Appendix : Vector Autoregression Model
A natural extension of our single equation model is a more general vector autoregressive model (VAR) where we can consider several endogenous variables together so that they are simultaneously determined, and we can accommodate a more generalized lag structure so that each variable evolves dynamically. The VAR captures the full dynamic interactions among the variables included in the model, so, for example, we can shock MSP and trace out the empirical response of inflation to that shock by quarter.
Based on the institutional processes for the determination of inflation, and tests of residual autocorrelation, we specify a lag length of 8 quarters. We assume a simple Choleski ordering with the global factors being the most exogenous, followed by output gap, wages, MSP and inflation. We assume that shocks to inflation do not affect any of the other variables within the quarter (so that inflation is last in the Choleski ordering). The results are similar if MSP is ordered before wages.
The resulting impulse responses are plotted in Figure 7. The impulse responses suggest that a one standard deviation shock to growth of MSP increases inflation by 0.3 percentage points, which is statistically significant. The effect, however, is not persistent, and is statistically indistinguishable from zero by the second quarter. Wages have a much smaller effect than MSP, and are not persistent. About 50% of the variability in inflation over the entire sample is explained by output gap, 30% by MSP, and 10% by dynamics of inflation. Although the direction of change in the output gap does not play a role in explaining the recent disinflation, the output gap, per se, does play a dominant role in explaining the variability over the sample, confirming the existence of a Phillips curve in India.
The VAR broadly validates our single equation results vis-à-vis the drivers of the disinflation. Lagged inflation, MSP and the regime change dummy still account for the largest share of the disinflation between 2013/14 and 2014/15. The role of MSPs is almost identical in both the models. Like the single equation model, crude and the exchange rate only played a minor role in the disinflation, in the time-period under consideration, whereas a closing output gap and a bad monsoon actually put upward pressure on inflation.
Anand, Rahul, Naresh Kumar, and Volodymyr Tulin, 2016, “Understanding India’s Food Inflation: The Role of Demand and Supply Factors”, IMF Working Paper No. 16/2.
Anand, Rahul, Ding Ding, and Volodymyr Tulin, 2014, “Food Inflation in India: The Role for Monetary Policy”, IMF Working Paper No. 14/178.
Ball, L., A. Chari, P. Mishra (2015). Understanding Inflation in India. India Policy Forum, National Council for Applied Economic Research, July 14-15, 2015.
Ball, L. and Sandeep Mazumder, 2011, “Inflation Dynamics and the Great Recession”, Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 42(1 Spring), pages 337–405.
Bhattacharya, Rudrani, Ila Patnaik, and Ajay Shah, 2008, “Exchange Rate pass-through in India”, 2nd Research Meeting of NIPFP-DEA Research Pro gram, New Delhi.
Clemente, J., A. Montanes, and M. Reyes (1998). Testing for a unit root in variables with a double change in the mean. Economics Letters 59: 175—182.
Hodrick, R. J. and E. C. Prescott (1997). Postwar U.S. Business Cycles: An Empirical Investigation. Journal of Money, Credit, and Banking, 29(1), 1–16.
Reserve Bank of India (2014). Report of the Expert Committee to Revise and Strengthen the Monetary Policy Framework (Chairman: Dr. Urjit Patel). January 2014.
The views represent those of the authors and not of the Reserve Bank of India, or any of the institutions to which the authors belong. The authors thank Paul Cashin, Volodymyr Tulin, and Mehdi Raissi of the IMF, and the India Executive Director’s Office at the IMF for very helpful comments and suggestions.
The authors institutions are JP Morgan (Chinoy) and Reserve Bank of India (Mishra and Kumar).
However, core inflation was persistently below headline for most of the period between 2006 and 2010. The purpose of a core inflation index is to get an accurate measure of the current inflation trend. Since core inflation was lower than the headline till 2010, that may have been suggestive of a downward pressure on future headline inflation (see for example Anand et. al., 2014 and also Cecchetti, 2007 for a critique of using core as a forecast for future headline inflation).
Core excludes food, fuel, and transport and communication. The latter is included in the contribution of the fuel category.
See Reserve Bank of India (2014) for a hybrid model of expectation formation, and Ball, Chari, and Mishra (2015) for estimation of a partial-adjustment model of expectations for India. See also Ball and Mazumder (2011), and references therein for a review of the voluminous literature on estimating inflation dynamics.
See RBI monetary policy statement, January 2014.
Note that actual crude prices are already controlled for in the empirical framework, therefore the dummy could only reflect the effect of crude prices on expectations.
We use a standard HP filter with a smoothing parameter λ equal to 1600. HP filter is likely to suffer from an end-point bias i.e. potential output may be affected by actual output at the end point of the sample; we also use other measures of potential output which may be less subject to this concern (see Table 4 and the robustness section).
Our choice of an 85% threshold to set the dummy is guided by earlier work, see, for example, “India’s food inflation: worrying about the wrong problem,” JP Morgan, July 30, 2015. Furthermore, there is significant variation in rainfall across geographic regions in India. If rainfall is, for example, below normal, in regions where crops with high weight in the food basket are grown, that may have a larger impact on food and overall inflation. However, given the absence of a good measure of the spatial distribution of rainfall, it is not included in the empirical analysis. In addition, food inflation is also determined by food management policies of the government, which could be interacted with the monsoon dummy. Again, the lack of good proxies for the latter preclude their inclusion in the empirical specification.
The results are unchanged if we use the nominal effective exchange rate (NEER) instead of the Rs./ rate. We keep the latter in the baseline as most imports are invoiced in US.
We tested for non-stationarity in the three key variables of interest – inflation, MSP growth, and wage growth. Using the methodology in Clemente, Montañés, Reyes (1998), we rejected the null hypothesis of a unit root in the series for inflation and MSP growth at the 10 percent level of significance. We could not, however, reject the null of a unit root in the wage growth series. Therefore, we included the first difference of wage growth in the single equation model for robustness, but the main findings remained unchanged (see Table 5).
Because we year-on-year inflation rates and a quarterly data, concerns may arise that the serial correlation is by construction. However, even if we use annual data, where there is no correlation by construction, we find lagged CPI to be economically and statistically significant – suggesting it is proxying inflation expectations.
See, for example, “India’s food inflation: worrying about the wrong problem,” JP Morgan, July 30, 2015.
The exchange rate is represented as US per rupee; so an increase is an appreciation which should be disinflationary, and hence the negative sign.
There could be a legitimate concern that the high R^2 is a sign of overfitting given that we have 60 observations and 24 explanatory variables. However, even if we drop several lags to generate a more parsimonious model, the R^2 is still 91%, which should allay concerns about overfitting.