A Brief Historical Journey

The quest for monetary policy rules has been traced back to the writings of Wicksell³ who argued that the central bank should aim to maintain price stability. This simple interest rate rule did not attract much attention in policy discussions, perhaps because its exclusive focus on price stability and lack of explicit reference to developments in real economic activity did not go down well with the ruling orthodoxy of the day.

An early influential case for rules is reflected in the Chicago view which produced non-activist formulations (Friedman, 1960; Lucas, 1980). A simple but operable policy rule developed and revolutionized thinking on monetary policy in its time and beyond - that the central bank maintain a constant rate of growth of the money supply equivalent to the rate of growth of real GDP or the celebrated k-percent rule⁴. Giving governments any flexibility in setting money growth was believed to lead to inflation; countercyclical Keynesian-type monetary policy was to be avoided at all costs. During the 1960s and 1970s, Friedman’s recommendation was that the Federal Reserve control the rate of money supply growth at 4 percent. The advantage of the constant money growth was that very little information was required to implement it. If velocity does not exhibit a secular trend, the only required element for calibrating the rule is the economy’s natural growth of output. In addition, the calibration of this rule does not rest on the specification of any particular model and is stable across alternative models of the economy. Despite its intuitive appeal, however, the Friedman rule became difficult to operate in the face of real world developments as is well known. High inflation and a breakdown in the stability of the velocity of money brought on by deregulation of financial markets, innovations and advances in transactions technology made control of money supply futile. It suffered from logical weaknesses too. Ruling out policy feedback implied a belief that money was the exclusive determinant of GDP. Moreover, if a particular money rule would stabilize the economy, discretion preferring policy makers could always behave that way and still retain the flexibility to change the rule as needed (Fischer, 1988).

Two Modern Formulations

The McCallum and Taylor rules are essentially efforts to develop simple and transparent rules that could deliver improved macroeconomic performance. They belong in the suite of rules driven by the belief that central banks should respond to evolving conditions in a relatively activist manner, in contrast to the types of rules proposed by the Chicago school.

The McCallum rule (McCallum, 2000) specifies the growth rate of the monetary base (instrument) in a non-discretionary feedback rule for nominal GDP (target) as

Δb_t = Δx* − Δv_t + 0.5(Δx* − Δx_t-1),

where Δb_t is the rate of growth of the monetary base; Δv_t is the rate of growth of base velocity averaged over previous four years⁵; Δx_t is the rate of growth of nominal GDP and Δx* is the target rate of growth of nominal GDP (assumed at 5 percent by McCallum for the US) taken to be the sum of π*, the target inflation rate (2 percent), and the long-run average rate of growth of real GDP (3 percent per year). Since technological and regulatory changes alter the growth of base velocity from year to year, a problem that undermined Friedman’s rule, Δv_t is averaged over the past four years and is intended as a forecast of the average growth rate of velocity over the foreseeable future rather than a reflection of current cyclical conditions which are represented by the term Δx* − Δx_t-1. In substance, base money growth must equal the targeted growth of nominal GDP. There is a proportional feedback to the growth rate of base money from the gap between nominal GDP growth and its targeted rate. If the relationship between the monetary base and nominal income changes (say on account of financial innovations), the growth rate of the monetary base must be adjusted accordingly.

The Taylor rule (Taylor, 1993) prescribes the adjustment of interest rate policy instrument in a systematic manner in response to developments in inflation and macroeconomic activity. It can be written as

R_t = r + Δp_t + 0.5(Δp_t − π*) + 0.5 ý_t

where R_t is the nominal policy interest rate; r is the average equilibrium real interest rate; Δp_t is the inflation rate, recent or expected future value; π* is the target rate of inflation, and ý_t is the deviation of current real GDP from its potential or natural rate.

Taylor has used 2 percent for the average real rate of interest and has also assumed that 2 percent per year is the target rate of inflation. Different values could be specified for the coefficients on the terms (Δp_t − π*) and y_t, but the values of 0.5 were used in Taylor’s original work. The presence of the term Δp_t on the right hand side implies that a measure of the real rate of interest, Rt − Δpt, is adjusted up or down relative to the average real rate r in response to departures of inflation and output from their target values. Taylor also noted that if the deviation of real quarterly output from a linear trend is used to measure the output gap, and the year-over-year rate of change of the output deflator to measure inflation, this parameterization appeared to describe Federal Reserve behavior well in the late 1980s and early 1990s.

Methodological Issues

In essence, a rule is a restriction on the monetary authority’s discretion. Most rules proposed in the literature do not, however, eliminate discretion completely⁶. Modern policy rules recognize the desirability of some discretion in the monetary authority’s response to the evolving state of the economy, and, therefore, incorporate feedback that allow it to react in a manner that minimizes the persistence of shocks. Both the McCallum rule and the Taylor rule incorporate feedback. While some evidence suggests improved performance, responding to the state of the economy can also be destabilizing. It is also important to take note of the Lucas (1975) critique and carefully consider the implications of changes in policies for expectations – what expectations of prior policy are built into the model and how the model will change with a new policy.

Methodological issues surrounding the operationalisation of rules essentially relate to the manner in which feedback is incorporated – the choice of policy instrument that the monetary authority can control directly and/or accurately – base money for McCallum and the short-term policy rate for Taylor (in some cases, the exchange rate); the target variable(s) – deviation of nominal GDP growth from its target for McCallum and deviations of inflation/real output from target/potential for Taylor (variants also incorporate the exchange rate); the baseline for the target variable – long run rate of nominal output growth for McCallum and the real rate of interest for Taylor; the monetary policy response parameter – the coefficients on the target variables; and the smoothing parameter (the coefficient on the lagged policy variable) which empirical analysis has shown to be important in gauging the pace of policy response.

(a) McCallum Rule

Turning to specific methodological issues, first, it is important to note that the policy instrument in the McCallum’s rule i.e., the monetary base implicitly sums the effects of pure changes in high-powered money and those induced by changes in reserve requirements. Given the tendency of the central bank to systematically offset changes in reserve requirements with open market operations, the explanatory power of the monetary base as a policy instrument is significantly improved by adjusting for the short-run dynamics embodied in discrete changes in reserve requirements (McCallum, 1990; Haslag and Hein, 1995).

Second, the McCallum rule employs average velocity growth because trends in velocity growth can shift over time, but not every change in base velocity represents a long-lasting shift in the trend (McCallum and Nelson, 1999). The velocity growth adjustment is intended to reflect long-lasting institutional/technological changes affecting the demand for the monetary base⁷.

Third, the term for deviations of nominal GDP growth from target is intended to account for cyclical influences and acts as an error-correction mechanism. As in all error-correction models, this confronts a trade-off between gradualism and immediate restoration of the target. Thus, the key element in McCallum’s rule is the monetary response coefficient which determines how much base money – and eventually money stock – must change when nominal GDP deviates from its target. If the monetary response factor is too large, it can induce an explosive reaction or instability in the economy. On the other hand, a monetary response factor that is too small implies that monetary policy does not affect the economy much. There seems to be a range of ideal values for the monetary response factor (Croushore and Stark, 1996). McCallum’s own research and other efforts (Hall, 1990) suggests using a factor of 0.5 for the US economy. In contrast, a lower feedback value (0.25) is needed for Japan (McCallum, 1993). For developing countries such as China, a smaller monetary response factor is found to be appropriate (Sun et al, 2010). Clearly, instrument instability is an important issue that has to be dealt with in a country-specific manner in the context of estimating McCallum’s rule.

