Modeling and Forecasting Inflation in India

7/30/2019 Modeling and Forecasting Inflation in India

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IMF Working Paper 1999 International Monetary Fund

This is a Working Paper and the author(s) would welcomeany comments on the present text. Citations should refer toa Working Paper of the International Monetary Fund. Theviews expressed are those of the author(s) and do notnecessarily represent those of the Fund.

WP/99/119 INTERNATIONAL MO NETAR Y FUNDAsia and Pacific Dep artme nt

Modeling and Forecasting Inflation in IndiaPrepared by Tim Callen and Dongkoo Chang1

Authorized for distribution by Ajai ChopraSeptember 1999

AbstractThe Reserve Bank of India (RBI) has moved away from a broad money target toward a "multipleindicators" approach to the conduct of monetary policy. In adop ting such a framework, it isnecessary to k now which of the many potential indicators prov ide the m ost reliable and timelyinformation on future developments in the target variable(s). This paper assesses which indicatorsprovide the m ost useful information about future inflationary trends. It concludes th at while thebroad money target has been de-emphasized, developments in the monetary aggregates remain animportant indicator of future inflation. The exchange r ate and im port prices ar e also relevant,particularly for inflation in the manufacturing sector.JEL C lassification Num bers: C51, E3 1Keywords: India, inflation, cointegrationAuthor's E-Mail Address: [email protected], [email protected]

1Theauthors would like to thank, without implication, Tamim Bayoumi, Narendra Jadhev,Patricia Reyno lds, Christopher T owe, and participants at an Asia and Pacific Dep artme nt seminarfor their comments, and Siddhartha Choudhury, Ioana Hussiada, and Aung Win for researchassistance.


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- 2 -Contents Page

I. Introduction and Motivation 3II. M easu res of Inflation in India 4II I Inflation During the 1980s and 1990s 5IV. M ode ling Inflation in India 9V. Estimation Methodology and Results

A. Da ta 13B. Empirical Results 13C. Lead ing Indicator s of Inflation 21

VI. Conclu sions and Policy Implications 21Text Tables1. Charac teristics of Inflation: 198 3-1 999 62. Cointegrating Vectors for LWPI and LW PIM 153. Inflation Equa tions 16Text Charts1. CPI and W PI Inflation 72. Components of the WPI 83. M anufac tured Inflation and the Outp ut Gap 144. Actual and Fitted Values of the Equations 185. Ou t of Sam ple Fore cast of Inflation 19References 24Appe ndix I. Da ta Definitions and Sources 26App endix II. Details of Empirical Results 27Appendix Tables1. Unit Root Tests 272. Johansen Max imum Likelihood App roach 283. Cointegration Using a Residuals Based App roach 304. Estimates of Output Gap Models 315. Estimates of Inflation Equations on Annual data 326a. Lead ing Indicators of Inflation: Bivariate Gra nger Causality Tests 336b. Lead ing Indicators of Manu factured Inflation: Biva riate Gran ger Causality Tests 347a. Foreca st Error Variance of Inflation Explained by Variable 357b. Foreca st Error Variance of Manufactured Inflation Explained by Variable 36


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I . INTRODUCTION AND MO TIVA TIONMaintaining a reasonable degree of price stability while ensuring an adequ ate

expansion of credit to assist economic growth have been the primary goals of mon etary policyin India (Rangarajan, 1998). The concern with inflation emanates not only from the need tomaintain overall macroeconomic stability, but also from the fact that inflation hits the poorparticularly hard as they do not possess effective inflation hedges. Prime Minister Vajpayeerecently stated that "inflation is the single biggest enemy of the poor." Con sequen tly,maintaining low inflation is seen as a necessary part of an effective anti-poverty strategy.By th e standards of many developing countries, India h as been reasonably successful inmaintaining an acceptable rate of inflation. Since the early 1980s, inflation has not exceeded17 percent (measured by the year-on-year change in the monthly wholesale price index (W PI))and has averaged about 8 percent. While this is only on par w ith other countries in the Asian

region, it compares well with an average inflation rate in all developing countries of around35 p ercent.During this period, the Reserve Bank of India (RB I) has largely condu cted monetarypolicy through an intermediate target for credit or broad money growth. Prior to 1985/86, theimplementation of m onetary policy was based on an annual target for credit expansion (eithera nominal target for total or non-food credit, or a targeted incremental credit-to-deposit ratio).In 1985/86, the RBI switched to an annual target for the growth of broad money. Initially thiswas fixed on the basis of actual monetary grow th in the preceding y ear (or average of severalyears). In 1990/91, the target became more forward looking being based on projections forreal GDP grow th, inflation, and velocity. How ever, success in achieving the announcedtargets has been limited, with broad m oney growth being in line with the targ et in only fouryears between 1985/86 and 1997/98 (Mohanty and Mitra, 1999).2In its April 1998 Monetary and Credit Policy Statement the RBI announced a moveaway from the broad money target toward a "multiple indicators" approach to the conduct ofpolicy (although it still announced a projected range for M 3 gro wth, which con tinues to be anintegral part of the policy framework). However, as Kannan (1999) points out, this changewas not really a discrete shift in the way policy is conducted, but rather the formal recognitionof changes that have gradually taken place in the policy framework over several years. Theappropriateness of using broad money as the intermediate target for monetary policy hadincreasingly become an issue. While the majority of empirical studies still point to a stablemoney dem and function in India despite the ongoing pro cess of financial deregulation

2Whilebroad money growth was the main policy target, other indicators were alsoemphasized at different times depending on the prevailing conditions. This may explain thelack of success in meeting the announced m onetary targ et.


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(Arif, 1996, and Reserv e Bank of India, 1998),3 the exp eriences with mo netary targ ets inother countries following financial deregulation, and India's own limited success in meeting itsannounced targets, raised doubts about the continued usefulness of the monetary target.In ad opting a multiple indicators approach, it is necessary to know which of the manypotential indicators provide the m ost reliable and timely indications of future developments inthe target variable(s), and which should therefore be m ost closely m onitored. In this paper, weassess which variables are the most useful indicators of future inflation developments. Weapproach this in two w ays. First, we estimate tw o m odels of the inflation process in India (onebased on a mon etary approach, the other using an ou tput gap) and then assess their ability toforecast recent inflation developments. Second, we use a series of vecto r autoregressions(VARs) to identify the indicators that contain predictive information about future inflation.The remainder of the paper is organized as follows: Section II discusses the m easuresof inflation available in India; Section III describes recent inflation developments; Section IVdiscusses previous studies of inflation in India and outlines the models of the inflationaryprocess used in the empirical work; Section V presents the estimation resu lts, and discussesthe results of the VA R analysis; and Section VI conclud es with a discussion of the policyimplications of the results.

I I. MEASURE S OF INFLATION IN INDIAThree different price indices are published in India: the wholesale price index (WPI);the consum er price index (CPI), which is calculated for three different types of worke rs (thosein the industrial, urban non-manual, and agricultural/rural sectors); and the GD P deflator. TheWP I is available weekly, with a lag of two weeks for the provisional index and ten w eek lagfor the final index. The C PI is available monthly, with a lag of about one m onth, and th e GDPdeflator is available only annually (and is not considered further in this paper).In m ost cou ntries, the main focus is placed on the CPI for assessing inflationary trend s,both b ecause it is usually the index where m ost statistical resources are placed and because itmost closely represents the co st of living (and is therefore m ost ap propriate in terms of thewelfare of individuals in the economy). In India, however, the m ain focus is placed on theW PI becau se it has a broader coverage and is published on a m ore frequent and timely basis

3Financial deregulation began in earnest in the early 1990s, although impo rtant changes in thestructure of the financial sector had already started in the 1980s with the grow th of thenonbank finance companies (NBFCs). The rapid growth of deposits into these institutions mayalready have begun to effect the interpretation of the mon etary aggregates p re-199 0.


