Abstract
The relation between the Producer Prices Index (PPI) and the Consumer Price Index (CPI) in the U.S. is analyzed for two sub-periods: one spanning from 1947 to 1982, the post-war period marked by demand-side economic policies, and the other one starting by 1983 when supply-side policies pioneered by the Reagan government came into effect. As the series in question are found to be cointegrated, a Vector Error Correction Model is employed for the analysis. Regarding the long-run equilibrium relationships, it is found that the loading for the PPI series are statistically significant for both periods, while the loading for the CPI is barely significant for the first period, and it is insignificant at any acceptable level for the second. Thus, the CPI represents the common trend in the system in both periods, but it does more clearly so in the second period.
TopIntroduction
The relationship between the Producer Prices Index (PPI) and the Consumer Price Index (CPI) has long been an essential question for academic and policy-making purposes. Numerous empirical studies have investigated this relationship and identified unidirectional or bidirectional causal relations for different samples.
In early studies for the U.S. market, Colclough and Lange (1982) found a unidirectional causality from CPI to PPI (called Wholesale Price Index at the time) by using Sims and Granger causality tests, while Jones (1986) found a bidirectional causal relationship. Bloomberg and Harris (1995) and Clark (1995) reveal that the PPI does not help to predict the CPI. These empirical results casted doubt on the conventional wisdom according to which there is unidirectional causality running from producer to consumer prices.
The supply-side approach claims that there is a causal relationship from PPI to CPI. This conventional explanation is based on the well-known cost-push mechanism: through the production chain, increases in prices of raw materials and intermediary goods are reflected in the prices of finished goods. The causality from CPI to PPI is explained through a less intuitive mechanism: the demand-side approach refers to the demand-pull effect according to which increased demand for final goods leads to an increase in demand for inputs (Cushing & McGarvey, 1990; Caporale, Katsimi, & Pittis, 2002).
More recent empirical evidence is mixed as the results depend on both the method and the data used. Using Toda and Yamamoto’s (1995) causality approach, Caporale, Katsimi and Pittis (2002) found that there is a unidirectional causality from PPI to CPI for the G7 countries for the period of 1976 to 1999. Unidirectional causality from PPI to CPI is also found by Ghazali, Yee, and Muhammed (2008) in their study on the Malaysian economy and by Sidaoui, Capistrán, Chiquiar and Ramos-Francia (2010) for Mexico. Moreover, Liping, Gang, and Jiani (2008) showed that there is a unidirectional causality from CPI to PPI in China.
Vector Autoregressive (VAR) models or Vector Error Correction (VEC) models are employed for these types of analyses where the variables in question are potentially interrelated. For VAR models to be reliable, the series should all be stationary. However, many empirical time-series tend to exhibit time-varying moments. Through differencing, non-stationary series may be transformed into stationary series that are suitable for VAR analysis at the expense of valuable information about long-term dynamics. Instead, cointegration analysis may be conducted to identify long-term stable relationships between variables. Identified cointegration relationships may then be integrated into the VAR model with differenced series to form a VEC model. Through a VEC model, it is possible to analyze not only how the variables react to any innovations but also how the system reverts to the long-run equilibrium after any deviance.
In this chapter, the relationship between the PPI and CPI in the U.S. is analyzed for two sub-periods: one spanning from 1947 to 1982, the post-war period marked by demand-side economic policies, and the other sub-period starting in 1983 when supply-side policies pioneered by the Reagan administration came into effect. The primary purpose of this chapter is principally pedagogical: through the empirical analysis, VAR and VEC models are exhibited, related statistical concepts such as stationarity and cointegration are explained, and econometrical tests that are employed to identify these statistical properties are presented in detail. The comparative analysis employed in this chapter is also expected to enhance the comprehension as it permits to expose how different results lead to different interpretations.
The remainder of the chapter is organized as follows. First, technical and non-technical explanations of VAR and VEC models along with the related statistical concepts are provided. Then, the data used in the empirical analysis are presented. The empirical application section introduces the econometrical tests and methods that are employed to identify the appropriate empirical model. Empirical results are then presented and interpreted.
Key Terms in this Chapter
Stationarity: An important property in time-series econometrics. A time-series is stationary if it has a constant mean, a finite variance, and a constant auto-covariance structure throughout the sample. If any one of these conditions is not satisfied, the time-series would be non-stationary.
Unit-Root: A form of non-stationarity that can be easily coped with by differencing. Consider for instance a simple autoregressive process, X t =??X t -1 + u t , where u t is white noise. This equation may be rewritten as (1 – a B ) X t =u t , where B is the backshift operator ( BX t =X t -1 ). As u t is a white noise process with mean 0, this equation has a unique root at 1/a. Thus, the process would have a unit root when a=1. Note that this with unit root series will consist of the cumulative sum of the white noise series which would not be stationary, while the first difference of this series would be equal to the white-noise series, which is clearly stationary.
Long-Run Disequilibrium: Any deviance of a cointegrating variable from the cointegrating relationship.
Cointegration: Cointegration is a statistical property about the relationship between a group of integrated series. If there is a linear combination of several I(d) series which results in an I(b) series where b<d , the series are cointegrated. For instance, when there are two I(1) series, while a linear combination of these series gives a stationary variable, then there is cointegration. This linear combination is generally normalized to one of the cointegrating variables to define the cointegration relation. The coefficients of the cointegration relation are included in a cointegrating vector.
Adjustment Parameter: A parameter that determines the adjustment speed of a variable when a long-run disequilibrium occurs. It is estimated within a VEC model.
White Noise: A white noise process is also a stationary series but with additional strict conditions. A white noise series also has constant mean, constant and finite variance, and a constant auto-covariance structure, but the mean should be zero, and there should be no serial autocorrelations in white noise series.
Order of Integration: The order of integration is a statistic about data indicating the number of unit roots in the series. A series that is integrated of order d is shown as I(d). An I(2) series, for instance, should be differenced twice to obtain a stationary, I(0) , series.