Fourth, McCallum rule also features feedback adjustments in velocity changes in response to cyclical departures of nominal income from the target path with the coefficient chosen to balance against the danger of instrument instability. However, the velocity correction term could be omitted without any appreciable effect on results, attesting to the non-dependence of the McCallum rule on base velocity growth (McCallum, 2002).

In empirical analysis McCallum showed that if a rule such as his had been followed, the performance of the U.S. economy likely would have been considerably better than actual performance, especially during the 1930s and 1970s, the two periods of the worst monetary policy mistakes in the history of the Federal Reserve (McCallum, 2002). Several studies present supportive evidence for McCallum’s rule in different developed countries (Hall, 1990; Judd and Motley, 1991; 1993; Razzak, 2003; Diez de los Rios, 2009). In the Indian context, a backward-looking version of McCallum’s rule, with real exchange rate changes as an additional variable, has been found to work best. The nominal income gap is significant and correctly signed, suggesting that nominal income could be an implicit final target in the conduct of monetary policy (Virmani, 2004). The McCallum rule has been evaluated along with Taylor-type and hybrid rules for Russia with the finding that monetary aggregates can indeed be used as an effective policy instrument (Esanov et al, 2004). In the Chinese context, the monetary base has been substituted with broad money first by using the coefficients specified by McCallum, and then by allowing the data to determine the actual coefficient estimates. The actual developments of the monetary base were found to follow the values implied by the McCallum rule more closely than was the case with broad money since 2003. Monetary growth was observed to have been faster than what the McCallum would have suggested in the more recent period, partly due to hikes in reserve requirements boosting the monetary base (Koivu et al, 2009). For Turkey, the monetary response coefficient was found to be 0.1 (as against McCallum’s original proposition of 0.5) in view of the history of high inflation. Monetary policy appears to be closely simulated by McCallum’s rule over the whole period (2002-2008) whereas the Taylor rule provides a good approximation only from 2006 when prerequisites of an inflation targeting regime were in place. The smoothing component was also found to be higher under the McCallum rule (Khakimov et al, 2009).

Drawing on the results of estimating McCallum and Taylor rules as well as hybrids mixing instruments and targets for 20 emerging countries across Africa, Asia, emerging Europe and Latin America, it is observed that while the McCallum rule works well for countries that adopt leaning against the wind strategies, it is the hybrid McCallum-Taylor specifications with an interest rate instrument and a nominal income gap perform better than benchmark Taylor or McCallum rules. Instrument smoothing is significant across all specifications, but the exchange rate is not consistently significant (Mehrotra et al, 2011).

(b) Taylor Rule

The confluence of the econometric evaluation evidence and its usefulness for understanding historical monetary policy has generated widespread interest in the Taylor rule among numerous central banks to provide guidance in policy decisions. A generalized Taylor rule that nests the original specification and also allows for interest rate smoothing has been favoured in the empirical literature (Clarida, Gali and Gertler, 1998, 2000).

A key issue in the context of estimating the Taylor rule is, first, the size of the coefficients on the inflation and output gaps. The coefficient on inflation is 1.5, the coefficient on real output is 0.5 and the intercept term is r – 0.5 π* (Taylor, 1993, 1999a). Some studies have shown that that the coefficient on real output is close to 1 (Brayton et al, 1997). However, higher weight to output in a policy rule gives a lower variance of output but may give a higher variance of inflation. Raising the coefficient on real output from 0.5 to 1.0 represents a trade-off between inflation variance and output variance, but the increase in average inflation variability is small compared with the decrease in average output variability, and moreover, interest rate variance is higher (Taylor, 1999b)

There is less ambiguity around the coefficient on the inflation gap. If the coefficient on inflation is less than one, the real interest rate would fall rather than rise when inflation rose (US in 1960s and 1970s), leading to even higher inflation and inflation would turn highly volatile. There can be bursts of inflation and output fluctuations that result from self-fulfilling changes in expectations (Clarida et al, 1998).

Second, methodological issue relating to operationalising the Taylor rule is about whether it should be forward-looking, contemporaneous or backward-looking. While Clarida et al (1998) demonstrate the case for a purely forward-looking rule in the context of the US, the UK and Japan, it is also argued that a rule that uses only information about the recent behavior of inflation and output does quite well (Taylor and Williams, 2010), as compared to one that uses forecasts of future inflation and output. Performance under the best kind of rule of this kind (measured in terms of variability of inflation, output and interest rates) is not significantly reduced if lagged inflation data is used (Rotemberg and Woodford, 1999; Feldstein, 1999). Thus lags in the availability of accurate measurement of inflation are not necessarily a serious problem for the implementation of such a rule. Accordingly, backward looking rules are quite good approximations of optimal policy (Rotemberg and Woodford, op cit.). It is argued that there is no need for policy to be forward-looking as long as the private sector is. A commitment to raise interest rates later, after inflation increases, is sufficient to cause an immediate contraction of aggregate demand in response to a shock that is expected to give rise to inflationary pressures – aggregate demand depends on future interest rates and not simply on current short rates as long as the monetary authority is understood to be committed to adhering to the contemplated policy rule in the future and not only at the present time; and as long as the private sector has model-consistent rational expectations. However, for the euro area, there is evidence that policy-makers are neither purely backward nor forward-looking, but react to a synthesis of the available information on the current and future state of the economy (Blattner and Margaritov, 2010).

Third, adding the exchange rate - either though a monetary conditions index (weighted average of exchange rate and inflation rate) to replace the interest rate as the policy instrument or by introducing an exchange rate term in the right hand side - to the simple Taylor-type policy rules may improve macroeconomic performance (Ball, 1999).

Mohanty and Klau (2004) estimated an open economy Taylor rule for India, along with other emerging market economies (EMEs) in which the relationship between the short-term interest rate and the inflation rate turned out to be relatively weak, whereas the output gap was statistically significant. Similar findings are reported in other efforts (Inoue and Hamori, 2009; Singh, 2006; Jha, 2008; Hutchison et al, 2010; and Anand et al, 2010). On the other hand, a comprehensive analysis of monetary policy rules across different specifications in both backward- and forward-looking versions found monetary policy’s reaction to inflation to be stronger than to the output gap for the period 1988-2009 (Singh, 2010). On the basis of a variety of alternative simulations, a forward-looking Taylor rule performed best for India in term of consistency with the Taylor principle. The coefficient on the inflation gap turned out to be greater than unity, while that on the output gap was unity (Patra and Kapur, 2012).

Methodological issues that arise in the actual estimation of the Taylor rule and its extensions have been comprehensively surveyed recently (Patra and Kapur, 2012). First, it is observed that while a forward-looking specification is recommended in theory (the target variables depend not only on the current policy stance but also on expectations about future policy), from practical considerations, a general specification with forward-looking terms and incorporating the well-documented interest rate smoothing by central banks (inertia in policy response) is preferred in the empirical literature (Clarida et al., 2000; Paez-Farrell, 2009). Second, exchange rate smoothing is found to be an important consideration in the policy reaction function of emerging economies, including India, in some studies.⁸ Third, the use of the output gap, a variable which is not observed, presents a challenge particularly in view of frequent and often sizable revisions which can produce large divergences between real time data on which authorities make their policy judgments and the final revised data that are used in empirical work. Accordingly, it may be optimal to replace the output gap variable with its first difference (Taylor and Williams, 2010).

