Reklamlari:  Indir 82.61 Kb.

The Relationship Between Different Price Indices: Evidence from TurkeyYilmaz AkdiDepartment of Statistics, Faculty of Science, Ankara University 06100 Tandogan Ankara, Turkey Hakan Berument^{*}Department of Economics, Bilkent University 06800 Bilkent Ankara, Turkey Seyit Mümin CilasunDepartment of Economics, Atilim University 06836 Incek Ankara, Turkey Abstract: A possible relationship between the Consumer Price Index and the Wholesale Price Index has been analyzed for long and shortrun relationships. Conventional Engle and Granger (1987) and Johansen’s (1988) cointegration tests give mixed evidence for a possible longrun relationship between those two series. The modelfree and seasonality robust periodiogram based test fails to reject the null of nocointegration relationship. However, these two series move together in the shortrun. ^ C22, E31. Key words: Cointegration, Periodogram and Price Indices.
Inflation or price level targeting is becoming more popular as a policy goal among central banks for guiding their monetary policies. The selection of the basket on which price level is calculated is as vital as the level of targeted inflation rate because different indices could yield different inflation rates. Various central banks used different baskets to implement their policies. The price indices are the weighted averages of the prices of individual items. These prices are not all affected in the same way by the policies of central banks. For example, central banks’ exchange rate policies are more likely to affect the prices of tradable than nontradable goods. Moreover, central bank interest rate policies affect the prices of goods and services differently (services are less likely to be affected by the interest rates relative to goods prices). Therefore, the selection of the price index could be detrimental to the credibility of the central bank policies as well as to their sucess. The purpose of this study is to assess any long and shortrun relationships between two widely used indexes: the Consumer Price Index (CPI) and the Wholesale Price Index (WPI) series. The CPI includes both tradable goods and nontradable goods/services in its composition; however, the WPI consists only of tradable goods. It might be the case that these two indexes are affected differently by exchange rate and interest rate based policies. Therefore, it is plausible that these two indexes do not move together. If these two indexes are not cointegrated –there is no longrun relationship–, then this means their values may diverge persistently over time. Therefore, the announced inflation target might be reached for some of the price indexes but missed for some others. This will threaten the credibility of the Central Bank. In order to avoid that, the selection of the price index is vital for the implementation and success of any inflation target based monetary policy. However, if there is a shortrun relationship, this means their longrun deviation will not affect their respective behaviors in the short run. To the best of our knowledge, there is no other study that looks at the relationship between different price indexes. On the other hand, there are various studies that suggest that these series are affected differently by various economic shocks. For example, technology shocks and increasing return to scale (Murphy et al: 1989); different stickiness of intermediate product prices (Basu: 1995); tight monetary policy (Clark: 1999); oil price shocks (Doroodian and Boyd: 2003); and real exchange rates (Kim: 2004) affect the prices of different products differently. The purpose of this paper is to analyze the dynamic relationship between these two series directly rather than assessing the third variable effect on these two series. This paper studies a direct relationship between the two most popular price indexes (WPI and CPI) using Turkish data, which has various advantages. Firstly, Turkey has been experiencing a high and persistent level of inflation without running into hyperinflation since the mid1970s. The high variability in the level of inflation allows us to minimize the type 2 error – an error made when an incorrect null hypothesis is not rejected. Secondly, unlike some central banks, the Central Bank of the Republic of Turkey used both exchange rate and interest rate based stabilization policies to hamper inflation. Therefore, the effects on prices of both central bank policy tools do exist for the Turkish data. Thirdly, Turkey has relatively welldeveloped and liberal markets; therefore, prices move with market forces rather than being regulated by price controls or freezes. All these allow the use of the Turkish data for any relationship that could exist among price indexes. This study, in particular, investigates a possible relationship between the WPI and CPI series for the period January 1987 – August 2004 in Turkey by using conventional cointegration tests such as Engle and Granger’s (1987) single equation, Johansen’s (1988) multivariate cointegration tests as well as the periodogram based cointegration test. The main contribution of this paper is to use this third test to determine if there is a (long run) relationship between these two indexes. Note that both the CPI and the WPI are quite seasonal series. Maravall (1995), Hecq (1998), Cubadda (1999) and Cheung and Westermann (2003) argue that addressing the seasonality in the data could alter the basic inference gathered from the data. In order to account for this, we used the periodogrambased cointegration tests as developed by Akdi (1995) and Akdi and Dickey (1998). This method has the advantage of being model free and seasonality robust. The next section introduces the data and the conventional as well as the periodiogram based testing methods, section three presents the empirical evidence and the last section concludes the paper.
