In India, year-on-year percentage changes of price indexes are widely used as the measure of inflation. In terms of monthly data, each observation of a one-year change in inflation is the sum of 12 one-month changes. This suggests that better information about inflationary pressures can be obtained using point-on-point monthly changes. This requires seasonal adjustment. We apply standard seasonal adjustment procedures in order to obtain a point-on-point seasonally adjusted monthly time-series of inflation in India. In three interesting high inflation episodes - 1994-95, 2007 and 2008 - we find that this data yields a faster and better understanding of inflationary pressures.
SPECIAL ARTICLEdecember 6, 2008 EPW Economic & Political Weekly62Early Warnings of Inflation in IndiaRudrani Bhattacharya, Ila Patnaik, Ajay ShahIn India, year-on-year percentage changes of price indexes are widely used as the measure of inflation. In terms of monthly data, each observation of a one-year change in inflation is the sum of 12 one-month changes. This suggests that better information about inflationary pressures can be obtained using point-on-point monthly changes. This requires seasonal adjustment. We apply standard seasonal adjustment procedures in order to obtain a point-on-point seasonally adjusted monthly time-series of inflation in India. In three interesting high inflation episodes – 1994-95, 2007 and 2008 – we find that this data yields a faster and better understanding of inflationary pressures. 1 Introduction The focus of inflation measurement in India is the year-on-year (YOY) change in the wholesale price index (WPI). As a thumb-rule, in the present environment, inflation of roughly 3% is considered acceptable and inflation of 6% and above is considered an alarming high inflation episode. Figure 1 (p 63) shows the time-series of YOY inflation with a horizontal line at 6%. This highlights the two recent high inflation episodes, in 2007 and 2008. In the high inflation episode of 2007, YOY infla-tion exceeded 6% in January 2007 and dropped below 6% in April 2007. In the high inflation episode of 2008, YOY inflation exceeded 6% in March 2008. Inflation monitoring in India is almost entirely done using YOY price changes. As an example, theAnnual Report released by the Reserve Bank of India is entirely couched in terms of YOY changes in price indexes.1 The measure of inflation used in the Economic Survey released by the Ministry of Finance is the percentage dif-ference between a moving average of the price index over the latest 12 months when compared with the identical value of a year ago. YOY inflation measures have a weakness in that they represent the sum of 12 monthly changes in the price level. In working with monthly data on inflation, each observation of month-on-month (mOm) inflation can be thought of as one shock or one innovation in the time-series. The YOY inflation is then an equally weighted moving average of the latest 12 shocks. Analysing the individual mOm price changes can yield more timely information about inflation. When innovations arise in the inflation process, the analysis of point-on-point (POP) inflation can yield early warn-ings about the onset or ending of high inflation episodes, when compared with the slow response ofYOY inflation. Our main objective is to investigate whether tracking the changes in price indices in a shorter time frame (WOW or MOM), instead ofYOY is able to give us a more accurate sense of price pressure. Tracking the price pressure in turn will be helpful in timely adoption of appropriate policies. However, exploring the inflation dynamics following a purely statistical approach has limitations as it does not capture the behavioural structure of the economy (Srinivasan 2008). The fuller agenda of research on inflation involves incorporating real activities summarised by the output gap, supply shock, expectation formation by the economic agents and the interaction with monetary policy. This paper contributes to that larger task in one respect: better measurement of inflation.WhilePOP measurement of inflation is attractive, POP inflation measures are contaminated by seasonal effects that are not influ-enced by monetary policy. As an example, the arrival of a harvest This work was initiated at the request of the Planning Commission. It is part of the NIPFP-DEA Research Program on Capital Flows and their Consequences. We are grateful to Montek Singh Ahluwalia, Kirit Parikh, Abhijit Sen, Josh Felman, Jahangir Aziz, Shubhashis Gangopadhyay and seminar participants at the Planning Commission and the anonymous referee of EPW, for many useful discussions which greatly improved the work. The implementation of this research was done by Ankur Shukla (IIT Kharagpur), Mohd Farhan Ansari, Himanshu Gupta and Sayeed Hussain (IIT Roorkee), Kushdesh Prasad (ISI Delhi) and Apoorva Kapavarapu (Christ’s College, Cambridge University). An earlier version was released as NIPFP Working Paper 54. The key data involved in this paper has been placed at http://www.mayin.org/ajayshah/A/BPS2008_ew.csv on the web.Rudrani Bhattacharya (rudrani.isi@gmail.com), Ila Patnaik (ilapatnaik@gmail.com) and Ajay Shah (ajayshah@mayin.org) are with the National Institute for Public Finance and Policy, New Delhi.