The greater prominence of the Taylor rule is attributed to it being more realistic in describing the conduct of actual monetary policy since 1986. Modern central banks focus upon interest rates, not the monetary base, in designing their policy actions. The ascendency of the new Keynesian framework from the late 1990s has also implied a downgrading of monetary aggregates in explaining the operational conduct of monetary policy. These developments notwithstanding, considerable academic support for nominal spending targets has existed since 1980 (Meade, 1978; Tobin, 1980). Keeping nominal GDP close to a target growth path would maintain inflation close to its desired value on average and would diminish fluctuations in real cyclical aggregates. This helps the policy maker to balance the two goals without having to control or accurately predict how nominal GDP divides between its constituents (McCallum, 1988). It also eliminates policy surprises due to undesirable fluctuations arising from pursuit of an optimal policy decision. Also, there is an observable tendency for an interest rate instrument to become something of a target variable that is thus adjusted too infrequently and too timidly (Taylor, 1999b).

In some ways, nominal income targeting rules can claim analytical superiority over pure interest rate formulations in the Taylor rule tradition. Illustratively, the growth rate version of nominal income targeting avoids the need to measure unobservables such as capacity or natural-rate output (for the output gap) or the real interest rate, as is required by Taylor’s rule⁹ (Orphanides, 2003). While Clarida et al (1998) provided formal econometric support for Taylor’s findings in the context of US monetary policy, it has been shown that replacing expected future inflation in Clarida et al by expected current nominal income growth produces standard errors that are lower, and nominal income growth is significant with higher explanatory power (McCallum, 2000). Especially in an environment with near-zero short-term interest rates, the McCallum rule may be of interest – (Goodfriend, 2000; Krugman, 1998; Meltzer, 1998). Moreover, in the case of emerging economies, it has been claimed that a monetary base or some other monetary aggregate can still be a reasonable monetary policy instrument (Taylor, 2000; Beck and Wieland, 2008).

Experiments with hybrid rules have yielded promising results. Replacing the monetary base in the McCallum rule with the interest rate as the policy instrument produces a modified rule that is highly cointegrated with the standard Taylor rule. With similar degrees of sufficiently high instrument smoothing, each of these rules performs as well as the other – equality of unconditional variance of inflation and output cannot be rejected (Razzak, 2003). This seems to be the desirable direction of future research – a consensus approach.

Contemporaneous/Backward-looking Versions

Taylor Rule:

i_t = a0 + a1*(π_t – π*) + a2*y_t + a3*Δe_t-1+ a4*i_t-1

McCallum Rule

Δb_t = b0 + b1*(Δx_t* − Δx_t-1) + b2*Δe_t-1+ b3*Δb_t-1,

Hybrid McCallum-Taylor Rule

i_t = c0 + c1*(Δx_t* − Δx_t-1) + c2*Δe_t-1 + c3*i_t-1

Hybrid McCallum-Hall-Mankiw Rule

Δb_t = d0 + d1*(π_t – π* + y_t) + d2*Δe_t-1 + d3*Δb_t-1

Forward-looking Versions

Taylor Rule:

i_t = a0 + a1*(E_tπ_t+i – π*) + a2*E_ty_t+i + a3*Δe_t-1 + a4*i_t-1

McCallum Rule

Δb_t = b0 + b1*(Δx_t* − E_tΔx_t+i) + b2*Δe_t-1 + b3*Δb_t-1,

Hybrid McCallum-Taylor Rule

i_t = c0 + c1*(Δx_t* − E_tΔx_t+i) + c2*Δe_t-1 + c3*i_t-1

Hybrid McCallum-Hall-Mankiw Rule

Δb_t = d0 + d1*[(E_tπ_t+i – π*) + E_ty_t+i)] + d2*Δe_t-1 + d3*Δb_t-1

Variables

We use quarterly data for the period April 1996 to March 2011, the choice of period being determined by the availability of quarterly data on real GDP for India. All series which are in gap form (such as output gap, non-agricultural output gap, industrial output gap and real effective exchange rate gap) are based on seasonally adjusted data using the X-11 algorithm of the US Department of Commerce. Variables measured on a year-on-year (y-o-y) basis such as inflation and GDP growth are not seasonally adjusted. Also, the policy instruments – the policy interest rate and the y-o-y base money growth – are not adjusted for seasonality.

The output gap is measured by the difference between real GDP (seasonally adjusted) and its trend obtained by the HP filter. Headline inflation in India is measured by y-o-y variations in the wholesale price index (WPI). For the purpose of estimation, we use headline WPI inflation as well as the core inflation indicator (non-food manufactured products WPI inflation).

Turning to policy variables, the McCallum rule requires the use of the monetary base. In view of frequent changes in the cash reserve ratio (CRR) in the conduct of monetary policy, the concept of adjusted reserve money (i.e., adjusted for the CRR impact) is important in the Indian context. Over the period of study, the CRR was initially reduced from 13.5 per cent (April 1996) to 4.5 per cent by June 2003. It was then raised to 9.0 per cent by September 2008, but in response to the global financial crisis it was lowered to 5.0 per cent by January 2009. It was increased to 6.0 per cent by April 2010 and is 4.75 per cent currently (March 2012) Accordingly, we compute an adjusted reserve money series as the base money aggregate as it would have been if the CRR had remained unchanged at 5 per cent i.e., its initial value at the beginning of the sample period. For the periods for which the actual CRR is 5 per cent, the unadjusted and adjusted series coincide.

As regards the policy interest rate, we follow Patra and Kapur (2012), in using the effective policy rate i.e., the interest rate through which the RBI engaged in its liquidity operations with market participants, depending on prevailing liquidity conditions - the Bank Rate until February 2002; the reverse repo rate during March 2002-June 2006 and December 2008-May 2010 when liquidity was abundant and the RBI was in absorption mode; and the LAF repo rate in all other phases of the period of study (July 2006-November 2008 and June 2010-March 2011) when liquidity was tight and the RBI injected liquidity through repo operations.

Data Sources

All data are taken from published sources. Data on global real GDP growth and the index of world non-fuel commodity prices are from the IMF’s World Economic Outlook and database on Primary Commodity Prices, respectively. Data on the US federal funds rate target are from the Fred database of the Federal Reserve Bank of St. Louis (http://research.stlouisfed.org/fred2/). All data on the Indian economy - quarterly real and nominal GDP, components of GDP, reserve money and CRR changes, the various measures of inflation, the policy rates, the nominal exchange rate of the Indian rupee against the US dollar and the real effective exchange rate (REER) index covering 36 partner countries are taken from the RBI’s “Handbook of Statistics on Indian Economy 2010-11” supplemented by information from the RBI’s Monthly Bulletin and data put out on the website of the Central Statistical Organisation (CSO) of the Government of India (http://www.mospi.gov.in/mospi_press_releases.htm).

