be clearly retained and offers an efficiency again over the LSDV model, though this is not apparent from the reported estimates for the standard errors in columns 5 and 6.

Despite the failure to reject the random effects model a question mark still hangs over its use in this particular study. In general, a favoured application of the random effects model would be in cases where the sampled cross- sectional units are drawn at random from a population. The cross-sectional units employed in this particular study cannot be said to satisfy this particular criterion. Nevertheless, the consistent nature of the results obtained using the LSDV model and the fixed effects model is heartening.

V

CONCLUSIONS

This paper has attempted to address the perennial question of the relationship between unemployment and crime. The econometric problems posed by auto- correlation, heteroscedasticity and cross-sectional correlation were addressed within the FGLS framework. Estimates based on a fixed effects model and an FGLS random effects model were also presented. Cross-sectional correlation in the errors of the crime rate equations was detected in the regional level data employed in this study. The presence, also, of both random effects and fixed effects across regions could not be rejected by the data.

Greene (1990) outlines the calculation of the Hausman test employed in this study. It is based on the idea that under the null of no correlation between random effects and the regressors the OLS estimates of the LSDV model and the FGLS estimates of the Random Effects model are consistent but OLS is inefficient. Under the alternative hypothesis of correla- tion between the random effects and the regressors, OLS is consistent but the FGLS is not. Therefore, under the null hypothesis of no correlation, the two estimates should not differ systematically and a test can be based on the difference. Following Greene (p. 495) the follow- ing Wald statistic is defined

w = [ b - f l ] v - " b - f l ] where b is the vector of slope coefficients from the LSDV model and f l is the vector of slope coefficients from the Random Effects model. V-' is the inverse of the difference between the LSDV variance covariance matrix and the random effects variance covariance matrix. The number of restrictions under test in this case is two, the slope coefficients, and the Wald is distributed as x 2 .

CRIME AND UNEMPLOYMENT IN SCOTLAND 227

The strongest finding in this paper was the extremely robust positive coefficient on the unemployment rate, a result which was invariant to the esti- mator used. The magnitude of this effect ranged from 0.15 to 0.35. In all cases but one this effect was significant at the 5% level using a two-tailed test. Thus, the general finding across the six estimates was for a strong well determined positive relationship between the crime rate and the unemployment rate.

The coefficient on the public housing completion variable was more sensitive across the estimators. Using both the random effects and the fixed effects models a negative and significant effect was detected. This is in line with one's priors. The exclusion of the flow of housing variable had no substantive impact on the unemployment coefficients reported in Table 2. Thus, the robustness of the relationship between crime and unemployment is not sensitive to the inclusion or exclusion of the flow of public housing variable.

However, even given the relatively robust relationship exhibited above, it must be stressed that the specification estimated is a relatively simple one. More complex factors omitted from the specification may have as important a role in determining the crime rate as unemployment. If these factors were quan- tifiable and available to the econometrician, then, it is conceivable that the effect of unemployment on crime could be diminished somewhat. Nevertheless, if these crucial omitted factors are either fixed or random across regions, then, one would expect the fixed effects model and the random effects model respect- ively to allow for them. It should be recalled that the strongest results obtained in Table 2 were for these two particular models.

A conclusion of this paper must be that unemployment cannot be dismissed as one (of perhaps a number) of the determinants of the crime rate in Scotland. It, therefore, follows that policies designed to reduce regional unemployment in Scotland could also lead to a diminution in the regional crime rate. The official view held by the Home Office and mediated through the Scottish Office is that there exists no relationship between unemployment and crime. The evidence presented in this paper does not appear to support this view.

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