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In Search of Optimal Inflation

Evidence from CPI Data

Sartaj Rasool Rather (sartajrasool@gmail.com) is with the Department of Humanities and Social Sciences, Birla Institute of Technology and Science, Pilani, Dubai Campus, Dubai, UAE.

The impact of inflation on dispersion of relative prices is examined in a cointegration framework using a data set of all seven components of the consumer price index from India. The empirical evidence indicates that the dispersion of relative price increases with an increase in deviation of inflation from a certain threshold rate in either direction but not with inflation per se, as is traditionally believed. The crucial inference that emerges from the empirical findings is the presence of a threshold inflation rate corresponding to which the dispersion of relative prices is minimised, and this threshold turns out to be 5%.

The author would like to thank the anonymous referees for their valuable comments and suggestions on the earlier draft of this article.

In an economy, the structure of relative prices varies due to changes in both real factors (which include tastes/preferences, real income, technology, etc) and the nominal factors such as inflation (Parks 1978). The variability in relative prices due to changes in real factors is considered useful for the efficient allocation of resources, as these changes reflect signals purely from the market forces and real sector of an economy. However, the changes in relative price structure mainly due to inflation are believed to generate adverse distortions by: (i) reducing the information content of relative prices; (ii) increasing search activities which are costly; (iii) shortening the length of optimal contracts and triggering more frequent contract revisions, and thereby impeding the efficient allocation of resources.1 In fact, as emphasised by the new Keynesian dynamic general equilibrium models, the distortionary impact of inflation on the structure of relative prices is one central channel through which the negative effects of inflation transmit to the real sector of an economy (Green 2005; Becker and Nautz 2012). In this context, in order to ensure that the fluctuations in inflation rate do not trigger any significant changes in relative prices, the monetary authority’s commitment to the objective of price stability is very critical. Also, equally important is choosing an appropriate optimal/desired inflation target for the effective operation of monetary policy.

Theoretically, the link between variability of relative prices and inflation originates from the models based on misperceptions and incomplete information (Lucas 1973; Head and Kumar 2005), and the models assuming menu costs in price adjustment of firms (Sheshinsky and Weiss 1977; Rotemberg 1983; Ball and Mankiw 1994, 1995). More specifically, in models based on ­incomplete ­information, the firms with relatively price elastic supply adjust the quantity of output quite often in res­ponse to the shocks in demand. However, the firms whose supply is relatively inelastic will adjust prices (rather than quantity of output) in ­response to the demand shocks. Hence, the demand shocks that result in higher inflation tend to generate more variability in relative prices. The menu cost models demonstrate that firms adjust prices only at discrete intervals and the adjustment is heterogeneous as it incurs costs, which differ across firms. Under these conditions, the price changes get more dispersed during the periods of higher infl­ation, which in turn result in larger variability in relative prices. Building on Friedman (1977), Ball (1992) provided an alternative explanation that during the periods of high inflation, the public expects/perceives erratic policy response by the monetary authorities as policy changes from one direction to another. In such a situation, predicting the short-term fluctuations as well as the long-term trend in inflation become more difficult (Friedman 1977), and more importantly, the individual prices drift apart signi­ficantly in a dynamic manner, thereby causing higher dispersion of relative price over time (Shoesmith 2000).

In the literature, the empirical studies have mainly focused on the relationship between inflation and a measure of relative price variability (traditionally calculated as variance of cross-sectional price changes in a given point of time) and provided evidence in favour of both linear as well as non-linear relationship ­depending on the monetary policy stance and the inflation regime prevailing in an economy (Caraballo and Dabus 2013; Choi 2010; Fielding and Mizen 2008). Using an alter­native approach of Johansen (1991, 1995) cointegration test to capture the dispersion in relative prices over time, Shoesmith (2000) demonstrated that this dispersion in the United States (US) consumer price index (CPI) sub-prices over time increases more during the ­periods characterised with high inflation.2 Extending this strand of literature, Rather et al (2018), using component CPI data from the US and Japan, found that the dispersion of relative prices increases with the increase in deviation of inflation from a certain threshold rate in either direction rather than inflation per se. In particular, they have shown that the relationship between relative price dispersion and inflation is U-shaped; that is, a larger deviation of inflation from its threshold cause a higher dispersion in relative prices. It is important to note that the U-shape profile of this relationship has very crucial implication for the conduct of monetary policy. In particular, Head and Kumar (2005) and Becker and Nautz (2012) argue that the rate of inflation, which generates minimum variability/dispersion in relative prices, can serve as a proxy for the threshold/target inflation rate that minimises the welfare cost of inflation. Hence, the rate of inflation corresponding to which the dispersion of relative prices is minimum can be perceived as the target/threshold inflation rate for the conduct of monetary policy (Fielding and Mizen 2008).

