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Some Insights from India

A Horse Race among the Alternative Taylor Rule Specifications

The paper estimates a slew of augmented Taylor rule specifications using call and treasury bill rates. After accounting for break points, we calculate the output gap based on a single-index dynamic factor extracted from monthly high-frequency indicators that are representative of broad sectoral activity. In our study, we found that interest rates in India are mostly in line with the augmented Taylor rule specifications after the Reserve Bank of India started using flexible inflation targeting.

Over the past few decades, the Taylor rule has been considered one of the guiding forces of the central banks’ policy rate decisions, though it is well known that central banks do not necessarily follow it as a hard rule and take interest rate decisions by integrating judgment and discretion. Empirical research and discussions surrounding the policy reaction function have taken centre stage following the seminal paper by John B Taylor (1993). Thereafter, several dynamic stochastic general equilibrium (DSGE) models have used the Taylor rule to provide an effective closure for the indeterminacy problem. Galí and Gertler’s paper (1999) shows that the dynamic stability condition converges with the Taylor principle, providing micro-foundations to this macroeconomic rule. Central banks take policy decisions based on several considerations, for example, high-frequency data releases, nowcasts of major macro variables, and judgments. However, the Taylor rule is regularly estimated in many central banks to compare actual policy rates vis-à-vis the rule-prescribed rates with due caution against its mechanical use. Accordingly, researchers have augmented the standard Taylor rule to capture the policy rate dynamics of different countries and time periods. Thus, different variants of the Taylor rule have subsequently evolved: the forward-looking Taylor rule, backward-looking Taylor rule (Clarida et al 1999), Taylor rule with error correction (Judd and Rudebusch 1998), Taylor rule augmented with output gap dynamics (Walsh 2003), etc.

Among the emerging market economies, India has a long history of monetary policymaking where policy and operating frameworks have evolved with the economy. India’s monetary policy framework has transitioned from a credit-planning regime to monetary targeting, a multiple indicator approach, preconditions for inflation targeting, and finally to a flexible inflation targeting (FIT) framework. However, call rates have played the role of a key money market rate for a long time. So, the immediate questions that arise are (i) which class of Taylor rule best fits the monetary policy rate dynamics? (ii) how has the relationship between the policy interest rate, inflation gap, and output changed in different monetary policy regimes? and (iii) whether there has been a change in this over the past few years? This paper involves estimating a slew of augmented Taylor rule specifications for India that look at the relationship between the policy interest rate and output gap and inflation gap over a period of time.

In the Indian context, the Taylor rule has been estimated by Cavoli and Rajan (2008) and Singh (2010). Cavoli and Rajan (2008) find that the persistence specification and inflation gap are important and that the output gap is not significant in explaining treasury bill (T-bill) rate movements, using monthly data from 1993 to 2007. However, their work primarily concentrates on the pre-global financial crisis (GFC) period of 2008–09. Since then, the Indian policy scenario has evolved significantly, including with the adoption of FIT. Singh (2010), however, estimates a slew of alternative model specifications but with annual data. Similar to Singh (2010), we do find evidence that interest rates follow a backward Taylor specification in India.

Taking a cue from these studies, we explore different model specifications using higher frequency data for a longer sample period with both the weighted average call rate (WACR) and 91-day T-bill rate. Additionally, we adopt a novel estimation strategy wherein the output gap is measured using a single-index dynamic factor to account for economic activities pertaining to different sectors. In this way, we include the representation of multiple sections of the economy—for instance, services and the external sector in addition to the index of industrial production (IIP), which we use in our monthly models.

Our findings suggest that the inflation gap plays an important role in explaining fluctuations in policy rates, which is generally the case across countries. Monthly frequency data give a better model fit across all Taylor rule specifications. When we augment the model with the GFC and FIT dummies,1 the performance of the model improves. The major contribution of our study lies in its use of a monthly single-indexed dynamic factor output gap–augmented Taylor rule instead of using a monthly IIP gap. The model fit improves when we measure the output gap using a dynamic factor that represents broad-based sectoral activity instead of using IIP as a proxy for a gap measure.

