- Email: [email protected]
New evidence from the misery index in the crime function
Economics Letters 102 (2009) 112–115
Contents lists available at ScienceDirect
Economics Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o n b a s e
New evidence from the misery index in the crime function Chor Foon Tang a, Hooi Hooi Lean b,⁎ a b
College of Arts and Sciences (Economics), Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia Economics Program, School of Social Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
a r t i c l e
i n f o
Article history: Received 2 October 2007 Received in revised form 20 November 2008 Accepted 22 November 2008 Available online 3 December 2008
a b s t r a c t We propose a parsimony model which is clear from multicollinearity and specification problems in the standard crime function. This study examines the relationship between the misery index and the crime rate in the Unites States from 1960 to 2005. © 2008 Elsevier B.V. All rights reserved.
Keywords: Cointegration UECM Multiple-rank F-test Misery index Crime
1. Introduction The unemployment–crime (U–C) hypothesis has been heatedly debated in the literature. Two theories have essentially rooted this countervailing relationship; they are the positive motivation effect and the negative opportunity effect. Becker (1968) postulated that unemployment is positively related to the crime rate because when an individual is unemployed, the marginal return from legitimate earning activities are lower than before, hence one is more likely to engage in criminal activities. Smith et al. (1992), and Carmichael and Ward (2001) also found the same positive relation between the two variables. On the other hand, Cantor and Land (1985) documented that unemployment and crime rates are in negative relationship because when people are unemployed, the expenditure on property and luxury goods are reduced. Furthermore, people prefer to be at home or stay close-by within the neighbourhood. Thus, they have more protection to their property and thus reducing the crime incidence. Box (1987) and Chiricos (1987) identified a mixture of results from various empirical studies on the U–C hypothesis. Allen (1996), and Narayan and Smyth (2004) also found a mixed result for different types of crime. A survey in the American inner cities reported that the inflation rate plays a crucial role on crime (see Curtis, 1981). Chungviwatanant (1981) found that the inflation rate in the United States is positively correlated with the crime rate. Devine et al. (1988) documented the basic notion that the inflation rate causes the crime rate to change
⁎ Corresponding author. Tel.: +60 604 653 2663; fax: +60 604 657 0918. E-mail address: [email protected] (H.H. Lean). 0165-1765/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2008.11.026
positively because hard economic times always motivate criminal behaviour and reduce the capacity of communities to deter crime. Similarly, Ralston (1999) found that inflation and crime rates are positively related. Deadman and MacDonald (2002) commented that
Table 1 The estimated UECM Dependent variable: ΔlnCRt Independent variable
Coefficient
t-Statistic
Constant lnCRt − 1 lnMIt − 1 ΔlnCRt − 1 ΔlnMIt ΔlnMIt − 1 ΔlnMIt − 2 ΔlnMIt − 3 Bounds test: F-statistics
0.670 −0.095 0.060 0.484 0.165 0.012 −0.092 −0.082 6.686⁎⁎
3.525⁎ −3.635⁎ 2.946⁎ 4.238⁎ 5.005⁎ 0.299 −2.465⁎⁎ −2.473⁎⁎
# Critical bounds (F-test):
Lower
Upper
1% 5% 10% Conclusion:
7.740 5.235 4.225 Cointegrated
8.650 6.135 5.020
Note: ⁎, ⁎⁎, ⁎⁎⁎denote significance at 1%, 5% and 10% level. #Unrestricted intercept or constant and no trend (k = 1 and T = 45) from Narayan (2005, pp. 1988). R-squared: 0.833; Adjusted R-squared: 0.799; F-Statistic: 24.297 (0.000) Jarque-Bera:1.136 (0.567); Ramsey RESET (1):8.15E-05 (0.993), (2): 0.084 (0.920); Breusch–Godfrey LM test (1):0.110 (0.740), (2):3.501 (0.174); ARCH test (1):0.036 (0.850), (2):0.293 (0.864) ( ) refer to p-value
C.F. Tang, H.H. Lean / Economics Letters 102 (2009) 112–115
113
Fig. 1. Plots of CUSUM and CUSUM of squares statistics for UECM.