Estimation Procedure

For forward-looking specifications of the monetary policy rules, we estimate the equations using Generalised Method of Moments (GMM) following Clarida et al. (1998, 2000)¹³. For the contemporaneous/backward-looking specifications as well as equations which use RBI’s publicly available projections, estimation is done through ordinary least squares (OLS) estimates.

Results

(a) McCallum Rule

While the original McCallum rule is backward-looking, we estimate both forward-looking and backward-looking versions of the rule. We also assess the monetary policy response to exchange rate dynamics. Given the volatility imparted by agricultural shocks to both growth and inflation in India, we estimate McCallum rules separately for total nominal income and its core component, non-agricultural income. Here, it is necessary to note an important caveat: in the McCallum rule, the income growth term is defined as trend growth minus actual growth, in contrast to a Taylor-type rule which typically defines it as actual growth minus trend growth. Consequently, we expect the income gap term to have a positive coefficient – illustratively, when it increases i.e., actual income growth is declining relative to trend growth, monetary policy is expected to be accommodative and base money expands.

The empirical results are summarized in Table 1. All specifications indicate a sizable degree of policy smoothing, and this is true of all specifications estimated in this paper. Turning to specific findings, first, consistent with a priori expectations, we find a positive and statistically significant (at the 10 percent level) reaction of base money growth – the policy instrument – to deviations of trend growth in nominal income from its expected growth in the next quarter (Column 7). However, the response of base money to deviations in nominal income growth is found to be stronger and significant at the 1 percent level for the core component of GDP (i.e., non-agricultural GDP) one quarter forward (Columns 10 and 11) and two quarters forward (Column 13). In either case, whether it is overall GDP growth or non-agricultural GDP growth, the policy response is stronger – between 0.6 and 2.1 - vis-à-vis the range suggested by McCallum – 0.25 to 0.50 for mature economies such as Japan and the US. Second, an important finding in this context is that the expected relationship between base money growth and deviations in nominal income/non-agricultural nominal income growth does not materialize in the backward-looking specification that characterizes the conventional McCallum rule - the coefficient is sometimes wrongly signed and insignificant in all cases (Columns 2-5). Third, the term for exchange rate changes which enters with a one-quarter lag is found to have the correct sign and is statistically significant in all specifications - monetary policy reacts to, rather than preempts, large movements in exchange rates out of line with fundamentals through smoothing interventions that affect its net foreign assets and thereby base money. While this may produce a tightening of monetary conditions, it is not necessarily associated with a tightening of monetary policy. As the empirical results from Taylor rule estimations will show subsequently, the RBI does not respond to exchange rate movements with changes in policy interest rates which, in the current framework, more accurately reflect the policy stance. Moreover, the long run coefficient on exchange rate changes is low at 0.19 to 0.30 relative to the monetary response coefficient on nominal income growth.

Table 1:

Estimates of McCallum Rule

(Dependent Variable: Growth in Base Money (Δb_t))

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-13 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, Δb, Δe, DNFC, DM3, FEDTARGET, and the relevant lag of nominal income deviation term.

Table 1:

Estimates of McCallum Rule

(Dependent Variable: Growth in Base Money (Δb_t))

1	2	3	4	5	6	7	8	9	10	11	12	13
Constant	4.54	4.94	4.95	5.26	4.81	4.02	4.48	4.48	4.73	4.13	4.26	3.75
	(2.52)	(3.45)	(3.02)	3.93	1.78	1.40	1.56	1.36	1.74	1.99	1.29	1.23
Δxt* − Δxt-1	-0.09	-0.09
	(1.36)	(1.25)
Δxct* − Δxct-1			0.05	0.03
			(0.54)	(0.35)
Δxt* − EtΔxt+1					0.08	0.18
					(1.00)	(1.80)
Δxt* − EtΔxt+2							0.01	0.07
							(0.06)	(0.56)
Δxct* − EtΔxct+1									0.39	0.49
									(2.74)	(5.08)
Δxct* − EtΔxct+2											0.15	0.34
											(1.33)	(2.27)
Δeqt-1		-0.05		-0.05		-0.05		-0.05		-0.07		-0.06
		(1.79)		(1.69)		(2.95)		(2.16)		(5.29)		(2.64)
Δbt-1	0.68	0.66	0.66	0.64	0.68	0.74	0.70	0.70	0.71	0.77	0.73	0.78
	(5.92)	(6.87)	(6.27)	(7.23)	(3.86)	(3.72)	(3.72)	(3.09)	(3.84)	(5.41)	(3.29)	(3.68)
${\overline{\mathrm{R}}}^2$	0.44	0.46	0.43	0.45	0.44	0.46	0.42	0.44	0.46	0.47	0.41	0.42
LB-Q(8)	0.15	0.15	0.17	0.16	0.16	0.12	0.16	0.12	0.14	0.13	0.12	0.09
J-test					0.14	0.09	0.15	0.10	0.11	0.11	0.15	0.11

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-13 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, Δb, Δe, DNFC, DM3, FEDTARGET, and the relevant lag of nominal income deviation term.

View Table

Table 1:

Estimates of McCallum Rule

(Dependent Variable: Growth in Base Money (Δb_t))

1	2	3	4	5	6	7	8	9	10	11	12	13
Constant	4.54	4.94	4.95	5.26	4.81	4.02	4.48	4.48	4.73	4.13	4.26	3.75
	(2.52)	(3.45)	(3.02)	3.93	1.78	1.40	1.56	1.36	1.74	1.99	1.29	1.23
Δxt* − Δxt-1	-0.09	-0.09
	(1.36)	(1.25)
Δxct* − Δxct-1			0.05	0.03
			(0.54)	(0.35)
Δxt* − EtΔxt+1					0.08	0.18
					(1.00)	(1.80)
Δxt* − EtΔxt+2							0.01	0.07
							(0.06)	(0.56)
Δxct* − EtΔxct+1									0.39	0.49
									(2.74)	(5.08)
Δxct* − EtΔxct+2											0.15	0.34
											(1.33)	(2.27)
Δeqt-1		-0.05		-0.05		-0.05		-0.05		-0.07		-0.06
		(1.79)		(1.69)		(2.95)		(2.16)		(5.29)		(2.64)
Δbt-1	0.68	0.66	0.66	0.64	0.68	0.74	0.70	0.70	0.71	0.77	0.73	0.78
	(5.92)	(6.87)	(6.27)	(7.23)	(3.86)	(3.72)	(3.72)	(3.09)	(3.84)	(5.41)	(3.29)	(3.68)
${\overline{\mathrm{R}}}^2$	0.44	0.46	0.43	0.45	0.44	0.46	0.42	0.44	0.46	0.47	0.41	0.42
LB-Q(8)	0.15	0.15	0.17	0.16	0.16	0.12	0.16	0.12	0.14	0.13	0.12	0.09
J-test					0.14	0.09	0.15	0.10	0.11	0.11	0.15	0.11

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-13 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, Δb, Δe, DNFC, DM3, FEDTARGET, and the relevant lag of nominal income deviation term.

