Producer & Consumer Prices Nexus: ARDL Bounds Testing Approach

Transcription

1 Producer & Consumer Prices Nexus: ARDL Bounds Testing Aroach Muhammad Shahbaz COMSATS Institute of Information Technology, Lahore Camus, Pakistan Rehmat Ullah Awan University of Sargodha, Sargodha, Pakistan Najeeb M. Nasir College of Business Administration, King Saud University, Riyadh Saudi Arabia Abstract The resent endeavor exlores relationshi between roducer and consumer rice indices by emloying new techniques. We have utilized the time series monthly (1992M1-2007M6) data while ARDL Bounds Testing and Johanson Cointegration Aroach is used to determine the long run association and robustness of long run results. Toda & Yamamato (1995) and Variance Decomosition for causal raort between roducer and consumer rices are alied. DF-GLS & Ng-Perron Tests are also alied to inquire the order of integration for running variables. Results have verified the existence of long run relationshi between roducer and consumer rices, and their association is robust in long san of time in the case of small develoing economy like Pakistan. Causal results through Toda and Yamamato s (1995) technique asserts that there is two-way causality but it is stronger from roducer to consumer rices and same with Variance Decomosition Method. Finally Feed back imacts show that feedback influence from PPI to CPI is stronger or dominating as comared to feedback from CPI to PPI, which suort Cushing and McGarvey (1990) hyothesis. Keywords: D24, D12, C20 Introduction The relevant literature reveals that consumer and roducer rice indices are considered as indicators of inflation and current roducer rices lead consumer rices in future [Caorale, (2002) & Darestani and Arjomand, (2006)]. Researchers found causal relationshi between roducer rice and consumer rice from both sides simultaneously [Engle, (1978); Sims, (1972); Silver and Wallace, (1980); and Guthrice, (1981)] (Note 1). But Colclough and Langee (1982) argued that causality between the said variables can run from roducer rices to consumer rices or might be bidirectional after alying the Granger & Sims tests and theoretically causality exects to run from consumer to roducer rices. Over a long san of time, Mehra (1991) & Huh and Trehan (1995) concluded that consumer rice index leads labor cost, which is major art of roduce rice index and this mechanism contradicts the chain view. In contrary, Emery and Chang (1996) summed u workers comensation growth adjusted for roductivity has no ower to anticiate the inflation. Further more Cushing and McGarvey (1990) indicated that feedback from roducer rices to consumer rices is greater than that from consumer to roducer rices that can be concluded as consumer rices have very light incremental ower. Further more, they argued that addition of money suly does not affect revailing feedback from roducer to consumer and causal link is consistent with the sule rice model showing strong demand effects. Contrarily, Clark (1995) concluded that ass-through effect from roducer rices to consumer rices may be weak and found causality is unidirectional that runs from roducer rices to consumer rices. 1. Theoretical Background In literature roducer rice index is utilized frequently as an imortant indicator for consumer rice index. Mostly causal relationshi is related to suly-side that is an indication from roduction timing while retail sector also adds value in existing roduction after a lag eriod. According to standard oen macro economy model, retail sector uses 78