SPECIAL ARTICLEEconomic & Political Weekly EPW December 6, 200863in a particular month would yield a lowered estimate of POP inflation. POP inflation meas-ures are hence likely to be inappropriate in obtaining information about inflation as a macroeconomic phenomenon. The resolution of this problem lies in sea-sonal adjustment. In this paper, we apply standard methodologies of seasonal adjust-ment to Indian inflation data. This gives us estimates of POP seasonally adjusted (POPSA) inflation. We then explore the usefulness of this information for the purpose of analysing inflation in three interesting high inflation episodes: 1994-95, 2007 and 2008. We do not, however, deal with deeper con-cerns regarding the WPI and its relevance to economic agents. These concerns, highlighted by Srinivasan (2008), are very important in thinking about inflation measurement in India. Problems of sampling, composition, consolidation and reporting need to be addressed in improving inflation measurement.2This paper, how-ever, focuses on the narrow issue of how POPSA inflation is a use-ful and important new way of thinking about inflation.Our main finding is thatPOPSA inflation helps in obtaining superior information about inflationary pressures in the economy. This finding is not unusual in an international perspective. As an example, theInflation Report of the Bank of England is almost entirely couched in terms of seasonally adjustedpOpinflation. 2 Methodology for Seasonal Adjustment Statisticians have grappled with problems of seasonal adjustment for almost 100 years. The first tools developed for seasonal adjustments were data-driven filters, such as moving averages, aimed at smoothing out the seasonal fluctuations (Bell and Hillmer 1984). This strategy can decompose a time-series into trend, seasonal and irregular components. These components do not need explicit models of each of these elements. The irregular component is defined as what remains after the trend and sea-sonal components have been removed by filters. Given the limita-tions of this methodology, the estimated irregular component is not white noise. In the late 20th century, model-based approaches came to be applied to this problem. These were based on writing a model that expressed seasonal fluctuations, and arriving at estimates of seasonality through estimation theory applied to the data. The simplest of these strategies is the dummy variable regres-sion. As an example, log WPI can be regressed on 12 month dum-mies while excluding an intercept. This regression can be estimated by Ordinary Least Squares (OLS) or by robust regression tech-niques. This is a simple and readily implemented strategy. How-ever, it is not effective at dealing with changing seasonality. The way forward lay in the Box-Jenkins approach, with the seasonal ARIMA model, where the seasonal pattern of one period is assumed to repeat in the next period with an additive random perturbation. We conduct seasonal adjustment using theX-12-ARIMA system developed by the US Bureau of Census which combines all these three approaches. It conducts dummy varia-ble regression for fixed seasonal effects, trading day effects, moving holiday effects (such as Easter and Thanksgiving Day) and outliers; and fits a seasonal ARIMA model thus modelling the changing seasonal pat-tern. X-12-ARIMA fits the following model: yt = ∑βixit+ ztwhere zt follows a seasonal ARIMA(p,d,q) (P, D, Q) model. The ARIMA identification is done automatically by analysing the auto-correlation function (ACF) and the partial autocorrelation function (PACF). A set of dummy variables reflecting various kinds of seasonal effects are used in a regression model. An iterative GLS algorithm is then used, which works in two consecutive steps. In step 1, given values ofAR andMA para-meters, coefficients of dummies are estimated byGLS using the covariance structure of the regression errors determined by the ARIMA model, and in step 2, given estimates of regression para-meters, regression errors are calculated and the ARIMA model is estimated using MLE. These two steps are iterated till conver-gence is achieved. The fitted series, adjusted for effects of regressors, including outliers, is passed through seasonal and trend filters to obtain seasonally adjusted series, trend and irregular components. X-12-ARIMA checks that the regression residuals are white noise using the Box-Ljung q statistic. It also checks for residual season-ality in the seasonally adjusted series and irregular components using F-tests and spectral plots of these series. If seasonality is still present in the adjusted series, the programme warns of visu-ally significant peaks at seasonal frequencies for monthly series of k/12 cycles per month (ork cycles per year) where 1<k < 5 and trading day frequencies of 0.348 and 0.432 cycles per month (or 4.176 and 5.184 cycles per year). In terms of data resources, we use the monthly WPI series from CMIE’sBusiness Beacon database. Each observation for a month is the average of all observations of WPI in the month. Our dataset runs from April 1990 to July 2008 and has 220 observations.3 121086420 | | | | | | | | | | | | | | |4/06 6/06 8/06 10/06 12/06 2/07 4/07 6/07 8/07 10/07 12/07 2/08 4/08 5/08 7/08Figure 1: High Inflation Episodes of 2007 and 2008YOY WPI inflationTable 1: Correlation Matrix of Alternative Measures of POP Changes of the WPI NSA X-12-ARIMA Dummy Variable Reg STLNSA 1 X-12-ARIMA 0.91 1 Dummy variable reg 0.93 0.96 1 STL 0.82 0.93 0.87 1Table 2: Examples of Numerical Values Obtained with Different Methods of Seasonal AdjustmentMonth Raw X-12-ARIMA Dummy Var Reg STL2007-10 0.553.16 1.31 1.812007-11 3.896.37 6.17 6.002007-12 2.7710.94 9.1713.052008-01 9.9413.24 12.47 20.612008-02 9.3111.92 10.89 13.452008-03 30.17 31.14 31.63 23.012008-04 15.85 9.08 8.88 9.112008-05 12.01 7.95 10.95 9.182008-06 29.78 26.59 25.78 35.722008-07 12.86 8.57 10.15 12.11