the sustained period of economic growth, low inflation and unemployment in the United States had resulted in a fall in the crime rate for a short period of time. Teles (2004) found that if the quantity of money held by an economics agent affects the marginal utility of crime, then the inflation rate will affect the incidence of crime in the economy. Assuming that wages are constant, a rise of the inflation rate will reduce a person's purchasing power and the cost of living will be relatively higher than before. From the literature, it is clear that both unemployment and inflation rates explain the change in the crime rate via motivation and opportunity effects; however it does not provide clear evidence of those catalysts which have strong effects on and can exert the most influence on the crime rate. In other words, what is the net effect on crime? In addition, if these two variables are included into the crime model, it may lead to the occurrence of the multicollinearity problem1 (see Ralston, 1999, pp. 418). Furthermore, if we include the variables separately, we will lose valuable information and cause the misspecification problems. Thus, to avoid these mis-specification problems, we are motivated to take both unemployment and inflation rates together. In this study, we employ the misery index2, which is the unemployment rate plus the inflation rate to examine the crime function in the United States from 1960 to 2005. There are several advantages of using the misery index. First, it is able to examine both unemployment and inflation effects on crime with no multicollinearity problem. Second, it is able to examine the net effect of unemployment and inflation on the crime rate. Third, it may improve on the methodological flaws by earlier studies. This contributes to a new methodology to crime literature. 2. Data and methodology This study uses annual data of the misery index and the crime rate index from 1960 to 2005 in the United States extracted from the Department of Labour and Federal Bureau of Investigation Uniform Crime Report3 respectively.
The following double-log linear equation is estimated. lnCRt = α + βlnMIt + εt
ð1Þ
where lnCRt is the natural log of the crime rate index/100,000 population, lnMIt is the natural log of the misery index and εt are the residuals. The bounds test for cointegration is based on an estimation of the Unrestricted Error-Correction Model (UECM) as follows: p
q
i=1
j=0
ΔlnCRt = β 0 + π 1 lnCRt−1 + π 2 lnMIt−1 + ∑ λi ΔlnCRt−i + ∑ δj ΔlnMIt−j + μ t
ð2Þ To test the presence of long run relationship, we set H0:π1 = π2 = 0 versus H1:π1 ≠ π2 ≠ 0. We use the critical values provided by Narayan (2005) because the critical values in Pesaran et al. (2001) are inappropriate for small sample sizes. Gordon and Sakyi-Bekoe (1993), and Ansari et al. (1997) documented that the standard parametric causality tests by Granger (1969) and others are based on classical assumptions. Violation of these conditions will affect the causality conclusions. But, the nonparametric causality approach does not limit to these classical assumptions. Holmes and Hutton (1990) suggested an alternative procedure for causality testing based on the rank ordering (R) of each variable. This ranking approach is more robust than the conventional parametric approach. Furthermore, if the classical assumptions for Granger estimation are satisfied, the multiple-rank F-test results are similar to the Granger results. Otherwise, Holmes–Hutton procedure is superior to the Granger's test. The multiple-rank F-test is performed in the following ARDL model.4 Each variable is ranked and the ranked value of each observation is used to test for the causality relationship. The optimal lag lengths are selected by AIC criterion. p q RðlnCRt Þ = α + ∑ ui RðlnCRt−i Þ + ∑ /j R lnMIt−j + nt
ð3Þ
p q RðlnMIt Þ = β0 + ∑ ηi RðlnMIt−i Þ + ∑ γ j R lnCRt−j + mt
ð4Þ
i=1
i=1
j=1
j=1
1
According to the trade-off Phillips curve, when the unemployment rate is low, the inflation rate tends to be high and vice-versa (Phillips, 1958). 2 The misery index was initiated by Arthur Okun, an adviser to President Lyndon Johnson in the 1970's. It is simply the unemployment rate added to the inflation rate. It is assumed that a higher rate of unemployment and a worsening of inflation both create economic and social costs to the society. A combination of rising inflation and more people out of work imply deterioration in economic performance and a rise in the misery index (http://www.miseryindex.us/). 3 The crime rate index can be obtained from (http://www.disastercenter.com/crime/ uscrime.htm). The misery index can be obtained from (http://www.miseryindex.us/ indexbyyear.asp). Unreported correlation analysis shows that the misery index correlates more strongly to the inflation rate than the unemployment rate.
R(.) represents the rank order transformation, p and q are referred to the maximum lag order; ξt and vt are serially uncorrelated whitenoise residuals. From Eq. (3), ϕj ≠ 0∀j implies causality from the misery 4 We note that the standard Granger causality test uses VAR model to examine the causal link. In this study, we use the ARDL model due to the assumption that the nonuniform lag orders reflect the relationship better than the uniform lag order. We do not include the current variables (lnMIt & lnCRt)in the ARDL model because the present or future cannot cause the past (see Granger, 1969).
114
C.F. Tang, H.H. Lean / Economics Letters 102 (2009) 112–115
Table 2 Results of multiple-rank F-test causality test Null hypothesis
χ2- statistic
Misery index does not Granger-cause crime Crime does not Granger-cause misery index
4.870⁎ 1.591
Note:⁎, ⁎⁎, ⁎⁎⁎ denote significance at 1%, 5% and 10% level.