2 International Journal of Marketing Studies November, 2009 running domestic roduction as an inut. Literature indicates that consumer rices deend uon roducer rices of goods, imorted goods rices, exchange rate, rate of indirect taxes imlementation, marginal cost of retail roduction and marku ossibly. Theoretical basis for causal relationshi running from wholesale rice has been develoed by Cushing and McGarvey (1990). The roduction of final goods in each eriod uses rimary goods roduced in lagged eriod as inuts which indicate that suly-side turbulence in rimary goods market influence wholesale and consumer rices in ucoming eriod. Cushing and McGarvey (1990) find that rimary goods are used as inut with lag eriod in roduction rocess of consumtion goods that s why wholesale rices will lead consumer rices indeendently. Contrarily, Colclough and Langee (1982) argued that causal relationshi from consumer rices to roducer rices did not receive much attention to be investigated in the literature. Their theoretical argument stems from derived demand and was develoed by Marshall (1961). Demand for inuts determined by demand for final goods and services between cometing utility items and this framework indicates that oortunity cost of resources and intermediate materials is reflected by the roduction cost that influences the demand of final goods and services in resonse. This shows that consumer rices should affect roducer rices. Cushing and McGarvey (1990) examined said link by allowing for demand side effects, while demand for rimary goods determines exected future rices of consumer goods. Under this assumtion, current demand and ast exectations of current demand determine consumer rice while wholesale rice deends on exected future demand (Cushing and McGarvey, 1990). So causality running from consumer rices to wholesale rices would exist only for certain values of disturbance arameters (Cushing and McGarvey, 1990). Caorale, et al. (2002) exlain this link through labor suly channel, consumer rices also affect roducer rices through suly shocks in labor market, if wage earners in the wholesale sector want to reserve the urchasing ower of their incomes. This effect occurs with lag-eriod, it robably deends on the nature of wage-setting rocess along with exectations of machinery formation. Finally, Yee and Mummad (2008) find unidirectional causal relation running from roducer rice index to consumer rice index in Malaysia. Insert Figure 1 here Figure-1 shows the behavior of Consumer Prices and Producer Prices and for this, Monthly Consumer Price and Producer Price Indices are utilized. Data set has been obtained from International Financial Statistics (IFS, 2007) and State Bank Monthly Bulletins (Various issues). Remaining art of the study is designed as follows: art B exlains the methodological framework; Interretations are in art C of the study and conclusions are drawn in art D. 2. Methodological Framework To investigate the long run association between Producer Price and Consumer rices indices, ARDL bounds testing aroach for cointegration by Pesaran, (2001) has been alied. This technique is advantageous over traditional econometric rocedures and has been utilized to study the Producer and Consumer rices relationshi in the available literature. This is the study of two vectors namely Z t where Z t ( LPPI, LCPI). LPPI and LCPI are used as deendent and indeendent variables one by one. The ARDL bounds testing in the form of conditional error correction models are given below: li 1 2lit1 3lcit1 1liti 2lcit j i (1) lci li lci i1 lci 1 2 t1 3 t1 1 t j 2 ti i (2) j1 i0 j0 li Where, is the difference oerator while LCPI is the log of consumer rice index (roxy for consumer rices) and LPPI is indicating log of roducer rice index (reresenting roducer rice) 2 2, 3 3 are showing the long run coefficients and 1 1 indicating drifts of both equations of the study. One may be noted that LPPI and LCPI are deendent variables simultaneously in both equations. Current and lagged values of differences for LPPI & LCPI are utilized in the model for short run dynamic structure. Lag length selection namely Pesaran, et al. (2001, age-308) described that there is delicate balance between choosing sufficiently large to mitigate the residual serial correlation roblem and, at the same time, sufficiently small so that the conditional ECM is not unduly over-arameterized, articularly in the view of limited time series data. In this study, time series data set is monthly ranging from 1992M1 to 2007M6 (186 observations). The bounds testing aroach for the absence of any level association between PPI and CPI is through the exclusion of lagged levels of running actors like LPPI t 1 and LCPI t1. This lends suort for following not only for null hyothesis but also for the alternative hyothesis: H : 2 2 0, (3) H : 0, 0.(4) a The F-statistics, which has been a non-standard distribution, deends not only on non-stationarity of the data and number of indeendent actors but also on the samle eriod and samle size. The asymtotic distributions of the F-statistics are non-standard under the null hyothesis of no co-integration relationshi between the examined variables, irresective of whether the variables are urely I(0) or I(1), or mutually co-integrated. Two sets of asymtotic critical 79