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than the CPI. However, the CPI remains important because it is used for indexation purposesfor many wag e and salary earners (including governm ent employees).The W PI covers 44 7 commodities and is heavily weighted tow ard manufactured

prod ucts w hich com prise 57 percent of the index. Primary articles, consisting mainly of fooditems, accoun t for 32 percen t of the index, and fuel and energy the remaining 11 percent (theprices of many of these items are administered by the governm ent, although they are beinggradually deregulated). However, being a combination of primary and intermediate products,the WPI is not representative of the consumption basket of the average Indian household. TheCPI is more relevant in measuring inflation as it impacts on households, b ut its coverage andquality are often questioned. The CPI for industrial workers, the most commonly quoted ofthe three CPI measures, covers 260 commodities, and is more heavily weighted toward fooditems which account for nearly 60 percent of the total index.In recen t years, a number of countries, particularly those w ho hav e adop ted explicitinflation targets, have developed m easures of "underlying" or "core" inflation which attem pt toidentify permanent trends in inflation by eliminating temporary price fluctuations from theindex. Core inflation is generally associated with the demand pressure co mp onent of measuredinflation and is often viewed as being important for the determination of inflation expectations.A further problem in many countries is that elements o f the index are under go vernment pricecontrol, and prices of these items generally adjust slowly, and not always completely, tochanges in underlying market prices. Consequently, th e m easured price index may not fullyreflect underlying inflationary trends.In India, no measure of "core" inflation is publicly available. However, given theimportance of supply shocks on primary prices (see discussion below) and the presence ofprice con trols on a num ber of items in the m easured indices, a notion of underlying inflation isimportant from a monetary policy perspective. An o bvious and immediately available proxyfor core inflation is the manufactured price sub-compon ent of the W PI. This eliminatesprimary products (whose prices are most likely to be subject to temporary supply shocks) andfuel and energy (whose p rices are often administered), from the W PI. Ho wev er, this is farfrom a perfect proxy because the processing of agricultural produ ce is an important aspect ofIndian manufacturing so agricultural supply still influences the manufacturing price index.Further, th e mean of primary product inflation has exceeded that of the manufacturinginflation indicating that a focus on manufacturing inflation alone will likely underestimate"permanent" inflation.

I I I . INFLATION DURIN G THE 198 0S AND 19 90 SW PI inflation w as relatively stable between 1983 and 1990, averaging 6 3/4percent,recording a low o f 3 percent in early 1986, and a high of a little over 10 percent in early 1988(Chart 1 and Table 1). In the 1990s, inflation has, on averag e, been higher at 8 3/4percent, andconsiderably m ore variable. Inflation ro se sharply in the early 1990s, reaching a peak of a littleover 16 percent in late 1 991, as primary product prices rose sharply and the balance ofpayments crisis resulted in a sharp depreciation of the rupee and upward pressure on the price


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- 6 -of industrial inputs. How ever, as the agricultural sector rebou nded, industrial activity slowed,and financial stability wa s restored, inflation declined to 7 percent by m id-19 93, but then againaccelerated to over 10 percent during 1994 and 1995 as economic activity recovered strongly.In response, the RBI moved to tighten monetary policy, and inflation was brought downgradually, reaching a low of 33/4 percent in mid-1997 . Howe ver, mo re recently, inflation againaccelerated in the second half of 1998 as adverse supply conditions in key commodity markets(although overall monsoon conditions were regarded as normal) put upward pressure on foodprices. As these conditions have eased, inflation has again fallen sharply.

Table 1: Characteristics of Inflation: 198 3-19 99~~ ____ _ _ _ _ _ _ _ _ _ _ _ _ _ _Mean inflation rateOverall WPIPrimary sectorManufacturing sectorFuel and energy

7.848.337.518.29

6.756.397.235.68

8.659.807.7310.27CPI (industrial work ers) 9.19 8.31 9.86

Standard devia t ionOverall W PI 2.72 1.65 3.08Primary sector 5.04 4.56 4.94Manufacturing sector 2.85 2.53 3.08Fuel and energy 5.24 2.50 5.91CPI (industrial workers) 2.73 2.40 2.81

Within the three sub-components of the WPI, prices in the manufacturing sector havebeen lower and more stable, ranging from 2 to 13 percen t (Ch art 2) . Inflation in both primaryprod ucts and fuel and energy categories has been considerably higher in the 1990s than in the1980s. Bot h indices have also been volatile. Within the fuel and energy category , th e sharprise in prices in recent years is partly due to th e government moving m ore tow ard marketbased prices, although given the administered n ature of these prices such adjustments havetended to occur at irregular intervals leading to sharp movements in the index.


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- 9 -Inflation in the primary products category has ranged from a peak of ov er 21 percentin late 1991 to a low of negative 2 percent in 1 985. While the government intervenes in thedetermination of the prices of essential food items by fixing procure men t or minimum supportprices for prod ucers and issue prices for consum ers, at the m argin, agricultural prices are

determined by market forces.4 With around two -thirds of agricultural land in India stillunirrigated, the monsoon remains the key factor for agricultural production and prices(imports o f agricultural prod ucts are heavily restricted so that shortfalls in domesticproduction quickly translate into higher prices). Consequently, years of drought (1982/83,1985/86, 1987/88 , and 1990/91) have been associated w ith a sharp rise in inflation, w hileyears following these d rough ts, or years with bum per h arvests, have seen a decline in inflation.Although the C PI has tended to give a higher estimate of inflation than the W PI or themanufacturing price index during this sample period,5 the choice between the three indices asthe main policy measure of inflation has been largely irrelevant for most of the 1980s and1990s as there has been little sustained difference in their broad trends. H ow ever, there havebeen several periods where this has not been the case: (i) from mid-1983 to mid-1984 whenCPI inflation increased to nearly 14 percent, but the W PI rate remained b roadly unchanged ataround 7 percent; (ii) from early 1995 to late 1996 when WPI inflation fell sharply from12 percent to 4 percent, but CPI inflation remained around 8-10 percent; and (iii) during 1997and 1998 when manufactured price inflation has remained broadly unchanged in the 4- 5percent range while the rates of overall WPI and CPI inflation have swung quite widely.Further, during 1998, CPI inflation accelerated much more rapidly than W PI inflation and asignificant gap opened between the two measures. Samanta and Mitra (1998) find that thedifference in the com modity basket and weighting patterns in the tw o indices explain part ofthis divergence, with the much higher weighting on food items in the CPI being important.However, other factors also appear to be at work, although their study does not identify these.

