Evaluating inflation targeting as a monetary policy objective for India

Economic Modelling 29 (2012) 1053–1063

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Evaluating inflation targeting as a monetary policy objective for India Ankita Mishra a, 1, Vinod Mishra b,⁎ a b

School of Economics, Finance and Marketing, RMIT University, VIC 3000, Australia Department of Economics, Monash University, VIC 3800, Australia

a r t i c l e

i n f o

Article history: Accepted 26 February 2012 JEL classification: E52 E58 E63 Keywords: India Inflation targeting CPI Taylor's rule Monetary policy

a b s t r a c t This study formulates a small open economy model for India with exchange rate as a prominent channel of monetary policy. The model is estimated using the Instrumental Variable-Generalized Methods of Moments (IV-GMM) estimator and evaluated through simulations. This study compares different cases of domestic and CPI inflation targeting, strict and flexible inflation targeting, and simple Taylor type rules. The analysis highlights the unsuitability of simple Taylor-type monetary rules in stabilizing the Indian economy and suggests that discretionary optimization works better in stabilizing this economy. There seems to be a trade-off between output gap stabilization and exchange rate stabilization in flexible domestic inflation targeting and CPI inflation targeting respectively. However, flexible domestic inflation targeting seems a better alternative from an overall macro stabilization perspective in India where financial markets are still not sufficiently integrated to ensure quick transmission of interest rate impulses and existence of rigidities in the economy. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Inflation targeting has emerged as a powerful and effective monetary policy regime since the early 1990s. It has been adopted by a number of industrial countries starting with New Zealand in 1990, Canada in February 1991, Israel in December 1991, the United Kingdom in 1992, Sweden and Finland in 1993 and Australia and Spain in 1994. Many of the empirical studies show that an inflation targeting regime has been successful in significantly reducing inflation in these countries. Bernanke et al. (1999), for example, found that inflation remained lower after inflation targeting than would have been the case if forecasted by using Vector Auto-Regressions (VARs) estimated with the data from the period before inflation targeting started. Inflation targeting also helped to maintain price stability once it was achieved. Inspired by the success of inflation targeting in industrialized economies, many Emerging Market Economies (EMEs) also adopted an inflation-targeting approach to monetary policy, including Chile in 1991, Brazil in 1999, Czech Republic in 1997, Poland in 1998 and Hungary in 2001. Inflation targeting is currently practiced by a group of advanced economies and several medium to small sized EMEs. The applicability of this regime to a large, growing, developing economy like India is still a researchable area. There has been growing interest in analyzing

⁎ Corresponding author. Tel.: + 61 3 99047179. E-mail addresses: [email protected] (A. Mishra), [email protected] (V. Mishra). 1 Tel.: + 61 3 99251638. 0264-9993/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2012.02.020

the applicability and suitability of inflation targeting as a monetary policy regime for India, primarily because the current multiple indicator monetary policy approach2 of the Reserve Bank of India (RBI) seems to have lost its relevance and does not appear to work effectively.3 Many studies in the literature have attempted to analyze India's preparedness for inflation targeting. Indeed. several studies have examined financial sector reforms as the essential pre-condition for adoption of inflation targeting, and analyzed the preparedness of India for inflation targeting from that perspective (see, Jha, 2008; Kannan, 1999). Following Kannan's (1999) suggestion that implementation of inflation targeting in India should wait until financial sector reforms have been completed, Singh (2006) argued that the first phase of financial sector reforms is complete and macroeconomic performance in terms of level of inflation and interest rates is satisfactory and stable suggesting that conditions are favorable in India for the adoption of inflation targeting. Singh advocated addressing a few issues, namely, use of both fiscal and monetary instruments to control inflation, publication of fullfledged inflation reports, and establishing an inflation committee to bring transparency in its operation before an actual inflation targeting framework could be adopted in India. Khatkhate (2006) asserted that inflation targeting might be a good policy framework for India as the RBI always has to be on alert to maintain its credibility and authority

2 Post global financial crisis, financial stability has become one of the major concerns of central banks across the world. However, if implemented in a flexible manner, inflation targeting is perfectly compatible with a financial stability objective (Walsh, 2009). 3 Refer to D'souza (2003), Shah (2007), Mishra and Mishra (2009), Mishra and Mishra (2010).

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in controlling inflation, even though the sources of inflation in India are often non-monetary. 4 She suggested that in operational terms India ought to target headline inflation. Mishra and Mishra (2009) analyzed the preconditions for inflation targeting in India, namely, the independence of monetary policy from fiscal, external, structural and financial concerns, and assessing its suitability as a monetary policy framework for India. They found that the Indian economy satisfies the preconditions for inflation targeting. Extending the analysis of Mishra and Mishra (2009), this study attempts to answer the question of the probable consequences of shifting to an inflation targeting framework of monetary policy, and how different shocks will affect the economy under this framework by using a general linear model of the economy with quadratic loss function to be minimized by the central bank for India. Inflation targeting is conducted in conjunction with a Monetary Policy Rule (MPR). MPR is part of the overall monetary policy of the central bank or monetary authority, and specifies how the instrument of monetary policy is to be changed given the characteristics of the macro economy and the policy objective of the central bank. This study compares different cases of strict and flexible domestic and CPI (Consumer Price Index) inflation targeting (Optimal MPR) with simple Taylor type rules (simple MPR) to examine the most suitable 5 inflation targeting framework for India. Modeling inflation targeting as the announcement and assignment of a relatively specific loss function to be minimized by the central bank, this study suggests that simple Taylor type rules are inadequate in stabilizing the economy, and that optimal rules work better. Further, though there seems to be a trade-off between output gap stabilization and exchange rate stabilization in flexible domestic inflation targeting and CPI inflation targeting respectively, flexible domestic inflation targeting appears to be a better policy option for India from an overall macro stabilization aspect. The organization of the rest of this paper is as follows: Section 2 presents a brief review of the models used in literature to examine the monetary policy rules; Section 3 outlines the structure of the theoretical model and the description of its main equations; Sections 4 and 5 present empirical and simulation results respectively; and the final section presents the conclusions and policy implications of this study. 2. Literature review There are a wide variety of models developed in the literature to investigate monetary policy rules. These models differ in size, degree of openness and degree of ‘forward lookingness’ assumed. Some of these models are developed in closed economy settings to examine the performance of policy rules that are consistent with a monetary policy regime of inflation targeting, for example, Rudebusch and Svensson (1999), and Clarida et al. (1999) among others. Many of the studies extended the analysis of monetary policy from closed economy settings to open economy settings. These open economy models differ from their closed counterparts as the real exchange rate affects both aggregate demand and inflation. This complicates monetary management as the impact of exchange rate on real activity and inflation must be accounted for while formulating monetary policy. Some of the notable studies are Ball (2000) 6, Walsh (1999), Svensson (2000), and Clarida et al. (2001). The above models study inflation-targeting regimes for developed countries; however, for the purpose of the current study, more relevant are those studies that look at inflation targeting as a monetary policy regime for EMEs. Many of the studies modify the models 4

