Are Second-Round Effects Important in India?

To formalize the relationship between food inflation and its pass-through to core inflation, it is worth assessing the dynamics of headline inflation with respect to core inflation. To do so, we ask the following questions:

• Does headline inflation revert to core inflation?—If headline inflation reverts quickly to core inflation, then the impact of food and fuel price shocks is temporary, and second-round effects are probably limited. But if headline inflation does not revert to core, either the shocks are persistent or the second-round effects are large because of higher inflation expectations and accelerating wages.

• Does core inflation revert to headline inflation?—If core inflation reverts to headline inflation, it would indicate that shocks to headline inflation, such as those caused by commodity price spikes, feed into inflation expectations and price setting, driving core inflation to catch up with headline inflation.

The empirical results suggest that second-round effects are indeed significant (Box 9.1). It can therefore be concluded that headline does not revert to core, suggesting that either food shocks are persistent or second-round effects are large. This suggests that core inflation catches up with headline inflation and reverts to headline quickly. Thus, large second-round effects are present.³

^{Box 9.1}

How Important Are Second-Round Effects in India?

We follow Cecchetti and Moessner (2008) and Clark (2001) to estimate the following equations, using monthly inflation data for 1996–2013, to answer these two questions:

Does headline inflation revert to core inflation?

${\pi }_t^{headline}-{\pi }_{t-12}^{headline}=\alpha +\beta ({\pi }_{t-12}^{headline}-{\pi }_{t-12}^{core})+{\varepsilon }_t$

Does core inflation revert to headline inflation?

${\pi }_t^{core}-{\pi }_{t-12}^{core}=\delta +\gamma ({\pi }_{t-12}^{core}-{\pi }_{t-12}^{headline})+{\varepsilon }_t$

where ${\pi }_t^{headline}$ and ${\pi }_t^{core}$ denote headline and core year-over-year CPI inflation, respectively.

The empirical results suggest that second-round effects are indeed significant (Table 9.1.1). Specifically, if headline reverts to core, the coefficient β is expected to be negative. The results, however, suggest that the null of β = 0 cannot be rejected, which implies that headline inflation does not revert to core inflation. At the same time, individually both the hypothesis that β = −1 and that β = −1 and α = 0, (that is, that headline fully reverts to core within a year) are rejected. Therefore, it can be concluded that headline does not revert to core, suggesting that either food shocks are persistent or second-round effects are large. On the other hand, the estimate of γ is −0.68, which is highly statistically significant, suggests that core inflation reverts to headline inflation. At the same time, the null hypothesis of γ = 0, which corresponds to a situation where core does not revert to headline, is rejected. Moreover, both the hypothesis that γ = −1 and that γ = −1 and δ = 0 cannot be rejected. This suggests that core inflation catches up with headline inflation and reverts to headline quickly. Therefore, large second-round effects are present.

Table 9.1.1.

Regression Analysis of Noncore Inflation Pass-Through

Source: IMF staff estimates. Note: Robust standard errors in parenthesis. *** p < .001.

Table 9.1.1.

Regression Analysis of Noncore Inflation Pass-Through

Dependent Variable	${\pi }_t^{headline}-{\pi }_{t-12}^{headline}$	${\pi }_t^{core}-{\pi }_{t-12}^{core}$
${\pi }_{t-12}^{headline}-{\pi }_{t-12}^{core}$	−0.31
	(0.27)
${\pi }_{t-12}^{core}-{\pi }_{t-12}^{headline}$		−0.68***
		(0.21)
Constant	0.136	−0.11
	(0.59)	(0.49)
Sample: 1997–2013

Source: IMF staff estimates. Note: Robust standard errors in parenthesis. *** p < .001.

View Table

Table 9.1.1.

