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GLOBAL CRIME VOLUME 8 NUMBER (NOVEMBER 200) Will Inflation Increase Crime Rate? New Evidence from Bounds and Modified Wald Tests Chor Foon Tang & Hooi Hooi Lean This paper employs the modified Wald (MWALD) causality test to re-examine the relationship between crime and its determinants (inflation and unemployment) in the United States from 1960 to 2005. Bounds test approach is employed to investigate the existence of a long-run relationship. The empirical evidence suggests that inflation and crime rates are cointegrated with a positive relationship. Moreover, the causal link is from inflation and unemployment to crime. Keywords cointegration; MWALD; inflation; crime; JEL Classification Code C22; E31 Introduction Empirical studies on the relationship between unemployment and crime (U C) is an old issue in the social sciences literature. There have been many studies on the U C hypothesis, among them are Becker, 1 Freeman, 2 Carmichael and Ward. 3 Chor Foon Tang obtained his Master of Economics Management from Universiti Sains Malaysia and is currently a consultant with Media Utara Resources Enterprise. Hooi Hooi Lean is currently a lecturer with the School of Social Sciences, Universiti Sains Malaysia. She obtained her PhD from the National University of Singapore. She is also an active researcher with Asian Business and Economics Research Unit (ABERU) of Monash University, Australia. Dr Lean has written extensively and published her research in major international journals such as Applied Economics, Journal of Financial Markets, Journal of Multinational Financial Management, Pacific Basin Finance Journal, Mathematics and Computers in Simulation and Tourism Economics. In 200, she was awarded the ASEAN-ROK Academic Exchange Fellowship. Correspondence to: Hooi Hooi Lean, School of Social Sciences, Universiti Sains Malaysia 11800 USM, Penang, Malaysia. Tel: 60-653 2663. Fax: 60-65 0918. Email: hooilean@usm.my 1. Becker, G. (1968) Crime and Punishment: An Economic Approach, Journal of Political Economy, vol. 6, pp. 1169 121 2. Freeman, R. B. (1980) Crime and Unemployment, in Crime and Public Policy, ed. Wilson, J. Q., ICS Press, San Francisco, pp. 89 106. 3. Carmichael, F. & Ward, R. (2001) Male unemployment and crime in England and Wales, Economics Letters, vol. 3, pp. 111 115. ISSN 1-052 print/1-0580 online /0/00311-323 q 200 Taylor & Francis DOI: 10.1080/1050013969
312 TANG & LEAN Besides, Masih and Masih and Narayan and Smyth 5 etc. have adopted econometrics techniques like Granger causality and cointegration tests to study the relationship. However, Cantor and Land 6 quoted that the strong U C relationship has been hypothesized over a century in the social sciences literature. Allen added that by stressing on unemployment, crime theory generally ignores the effects of inflation on criminal activities. Brenner 8,9,10,11 indicated that the basic idea of a positive U C relationship is that an individual is unable to maintain a particular standard of living as consequence of unemployment and he/she is likely to indulge in criminal activities. Therefore, unemployment is a shock effect that causes an individual to engage in criminal activities. On the other hand, inflation causes the purchasing power to reduce and cost of living to increase. As a result crime rate may increase because an individual is unable to maintain his/her standard of living as before. However, this phenomenon does not happen immediately because it takes time for inflation to gradually reduce the purchasing power. In the literature, several studies have observed the crucial effect of inflation on crime. 12,13,1 However, the focus of. Masih, A. M. M. & Masih, R. (1996) Temporal Causality and the Dynamics of Different Categories of Crime and their Socioeconomics Determinants: Evidence from Australia, Applied Economics, vol. 28, pp. 1093 110. 5. Narayan, P. K. & Smyth, R. (200) Crimes Rates, Male Youth Unemployment and Real Income in Australia: Evidence from Granger Causality Tests, Applied Economics, vol. 36, no. 18, pp. 209 2095. 6. Cantor, D. & Land, K. (1985) Unemployment in Crime Rates I Post World War II United States: A Theoretical and Empirical Analysis, American Sociological Review, vol. 50, pp. 31 332.. Allen, R. C. (1996) Socioeconomic Conditions and Property Crime: A Comprehensive Review and Test of the Professional Literature, American Journal of Economics and Sociology, vol. 55, no. 3, pp. 293 308 8. Brenner, H. M. (191) Time Series Analysis of Relationships Between Selected Economic and Social Indicators, vol. I. Final Report on Contact no. 81-0-62-22. US Department of Labor, Manpower Administration. 