From Table 2, we find that the misery index (unemployment and inflation rates together) Granger causes the crime rate over the sample period. The result is consistent with Tang and Lean (2007) who found uni-directional causality from both inflation and unemployment rates to crime in the United States. Hence, the misery index is affirmed as an exogenous variable in the crime function.8 4. Conclusions
index to the crime rate; whereas in Eq. (4), crime Granger causes the misery index, if γj ≠ 0∀j. 3. Empirical results
This article examines the effect of both unemployment and inflation on crime by using one variable—the misery index. We propose a parsimony model which is clear from multicollinearity and mis-specification problems in the standard crime function. We find that the variables are cointegrated and the misery index is positively related to the crime rate. Moreover, the criminal motivation effect is stronger than the criminal opportunity effect and the misery index Granger causes the crime rate. We note that macroeconomic policies which are used to reduce the unemployment rate may not guarantee to reduce the crime rate correspondingly, because the decrease of the unemployment rate will indirectly increase the inflation rate (due to the trade-off Phillips curve effect) and may eventually increase the crime rate. We argue that policy directed to the misery index will tackle both effects together. This finding may shed some light to the policymakers in formulating policy to reduce crime rates based on the misery index. One may ask questions about the proportional impact of unemployment and inflation rate in the misery index. We argue that the supply-side economic policy which will reduce both rates simultaneously could be considered (see Tang and Lean, 2007).
We find that UECM (1,3) is the best model and the estimated results are presented in Table 1. All the estimated coefficients are significant at the 5% level except ΔlnMIt − 1. The UECM passes a numbers of diagnostic tests.5 The plots of CUSUM and CUSUM of Squares tests are always inside the 5% confident lines (Fig. 1). This implies that the estimated parameters in the UECM are stable over the analysis period. To examine the presence of long run relationship, we compute the F-statistics for the lagged level variables, lnCRt − 1 and lnMIt − 1 in Eq. (2). We find that the computed F-statistic (6.686) is greater than the 5% upper bounds critical value. This implies that the crime rate and the misery index are cointegrated. Cantor and Land (1985, 2001), Greenberg (2001), and Paternoster and Bushway (2001) documented that the criminal opportunity effect is a short run phenomenon while the motivational effect is a long run phenomenon. Bardsen's (1989) method is used to compute the short and long run coefficients. We find that the short run misery index coefficient is 0.003 but insignificant while the long run coefficient is 0.63 and statistically significant at the 1% level. These results show two remarkable conclusions. First, the positive sign of the short run coefficient shows that the opportunity effect may not exist in the United States over our analysis period. This is in harmony with the findings of Hale and Sabbagh (1991) that the changes of unemployment rates are positively related to the property crime rate. Second, the long run coefficient is bigger than the short run coefficient inferring that the motivational effect is stronger than the opportunity effect. As noted by Cantor and Land (1985, 2001), most workers have savings and welfare benefit to sustain them for some time after they lose a job. Same argument can be made here for the case of inflation and thus the misery index. In addition, we run separate regressions estimating the effects of (1) the unemployment rate, (2) the inflation rate and (3) both rates on crime. These additional regressions were compared with the result of the misery index.6 We found that only the inflation rate was cointegrated with a positive sign on short and long run coefficients. A plausible explanation is that the separate regression model may be mis-specified and cause unstable cointegration results (see Miller, 1991, pp. 144). He and Maekawa (2001) stated that F-statistics for Granger causality often leads to spurious causality results when one or both of the estimated series are non-stationary. We perform the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) unit root test to investigate the degree of integration7 and find that all variables are I(1). Thus, we monotonically transformed the first differenced variables into rank ordering R(.) to avoid spurious causality conclusion. The result for the multiple-rank F-test is reported in Table 2.