SPECIAL ARTICLEDecember 6, 2008 EPW Economic & Political Weekly64The log of WPI is used for adjustment and a multiplicative model is chosen. The iterative GLS procedure of the programme fits the first difference of the series to an ARIMA (1 2). It implies that the WPI series reflects a fixed seasonal pattern captured by the monthly dummies and hence the series, net of seasonal effects, follows a pure ARIMA (1, 1, 2) structure. In other words, the WPI in India is non-stationary, but WPI inflation is a stationary process.3 Definitions and Notation POP: Point-on-point inflation. Computed asπt = 1200(log pt – log pt–1) where pt is the level of the price index of monthly frequency at time t. This yields an annualised measure. As an example, if a price index goes up from 100 to 101 in a month, this corresponds to an annual-ised rate of inflation of 11.94%. SA: Seasonally adjusted. NSA: Not seasonally adjusted. POPSA: POP inflation (as defined above) computed using the time-series of seasonally adjusted levels. POPNSA: POP inflation (as defined above) computed using the raw time-series of unadjusted levels. 4 Robustness 4.1 Outliers X-12-ARIMA detects outliers and ensures that they do not have a disproportionate impact on the estimated results. This addresses one key concern in real world applications.4.2 Sensitiveness to Alternative Techniques of Seasonal AdjustmentIn order to obtain an empirical sense on how sensitive the results are to alternative algorithms of seasonal adjustment, we implement three different strategies: (a) X-12-ARIMA, (b) dummy variable regression using a robust regression (Venables and Ripley 2002) and (c) decomposition into trend, seasonality and irregular component using a non-parametric “STL” algorithm (Cleveland et al 1990) using LOESS (Cleveland et al 1992). Of these, X-12-ARIMA and the variable regression are parametric methods; however in both cases robust estimation is done to reduce the influence of extreme observations. STL is an explicitly non-parametric method. Table 1 (p 63) shows the correlation matrix of four different time-series of POP changes of the WPI: the raw data, and the three alternative seasonal adjustment methods. All three seasonal adjustment strategies explicitly deal with outliers, which would inevitably generate a loss of correlation against the raw data series. The lowest correlation in this table, of 0.82, is between the raw data and the seasonal adjustment done through STL. All the other correlations are higher than this. Table 2 (p 63) shows the numerical values obtained in recent months, which allows us to compare the results obtained by the three different methods of seasonal adjustment. As an example, in January 2008, while the raw data showed inflation of 9.94%, the three different seasonal adjustment algorithms showed values of 13.24%, 12.47% and 20.61%. The three SA series are remarkably alike. This fact, coupled with the high correlations seen in Table 1,helps us have confidence that the results are not unduly sensitive to the choice of strategy for seasonal adjustment. 4.3 Extent to Which Seasonal Adjustment Removes Seasonality The intuition of spectral analysis is particularly useful in inter-preting the goals and the results of seasonal adjustment procedures. Figure 2 shows the Fourier decomposition of POP changes inWPI, comparing the raw series (termed NSA or not seasonally adjusted) against the X-12-ARIMA seasonally adjusted (termedSA) series.This shows that the raw series has an extremely strong peak at the wavelength of one year.4 This peak is removed by seasonal adjustment. At low and high frequencies compared with this peak, the spectrum of the raw data is close to the spectrum of the seasonally adjusted data, which suggests that other features of the time-series have been unaffected by the process of seasonal adjustment. 5 EarlyWarnings Seasonally adjusted data is well suited for short-term forecast-ing. For this, a variety of econometric models can be applied to the seasonally adjusted data. The efforts of many researchers are required in modelling inflation in India usingPOPSA data. In order to obtain intuition into the usefulness of seasonal adjust-ment, we merely examine the data looking for large values. 20015010050 | | | | | |0.00 0.050.100.150.200.25FrequencyRaw dataSA (x 12 ARIMA)Period = 1 yearFigure 2: Spectrum of NSA and SA POP Changes in WPISpectrum (decibles)Figure 3: Short-term Interest Rate(expressed in real terms (smoothed)) | | | | | | | | | | | | | | |4/05 10/95 10/96 10/97 10/98 10/99 10/2000 10/01 10/02 10/03 10/04 10/05 10/06 10/07 4/086420–2Real rate (in %)
SPECIAL ARTICLEEconomic & Political Weekly EPW December 6, 200865The 6% threshold for a “high inflation episode” works out to the 60th percentile of the data. The 60th percentile of thePOPSA WPI inflation works out to an annualised value of 6.65%. Hence, we define a high inflation episode asYOY inflation exceeding 6%5 and consider the consequences of putting out an early warning when the POP SA inflation exceeds 6.65%. In the following tables, these “high inflation episode” or “warning” values are shown in boldface. In order to obtain estimates of the real interest rate at the short-end of the yield, forward-looking estimates of inflation are required. In this, we seek to adjust the nominal rate for the 90-day maturity using inflation forecasts for a 90-day horizon. To achieve this, the POP SA data is used to make forecasts, using an AR(6) model, for the coming three months.6 At each month, information available till that month is used to estimate theAR model, and to make forecasts for POPSA inflation over the coming three months using this model. The average of these three forecasts is used to convert the nominal short-term interest rate into the short-term real rate. Figure 3 (p 64) shows the smoothed time-series of the real rate computed in this fashion.75.1 High Inflation Episode of 1994-95 Table 3 shows YOYWPI inflation, POPSAWPI inflation, and the responses of monetary policy in the high inflation episode of 1994-95.8 A large POP SA change took place in April 1994. This may be partly related to statistical measurement issues ofWPI. At this time, the 90-day interest rate in the economy was 7.36%. In the following two months,POPSA inflation showed large values of 7.17% and 16.78%. Large values for POPSA inflation are visible till May 1995. In this period, the short-term rate became negative in real terms. The short-term rate was negative in real terms all the way till January 1995. From June 1995 onwards,POPSA inflation dropped sharply. However, large values for YOY inflation continued to be recorded, since YOY inflation is the average of the last 12 values for POP inflation. Monetary policy tightening is visible right from the start. The real rate, which was nega-tive, started rising. In June 1995, whenPOPSA inflation had started easing, the real rate was +2.21%. The short-term rate stayed above 2% in real terms till August 1996. Over this period, YOY WPI inflation ebbed away. However, when judged byPOPSA data, WPI inflation had sub-sided 14 months earlier, by June 1995. Examining POP SA data does not substan-tially alter the date at which the tightening began. However,POPSA inflation had subsided by June 1995, which suggests that the easing could have begun earlier and progressed faster. In this period, the use of POPSA data would have given a useful early warning that inflation had subsided. 5.2 Example: High Inflation Episode of 2007 Table 4 (p 66) shows the events of the high inflation episode of 2007. Going by the YOY series, the high inflation episode erupted in January 2007 and ended in April 2007. The POPSA data, how-ever, shows a very different picture. It shows that the episode began in May 2006: an early warning of eight months. POPSA inflation was high in the period from May 2006 till October 2006: over this period, inflation averaged 7.81%. The inflationary pressures subsided by October 2006, before the high inflation episode had even showed up in the YOY data. To the extent that policy responses took place after October 2006, they were possibly in the wrong direction. In the critical period from May 2006 to October 2006, when there was high inflation, monetary policy was expansionary. Monetary policy tightening is visible much later. The real rate went up from –0.55% in September 2006 to 3.35% in June 2007. Inflation had subsided before the tightening began. 