9. Brenner, H. M. (196) Estimating the Social Costs of National Economic Policy: Implications for Mental and Physical Health and Criminal Aggression. Paper no. 5, Joint Economic Committee, Congress of the United States, US Government Printing Office, Washington, DC. 10. Brenner, H. M. (198a) Crime in Society, in Economic Crises and Crime, eds L. Savitz & N. Johnston, Wiley, New York, pp. 555 52. 11. Brenner, H. M. (198b) Impact of Economic Indicators on Crime Indices, pp. 20 5. in Unemployment and Crime. Hearings before the Subcommittee on Crime of the Committee on the Judiciary, US House of Representatives. Serial no.. 12. Curtis, L. A. (1981) Inflation, economic policy, and the inner city, Annals of the American Academy of Political and Social Science, vol. 56, pp. 6 59. 13. 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, vol. 58, no. 3, pp. 05 3. 1. Teles, V. K. (200) The Effects of Macroeconomic Policies on Crime, Economics Bulletin, vol. 11, no. 1, pp. 1 9.
WILL INFLATION INCREASE CRIME RATE? 313 these studies is only on explaining the relationship and they do not provide any empirical evidence for the causal relation. Recently, Bunge, Johnson and Baldé 15 found that crime rate and socio-economic indicators 16 are moving in the same direction, but they did not test the causal link between them. A survey in the American inner cities reported that crime was not merely affected by unemployment but inflation rate also played a crucial role in crime. 12 Chungviwatanant 1 found that the inflation rate in United States was positively correlated with crime rate, particularly for property, robbery and violent crime rate. Assuming the wages is constant, rise of inflation rate will reduce a person s purchasing power and the cost of living will be relatively higher (or an individual is relatively poorer) than before. Hence, an individual is likely to engage in criminal activities to maintain or/and improve his/her purchasing power. Long and Witte 18 documented that crime rate increases as inflation rate rises because hard times motivate criminal behaviours and inflation inhibits the capacity of communities to deter crime. Devine, Sheley and Smith 19 documented three factors that create a positive inflation to crime relationship. First, because of the lag between price and wage adjustments, inflation lowers the real income of low-skilled labour. Conversely, inflation rewards property criminals due to the rising demand and subsequent high profits in the illegal market. Second, inflation destroys the confidence in the existing institutions arrangements, resulting in a loss of social control. Third, inflation erodes the economic ability of communities to maintain real level for deterrence. Lott 20 postulated that the poor are more likely to commit crime due to their relatively limited access to capital markets and property crime is a method of borrowing against future human capital for poor people. Deutsch, Spiegel and Templeman 21 added that poor people are more likely to engage in crime because the cost of engaging in crime is less for low-income people than for high-income people who have more wealth to lose. Thus, the willingness to engage in criminal activities is greater for the poor than for the rich. In a more recent paper, Deadman and MacDonald 22 commented that a sustained period of economic growth, low inflation and unemployment in the United States has 15. Bunge, V. R., Johnson, H. & Baldé, T. A. (2005) Exploring Crime Pattern in Canada, Crime and Justice Research Paper Series. 16. Socio-economic indicators include age structure of population, unemployment, inflation and per capita alcohol consumption. 1. Chungviwatanant, S. (1981) Inflation and Incidence of Crime in the United States. Unpublished PhD Dissertation, United States International University. 18. Long, S. & Witte, A. D. (1981) Current Economic Trends: Implications for Crime and Criminal Justice, in Crime and Criminal Justice in a Declining Economy, ed. K. Wright, Oelgeschlager, Gunn and Hain, Cambridge, MA. 19. Devine, J. A., Sheley, J. F. & Smith, M. D. (1988) Macroeconomic and Social-control Policy Influences on Crime-rates Changes, 198 1985, American Sociological Review, vol. 53, pp. 0 20. 20. Lott, J. R. (1990) A Transaction-cost Explanation for Why the Poor are More Likely to Commit Crime Journal of Legal Studies, vol. 19, pp. 23 25. 21. Deutsch, J., Spiegel, R. & Templeman, J. (1992) Crime and Economic Inequality: An Economic Approach, Atlantic Economic Journal, vol 20, no., pp. 5 5. 22. Deadman, D. & MacDonald, Z. (2002) Why has Crime Fallen? An Economic Perspective, Institute of Economic Affairs, Blackwell Publisher, pp. 5 1.
