The Short- and the Long-run Relationships of CPI, GNP, Underemployment and Crime Rate: The Philippine Setting by

Annalyn Domingo-Cuaton and Agustina Tan-Cruz1

1 M.S. Econometrics student and Faculty member, respectively, School of Applied Economics, University of Southeastern Philippines, Obrero, Davao City.

INTRODUCTION

ECONOMICS

CRIME

2

Country’s Stability

MACROECONOMICS (Relationship of CPI, GNP and Underemployment)

INTRODUCTION Objectives: • To test for the existence of a short-run and a longrun model among the following variables: CPI, per capita GNP, underemployment and some categories of crime. • To test for causality between categories of crime and the remaining macroeconomic variables (CPI, per capita GNP and underemployment) and carry out innovation accounting.

METHODOLOGY Time Series Analysis Test for Stationarity a. Dickey – Fuller Test b. Augmented Dickey-Fuller Test

METHODOLOGY Testing for Cointegration: The Johansen Methodology a. Estimate the Vector Autoregression (VAR) and determine the appropriate lag length p xt = A0 + A1xt-1 + A2xt-2 + . . . + Apxt-p + e1

(3)

Where: xt = an (n x 1) vector containing each of the n variables

included in the VAR Ao = an (n x 1) vector of intercepts Ai = (n x n) matrices of short-run coefficients

ei

= an (n x 1) vector of error terms

In the multivariate context, the existence of a stationary linear combination of nonstationary variables that are integrated of the same order is referred to as cointegration and move around a long-run equilibrium.

METHODOLOGY b. Determine cointegrating rank r of π and proceed with a Vector Error Correction Model (VECM) Short-run changes

p-1

Long-run dynamics (Error Correction)

Δ xt = π0 + ∑ πi Δ xt-1 + π xt-p + εt i=1

(6)

Short-run dynamics

For cointegration to hold, cointegrating rank r of π must lie within: 0
ECM expresses the short-run changes of the variables in the system as a function of their short-run dynamics (lagged changes) and the long-run dynamics (the error correction term)

METHODOLOGY c. Analyze the normalized estimates of the cointegrating vector and speed of adjustment p-1

Error Correction

Δ xt = π0 + ∑ πi Δ xt-1 + π xt-p + εt i=1

(9)

π = α β’ Cointegrating Vector - Interpreted as long-run elasticities

Speed of Adjustment - A measure of response to a deviation from longrun equilibrium - Must not be too large in absolute value. The point estimates should imply that the short-run changes in the variables converge to the longrun equilibrium relationship

METHODOLOGY d. Innovation Accounting d.1. Impulse response analysis d.2. Forecast error variance decomposition

Plotting the impulse response functions is a practical way to visually represent the behavior of the {CRt}, {GNPt}, {CPIt} and {Ut} series in response to the various shocks Forecast error variance decomposition tells us the proportion of the movements in a sequence due to its own shocks versus shocks to the other variable

METHODOLOGY Granger Causality - A test whether or not the lags of one variable enter into the equation for another variable to determine whether one time series is useful in forecasting another

RESULTS AND DISCUSSION

Long-run Relationship Table 1. Coefficients of the Cointegrating Vector (β’) for Crime against Property and Total Crime (ceteris paribus). Crime Category Variable CPR CT CRIMEt-1 1.000000 1.000000 GNPt-1

3.160612*** (1.12366)

1.797791*** (0.28419)

CPIt-1

-2.597068*** (0.63212)

-0.893103*** (0.15414)

Ut-1

1.243402*** (0.33897)

0.283122*** (0.07616)

-41.26422

-24.75704

C *** significant at 1% level ** significant at 5% level significant at 10% level

RESULTS AND DISCUSSION Table 2. Speed of Adjustment Estimates (α). Crime Category (Model)

Error Correction (α) ΔCRIME

ΔGNP

ΔCPI

ΔU

CPR

-0.301720*** (0.07660)

-0.023697 (0.01546)

0.004604 (0.01126)

0.141495 (0.12942)

CT

-0.529819*** (0.18759)

0.066067 (0.05059)

-0.000483 (0.03675)

0.721164* (0.39493)

( ) Standard error *** significant at 1% level ** significant at 5% level * significant at 10% level

* Speed of adjustment tells the adjustment of a variable to the previous period’s deviation from long-run equilibrium

RESULTS AND DISCUSSION SHORT-RUN RELATIONSHIP +CPE(t-1), +CPE(t-3)

CPE

-ΔCPR(t-1), +ΔGNP(t-1), +ΔGNP(t-3), +ΔGNP(t-4) , +ΔU(t-1)

ΔCPR

-ΔCT(t-3), -ΔCPI(t-1)

ΔCT

RESULTS AND DISCUSSION GRANGER CAUSALITY

GNP CPI U ALL

ΔGNP ΔCPI ΔU ALL ΔGNP ΔCPI ΔU ALL

RESULTS AND DISCUSSION Impulse Response Analysis

Figure 16. Response of CPE to Choleskey One SD Innovation to CPE.