5.3 Example:HighInflationEpisode of 2008 Table 5 (p 66) shows facts about inflation in the high inflation episode of 2008. From December 2007 onwards, inflation pressures were visible in the POP SA data. They burst into the public consciousness in March 2008, with reports of highYOYWPI inflation. The use of POP SA data would have given an early warning by three months. A high rate ofPOPSA inflation is visible all the way to the latest data for July 2008. The future evolution of this high inflation episode is as yet unclear. The short term real interest rate was at 2.59% in November 2007, the last month prior to large inflation shocks. This plunged to –4.50% in March 2008. At a time of positive inflationary shocks, monetary policy was expansionary. Real rates remain very low when compared with those required to rein in inflation. The last observation of the real rate, –0.88% in July 2008, remained much below the level of +2.59% in November 2007, before this inflationary episode began. This suggests that until July 2008, monetary policy tighten-ing aiming to combat inflation has not taken place. 6 Areas for Further Research on Seasonal Adjustment There are two key areas where further work is required. The first is the issue of seasonal adjustment of weekly data. When working with monthly Table 3: WPI Inflation and Monetary Policy in High Inflation Episode of 1994-95(in %)Month WPIShort-termRate YOY POP SA Nominal Real 1994-04 7.50 79.84 7.36 -2.70 1994-05 8.30 7.17 7.48 -2.19 1994-06 10.00 16.78 8.25 -2.71 1994-07 11.10 5.56 8.83 -0.62 1994-08 11.80 8.00 8.13 -1.61 1994-09 11.90 3.32 8.58 -0.75 1994-10 12.70 10.68 8.77 -1.15 1994-11 13.20 7.89 8.50 -1.70 1994-12 14.50 17.40 9.42 -0.47 1995-01 16.20 20.42 10.68 -0.14 1995-02 16.90 7.57 11.29 2.64 1995-03 16.90 3.44 11.65 2.38 1995-04 10.97 15.31 11.72 0.74 1995-05 10.98 7.97 12.01 1.11 1995-06 9.72 3.19 12.46 2.21 1995-07 9.63 5.02 12.84 3.12 1995-08 8.94 1.18 12.63 3.86 1995-09 8.93 3.18 12.61 3.10 1995-10 8.42 4.56 12.78 4.12 1995-11 8.21 5.16 12.97 5.02 1995-12 6.63 -0.41 12.97 6.45 1996-01 4.99 3.20 12.97 6.40 1996-02 4.53 1.92 12.97 6.73 1996-03 4.53 3.09 12.97 6.81 1996-04 3.68 4.47 12.71 6.42 1996-05 3.57 7.12 12.39 6.06 1996-06 3.64 4.00 12.41 6.22 1996-07 4.26 13.14 10.80 2.79 1996-08 4.92 9.16 9.20 1.36 1996-09 5.08 4.66 10.07 2.78 1996-10 4.58 -2.49 9.50 2.96 1996-11 4.48 3.84 7.54 0.41 1996-12 5.24 8.82 8.10 -0.33 1997-01 5.16 3.60 8.12 1.64
SPECIAL ARTICLEEconomic & Political Weekly EPW December 6, 200867Notes1 In 2007, the RBI released a Report of the Internal Technical Group on Seasonal Movements in Inflation chaired by Balwant Singh. However, these ideas have not filtered into monetary policyformulation and official communications of the RBI. 2 Most notably, the composition of the WPI excludes the services sector, which composes over 60% of GDP. 3 There are concerns about utilising this full series given the change of base year which generates a large outlier in April 1994. While X-12-ARIMA detects and treats outliers, the analysis of the paper has hence been repeated using the data from May 1994 onwards. The broad results hold with this shorter time-series also. 4 The y axis shows 10 log10I(ω) in units of decibels where I(ω) = 1/n [{n∑(t=1) Xtsin(ωt)}2+ {n∑(t=1) Xtcos(ωt)}2] is the spectral density. Smoothing is done using modified Daniell smoothers (Venables and Ripley 2002). 5 We choose 6% as the threshold value since the target rate of inflation in India is spread up to 5%.6 This is a purely statistical approach to estimating expected inflation, and does not reflect any spe-cific theory or assumptions regarding formation of inflation expectations. It also does not take into account varying expectations of varying agents in the economy. 7 Special difficulties are faced in the period from April 1993 to April 1994, where the WPI shows a value of 100 for all the months of 1993-94 and then shows a sharp jump in April 1994. Hence, the POP SA value for WPI for these months was forced to be missing before computing the real rate using the procedure described in the text.8 A deeper economic analysis of the exchange rate regime, loss of monetary policy autonomy and infla-tion in this episode is presented in Patnaik (2005).References Bell, W and S Hillmer (1984): “Issues Involved with the Seasonal Adjustment of Economic Time Series”, Journal of Business and Economic Statis-tics, 2(4), 291-320. Cleveland, R B, W S Cleveland, J E McRae and I Terpenning (1990): “A Seasonal-trend Decom-position Procedure Based on Loess”, Journal of Official Statistics, 6, 3-73. Cleveland, W S, E Grosse and W M Shyu (1992): “Local Regression Models” in J M Chambers, T J Hastie, eds. “Statistical Models in S”, chapter 8 (Wadsworth and Brooks/Cole). Harvey, A, S Koopman and M Riani (1997): “The Modelling and Seasonal Adjustment of Weekly Observations”,Journal of Business and Economic Statistics, 15(3), 354-68. Hood, C and D Findley (2001): “Comparing Direct and Indirect Seasonal Adjustments of Aggregate Series”, Proceedings of the Annual Meeting of the AmericanStatisticalAssociation. Mistry, P (2007): Making Mumbai an International Financial Centre: Committee Report (Sage Publish-ing and Ministry of Finance, Government of India), URL http://finmin.nic.in/mifc.html. Patnaik, I (2005): “India’s Experience with a Pegged Exchange Rate” in S Bery, B Bosworth, A Pana-gariya, eds.The India Policy Forum 2004 (Brook-ings Institution Press and NCAER) pp 189-226, URL http://openlib.org/home/ila/PDFDOCS/Patnaik2004_implementation.pdf. Pierce, D A, M R Grupe and W P Cleveland (1984): “Seasonal Adjustment of the Weekly Mone-tary Aggregates: A Model-based Approach”, Journal of Business and Economic Statistics, 2(3), 260-70. Rajan, R (2008): Committee for Financial Sector Reforms, Committee Report (Planning Commis-sion: Government of India). Singh, B (2007): Report of the Internal Technical Group on Seasonal Movements in Inflation, Reserve Bank of India. Srinivasan, T N (2008): “Price Indices and Inflation Rates”, Economic & Political Weekly, Special Volume (June), 217-23. – (2008): “Some Aspects of Price Indices, Inflation Rates and the Services Sector in National Income Statistics” in N Jayaram, R S Deshpande, eds. Footprints of Development and Change: Essays in Memory of Professor V K R V Rao (Delhi: Academic Foundation), pp 437-74. Venables, W N and B D Ripley (2002): Modern Applied Statistics with S (Springer, 4th edition).