31 TANG & LEAN resulted in a fall in the crime rate. However, this is usually for a short period only. The reduction in property crime rate is due to the implementation of punishment and new technology like CCTV. Teles 1 constructed an intertemporal general equilibrium model with micro-fundamentals to explain the relationship between macroeconomic policies and criminal activities. The author found that if the quantity of money held by an economic agent affects the marginal utility of crime, then inflation rate will affect the incidence of crime in economy. We note that there are many possible causes for crime. However, the objective of this study is to examine the shock effect on crime with particular focus on the impact of inflation on crime function. The major contribution of this study is the employment of the newly developed cointegration and causality tests to reexamine the relationship between inflation and crime rates in the United States. Specifically, we use the bounds testing approach for cointegration developed by Pesaran, Shin and Smith 23 and modified Wald (MWALD) test developed by Toda and Yamamoto 2 and Dolado and Lütkepohl, 25 hereafter TYDL, to fill the gap in the previous empirical works. Narayan and Narayan 26 and Narayan and Smyth 2 noted that the bounds testing approach has superior small samples properties. Mah, 28 Tang and Nair 29 documented that the conventional cointegration techniques such as Engle and Granger technique 30 and Johansen and Juselius technique 31 require the knowledge of the degree of integration of the underlying variables and thus pre-testing for determining the order of integration is necessary. Since, unit root test suffers from the problem of low power, especially in the finite sample study; the results achieved by the conventional cointegration tests might be misleading because they push the short-run dynamics into the residual term as in the Engle Granger approach. 28,32 However, both bounds testing and TYDL approaches do not require any pre-testing for unit roots. 23. Pesaran, M. H., Shin, Y. & Smith, R. J. (2001) Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics, vol. 16, pp. 289 326. 2. Toda, H. Y. & Yamamoto, T. (1995) Statistical Inference in Vector Autoregressions with Possibly Integrated Processes, Journal of Econometrics, vol. 66, pp. 225 250. 25. Dolado, J. J. & Lütkepohl, H. (1996) Making Wald Tests Work for Cointegrated VAR System, Econometric Reviews, vol. 15, pp. 369 386. 26. Narayan, S. & Narayan, P. K. (2005) A Empirical Analysis of Fiji s Import Demand Function, Journal of Economic Studies, vol. 32, no. 2, pp. 158 168. 2. Narayan, P. K. & Smyth, R. (2006) Higher Education, Real Income and Real Investment in China: Evidence from Granger Causality Tests, Education Economics, vol. 1, no. 1, pp. 10 125 28. Mah, J. (2000) An Empirical Examination of the Disaggregated Import Demand of Korea: The Case of Information Technology Products, Journal of Asian Economics, vol. 11, pp. 23 2. 29. Tang, T. C. & Nair, M. (2002) A Cointegration Analysis of Malaysia Import Demand Function: Reassessment from Bounds Test, Applied Economics Letters, vol. 9, pp. 293 296. 30. Engle, R. F. & Granger, C. W. J. (198) Co-integration and Error Correction: Representation, Estimation and Testing, Econometrica, vol. 55, no. 2, pp. 251 26. 31. Johansen, S. & Juselius, K. (1990) Maximum Likelihood Estimation and Inference on Cointegration with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics, vol. 52, pp.169 210. 32. Pattichis, C. A. (1999) Price and Income Elasticities of Disaggregated Import Demand: Results from UECMs and an Application, Applied Economics, vol. 31, pp. 1061 101.