The rest of the paper is organised as follows. In the data and methodology, we describe the alternative model specifications. This is followed by the section where estimations of different Taylor rule specifications and model estimates are provided. In the next section, we measure the Taylor rule using the dynamic factor-based output gap. Following this, the discussion on the policy space reports the difference between the model-estimated short-term interest rates and observed or actual short-term interest rates. A summary of the model findings is provided in the conclusion.

Data and Methodology

We estimate several Taylor rule specifications, which are supported by the literature, using different data frequencies. The Taylor rule captures the relationship between the policy interest rate, the output gap, and the inflation gap. To estimate this relationship, we consider both quarterly and monthly data for the period 1998–2020. In the case of quarterly frequency, a traditional output gap measure is taken where the potential output is determined using a Hodrick–Prescott filter. For monthly frequency, we use the IIP gap instead of the output gap. While IIP has limitations in representing the health of the entire economy, this measure is widely used in the field (Cavoli and Rajan 2008; Cristadoro and Veronese 2011). We attempt to overcome this issue by using dynamic factor-based approaches.

For the inflation gap, we use consumer price index (CPI) inflation (industrial worker),2 which is highly correlated with the combined CPI published in 2011. Since India did not explicitly follow a FIT framework until February 2016, we use the strategy employed by Singh (2010) to construct the inflation gap—taking the difference between inflation and a decadal average of inflation. We take two measures of interest rate: WACR (Singh 2010) and the 91-day T-bill rates (Cavoli and Rajan 2008) and run all the Taylor rule model specifications for both the rates. It should be noted that while the WACR is the operational target of the Reserve Bank of India (RBI), the volume of transactions in the WACR window is relatively limited; T-bills in India are auction-based and incorporate both short-term rate movements and liquidity conditions. All the data sets used in this exercise are sourced from the CEIC database and the Database on Indian Economy (DBIE) of the RBI.3

In most emerging economies, policy persistence plays an important role in determining the current interest rate (Caporale et al 2018; Singh 2010; Cavoli and Rajan 2008). Therefore, the basic model that we consider as the Taylor rule in this section is as follows:

i= γ+ γrt-1 + (1-γ1) (θπ π+ θy yt) + ε… (Taylor rule with real persistence) … (1)

where, i ≡ WACR or 91-day T-bill rate, r ≡ real interest rate, itinflation, π ≡ CPI (industrial worker) inflation and y ≡ output gap (in case of quarterly data) or IIP gap (in case of monthly data). For different variants of the Taylor rule, we consider both forward- and backward-looking rules, described as

i= γ+ γ1 rt-1 + (1-γ1) Et-j (θπ πt+k + θy yt+m) + ε… (2)

If, k|m < 0, then it is a backward-looking Taylor rule, and if k|m > 0, then it is a forward-looking Taylor rule. We also experiment with two major variants of the Taylor rule, as explained by Walsh (2003) and Rudd and Rudebusch (1998), which are documented as follows:

i= γ+ γ1 rt-1 + (1-γ1) (θπ Et-j πt+k + θ1y Δ yt) + ε… (Walsh 2003)
… (3)

i= γ+ γ1rt-1 + γ2Δrt-1 + (1-γ1) (θππt-k + θyyt-k) + ε… (Judd and Rudebusch 1998) … (4)

Walsh (2003) assumes that under a discretionary policy, the central bank may maximise social welfare by reacting to the change in the output gap. Meanwhile, Judd and Rudebusch (1998) argue that the Taylor rule can be better characterised after incorporating an error correction form (that is, it includes Δrt-1 as error correction). Additionally, we augment all these variants with the GFC and FIT dummies. Therefore, the most general form of the Taylor rule under consideration can be described as follows:

­γ4 DtFIT+εt … (5)

We use the ordinary least squares (OLS) and generalised method of moments (GMM) methodologies as required to estimate the different variants of the Taylor rule. We use the GMM methodology to address the correlation between the expectational error and future inflation used as an independent variable (the endogeneity issue) in the forward-looking specification. We use the system GMM approach,4 which depends on the lag values of the dependent variables as instruments.