SPECIAL ARTICLEdecember 6, 2008 EPW Economic & Political Weekly62Early Warnings of Inflation in IndiaRudrani Bhattacharya, Ila Patnaik, Ajay ShahIn India, year-on-year percentage changes of price indexes are widely used as the measure of inflation. In terms of monthly data, each observation of a one-year change in inflation is the sum of 12 one-month changes. This suggests that better information about inflationary pressures can be obtained using point-on-point monthly changes. This requires seasonal adjustment. We apply standard seasonal adjustment procedures in order to obtain a point-on-point seasonally adjusted monthly time-series of inflation in India. In three interesting high inflation episodes – 1994-95, 2007 and 2008 – we find that this data yields a faster and better understanding of inflationary pressures. 1 Introduction The focus of inflation measurement in India is the year-on-year (YOY) change in the wholesale price index (WPI). As a thumb-rule, in the present environment, inflation of roughly 3% is considered acceptable and inflation of 6% and above is considered an alarming high inflation episode. Figure 1 (p 63) shows the time-series of YOY inflation with a horizontal line at 6%. This highlights the two recent high inflation episodes, in 2007 and 2008. In the high inflation episode of 2007, YOY infla-tion exceeded 6% in January 2007 and dropped below 6% in April 2007. In the high inflation episode of 2008, YOY inflation exceeded 6% in March 2008. Inflation monitoring in India is almost entirely done using YOY price changes. As an example, theAnnual Report released by the Reserve Bank of India is entirely couched in terms of YOY changes in price indexes.1 The measure of inflation used in the Economic Survey released by the Ministry of Finance is the percentage dif-ference between a moving average of the price index over the latest 12 months when compared with the identical value of a year ago. YOY inflation measures have a weakness in that they represent the sum of 12 monthly changes in the price level. In working with monthly data on inflation, each observation of month-on-month (mOm) inflation can be thought of as one shock or one innovation in the time-series. The YOY inflation is then an equally weighted moving average of the latest 12 shocks. Analysing the individual mOm price changes can yield more timely information about inflation. When innovations arise in the inflation process, the analysis of point-on-point (POP) inflation can yield early warn-ings about the onset or ending of high inflation episodes, when compared with the slow response ofYOY inflation. Our main objective is to investigate whether tracking the changes in price indices in a shorter time frame (WOW or MOM), instead ofYOY is able to give us a more accurate sense of price pressure. Tracking the price pressure in turn will be helpful in timely adoption of appropriate policies. However, exploring the inflation dynamics following a purely statistical approach has limitations as it does not capture the behavioural structure of the economy (Srinivasan 2008). The fuller agenda of research on inflation involves incorporating real activities summarised by the output gap, supply shock, expectation formation by the economic agents and the interaction with monetary policy. This paper contributes to that larger task in one respect: better measurement of inflation.WhilePOP measurement of inflation is attractive, POP inflation measures are contaminated by seasonal effects that are not influ-enced by monetary policy. As an example, the arrival of a harvest This work was initiated at the request of the Planning Commission. It is part of the NIPFP-DEA Research Program on Capital Flows and their Consequences. We are grateful to Montek Singh Ahluwalia, Kirit Parikh, Abhijit Sen, Josh Felman, Jahangir Aziz, Shubhashis Gangopadhyay and seminar participants at the Planning Commission and the anonymous referee of EPW, for many useful discussions which greatly improved the work. The implementation of this research was done by Ankur Shukla (IIT Kharagpur), Mohd Farhan Ansari, Himanshu Gupta and Sayeed Hussain (IIT Roorkee), Kushdesh Prasad (ISI Delhi) and Apoorva Kapavarapu (Christ’s College, Cambridge University). An earlier version was released as NIPFP Working Paper 54. The key data involved in this paper has been placed at http://www.mayin.org/ajayshah/A/BPS2008_ew.csv on the web.Rudrani Bhattacharya (rudrani.isi@gmail.com), Ila Patnaik (ilapatnaik@gmail.com) and Ajay Shah (ajayshah@mayin.org) are with the National Institute for Public Finance and Policy, New Delhi.