WILL INFLATION INCREASE CRIME RATE? 315 The remainder of this paper is set as follows. Section II briefly discusses the data and model specification used in this study. The empirical results are reported in Section III and Section IV concludes. Data and Model Specification This study uses annual data of consumer price index (CPI), unemployment rate and crime rate index from 1960 to 2005 in United States extracted from the International Financial Statistics (IFS), Department of Labour and Federal Bureau of Investigation (FBI) Uniform Crime Report 33, respectively. Annual data are applied to avoid biases in seasonally adjusted data. Hakkio and Rush 3 documented that cointegration is a long-run concept and hence requires longspan data to get more power than merely using large numbers of observations from high-frequency data. Although any interpolation techniques that are used to increase the frequency of data will improve the result of cointegration, 35 Alias and Tang 36 argued that using raw data in empirical studies results in lesser measurement errors than interpolated series. In order to examine the impact of inflation on crime function in the United States by controlling unemployment rate 3, the following log-linear equation is estimated: In CR t ¼ a þ b 1 INF t þ b 2 UR t þ 1 t ð1þ where In CR t is the natural log of crime rate index per 100,000 population, INF t is the inflation rate computed by CPI (2000 ¼ 100) and UR t represents the unemployment rate. We use the bounds testing approach to test the existence of a long-run relationship between crime and its determinants. If the variables are cointegrated, the long-run and short-run coefficients can be derived by Bardsen 38 procedure. To implement the bounds test approach, the following unrestricted error-correction model (UECM) equation is estimated. Dln CR t ¼ a 1 þ p 1 ln CR t21 þ p 2 INF t21 þ p 3 UR t21 þ Xp d i Dln CR t2i þ Xq j¼0 l j DINF t2j þ Xr k¼0 f k DUR t2k þ j t i¼i ð2þ 33. The crime rate index is obtained from http://www.disastercenter.com/crime/uscrime.htm 3. Hakkio, C. S. & Rush, M. (1991) Cointegration: How Short is the Long Run? Journal of International Money and Finance, vol. 10, no., pp. 51 581. 35. Zhou, S. (2001) The Power of Cointegration Tests Versus Data Frequency and Time Spans, Southern Economic Journal, vol. 6, no., pp. 906 921. 36. Alias, M. H. & Tang, T. C. (2000) Aggregate Import and Expenditure Components in Malaysia: A Cointegration and Error Correction Analysis, ASEAN Economic Bulletin, vol. 1, no. 3, pp. 25 269. 3. We thank the anonymous referee for the suggestion. We note that there are many control variables for crime, but due to the limited availability of data, we include only the unemployment rate in the study. 38. Bardsen, G. (1989) Estimation of Long Run Coefficients in Error Correction Models, Oxford Bulletin of Economics and Statistics, vol. 51, pp. 35 350
316 TANG & LEAN where p 1, p 2 and p 3 are the long-run parameters; a 1 and j t are the constant and error term, respectively. The existence of a long-run relationship is tested by restricting the lagged level variables ln CR t21, INF t21 and UR t21 in Equation 2. It is a joint significance F-test for the null hypothesis of no cointegrating relation ðh 0 : p 1 ¼ p 2 ¼ p 3 ¼ 0Þ against the alternative hypothesis of a cointegrating relation ðh 1 : p 1 p 2 p 3 0Þ. We are aware that the critical values provided by Pesaran, Shin and Smith 23 are not suitable for our small sample size and we choose to use the small sample critical values provided by Narayan. 39 If the computed F-statistics exceeds the respective upper critical bounds value, we conclude that the variables are cointegrated. If the F-statistics falls below the respective lower critical bounds, we fail to reject the null hypothesis of no cointegrating relationship. If the F-statistics falls between its upper and lower critical bounds values, the inference is inconclusive. 