Allen, R.C., 1996. Socioeconomic conditions and property crime: a comprehensive review and test of the professional literature. American Journal of Economics and Sociology 55 (3), 293–308. Ansari, M.I., Gordon, D.V., Akuamoah, C., 1997. Keynes versus Wagner: public expenditure and national income for three African countries. Applied Economics 29, 543–550. Bardsen, G., 1989. Estimation of long run coefficients in error correction models. Oxford Bulletin of Economics and Statistics 51, 345–350. Becker, G., 1968. Crime and punishment: an economic approach. Journal of Political Economy 76, 1169–1271. Borland, J., Hunter, B., 2000. Does crime affect employment status? The case of Indigenous Australians. Economica 67, 123–144. Box, S., 1987. Recession, Crime and Punishment. Macmillan, London. Cantor, D., Land, K.C., 1985. Unemployment in crime rates I post World War II United States: a theoretical and empirical analysis. American Sociological Review 50, 317–332. Cantor, D., Land, K.C., 2001. Unemployment and crime rate fluctuations: a comment on Greenberg. Journal of Quantitative Criminology 17 (4), 329–341. Carmichael, F., Ward, R., 2001. Male unemployment and crime in England and Wales. Economics Letters 73, 111–115. Chiricos, T.G., 1987. Rates of crime and unemployment: an analysis of aggregate research evidence. Social Problems 34, 187–212. Chungviwatanant, S., 1981. Inflation and incidence of crime in the United States. Unpublished Ph.D Dissertation, United States International University. Curtis, L.A., 1981. Inflation, economic policy, and the inner city. Annals of the American Academy of Political and Social Science 456, 46–59. Deadman, D. and MacDonald, Z., 2002. Why has crime fallen? An economic perspective. Institute of Economic Affairs, Blackwell Publisher, 5–14.
5 The diagnostic tests confirm the error term is normally distributed (Jarque-Bera test), absent of heteroskedasticity (ARCH test), the Breusch-Godfrey LM test shows that the model is free from serial correlation problem. In addition, the model is correctly specified (Ramsey RESET test). 6 We thank the anonymous referee for the suggestion. Due to space constraint, the results are not reported here but are available upon request. 7 The KPSS results are available upon request.
8 It would be very surprising if the Granger causality runs the other way. However, Grogger (1992), and Borland and Hunter (2000) explained that a person who has been arrested and/or convicted of an offence might be stigmatised and/or discriminated by employers and thus reduce the likelihood of employment in the legal labour market.
Acknowledgements The authors would like to thank the anonymous referee and the editor for their insightful comments and suggestions. The usual disclaimer applies. References
C.F. Tang, H.H. Lean / Economics Letters 102 (2009) 112–115 Devine, J.A., Sheley, J.F., Smith, M.D., 1988. Macroeconomic and social-control policy influences on crime-rates changes, 1948–1985. American Sociological Review 53, 407–420. Gordon, D.V., Sakyi-Bekoe, K., 1993. Testing the export-growth hypothesis: some parametric and nonparametric results for Ghana. Applied Economics 25, 553–563. Granger, C.W.J., 1969. Investigating causal relations by econometric models and crossspectral methods. Econometrica 37, 428–438. Greenberg, D.F., 2001. Time series analysis of crime rates. Journal of Quantitative Criminology 17 (4), 291–327. Grogger, J., 1992. Arrests, persistence youth joblessness, and black/white employment differentials. Review of Economics and Statistics 74 (1), 100–106. Hale, C., Sabbagh, D., 1991. Testing the relationship between unemployment and crime: a methodological comment and empirical analysis using time series data from England and Wales. Journal of Research in Crime and Delinquency 28 (4), 400–417. He, Z., Maekawa, K., 2001. On spurious Granger causality. Economics Letters 73 (3), 307–313. Holmes, J.M., Hutton, P.A., 1990. On the causal relationship between government expenditure and national income. Reviews of Economics Statistics 72 (1), 87–95. Miller, S.M., 1991. Monetary dynamics: an application of cointegration and errorcorrection modelling. Journal of Money, Credit and Banking 23 (2), 139–154. Narayan, P.K., 2005. The saving and investment nexus for China: evidence from cointegration tests. Applied Economics 37, 1979–1990.
115
Narayan, P.K., Smyth, R., 2004. Crimes rates, male youth unemployment and real income in Australia: evidence from Granger causality tests. Applied Economics 36, 2079–2095. Paternoster, R., Bushway, S.D., 2001. Theoretical and empirical work on the relationship between unemployment and crime. Journal of Quantitative Criminology 17 (4), 391–407. Pesaran, M.H., Shin, Y., Smith, R.J., 2001. Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics 16, 289–326. Phillips, A.W.H., 1958. The relationship between unemployment and the rate of change of money wages in United Kingdom, 1861–1957. Economica 15, 283–300. Ralston, R.W., 1999. Economy and race: interactive determinants of property crime in the United States, 1958–1995. Reflection on the supply of property crime. American Journal of Economics and Sociology 58 (3), 405–434. Smith, M.D., Devine, J.A., Sheley, J.F., 1992. Crime and unemployment: effects across age and race categories. Sociological Perspective 35, 551–572. Tang, C.F., Lean, H.H., 2007. Will inflation increase crime rate? New evidence from bounds and modified Wald tests. Global Crime 8 (4), 311–323. Teles, V.K., 2004. The effects of macroeconomic policies on crime. Economics Bulletin 11 (1), 1–9.