Regression Analysis of Noncore Inflation Pass-Through

Dependent Variable	${\pi }_t^{headline}-{\pi }_{t-12}^{headline}$	${\pi }_t^{core}-{\pi }_{t-12}^{core}$
${\pi }_{t-12}^{headline}-{\pi }_{t-12}^{core}$	−0.31
	(0.27)
${\pi }_{t-12}^{core}-{\pi }_{t-12}^{headline}$		−0.68***
		(0.21)
Constant	0.136	−0.11
	(0.59)	(0.49)
Sample: 1997–2013

Source: IMF staff estimates. Note: Robust standard errors in parenthesis. *** p < .001.

Quantifying the Size of Second-Round Effects

Analysis of inflation dynamics suggest that second-round effects are big, and policymakers need to pay close attention to food price shocks.⁴ Incorporating the second-round effects of food price inflation is essential for monetary policy formulation in India, and estimating their size is important for understanding the country’s inflation dynamics and monetary transmission. We estimate these effects using a variant of the small New Keynesian macroeconomic model with rational expectations developed by Berg, Karam, and Laxton (2006a, 2006b).

We then estimate a New Keynesian Phillips curve in a dynamic small open economy model, and analyze the effect of the output gap, lagged inflation, exchange rate, and inflation expectations on current inflation. To estimate the second-round effects, we modify the model to capture the pass-through from headline to core inflation. Although this model is simple and abstracts from many important features of the economy, such specifications have long been the workhorse of monetary policy analysis at the IMF. In addition to effectively capturing the key channels of monetary policy transmission, this framework has the virtues of clarity and tractability.

The Model

The model features a small open economy, including forward-looking aggregate supply and demand with micro foundations, and with stylized (realistic) lags in the different monetary transmission channels. Output developments in the rest of the world feed directly into the small economy because they characterize foreign demand for Indian products. Changes in foreign inflation or interest rates affect the exchange rate, and, subsequently, demand and inflation in the Indian economy. The model is set up in gap terms (that is, deviation of variables from their respective steady-state value). To estimate the second-round effects, we add an equation to capture the pass-through from headline to core inflation.

The baseline model has five behavioral equations: (1) an aggregate demand curve that relates the level of real activity to expected and past real activity, the real interest rate, the real exchange rate, and the foreign output gap; (2) a price-setting or Phillips curve equation that relates core CPI inflation to past and expected inflation, the output gap, and the exchange rate, as well as the pass-through from the headline to core inflation; (3) a food inflation equation that relates food inflation to past and expected inflation, the output gap, and the exchange rate; (4) an uncovered interest parity condition for the exchange rate, with some allowance for backward-looking expectations; and (5) a rule for setting the policy interest rate as a function of the output gap and expected inflation.

The output gap equation is given by:

in which ygap is the output gap, RRgap the real interest rate gap, zgap the gap of real exchange rate, ygap^RW the output gap in the rest of the world, P a series of parameters attached to those variables, and ε^ygap an error term, which captures other temporary exogenous effects.⁵

The headline inflation equation is given as the aggregation of the core and food and fuel inflation:

in which ${\text{π}}_t^c$ is core inflation rate, ${\text{π}}_{c,t}^{ff}$ is noncore (food and fuel), ϑ is the weight on noncore inflation, and ${\text{ɛ}}_t^{\text{π}}$ an error term. A residual captures other temporary exogenous effects that are not explicitly modeled.

We then have two pricing equations for core inflation and food and fuel inflation, which have a very similar structure except for an additional term in the former to capture the pass-through from headline to core inflation, or the second-round effects.