0 In addition, we employ the conventional cointegration techniques such as Johansen and Juselius 31 and Gregory and Hansen 1 tests. These additional econometric exercises are vital to compare the result of bounds tests with that of the conventional tests. The testing procedure and result for Gregory and Hansen 1 cointegration test are cited in Appendix. Empirical Results The estimated UECM and the F-statistics for bounds cointegration test and their critical values are presented in Table 1. From the estimated UECM in Table 1, we find that most estimated coefficients are statistically significant at the conventional level and the F-statistics for bounds test is greater than the 10% upper bound critical values. This indicates that there is a long-run relationship between the crime rate and inflation and unemployment rates in the United States from 1960 to 2005. Thus, we conclude that the inflation and unemployment rates are moving together with the crime rate to achieve their long-run equilibrium; even they might deviate in the short run. Moreover, the estimated model passes a battery of diagnostic tests. 2 Furthermore, the plot of CUSUM and CUSUM of squares tests values always stay within 5% confidence lines (Figure 1). 3 This implies that the estimated parameters are stable over the sample period. 39. Narayan, P. K. (2005) The Saving and Investment Nexus for China: Evidence from Cointegration Tests, Applied Economics, vol. 3, pp. 199 1990. 0. Pesaran, Shin and Smith 23 suggest that the order of integration for the series must be known before any conclusion can be drawn. 1. Gregory, A. W. & Hansen, B. E. (1996) Residual-based Tests for Cointegration in Models with Regime Shift, Journal of Econometrics, vol. 0, pp. 99 126. 2. The diagnostic tests confirm that the residuals have normal distribution (Jarque Bera test), no heteroskedasticity problem (ARCH test) and are absent from serial correlation (Breusch Godfrey LM test). The Ramsey RESET tests show no specification errors for the estimated model. 3. We noted that, in the presence of lagged dependent variables, the confidence lines for the CUSUM and CUSUM of squares tests are incorrect. However, this could not be discarded as a useless stability test.
Table 1 The estimated UECM Dependent variable: Dln CR t Method: Ordinary least squared Sample(adjusted): 1963 2005 WILL INFLATION INCREASE CRIME RATE? 31 Variable Coefficient t-statistic Constant 0.668 3.01* ln CR t21 20.08 23.826* INF t21 0.003 1.05 UR t21 0.010 1.953** 0.3.056* DINF t 0.015.589* DUR t 0.012 1.66 DUR t21 20.010 21.*** DUR t22 20.015 22.800* Bounds test F-statistics 5.116*** # Critical bounds (F-test): Lower Upper 1% 5.920.19 5%.083 5.20 10% 3.330.3 Conclusion Cointegrated Note: The asterisks *, **, *** denote significant at 1, 5 and 10% levels. #Unrestricted intercept or constant and no trend (k ¼ 2 and T ¼ 5) from Narayan (2005, pp. 1988). 39 R 2 : 0.830; F-statistic: 20.851 (0.000); Jarque Bera: 1.55 (0.55); Ramsey RESET [1]: 0.096 (0.5), [2]: 0.115 (0.832); Breusch Godfrey LM test [2]: 0.6 (0.689), [3]: 1.986 (0.55); ARCH test [1]: 0.52 (0.68); [ ] refers to the order of diagnostic tests; ( ) refers to the p-value. Since the variables are cointegrated, the long-run coefficients are derived from the UECM; i.e. the estimated coefficient of the one lagged level independent variable divided by the estimated coefficient of the one lagged level dependent variable and multiplied with a negative sign. 38 Thus, the long-run inflation and unemployment coefficients are 2ðp 2 =p 1 Þ and 2ðp 3 =p 1 Þ, respectively. On the other hand, the short-run inflation and unemployment coefficients are the estimated Figure 1 Plots of CUSUM and CUSUM of squares statistics for UECM.