Contents lists available at ScienceDirect
Economics Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o n b a s e
New evidence from the misery index in the crime function Chor Foon Tang a, Hooi Hooi Lean b,⁎ a b
College of Arts and Sciences (Economics), Universiti Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia Economics Program, School of Social Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
a r t i c l e
i n f o
Article history: Received 2 October 2007 Received in revised form 20 November 2008 Accepted 22 November 2008 Available online 3 December 2008
a b s t r a c t We propose a parsimony model which is clear from multicollinearity and specification problems in the standard crime function. This study examines the relationship between the misery index and the crime rate in the Unites States from 1960 to 2005. © 2008 Elsevier B.V. All rights reserved.
Keywords: Cointegration UECM Multiple-rank F-test Misery index Crime
1. Introduction The unemployment–crime (U–C) hypothesis has been heatedly debated in the literature. Two theories have essentially rooted this countervailing relationship; they are the positive motivation effect and the negative opportunity effect. Becker (1968) postulated that unemployment is positively related to the crime rate because when an individual is unemployed, the marginal return from legitimate earning activities are lower than before, hence one is more likely to engage in criminal activities. Smith et al. (1992), and Carmichael and Ward (2001) also found the same positive relation between the two variables. On the other hand, Cantor and Land (1985) documented that unemployment and crime rates are in negative relationship because when people are unemployed, the expenditure on property and luxury goods are reduced. Furthermore, people prefer to be at home or stay close-by within the neighbourhood. Thus, they have more protection to their property and thus reducing the crime incidence. Box (1987) and Chiricos (1987) identified a mixture of results from various empirical studies on the U–C hypothesis. Allen (1996), and Narayan and Smyth (2004) also found a mixed result for different types of crime. A survey in the American inner cities reported that the inflation rate plays a crucial role on crime (see Curtis, 1981). Chungviwatanant (1981) found that the inflation rate in the United States is positively correlated with the crime rate. Devine et al. (1988) documented the basic notion that the inflation rate causes the crime rate to change
⁎ Corresponding author. Tel.: +60 604 653 2663; fax: +60 604 657 0918. E-mail address: [email protected] (H.H. Lean). 0165-1765/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2008.11.026
positively because hard economic times always motivate criminal behaviour and reduce the capacity of communities to deter crime. Similarly, Ralston (1999) found that inflation and crime rates are positively related. Deadman and MacDonald (2002) commented that
Table 1 The estimated UECM Dependent variable: ΔlnCRt Independent variable
Coefficient
t-Statistic
Constant lnCRt − 1 lnMIt − 1 ΔlnCRt − 1 ΔlnMIt ΔlnMIt − 1 ΔlnMIt − 2 ΔlnMIt − 3 Bounds test: F-statistics
0.670 −0.095 0.060 0.484 0.165 0.012 −0.092 −0.082 6.686⁎⁎
3.525⁎ −3.635⁎ 2.946⁎ 4.238⁎ 5.005⁎ 0.299 −2.465⁎⁎ −2.473⁎⁎
# Critical bounds (F-test):
Lower
Upper
1% 5% 10% Conclusion:
7.740 5.235 4.225 Cointegrated
8.650 6.135 5.020
Note: ⁎, ⁎⁎, ⁎⁎⁎denote significance at 1%, 5% and 10% level. #Unrestricted intercept or constant and no trend (k = 1 and T = 45) from Narayan (2005, pp. 1988). R-squared: 0.833; Adjusted R-squared: 0.799; F-Statistic: 24.297 (0.000) Jarque-Bera:1.136 (0.567); Ramsey RESET (1):8.15E-05 (0.993), (2): 0.084 (0.920); Breusch–Godfrey LM test (1):0.110 (0.740), (2):3.501 (0.174); ARCH test (1):0.036 (0.850), (2):0.293 (0.864) ( ) refer to p-value
C.F. Tang, H.H. Lean / Economics Letters 102 (2009) 112–115
113
Fig. 1. Plots of CUSUM and CUSUM of squares statistics for UECM.