in which ${\text{π}}_t^c{4}_{t+4}$ and ${\text{π}}_t^{ff}{4}_{t+4}$ are the four-quarter-ahead year-over-year core and food and fuel inflation rates, respectively,⁶ ${\text{π}}_t^c{4}_{t-1}$ and ${\text{π}}_t^{ff}{4}_{t-1}$ are their one-quarter lagged year-over-year inflation rates, ygap the output gap, z_t − z_t−1 the real depreciation, α_c a series of parameters, and ${\text{ɛ}}_t^{\pi ,c}$ and ${\text{ɛ}}_t^{\pi ,\mathrm{ff}}$ are error terms. The additional term (π4_t−1 – π4_c,t−1) is added to the core inflation equation to allow for the possibility of relative price and real wage resistance; or more precisely that workers and other price setters may try to partially keep their prices rising in pace with past movements in headline CPI (Berg, Karam, and Laxton 2006b). Expected inflation enters the equation due to the assumption of staggered price-setting (Calvo 1983), while indexation schemes can rationalize the backward-looking inflation component. The real exchange rate z reflects the effect of the prices of imported goods on inflation in an open economy.⁷

The real exchange rate equation is given by:

in which z_t is the real exchange rate (an increase represents a depreciation), RR_t the real interest rate, $R{R}_t^{RW}$ the real interest rate in the United States, ρ* the equilibrium risk premium on the domestic currency, δ_z parameters, and ${\text{ɛ}}_t^z$ an error term. A residual captures other temporary exogenous effects.

Finally, the monetary policy rule is given by:

in which RS_t is the nominal interest rate, RR* the equilibrium real interest rate, π* the inflation objective, γ parameters, and ${\text{ɛ}}_t^{RS}$ an error term.

The model is a two-country model where the home country is small and open, whereas the foreign country—the home country’s main trading partner—is relatively large and closed; in effect, exogenous to the home country. Thus, the foreign country enters the home country equations through the impact of its activity on the home country demand, and the impact of its real interest rate on the bilateral exchange rate. Conversely, the home country does not affect the foreign country, which implies that the output gap of the foreign country does not depend on the bilateral exchange rate or the home country activity; and foreign country inflation does not depend on the bilateral exchange rate. Hence, the uncovered interest rate parity condition is irrelevant for the foreign country model. So there are three additional behavioral equations that describe the foreign sector: an output-gap equation, an inflation equation, and a policy reaction function, except that no rest-of-the-world (RW) variables appear.

Estimation

The parameter values are chosen based on the modeling experience of other country models, but adapted to our knowledge about the characteristics of the Indian economy and policy making. The model is estimated as an open economy, where the United States is treated as the relevant foreign sector for India. For the United States, we use the prior distributions used in Berg, Karam, and Laxton (2006b).

The long-term steady-state values for key parameters—the inflation objective, real exchange rate, and real interest rate—are chosen to match the historical average of these variables. The equilibrium real interest rate for the rest of the world is set at 1.5 percent and the inflation rate at 2.4 percent. We set India’s long-term headline CPI inflation rate at 6.5 percent and the equilibrium real interest rate at 1.5 percent. This implies an equilibrium nominal short-term interest rate of about 8 percent. Because we use a detrended real exchange rate series, which removes average real appreciation of about 1 percent a year, we make a technical assumption of zero equilibrium risk premium. All gaps that measure deviations of actual variables from their long-run equilibrium are, by definition, zero.

To estimate the model, we use key macroeconomic variables for India from the first quarter of 1996 to the fourth quarter of 2013. The three-month Treasury bill rate is used as a proxy for nominal interest rate, and real exchange rate (CPI-based) is used as a proxy for real exchange rate. For India’s inflation, we use a backcasted CPI-Combined based on the CPI-IW. We use U.S. GDP, inflation, and interest rate data for the rest of the world in the model. Variables are seasonally adjusted using an X12 filter.

