Evaluating the Statistical Measures of Core Inflation in Pakistan

Transcription

1 Evaluating the Statistical Measures of Core Inflation in Pakistan Riaz. H. Soomro Assistant Professor Hamdard Institute of Management Sciences and PhD Research Scholar in Hamdard Institute of Education and Social Sciences Hamdard University Karachi, Pakistan. Saghir Pervaiz Assistant Director State Bank of Pakistan Karachi, Pakistan. Ameer Haider Associate Professor Hamdard Institute of Management Sciences Hamdard University Karachi, Pakistan. Riaz. H. Soomro (Corresponding Author) Assistant Professor Hamdard Institute of Management Sciences Hamdard University Karachi, Pakistan. Abstract There are some volatile items in the consumer price index of Pakistan. It is important to identify and separate the core components from the consumer price index for policy implications. There are different methods adopted by different countries to identify persistent or core component. The reason for such difference in the method is the structure of the economy. This paper analyzes the non food and non energy, twenty percent, thirty percent and forty percent trimmed mean methods after computing them and investigates which measure is the most appropriate for finding the core component. Further this paper also finds out that whether or not the each measure satisfy the four properties of best measure of core inflation. The Core inflation is computed on the basis of weighted year on year and weighted consecutive month. Consumer price index basket of ninety two items from July 2002 to September 2007 is taken from Federal Bureau of Statistics. The distribution of price changes is skewed to the left. The degree of kurtosis is 456

2 below three suggesting platykurtic curve which means that mean is the most appropriate and efficient measure of core inflation. There was a decline in the average standard deviation confirming reduction of noise in the data on the basis of year on year as compare to basis of consecutive month s methods. Further this research finds out that all the methods satisfy the four properties of best measures of core inflation. Keywords: Core inflation, trimmed mean, non-food non-energy, volatile items, consumer price index. 1. Introduction Every government announces monetary policy in order to stabilize prices within an economy. State Bank of Pakistan (SBP) is assigned with such a task in Pakistan. Instability in prices is because of many reasons like monetary shocks, real shocks, internal and institutional factors. Real shocks are unpredictable therefore causing volatility in the prices. There are some volatile items in the consumer price index (CPI) of Pakistan. It is important to identify and separate the core components from the consumer price index for policy implications. There are different methods adopted by different countries to identify persistent or core component. The main purpose of finding core inflation is to get rid of volatile items which have inconsistent behavior so that the inflation can be forecasted and targeted properly. Items with noisy shocks in the CPI data are either to be taken out of CPI basket or trimmed from top and bottom. Statistical tools can also be applied to capture the moments with the help of Auto Repressors Integrated Moving Average models. This paper analyzes and interprets and computes and Non Food and Non Energy (NFNE), twenty percent, thirty percent and forty percent trimmed mean methods of core inflation and finds out whether or not the each measures satisfies Scott Rogers four properties of best measure of core inflation (Roger, March 1997). Core inflation is computed on the basis of weighted year on year (YoY) and weighted consecutive month. CPI basket of ninety two items from July 2002 to September 2007 is taken from Federal Bureau of Statistics (FBS). SBP defined core inflation as persistent component of measured inflation that excludes volatile and controlled prices (Pakistan, May 2006). Several studies have been done at national and international on the evaluation of methods of core inflation. One of the most common methods of core inflation used worldwide is the trimmed mean (Figueiredo, Marcos, & Staub, 2002). Trimmed mean is considered as high-frequency estimator of inflation. In some countries it is observed that trimmed mean and CPI excluding energy work as good estimator (Clark, 2001). Specifically the observation that show the high levels of kurtosis suggest that mean with outing trimming are not efficient measure of core inflation. Trimmed means produce superior estimates of core inflation, which is a long-run centered moving average of CPI inflation. Many researchers have performed procedures of trimming from each tail trimmed 9% from each tail of the CPI pricechange distribution and suggested that it is an efficient estimator of core inflation. 457