Such as changes in food output, marketed surplus, lax fiscal policy etc. The ‘most suitable’ implies the framework which is capable of bringing in overall macro stabilization and not just inflation stabilization. 6 For a closed economy version of the model, refer to Ball (1997). 5

developed in the literature to include characteristics mainly present in EMEs, for example, Moron and Winkelried (2003) modified the model of Svensson (2000) to incorporate financial vulnerability characteristics (which are commonly present in EMEs) to examine inflation targeting monetary policy rules. Fraga et al. (2003) analyzed the case for inflation targeting in EMEs and asserted that the problems faced by EMEs with respect to their fiscal, financial and external sectors are more acute when compared to developed economies. They use a small open economy model where imports enter as intermediate goods rather than as consumption goods. This assumption seems more plausible for the developing economy as capital and intermediate goods form a larger proportion of total imports in developing countries than do consumption goods. Goyal (2008a) adapted a standard IS-LM-UIP framework to build in the dualistic labor market and wage price rigidities present in the Indian economy. She found that in a simple open EME model calibrated to typical institutions and shocks of a densely populated EME like India, a monetary stimulus preceding a temporary supply shock can help stabilize inflation at minimum output cost, because of the exchange rate appreciation that accompanies a fall in interest rates and rise in output. In another study, Goyal (2008b) adapted the dynamic, stochastic, general equilibrium models 7 to analyze optimal monetary policy rules to the labor market structure of the small open emerging economy of India. By examining the welfare effects of different types of inflation targeting regimes for India, she concluded that flexible CPI inflation targeting without lags 8 works best and even more so when the degree of openness increases. However, due to welfare loss from the lags of CPI, domestic inflation targeting continues to be more robust and effective. 3. A macro structural model of a small open economy The formulation of the model of monetary policy used to analyze different inflation targeting monetary policy rules is based on the literature (in particular the models by Batini and Haldane, 1999, Svensson, 2000 and Goyal, 2008a) and broad conclusions derived by Mishra and Mishra (2010). Their model suggests that the monetary policy has real effects. It suggested that a ‘New Keynesian’ framework incorporating some form of stickiness in the prices which gives rise to non-neutral effects of monetary policy is needed to prepare the framework suitable for the evolution of monetary policy. Second, since the mid 1990s rate variables have been better at signaling the stance of monetary policy for India than quantity variables, and this implies the use of nominal interest rate (rather than money supply) as an instrument of monetary policy. Third, there is a growing importance of the exchange rate channel in the transmission of monetary policy in India, with exchange rate shocks playing a central role in explaining the volatility of inflation, interest rate, growth of credit and money supply in that country. Thus, exchange rate shocks as well as shocks originating from the rest of the world (transmitted through exchange rate) are important in conducting monetary policy, and the model for evaluation of monetary policy should incorporate this. Against this background we set up a model of monetary policy 7 Notable models of the type include models by Clarida et al. (1999, 2001), Svensson (2000), Woodford (2003) and Gali and Monacelli (2005). 8 CPI is available only at a monthly frequency in India, with a two month lag. Further, four distinct CPI measures are compiled for different reference populations. These are Consumer Price Index for Industrial Workers (CPI-IW), Consumer Price Index for Urban Non-Manual Employees (CPI-UNME), Consumer Price Index for Agricultural Labourers (CPI-AL) and Consumer Price Index for Rural Labourers (CPI-RL). These indices differ from each other in reference population, basket of goods and services and their weights, geographical areas and base-periods etc. None of these measures presents all the spectrum of the population of the country. There is a need to develop a harmonized measure of consumer price index which is computed on an all India basis and reflects the purchasing power of domestic currency in domestic market and thus facilitates international comparisons. Therefore, there are both information and price adjustment lags in the CPI.

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for India which is then used to evaluate different monetary policy rules. All the variables in the model (other than interest rate) are taken in logs and are expressed as deviations from their respective means. The aggregate supply 9 in period t is given by the following short run open economy Phillips equation: p

πt ¼ b1 πt−1 þ ð1−b1 ÞEt πtþ1 þ b2 yt þ b3 ðqt−1 −qt−2 Þ þ et :

ð1Þ

Here, πt denotes domestic or Wholesale Price Index (WPI) inflation. We assume that there is some inertia in inflation and it is not completely forward-looking. The degree of forward-lookingness depends on the values of the parameter ‘b1’. Thus, inflation depends on its lag, its expected value in period ‘t + 1’, output gap (Yt), lag of (log change in) real exchange rate (qt) (or lag of depreciation rate) and zero mean i.i.d. inflation shock (etp). Etπt + 1 as the expected inflation rate in period ‘t + 1’ is observed from period ‘t’. 10 The variable output gap yt is defined as: yt ¼

d p yt −yt :

ð2Þ

Here, ytd is (log) aggregate demand and ytp is potential output 11. The variable qt − 1 is the (log) lag real exchange rate. The real exchange rate in the economy is defined by following the ‘Purchasing Power Parity (PPP)’ condition: 

qt ¼ et þ pt −pt :

The variable rt is defined as: r t ¼ it −Et πtþ1 :