3 values rovided by Pesaran and Pesaran, (1997). The first set assumes that all variables are I(0) while the second set assumes that all variables are I(1). If the comuted F-statistics is greater than the uer bound critical value then we reject the null hyothesis of no co-integration and conclude that there exists steady state equilibrium between the variables. If the comuted F-statistics is less than the lower bound critical value, then we cannot reject the null of no co-integration. If the comuted F-statistics falls within the lower and uer bound critical values, then the result is inconclusive; in this case, following Kremers, (1992) and Bannerjee, (1998), the error correction term will be a useful way of establishing co-integration(note 2). For granger causality, Rambaldi and Doran (1996) formulating for Toda-Yamamato s (1995) is emloyed. dmax is indicating the maximum order of integration in the system (in this study, it is 1) and a VAR(k + dmax) has to be estimated to use the Wald test for linear restrictions on the arameters of a VAR(k) which has an asymtotic 2 distribution. In our case, k is determined to be by using the Akaike Information Criterion (AIC). LPPI & LCPI can be reresented by X and Y resectively and for a VAR following system of equations can be alied: LPPI 1 1LPPI t 2LCPI (5) i1 LCPI 1 1LCPI t j 2LPPI ti i (6) j1 i1 For the above described system, F-statistics and Wald tests alied to examine the causality relation between said variables. If one wants to test that LCPI does not Granger-cause LPPI, null hyothesis will be as H : 2 0 and alternative H : 2 0 while null hyothesis will be as H : 2 0 and alternative H : 2 0 for second equation. 3. Interreting Style At the revious ste standard tests are emloyed like DF-GLS and Ng-Perron in order to investigate the order of integration for said variables in the concerned models. Mostly in available literature to find out the order of integration ADF (Dicky & Fuller, 1979) and P-P (Phili & Perron, 1988) tests are often used resectively. Due to their oor size and ower roerties, both tests are not reliable (Dejong et al, 1992 and Harris, 2003). As earlier mentioned they conclude that these tests seem to over-reject the null hyotheses when it is true and accet it when it is false. While, these newly roosed tests seem to solve this arising roblem: the Dicky-Fuller generalized least square (DF-GLS) de-trending test develoed by Elliot (1996) and Ng-Perron test following Ng-Perron (2001). The results of Table-1 indicate that PPI & CPI are I(1) variables. Lag selection criteria does not allow to take lag more and less than 8 because at lag-8 AIC values is minimum. Insert Table 1 here Insert Table 2 here Insert Table 3 here The first ste is to select the lag length of ARDL model with 8 on the basis of AIC (Akaike Information Criteria). The total number of regressions estimated following the ARDL method in the equation 6 is ( 8 1) As results reorted in Table 3 of F-Statistics, exceeds the critical bounds, 2.79 is lower bounds and 4.10 is uer bounds resectively at 1% level of significance and values of arsimonious model (Wald-Statistics) are given with their stability ower in arenthesis. ARDL F-statistics and Wald-statistics ush to accet the hyothesis of Cointegration between PPI and CPI. So, one may conclude that Consumer and Producer rice indices are tied together in long run relationshi. To investigate the robustness of long run relationshi between PPI & CPI, Table-4 shows the outut of Johansen Likelihood test and indicates the existence of long run association between Producer rice index and Consumer rice index in the long run. Insert Table 4 here Insert Table 5 here Table 5 reorts the regression results both by OLS and Johansen Normalized equation. One ercent increase in roducer rices lead to raise consumer rices in current eriod by more than 90 % in future while there is 88 ercent increase in Consumer rices due to one ercent increase in roducer rices according to the Johanson normalized equation. From oosite side, one may conclude that roducer rices are influenced more than 100 ercent due to rise in consumer rices in the country. This roves the existence of derived demand hyothesis in Pakistan which was develoed by Marshall (1961). For Causal relationshi between PPI and CPI Toda and Yamamato (1995) has alied and results in Table-6 reveal that there is bidirectional causality between Producer and consumer rices. Insert Table 6 here i j1 t j i 80