(b) Hybrid McCallum-Taylor Rule

We followed the encouraging results thrown up in the literature (see Section II) on hybrid McCallum-Taylor rules by estimating formulations in which the effective policy interest rate as the policy instrument reacts to deviations of nominal income growth from its trend. The results are again presented for both backward- and forward-looking specifications as well as for overall growth in nominal income and in its non-agricultural component. Here, the expectation is that the income term will be negatively signed i.e., when it is increasing or nominal output growth is falling relative to trend, monetary policy turns accommodative and policy interest rates are reduced, and vice versa.

Our results provide strong support for such hybrid rules (Table 2). First, the coefficient on the nominal income growth deviation term is negative in all cases consistent with a priori expectations and is also statistically significant in most cases. This is true both for backward-and forward-looking specifications. Second, the policy response is found to be stronger for specifications using forward-looking versions (absolute long-run coefficient is 1.1-1.7) vis-a-vis backward-looking specifications (0.4). Finally, in contrast to the conventional McCallum rule and consistent with our results for the Taylor rule, the exchange rate coefficient is wrongly signed and insignificant in all specifications.

Table 2:

Estimates of Hybrid Taylor-McCallum Rule

(Dependent Variable: Effective Policy Interest Rate (INT))

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-13 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, INT, Δe, DNFC, DM3, FEDTARGET, and the relevant lag of nominal income deviation term.

Table 2:

Estimates of Hybrid Taylor-McCallum Rule

(Dependent Variable: Effective Policy Interest Rate (INT))

1	2	3	4	5	6	7	8	9	10	11	12	13
Constant	0.78	0.75	0.79	0.75	0.54	0.04	0.45	-0.37	0.49	0.14	0.38	-0.18
	(3.09)	(2.25)	(3.05)	(2.22)	(2.11)	(0.07)	(1.61)	(0.50)	(1.76)	(0.36)	(1.16)	(0.28)
Δxt* − Δxt-1	-0.05	-0.05
	(1.78)	(1.85)
Δxct* − Δxct-1			-0.05	-0.05
			(1.37)	(1.50)
Δxt* − EtΔxt+1					-0.11	-0.15
					(3.26)	(2.74)
Δxt* − EtΔxt+2							-0.10	-0.11
							(2.01)	(2.01)
Δxct* − EtΔxct+1									-0.16	-0.19
									(3.33)	(2.73)
Δxct* − EtΔxct+2											-0.16	-0.18
											(1.92)	(2.09)
Δeqt		0.00		0.00		-0.03		-0.05		-0.02		-0.03
		(0.20)		(0.21)		(0.92)		(1.18)		(1.11)		(0.93)
INTt-1	0.87	0.87	0.86	0.87	0.90	0.97	0.91	1.05	0.89	0.94	0.90	0.99
	(23.76)	(20.25)	(23.39)	(18.78)	(23.47)	(12.21)	(22.28)	(8.89)	(20.57)	(16.73)	(20.57)	(9.99)
${\overline{\mathrm{R}}}^2$	0.83	0.83	0.83	0.83	0.83	0.79	0.82	0.75	0.84	0.81	0.81	0.77
LB-Q(8)	0.77	0.81	0.73	0.79	0.48	0.49	0.63	0.10	0.32	0.48	0.60	0.25
J-test					0.28	0.23	0.33	0.50	0.23	0.18	0.30	0.37

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-13 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, INT, Δe, DNFC, DM3, FEDTARGET, and the relevant lag of nominal income deviation term.

View Table

Table 2:

Estimates of Hybrid Taylor-McCallum Rule

(Dependent Variable: Effective Policy Interest Rate (INT))

1	2	3	4	5	6	7	8	9	10	11	12	13
Constant	0.78	0.75	0.79	0.75	0.54	0.04	0.45	-0.37	0.49	0.14	0.38	-0.18
	(3.09)	(2.25)	(3.05)	(2.22)	(2.11)	(0.07)	(1.61)	(0.50)	(1.76)	(0.36)	(1.16)	(0.28)
Δxt* − Δxt-1	-0.05	-0.05
	(1.78)	(1.85)
Δxct* − Δxct-1			-0.05	-0.05
			(1.37)	(1.50)
Δxt* − EtΔxt+1					-0.11	-0.15
					(3.26)	(2.74)
Δxt* − EtΔxt+2							-0.10	-0.11
							(2.01)	(2.01)
Δxct* − EtΔxct+1									-0.16	-0.19
									(3.33)	(2.73)
Δxct* − EtΔxct+2											-0.16	-0.18
											(1.92)	(2.09)
Δeqt		0.00		0.00		-0.03		-0.05		-0.02		-0.03
		(0.20)		(0.21)		(0.92)		(1.18)		(1.11)		(0.93)
INTt-1	0.87	0.87	0.86	0.87	0.90	0.97	0.91	1.05	0.89	0.94	0.90	0.99
	(23.76)	(20.25)	(23.39)	(18.78)	(23.47)	(12.21)	(22.28)	(8.89)	(20.57)	(16.73)	(20.57)	(9.99)
${\overline{\mathrm{R}}}^2$	0.83	0.83	0.83	0.83	0.83	0.79	0.82	0.75	0.84	0.81	0.81	0.77
LB-Q(8)	0.77	0.81	0.73	0.79	0.48	0.49	0.63	0.10	0.32	0.48	0.60	0.25
J-test					0.28	0.23	0.33	0.50	0.23	0.18	0.30	0.37

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-13 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, INT, Δe, DNFC, DM3, FEDTARGET, and the relevant lag of nominal income deviation term.

(c) Hybrid McCallum-Hall-Mankiw Rule

We also estimate the hybrid McCallum-Hall-Mankiw rule in which the policy instrument - base money growth – reacts to the sum of the inflation gap and the output gap. As before, we examine both backward- and forward-looking specifications and versions based on growth in overall nominal income and its non-agricultural component.

Our empirical evidence does not support such rules (Table 3). First, while the coefficient on the inflation gap plus output gap term is correctly signed (negative) in the contemporaneous versions, it is incorrectly signed in the forward-looking versions. In all formulations, however, the coefficients are statistically insignificant. Second, consistent with our findings for the McCallum rule, the exchange rate coefficient is correctly signed but insignificant in all specifications.

Table 3:

Estimates of Hybrid McCallum-Hall-Mankiw Rule

(Dependent Variable: Growth in Base Money (Δb_t))

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-9 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, Δb, [(π – π*) + YGAP], [(π_MPNF – π*_MPNF) + YGAP^C], Δe, DNFC, DM3, and FEDTARGET.