IV. MO DELIN G INFLATION IN INDIARecen t studies of inflation in India have generally followed either a m onetarist or"structuralist" approach. The monetarist approach is well known, and recent examples of itsapplication to India include Kumar Das (1992) and Pradhan and Subramanian (1998). Thestructuralist approach sees inflation as the result of structural disequilibrium in the economy,

4Major foodgrains such as rice and wheat and comm odities such as sugar and edible oil arepartly supplied thro ugh the public distribution system (PD S) which ru ns in parallel with themarket system. Supplies for the PDS are purchased from producers at pre-announcedprocurem ent prices and are sold to consumers at a subsidized issue price (any individual witha registered residential address is eligible for a ration card that entitles them to buy a fixedquota of goods at the issue price). The Food Corporation of India (FCI) maintains a bufferstock of items sold through the PDS.5How ever, this does not appear to be true over longer time periods (see Reserve Bank ofIndia, Annual Report, 1996/97, page 64).


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- 10-and examines inflation in a sector specific manner. In general, with agricultural output given inthe short-run by the size of the crop (unless imports are freely allowed or significant stocksare held), agricultural prices are viewed as adjusting to clear excess demand. Withinagricultural prices, the price of foodgrains (wheat and rice in particular) are co nsidered to b ethe mo st impo rtant given their large share in family bud gets (B uragohain (199 7)). In theindustrial sector, scope is seen for changes in ou tput even with fixed capacity in the short-run,and industrial prices are not so much driven by demand as by cost factors. Price developmentsin the agricultural sector have implications for industrial c osts and p rices; excess demand foragricultural products leads to higher agricultural prices, and this, in turn, feeds into industrialprices because agricultural prices are a direct input into the production process and becausewag e pressure s increase as the price of food items rise (as noted earlier, many w ages andsalaries are directly indexed to the C PI).

In applying the structuralist approach to India, Balakrishnan (1991, 1992) m odelsmanufactured prices throug h an error-correction specification based on a m ark-up pricing ruleusing annual data for 195 2-80. Labor and raw material costs are both found to b e significantdeterminants of inflation in the industrial sector. Agricultural (foodgrain) prices are modeledas a function of per capita output, per capita income of the nonagricultural sector, andgovernment procurement of foodgrains through the public distribution system (PDS).Balakrishnan (1994) finds the structuralist model outperforms the monetarist model on thebasis of F-tests and the Cox test when estimated on annual data over the period 1952-80. Thisview of the sup eriority of the structuralist model ov er the monetarist m odel in the case ofIndia is supported by Bhattacharya and Lodh (1990).

Dem and pull models of inflation have been less commonly applied t o India. Anexception is Chand (1996) who modeled the GDP deflator over the period 1972-91 using anoutput gap approach. H is results indicated that excess demand is an impo rtant determinant ofinflation, and that the re is some weak evidence of asymmetry in the effect of periods of excessdemand and excess supply, with periods of excess demand exerting greater upward pressureon inflation than periods of excess supply exert in a downward direction.6 How ever, Coe andMcDermott (1997), in a study of the output gap model in Asia, found that India was one ofthe few countries where the output gap model did not work (to derive a satisfactory model ofthe Indian inflation process they had to add a "money gap" term into the eq uation).Indeed, while considerable empirical support is provided for the output gap model instudies of industrial co untries, and by Coe and Mc Dermo tt for a number of Asian countries, itis not clear how applicable such a specification is for India, which has a large (and protected)agricultural sector and is subject to num erous supply shocks. The usual in terpretation of theoutput gap model is that (say) a positive demand shock causes output to rise above itspotential level (i.e., a positive output gap develops) and this leads to an increase in inflationarypressures. Ho wev er, if instead, output rises above its potential level because of a positive

6Several studies on industrial countries have argued th at a non-linear Phillips curve provides abetter representation of the data than the linear curve (see Debelle and Laxton (1997)).


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-11 -supply shock (a favorable m onsoon that leads to a large increase in agricultural p roduction),this is likely to result in lower inflation in the agricultural sector and a decline in generalinflation, at least in the first round.7 The appropriateness o f the outpu t ga p m odel is likely todepend on whether demand or supply shocks dominate in the economy.8 For India, thissuggests tw o po ssible lines could be considered for estimating an ou tput gap m odel: (i) theestimation could be confined to manufactured prices where the output gap specification islikely to be relevant; or (ii) separate output gap term s reflecting the state of th e industrial andagricultural sec tors could be used with the expectation that a move in industrial ou tput abovepotential will, other things being equal, result in an increase in inflationary pressures, but that amov e in agricultural prod uction above trend will result in a decline in inflation.

Most of the studies discussed above used annual data in the estimation. However, asthe primary interest here is to develop a model that could be used to derive inflation forecastsas an input into the formulation of monetary policy a m ajor consideration is to use variablesfor which d ata are published on a regular and timely basis. This places a constraint onadopting some of the approaches discussed above; the lack of information on the cost side,particularly on w ages and productivity, means that the cost-push mod els of industrial pricesestimated by B alakrishnan could not be considered.9Our empirical work focuses on modeling and forecasting both the overall WPI and themanufacturing price subcomponent of the index. We follow two approaches. First, we derivea simple monetarist equation for the price level, apply co-integration techn iques to model thelong-run behavior of prices, and then derive a dynamic equation for inflation based on theseresults. Second, w e model inflation through an output gap equation. W e start from a simplemodel of price determination in which the price level, P t, is a weighted av erage of tradableprices, P tT, and no ntradable prices, P tN:

P t = 0PtN + (l-0)P tT (1)and 0 is the w eight on n ontradable prices in the price index. Th e price of tradable good s isdetermined in the world m arket, with their price in the domestic econom y being a function ofthe foreign currency price, Ptf, and the exchange rate , E t (with an increase representing a

7Of c ourse, second round effects from the rise in incomes in the agricultural sector m ay leadto higher demand for manufactured products and a rise in inflation.8On similar lines, De Masi (1997) argues that "the concep t of potential ou tput is lessmeaningful for countries in which a large proportion of outpu t is accounted for by primarycomm odities whose prod uction is supply determined, o r which are experiencing large inflowsor outflows of labor."9While annual data on wages and productivity were published in the Labour B ulletin until theearly 1980s, no data cu rrent appears to be published. Presumably this is why Ba lakrishnan'sstudies, which were published in the early 1990s, only used data up until 1980.


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- 1 2 -depreciation of the rupee). T he price of nontradables is determined in the d om estic moneymarket: LogPtN = a (LogM t - LogM td) (2)where M t is the outstanding stock of money, M td is the demand for real money balances, and ais a scale factor representing the relationship betw een economy w ide demand and demand fornontradable goods. The demand for real money balances is assumed to be determined by thelevel of real income, Y t, and the opportunity cost o f holding money vis-a-vis other assets (realor financial), it. Consequently, the price of nontradables can be rewritten a s:

LogPtN - a (LogM t -a1LogY t + a2it) (3)An increase in the outstanding m oney stock is expected to result in higher prices, an increasein real income is expected to expand the demand for money for transa ctions and, in turn, leadto a decline in prices, and an increase in the oppo rtunity cost of holding m oney, by reducingthe demand for money balances, will result in an increase in prices.

So, with uncapitalized letters representing log s, prices, p t, can be written as:p t = a0(m t - aiyt + a2i1) + (l-0 )(e t + ptf) (4)

and a dynamic specification of this long-run relationship can be written for inflation, 7 t, as:Tit = b0 + bi(L)7it + b2(L)Am t - b3(L)Ayt + b4(L)Ait + b5(L)Aet + b6(L)Ap tf -b7ECMt-1+ u t (5 )whe re = Apt, A is the first difference operator, L is the lag operato r, and ECM is thedeviation of actual prices from their estimated long-run equilibrium level obtained from (4).