ð6Þ

Here, it is short-run nominal interest rate and is the instrument of the central bank. Using Eq. (6) and assuming pt* and it* are normalized to zero, the real interest rate parity condition is defined as: e

qt ¼ qtþ1jt þ πtþ1jt −it þ εt :

ð7Þ

We define CPI inflation as weighted average of domestic inflation and domestic currency inflation of foreign goods, given by the following equation: c

f

πt ¼ ð1−ωÞπt þ ωπt :

ð8Þ

Here, ω is the share of imported goods in the CPI and πtf denotes domestic currency inflation of imported foreign goods which in turn is defined as: f

f

f

π t ¼ pt −pt−1 ptf ¼ pt þ et

and

And since, pt* = 0, ptf = et So, πtf = et − et − 1 and substituting the value of et, from Eq. (3)

ð3Þ

Here, pt is the (log) price level of domestic (ally produced) goods, pt* the (log) foreign price level and et represents (log) nominal exchange rate. The variable et fulfills the following interest rate parity condition:

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f

πt ¼ ðqt þ pt Þ−ðqt−1 −pt−1 Þ ¼ πt þ ðqt −qt−1 Þ Substituting this value in Eq. (8): c



e

et ¼ Et etþ1 þ it −it þ εt

ð4Þ

where it and it* are domestic and foreign nominal interest rates respectively, and εte is a combined shock in foreign interest rate and other disturbances in the foreign exchange market, including shocks to foreign exchange risk premium. 12 The aggregate demand (defined in terms of ‘output-gap’) in the economy in period t is given by the following equation: y

yt ¼ a1 yt−1 −a2 r t þ a3 ðqt−1 −qt−2 Þ þ εt :

πt ¼ ð1−ωÞπt þ ωðπt þ qt −qt−1 Þ ¼ πt þ ωðqt −qt−1 Þ:

ð9Þ

Thus, the model consists of aggregate supply Eq. (1), aggregate demand Eq. (5), real interest rate parity Eq. (7), and the CPI Eq. (9). 3.1. The Loss function The optimal monetary policy rules can be derived from central bank's explicit loss function. We assume the following loss function of RBI:

ð5Þ 2

c

c2

2

2

2

Lt ¼ μ π πt þ μ π πt þ μ y yt þ μ i it þ μ Δi ðit −it−1 Þ : The aggregate demand curve is backward looking. It depends on its own past lag, real interest rate (rt), depreciation rate and demand shocks. The term εty is a zero mean i.i.d. aggregate demand shock. 9 This Phillips curve is similar to the Phillips curve emerging from a Calvo type staggered price setting framework from the inter-temporal maximization of a representative agent that demands domestic and foreign goods, and also to Fuhrer and Moore Phillips curve in that inflation depends on both lagged inflation and future expected inflation. Further, the motivation for this empirical version of Phillips curve comes from the results of Mishra and Mishra (2010). They found that the (change in) exchange rate affects inflation with a lag. External factors like oil prices and foreign interest rates were also significant in explaining inflation. We assumed that effects of all these external factors would be transmitted to domestic inflation via a change in exchange rate. 10 For estimation, the ‘expected inflation’ is taken as a forecast obtained from fitting AR(1) model in WPI inflation series. 11 Potential output is obtained with Hodrick–Prescott filter method. It is thus a longterm trend component in (log) of ‘Index of Industrial Production’ (IIP) series, which is the measure of output (aggregate demand) in our model. 12 This assumption is motivated by Batini and Haldane's (1999) model and the response of exchange rate to monetary policy shock as discovered by Mishra and Mishra (2010) where we see some prolonged appreciation of exchange rate to a positive interest rate shock.

ð10Þ

Here, all the weights are non-negative; thus, the loss function is the weighted sum of the respective unconditional variances and defined in the following way:
c c E½Lt  ¼ μ π Var ½πt  þ μ π Var πt þ μ y Var½yt  þ μ i Var½it  þ μ Δi Var ½it −it−1 :

ð11Þ

Here, μπ, μπc , μy, μi and μ Δi are policy parameters that relate to domestic inflation, CPI inflation, output, interest rate and interest rate smoothing. The ‘strict domestic inflation targeting’ corresponds to μπ positive and all other weights are equal to zero. ‘Flexible domestic inflation targeting’ refers to positive weights to other policy parameters also. ‘CPI inflation targeting’ will have μπc positive rather than μπ. Thus, the decision problem of the central bank is to choose the instrument it conditional upon the information available in period ‘t’ so as to minimize Eq. (10).

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The above loss function can be seen as a limit of the inter-temporal loss function: min Et

∞ X

h i j 2 c c2 2 2 2 β μ π π t þ μ π πt μ y yt þ μ i it þ μ Δi Δit :

ð12Þ

j¼0

Here, β is the discount factor (fulfilling 0 b β b 1 representing central bank's rate of time preference). 4. Data and empirical estimations The aggregate demand and aggregate supply equations are estimated with an Instrumental Variable-Generalized Method of Moments (IV-GMM) estimator. 13 We use monthly data for the period January 1996 to March 2007. The data is sourced mainly from the IFS (IMF) and the RBI (www.rbi.org.in). All the variables other than interest rates are transformed as annual changes in log values. Thus, all the variables denote year-on-year changes in the original series which take care of seasonality issues in the monthly sample. All the variables are for the 1993–94 base period. All the variables entering into the estimation are stationary. 14 As there are expectation variables in the equations, we estimated the equations by replacing these expected values with their corresponding realized values and thereby introducing expectation errors into the equations' composite disturbances. 4.1. Variable description Domestic inflation and CPI inflation are measured as year-to-year changes in ‘Wholesale Price Index’ (WPI) and ‘Consumer Price Index for Industrial Workers’ (CPI-IW). Output gap is measured as the difference between (log of) ‘Index of Industrial Production’ (IIP) and its long term trend, proxied by (log of) Hodrick–Prescott trend. Real exchange rate is measured by ‘real effective exchange rate’ (REER) trade weighted. The call money rate (CMR) is taken as the short-run nominal interest rate. 4.2. Estimation of aggregate supply equation The specification of aggregate supply equation is kept as close as possible to the theoretical specification as described in Section 3. The annual WPI inflation (ΔWPI) is the dependent variable. The lag of inflation (ΔWPIt−1 ) and lag of (log) change in real effective exchange rate (ΔREERt−1 ) are the ‘included instruments’. The endogenous regressors are output gap ( ΔY) and expected inflation (E [WPI]). They are instrumented with a number of variables and their lags (excluded instruments) 15 in the regression. The estimation results of aggregate supply equation suggest that both lagged inflation rate and expected inflation are highly significant (at 1% level). The inflation in India shows substantial inertia along with the degree of forward-lookingness. This confirms our assumption in the theoretical section that hybrid Phillips curve could better explain inflation dynamics in India. The lag of (log) change in real 13