3 Sometimes lesser trims also produce substantial efficiency gains. Historically, the optimal trimmed estimators are found to be nearly 23% more efficient than the standard mean CPI in terms of root-mean-square error. The efficient estimators were found robust to short period as well as underlying long-run trend in inflation.(bryan, Cecchetti, & Winggins II, September 1997) Core inflation should serve its purpose of finding consistent component. In Pakistan the exclusion based approach does not satisfy the basic conditions proposed by Marques (Marques, April 2000) where as all trimmed-based core inflation measures do but systematically underestimate true core inflation (Lodhi, 2007). The sample mean becomes nearly inefficient and less robust estimator of the population than the median in case when there is high kurtosis. Sometimes median is not an appropriate measure of core inflation. In order to bring the robustness and efficiency in the data series may be trimmed. Statistical noise can be removed from the data by trimming data from both sides as this would improve the Root Mean Square Error (Aidan, April 1999). The best statistical measure should be timely, robust and unbiased and verifiable by the general public (Roger, March 1997). The policymakers should balance the official exclusion-based measure with internal estimates using alternative methods in assessing the inflation environment because alternative methods are more efficient in assessing inflation (Guinigundo, April 2004). Ideal measure of inflation should reflect long-run price movements driven by actual demand in the economy and exclude short-term supply shocks (Uzagalieva) Waveletbased measures perform better, and sometimes much better than the traditional CPI based measures of inflation (Cotter, 2006). In the data driven approach must be followed due to lack of consistency in the country studies results. The measures are tested on the basis of exclusion-based methods, limited influence estimators, reweighting, and economic modeling. In this case criteria for judging the best approach is the credibility, control, deviations from a smoothed reference series, volatility, predictive ability, causality and co-integration tests, and correlation with money supply (Silver, 2007). Core inflation is to purge the components of transitory and non-monetary changes from the CPI basket. This is all the more desirable when distribution of price changes departs from normality, as is the case in Pakistan as well as in other countries. Further in Pakistan, trim-based measure compared favorably with those based on methods of excluding fixed items from the basket of CPI (Tahir, 2006). In section two of this paper measurement of core inflation is done. The third section discusses the best method of core inflation and in fourth section the statistical analysis of the methods of core inflation is done and finally conclusion is drawn. 458

4 2. Measurement of core inflation CPI headline inflation series has two components as discussed by the Scott Roger which includes idiosyncratic shocks and core inflation (Roger, March 1997). 2.1 Non food and non energy This method excludes items of energy and food from CPI basket of ninety two items provided by the SBP to the general public for verification. The items that are excluded from CPI basket are six energy items, kerosene, diesel, electricity, natural gas, petrol and CNG filling charges and all food items (Inflation Monitor, July 2007). The graphical Representation of computations on the basis of YoY and consecutive months are shown in Figure 1 and Figure 2 respectively. From the month July 2002 to January 2004 there was consistency in NFNE inflation. There was significant rise in the price of NFNE items showing high rate of NFNE till September This shows that core inflation of NFNE on the basis of YoY may not be a reliable measure. Core inflation of NFNE on the basis of consecutive month is to be an appropriate method as per diagrams. Figure 1: Core inflation YoY-NFNE v/s Headline inflation from June 2003 to September 2007 Core Inflation (NFNE) v/s Head Line Inflation CPIYOY NFNE Source: Federal Statistics Bureau-CPI based on 92 items 459

5 Figure 2: Core inflation Consecutive months -NFNE v/s Headline inflation (Monthly) from June 2005 to September 2007 Core Inflation (NFNE) v/s Head Line Inflation (Monthly) CPIMON NFNE Source: Federal Statistics Bureau-CPI based on 92 items 2.2 Trimmed mean at twenty percent, thirty percent and forty percent The second method used by SBP is twenty percent trimmed mean however the trimmed mean of thirty and forty percent are also computed for the analysis. Ten percent, fifteen percent and twenty percent of the cumulative weights are excluded from the top and bottom of the CPI services. The following are the results used, which explain the computation of core inflation for July 2007 in terms of twenty percent, thirty percent and forty percent weighted trimmed measure of CPI (Inflation Monitor, July 2007). The core inflation of ninety items with the methods twenty percent trimmed mean, thirty percent trimmed mean and forty percent trimmed mean is computed. The basis of computing these all the methods are YoY and Consecutive Monthly CPI. Figure 3 and 4 shows twenty percent trimmed mean computed on YoY basis and Consecutive monthly basis. 460