To derive the output gap model, we start from equation (1), but specified in inflationrates (rather than price levels). Again, with the price of imported goods determined in theworld mark et, impo rted inflation is a function of the change in foreign prices and the exchangerate. Inflation in the nontradables sector is assumed to be determined by an expectationsaugmented Phillips curve of the form:mN = ite + B(yt-yt*)/yt* (6)

so that,7tt = c0 + C1(L)7tt + c2(L)(yt - y t*)/yt* + c3(L)Aet + c4(L)7rtf + w t (7)

where th e lags of actual inflation are used as a proxy for inflation expec tations in the absenceof any survey m easures of inflation expectations.


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- 1 3 -V . ES TIMA TIO N METH O D O LO G Y AN D R ES U L TS

A. DataAn extended time series for quarterly G DP data is not available in India.10Consequen tly, industrial production is used as a proxy for activity in the estimation w ork. Onan annual basis, GDP growth and growth in the industrial sector have a correlation of around75 perc ent. N o timely data is available on agricultural pro duction on a quarterly basis.The sample period used in the estimation work was 1982Q2 to 1998Q2. The data usedare as follows (all data except interest rates and rainfall are in logs; exact definitions arecontained in Appendix I) : the overall WPI (LWPI); the manufacturing subcomponent of theWP I (LW PIM); the primary product subcomponent of the WPI (LW PIP); the CPI forindustrial workers (LCPI); the industrial production index (LIP) as a proxy for realoutput/incomes; the output gap (OGAP), with trend industrial production, y*, derived fromthe Ho drick-P rescott filter (the industrial output g ap and m anufactured inflation are shown inChart 3); narrow money (LM1); broad money (LM3); overnight interest rates (CALL) 11; thedeviation of rainfall from average (RAIN D), which is used as a proxy for changes inagricultural production; foreign prices, approximated by US producer prices (LUSPPI); therupee/dollar exchange rate (LERATE); and oil prices (LOIL). All data were non-seasonallyadjusted, and seasonal dumm ies were included in the estimation (these are n ot rep orted in theresults tables).Based on the Augmented Dickey-Fuller and Phillips-Perron procedures, the hypothesisof a unit roo t in the levels of all variables except rainfall, the output gap , and th e call ratecould not be rejected (Appendix II, Table 1).

B. Empirical ResultsWhile our main focus was on modeling LWPI and LWPIM, and the results for theseare discussed in detail below, the equations were also run with LCPI as the dependentvariable. The results obtained were very similar. Our modeling procedure was as follows:given the closed nature of the Indian economy (over the sample period, imports averaged lessthan 10 percent of GDP) we began w ith only the d om estic variables in the analysis with theintention of adding further variables if cointegration relationships could not b e found amongthis initial group . Even though the call rate was bord erline I(1), it wa s included in the

cointegrating regressions to be consistent with the model outlined ab ove. A s a first step w etested for cointegration between prices, money, output, and interest rates. Tests of

10The Cen tral Statistical organization has recently published quarterly G DP data, but onlyfrom 1996 onward.11Given the repressed state of the financial sector in India during the 1980s, interest ra tesshow little movem ent for m uch of this period.


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- 1 5 -cointegration were carried out both via the Johansen procedure and a residuals-basedapproach (see Appendix II Tables 2 and 3 for the results). The results from the tw oprocedures were generally consistent, with a couple of exceptions. Results for LWPI from theJohansen p rocedure indicate the presence of one cointegrating vector when either LM3 orLM1 is used (the maximum eigen value statistic suggests there may be two cointegratingvectors when LM3 is included). The residuals based approach, however, indicatedcointegration only when LM1was used. For LW PIM , co integration is rejected in all cases.The search was therefore widened to include LUS PPI and LERAT E, The inclusion ofLU SPPI w as found to yield a cointegrating vector under the Johansen procedu re, but onlywith LM1 under the residuals-based approach. Inclusion of LERATE on its own did not yielda cointegrating relationship, and the inclusion of LUSPPI and LERATE together resulted inincorrect signs on the variables in the vector.

The cointegrating vectors for LW PI and LWPIM from the Johansen proced ure witheach of the two measures of money are set out in Table 2. The param eters in the equations arecorrectly signed, except the interest rate term in equations I and II.12 The coefficient valuesare generally similar to those from the OLS regressions (Appendix II, Table 3). Thesestationary cointegrating relationship can be interpreted as representing the long-run orequilibrium relationship between prices, money, interest rates, and output (and foreign prices).

Table 2: Cointegrating Vectors for LW PI and LW PIM

I. LW PI = 0.68*LM3 - 0.42*LIP -0.031* CA LLII LWPI = 0.78*LM1 - 0.56*LIP - 0.006*CALLIII. LWPIM = 0.94*LM3 - 1.10*LIP + 0.01*CALL + 0.42*LUSPPIIV. LWPIM = 0.76*LM1 - 0.64*LIP + 0.002*CALL + 0.48*LUSPP I

We interpreted the above results as indicating the presence of a single cointegratingrelationship in all cases. Dynamic equations were then estimated for both DLWPI (where Dsignifies th e first difference of a variable) and DLWPIM using ordinary least squares, and ageneral-to-specific modeling strategy was employed starting with four lags of each variable inthe system. Th e final preferred specifications are presen ted in Table 3 (repor ted re sults areusing LM3). The error-correction terms (EC M) of the deviation of actual prices from their

12The nominal call money rate used in these regressions is probably a poor proxy for theopportunity cost of holding broad money balances given that about 70 percent of broadmoney is held in interest bearing time deposits. Unfortunately, data on th e retu rn on these timedeposits is not available to calculate a more realistic opportun ity cost.


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Table 3: Inflation Equations(1) (2) (3) (4)Dependent variable DLWPI DLWPI DLWPIM DLWPIM

ConstantDLW PI (-1)DLW PI (-2)DLWPI (-3)DLWPI(-4)DLM3 (-1)DLIP (-1)M0NG3 ( -1 )DLERATE (-3)DLUSPPI (-1)

DLUSPPI (-3)

DLWPIP (-3)

ECM (-4)

R 2R 2L M ( 1 )WhiteJarque-bera

0.013(2.78)0.306(2.72)-0.024(0.21)-0.368(3.03)-0.320(2.66)0.161(2.18)-0.122(4.19)

...

...

...

-0.083(2.59)0.5050.4047.49

20.030.9

0.015(4.22)0.308(2.76)-0.030(0.26)0.363(3.03)0.309(2.63)

0.126(4.56)

...

...

-0.084(2.61)0.5020.4128.21

19.390.91

0.004(0.94)

...

...0.174(2.63)-0.098(3.66)

0.063(2.73)0.230(2.53)0.322(3.38)0.207(4.49)-0.116(3.24)0.7220.6664.54

18.752.97

0.007(3.19)

...

...

...

...

0.107(4.22)0.066(2.86)0.229(2.53)0.312(3.29)0.202(4.39)

-0.118(3.29)

0.7160.6664.88

16.581.53

No te: Sam ple: 1982 Q2-1998Q2 . t-statistics in parentheses.