The GMM estimator applied here is the two-step efficient generalized method of moments (GMM) estimator. The efficient GMM estimator minimizes the GMM criterion function J = N * g′ * W * g, where N is the sample size, g is the orthogonality or moment conditions (specifying that all the exogenous variables or instruments in the equation are uncorrelated with the error term) and W is the weighting matrix (inverse of an estimate of the covariance matrix of orthogonality conditions). These moments' conditions are tested using Hansen J statistic. 14 The unit root tests of stationarity are reported in Appendix Table A.1. 15 List of ‘excluded instruments’ in aggregate supply equation is given in Appendix Table A.2. We also estimated alternative specifications of IV regressions using a subset of 12, 8, 6 instruments respectively. The results of these alternative specifications were very close (sign, significance and magnitude) to the results reported in Table 1, suggesting that the model is robust to alternative specifications of choice of instruments.

effective exchange rate (or lag of depreciation) is also significant. The coefficient on output gap is a very small positive number suggesting that the supply curve in India is sufficiently elastic and there is an excess (or unused) capacity in the economy. However, this coefficient is not significant which reconfirms the findings of Mishra and Mishra (2010) that inflation in India is not markedly governed by demand pull factors. The overall goodness of fit as measured by R-square is 0.73 (centered), suggesting that the included regressors explain much of the movements in the inflation. The next step in instrumental variable estimation is to check the validity of instruments. We performed two tests, that is, the Hansen–Sargan test of over-identifying restrictions and the LM test of under-identification (Kleibergen–Paap rk statistic). The joint null hypothesis of Hansen–Sargan test is that the instruments are valid instruments, that is, uncorrelated with the error term, and that the excluded instruments are correctly excluded from the estimation equation. From Table 1 we see that we fail to reject the null of instrument validity. For the under-identification test, null hypothesis is that the matrix of reduced form coefficients has rank equal to K-1 (such that K is the number of a regressor). The statistic provides a measure of instrument relevance and the rejection of null indicates that the model is identified. We reject null at 1% level (p-value 0.000) of under-identification, which means that the aggregate supply equation has been properly identified. The next step was to check whether or not GMM estimator is the appropriate estimator. In the presence of heteroskedasticity, GMM estimator is more efficient than the simple IV estimator. However, in the absence of heteroskedasticity, GMM estimator is asymptotically no worse than the IV estimator. Pagan and Hall (1983) proposed the test of heteroskedasticity for instrumental variable estimation. The results of the Pagan–Hall test statistic for our aggregate supply equation did indicate the presence of heteroskedasticity in aggregate supply equation and thus justified the use of GMM estimator. 4.3. Estimation of aggregate demand equation The aggregate demand equation of the model is also estimated with the IV-GMM estimator. The ‘output gap’ is the dependent variable in the regression. The lag of the output gap ðΔY t−1 ) and lag of log change in real effective exchange rate (ΔREERt−1 ) are ‘included Table 1 IV-GMM estimates of the aggregate supply equation. Dependent variable: ΔWPI Variable

Coefficient

Standard error

P-value

ΔY ΔWPIt−1 E(WPI) ΔREERt−1 Constant Number of observations Centered R-square Uncentered R-square Root MSE F (4,128) Underidentification test (Kleibergen–Paap rk LM statistic) Hansen J statistic

0.0109 0.5931⁎⁎⁎ 0.4226⁎⁎⁎ − 0.057⁎⁎ − 0.0005 133 0.7387 0.7939 .0039 498.80⁎⁎⁎ 36.39⁎⁎⁎

0.0078 0.0498 0.0570 0.0072 0.0011

0.168 0.00 0.00 0.019 0.638

Test for the presence of heteroskedasticity Pagan–Hall test statistic(using levels of IVs) Pagan–Hall test statistic (using levels and squares of IVs) Pagan–Hall test statistic (using level and cross products of IVs)

0.00 0.00

11.072

0.1976

33.854⁎⁎ 76.349⁎⁎⁎

0.0508 0.0013

123.027

0.6550

Note: ΔWPI : WPI inflation; ΔY: Output gap; ΔREER: (change in) real effective exchange rate; E(WPI) : expected WPI inflation. ***, **, * indicate 1%, 5% and 10% significance levels respectively.

A. Mishra, V. Mishra / Economic Modelling 29 (2012) 1053–1063

instruments’. Variable ‘real interest rate’ (RIR) is the endogenous regressor, which has been instrumented with a number of exogenous variables (excluded instruments). 16 The estimation results of the aggregate demand equation suggest that lag of output gap is significant at 1% level and the depreciation rate is significant at 5% level. The real interest rate coefficient is significant only at 10% level. The coefficient on ‘real interest rate’ is a very small negative number indicating the low interest elasticity of the aggregate demand in the Indian economy. Model selection statistics such as F-statistic, Root Mean Square Error and R-square are significant and support the tight fit for the model. The tests of validity of instruments, that is, Hansen J test and Kleibergen–Paap LM test, suggest that instruments are valid instruments; thus excluded instruments are correctly excluded from estimation equation and the equation is identified. The Pagan–Hall test suggests the presence of heteroskedasticity. 5. Simulations 5.1. Results on optimal policies We simulated the model 17 using the estimates of aggregate demand and supply from Tables 1 and 2 (taking the values of b1 = 0. 5931, b2 = 0. 0109, b3 = −0.057 for aggregate supply and a1 = 0.2437, a2 = −0.0032, a3 = 0.1536 for aggregate demand), an estimate for (ω), the share of imported goods (ω) in CPI 18 and the variance of various shock parameters in our model, demand shocks (σy2), supply shocks (σp2) and exchange rate shocks (σq2)). Also we assumed that the model is subjected to historical shocks, thus the variance of demand shocks (σy2) and supply shocks (σp2) is assumed to be 1 and the variance of exchange rate shocks (σq2) is to be 0.5).