318 TANG & LEAN Table 2 Variables The summary of long-run and short-run coefficients Coefficients Long run INF t 0.039 UR t 0.109 Short P Run P DINFt2j 0.015 DURt2k 20.013 coefficients of the first differenced variables P l j and P f k in the Equation 2. Both the short-run and long-run coefficients are summarized in Table 2. From the estimated results, the long-run inflation and unemployment coefficients are 0.039 and 0.109, respectively, while the short-run inflation and unemployment coefficients are 0.015 and 20.013, respectively. These imply that the crime rate and inflation rate are positively related for both short and long run, while unemployment rate and crime rate are negatively related in the short run. An interesting finding emerging from this analysis is that Cantor and Land s 6 opportunity effect is a short-run phenomenon only, whereas in the long run, Becker s 1 motivation effect is proven to be stronger than the opportunity effect. This indicates that both motivational and opportunity effects are exist in the United States. In addition to the bounds test, we employ the Johansen and Juselius 31 multivariate cointegration test to affirm the presence of a long-run relationship. We found that vector autoregressive (VAR) lag one is the most appropriate model. The JJ test results are given in Table 3. The trace ðl trace Þ and eigenvalues ðl max Þ likelihood ratio statistics consistently reject the null of no cointegrating vector at the corrected 5% significant level. Furthermore, the test statistics fail to reject the null of one cointegrating vector. It is interesting to note that both the bounds test and JJ cointegration test consistently suggest that the variables are coalescing in the long run. Thus, we confirm that crime rate and its determinants are cointegrated. He and Maekawa 5 argued that F-statistics for Granger causality often leads to spurious causality results when one or both of the estimated series are nonstationary. Thus, we use the TYDL causality approachÿÿmwald testÿÿin this study. Zapata and Rambaldi 6 documented that both likelihood ratio test and Wald test are very sensitive to the specification of the short-run dynamics in error correction models (ECMs) even in large samples. Further, they noted that given the performance of the tests in larger samples, the MWALD test is a better appeal because of its simplicity. In order to employ the MWALD test,. The optimal lag order is chosen based on Schwarz Bayesian criterion (SBC). 5. He, Z. & Maekawa, K. (2001) On Spurious Granger Causality, Economics Letters, vol. 3, no. 3, pp. 30 313. 6. Zapata, H. O. & Rambaldi, A. N. (199) Monte Carlo Evidence on Cointegration and Causation, Oxford Bulletin of Economics and Statistics, vol. 59, pp. 285 298.
Table 3 The results of Johansen Juselius test Hypothesis Tests statistics Corrected 5% critical values H 0 H 1 WILL INFLATION INCREASE CRIME RATE? 319 l trace r ¼ 0 r $ 1 0.31** 38.695 r # 1 r $ 2 11.32 21.52 r # 2 r $ 3 2.81.218 l max r ¼ 0 r ¼ 1 28.885** 2.3 r # 1 r ¼ 2 8.651 20.253 r # 2 r ¼ 3 2.81.229 Note: The test assumption is linear deterministic trend in the data. The asterisk ** denotes statistically significant at 5% level. Due to limited sample size, the critical values are corrected through the Cheung and Lai 52 surface response procedure. we pre-specify the maximal order of integration (d max ) for the series in the system and the optimal lags order for the autoregressive distributed lag (ARDL) model.,8 We use d max ¼ 1 as it performs better than other orders of d max. 25 In order to ascertain the causal link between inflation, unemployment and crime rates, we estimate the following ARDL equations. 2 3 2 3 2 32 3 2 32 3 lncr t a 1 A 11;1 A 12;1 A 13;1 lncr t21 A 11;k A 12;k A 13;k lncr t2k INF 6 t 5 ¼ a 6 2 5 þ A 21;1 A 22;1 A 6 23;1 INF 6 t21 5 5 þ þ A 21;k A 22;k A 23;k INF 6 t2k 6 5 5 UR t a 3 A 31;1 A 32;1 A 33;1 UR t21 A 31;k A 32;k A 33;k UR t2k 2 32 3 2 A 11;p A 12;p A 13;p lncr t2p þ A 21;p A 22;p A 6 23;p INF t2p 6 5 5 þ 6 A 31;p A 32;p A 33;p UR t2p 1 1t 1 2t 1 3t 3 5 ð3þ where the order of p represents the ðkþd max Þ. The optimal lag length k is selected based on the Akaike s information criterion (AIC). 9,50,51. We note that the standard Granger causality test uses VAR model to examine the causal link. In this study, we use the ARDL due to the assumption that the non-uniform lag order reflects the relationship better than the uniform lag order. We do not include the current variables in the ARDL model because the present or future cannot cause the past (Granger, 1969). 8. Investigating Causal Relations by Econometric Models and Cross-spectral Methods, Econometrica, vol. 3, pp. 28 38. 9. In finite sample study (T, 60), AIC and final prediction error (FPE) are superior to other information criterion such as SBC (see Liew, 200, Lütkepohi, 1991). 50. Liew, K. S. (200) Which Lag Length Selection Criteria should we Employ? Economics Bulletin, vol. 3, no. 33, pp. 1 9. 51. Lütkepohl, H. (1991) Introduction to Multiple Time Series Analysis, Springer-Verlag, Germany. 52. Cheung, Y. W. & Lai, K. S. (1993) Finite-sample Size of Johansen s Likelihood Ratio Tests for Cointegration, Oxford Bulletin of Economics and Statistics, vol. 55, no. 3, pp. 313 328.