Estimated Aggregate Demand Equation

Coefficient estimates for the output gap equation are reported in Table 9.2:

^{Table 9.2}

Aggregate Demand Equation

^{Table 9.2}

Aggregate Demand Equation

Parameter	Prior Mean	Posterior Mean
βld	0.40	0.19
βlag	0.60	0.59
βRRgap	0.05	0.04
βZgap	0.05	0.04
βRWygap	0.15	0.10

View Table

^{Table 9.2}

Aggregate Demand Equation

Parameter	Prior Mean	Posterior Mean
βld	0.40	0.19
βlag	0.60	0.59
βRRgap	0.05	0.04
βZgap	0.05	0.04
βRWygap	0.15	0.10

$\begin{array}{cc}yga{p}_t=& {\text{β}}_{ld}yga{p}_{t+1}+{\text{β}}_{ld}yga{p}_{t-1}-{\text{β}}_{RRgap}RRga{p}_{t-1}+{\text{β}}_{Zgap}zga{p}_{t-1}\\ & +{\text{β}}_{RWygap}yga{p}_t^{RW}+{\text{ɛ}}_t^{ygap}\hfill \end{array}$

The β parameters in the output gap equation depend to a large extent on the degree of inertia in the economy, the effectiveness of monetary policy transmission, and the openness of the economy. Drawing on the experience of several applied country modeling efforts, Berg, Karam, and Laxton (2006b) suggest that the value of β_lag should lie between 0.5 and 0.9, with a lower value for countries more susceptible to volatility.

The estimated coefficient of 0.6 for β_lag is comparable to other emerging markets. The lead of the output gap β_ld is typically small, and the estimated value for India is 0.2. The coefficient estimate on the lead of the output gap indicates that expectations on the future level of the output gap are important. This corroborates the importance of confidence effects in promoting economic activity in India (Anand and Tulin 2014). The parameter β_RRgap depends on the effectiveness of monetary transmission mechanism, while β_zgap and β_RWygap depend on the importance of the exchange rate channel and the degree of openness. Significant lags in the transmission of monetary policy imply that the sum of β_RRgap and β_zgap should be small relative to the parameter on the lagged gap in the equation. A β_RRgap coefficient of 0.04 implies that a one percentage point increase in real interest rates would lead a 0.04 percent fall in the output gap the following period. The value for β^RWygap of 0.1 implies that a 1 percentage point increase in the foreign output gap leads to a contemporaneous 0.1 percentage point increase in the Indian output gap.

Estimated Philips Curve Equations

Coefficient estimates for the core and headline CPI inflation equations are reported in Tables 9.3 and 9.4:

^{Table 9.3}

Phillips Curve Equation for Core Inflation

^{Table 9.3}

Phillips Curve Equation for Core Inflation

Parameter	Prior Mean	Posterior Mean
αc,πld	0.20	0.26
αc,ygap	0.25	0.25
αc,z	0.30	0.15
αc,π	0.30	0.32

View Table

^{Table 9.3}

Phillips Curve Equation for Core Inflation

Parameter	Prior Mean	Posterior Mean
αc,πld	0.20	0.26
αc,ygap	0.25	0.25
αc,z	0.30	0.15
αc,π	0.30	0.32

^{Table 9.4}

Phillips Curve Equation for Food Inflation

^{Table 9.4}

Phillips Curve Equation for Food Inflation

Parameter	Prior Mean	Posterior Mean
αff,πld	0.20	0.22
αff,ygap	0.25	0.28
αff,z	0.30	0.33

View Table

^{Table 9.4}

Phillips Curve Equation for Food Inflation

Parameter	Prior Mean	Posterior Mean
αff,πld	0.20	0.22
αff,ygap	0.25	0.28
αff,z	0.30	0.33

$\begin{array}{cc}{\text{π}}_t^c=& {\alpha }_{c,\text{π}ld}{\text{π4}}_{t+4}^c+(1-{\alpha }_{c,\text{π}ld}){\text{π4}}_{t-4}^c+{\alpha }_{c,ygap}yga{p}_{t-1}+{\alpha }_{c,z}(z_t-z_{t-1})\hfill \\ & +{\alpha }_{c,\text{π}}(\text{π}{4}_{t-1}-\text{π}{4}_{c,t-1})+{\text{ɛ}}_t^{\text{π,c}}\hfill \\ {\text{π}}_t^{ff}=& {\alpha }_{ff,\text{π}ld}{\text{π4}}_{t+4}^{ff}+(1-{\alpha }_{ff,\text{π}ld}){\text{π4}}_{t-1}^c+{\alpha }_{ff,ygap}yga{p}_{t-1}+{\alpha }_{ff,z}(z_t-z_{t-1})+{\text{ɛ}}_t^{\text{π,}ff}\hfill \end{array}$