Table 3:

Estimates of Hybrid McCallum-Hall-Mankiw Rule

(Dependent Variable: Growth in Base Money (Δb_t))

1	2	3	4	5	6	7	8	9
Constant	5.28	5.64	5.24	5.58	6.21	5.85	6.46	5.88
	(3.00)	(3.94)	(2.89)	(3.73)	(5.22)	(4.97)	(5.14)	(4.68)
[(π – π*) + YGAP]t	-0.01	-0.01
	(0.08)	(0.16)
[(πMPNF – π*MPNF) + YGAPC]t			-0.04	-0.06
			(0.37)	(0.62)
[(π – π*) + YGAP]t+1					0.12	0.10
					(1.16)	(0.90)
[(πMPNF – π*MPNF) + YGAPC]t+1							0.08	0.03
							(0.82)	(0.29)
Δeqt-1		-0.04		-0.04		-0.03		-0.03
		(1.42)		(1.48)		(1.33)		(1.39)
Δbt-1	0.63	0.61	0.63	0.61	0.57	0.60	0.57	0.61
	(5.49)	(6.30)	(5.32)	(6.03)	(7.10)	(7.44)	(6.81)	(7.10)
${\overline{\mathrm{R}}}^2$	0.38	0.39	0.38	0.39	0.33	0.34	0.35	0.37
LB-Q(8)	0.11	0.13	0.11	0.13	0.14	0.12	0.15	0.14
J-test					0.72	0.68	0.71	0.64

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-9 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, Δb, [(π – π*) + YGAP], [(π_MPNF – π*_MPNF) + YGAP^C], Δe, DNFC, DM3, and FEDTARGET.

View Table

Table 3:

Estimates of Hybrid McCallum-Hall-Mankiw Rule

(Dependent Variable: Growth in Base Money (Δb_t))

1	2	3	4	5	6	7	8	9
Constant	5.28	5.64	5.24	5.58	6.21	5.85	6.46	5.88
	(3.00)	(3.94)	(2.89)	(3.73)	(5.22)	(4.97)	(5.14)	(4.68)
[(π – π*) + YGAP]t	-0.01	-0.01
	(0.08)	(0.16)
[(πMPNF – π*MPNF) + YGAPC]t			-0.04	-0.06
			(0.37)	(0.62)
[(π – π*) + YGAP]t+1					0.12	0.10
					(1.16)	(0.90)
[(πMPNF – π*MPNF) + YGAPC]t+1							0.08	0.03
							(0.82)	(0.29)
Δeqt-1		-0.04		-0.04		-0.03		-0.03
		(1.42)		(1.48)		(1.33)		(1.39)
Δbt-1	0.63	0.61	0.63	0.61	0.57	0.60	0.57	0.61
	(5.49)	(6.30)	(5.32)	(6.03)	(7.10)	(7.44)	(6.81)	(7.10)
${\overline{\mathrm{R}}}^2$	0.38	0.39	0.38	0.39	0.33	0.34	0.35	0.37
LB-Q(8)	0.11	0.13	0.11	0.13	0.14	0.12	0.15	0.14
J-test					0.72	0.68	0.71	0.64

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Columns 2-5 report OLS estimates. Columns 6-9 report estimates by GMM methodology using one lag each of the following variables as instruments: constant, Δb, [(π – π*) + YGAP], [(π_MPNF – π*_MPNF) + YGAP^C], Δe, DNFC, DM3, and FEDTARGET.

(d) Taylor Rule

In this paper, we refine and broaden the Taylor rule estimations conducted in the context of operationalisation of the new Keynesian model in Indian conditions in Patra and Kapur (2012). They estimated a monetary policy reaction function for India using the output gap, inflation (measured by the y-o-y change either in the GDP deflator or in WPI inflation) and the effective policy rate. Robustness properties were explored by estimating contemporaneous and forward-looking versions of the Taylor rule and across alternative sample periods.

At the outset of this sub-section, it is useful to set out a critical issue in the empirical estimation of Taylor rules. The Taylor principle is that the long-run coefficient on the inflation term should be more than unity. As pointed out in Section II, a coefficient of less than unity implies that the real interest rate falls when inflation is rising, characteristic of the policy mistakes found in the US in the 1960s and 1970s, and this will lead to even higher inflation. Patra and Kapur (2012) show that the Taylor principle is amply satisfied in the Indian context for forward-looking versions of the rule. For contemporaneous versions, the long-run coefficient was found to be less than unity, thus violating the Taylor principle. In contrast to Patra and Kapur (2012), others such as Anand et al (2010), Hutchison et al (2010) and Mohanty and Klau (2004) obtained a long-run inflation coefficient less than unity. Patra and Kapur (2012) suggested that this counter-Taylor principle result could be the outcome of a number of factors such as (a) use of contemporaneous reaction functions, ignoring the normal lags associated with the operation of monetary policy; (b) use of call money rate/Treasury bill rate as a proxy for the policy rate; and (c) use of industrial output as the activity variable rather than overall GDP.

In this paper, we empirically revisit this issue and in doing so, we examine additional aspects such as: (a) use of actual GDP growth rates rather than the unobservable output gap; (b) use of the output gap based on industrial GDP rather than overall GDP; (c) use of provisional/preliminary data i.e., data actually used by the central bank at the time of taking policy action) and not the revised estimates¹⁴; (d) using the RBI’s monetary policy projections for growth and inflation (semi-annual up to mid-2005 and quarterly thereafter), which can obviate the need for use of instruments and, therefore, estimable by OLS; (e) use of non-food manufactured products WPI inflation (in lieu of headline inflation) recently articulated by the Reserve Bank as an indicator of core demand pressures and the non-agricultural output gap to abstract from volatility caused by supply shocks; and (f) use of the call money rate instead of the effective policy rate. For the various potential combinations, we present results for both forward-looking and contemporaneous specifications. In all cases, we also assess as to whether exchange rate dynamics play any role in the policy reaction functions.

The results for these alternative explanatory variables/combinations are presented in Tables 4 and 5. The main findings are summarized below: First, the estimation results obtained in Patra and Kapur (2012) are robust to using various alternative indicators of inflation and growth.

Second, the coefficients on inflation and output gap terms are statistically significant and satisfy the Taylor principle in almost all the forward-looking specifications (Table 4). The coefficient estimates indicate stronger policy response to non-food manufactured products inflation dynamics, consistent with the Reserve Bank’s recent emphasis on this indicator of underlying demand pressures in the context of the 2010-11 inflation episode.

Table 4:

Estimates of Taylor Rule (Forward-looking Specifications)

(Dependent Variable: Effective Policy Interest Rate (INT))

Note:

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Estimation is by GMM methodology for the sample period 1997:2 to 2011:1 using one lag each of the following variables as instruments: int, ygap, πgap^gdpd, πgap^cpi, πgap^wpi, INFG, oil, Δe, DNFC, DM3 and fedtarget for the specification in columns 2-3 and 6-15; for columns 14 and 15, the instrument ‘int’ is replaced by ‘call’. Columns 4 and give are OLS estimates.