the sustained period of economic growth, low inflation and unemployment in the United States had resulted in a fall in the crime rate for a short period of time. Teles (2004) found that if the quantity of money held by an economics agent affects the marginal utility of crime, then the inflation rate will affect the incidence of crime in the economy. Assuming that wages are constant, a rise of the inflation rate will reduce a person's purchasing power and the cost of living will be relatively higher than before. From the literature, it is clear that both unemployment and inflation rates explain the change in the crime rate via motivation and opportunity effects; however it does not provide clear evidence of those catalysts which have strong effects on and can exert the most influence on the crime rate. In other words, what is the net effect on crime? In addition, if these two variables are included into the crime model, it may lead to the occurrence of the multicollinearity problem1 (see Ralston, 1999, pp. 418). Furthermore, if we include the variables separately, we will lose valuable information and cause the misspecification problems. Thus, to avoid these mis-specification problems, we are motivated to take both unemployment and inflation rates together. In this study, we employ the misery index2, which is the unemployment rate plus the inflation rate to examine the crime function in the United States from 1960 to 2005. There are several advantages of using the misery index. First, it is able to examine both unemployment and inflation effects on crime with no multicollinearity problem. Second, it is able to examine the net effect of unemployment and inflation on the crime rate. Third, it may improve on the methodological flaws by earlier studies. This contributes to a new methodology to crime literature. 2. Data and methodology This study uses annual data of the misery index and the crime rate index from 1960 to 2005 in the United States extracted from the Department of Labour and Federal Bureau of Investigation Uniform Crime Report3 respectively.
The following double-log linear equation is estimated. lnCRt = α + βlnMIt + εt
ð1Þ
where lnCRt is the natural log of the crime rate index/100,000 population, lnMIt is the natural log of the misery index and εt are the residuals. The bounds test for cointegration is based on an estimation of the Unrestricted Error-Correction Model (UECM) as follows: p
q
i=1
j=0
ΔlnCRt = β 0 + π 1 lnCRt−1 + π 2 lnMIt−1 + ∑ λi ΔlnCRt−i + ∑ δj ΔlnMIt−j + μ t
ð2Þ To test the presence of long run relationship, we set H0:π1 = π2 = 0 versus H1:π1 ≠ π2 ≠ 0. We use the critical values provided by Narayan (2005) because the critical values in Pesaran et al. (2001) are inappropriate for small sample sizes. Gordon and Sakyi-Bekoe (1993), and Ansari et al. (1997) documented that the standard parametric causality tests by Granger (1969) and others are based on classical assumptions. Violation of these conditions will affect the causality conclusions. But, the nonparametric causality approach does not limit to these classical assumptions. Holmes and Hutton (1990) suggested an alternative procedure for causality testing based on the rank ordering (R) of each variable. This ranking approach is more robust than the conventional parametric approach. Furthermore, if the classical assumptions for Granger estimation are satisfied, the multiple-rank F-test results are similar to the Granger results. Otherwise, Holmes–Hutton procedure is superior to the Granger's test. The multiple-rank F-test is performed in the following ARDL model.4 Each variable is ranked and the ranked value of each observation is used to test for the causality relationship. The optimal lag lengths are selected by AIC criterion. p q RðlnCRt Þ = α + ∑ ui RðlnCRt−i Þ + ∑ /j R lnMIt−j + nt
ð3Þ
p q RðlnMIt Þ = β0 + ∑ ηi RðlnMIt−i Þ + ∑ γ j R lnCRt−j + mt
ð4Þ
i=1
i=1
j=1
j=1
1
According to the trade-off Phillips curve, when the unemployment rate is low, the inflation rate tends to be high and vice-versa (Phillips, 1958). 2 The misery index was initiated by Arthur Okun, an adviser to President Lyndon Johnson in the 1970's. It is simply the unemployment rate added to the inflation rate. It is assumed that a higher rate of unemployment and a worsening of inflation both create economic and social costs to the society. A combination of rising inflation and more people out of work imply deterioration in economic performance and a rise in the misery index (http://www.miseryindex.us/). 3 The crime rate index can be obtained from (http://www.disastercenter.com/crime/ uscrime.htm). The misery index can be obtained from (http://www.miseryindex.us/ indexbyyear.asp). Unreported correlation analysis shows that the misery index correlates more strongly to the inflation rate than the unemployment rate.
R(.) represents the rank order transformation, p and q are referred to the maximum lag order; ξt and vt are serially uncorrelated whitenoise residuals. From Eq. (3), ϕj ≠ 0∀j implies causality from the misery 4 We note that the standard Granger causality test uses VAR model to examine the causal link. In this study, we use the ARDL model due to the assumption that the nonuniform lag orders reflect the relationship better than the uniform lag order. We do not include the current variables (lnMIt & lnCRt)in the ARDL model because the present or future cannot cause the past (see Granger, 1969).
114
C.F. Tang, H.H. Lean / Economics Letters 102 (2009) 112–115
Table 2 Results of multiple-rank F-test causality test Null hypothesis
χ2- statistic
Misery index does not Granger-cause crime Crime does not Granger-cause misery index
4.870⁎ 1.591
Note:⁎, ⁎⁎, ⁎⁎⁎ denote significance at 1%, 5% and 10% level.