Estimation of Different Taylor Rule Specifications

Now we discuss four sets of results. In the first set, we use the call rate, quarterly gross domestic product (GDP) gap, and inflation gap. In the second set, we use the same specifications with T-bill rates instead of the WACR. In the third and fourth sets, we use monthly data by replacing the GDP-based output gap with the IIP-based output gap for each of the aforementioned specifications. For each of the sets, we report 11 estimates obtained for the five equations mentioned in the data and methodology section. We use OLS for all sets and GMM wherever applicable.

Appendix 1 (p 54) tabulates results for every specification. We start with the quarterly frequency data specifications for both the WACR and T-bill rates. Appendix 1 Table A3 (p 54) describes the parameter estimates of different Taylor specifications for the quarterly WACR. First we estimate all the models without including the GFC and FIT dummies. Subsequently, we test all the model specifications including the two dummies. In the case of the standard Taylor rule with real persistence,5 we use the GMM methodology to correct for the causal loop between the independent and dependent variables, which would lead to the endogeneity problem. The parameter estimates are broadly similar in the two methodologies. However, the Taylor coefficient for inflation gap becomes insignificant when using GMM. In the case of the forward-looking Taylor rule as well, we use GMM as a regression methodology while the Taylor coefficient for inflation gap remains insignificant. Judd and Rudebusch’s (1998) Taylor rule specification without including the GFC and FIT dummies shows that both the inflation and output gaps are statistically significant. Additionally, the Taylor rule coefficient for inflation gap is higher in magnitude than the output gap, which is in line with the existing findings.

When we consider the 91-day T-bill rate at a quarterly frequency in Appendix 1 Table A4 (p 54), the standard Taylor rule with real persistence shows consistent results across the two methodologies in terms of statistical significance. In the case of the quarterly 91-day T-bill, the inclusion of the GFC and FIT dummies while estimating the backward-looking Taylor rule and Judd and Rudebusch’s (1998) specification provides parameter estimates that are in line with theoretical findings. Note that when we use the quarterly frequency data series, the magnitudes of the Taylor coefficients’ estimates are quite sensitive to the model specification and estimation methodologies. This issue is resolved when we estimate all the previous specifications in the monthly frequency data, using the IIP gap instead of the GDP gap to measure the output gap.

These results are the same for the WACR and 91-day T-bill. The magnitudes are all consistent with the theoretical findings, that is, the Taylor coefficient for inflation gap is higher in magnitude than the output gap. However, the Taylor coefficient for output gap does not remain statistically significant for the monthly 91-day T-bill rate after the inclusion of the GFC and FIT dummies. While using a monthly WACR, the output gap remains statistically significant and the magnitude is also lower than the inflation gap coefficients even after the inclusion of the GFC and FIT dummies. It is also important to mention that in all the model specifications across both the policy rates, the persistence term and both dummies were statistically significant. These results indicate that an appropriately augmented Taylor’s rule augurs well for India irrespective of policy regimes and that both GFC and FIT episodes could be considered as break points in the Indian macroeconomic scenario in their own different ways. The GFC constituted an unprecedented disruptive shock, while the FIT represented a structural shift in the monetary policy operating framework.

Here, we mention only the best-fit model in the WACR and 91-day T-bill rate. The model performance improves after the inclusion of the GFC and FIT dummies consistently across all specifications. The best-fit Taylor rule comes with a time dummy and in monthly frequency data instead of quarterly frequency data. The error correction specification coined by Judd and Rudebusch (1998) and the backward-looking Taylor rule augmented with dummies perform particularly well at tracking policy rates (Appendix 1). To choose the best model, we use the minimum root-mean-square error (RMSE). The model characteristic that has the minimum RMSC is the backward-looking Taylor rule estimated using the OLS technique. Estimation based on the monthly series performs better than the quarterly series across all model specifications. The following are the best estimated models for the monthly WACR and the monthly 91-day T-bill:

… (6)

Equation (6) is the estimated model for WACR using OLS.