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- 1 7 -long-run equilibrium level were found to be significant and correctly signed with a lag of fourquarters. H ow ever, the speed of adjustment to the equilibrium is slow, while sum of thecoefficients on lagged inflation in the DLW PI regression, at around 0.3, also sug gests inertiain the inflation process. T he first lags of money and o utpu t gro wth were found to besignificant in both eq uations, and imposing equal and o pposite coefficients on these term s wasaccepted. The term (D LM3-DLIP) can be interpreted as a "money gap " (M 0N G3 ) withmon etary gro wth in excess of output leading to an increase in inflationary pressures .Ho wev er, its short-run elasticity is quite low in both cases (0.13 and 0.11 respectively)indicating that excess monetary growth feeds slowly into inflation. The inclusion of RAIN D asa proxy for agricultural production w as not successful, entering the equation w ith a positivesign and being significant in its first and second lags. 13 The fit of the equation for DLC PI wasactually slightly better than for DLW PI, but of the same basic stru cture.

For manufactured price inflation (DLWPIM), the first and third lags of importedinflation and th e third lags of the exchange rate and primary produc t inflation (DLW PIP) w erealso found to be significant and correctly signed. The significance of imported inflation formanufactured inflation, but not overall inflation, reflects the greater import propensity of themanufacturing sector. Indeed, one important factor behind the relatively subdued inflation inthe m anufacturing sector in recent years is likely to have been the o pening up of dom esticindustry to greate r external competition. Indeed, this equation specification will not c apturethe full impact of trade liberalization on industrial price inflation given it uses U.S. producerprices rather than actual Indian import prices. The significance of primary p rodu ct inflation isconsistent with the feed through from the agricultural sector to the industrial sectoremphasized by the structuralist models. As would be expected given the difficulties inmodeling the variability of primary prices, the fit of the equation for DL W PIM is superior tothat for DLWPI.Tests on the equation residuals showed no signs of serial correlation orheteroskedasticity and also appeared normal at the 5 p ercent confidence level. The actual andfitted values of equations (1) and (3) are plotted in Chart 4. T he dynamic forecasts over theperiod 1997Q2 to 1998Q2 indicate that while the equations predict inflation developmentsmoderately well, there is considerable uncertainty around the forecasts (Chart 5). As expected,the results are better for LWPIM than LWPI. To see whether any structural breaks could bedetected in the estimated relationships due to the effects of financial d eregulation, Chow testswere conducted with the sample being split in 1992Q2. These tests did not indicate thepresence of a break in either equation.14 The choice of this quarter as the start of the period of

financial deregulation is somewhat arbitrary, but the results did not appear to be sensitive to13Most studies of inflation in developing countries find a neg ative relationship betw eenrainfall and inflation. However, excessive deviations from "normal" rainfall in eitherdirection, ie. droughts or floods will hurt agricultural production and result in higherinflation.14On a larger sample, Jadhev (1994), finds structural breaks in a quarterly moneydemand function in 1975 and in 1992/83.


18/36


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20/36

- 2 0 -

the exact breakpoint chosen. However, while these statistical tests did not detect a structuralbreak, re-estimation of the equations over the more recent time period suggested someinteresting changes (although caution should be attached to these results given the shortsample period). First, the fit of both equations improved. Second, the im portance of themonetary terms and imported inflation increased significantly. Third, for manufacturedinflation, the im portance of primary product inflation declined, possibly suggesting that as thedomestic economy has been opened to foreign competition the links between domesticagriculture and industry have w eakened.

Estima tes of the outpu t gap model for overall and manufactured price inflation arepresented in Appendix II, Table 4. While the sum of the output gap term s is correctly signedand significant for overall WPI inflation, it is incorrectly signed and significant formanufactured prices. Given the output gap is based on industrial prod uction, rather thanoverall G DP , these results are counter intuitive.14 The o utput gap was also insignificant and/orincorrectly signed when included in the preferred mon etary equation.To further explore the properties of the output gap model, and to check the robustnessof the other results derived from the quarterly data, the equations reported above were re-estimated for LWPI using annual data (1957/58-1997/98) with real GDP as the activityvariable instead of industrial production (results reported in Appendix II, Table 5). The resultswere broadly similar to tho se obtained from the qu arterly data, again show ing a relatively slowpace of adjustment to the long-run equilibrium. In these regressions, LOIL was found tooutperform LU SPPI being highly significant in all the regressions. A gain the o utput gap m odelwas not supported by the data, with the coefficient on the outpu t gap term being incorrectlysigned and insignificant.15The earlier discussion suggested that for the Indian economy it is likely to b eimportant to distinguish between the agricultural and industrial sectors w hen estimating anoutput gap model Using annual data, it is possible to split the output gap into separateindustrial and agricultural components (again using the Hodrick-Prescott filter to deriveestimates of trend output). Both the agricultural (OGAPA) and industrial (OGAPI) outputgaps we re correctly signed when entered individually (i.e., agricultural outp ut above trendresults in lower inflation, while industrial output above trend leads to higher inflation),although only the agricultural gap w as significant. This highlights the im portance of sectoralaspects of the Indian inflation process, and indicates the im portance o f accounting for supplyshocks in explaining inflation.

15Of course, this does not necessarily imply that the output gap model does not workfor India. It may be that the Hodrick-Prescott filter does not provide a goodcharacterization of potential output in India,


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- 2 1 -C. Leading Indicators of Inflation

In this section we assess the leading indicator prope rties of a num ber of variables forfuture inflation through the estimation of bivariate vector autoregressions (VARs) and a seriesof Granger causality tests and variance decompositions. The variables used in the bivariatetests are those used in the model estimation above together with stock prices.

The results of the bivariate G ranger-causality tests a re presented in Appendix II, Table6. Likelihood ratio tests were carried out for the null hypothesis that the variable underconsideration d oes not G ranger-cause inflation. The resu lts indicate that the money gap(MONG1 and MONG3 using Ml and M3 respectively) has the highest degree of predictivecontent for inflation, although this comes mainly from industrial prod uction rather than th emonetary aggregates over the whole sample period. However, during the more recent period(1992 Q2 to 1998Q2 ), the predictive content of the monetary agg regates, particularly M l,increases, especially at short time horizons. Foreign inflation also has some predictive contentover short time horizons. W hile the output gap also app ears to have predictive con tent afterone- quarter, the term s are incorrectly signed and the results are only included forcompleteness. For manufactured price inflation, the money gap again has significant predictivepower, although in this case M l on its own is significant. Fo reign inflation and stock pricesalso have strong predictive content, while primary prod uct inflation has som e predictivecontent. However, in contrast to the results for the aggregate WPI, the predictive content ofthe money gap terms weaken substantially, particularly over short time horizons, during themore recent period.