4 International Journal of Marketing Studies November, 2009 Insert Table 7 here In table-7, Variance decomosition is an alternative method to imulse resonse function for investigating the resonse of deendent variable due to the effects of shocks by exlanatory actors. This method exlains that how much of redicted error variance for any variable is described by innovations through each indeendent variable in a system over the horizons. The shocks also affect other variables in the system due to shocks exlained by error variance. From the above test it can be concluded that each time series describes the revalence of its own values. Consumer rice exlains over % of its forecast error variances or exlain through its own innovative shocks. Whereas, roducer rice shows innovative imact through its own shocks nearly %. This shows that consumer rice redominately exlains by its ast values or innovative shocks and ercent through Producer rice. This can also be concluded that current consumer rice influences future consumer rice. PPI lead CPI not more than % through its innovative shocks while PPI leads CPI more than 23 % through their innovative shocks on each. The results of VDC have also roved that there revails bidirectional causality between PPI & CPI. Insert Table 8 here For short term behavior, Error Correction Model (ECM) is alied. Table-8 shows that more than 11 ercent CPI is raised by lag and PPI ushes the CPI to raise almost 39 ercent but lag imact of PPI is ositive with insignificance. Lag imact CPI is negative but in future it converts into ositive and imacts PPI ositively and significantly. Further more, lag of PPI raises PPI by more than 23 ercent with high level of significance. Feed back imacts show that feedback influence from PPI to CPI is stronger or dominating as comared to feedback from CPI to PPI suorting Cushing and McGarvey (1990) hyothesis. According to Pesaran and Shin (1999) the stability of the estimated coefficient of the error correction model should also be emirically investigated. Grahical reresentations of CUSUMsq are shown in figure1 and 2 for both models. Following Bahmani-Oskooee (2004) the null hyothesis (i.e. that the regression equation is correctly secified) cannot be rejected if the lot of these statistics remains within the critical bounds of the 5% significance level (see figure given in aendix-a). As it is clear from Fig. 1 and 2, the lots of both the CUSUMsq are with in the boundaries and hence these statistics confirm the stability of the long run coefficients of regressors. 4. Conclusion The resent endeavor analyzed the link between roducer and consumer rices in Pakistan. For this urose, we alied ARDL (Auto Regressive Distributive Model) and Johansson for its robustness. Time series data ranging for the eriod of 1992M1-2007M6 was utilized. DF-GLS and Ng-Perron tests were alied for the existence of a unit root in the level and first difference of both variables. Stationarity was found at the level 1(1). Results of articular study verified that there exists a long run relationshi between roducer and consumer rice indices and their association is robust in long run in the case of small develoing economy like Pakistan. Causal results through Toda and Yamamato s (1995) technique assert that there is two-way causality but stronger from roducer to consumer rices while same by Variance Decomosition Method. Finally, Feed back imacts show that feedback influence from PPI to CPI is stronger or dominating as comared to feedback from CPI to PPI suorting Cushing and McGarvey (1990) hyothesis. References Bannerjee, A., J. Dolado and R. Mestre. (1998). Error-correction mechanism tests for Cointegration in single equation framework. Journal of Time Series Analysis, 19, Caorale, Katsimi and Pittis. Causality between Consumer and Producer Prices: Some Emirical Evidence. Southern Economic Journal, Vol. 68, Clark. T. (1995). Do Producer Prices Lead Consumer Prices?. Federal Reserve Bank of Kansas City Economic Review, Vol. 80, Colclough and Lange. (1982). Emirical Evidence of Causality from Consumer to Wholesale Prices. Journal of Econometrics, Vol. 19, Cushing and McGravey. (1990). Feedback between Wholesale and Consumer Inflation: A Re-examination of the Evidence. Southern Economic Journal, Vol. 56, Darestani and Arjomand. (2006). An Emirical Study of the Relationshi between Consumer and Producer Index: A Unit Root and Test of Cointegration. The Coastal Business Journal, Vol. 5, Dejong, D.N., Nankervis, J.C., & Savin, N.E. (1992). Integration versus Trend Stationarity in Time Series. Econometrica, 60, Dickey, D. and Fuller, W. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, Vol. 74,

5 Elliot, G., Rothenberg, T.J., & Stock, J.H. (1996). Efficient Tests for an Autoregressive Unit Root. Econometrica, 64, Engle. R. (1978). Testing the Price Equations for Stability across Sectral Frequency Bands. Econometrica, Vol. 46, Gordon, (1988). The Role of Wages in the Inflation Process. American Economic Review, Vol. 78, Guthrie, Richard S. (1981). The Relationshi between Wholesale and Consumer Prices. Southern Economic Journal, Vol. 47, Harris, R., Sollis, R. (2003). Alied Time Series Modeling and Forecasting, Wiley, West Sussex. Huh and Trehan. (1995). Modeling the Time Series Behavior of Aggregate Wage Rate. Federal Reserve Bank of San Francisco Economic Review, Kremers, J.J.M., Ericsson, N.E., & Dolado, J.J. (1992). The Power of Cointegration Tests, in. Oxford Bulletin of Economics and Statistics, Vol. 54, Marshall, Alfred. (1961). Princiles of Economics, 9 th Edition, London, Macmillan. Mehra. (1991). Wage Growth and Inflation Process: An Emirical Note. American Economic Review, Vol. 81, Ng, S., Perron, P. (2001). Lag Length Selection and the Construction of Unit Root Test with Good Size and Power. Econometrica, 69, Ooi Ai Yee and Mohd Zulkifli Muhammad. (2008). Do Producer Prices Cause Consumer Prices? Some Emirical Evidence. International Journal of Business and Management, Vol. 3, Pesaran MH, Shin Y. (1999). An Autoregressive Distributed Lag Modeling Aroach to Cointegration Analysis. Chater 11 in Econometrics and Economic Theory in the 20th Century: The Ragnar Frisch Centennial Symosium, Strom S (ed.). Cambridge University Press: Cambridge. Pesaran, M. H., Pesaran, B. (1997). Working with Microfit 4.0: Interactive Econometric Analysis. Oxford: Oxford University Press. Pesaran, Shin and Smith. (2001). Bounds Testing Aroaches to the Analysis of Level Relationshis. Journal of Alied Econometrics, Vol. 16, Phillis, P.C.B., & Perron, P. (1988). Testing for a Unit Root in Time Series Regression. Biometrica, 75, Rambaldi, A. N. and H. E. Doran. (1996). Testing for Granger non-causality in cointegrated systems made easy. Working Paers in Econometrics and Alied Statistics 88, Deartment of Econometrics, The University of New England. Silver and Wallace. (1980). The Relationshi between Wholesale and Consumer Prices. Journal of Econometrics, Vol. 12, Sims, Christoher A. (1972). Money, Income, and Causality. American Economic Review, Toda, H.Y. and T. Yamamoto. (1995). Statistical Inference in Vector Auto- regressions with Possibly Integrated Processes. Journal of Econometrics, 66, Notes Note 1. On contrary, Gordon, (1988) found relationshi between consumer and roducer rices insignificantly Note 2. To ascertain the goodness of fit of the ARDL model, the diagnostic and the stability tests are conducted. The diagnostic tests examine the serial correlation, functional form, normality of error term, autoregressive conditional heteroscedisticity and heteroscedisticity associated with the model. The stability test is conducted by emloying the cumulative sum of recursive residuals (CUSUM) and the cumulative sum of squares of recursive residuals (CUSUMsq). Examining the rediction error of the model is another way of ascertaining the reliability of the ARDL model. Note 3. Reresents the significance at 1% level of significance. 82