6 Figure 3: Core inflation YoY-TWTRM and Headline inflation from June 2003 to September 2007 Core Inflation (TWTRM) v/s Head Line Inflation CPIYOY TWTRM Source: Federal Statistics Bureau-CPI based on 92 items Figure 4: Core inflation Consecutive months -TWTRM and Headline inflation (Monthly) from June 2005 to September 2007 Core Inflation (TWTRM) v/s Head Line Inflation (Monthly) CPIMON TWTRM Source: Federal Statistics Bureau CPI based on 92 items Trimmed mean 30% computed on the basis of NFNE and Consecutive months is given in the figure 5 and 6 below. 461

7 Figure 5: Core inflation YoY-THTRM and Headline inflation from June 2003 to September 2007 Core Inflation (THTRM) v/s Head Line Inflation CPIYOY THTRM Source: Federal Statistics Bureau CPI based on 92 items Figure 6: Core inflation Consecutive months -THTRM and Headline inflation (Monthly) from June 2005 to September 2007 Core Inflation (THTRM) v/s Head Line Inflation CPIMON THTRM Source: Federal Statistics Bureau CPI based on 92 items Figure 7 and 8 are the core inflation measures computed on the basis of YoY and Consecutive months. 462

8 Figure 7: Core inflation YoY-FOTRM and Headline inflation from June 2003 to September 2007 Core Inflation (FOTRM) v/s Head Line Inflation CPIYOY FOTRM Source: Federal Statistics Bureau CPI based on 92 items Figure 8: Core inflation Consecutive months -FOTRM and Headline inflation (Monthly) from June 2005 to September 2007 Core Inflation (FOTRM) v/s Head Line Inflation(Monthly) CPIMON FOTRM Source: Federal Statistics Bureau CPI based on 92 items 463

9 3. Best core inflation method There are various methods of computing core inflation, for choosing the best method it is necessary to some establish criteria by which countries can choose among measures. Core inflation is computed on the basis of determinants of inflation for example when there are supply shocks in the head line inflation the best method to compute core inflation would be the exclusion of the volatile items. There are four properties of best measure of core inflation (Roger, March 1997). First, the measure must be available on a timely basis, ideally simultaneous with the publication of the actual inflation data. SBP publishes monthly bulletin and measures core inflation on timely basis as soon as the data of the inflation is available from FBS. The policy makers will not be able to decide on the monetary policy if it is not available on timely basis. Second, the measure should be easily understood. SBP contribution towards its methods of computing core inflation is that it has provided a guideline for preparing core inflation as the inflation is very important determinant of many economic variables. Thirdly; the measure should be free from revisions. If the measures of core inflation are changed retrospectively on the consistent basis this creates confusion among the policy makers therefore policy implementations problems will occur. SBP does not revise the methods of core inflation. Finally, a long term and medium term measures of core inflation should not differ significantly so that nobody can use the measure for once own interest. This property has also been verified by the SBP (Pakistan, May 2006) (Bryan, Cecchetti, & Winggins II, September 1997). The measure of core inflation should also be computable in real time; robust and unbiased; forward looking in some sense; The measures should have track record of some sort; should have some theoretical basis, should ideally in monetary theory; should be familiar and understandable to the general public; and should not be subject to revisions. These features are only important to the extent that the central bank seeks to use a measure of underlying inflation with the public to explain policy decisions (Wynne, 1999). 4. Statistical analysis of measures of core inflation The statistics like mean, variance, kurtosis and skewness are the basis of knowing the efficiency of any series. The standard normal distribution has a mean of zero, standard deviation of one, skewness of zero although skewness in itself does not mean that distribution is symmetric, and kurtosis of three. The sample mean is simply the weighted sum of the individual price changes. The standard deviation is the square root of the variance. This measure is used to scale the third and fourth moments, to obtain measures of the skewness and kurtosis of the distribution. If the skewness is positive, this means the distribution is skewed to the right showing the right-hand tail is longer than the left-hand tail and vice-versa if the skewness is negative. Kurtosis captures the weight of the distribution in the tails. A distribution with high kurtosis has a relatively large weight in the tails of the distribution. This means that one is relatively more likely to obtain a sample from the tails of the distribution. A normal distribution has a kurtosis of three 464