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Table 2 IV-GMM estimates of the aggregate demand equation. Dependent variable: ΔY Variable

Coefficient

Standard error

P-value

ΔY t−1 RIR ΔREERt−1 Constant Number of observations Centered R-square Uncentered R-square Root MSE F (3,122) Underidentification test (Kleibergen–Paap rk LM statistic) Hansen J statistic

0.2437⁎⁎⁎ − 0.0032⁎ 0.1536⁎⁎ − 0.0446⁎⁎⁎

0.0818 0.0018 0.0653 0.0123

0.00 0.087 0.019 0.00

Test for the presence of heteroskedasticity Pagan–Hall test statistic (using levels of IVs) Pagan–Hall test statistic (using levels and squares of IVs) Pagan–Hall test statistic (using level and cross products of IVs)

125 0.4210 0.4210 .03015 12.24 54.363

0.00 0.00

9.433

0.8538

78.945⁎⁎⁎ 137.814⁎⁎⁎

0.000 0.000

253.931***

0.000

Note: ΔY: output gap; ΔREER: (change in) real effective exchange rate; RIR: real interest rate. ***, **, * indicate 1%, 5% and 10% significance levels respectively.

inflation targeting (domestic or CPI) are defined as weight only on inflation stabilization (domestic or CPI inflation depending on the targeted inflation of the central bank), while in the cases of flexible inflation targeting there is a weight on output stabilization but with preference (represented by higher weight) toward inflation stabilization.

5.2. Inflation targeting cases and Taylor rules 5.3. Unconditional standard deviations The different cases of inflation targeting are identified by the weights of policy parameters in the loss function of the RBI. We examined four targeting cases depending on whether the instruments correspond to WPI (domestic inflation) or CPI inflation along with two closed economy versions and one open economy 19 version of Taylor rules. 20 The weights given to the policy parameters under different targeting cases 21 are given in Table 3. The cases of strict 16 The list of ‘excluded instruments’ in aggregate demand equation is given in Appendix Table A.3. We also estimated alternative specifications of IV regressions using a subset of 12, 8, 6 instruments respectively. The results of these alternative specifications were very close (sign, significance and magnitude) to the results reported in Table 2, suggesting that the model is robust to alternative specifications of choice of instruments. 17 We modified a GAUSS code for solving optimal monetary policy under discretion and simple rules, made available by Paul Soderlind on his website http://home. tiscalinet.ch/paulsoderlind. The detailed solution of the model is with the authors and available on request. 18 We took the value of ω = 0.3. The share of imported goods in CPI is not very high in India. We also experimented with a number of values for ω; these do not affect our results qualitatively. 19 In an open economy version of Taylor rule, exchange rate enters with non-zero coefficient. In particular the coefficient on exchange rate should be less than zero and coefficient on lag of exchange rate should be a small positive number representing partial adjustment. (for more discussion on this refer to Taylor (2001) and Cavoli and Rajan (2005)). Using model simulations, recent literature find the optimal coefficient values for exchange rate range between − 0.45 and − 0.25 and lag of exchange rate range between 0.15 and 0.45 (refer to Cavoli and Rajan 2005). 20 We also tested Taylor rules with weight on interest rate smoothing at 0.50, 0.75 and 0.95. We find that Taylor rules with interest rate smoothing do bring down the volatility in interest rate (the higher the weight on interest rate smoothing, the lesser the variability in interest rate). However, their performance in terms of overall stabilization is even worse than optimal rules. These results are available from the authors on request. 21 The case of strict CPI inflation targeting does not converge without adding a small weight on interest rate smoothing. Therefore, for uniformity we added a small weight of 0.01 to interest rate smoothing parameter under all rules.

The unconditional standard deviation results highlight the unsuitability of ‘simple Taylor type monetary policy rules’ over ‘optimal monetary policy rules’. Closed economy simple monetary policy rules with only weight on output and inflation result in huge volatility in exchange rate and interest rate. The performance of ‘simple Taylor rule CPI inflation’ is worse than the ‘simple Taylor rule domestic inflation’. The open economy Taylor rule with weight on exchange rate generates lesser volatility in exchange rate than its closed economy counterpart. However, the performance of open economy Taylor rule is worse in stabilizing inflation and output in comparison to closed economy Taylor rules and exchange rate and interest rate in comparison to optimal monetary policy rules (Table 4). The results also indicate that there exists a trade-off between inflation variability and variability of other macro variables (output, exchange rate and interest rate) in strict inflation targeting cases. When we move from strict (both domestic and CPI) targeting cases to flexible targeting cases, the variability of inflation rises and the variability of other macro economic variables reduces. In CPI targeting cases the

Table 3 Targeting cases and Taylor rules. Optimal MPR Strict domestic-inflation targeting Flexible domestic inflation targeting Strict CPI targeting Flexible CPI targeting

μπ = 1 μπ = 1 μπ = 0 μπ = 0

Simple MPR Taylor rule, domestic inflation Taylor rule, CPI inflation Taylor rule, open economy

it = 1.5πt + 0.5yt it = 1.5πtc + 0.5yt it = 0.5yt + 1.5πt − 0.4qt + 0.2qt − 1

μπc = 0 μπc = 0 μπc = 1 μπc = 1

μy = 0 μy = .5 μy = 0 μy = .5

μi = 0 μi = 0 μi = 0 μi = 0

μΔi=.01 μ Δi ¼ :01 μΔi=.01 μ Δi ¼ :01

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Table 4 Unconditional standard deviations. Targeting cases

yt

πt

πtc

qt

it

Strict domestic-inflation targeting Flexible domestic inflation targeting Strict CPI targeting Flexible CPI targeting Taylor rule, domestic inflation Taylor rule, CPI inflation Taylor rule, open economy