320 TANG & LEAN From Equation 3, A 12;k 0; k implies that there is causality from inflation to crime; whereas A 21;k 0; k means crime Granger causes inflation. Furthermore, A 13;k 0; k and A 31;k 0; k can be interpreted in the same way in terms of unemployment rate and crime rate. Table presents the results of the MWALD causality tests. The augmented ARDL model for MWALD test passes a number of diagnostic tests, except when the residuals in the crime equation are serially correlated. Serial correlation problem will not affect the unbiasedness and consistency of the ordinary least squares regression estimators, but it does affect their efficiency, hence the standard error is no longer valid. 53 The usual Newey and West 5 procedure is applied to correct the standard error. Overall, we find no evidence of the violation from the classical assumptions and the models are correctly specified through a number of diagnostic tests. Furthermore, the MWALD causality test suggests that both the inflation and unemployment Granger cause crime at a 5% significance level, but it fails to reject the null hypothesis that crime does not Granger causes inflation (unemployment). Hence, there is unidirectional causality from inflation and unemployment rates to crime rate. In addition to the MWALD test, we employ the Granger causality test within the VAR framework to affirm the causal link among the interested variables. The VAR model with the one period lagged level error correction term ðect t21 Þ is expressed in Equation. 55 2 3 2 Dln CR t 6 DINF t 5 ¼ 6 DUR t a 1 a 2 a 3 2 þ 6 3 2 3 2 3 B 11;1 B 12;1 B 13;1 Dln CR t21 5 þ 6 B 21;1 B 22;1 B 23;1 5 6 DINF t21 5 B 31;1 B 32;1 B 33;1 r 1 r 2 r 3 3 2 5 ½ ECT t21šþ 6 1 1t 1 2t 1 3t DUR t21 3 5 ðþ Table 5 presents the results of Granger causality test. We find that inflation and unemployment rates are significant at 1% in the crime equation, but the crime rate is not significant in both inflation and unemployment equations at 5% level. This implies that there is unidirectional Granger causality from inflation and unemployment rates to crime in the short run but no evidence of reverse causality. 56 Moreover, the series is non-explosive and the long-run equilibrium 53. Pindyck, R. S. & Rubinfeld, D. L. (1998) Econometric Models and Economic Forecasts, th edn, McGraw-Hill, Singapore. 5. Newey, W. & West, K. (198) A Simple Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica, vol. 55, pp. 03 08. 55. The optimal lag order for the VAR model is determined by SBC. 56. There is weak bilateral causality evidence (at 10%) between crime and unemployment rates.
Table The results of TYDL causality test Dependent variables WILL INFLATION INCREASE CRIME RATE? 321 Independent variables P ln CRt P INFt P URt x 2 ÿ Statistics ln CR t 10.595**.32** INF t 0.955.339** UR t 5.960 5.161*** Note: The above TYDL was performed through the ARDL framework. The asterisks *, ** and *** denote statistically significant at 1, 5 and 10% levels. relationship is attainable. The long-run causality is running from inflation and unemployment rates to crime, but not the reverse. Therefore, we conclude that both the Granger and MWALD tests affirm the existence of unidirectional causality evidence from inflation and unemployment rates to crime in the United States over the period of 1960 2005. Conclusion The objective of this paper is to re-examine the impact of inflation rate on crime in the United States over the period of 1960 2005. In order to ascertain a reliable relationship between inflation (by controlling unemployment rate) and crime rates, we employ the newly developed econometrics techniques, i.e. bounds testing approach for cointegration test and TYDL causality test. Using annual data from 1960 to 2005, all the results consistently indicate that the crime rate is cointegrated with inflation and unemployment rates. Table 5 The results of Granger causality test on VAR Dependent variables Independent variables P Dln CRt P DINFt P DURt ECT t21 t-statistic x 2 ÿ Statistics Dln CR t 8.22*.821* 20.03** DINF t 0.05 12.18* 20.360 DUR t 2.8*** 0.21 1.080 Note: The ECT is the error correction term. The asterisks *, ** and *** denote statistically significant at 1, 5 and 10% levels. The serial correlation LM tests: [1] 11.3 (0.25), [2] 1.609 (0.102) and [3] 11.15 (0.28); [ ] refers to the order of serial correlation and ( ) refers to the p-values.