Table 4:

Estimates of Taylor Rule (Forward-looking Specifications)

(Dependent Variable: Effective Policy Interest Rate (INT))

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Constant	0.64	0.58	-1.45	-1.45	0.46	0.51	0.41	-0.03	-0.21	-0.43	0.50	0.34	1.72	2.66
	(2.41)	(1.20)	(1.99)	(1.96)	(2.06)	(1.67)	(1.87)	(0.08)	(0.60)	(1.08)	(2.16)	(1.06)	(3.10)	(2.18)
(π – π*)t+2	0.16	0.15							0.11	0.10	0.15	0.15
	(2.63)	(2.10)							(2.62)	(1.83)	(2.51)	(2.38)
YGAPt+2	0.18	0.17
	(2.16)	(1.60)
(πPROV - π*)t+2			0.09	0.09
			(1.72)	(1.49)
GDPPROJ{+1}			0.26	0.26
			(3.07)	(3.29)
(πMPNF – π*MPNF)t+2					0.21	0.21
					(5.23)	(5.02)
YGAPCt+2					0.15	0.16
					(2.75)	(2.01)
(π – π*)t+1							0.14	0.19					0.17	0.09
							(4.50)	(4.04)					(2.28)	(1.09)
Δ(YGAP)t+2							0.37	0.31
							(1.50)	(0.85)
GDPRG									0.06	0.07
									(1.70)	(1.80)
YGAPINDt+2											0.11	0.10
											(2.82)	(2.60)
YGAPt+1													0.48	0.48
													(2.68)	(2.18)
Δet		-0.01		0.00		0.00		-0.03		-0.01		-0.01		0.08
		(0.29)		(0.11)		(0.27)		(2.13)		(0.86)		(0.89)		(1.86)
INTt-1	0.88	0.89	0.94	0.94	0.91	0.91	0.92	0.99	0.95	0.98	0.91	0.93
	(24.02)	(11.90)	(34.87)	(24.89)	(29.54)	(18.84)	(27.61)	(18.74)	(28.52)	(18.46)	(26.95)	(19.30)
CALLt-1													0.71	0.58
													(7.67)	(3.03)
${\overline{\mathrm{R}}}^2$	0.85	0.84	0.90	0.90	0.86	0.86	0.82	0.81	0.85	0.84	0.84	0.83	0.26	0.32
LB-Q(8)	0.79	0.79	0.76	0.75	0.57	0.57	0.75	0.41	0.67	0.63	0.66	0.56	0.70	0.80
J-test	0.55	0.44			0.71	0.64	0.68	0.64	0.57	0.47	0.56	0.54	0.77	0.71
Long-run coefficients
Inflation	1.33	1.40	1.45	--	2.43	2.24	1.77	16.14	2.39	4.73	1.60	2.28	0.58	--
Output	1.51	1.58	4.16	4.25	1.71	1.71	--	--	1.21	3.12	1.18	1.53	1.69	1.15

Note:

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Estimation is by GMM methodology for the sample period 1997:2 to 2011:1 using one lag each of the following variables as instruments: int, ygap, πgap^gdpd, πgap^cpi, πgap^wpi, INFG, oil, Δe, DNFC, DM3 and fedtarget for the specification in columns 2-3 and 6-15; for columns 14 and 15, the instrument ‘int’ is replaced by ‘call’. Columns 4 and give are OLS estimates.

View Table

Table 4:

Estimates of Taylor Rule (Forward-looking Specifications)

(Dependent Variable: Effective Policy Interest Rate (INT))

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Constant	0.64	0.58	-1.45	-1.45	0.46	0.51	0.41	-0.03	-0.21	-0.43	0.50	0.34	1.72	2.66
	(2.41)	(1.20)	(1.99)	(1.96)	(2.06)	(1.67)	(1.87)	(0.08)	(0.60)	(1.08)	(2.16)	(1.06)	(3.10)	(2.18)
(π – π*)t+2	0.16	0.15							0.11	0.10	0.15	0.15
	(2.63)	(2.10)							(2.62)	(1.83)	(2.51)	(2.38)
YGAPt+2	0.18	0.17
	(2.16)	(1.60)
(πPROV - π*)t+2			0.09	0.09
			(1.72)	(1.49)
GDPPROJ{+1}			0.26	0.26
			(3.07)	(3.29)
(πMPNF – π*MPNF)t+2					0.21	0.21
					(5.23)	(5.02)
YGAPCt+2					0.15	0.16
					(2.75)	(2.01)
(π – π*)t+1							0.14	0.19					0.17	0.09
							(4.50)	(4.04)					(2.28)	(1.09)
Δ(YGAP)t+2							0.37	0.31
							(1.50)	(0.85)
GDPRG									0.06	0.07
									(1.70)	(1.80)
YGAPINDt+2											0.11	0.10
											(2.82)	(2.60)
YGAPt+1													0.48	0.48
													(2.68)	(2.18)
Δet		-0.01		0.00		0.00		-0.03		-0.01		-0.01		0.08
		(0.29)		(0.11)		(0.27)		(2.13)		(0.86)		(0.89)		(1.86)
INTt-1	0.88	0.89	0.94	0.94	0.91	0.91	0.92	0.99	0.95	0.98	0.91	0.93
	(24.02)	(11.90)	(34.87)	(24.89)	(29.54)	(18.84)	(27.61)	(18.74)	(28.52)	(18.46)	(26.95)	(19.30)
CALLt-1													0.71	0.58
													(7.67)	(3.03)
${\overline{\mathrm{R}}}^2$	0.85	0.84	0.90	0.90	0.86	0.86	0.82	0.81	0.85	0.84	0.84	0.83	0.26	0.32
LB-Q(8)	0.79	0.79	0.76	0.75	0.57	0.57	0.75	0.41	0.67	0.63	0.66	0.56	0.70	0.80
J-test	0.55	0.44			0.71	0.64	0.68	0.64	0.57	0.47	0.56	0.54	0.77	0.71
Long-run coefficients
Inflation	1.33	1.40	1.45	--	2.43	2.24	1.77	16.14	2.39	4.73	1.60	2.28	0.58	--
Output	1.51	1.58	4.16	4.25	1.71	1.71	--	--	1.21	3.12	1.18	1.53	1.69	1.15

Note:

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags. J-test reports p-value for test for over-identifying restrictions for GMM estimates.

^4.Estimation is by GMM methodology for the sample period 1997:2 to 2011:1 using one lag each of the following variables as instruments: int, ygap, πgap^gdpd, πgap^cpi, πgap^wpi, INFG, oil, Δe, DNFC, DM3 and fedtarget for the specification in columns 2-3 and 6-15; for columns 14 and 15, the instrument ‘int’ is replaced by ‘call’. Columns 4 and give are OLS estimates.

Third, the only instance in the forward-looking specifications when the coefficient on the inflation term is insignificant is when we use call rate as the policy instrument in lieu of the effective policy rate (Table 4, columns 14-15). Moreover, the ${\overline{\mathrm{R}}}^2$ drops substantially to 0.26 vis-à-vis 0.80-0.90 in the specifications using the effective policy rate. Over the period of evolution of the current monetary policy regime in India, there have been brief periods when the call rate has exhibited significant volatility and has moved significantly away from the policy corroder set by the repo and the reverse repo rate.

Fourth, in the contemporaneous specifications, the inflation coefficient is correctly signed (positive) and statistically significant in almost all cases; however, the long-run inflation coefficient is below unity in all permutations with the notable exception when non-food manufactured products inflation is used as an indicator of inflation (Table 5).

Table 5:

Estimates of Taylor Rule (Contemporaneous Specifications)

(Dependent Variable: Effective Policy Interest Rate (INT))

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags.