The α parameters in the core inflation equations depend on the role of expectations and aggregate demand on inflation, and the degree of pass-through from the exchange rate to prices. The α_c,πld parameter in the core inflation equation determines the forward component of inflation (while its inverse, 1 – α_c,πId, determines the backward component). This can be interpreted as depending in part on the credibility of the central bank, and in part on institutional arrangements regarding wage indexation and other price-setting mechanisms. A higher value of α_c,πld close to 1 would suggest that small changes in monetary policy cause large changes in price expectations; a low value would suggest that inertia and backward-looking expectations cause prices to respond with greater delays to changes in monetary policy. The estimated Philips curve for India is backward looking (the backward-looking component in the core inflation is 0.8), suggesting that inflation is highly inertial and that shocks to inflation are persistent. Patra and Kapur (2010) have found similar estimates for the forward- and backward-looking components.⁸

The α_c,ygap parameter depends on the extent to which output responds to price changes and, conversely, how much core inflation is influenced by real demand pressures, and is typically between 0.25 and 0.50. This parameter is estimated to be 0.25 for India. This is in line with the literature estimates of 0.20–0.30 (Patra and Kapur 2010). The α_c,zgap parameter represents the short-term pass-through of (real) exchange rate movements into prices, and depends on trade openness, price competition, and monetary policy credibility. The exchange rate pass-through coefficient is estimated to be 0.15 in India. This is in line with the findings of Patra and Kapur (2010) and other cross-country findings that estimate exchange rate pass-through to be about 0.16 for countries with low (less than 10 percent) inflation (Choudhuri and Hakura 2001).

Finally, the parameter α_c,π represents the pass-through coefficient from headline to core inflation; that is, the extent to which price setters keep their prices rising in step with past movements in headline CPI. If α_c,π is zero, the gap between past headline and core inflation (namely, inflation of food and energy prices) will have no effect on core inflation. In other words, there will be no second-round effects in the economy. Our estimation of the second-round effect coefficient indicates that if headline inflation exceeds core inflation by 1 percentage point, it will lead to a 0.3 percentage point increase in core inflation in the next quarter. As expected, the pass-through from headline to core inflation is relatively large. This estimate is consistent with our analysis of year-over-year inflation dynamics in India, as discussed in an earlier section. However, some caution is warranted in interpreting a rather large pass-through coefficient. An alternative interpretation of a strong pass-through coefficient estimate may reflect a faster response of food inflation to aggregate demand, because commodity prices, including food items, tend to be more flexible than nonfood prices. Another reason could be that food inflation may also react faster than nonfood inflation when inflation expectations are not firmly anchored.

Estimated Uncovered Interest Parity Equation

$z_t={\delta }_z{z}_{t+1}+(1-{\text{δ}}_z)z_{t-1}-(R{R}_t-R{R}_t^{RW}-\text{ρ*})/4+{\text{ɛ}}_t^z$

The δ_z parameter in the real exchange rate equation determines the relative importance of forward- and backward-looking real exchange rate expectations. If δ is equal to 1, the equation behaves as in the Dornbusch overshooting model; that is, the real exchange rate is a function of the future sum of all real interest rate differentials. The estimated coefficient of 0.5 makes monetary policy potentially a more effective tool, though the incomplete exchange rate pass-through in India somewhat reduces its efficacy (Table 9.5).