322 TANG & LEAN Furthermore, Bardsen s 38 estimation results suggest that crime rate and inflation rate have a positive relationship in both the short and long run. This finding is corroborated with Becker s 1 motivation effect that an individual will engage in criminal activities because he/she is unable to maintain a particular level of living as a consequence of inflation and unemployment. On the other hand, Cantor and Land 6 opportunity effect is valid merely in the short run. Moreover, this study provides evidence that crime function in the United States is stable over the sample period. The results also imply that inflation and unemployment rates Granger cause crime rate, but there is no strong evidence of reverse causality. These findings may reveal to policymakers and economic agents that low unemployment rate does not mean low crime rate because inflation rate is positively related to crime rate. 5,58 Thus, supply-side economic policy by reducing both inflation and unemployment rates simultaneously could be one of the alternatives to reduce crime rate. As inflation and unemployment rates are the only variables used in this study, the results may not fully capture the criminal behaviour in the United States. There are some other potential variables such as the benefit or cost of crime 59 and government expenditure on internal security. Nevertheless, the use of inflation and unemployment rates is in parallel with the objective of this study and they should not be discarded as useless tools. Thus, the future study can be extended by including these potential variables. Acknowledgements The authors would like to thank the anonymous referee and the editor for their insightful comments and suggestions. The usual disclaimer applies. Appendix A: Phillips Perron Stationarity Test The Phillips Perron stationarity test results show that ln CR t, INF t and UR t are not stationary at level. However, all the variables are stationary after first differencing. Thus, we conclude that all the estimated variables are integrated at order one, I(1) and we can proceed to the cointegration tests. Appendix B: Gregory and Hansen 1 cointegration test with structural breaks 5. When the unemployment rate is low, inflation rate tends to be high and vise versa (Phillips, 1958). 58. Phillips, A. W. H. (1958) The Relationship Between Unemployment and the Rate of Change of Money Wages in United Kingdom, 1861 195, Economica, vol. 15, pp. 283 300. 59. We thank the anonymous referee for the suggestion.
Table A1 Variables The results of Phillips Perron stationarity test Phillips Perron Test Statistics WILL INFLATION INCREASE CRIME RATE? 323 Without constant and trend Constant only Constant and trend Level ln CR t 1.08 23.06** 21.063 INF t 20.915 22.095 21.850 UR t 20.2 22.223 22.180 First difference Dln CR t 23.00* 23.162** 2.39* DINF t 25.286* 25.12* 25.3* DUR t 25.83* 25.39* 25.28* Note: The asterisks *, ** and *** denote the significance at 1, 5 and 10% levels, respectively, based on Mackinnon 60 critical values. This study has employed three models, C, C/T and C/S as suggested by Gregory and Hansen. 1 In this study, we choose Model () which is the most significant model for cointegration test. The ADF* test for Model () rejects the null hypothesis of no cointegration at 5% level. Thus, we conclude that crime rate and its determinants in the United States are cointegrated with a regime shift in 191. This is consistent with our bounds test finding. Table B1 Minimum ADF* t-statistics for the three Gregory Hansen tests Model ADF* TB1 2 (C) 2.990 196 3 (C/T) 23.803 1983 (C/S) 26.1** 191 Note: The asterisks *, **, *** represent the significant level at 1, 5 and 10%, respectively. Note: the critical values for 1, 5 and 10% levels are (25., 25.28 and 25.02), (26.05, 25.5 and 25.33) and (26.51, 26.00 and 25.5) for Model (2), Model (3) and Model (), respectively, obtained from Table 1 (pp. 109) of Gregory and Hansen. 1 TB1 denotes the potential breakpoint in the cointegrating vector. 60. Mackinnon, J. G. (1996) Numerical Distribution Function for Unit Root and Cointegration Tests, Journal of Applied Econometrics, vol. 11, pp. 601 618.