2.075 0.946

4.536 5.466

4.487 5.472

0.0039 0.0026

0.0039 0.0026

0.906 0.734 1.308 1.824 3.973

3.972 4.785 2.221 2.949 2.787

3.534 4.908 1.832 1.886 2.779

0.942 0.754 7.818 8.712 4.825

0.905 0.754 4.458 8.848 5.142

volatility of exchange rate and interest rate is higher when compared to their volatility in domestic inflation targeting cases. This suggests the extensive use of exchange rate in CPI targeting to bring about stabilization. The domestic inflation targeting rules in our model are quite successful in containing variability of exchange rate and interest rate but at the expense of high volatility in domestic and CPI inflation rates. The volatility of output is also higher in domestic inflation targeting rules (both strict and flexible) when compared to CPI inflation targeting rules. This creates a trade-off between domestic and CPI

1

Effect of 1 s.d. dd shock on y

0.5

0 0.1

0.1

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. dd shock on dom.inflation

0.001

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. dd shock on CPI inflation

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. dd shock on interest rate

1

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. shock on dom. inflation

0 1

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. shock on CPI inflation

0 0.001

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. shock on interest rate

0.0005

1 2 3 4 5 6 7 8 9 10 11 12

0.001 Effect of 1 s.d. dd shock on exchange rate 0.0005 0

0

0.5

0.0005

0

Effect of 1 s.d. shock on y

0.5

0.05 0

0.01

0.005

0.05

0

inflation targeting rules. Domestic inflation targeting rules are more successful in containing the volatility of exchange rate and interest rate while CPI targeting rules are better at controlling the variability of output and inflation. The simple Taylor type rules, though somewhat successful in curbing the volatility of output and domestic and CPI inflations, result in huge volatility in exchange rate and interest rate. The volatility of exchange rate and interest rate is higher in simple Taylor type CPI inflation rules than in the simple Taylor type domestic inflation rule. The above results indicate that a flexible form of inflation targeting does result in lower variability of major macroeconomic variables at a small inflation volatility cost when compared to their strict targeting counterpart. Therefore some form of flexible targeting is preferable for the Indian economy. On the other hand, the simple rules turned out to be completely unsuccessful in stabilizing the economy in the current volatile open environment. There is a trade-off between flexible domestic inflation and CPI inflation targeting and neither of them appears to be very successful from an overall macro stabilization perspective. However, flexible domestic inflation targeting with low to moderate volatility in all the variables seems to be a better option but at the expense of some higher volatility in inflation rates.

0

0.001

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. shock on exchange rate

0.0005

1 2 3 4 5 6 7 8 9 10 11 12

0

1 2 3 4 5 6 7 8 9 10 11 12

Fig. 1. Impulse response: domestic inflation targeting (cases: strict and flexible).

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Effect of 1 s.d. dd shock on y

1

0.01

1059

Effect of 1 s.d. π shock on y

0.005 0

0.5

-0.005 -0.01

0

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

Effect of 1 s.d. dd shock on dom.inflation 0.1

1

0.05

0.5

0

0

Effect of 1 s.d. π shock on dom. inflation

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12 Effect of 1 s.d. dd shock on CPI inflation

0.1

0.05

Effect of 1 s.d. π shock on CPI inflation

1

0.5

0

0 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

Effect of 1 s.d. dd shock on interest rate 0.01

0.1

0.005

0.05

0

0

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

0.01

Effect of 1 s.d. π shock on interest rate

Effect of 1 s.d. dd shock on exchange rate

0.1

Effect of 1 s.d. π shock on exchange rate

0.05

0.005

0

0 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

Fig. 2. Impulse responses: CPI inflation targeting (cases: strict and flexible).

5.4. Impulse response functions Next we discuss the impulse responses for six cases of major macroeconomic variables to one standard deviation shock in the model. These results help us to analyze how an economy reacts over time to exogenous impulse shocks under various monetary policy rules, and thus enables us to further evaluate the performance of different monetary policy rules in a dynamic context. In each case the model is subjected to one standard deviation positive demand shock to output gap and one standard deviation inflation shock to domestic inflation. We analyzed the responses of inflation, output, exchange rate and interest rate to these shocks across different optimal monetary policy rules and for simple Taylor rules for 12 time periods in Figs. 1 to 4. The optimal monetary policy response under different monetary policy rules is examined. The

purpose of this analysis is to identify the monetary policy rule, which quickly brings the economy back to equilibrium with limited volatility in the macroeconomic variables in the event of a shock. Also, these results throw light on the effect of the different shocks on the economy under alternative inflation targeting rules. 22

22 We found that patterns of impulse response functions to demand and inflation shocks are quite alike in strict and flexible domestic inflation targeting cases and in strict and flexible CPI inflation targeting cases. However, these response functions do differ in magnitude of volatility from strict to flexible targeting cases. For example, demand and cost push shocks generate greater volatility in output and exchange rate and lesser in inflation in strict targeting cases when compared to flexible ones. Given the similar pattern of impulse response function in strict and flexible cases, while discussing the results, we presented the results of strict domestic inflation targeting together with flexible domestic inflation targeting and strict CPI inflation targeting together with flexible CPI inflation targeting.

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Effect of 1 s.d. π shock on y

Effect of 1 s.d. dd shock on y 2 1 0 -1 -2

2 1 0 -1 -2

1 2 3 4 5 6 7 8 9 10 11 12

2

Effect of 1 s.d. dd shock on dom. inflation

1 2 3 4 5 6 7 8 9 10 11 12

2

Effect of 1 s.d. π shock on dom. inflation

1

1

0

0

-1

-1

-2

-2

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

2

Effect of 1 s.d. dd shock on CPI inflation

2 1

1 0

0

-1

-1

-2

-2 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

2

Effect of 1 s.d. π shock on CPI inflation

Effect of 1 s.d. dd shock on interest rate

2 1 0 -1 -2

1 0 -1

Effect of 1 s.d. π shock on interest rate

1 2 3 4 5 6 7 8 9 10 11 12

-2 1 2 3 4 5 6 7 8 9 10 11 12

2

Effect of 1 s.d. dd shock on exchange rate

4

Effect of 1 s.d. π shock on exchange rate

2

1

0

0

-2

-1

-4

-2

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12 Fig. 3. Impulse responses: simple Taylor rule domestic inflation.