^{Table 9.5}

Uncovered Interest Parity Equation

^{Table 9.5}

Uncovered Interest Parity Equation

Parameter	Prior Mean	Estimate (Posterior Mean)
δz	0.60	0.40

View Table

^{Table 9.5}

Uncovered Interest Parity Equation

Parameter	Prior Mean	Estimate (Posterior Mean)
δz	0.60	0.40

Estimated Open-Economy Taylor-Rule Equation

$R{S}_t={\gamma }_{RSlag}R{S}_{t-1}+(1-{\text{γ}}_{RSlag})*[R{R}_t^{*}+{\text{π4}}_t+{\text{γ}}_{\text{π}}({\text{π4}}_{t+4}-{\text{π4}}_{t+4}^{*})+{\text{γ}}_{ygap}yga{p}_t]+{\text{ɛ}}_t^{RS}$

The γ parameters in the monetary policy rule equation depend on the speed and aggressiveness with which the monetary authorities adjust the nominal interest rate, and the relative importance of the inflation target versus the real activity target (Table 9.6). There is a high degree of interest rate smoothing in India (the coefficient is 0.8), which is in line with the estimates of this parameter by Mohanty and Klau (2004) and Anand, Saxegaard, and Peiris (2010). The value of γ_π is 1.9. The estimate of γ_ygap is 0.6, suggesting that the RBI puts weight on stabilizing real activity, which is expected, considering that the central bank followed an approach of multiple objectives during most of the analysis period.

^{Table 9.6}

Taylor-Rule Equation

^{Table 9.6}

Taylor-Rule Equation

Parameter	Prior Mean	Estimate (Posterior Mean)
γRSlag	0.80	0.82
γπ	1.90	1.88
γygap	0.60	0.64

View Table

^{Table 9.6}

Taylor-Rule Equation

Parameter	Prior Mean	Estimate (Posterior Mean)
γRSlag	0.80	0.82
γπ	1.90	1.88
γygap	0.60	0.64

Key Results of the Model

Estimated results of the model suggest the following:

• A temporary increase of 100 basis points in the interest rate leads to a peak widening of the output gap by almost 1 percent in about four quarters, slowing in the core CPI inflation by about ¾ of a percentage point, an almost 1 percentage point decline in headline CPI inflation, and a nearly 2 percent peak real appreciation.

• With a 1.5 percentage point jump in food and fuel price inflation, the output gap widens at peak by about 0.5 percentage point, and headline and core inflation rise by about 0.5 percent. The interest rate increases by about 80 basis points, while the exchange rate appreciates by about 2.5 percent. Inflation shocks lead to widening of the output gap, a rise in inflation and the interest rate, and real appreciation. Furthermore, the headline inflation shock passes through to core inflation, which rises by about 0.2 percentage point.

We can use the estimated model to study the behavior of interest rates in India to examine its monetary policy stance since 2000. Figure 9.3 presents actual and model-predicted nominal interest rates. As is evident, since mid-2008 actual interest rates are consistently below those predicted by the model, suggesting that monetary policy shocks have been negative. The gap between the two rates (actual and predicted) was large during 2008–09. The gap again opened in late 2010 and averaged about 100 basis points during 2011–12. This was highlighted by successive IMF India Article IV Staff Reports, which argued for a tighter monetary stance to counter inflation and inflationary pressures (IMF 2011b, 2012, 2013, 2014a, 2014b).

Interest Rates in India: Predicted versus Actual

(Percent)

Sources: Anand and Tulin (2014); Haver Analytics; and IMF staff estimates.Note: Interest rates correspond to three-month Treasury bill yield.

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Interest Rates in India: Predicted versus Actual

(Percent)

Sources: Anand and Tulin (2014); Haver Analytics; and IMF staff estimates.Note: Interest rates correspond to three-month Treasury bill yield.

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Interest Rates in India: Predicted versus Actual

(Percent)

Sources: Anand and Tulin (2014); Haver Analytics; and IMF staff estimates.Note: Interest rates correspond to three-month Treasury bill yield.

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