Figure 17. Response of CPE to Choleskey One SD Innovation to GNP.

• IRF generate the effects of the various shocks on the time paths (i.e. on the current and future values ) of the variable sequences in the system. • The shocks are considered permanent if the responses do not return to equilibrium state or initial value. • Orthogonalization allows for the variables on the left side to have an instantaneous effect on the extreme right side variable in the ordered variables.

RESULTS AND DISCUSSION

Figure 18. Response of CPE to Choleskey One SD Innovation to CPI.

Figure 19. Response of CPE to Choleskey One SD Innovation to U.

RESULTS AND DISCUSSION

Figure 20. Accumulated Response of CPE to Choleskey One SD Innovation to CPE.

Figure 21. Accumulated Response of CPE to Choleskey One SD Innovation to GNP.

RESULTS AND DISCUSSION

Figure 22. Accumulated Response of CPE to Choleskey One SD Innovation to CPI.

Figure 23. Accumulated Response of CPE to Choleskey One SD Innovation to U.

RESULTS AND DISCUSSION

Figure 24. Response of CPR to Choleskey One SD Innovation in CPR, GNP, CPI and U.

Figure 25. Accumulated Response of CPR to Choleskey One SD Innovation in CPR, GNP, CPI and U.

RESULTS AND DISCUSSION

Figure 26. Response of CT to Choleskey One SD Innovation in CT, GNP, CPI and U.

Figure 27. Accumulated Response of CT to Choleskey One SD Innovation in CT, GNP, CPI and U.

RESULTS AND DISCUSSION Forecast Error Variance Decomposition

Figure 28. Forecast Error Variance Decomposition of CPE

Figure 29. Forecast Error Variance Decomposition of CPR

• Variance decomposition separates the variation (forecast error) in an endogenous variable into the component shocks to VAR/VECM • If the shocks in all other variables cannot explain the forecast error variance of one variable at all forecast horizons, the latter is exogenous. This means that the exogenous variable would evolve independently of the shocks in the other variables and their sequences.

RESULTS AND DISCUSSION

Figure 30. Forecast Error Variance Decomposition of CT

SUMMARY, CONCLUSION, RECOMMENDATION AND AREAS FOR FURTHER STUDIES MODEL 1 Crime against Person, GNP, CPI and Underemployment MODEL 2 Crime against Property, GNP, CPI and Underemployment MODEL 3 Total Crime, GNP, CPI and Underemployment

SUMMARY, CONCLUSION, RECOMMENDATION AND AREAS FOR FURTHER STUDIES MODEL 1 GNP, CPI and U are not strong determinants of CPE in the short run MODEL 2 Positive relationship of GNP to CPR may be accounted to increased expected gains and income inequality effects Negative relationship of CPI to CPR may be accounted to threshold level effects of inflation/price increases Positive relationship of U to CPR induces people to augment financial needs through property crimes

SUMMARY, CONCLUSION, RECOMMENDATION AND AREAS FOR FURTHER STUDIES MODEL 3 Positive relationship of GNP to CT may be accounted to the negative effects of overseas employment Negative relationship of CPI to CT may be accounted to the same effects on CPR considering that 20% of CT is CPR Positive relationship of U to CT may be accounted to the morale issues brought by underemployment

SUMMARY, CONCLUSION, RECOMMENDATION AND AREAS FOR FURTHER STUDIES RECOMMENDATION Economic and government policies considering macroeconomic variables in suppressing crime. - keep inflation/prices increases at acceptable levels - shocks in underemployment must be countered - growth in GNP must be paralleled with criminal countermeasures Implement programs and other innovative ways of reducing negative effects of high overseas employment rate to crime rate

SUMMARY, CONCLUSION, RECOMMENDATION AND AREAS FOR FURTHER STUDIES AREAS FOR FURTHER STUDIES To explore on more specific categories of crime. To include income inequality and poverty To study the effects of overseas employment rate to juvenile crime rate in the Philippines.