5.4.1. Strict and flexible domestic inflation targeting One standard deviation positive aggregate demand shock under domestic inflation targeting monetary policy rule (strict as well as flexible) increases output by 1% above its potential level in period 1. There is a smaller increase in domestic inflation due to these shocks and it increases by 0.1% in period 1. Monetary policy reacts to this development and there is an increase in nominal interest rate. As a result, real interest rate rises and there is an appreciation of real exchange rate. Due to this output gap contracts, domestic inflation falls and all the macro economic variables return to their steadystate values in about 5–6 periods. For one standard deviation inflation shock, domestic (and CPI) inflations rise by half a percent in period 1 and there is no response

from output gap in period 1. Reacting to rise in inflation, there is a rise in nominal interest rate and hence real interest rate. But the increase in real interest rate is very modest when compared to the increase in inflation. As a result, real interest rate falls in the subsequent periods. With this, output gap starts expanding. This expansion of output gap helps to bring down inflation and inflation reaches to its target level in 5–6 periods. 5.4.2. Strict and flexible CPI inflation targeting One standard deviation positive demand shock under CPI inflation targeting cases evokes similar reactions in output gap and inflation as under domestic inflation targeting cases. However, it evokes a stronger monetary policy response when compared to domestic inflation

A. Mishra, V. Mishra / Economic Modelling 29 (2012) 1053–1063

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Effect of 1 s.d. π shock on y

Effect of 1 s.d. dd shock on Y 2 1 0 -1 -2

2 1 0 -1 -2

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

2 1 0 -1 -2

Effect of 1 s.d. dd shock on dom.inflation

2 1 0 -1 -2

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

2 1 0 -1 -2

Effect of 1 s.d. dd shock on CPI inflation

2 1 0 -1 -2

2 1 0 -1 -2

Effect of 1 s.d. π shock on CPI inflation

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

rate

Effect of 1 s.d. π shock on dom.inflation

2 1 0 -1 -2

Effect of 1 s.d. π shock on interest rate

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

4 2 0 -2 -4

Effect of 1 s.d. dd shock on exchange rate

1 2 3 4 5 6 7 8 9 10 11 12

2 1 0 -1 -2

Effect of 1 s.d. π shock on exchange rate

1 2 3 4 5 6 7 8 9 10 11 12

Fig. 4. Impulse responses: simple Taylor rule CPI inflation.

targeting monetary policy rule. There is a bigger (as compared to domestic inflation targeting rules) rise in nominal interest rate and hence real interest rate, as well as a larger (compared to domestic inflation targeting rules) appreciation in real exchange rate. As a result, output gap starts contracting and inflation starts falling in the subsequent periods. The economy returns to its steady state after about 5–6 periods. Similarly one standard deviation inflation shock in CPI targeting cases causes a similar reaction in domestic and CPI inflation as under domestic inflation targeting cases, and they increase by half a percentage point in period 1. Output gap again does not respond to this shock in period 1. There is a very strong monetary policy reaction to this and a large increase in nominal interest rate and hence real

interest rate. This causes a large appreciation in real exchange rate. Following an increase in real interest rate, output gap starts falling from period 2 onward below its potential level and inflation starts decreasing. The economy returns to its steady state equilibrium in around 7–8 periods. 5.4.3. Taylor rules Demand and inflation shocks generate much larger variability in major macroeconomic variables in Simple Taylor Domestic Inflation monetary policy rule when compared to optimal monetary policy rules. The economy takes more time to recover from these shocks in this rule. In the event of one standard deviation demand shock in domestic inflation Taylor rule, output gap starts rising and inflation also

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increases. Additionally, there is an increase in nominal (hence real interest rate) and an appreciation in real exchange rate. Due to this, output gap contracts and inflation falls. Inflation turns negative after around 7–8 periods and consequently there is a fall in interest rate and hence exchange rate depreciates. This leads to the expansion of output gap which rises for a few periods before returning to its steady state. Inflation also returns to its steady state after around 12 periods. The supply shocks generate erratic response from all the major variables and the economy takes longer to stabilize. CPI Taylor type monetary policy rules cause very high variability in exchange rate. However, they result in very moderate volatility of output gap and thus are quite successful in curbing the volatility of the output gap. Under CPI Taylor rules (similar to domestic inflation Taylor rule), the economy takes more time to stabilize after a shock. In our model framework, CPI Taylor rule results in huge volatility of real exchange rate in line with Svensson (2000) observation that, “This might illustrate the danger of responding to a current forward-looking variable, and provides support for the warning in Woodford” 23 (p.23). 6. Conclusions

better alternative from an overall macro stabilization perspective in the present scenario where financial markets are still not integrated enough to ensure quick transmission of interest rate impulses (as suggested by low sensitivity of demand to interest rate impulses) and existence of rigidities in the economy (as indicated by flat Phillips curve). There are two main limitations to the study that provide useful directions and scope for future research. One of the limitations relates to the formulation of the model, in that the model is a simple three equation model and foreign variables are not explicitly modeled. The model is linear with quadratic loss function and there are different sources which can induce non-linearity in the model (like non negative nominal interest rate or non linear Phillips curve). The other limitation of the study is the application of general empirical methodology. We note that the GMM method exploits only part of the information implied by the model, while the currently more popular likelihood methods (with the Kalman filter) and Bayesian estimation can use all the implications of the DSGE model. It would be very desirable to test the results of the model using the abovementioned alternative empirical approaches, and thus provides an interesting area for future research. Appendix