The WPI and CPI indexes for the period from 1987:01 to 2004:08 were gathered from the Central Bank of the Republic of Turkey data delivery system (http://tcmbf40.tcmb.gov.tr/cbt.html). In our analysis, we used 1994based WPI and CPI indexes. The WPI index includes 678 goods chosen according to the share of sales values that are produced domestically and supplied to the domestic markets. The current prices of those goods from 1287 firms with the highest domestic endorsement are followed. The prices, except for the agriculture sector, are the final goods prices. For the agriculture sector, prices are taken from wholesale food markets. The 1994 based WPI uses ISIC Rev.3. classification and is calculated by employing fixedweight Laspeyres formulation. The 1994based CPI index, on the other hand, is calculated for 7 geographical provinces and 19 cities by employing fixedweight Laspeyres formulation. It covers 410 goods and services whose prices are gathered from 35 residential areas and uses Classification of Individual Consumption by Purpose (COICOP). Figure 1(a) reports the time series plots of the logarithms of these two series. These series are similar regarding persistency and both have increasing trends. The graphs of the calculated values of Autocorrelation and Partial Autocorrelation functions are reported in Figure 1(b) for the sample. Graphs of the autocorrelation functions decay very slowly, which may suggest a possible unit root for each series. Therefore, the unit root tests are warranted.
Table 1 reports the conventional DickeyFuller, PhillipsPeron Unit Root Tests as well as Dickey, Hasza and Fuller (1984) seasonal unit root tests for these two series. Panel A reports the series with an intercept term, Panel B gives the intercept term and the time trend and Panel C reports the tests on the first difference of the series for the DickeyFuller, PhillipsPeron Unit Root Tests and the twelfth difference for the Dickey, Hasza and Fuller test. Table 1 suggests that we cannot reject the null of a unit root in either series in levels (with and without time trend). However, we could reject the null of a unit root in the differenced of the series. Thus, we claim that both series are I(1).
Note: * indicates the level of significance at 5% and ** indicates the level of significance at 1%. The critical values are gathered from Hamilton (1994) and Franses and Hobijn (1997). Next, we will perform the Akdi and Dickey’s (1998) periodogram based unit root test for each series. For this test, one may use the trigonometric transformation of the series. Given a time series , the periodogram ordinate (without any model specification) is, (1) where , are the Fourier coefficients and defined as and . (2) Note that when, the following equality appears and this causes the Fourier coefficients to be invariant to the mean and therefore the periodogram ordinate is invariant to the mean. Moreover, periodogram based unitroot/cointegration tests have the advantage of being seasonality robust, and model free from the selection of the lag lengths (see Akdi, 1995 and Akdi and Dickey, 1998).^{1} In order to reject the null hypothesis of a unit root, one needs to observe small values of the periodiogram ordinates. Therefore, the values of the test statistics, can be used to test for a unit root where (3) The test statistics are distributed as a mixture of chisquares exactly for AR(1) series under the assumption of stationarity. In this case, the normalized periodogram will be distributed as chisquares with two degrees of freedom asymptotically. In conventional tests, the power of the tests is not exact. However, the power can be calculated analytically for the periodogram method to test for a unit root (see, Akdi, 1995). For higher order series, the same distribution is obtained asymptotically; that is, (4) where Z_{1} and Z_{2} are independent standard normal random variables and is the variance of the error term. Here, the notation “” stands for convergence in distribution. The critical values of this distribution are provided by Akdi and Dickey (1998). The results of both types of series are given in Table 2. ^
^ 