From Table 2, we find that the misery index (unemployment and inflation rates together) Granger causes the crime rate over the sample period. The result is consistent with Tang and Lean (2007) who found uni-directional causality from both inflation and unemployment rates to crime in the United States. Hence, the misery index is affirmed as an exogenous variable in the crime function.8 4. Conclusions
index to the crime rate; whereas in Eq. (4), crime Granger causes the misery index, if γj ≠ 0∀j. 3. Empirical results
This article examines the effect of both unemployment and inflation on crime by using one variable—the misery index. We propose a parsimony model which is clear from multicollinearity and mis-specification problems in the standard crime function. We find that the variables are cointegrated and the misery index is positively related to the crime rate. Moreover, the criminal motivation effect is stronger than the criminal opportunity effect and the misery index Granger causes the crime rate. We note that macroeconomic policies which are used to reduce the unemployment rate may not guarantee to reduce the crime rate correspondingly, because the decrease of the unemployment rate will indirectly increase the inflation rate (due to the trade-off Phillips curve effect) and may eventually increase the crime rate. We argue that policy directed to the misery index will tackle both effects together. This finding may shed some light to the policymakers in formulating policy to reduce crime rates based on the misery index. One may ask questions about the proportional impact of unemployment and inflation rate in the misery index. We argue that the supply-side economic policy which will reduce both rates simultaneously could be considered (see Tang and Lean, 2007).
We find that UECM (1,3) is the best model and the estimated results are presented in Table 1. All the estimated coefficients are significant at the 5% level except ΔlnMIt − 1. The UECM passes a numbers of diagnostic tests.5 The plots of CUSUM and CUSUM of Squares tests are always inside the 5% confident lines (Fig. 1). This implies that the estimated parameters in the UECM are stable over the analysis period. To examine the presence of long run relationship, we compute the F-statistics for the lagged level variables, lnCRt − 1 and lnMIt − 1 in Eq. (2). We find that the computed F-statistic (6.686) is greater than the 5% upper bounds critical value. This implies that the crime rate and the misery index are cointegrated. Cantor and Land (1985, 2001), Greenberg (2001), and Paternoster and Bushway (2001) documented that the criminal opportunity effect is a short run phenomenon while the motivational effect is a long run phenomenon. Bardsen's (1989) method is used to compute the short and long run coefficients. We find that the short run misery index coefficient is 0.003 but insignificant while the long run coefficient is 0.63 and statistically significant at the 1% level. These results show two remarkable conclusions. First, the positive sign of the short run coefficient shows that the opportunity effect may not exist in the United States over our analysis period. This is in harmony with the findings of Hale and Sabbagh (1991) that the changes of unemployment rates are positively related to the property crime rate. Second, the long run coefficient is bigger than the short run coefficient inferring that the motivational effect is stronger than the opportunity effect. As noted by Cantor and Land (1985, 2001), most workers have savings and welfare benefit to sustain them for some time after they lose a job. Same argument can be made here for the case of inflation and thus the misery index. In addition, we run separate regressions estimating the effects of (1) the unemployment rate, (2) the inflation rate and (3) both rates on crime. These additional regressions were compared with the result of the misery index.6 We found that only the inflation rate was cointegrated with a positive sign on short and long run coefficients. A plausible explanation is that the separate regression model may be mis-specified and cause unstable cointegration results (see Miller, 1991, pp. 144). He and Maekawa (2001) stated that F-statistics for Granger causality often leads to spurious causality results when one or both of the estimated series are non-stationary. We perform the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) unit root test to investigate the degree of integration7 and find that all variables are I(1). Thus, we monotonically transformed the first differenced variables into rank ordering R(.) to avoid spurious causality conclusion. The result for the multiple-rank F-test is reported in Table 2.