6 International Journal of Marketing Studies November, 2009 Table 1. DF-GLS & Ng-Perron Unit Root Test Variables DF-GLS at Level DF-GLS at 1 st Difference PPI * CPI * Ng-Perron at Level Variables MZa MZt MSB MPT CPI PPI Ng-Perron At 1 st Difference CPI * PPI * (Not e 3) Note: *Ng-Perron (2001, Table 1) & *Elliott-Rothenberg-Stock (1996, Table 1) Table 2. Lag selection criteria Lag order AIC SBC Log likelihood * Table 3. ARDL Estimation ARDL with Constant & Trend Deendent Variable PPI CPI F-Statistics Wald- Statistics (0.0025) (0.0081) Chi-square (0.0020) (0.0069) Critical Bounds Instability Level Lower Bound Uer Bound Pesaran, et, al (2001) 1% 5% 10% Table 4. Johansen First Information Maximum Likelihood Test for Co-integration Hyotheses Likelihood ratio Prob-value* 5 Percent critical value Maximum Eigen values 5 Percent critical value Prob-value** R = R Note: * & ** shows rejection at 5 ercent level & **MacKinnon-Haug-Michelis (1999) -values. 83

7 Table 5. Regression Results Deendent variable OLS Regression Normalized Cointegration Coefficients (Johanson OLS) Constant Coefficient Constant Coefficient CPI (22.982) ( ) (8.698) (67.083) PPI ( ) ( ) (-7.812) (67.829) Table 6. Toda and Yamama (1995) Wald Test Lags Wald Test Instability Instability Statistics Value Chi-Square Value Running from PPI to CPI Table 7. VDC by Cholesky Ordering Running from CPI to PPI Variance Decomosition of CPI Period CPI PPI Variance Decomosition of PPI Period CPI PPI

8 International Journal of Marketing Studies November, 2009 Table 8. Short Run Dynamics Deendent Variable: CPI Deendent Variable: PPI Variables Coefficient T.values Coefficient T.values Constant * CPI * CPI t *** ** PPI * - - PPI t * Ecm t * * R-squared = R-squared = F- Statistics = (0.000) F- Statistics = (0.000) Durban Watson = Durban Watson = PPI & CPI Behaviour PPI & CPI PPI CPI 1992M M M M M M M M M M01 Time Figure 1. Behavior of Producer and Consumer rice Indices in Pakistan CUSUM of Squares 5% Significance Figure 2. CPI is Deendent Variable Plot of Cumulative Sum of Squares of Recursive Residuals The straight lines reresent critical bounds at 5% significance level. 85

9 CUSUM of Squares 5% Significance Figure 3. PPI is Deendent Variable Plot of Cumulative Sum of Squares of Recursive Residuals The straight lines reresent critical bounds at 5% significance level. 86