SPECIAL ARTICLEEconomic & Political Weekly EPW December 6, 200863in a particular month would yield a lowered estimate of POP inflation. POP inflation meas-ures are hence likely to be inappropriate in obtaining information about inflation as a macroeconomic phenomenon. The resolution of this problem lies in sea-sonal adjustment. In this paper, we apply standard methodologies of seasonal adjust-ment to Indian inflation data. This gives us estimates of POP seasonally adjusted (POPSA) inflation. We then explore the usefulness of this information for the purpose of analysing inflation in three interesting high inflation episodes: 1994-95, 2007 and 2008. We do not, however, deal with deeper con-cerns regarding the WPI and its relevance to economic agents. These concerns, highlighted by Srinivasan (2008), are very important in thinking about inflation measurement in India. Problems of sampling, composition, consolidation and reporting need to be addressed in improving inflation measurement.2This paper, how-ever, focuses on the narrow issue of how POPSA inflation is a use-ful and important new way of thinking about inflation.Our main finding is thatPOPSA inflation helps in obtaining superior information about inflationary pressures in the economy. This finding is not unusual in an international perspective. As an example, theInflation Report of the Bank of England is almost entirely couched in terms of seasonally adjustedpOpinflation. 2 Methodology for Seasonal Adjustment Statisticians have grappled with problems of seasonal adjustment for almost 100 years. The first tools developed for seasonal adjustments were data-driven filters, such as moving averages, aimed at smoothing out the seasonal fluctuations (Bell and Hillmer 1984). This strategy can decompose a time-series into trend, seasonal and irregular components. These components do not need explicit models of each of these elements. The irregular component is defined as what remains after the trend and sea-sonal components have been removed by filters. Given the limita-tions of this methodology, the estimated irregular component is not white noise. In the late 20th century, model-based approaches came to be applied to this problem. These were based on writing a model that expressed seasonal fluctuations, and arriving at estimates of seasonality through estimation theory applied to the data. The simplest of these strategies is the dummy variable regres-sion. As an example, log WPI can be regressed on 12 month dum-mies while excluding an intercept. This regression can be estimated by Ordinary Least Squares (OLS) or by robust regression tech-niques. This is a simple and readily implemented strategy. How-ever, it is not effective at dealing with changing seasonality. The way forward lay in the Box-Jenkins approach, with the seasonal ARIMA model, where the seasonal pattern of one period is assumed to repeat in the next period with an additive random perturbation. We conduct seasonal adjustment using theX-12-ARIMA system developed by the US Bureau of Census which combines all these three approaches. It conducts dummy varia-ble regression for fixed seasonal effects, trading day effects, moving holiday effects (such as Easter and Thanksgiving Day) and outliers; and fits a seasonal ARIMA model thus modelling the changing seasonal pat-tern. X-12-ARIMA fits the following model: yt = ∑βixit+ ztwhere zt follows a seasonal ARIMA(p,d,q) (P, D, Q) model. The ARIMA identification is done automatically by analysing the auto-correlation function (ACF) and the partial autocorrelation function (PACF). A set of dummy variables reflecting various kinds of seasonal effects are used in a regression model. An iterative GLS algorithm is then used, which works in two consecutive steps. In step 1, given values ofAR andMA para-meters, coefficients of dummies are estimated byGLS using the covariance structure of the regression errors determined by the ARIMA model, and in step 2, given estimates of regression para-meters, regression errors are calculated and the ARIMA model is estimated using MLE. These two steps are iterated till conver-gence is achieved. The fitted series, adjusted for effects of regressors, including outliers, is passed through seasonal and trend filters to obtain seasonally adjusted series, trend and irregular components. X-12-ARIMA checks that the regression residuals are white noise using the Box-Ljung q statistic. It also checks for residual season-ality in the seasonally adjusted series and irregular components using F-tests and spectral plots of these series. If seasonality is still present in the adjusted series, the programme warns of visu-ally significant peaks at seasonal frequencies for monthly series of k/12 cycles per month (ork cycles per year) where 1<k < 5 and trading day frequencies of 0.348 and 0.432 cycles per month (or 4.176 and 5.184 cycles per year). In terms of data resources, we use the monthly WPI series from CMIE’sBusiness Beacon database. Each observation for a month is the average of all observations of WPI in the month. Our dataset runs from April 1990 to July 2008 and has 220 observations.3 121086420 | | | | | | | | | | | | | | |4/06 6/06 8/06 10/06 12/06 2/07 4/07 6/07 8/07 10/07 12/07 2/08 4/08 5/08 7/08Figure 1: High Inflation Episodes of 2007 and 2008YOY WPI inflationTable 1: Correlation Matrix of Alternative Measures of POP Changes of the WPI NSA X-12-ARIMA Dummy Variable Reg STLNSA 1 X-12-ARIMA 0.91 1 Dummy variable reg 0.93 0.96 1 STL 0.82 0.93 0.87 1Table 2: Examples of Numerical Values Obtained with Different Methods of Seasonal AdjustmentMonth Raw X-12-ARIMA Dummy Var Reg STL2007-10 0.553.16 1.31 1.812007-11 3.896.37 6.17 6.002007-12 2.7710.94 9.1713.052008-01 9.9413.24 12.47 20.612008-02 9.3111.92 10.89 13.452008-03 30.17 31.14 31.63 23.012008-04 15.85 9.08 8.88 9.112008-05 12.01 7.95 10.95 9.182008-06 29.78 26.59 25.78 35.722008-07 12.86 8.57 10.15 12.11