The variance decomposition results broadly support the Granger-causality tests(Appendix II, Table 7). The variance decompositions measure the proportion of the varianceof inflation that can be explained by the variance of the indicator variable. Variances of themoney gap terms, industrial production on its own, and stock prices explain a significantpropo rtion of the variance in inflation. Again the mo netary term s becom e m ore impo rtant inexplaining the variance of inflation in the more recent sample, as does imported inflation.Narrow money, the two money gap terms, primary product inflation, and stock prices appearto contain the most information about LWPIM.VI. CONCLUSIONS AND POL ICY IMPLICATION S

In its recent policy statements, the Reserve B ank of India has indicated that it ismoving away from a broad money target toward a "multiple indicators" approach to theconduct of monetary policy. In this paper we have attempted to assess which of the potentialindica tors available give the most reliable and timely indications of future inflationarydevelopm ents. This has been carried out both by developing a model of inflation, and byestimating a series of bivariate VARs. The results indicate a number of impo rtant issues inmodeling and forecasting inflation in India. Developing an adequate model of inflation is complicated by swings in the prices ofprimary pro ducts, w hich, year-to-year, are largely driven by climatic co nditions, and by


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- 2 2 -

changes in administered prices. A model of manufacturing prices fits better than onefor the overall WPI. Developm ents in the monetary aggregates (both M l and M3 ) appear to contain thebest information about future inflation, particularly w hen judg ed against d evelopmentsin activity. If anything, the information content of the m onetary ag grega tes appears tohave increased since financial deregulation. An output gap specification, unlike inmany other countries, does not perform well on Indian data. With regard to prices in the manufacturing sector, import prices, the exchange rate,stock prices, and the prices of primary produc ts also provide useful information aboutfuture price developments.In turn, the results have a number of policy implications and also raise a number of issues forthe monetary authorities: While the RB I is moving away from announcing an explicit mo netary target,developments in the monetary aggregates continue to provide important informationabout future inflationary developments and will need to continue to be closelymonitored. The development of a wider measure of liquidity which includes public deposits heldwith financial institutions and NBFC s, as set out in the report of the W orking Grou pon "Money Supply: Analytics and Methodology of Compilation," would provideimportant additional information given the growing importance of nonbankinstitutions. In this paper, the manufacturing subcomponent of the W PI has been used as a measureof core inflation. However, the Reserve Bank should develop a proper measure of coreinflation which excludes volatile items and tho se items w hose prices are notdetermined in the short-run by market forces. This index would give a better idea ofunderlying inflation developments in the economy than is available in the currentlypublished indices, and would aid the conduct of mon etary policy. Of co urse, in itscurrent conduct of policy, the Reserve Bank at times implicitly focuses on a coremeasure of inflation by discounting price movements that are expected to be reversedin the short-run (for example, the recent sharp rise and subsequ ent decline in primaryprod uct prices). But the publication of an explicit core inflation index would improvethe transparency of policy. However, this does not mean that developments in theheadline price index can be totally d iscounted. The results presented here indicate thatthere are important links between developments in the primary sector and other areasof the economy, and the RBI needs to take this into account in its policy actions. It should also be noted that the change in the RB Fs policy approa ch entails some risks.The broad money target has formed the backbone of monetary policy for a number of


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- 2 3 -

years and is well understood by the general public and prov ides an anchor for inflationexpectations (Rangarajan, 1998). During the transition period, th e RB I will need to beparticularly vigilant and quickly respond to any pick-up in inflation pressures t o ensurethere is no suggestion of a weakening of its commitment to maintain a reasonabledegree of price stability.

An important question, and one that has not been addressed in this paper, is whetherthe swings in the prices of primary products are accentuated by remaining restrictions on th eimports of many of these products and by poor distribution mechanisms. If so , liberalizing th eimport of agricultural products and improving distribution mechanisms would be an importantstep for improving macroeconomic stability.


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- 2 4 -

REFERENCES

Arif, R. 1996, "Money Demand Stability: Myth or Reality-An Econometric Analysis,"Development Research G roup Study 1 3, Reserve Bank of India, Mumbai.Balakrishnan, P., 1991, Pricing and Inflation in India, Oxford University Press, Delhi.Balakrishnan, P.,1 992, "Industrial Price Behaviour in India: An Error-Correction Model,"Journal of Development Econom ics, 37, pp.309-32 6.Balakrishnan, P., 1994, How Best to Model Inflation in India," Journal of Policy Mod eling, pp.677-83, December,Bhattachary a, B .B., and Madhum ita Lodh, 1990, "Inflation in India: An Analytical Survey,"Artha Vijnana, Vol. 32, pp.25-68.Burago hain, T., 1997, "The Role of Sectoral Prices in Indian Inflation," "Indian Journal ofQuantitative Economics, pp. 89-102.Chand, S., 1996, "Fiscal and O ther Determinants of the Indian Inflation R ate," NationalInstitute of Public Finance and Policy Working Paper No. 7.Coe, D., and J. McDermott, 1997, "Does the Gap Model Work in Asia?" IMF Staff Papers,Vol.44, No.l, March, pp. 59-80.Debelle, G., and D. Laxton, 1997, "Is the Phillips Curve R eally a Curve? Some Evidence forCanada, the United Kingdom, and the United States," IMF Staff Papers, Vol.44, No.2, June,pp . 249-282 .Debelle, G., and C. Lim, 1998, "Preliminary Considerations of an Inflation TargetingFramework for the Philippines," IMF Working Paper W P/98/39, January.De M asi, P., 1 997, "IMF Estimates of Potential O utput: T heory and Practice, "IMF WorkingPaper WP/97/177, December.

Kannan, R., 199 9, "Inflation Targeting: Issues and Relevance for India ," Economic andPolitical Weekly, January 16-23, pp. 115-122.Kumar Das, Debendra, 1992, "An Empirical Test of the Behaviour of Money Supply,Government Expenditure, Output and Prices: The Indian Evidence," Indian EconomicJournal, Vol. 40, pp. 63-81.Jadhev, N., 1994, Mon etary Economics for India, Macmillan India Ltd.


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- 2 5 -

Mohanty, D. and A. Mitra, 1999, "Experience with Monetary Targeting in India, "Economicand Po litical Weekly, January 16-23, pp. 123-132.Pradhan, B asanta K., and A. Subramanian, 1998, "Money and Prices: Som e Evidence fromIndia," Applied Economics, Vol. 30, pp. 821-2 7.Rangarajan, C., 1998, "Development, Inflation, and Mone tary Policy," in I. Ahluwalia and I.Little (eds), India's Econom ic Reforms and Developments: Essays for Man mohan Singh,New Delhi.Reserve Bank of India, 1998, "Money Supply: Analytics and Methodology of Compilation,"Report of the W orking Group, June.Reserve Bank of India, Annual Report, various issues.Reserve Bank of India, Monetary and Credit Policy Statement, various issues.Samanta, G. and S. Mitra, 1998, "Recent Divergence between Wholesale and ConsumerPrices In India - A Statistical Exploration," Reserve Bank of India Occasional Pap ers, Vol 19,N o. 4 December.


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- 2 6 - APPENDIX I

DA TA DEFINITIONS A N D S O U R C ESW holesale price index (WP I): Quarterly data, including the manufacturing and primary productssubcomponents, are from the Wharton Econometric Forecasting Associates (WE FA) database(1980/81 =1 00). Annual data are from International Financial Statistics (IFS) line 63 (1990=1 00).Consumer price index (CPI): Quarterly and annual data are from IFS line 64 (1990=100).Index of industrial production (IP): From IFS line 66 (1990=100).Real GDP (GDP): From IFS line 99b.p (at 1980/81 prices).Narrow money (M l): Quarterly and annual data are from IFS line 34, Money.Broad money (M3): Quarterly and annual data are from IFS. Defined as the sum ofMoney (line 34and Quasi-Money (line 35).Call rate (CALL): Quarterly data is from the WEFA database. For annual data, the money marketrate from IFS is used (line 60b).US producer prices (USPPI): From IFS line 63 (1990=1 00).Oil prices (OIL): Price of U.K. Brent, from IFS line 112.Exchange rate (ERATE): The period average U.S. dollar/Indian rupee rate from IFS line rf.Stock prices (STK): From IFS line 62.Rainfall (RAIND): Data provided by the Centre for Monitoring the Indian Economy (CME),