Our small macro model of the Indian economy was built on the results from the VAR model proposed by Mishra and Mishra (2010) and based on literature on small open economy models. In our model the exchange rate has a prominent role to play in both the determination of the aggregate demand and supply equation of the economy. Our model specification is different from other models of open economies in that we assumed both the aggregate supply and demand equation to be affected by the lag of (change in) exchange rate rather than its contemporaneous value. 24 Estimation results of aggregate supply justify the assumption of hybrid Phillips curve for India and suggest that backward dynamics (lag of inflation) are slightly more important than forward dynamics (expected inflation in the next period) to explain inflation outcomes in India. This further indicates the presence of rigidities 25 in price setting behavior in the Indian economy resulting in short-run trade-off between inflation and output. We found that the supply curve in India was flatter compared to a mature small open economy and that there was an excess capacity in the economy. We also found that the interest rate elasticity of the aggregate demand is low. Within this framework, the properties of strict vs. flexible domestic and CPI inflation targeting were examined and compared with the Taylor rules (domestic and CPI Inflations). The analysis highlights the unsuitability of simple Taylor type monetary rules in stabilizing the economy and suggests that discretionary optimization works better. There appears to be a trade-off between output gap stabilization and real exchange rate stabilization under domestic and CPI inflation targeting respectively. Flexible domestic inflation targeting seems a

23 Woodford analyzed the budding issue in monetary policy literature that a desirable monetary policy would be able to contain inflation before much had developed. This could be conducted by monetary indicators that are supposed to be good predictors of ‘future inflation’ rather than by concentrating on variables (such as money supply) that are thought to be probable causes of inflation. In his analysis, Woodford suggested that there were important advantages in finding indicators of the causes of inflation rather than of inflationary expectations. For more details, refer to Woodford (1994). 24 The assumption is motivated from the results of Mishra and Mishra (2010) and further verified by the estimations in this study where lag of exchange rate turned out to be statistically significant in both aggregate demand and supply equations. 25 The main sources of real rigidity in the Indian context relate to goods market and labor market imperfections. Both goods and labor markets are characterized by dualistic consumers and labors respectively, where one type of consumers and labors are at above subsistence level while others are at subsistence level (for more details refer to Goyal, 2011).

A.1. Unit root tests

ΔWPI ΔREER RIR ΔCPI Δ2 CPI ΔY ΔOIL ΔUSIIP Δ2 USIIP ΔUSCPI ΔM3 ffrate Δf f rate lrate5 Δlrate5 lrate10 Δlrate10 spread1 spread5

ADF test

Phillips–Perron test

− 3.020⁎⁎ (0.033) − 3.99⁎⁎ (0.011) − 5.495⁎⁎⁎ (0.00) − 1.992 (0.29) − 7.513⁎⁎⁎ (0.00) − 8.679⁎⁎⁎ (0.00) − 3.016⁎⁎ (0.033) − 2.160 (0.22) − 10.33⁎⁎⁎ (0.00) − 2.689⁎ (0.075) − 2.622⁎ (0.089) − 0.689 (0.84) − 5.874⁎⁎⁎ (0.00) − 1.815 (0.37) − 10.791⁎⁎⁎ (0.00) − 1.705 (0.43) − 11.009⁎⁎⁎ (0.00) − 3.656⁎⁎⁎ (0.0048) − 3.670⁎⁎⁎ (0.0046)

− 2.958⁎⁎ − 3.614⁎⁎⁎ − 5.290⁎⁎⁎ − 2.477 − 7.304⁎⁎⁎ − 8.799⁎⁎⁎ − 2.538 − 1.749 − 10.525⁎⁎⁎ − 2.72⁎ − 2.616⁎ − 1.088 − 5.985⁎⁎⁎ − 1.836 − 10.779⁎⁎⁎ − 1.710 − 11.009⁎⁎⁎ − 3.118⁎⁎ − 3.517⁎⁎⁎

(0.039) (0.0055) (0.00) (0.12) (0.00) (0.00) (0.10) (0.41) (0.00) (0.071) (0.089) (0.72) (0.00) (0.36) (0.00) (0.43) (0.00) (0.0252) (0.0076)

Notes: 1. ***, **,* indicate 1%, 5% and 10% significance levels respectively. 2. Figures in parenthesis indicate Mackinnon p-value. 3. The number of lagged difference terms included in testing for each series has been decided on the basis of no autocorrelation in the error terms for the ADF tests. For PP tests lags have been selected on the basis of Newey–West criterion.

A.2. List of ‘excluded instruments’ in aggregate supply equation Variable

Meaning

ΔY t−1 ΔT t−2 RIR ΔREER ΔOIL ΔOILt−1 ΔOILt−2 ΔOILt−4 Δ2 CPI Δ2 CPI t−1 ΔUSCPI ΔUSCPIt−1 Δ2 USIIP Δf f rate Δf f ratet−1 Δf f ratet−2

Lag one of output gap Lag two of output gap Real interest rate Log change in REER Oil price inflation Lag one of oil price inflation Lag two of oil price inflation Lag four of oil price inflation Change in CPI inflation Lag one of change in CPI inflation United States (US) CPI inflation Lag one of us CPI inflation Change in ‘Index of Industrial Production (IIP)’ growth rate in US Change in federal funds rate (US) Lag one of change in federal funds rate Lag two in federal funds rate

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A.3. List of ‘excluded instruments’ in aggregate demand equation Variable

Meaning

ΔY t−2 ΔY t−4 spread1

Lag two of output gap Lag four of output gap Difference between yield on SGL transaction on government security of 1 year maturity and 10 year maturity. Difference between yield on SGL transaction on government security of 5 year maturity and 10 year maturity. Change in yield on SGL transaction on government security of 5 year maturity Lag one of change in yield on SGL transaction on government security of 5 year maturity Change in yield on SGL transaction on government security of 10 year maturity Lag two of change in yield on SGL transaction on government security of 10 year maturity Lag one of real interest rate Lag two of real interest rate Log change in money supply (M3) Lag two of log change in M3 Log change in REER Lag two of log change in REER WPI inflation Lag one of WPI inflation Lag one of change in federal funds rate Lag two in federal funds rate

spread5 Δlrate5 Δlrate5t−1 Δlrate10 Δlrate10−t−2 RIRt − 1 RIRt − 2 ΔM3 ΔM3t−2 ΔREER ΔREERt−2 ΔWPI ΔWPIt−1 Δf f ratet−1 Δf f ratet−2

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