SPECIAL ARTICLEDecember 6, 2008 EPW Economic & Political Weekly64The log of WPI is used for adjustment and a multiplicative model is chosen. The iterative GLS procedure of the programme fits the first difference of the series to an ARIMA (1 2). It implies that the WPI series reflects a fixed seasonal pattern captured by the monthly dummies and hence the series, net of seasonal effects, follows a pure ARIMA (1, 1, 2) structure. In other words, the WPI in India is non-stationary, but WPI inflation is a stationary process.3 Definitions and Notation POP: Point-on-point inflation. Computed asπt = 1200(log pt – log pt–1) where pt is the level of the price index of monthly frequency at time t. This yields an annualised measure. As an example, if a price index goes up from 100 to 101 in a month, this corresponds to an annual-ised rate of inflation of 11.94%. SA: Seasonally adjusted. NSA: Not seasonally adjusted. POPSA: POP inflation (as defined above) computed using the time-series of seasonally adjusted levels. POPNSA: POP inflation (as defined above) computed using the raw time-series of unadjusted levels. 4 Robustness 4.1 Outliers X-12-ARIMA detects outliers and ensures that they do not have a disproportionate impact on the estimated results. This addresses one key concern in real world applications.4.2 Sensitiveness to Alternative Techniques of Seasonal AdjustmentIn order to obtain an empirical sense on how sensitive the results are to alternative algorithms of seasonal adjustment, we implement three different strategies: (a) X-12-ARIMA, (b) dummy variable regression using a robust regression (Venables and Ripley 2002) and (c) decomposition into trend, seasonality and irregular component using a non-parametric “STL” algorithm (Cleveland et al 1990) using LOESS (Cleveland et al 1992). Of these, X-12-ARIMA and the variable regression are parametric methods; however in both cases robust estimation is done to reduce the influence of extreme observations. STL is an explicitly non-parametric method. Table 1 (p 63) shows the correlation matrix of four different time-series of POP changes of the WPI: the raw data, and the three alternative seasonal adjustment methods. All three seasonal adjustment strategies explicitly deal with outliers, which would inevitably generate a loss of correlation against the raw data series. The lowest correlation in this table, of 0.82, is between the raw data and the seasonal adjustment done through STL. All the other correlations are higher than this. Table 2 (p 63) shows the numerical values obtained in recent months, which allows us to compare the results obtained by the three different methods of seasonal adjustment. As an example, in January 2008, while the raw data showed inflation of 9.94%, the three different seasonal adjustment algorithms showed values of 13.24%, 12.47% and 20.61%. The three SA series are remarkably alike. This fact, coupled with the high correlations seen in Table 1,helps us have confidence that the results are not unduly sensitive to the choice of strategy for seasonal adjustment. 4.3 Extent to Which Seasonal Adjustment Removes Seasonality The intuition of spectral analysis is particularly useful in inter-preting the goals and the results of seasonal adjustment procedures. Figure 2 shows the Fourier decomposition of POP changes inWPI, comparing the raw series (termed NSA or not seasonally adjusted) against the X-12-ARIMA seasonally adjusted (termedSA) series.This shows that the raw series has an extremely strong peak at the wavelength of one year.4 This peak is removed by seasonal adjustment. At low and high frequencies compared with this peak, the spectrum of the raw data is close to the spectrum of the seasonally adjusted data, which suggests that other features of the time-series have been unaffected by the process of seasonal adjustment. 5 EarlyWarnings Seasonally adjusted data is well suited for short-term forecast-ing. For this, a variety of econometric models can be applied to the seasonally adjusted data. The efforts of many researchers are required in modelling inflation in India usingPOPSA data. In order to obtain intuition into the usefulness of seasonal adjust-ment, we merely examine the data looking for large values. 20015010050 | | | | | |0.00 0.050.100.150.200.25FrequencyRaw dataSA (x 12 ARIMA)Period = 1 yearFigure 2: Spectrum of NSA and SA POP Changes in WPISpectrum (decibles)Figure 3: Short-term Interest Rate(expressed in real terms (smoothed)) | | | | | | | | | | | | | | |4/05 10/95 10/96 10/97 10/98 10/99 10/2000 10/01 10/02 10/03 10/04 10/05 10/06 10/07 4/086420–2Real rate (in %)
SPECIAL ARTICLEEconomic & Political Weekly EPW December 6, 200865The 6% threshold for a “high inflation episode” works out to the 60th percentile of the data. The 60th percentile of thePOPSA WPI inflation works out to an annualised value of 6.65%. Hence, we define a high inflation episode asYOY inflation exceeding 6%5 and consider the consequences of putting out an early warning when the POP SA inflation exceeds 6.65%. In the following tables, these “high inflation episode” or “warning” values are shown in boldface. In order to obtain estimates of the real interest rate at the short-end of the yield, forward-looking estimates of inflation are required. In this, we seek to adjust the nominal rate for the 90-day maturity using inflation forecasts for a 90-day horizon. To achieve this, the POP SA data is used to make forecasts, using an AR(6) model, for the coming three months.6 At each month, information available till that month is used to estimate theAR model, and to make forecasts for POPSA inflation over the coming three months using this model. The average of these three forecasts is used to convert the nominal short-term interest rate into the short-term real rate. Figure 3 (p 64) shows the smoothed time-series of the real rate computed in this fashion.75.1 High Inflation Episode of 1994-95 Table 3 shows YOYWPI inflation, POPSAWPI inflation, and the responses of monetary policy in the high inflation episode of 1994-95.8 A large POP SA change took place in April 1994. This may be partly related to statistical measurement issues ofWPI. At this time, the 90-day interest rate in the economy was 7.36%. In the following two months,POPSA inflation showed large values of 7.17% and 16.78%. Large values for POPSA inflation are visible till May 1995. In this period, the short-term rate became negative in real terms. The short-term rate was negative in real terms all the way till January 1995. From June 1995 onwards,POPSA inflation dropped sharply. However, large values for YOY inflation continued to be recorded, since YOY inflation is the average of the last 12 values for POP inflation. Monetary policy tightening is visible right from the start. The real rate, which was nega-tive, started rising. In June 1995, whenPOPSA inflation had started easing, the real rate was +2.21%. The short-term rate stayed above 2% in real terms till August 1996. Over this period, YOY WPI inflation ebbed away. However, when judged byPOPSA data, WPI inflation had sub-sided 14 months earlier, by June 1995. Examining POP SA data does not substan-tially alter the date at which the tightening began. However,POPSA inflation had subsided by June 1995, which suggests that the easing could have begun earlier and progressed faster. In this period, the use of POPSA data would have given a useful early warning that inflation had subsided. 5.2 Example: High Inflation Episode of 2007 Table 4 (p 66) shows the events of the high inflation episode of 2007. Going by the YOY series, the high inflation episode erupted in January 2007 and ended in April 2007. The POPSA data, how-ever, shows a very different picture. It shows that the episode began in May 2006: an early warning of eight months. POPSA inflation was high in the period from May 2006 till October 2006: over this period, inflation averaged 7.81%. The inflationary pressures subsided by October 2006, before the high inflation episode had even showed up in the YOY data. To the extent that policy responses took place after October 2006, they were possibly in the wrong direction. In the critical period from May 2006 to October 2006, when there was high inflation, monetary policy was expansionary. Monetary policy tightening is visible much later. The real rate went up from –0.55% in September 2006 to 3.35% in June 2007. Inflation had subsided before the tightening began. 