 … (7)

Equation (7) is the estimated model for the 91-day T-bill rate using OLS.

The model fit for the aforementioned specifications is demonstrated in Figure 1 (p 50).

In the case of monthly WACR, both inflation and IIP gaps are statistically significant at 10%. In the case of the 91-day T-bill rate, it turns out that although the inflation gap is statistically significant and explains a large part of the T-bill rate fluctuation, the output gap remains statistically insignificant.6 In the following sections, we adopt a single-indicator dynamic factorbased approach instead of the IIP gap and examine the model fit with respect to both the WACR and 91-day T-bill.

For robustness, we examine the Taylor rule results by breaking the data set into the pre- and post-GFC periods. Then, we run the same set of empirical exercises, done earlier, separately for the pre- and post-GFC periods. The pre- and post-GFC periods both show that the CPI inflation and IIP gaps have statistically significant impacts on the 91-day T-bill under the backward-looking Taylor rule specification (as mentioned in Equation 2). In the case of the WACR, the CPI inflation and IIP gaps are statistically significant under the backward-looking Taylor rule specification for the post-GFC period. In the pre-GFC period, the WACR is significantly explained by the CPI gap but not by the IIP gap. The lagged series of real rates (rt-1) remain statistically significant for all the specifications. The coefficient of the lagged IIP gap is larger during the pre-GFC period as compared to the post-GFC period while explaining the 91-day T-bill. In contrast, the coefficient of the lagged CPI inflation gap in the same backward-looking Taylor rule specification is smaller in the pre-GFC period than in the post.

We do not split the series into pre- and post-FIT because the number of observations for post-FIT is fewer than for the pre-FIT periods. Instead, we address the issue relating to structural changes by incorporating a FIT dummy.

Dynamic Factor-augmented Taylor Rule

Bernanke et al (2005) suggest that the measure of economic activity may not be perfectly represented in the IIP measure. To correctly gauge the effects of a policy change on the level of economic activity, it is useful to observe the effects of the policy on different sectors within an economy. This is only possible if we analyse the policy response in terms of multiple indicators that represent the labour market, consumption, sales, production, trade and financing, financial markets, etc. Unfortunately, the inclusion of multiple indicators in a regression specification may lead to degrees of freedom problems. For example, the inclusion of multiple indicators in a model can result in the number of explanatory variables in a model exceeding the number of observations associated with those variables. As a result, the degree of freedom required to estimate a complete model is insufficient. To conserve the degrees of freedom, it is preferable not to employ too many indicators in a regression specification. At the same time, a small number of variables is unlikely to adequately capture the information set used by policymakers who follow many data series.

Therefore, we use a dynamic factor model, which will help to extract a consensus trend on economic activity from diverse economic indicators and may indicate varied trends in activity. We begin with a universe of high-frequency indicators representing industry and construction, income/consumption, employment, services, external sector, prices, financial sector, miscellaneous economic activities, etc. Next, we employ several rounds of indicator screening by evaluating (i) the dynamic correlation of these indicators with the GDP, and (ii) the least absolute shrinkage and selection operator (LASSO) procedure and correlation values to identify indicators that are relevant around turning points in the GDP growth cycle. In our final step, we extract a single-index dynamic factor from the shortlisted high-frequency indicators following several rounds of screening. Appendix 2 Table A7 (p 57) represents high-frequency indicators and their sectoral representation.7

Following the current literature, the monetary policy reaction function for India is estimated using the best-fitting model employing the OLS methodology. Short-term interest rates, such as the WACR and 91-day T-bill rate, are used to capture the monetary policy stance of the RBI. The inflation gap is measured by taking the difference between the CPI inflation and the decadal average of the CPI inflation rate. We adopt a novel estimation strategy by taking the difference in the index of economic activity from trend activity measured using the Hodrick–Prescott filter. The economic activity is measured using the single-index dynamic factor obtained from the 9 and 15 high-frequency indicators, that is, dynamic factor-9 and dynamic factor-15. Additionally, we introduce du­mm­ies in our regression specification to account for the GFC and FIT, adopted by the RBI.