Allen, R.C., 1996. Socioeconomic conditions and property crime: a comprehensive review and test of the professional literature. American Journal of Economics and Sociology 55 (3), 293–308. Ansari, M.I., Gordon, D.V., Akuamoah, C., 1997. Keynes versus Wagner: public expenditure and national income for three African countries. Applied Economics 29, 543–550. Bardsen, G., 1989. Estimation of long run coefficients in error correction models. Oxford Bulletin of Economics and Statistics 51, 345–350. Becker, G., 1968. Crime and punishment: an economic approach. Journal of Political Economy 76, 1169–1271. Borland, J., Hunter, B., 2000. Does crime affect employment status? The case of Indigenous Australians. Economica 67, 123–144. Box, S., 1987. Recession, Crime and Punishment. Macmillan, London. Cantor, D., Land, K.C., 1985. Unemployment in crime rates I post World War II United States: a theoretical and empirical analysis. American Sociological Review 50, 317–332. Cantor, D., Land, K.C., 2001. Unemployment and crime rate fluctuations: a comment on Greenberg. Journal of Quantitative Criminology 17 (4), 329–341. Carmichael, F., Ward, R., 2001. Male unemployment and crime in England and Wales. Economics Letters 73, 111–115. Chiricos, T.G., 1987. Rates of crime and unemployment: an analysis of aggregate research evidence. Social Problems 34, 187–212. Chungviwatanant, S., 1981. Inflation and incidence of crime in the United States. Unpublished Ph.D Dissertation, United States International University. Curtis, L.A., 1981. Inflation, economic policy, and the inner city. Annals of the American Academy of Political and Social Science 456, 46–59. Deadman, D. and MacDonald, Z., 2002. Why has crime fallen? An economic perspective. Institute of Economic Affairs, Blackwell Publisher, 5–14.
5 The diagnostic tests confirm the error term is normally distributed (Jarque-Bera test), absent of heteroskedasticity (ARCH test), the Breusch-Godfrey LM test shows that the model is free from serial correlation problem. In addition, the model is correctly specified (Ramsey RESET test). 6 We thank the anonymous referee for the suggestion. Due to space constraint, the results are not reported here but are available upon request. 7 The KPSS results are available upon request.
8 It would be very surprising if the Granger causality runs the other way. However, Grogger (1992), and Borland and Hunter (2000) explained that a person who has been arrested and/or convicted of an offence might be stigmatised and/or discriminated by employers and thus reduce the likelihood of employment in the legal labour market.
Acknowledgements The authors would like to thank the anonymous referee and the editor for their insightful comments and suggestions. The usual disclaimer applies. References
C.F. Tang, H.H. Lean / Economics Letters 102 (2009) 112–115 Devine, J.A., Sheley, J.F., Smith, M.D., 1988. Macroeconomic and social-control policy influences on crime-rates changes, 1948–1985. American Sociological Review 53, 407–420. Gordon, D.V., Sakyi-Bekoe, K., 1993. Testing the export-growth hypothesis: some parametric and nonparametric results for Ghana. Applied Economics 25, 553–563. Granger, C.W.J., 1969. Investigating causal relations by econometric models and crossspectral methods. Econometrica 37, 428–438. Greenberg, D.F., 2001. Time series analysis of crime rates. Journal of Quantitative Criminology 17 (4), 291–327. Grogger, J., 1992. Arrests, persistence youth joblessness, and black/white employment differentials. Review of Economics and Statistics 74 (1), 100–106. Hale, C., Sabbagh, D., 1991. Testing the relationship between unemployment and crime: a methodological comment and empirical analysis using time series data from England and Wales. Journal of Research in Crime and Delinquency 28 (4), 400–417. He, Z., Maekawa, K., 2001. On spurious Granger causality. Economics Letters 73 (3), 307–313. Holmes, J.M., Hutton, P.A., 1990. On the causal relationship between government expenditure and national income. Reviews of Economics Statistics 72 (1), 87–95. Miller, S.M., 1991. Monetary dynamics: an application of cointegration and errorcorrection modelling. Journal of Money, Credit and Banking 23 (2), 139–154. Narayan, P.K., 2005. The saving and investment nexus for China: evidence from cointegration tests. Applied Economics 37, 1979–1990.
115
Narayan, P.K., Smyth, R., 2004. Crimes rates, male youth unemployment and real income in Australia: evidence from Granger causality tests. Applied Economics 36, 2079–2095. Paternoster, R., Bushway, S.D., 2001. Theoretical and empirical work on the relationship between unemployment and crime. Journal of Quantitative Criminology 17 (4), 391–407. Pesaran, M.H., Shin, Y., Smith, R.J., 2001. Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics 16, 289–326. Phillips, A.W.H., 1958. The relationship between unemployment and the rate of change of money wages in United Kingdom, 1861–1957. Economica 15, 283–300. Ralston, R.W., 1999. Economy and race: interactive determinants of property crime in the United States, 1958–1995. Reflection on the supply of property crime. American Journal of Economics and Sociology 58 (3), 405–434. Smith, M.D., Devine, J.A., Sheley, J.F., 1992. Crime and unemployment: effects across age and race categories. Sociological Perspective 35, 551–572. Tang, C.F., Lean, H.H., 2007. Will inflation increase crime rate? New evidence from bounds and modified Wald tests. Global Crime 8 (4), 311–323. Teles, V.K., 2004. The effects of macroeconomic policies on crime. Economics Bulletin 11 (1), 1–9.