5.3 Example:HighInflationEpisode of 2008 Table 5 (p 66) shows facts about inflation in the high inflation episode of 2008. From December 2007 onwards, inflation pressures were visible in the POP SA data. They burst into the public consciousness in March 2008, with reports of highYOYWPI inflation. The use of POP SA data would have given an early warning by three months. A high rate ofPOPSA inflation is visible all the way to the latest data for July 2008. The future evolution of this high inflation episode is as yet unclear. The short term real interest rate was at 2.59% in November 2007, the last month prior to large inflation shocks. This plunged to –4.50% in March 2008. At a time of positive inflationary shocks, monetary policy was expansionary. Real rates remain very low when compared with those required to rein in inflation. The last observation of the real rate, –0.88% in July 2008, remained much below the level of +2.59% in November 2007, before this inflationary episode began. This suggests that until July 2008, monetary policy tighten-ing aiming to combat inflation has not taken place. 6 Areas for Further Research on Seasonal Adjustment There are two key areas where further work is required. The first is the issue of seasonal adjustment of weekly data. When working with monthly Table 3: WPI Inflation and Monetary Policy in High Inflation Episode of 1994-95(in %)Month WPIShort-termRate YOY POP SA Nominal Real 1994-04 7.50 79.84 7.36 -2.70 1994-05 8.30 7.17 7.48 -2.19 1994-06 10.00 16.78 8.25 -2.71 1994-07 11.10 5.56 8.83 -0.62 1994-08 11.80 8.00 8.13 -1.61 1994-09 11.90 3.32 8.58 -0.75 1994-10 12.70 10.68 8.77 -1.15 1994-11 13.20 7.89 8.50 -1.70 1994-12 14.50 17.40 9.42 -0.47 1995-01 16.20 20.42 10.68 -0.14 1995-02 16.90 7.57 11.29 2.64 1995-03 16.90 3.44 11.65 2.38 1995-04 10.97 15.31 11.72 0.74 1995-05 10.98 7.97 12.01 1.11 1995-06 9.72 3.19 12.46 2.21 1995-07 9.63 5.02 12.84 3.12 1995-08 8.94 1.18 12.63 3.86 1995-09 8.93 3.18 12.61 3.10 1995-10 8.42 4.56 12.78 4.12 1995-11 8.21 5.16 12.97 5.02 1995-12 6.63 -0.41 12.97 6.45 1996-01 4.99 3.20 12.97 6.40 1996-02 4.53 1.92 12.97 6.73 1996-03 4.53 3.09 12.97 6.81 1996-04 3.68 4.47 12.71 6.42 1996-05 3.57 7.12 12.39 6.06 1996-06 3.64 4.00 12.41 6.22 1996-07 4.26 13.14 10.80 2.79 1996-08 4.92 9.16 9.20 1.36 1996-09 5.08 4.66 10.07 2.78 1996-10 4.58 -2.49 9.50 2.96 1996-11 4.48 3.84 7.54 0.41 1996-12 5.24 8.82 8.10 -0.33 1997-01 5.16 3.60 8.12 1.64 
SPECIAL ARTICLEEconomic & Political Weekly EPW December 6, 200867Notes1 In 2007, the RBI released a Report of the Internal Technical Group on Seasonal Movements in Inflation chaired by Balwant Singh. However, these ideas have not filtered into monetary policyformulation and official communications of the RBI. 2 Most notably, the composition of the WPI excludes the services sector, which composes over 60% of GDP. 3 There are concerns about utilising this full series given the change of base year which generates a large outlier in April 1994. While X-12-ARIMA detects and treats outliers, the analysis of the paper has hence been repeated using the data from May 1994 onwards. The broad results hold with this shorter time-series also. 4 The y axis shows 10 log10I(ω) in units of decibels where I(ω) = 1/n [{n∑(t=1) Xtsin(ωt)}2+ {n∑(t=1) Xtcos(ωt)}2] is the spectral density. Smoothing is done using modified Daniell smoothers (Venables and Ripley 2002). 5 We choose 6% as the threshold value since the target rate of inflation in India is spread up to 5%.6 This is a purely statistical approach to estimating expected inflation, and does not reflect any spe-cific theory or assumptions regarding formation of inflation expectations. It also does not take into account varying expectations of varying agents in the economy. 7 Special difficulties are faced in the period from April 1993 to April 1994, where the WPI shows a value of 100 for all the months of 1993-94 and then shows a sharp jump in April 1994. Hence, the POP SA value for WPI for these months was forced to be missing before computing the real rate using the procedure described in the text.8 A deeper economic analysis of the exchange rate regime, loss of monetary policy autonomy and infla-tion in this episode is presented in Patnaik (2005).References Bell, W and S Hillmer (1984): “Issues Involved with the Seasonal Adjustment of Economic Time Series”, Journal of Business and Economic Statis-tics, 2(4), 291-320. Cleveland, R B, W S Cleveland, J E McRae and I Terpenning (1990): “A Seasonal-trend Decom-position Procedure Based on Loess”, Journal of Official Statistics, 6, 3-73. Cleveland, W S, E Grosse and W M Shyu (1992): “Local Regression Models” in J M Chambers, T J Hastie, eds. “Statistical Models in S”, chapter 8 (Wadsworth and Brooks/Cole). Harvey, A, S Koopman and M Riani (1997): “The Modelling and Seasonal Adjustment of Weekly Observations”,Journal of Business and Economic Statistics, 15(3), 354-68. Hood, C and D Findley (2001): “Comparing Direct and Indirect Seasonal Adjustments of Aggregate Series”, Proceedings of the Annual Meeting of the AmericanStatisticalAssociation. Mistry, P (2007): Making Mumbai an International Financial Centre: Committee Report (Sage Publish-ing and Ministry of Finance, Government of India), URL http://finmin.nic.in/mifc.html. Patnaik, I (2005): “India’s Experience with a Pegged Exchange Rate” in S Bery, B Bosworth, A Pana-gariya, eds.The India Policy Forum 2004 (Brook-ings Institution Press and NCAER) pp 189-226, URL http://openlib.org/home/ila/PDFDOCS/Patnaik2004_implementation.pdf. Pierce, D A, M R Grupe and W P Cleveland (1984): “Seasonal Adjustment of the Weekly Mone-tary Aggregates: A Model-based Approach”, Journal of Business and Economic Statistics, 2(3), 260-70. Rajan, R (2008): Committee for Financial Sector Reforms, Committee Report (Planning Commis-sion: Government of India). Singh, B (2007): Report of the Internal Technical Group on Seasonal Movements in Inflation, Reserve Bank of India. Srinivasan, T N (2008): “Price Indices and Inflation Rates”, Economic & Political Weekly, Special Volume (June), 217-23. – (2008): “Some Aspects of Price Indices, Inflation Rates and the Services Sector in National Income Statistics” in N Jayaram, R S Deshpande, eds. Footprints of Development and Change: Essays in Memory of Professor V K R V Rao (Delhi: Academic Foundation), pp 437-74. Venables, W N and B D Ripley (2002): Modern Applied Statistics with S (Springer, 4th edition).