Table 5:

Estimates of Taylor Rule (Contemporaneous Specifications)

(Dependent Variable: Effective Policy Interest Rate (INT))

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
Constant	0.61	0.53	0.63	0.58	0.51	0.43	0.01	-0.01	-0.41	-0.46	-0.55	-0.56	0.74	0.73	3.84	4.06
	(2.60)	(1.92)	(2.21)	(1.81)	(2.39)	(1.49)	(0.03)	(0.03)	(0.64)	(0.81)	(1.38)	(1.49)	(3.10)	3.01	4.46	4.90
(π – π*)t	0.07	0.08			0.09	0.10	0.08	0.08					0.06	0.06	0.08	0.03
	(3.37)	(2.80)			(3.47)	(2.88)	(3.19)	(2.63)					(1.79)	(1.79)	(0.78)	(0.28)
YGAPt	0.19	0.19													0.50	0.53
	(2.88)	(3.09)													(3.08)	(2.95)
(πMPNF – π*MPNF)t			0.06	0.06
			(1.89)	(1.83)
YGAPCt			0.31	0.31
			(3.15)	(3.05)
Δ(YGAP)t					0.08	0.08
					(1.26)	(1.22)
GDPRG							0.08	0.08
							(2.15)	(2.51)
INFWPIPROJD EV									0.20	0.20
									(2.21)	(1.85)
GDPPROJ									0.13	0.13
									(1.53)	(1.71)
(πPROV - π*)t											0.08	0.09
											(3.08)	(2.37)
GDPRGPRELIM
											0.16	0.15
											(2.50)	(2.77)
YGAPINDt													0.18	0.17
													(1.83)	(2.16)
Δeqt		-0.01		-0.01		-0.01		0.00		-0.01		-0.01		0.00		0.05
		(0.61)		(0.54)		(0.56)		(0.27)		(0.45)		(0.54)		(0.07)		(1.90)
INTt-1	0.90	0.91	0.90	0.91	0.91	0.92	0.90	0.90	0.91	0.92	0.89	0.91	0.88	0.88
	(24.7)	(24.4)	(20.7)	(19.9)	(29.7)	(25.6)	(29.4)	(25.0)	(31.1)	(30.1)	(15.5)	(23.1)	(23.4)	(25.0)
CALLt-1															0.40	0.36
															(3.67)	(3.32)
${\overline{\mathrm{R}}}^2$	0.90	0.90	0.91	0.91	0.89	0.89	0.86	0.85	0.90	0.90	0.82	0.82	0.91	0.91	0.35	0.39
LB-Q(8)	0.95	0.93	0.79	0.81	0.79	0.85	0.86	0.87	0.76	0.77	0.51	0.59	0.74	0.74	0.77	0.84
Long-run coefficients
Inflation	0.70	0.90	0.55	0.65	0.99	1.26	0.77	0.86	2.12	2.42	0.74	0.95	0.47	0.48	---	---
Output	1.86	2.04	3.02	3.34	--	--	0.75	0.77	--	1.58	1.48	1.58	1.45	1.45	0.83	0.83

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags.

View Table

Table 5:

Estimates of Taylor Rule (Contemporaneous Specifications)

(Dependent Variable: Effective Policy Interest Rate (INT))

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
Constant	0.61	0.53	0.63	0.58	0.51	0.43	0.01	-0.01	-0.41	-0.46	-0.55	-0.56	0.74	0.73	3.84	4.06
	(2.60)	(1.92)	(2.21)	(1.81)	(2.39)	(1.49)	(0.03)	(0.03)	(0.64)	(0.81)	(1.38)	(1.49)	(3.10)	3.01	4.46	4.90
(π – π*)t	0.07	0.08			0.09	0.10	0.08	0.08					0.06	0.06	0.08	0.03
	(3.37)	(2.80)			(3.47)	(2.88)	(3.19)	(2.63)					(1.79)	(1.79)	(0.78)	(0.28)
YGAPt	0.19	0.19													0.50	0.53
	(2.88)	(3.09)													(3.08)	(2.95)
(πMPNF – π*MPNF)t			0.06	0.06
			(1.89)	(1.83)
YGAPCt			0.31	0.31
			(3.15)	(3.05)
Δ(YGAP)t					0.08	0.08
					(1.26)	(1.22)
GDPRG							0.08	0.08
							(2.15)	(2.51)
INFWPIPROJD EV									0.20	0.20
									(2.21)	(1.85)
GDPPROJ									0.13	0.13
									(1.53)	(1.71)
(πPROV - π*)t											0.08	0.09
											(3.08)	(2.37)
GDPRGPRELIM
											0.16	0.15
											(2.50)	(2.77)
YGAPINDt													0.18	0.17
													(1.83)	(2.16)
Δeqt		-0.01		-0.01		-0.01		0.00		-0.01		-0.01		0.00		0.05
		(0.61)		(0.54)		(0.56)		(0.27)		(0.45)		(0.54)		(0.07)		(1.90)
INTt-1	0.90	0.91	0.90	0.91	0.91	0.92	0.90	0.90	0.91	0.92	0.89	0.91	0.88	0.88
	(24.7)	(24.4)	(20.7)	(19.9)	(29.7)	(25.6)	(29.4)	(25.0)	(31.1)	(30.1)	(15.5)	(23.1)	(23.4)	(25.0)
CALLt-1															0.40	0.36
															(3.67)	(3.32)
${\overline{\mathrm{R}}}^2$	0.90	0.90	0.91	0.91	0.89	0.89	0.86	0.85	0.90	0.90	0.82	0.82	0.91	0.91	0.35	0.39
LB-Q(8)	0.95	0.93	0.79	0.81	0.79	0.85	0.86	0.87	0.76	0.77	0.51	0.59	0.74	0.74	0.77	0.84
Long-run coefficients
Inflation	0.70	0.90	0.55	0.65	0.99	1.26	0.77	0.86	2.12	2.42	0.74	0.95	0.47	0.48	---	---
Output	1.86	2.04	3.02	3.34	--	--	0.75	0.77	--	1.58	1.48	1.58	1.45	1.45	0.83	0.83

^1.Variable names are in Annex 1.

^2.Figures in parenthesis are t-statistics based on HAC standard errors corrected with Newey-West/Bartlett window and three lags.

^3.LB-Q test gives significance level (p-value) of Box-Pierce-Ljung Q-statistic for the null of no residual autocorrelation for 8 lags.

Fifth, the coefficient on the various alternative output terms is positive and statistically significant in almost all specifications, both in the forward-looking and contemporaneous specifications. Thus, the central bank focuses on both inflation and output stabilization.

Sixth, turning to the issue of whether the monetary authority uses the interest rate instrument to lean against exchange rate volatility, the coefficient is found to be wrongly signed and insignificant in all instances. This is true for both the forward-looking and the contemporaneous specifications (Tables 4-5). The results are consistent with the WPI inflation specifications in Patra and Kapur (2012). The only instance in which the exchange rate variable enters the regression with the correct sign (positive) is when the call rate is used as the policy rate; however, when we use the call rate, the inflation terms, as noted earlier, lose significance. The exchange rate variable being insignificant in the policy reaction function appears to reflect the RBI’s approach to exchange rate management. The exchange rate regime in India has been described as a “bounded float” (Gokarn, 2012) under which the exchange rate is determined by daily variations in demand and supply and in excessively volatile market conditions, “smoothing” interventions help to keep markets orderly and prevent large jumps that can induce further spirals. Notably, the use of policy interest rates to target any level or band of the exchange rate is never resorted to.

Finally, the alternative specifications in the forward-looking version indicate that the neutral policy rate is around 5.5 per cent.