To estimate the policy reaction function, we use a backward-looking Taylor rule augmented by the dynamic factor. For our an­alysis, two different mea­­sures of dynamic factors are used to calculate the output gap. We use the 9 and 15-indicator dynamic factors that track the GDP closely, especially during the post-pandemic period. The model coefficient estimates for the 91-day T-bill are presented in Table 1 (p 51). All coefficient estimates, including lagged real short-term interest, lagged inflation gap, and lagged output gap, remain significant at 5%. The model fit improves further when we account for structural breaks such as the GFC and inflation targeting regime using suitable dummies. Both the models suggest that the coefficient estimates for the inflation gap are significantly higher than the output gap, roughly three times the output gap coefficient estimate. From Figure 2, it is clear that the model-based estimates of the T-bill rate are able to track the observed T-bill rate particularly well. The 91-day T-bill estimates from models 1A and 1B are plotted as “91TBillF1A and 91TBillF1B” and the realised values are represented as “91TBill.” The in-sample fit, measured in terms of the RMSE, is marginally better for the dynamic factor-9 model as compared to the dynamic factor-15 model for the estimation period.

Table 2 reports the Taylor rule estimates for the WACR and Figure 3 represents the Taylor rule-based short-term interest and actual interest rate for the entire sample period from 2004M1 to 2020M2. The WACR estimates from models 2A and 2B are plotted as “CALL_MONEY2A” and “CALL_MONEY2B,” and the realised values are represented as “CALL_MO­N­EY.” We obser­ve that the coefficient estimates for the inflation gap are significantly higher than the output gap when measured for WACR. A consensus that arises from different model variants under the backward-looking Taylor rule suggests that the monetary policy reacts more strongly to inflation deviations from its long-run path than to the output gap. Additionally, we can represent the model estimates in Tables 1 and 2 and write them down under a general Taylor rule specification. Equations 1 and 2 represent the general backward-looking Taylor rule specification for the 91-day T-bill rate and WACR. Equation 1 reports the average coefficient estimate for the 91-day T-bill rate obtained from the regression coefficient in the model with dynamic factor-15 and dynamic factor-9. Similarly, Equation 2 reports the average coefficient estimates for WACR, which are obtained from the dynamic factor-9- and dynamic factor-15-based models.

 … (8)

 … (9)


Policy Space

The policy space is measured using the difference between the model-estimated short-term interest rates and observed or actual short-term interest rates. Therefore, positive values suggest that there could be room for further rate hikes. Negative values, however, hint at potential rate cuts. We use the best-fitting model specification to determine the estimated value of the short-term interest rate. As reported earlier, our best-fitting model specification is the backward-looking Taylor rule. Although the policy space is measured at a monthly frequency, we report the same at a quarterly frequency by taking a monthly average. For robustness, we measure the policy space using the 91-day T-bill rate, WACR, and the weighted average of the 91-day T-bill rate and WACR. Finally, we also do a robustness check with the policy space suggested by the dynamic factor-augmented backward-looking Taylor rule model, which supports our findings.

Most of the time, the estimated policy space is in the range of 25 basis points (bps). According to some measures of policy space, a minor blip was created recently, which could be attributed to the transient high food price-led inflation. However, given the magnitude of the output gap triggered by the pandemic, this space seems to taper off with time. Figure 4 (p 52), Figures 5, and 6 illustrate the policy space measured using the 91-day T-bill, WACR, and the weighted average of the T-bill and WACR, respectively. Though there were some differences in policy space estimates based on the different money market rates, in general, the policy rates are well-anchored and the policy space stayed in the 25 bps range.