10 known as mesokurtic distribution. A distribution with a kurtosis larger than three is known as a leptokurtic distribution and has a relatively larger weight in the tails. A distribution with a kurtosis smaller than three is known as a platykurtic distribution. The summary of the descriptive statistics computed on the basis of YoY is shown in Table. As shown in the table NFNE has the lowest mean showing the core components as comparative to the twenty percent, thirty percent and forty percent trimmed mean. Root Mean Square Error (RMSE) is the lowest in case of NFNE verifying the claim. All four methods show that the observations are negatively skewed with lowest standard deviation and range in NFNE verifying the consistency and reduction of noise in the data. The degree of kurtosis is below three suggesting platykurtic curve however, it is negative for all methods. In case of platykurtic curve mean is the most efficient measure of core inflation. Table 1: Summary of Statistics computed on the Basis of YoY from July 2002 to September DESCRIPTIVE STATISTICS CPI YOY NFNE TWTRM THTRM FOTRM Mean Standard Error Median Standard Deviation Kurtosis Skewness Range Minimum Maximum Count Source: Monthly Bulletin of Federal Bureaus of Statistics The summary of the descriptive statistics computed on the basis of CPI on the basis of consecutive months is given in Table 2. As shown in the table thirty percent has the lowest mean which as comparative to the NFNE, twenty percent and forty percent trimmed mean. Root Mean Square Error (RMSE) is the lowest in incase of NFNE verifying the claim. 465

11 Table 2: Summary of Statistics computed on the Basis of Consecutive Months from July 2002 to September DESCRIPTIVE STATISTICS CPIMON NFNE TWTRM THTRM FOTRM Mean Standard Error Median Standard Deviation Kurtosis Skewness Range Minimum Maximum Count Source: Monthly Bulletin of Federal Bureaus of Statistics The degree of skewness has significant implications for which measure of central tendency is unbiased. If the distribution has skewness of zero, the mean and the median coincide and both are unbiased. However, if the distribution is skewed, then the mean and median diverge, and the median will be a biased estimator of the central tendency of the distribution (Wynne, 1999). For example, in this case the distribution is negatively skewed the median will lie above the mean. So the values computed suggest median is biased estimator as the mean and median do not coincide. The results computed suggest that CPI computed on the basis of YoY Headline Inflation has the lower volatility as compare to the computations on the basis of Consecutive months. 5. Conclusion The paper computes core inflation methods and concludes that the degree of kurtosis is below three suggesting platykurtic curve which means that mean is the most efficient measure of core inflation. There was a decline in the average standard deviation confirming reduction of noise in the data on the basis of YoY as compare to basis of Consecutive Months. The results computed suggest that CPI computed on the basis of YoY Headline Inflation has the lower volatility as compare to the computations on the basis of Consecutive months. Further methods satisfy the four properties of measures of core inflation.. 466

12 References Aidan, M. (April 1999). A Statistical Measure of Core Inflation Central Bank of Ireland. Technical Paper, Central Bank of Ireland, 2/RT/99, April Bryan, M. F., Cecchetti, S. G., & Winggins II, R. L. (September 1997). Efficient Inflation Estimators. National Bureau of Economic Research. Clark, T. (2001). Comparing Measures of Core Inflation. Federal Reserve Bank. Kansas City: Economic Review. Cotter, J. a. (2006). U.S. Core Inflation: A Wavelet Analysis No../ retrieved August MPRA Paper, University College Dublin. Figueiredo, F., Marcos, R., & Staub, R. B. (2002). Evaluation and Combination of Core Inflation Measures for Brazil. Central Bank of Brazil, Research Department. Guinigundo, D. C. (April 2004). An Official Core Inflation Measure for the Philippines. Department of Economic Research. Bangko Sentralng Pilipinas. (July 2007). Inflation Monitor. State Bank of Pakistan. Lodhi, M. A. (2007). Evaluating Core Inflation Measures in Pakistan. State Bank of Pakistan. Marques, C. R. (April 2000). Evaluating core inflation indicators. Working paper, Banco de Portugal, Economic Research Department. Pakistan, S. B. (May 2006). Inflation Monitor May Karachi. Roger, S. (March 1997). A Robust Measure of Core Inflation in New Zealand, Reserve Bank of New Zealand. Silver, M. (2007). Core Inflation: Measurement and statistical Issues in choosing among the statistical measures. International Monetary Fund. Tahir, S. (2006). Core Inflation Measures for Pakistan. State Bank of Pakistan. Uzagalieva, A. Finding Optimal Measures of Core Inflation in the Kyrgyz Republic. Economics Institute of the Academy of Sciences of the Czech Republic, The Center for Economic Research and Graduate Education. Charles University. Wynne, M. A. (1999). Core inflation: A review of some conceptional issues. ECB. 467