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- 2 7 - APPENDIX II

DETAILS OF EMPIRICAL R ES U LTSTable 1: Unit Root Tests

Test StatisticAugmented Dickey-Fuller Test Phillips-Perron Test

Constant Constant and Trend Constant Constant and TrendVariable Level A Level A Level A Level ASample: 1982Q2-1998Q2LM 3LM 1LIPOGAPLWPILWPIMLWPIPLCPILERATELUSPPILOILRAINDLSTKCALL

-0.567-0.496-0.579-2.6660.256

-1.3010.2860.175

-0.057-0.963-1.717-4.938-1.662-3.121

-4.620-3.549-2.612-3.317-2.350-3.018-3.253-3.270-4.535-3.081-4.842-5.850-4.012-3.589

-2.639-2.595-2.090-2.632-2.086-1.074-3.137-3.226-1.843-2.158-2.233-4.922-0.534-3.187

-4.541-3.533-2.583-3.254-2.291-2.666-3.305-3.282-4.497-3.086-4.780-5.811-4.368-3.533

-1.164-0.079-0.607-4.0290.347

-0.4230.134-0.364-0.065-0.840-2.120-7.047-1.582-4.670

-9.528-4.871

-14.717-12.906

-5.713-7.641-7.067-7.497-5.729-6.043-7.410

-15.560-5.520

-13.613

-3.72-5.653-6.474-4.002-1.704-1.276-2.319-2.789-2.048-1.826-2.758-7.016-0.883-4.707

-9.597-14.781-14.574-12.825

-5.693-7.579-7.063-7.421-5.688-6.016-7.334

-15.419-5.685

-13.511Sample: 1957/58-1997/98LCPILGDPLM ILM 3LOILM MROGAPOGAPAOGAPI

02321-3-5-5-5

.415.017.712.285.114.674.052.397.022

-4.897-4.878-4.029-2.051-3.735-8.965-6.232-7.399-5.227

-4.287-0.409-0.902-3.583-1.180-5.855-4.984-5.322-5.006

-4.948-5.622-6.507-2.971-3.758-8.823-6.138-7.289-5.155

0.8951.9864.9293.543

-1.084-4.541-5.274-6.651-3.322

-4.479-6.970-6.777-2.984-6.352

-11.295-8.945

-11.809-5.245

-3.146-0.361-1.182-3.493-1.458-5.968-5.205-6.562-3.271

-4.470-8.042-10.332

-4.406-6.316

-11.243-8.796

-11.580-5.153

Note: A is the first difference of the variable. Mackinnon (1991) critical values for theAugmented Dickey-fuller (ADF) and Phillips-Perron (PP) tests at the 1%, 5% , and 10%significance levels are -3.533, -2.906, -2.590 (with constant) and -4.104, -3.479,-3.167 (withconstant and trend) respectively for the quarterly data. Values for the annual data slightly higher.Four lags were used in the A DF test on quarterly data, one on annual data. The truncation lag inthe PP test was set at three.


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- 2 8 -Table 2: Johansen Maximum Likelihood Approach

Sample Period: 1982Q2 to 1998Q2(I) Cointegrating v ector: LWPI, LIP, LM3 , CALL

APPENDIX1/

Null .

r= 0r=3)r=4(r>=4)

MaximumEigen Value28.92*21.85*

5.471.68

95% CriticalValue27.121 .014.1

3.8

(II) Cointegrating vector: LWPI, LIP, LM 1 , CAL LNull

r= 0r=3)r=4(r>=4)

MaximumEigen Value33.92**12.55

5.550.00

(III) Cointegrating vector: LWPIM, LIP, LM 3Null

r= 0r=3)r=4(r>=4)

MaximumEigen Value23.63

9.946.692.89

95% CriticalValue27.121 .014.13.8

CALL95% CriticalValue27.121 .014.13.8

Trace

57.92*29.007.151.68

Trace

52.03*18.11

5.550.00

Trace

43.1519.529.572.89

95% CriticalValue47.229.715.4

3.8

95% CriticalValue47.229.715.43.8


3.8


29/36

- 2 9 - APPENDIX II(IV) C ointegrating vector: LWPI, LIP, L M 1 , CALL

Null

r= 0r=3)r=4(r>=4)

MaximumEigen Value17.6813.007.221.04

95% CriticalValue27.121 .014.1

3.8(V) Cointegrating vector: LWPI, LIP, LM3, CALL, LUSPPI

Nullr= 0r=4)r=5(r>=5)

MaximumEigen Value45.33**21.4011.389.612.56

(VI) C ointegrating vector: LWPIM, LIP, LM3Null

r= 0r=4)r=5(r>=5)

MaximumEigen Value37.2023.5513.6813.270.42

95% CriticalValue33.527.121 .014.13.8

Trace

38.9421 .258.261.04

Trace90.28**44.9523.5512.172.56

, CALL, LUSPPI95% CriticalValue33.527.121 .014.1

3.8

Trace

88.13**50.93*27.3813.700.42


3.8

95% CriticalValue68.547.229.715.43.8

95% CriticalValue68.547.229.715.4

3.81/ On the basis of a series of F-tests, the lag length in the VARs was set at 5 in all cases.Alternative hypothesis for the trace statistic is in brackets. *: significant at the 5 percentlevel;**: significant at the 1 percent level.


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- 3 0 - APPENDIX II

Table 3: Cointegration Using A Residuals Based ApproachUnit root tests for residuals from the OLS regression. 1Sample period: 1 982Q2 to 1998Q2

(I) LW PI = 2.02 + 0.74* LM3 - 0.54*LIP - 0.0004*CALLDF = -3.18 (-4.27)(II) LW PI = 2.38 + 0.73*LM1 - 0.45*LIP - 0.0008*CALLDF = -5.57** (-4.27)(III) LW PIM = -1.59 + 0.59*LM3 -0.45*LIP - 0.0003*CALL + 0.94*LU SPPIDF = -3.94 (-4.63)(IV) LW PIM = 0.02 + 0.63*LM1 - 0.38*LIP - 0.0003*CALL + 0.59*LUSPPIDF = -6.2 9** (-4.63)

lags in the A DF test wa s chosen in all cases on the basis of the A kaike and Schwarzcriterion. 5 percent critical values are in brackets and are taken from Mackinnon (1991).**:significant at the 1% level.


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- 3 1 - APPENDIX IITable 4: Estimates of Output Gap Models

Sample Period: 1982Q2 to 1998Q2Dependent Variable

Constant

DLWPI (-1)

DLWPI (-3)

DLWPI (-4)

OGAP (-1)

OGAP (-2)

OGAP (-3)

OGAP (-4)

DLERATE(-3)

DLUSPPI (-1)

DLUSPPI (-3)

DLWPIP (-3)

R 2R 2L M ( 4 )WhiteJarque-bera

DLWPI

0.010(2.85)0.416(3.27)0.391(3.24)-0.307(2.37)-0.119(2.67)0.184(3.62)0.019(0.38)-0.075(1.68)

...

...

0.4190.303.75

24.350.57

DLWPIM

0.005(1.92)...

...

-0.155(3.64)0.054(1.12)0.064(1.40)-0.046(1.06)0.071(2.73)0.241(2.29)0.382(3.44)

0.209(4.07)0.6560.584.43

26.062.14

Note : t-statistics in p arentheses.