The Taylor principle plays a pivotal role in central banks’ policymaking. It suggests that the policy rate is a linear function of the output gap and inflation. Several augmented versions of the rule have evolved since 1990 to closely capture this relationship in different economies.

For India, there has been prior work relating to the estimation of the Taylor rule. However, anecdotal evidence suggests a possible change in this relation following the GFC and the adoption of the FIT in India. We use a slew of augmented Taylor rules to identify the best-fitting model specifications. Our empirical findings suggest that in the case of India, (i) a backward-looking Taylor rule captures the dynamics in the short-term policy rate well, and (ii) the model fit improves after acc­ounting for structural breaks such as the GFC and FIT using suitable dummies in the Taylor rule specification.

The best way to measure the policy space would be to use quarterly GDP data and the associated gap. However, to facilitate the monetary policy decision-making of a central bank, the policy space must be monitored at a higher frequency. Therefore, the output gap is measured using the IIP data, which is available at a monthly frequency. Given the criticism of IIP as an overall indicator of economic activity, we introduce a single-index dynamic factor extracted from several high-frequency indicators. This dynamic factor-augmented Taylor rule broadly supports our earlier findings suggesting that the inflation gap coefficient estimates are roughly three times higher than the output gap coefficient estimate, and the model fit improves after accounting for structural breaks such as the GFC and the adoption of FIT.

Finally, we compute the difference between the estimated and actual rates as the policy space. Barring a few episodes, the policy space largely remained well within the band of 25 bps after the adoption of the FIT. Although there were minor differences using different estimates, the space measured using the T-bill rate mostly remained within the 25 bps band.

In conclusion, it is important to highlight that the Taylor rule estimated in this paper is not a prescriptive one. Our estimates are based on historic data. Therefore, the estimate of the Taylor rule will be driven by how policy was conducted in the past. While we show that the policy rates in India have evolved broadly in line with the Taylor rule, the policy space is purely indicative because Taylor rule coefficients are based on the observed
historical data and time-invariant parameter estimates.


1 The GFC dummy runs from 2009 onwards and the FIT dummy runs from 2016 onwards.

2 The wholesale price index was also considered, but the CPI industrial worker proved a better fit.

The repo rate is a natural choice for a policy instrument that estimates the Taylor rule and a consequent measure of the policy space. Further, WACR is also an appropriate rate by virtue of being an operating target of the central bank and its close alignment with the repo rate. On a purely technical note, given the low variability in the repo rate, quarterly/monthly averages of WACR, and to make the empirical exercise robust, the policy space is obtained using an alternative policy instrument, namely the 91-day T-bill. It may be noted that the 91-day T-bill remains a key channel for transmission, broad-based (in terms of market participants), and liquid. Therefore, it is a natural alternative benchmark rate in our empirical estimations.

4 We use the GMM methodology to correct for the causal loop between the independent and dependent variables in the model, which leads to the endogeneity problem.

5 In estimating the Taylor rule equation, we used the real persistence specification for India, which is consistent with the Indian literature. For example, Singh (2010) found that this specification fits well in the Indian context. We also evaluated several other specifications for the Indian context and found that the model with a lagged value of real interest rate provided a more meaningful result.

6 If we relax the minimum RMSE, then the backward-looking Taylor rule with only the GFC dummy shows both an inflation gap and IIP gap as statistically significant even in the case of WACR.

7 A single-index dynamic factor (dynamic factor-9) is extracted from nine high-frequency indicators, which are chosen following several rounds of screening procedures. The indicator selection procedures involve tracking the GDP dynamics with a special focus on understanding the turning points in the GDP growth rate cycle. The bridge equation involving dynamic factor-9 has exhibited superior tracking ability of the GDP dynamics. Both in-sample as well as out-of-sample accuracy of such a model have been carefully assessed by Bhadury et al (2020) and Bhadury et al (2021); they document that the dynamic factors track the GDP well. A chart indicating the validity of the claim is also reported in Appendix 2.


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Updated On : 4th Jun, 2022
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