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- 32 - APPENDIX II

Table 5: Estimates of Inflation Equations on Annu al D ataSample Period: 1957/58-1997/98

Dependent VariableConstantDLWPI (-1)DLM3 (-1)DLGDP (-1)M0NG3(- l)DLOIL (-1)ECM(- l )OGAP (-1)OGAPA(- l)OGAPI (-1)R2R2L M ( 1 )WhiteJarque-bera

DLWPI0.025(1.24)0.206(1.91)-0.405(3.23)-0.571(3.62)

...0.079(4.28)-0.235(3.44)

...

...

...0.6850.6370.278.780.78

0.011(0.89)0.220(2.08)

0.467(4.53)0.078(4.24)-0.242(3.59)

...

...0.6780.6400.025.130.62

0.065(5.16)0.045(0.31)

...0.11(4.61)

-0.502(1.57)......

0.4280.3794.842.950.07

0.063(5.39)0.090(0.66)

...0.103(4.62)

...

-0.413(2.72)0.373(1.66)0.5160.4593.604.770.24

No te: t-statistics in parentheses. MO NG3 is defined as DLM 3-D LG DP in this table.


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- 33 - APPENDIX II

Table 6a: Leading Indicators of Inflation: Bivariate Granger Causality TestsIndicatorVariables

DLM1DLM3DLIPM0NG1M0NG3CALLOGAPDLUSPPIDLOILDERATEDSTKDLWPIM

DLM1DLM3M0NG1M0NG3

1Sample:0.2300.4550.0010.0000.0010.1920.4700.0200.0390.0870.1160.933Sample:0.0100.0600.0040.039

2 31982Q2-1998Q2

0.3530.7440.0050.0010.0030.2310.0070.0240.1300.2720.1880.608

0.2550.7110.0010.0000.0000.7100.0030.0810.3020.7340.5280.675

1992Q2-1998Q20.0390.2200.0120.235

0.1460.2840.0350.197

Lags of VAR4

0.3690.8280.0020.0000.0010.7750.0030.1550.0850.7720.5790.444

0.2650.4360.0570.244

5

0.4840.5120.0030.0000.0020.9420.0060.2810.1200.7200.6490.470

0.2130.3190.0660.322

6

0.3880.5370.0070.0020.0040.9250.0090.4080.1840.7010.5340.474

0.0490.4920.1090.443

7

0.4870.6370.0090.0010.0020.8700.0190.4800.2030.7550.5580.435

0.1320.6520.1260.245

8

0.4940.5320.0140.0020.0010.1010.0150.4770.1580.7100.4660.456

0.0620.5930.0580.122

Note: P-values shown for the likelihood ratio tests of the null hypothesis that the indicatorvariable does not Granger-cause inflation.


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- 34 - APPENDIX II

Table 6b: Leading Indicators of Manufactured Inflation: Bivariate Granger Causality TestsIndicatorVariables

DLM1DLM3DLIPM 0 N G 1MONG3CALLOGAPDLUSPPIDLOILDERATEDLWPIPDSTK

DLM1DLM3MONG1M 0 N G 3

1 2 3Sample: 1982Q2-1998Q20.041 0.0200.241 0.4910.009 0.0310.000 0.0000.003 0.0130.483 0.6960.140 0.0530.020 0.0620.076 0.1900.175 0.3920.812 0.2090.037 0.083

0.0530.3490.0200.0000.0100.8770.0340.0180.3810.2410.0970.303

Sample: 1992Q2-1998Q20.023 0.0490.176 0.4690.124 0.2030.450 0.803

0.0970.2120.0280.426

Lags of VAR4

0.1110.5950.0650.0000.0230.9870.0900.0730.4620.3010.1200.482

0.1560.3070.0270.480

5

0.1890.7130.1230.0010.0320.9960.1520.1370.5090.3140.1580.632

0.0430.2430.0140.566

0.0.0.0.0.0.0.0.0.0.0.0.

0.

0.0.0.

6

1 608331 540000579872 4 71 8761 331 72 2 842 9

049

35 60014 4 4

0.0.0.0.0.0.0.0.0.0.0.0.

0.

0.00.

7

2 4082 322200105498431 132 138 758835 63 36

1 09

5600014 90

000000000000

0

000

8

.286

.847

.303

.003

.095

.974

.345

.433

.495

.580

.493

.425

.044

.662

.001

.682

Note: P-values shown for the likelihood ratio tests of the null hypothesis that the indicatorvariable does not Granger-cause inflation.


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- 35 - APPENDIX II

Table 7a: Forec ast Erro r Variance of Inflation Explained by V ariable (In percent)

IndicatorVariable

DLM1DLM3M 0 N G 1M 0 N G 3DLIPOGAPDLUSPPIDLOILDLERATEDLSTKDLWPIM

DLM1DLM3MONG1M 0 N G 3DLUSPPI

1Sample:1.12 .46.311.46.33.09.82 .60.46.41.4Sample:

40.738.033.617.18.9

2

Horizon (in

31982Q2-1998Q21.12 .710.114.28.29.59.55.43.812.91.9

8.57.817.016.28.19.69.05.45.114.25.0

1992Q2-1998Q242.436.935.617.116.4

43.740.240.123.140.6

4

8.68.416.716.18.59.611.58.15.414.25.1

43.839.639.222.540.6

quarters)

6

12.412.416.716.29.19.611.510.99.413.67.2

48.341.643.921.648.1

8

12.713.616.815.09.29.511.811.19.314.77.1

51.244.347.722.950.4

12

13.713.817.615.69.49.512.412.39.815.57.4

49.343.147.122.660.1

2 4

13.813.817.916.09.59.512.512.410.015.77.3

55.543.047.723.975.5

N ote : Six lags included in the estimated VA R.


36/36

- 36 - APPENDIX II

Table 7b: Forecast Error Variance of Manufactured Inflation Explained by Variable(In percent)

IndicatorVariable

DLM1DLM3MONG1M 0 N G 3DLIPOGAPDLUSPPIDLOILDLERATEDLSTKDLWPIP

DLM1DLM3M 0 N G 1M 0 N G 3DLUSPPIDLWPIP

1Sample:8.83.0

28.019.4

9.16.74 .91.31.19.90.0

Sample:28.312.157.316.810.4

3.3

2

Horizon (in

31982Q2-1998Q212.1

3.129.919.3

9.38.94.91.31.0

14.44.6

12.03. 1

27.920.310.0

9.16.92 .11.3

15.616.5

1992Q2-1998Q233.612.161.116.010.5

3.0

29.111.162.015.910.9

4 .6

4

12.03.1

27.422 .412.511.312.0

3.91.9

16.317.2

26.610.066.725.210.9

5.3

quarters)

6

157

2 72 1121011

63

1518

4 71363251217

.0

.6

.7

.8

.9

.8

.4

.2

.7

.7

.0

.3

.8

.4

.2

.5

.7

8

15.37.7

26.421 .112.710.812.0

6.55.3

16.018.5

46.714.162.027.014.216.6

12

15.28.2

26.621.713.611.112.3

6.85.5

16.318.7

47.214.862.028.215.618.2

2 4

15.38.3

26.922.414.211.212.4

6.85.6

16.318.7

47.315.561.429.615.919.8

Modeling and Forecasting Inflation in India

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