In the context of India, Rather et al (2014) and Senapati et al (2018), focusing mainly on the relationship between inflation and traditional measure of relative price variability, have made attempts in this direction using the wholesale price index (WPI) component data and provided evidence in favour of 4.5% and 5.5% threshold inflation rate, respectively. However, no study till date has studied the relationship between dispersion of relative prices (measured over time) and inflation in a cointegration framework. In particular, no study has examined whether the relationship between inflation and relative price dispersion is of same profile as the traditional inflation–relative price variability relationship. Moreover, no study has explored new CPI component price series in the present context and examined the threshold inflation rate corresponding to which the dispersion of relative prices is minimised.

Following Rather et al (2018), this study uses the new CPI component price data from India and examines the dispersion of relative prices with respect to inflation for a sequence of rolling sub-samples. The results from the empirical analysis suggest that the divergence among component prices increases as inflation deviates farther from certain threshold rate in any direction; hence, indicating that it is the deviation of inflation from certain rate that matters for the relative price dispersion, but not the inflation per se as is traditionally beli­eved. The results provide evidence in ­favour of view that the relationship between inflation and relative price dispersion is of the same profile as the traditional inflation–relative price variability relationship. The more interesting inference that emerges from empirical exercise is the presence of a threshold inflation rate corresponding to which the dispersion of relative prices is minimised. The empirical findings provide the evidence in favour of 5% inflation target as proposed by the earlier literature.

Econometric Methodology

In order to estimate the dispersion of relative prices over time, Johansen (1991, 1995) cointegration test is used for a seq­uence of rolling subsamples, following Shoesmith (2000) and Rather et al (2018). In this framework, the wider (lesser) dispersion in relative prices over time is reflected by larger (smaller) number of common stochastic trends in the system of sub-price indices. In other words, the evidence of higher (lower) cointegration rank “r” in the system of price indices implies lesser (wider) dispersion among relative prices over time. Unlike the traditional approach of simply using an estimate of variance of cross-sectional distribution price changes in a given point of time, this procedure measures the dispersion of relative prices by evaluating the divergence among sub-prices over period of time. The cointegration rank “r” (number of significant cointegrating vectors/relations) among the component price indices is estimated for each rolling subsample characterised with different inflation rate. The advantage of conducting rolling cointegration tests is that it provides the scope for capturing the dynamics of this relationship and helps to identify the threshold inflation rate. It also provides insights about any time variation and the stability of this relationship over the different inflation regimes. Moreover, given the changing dynamics of inflationary process in India, as reported by Dholakia and Kadiyala (2018), the procedure of carrying out rolling cointegration tests is more appropriate.

Before proceeding to Johansen cointegration test, first, time series properties of each variable is examined using Augmented Dickey-Fuller and Phillip-Perron tests. Once it is found that each price series contains a single unit root and thus integrated of same order, the Johansen’s cointegration tested is carried out for a sequence of rolling subsamples.3

To examine the relationship between inflation and relative price dispersion, in the first stage, the total number of significant cointegrating relations in the system of component prices is estimated for each rolling subsample of a given window size. In the next stage, the number of significant cointegrating relations obtained from each subsample is compared with the corresponding period’s average inflation rate.

Empirical Results and Discussions

To carry out the empirical analysis, the study uses monthly data on all six major components of CPI, which include food and beverages, pan, tobacco and intoxicants, clothing and footwear, housing, fuel and light, and miscellaneous. The data is collected from the official website of the Ministry of Statistics and Programme Implementation, Government of India. The data is collected for the period from January 2013 to December 2018.

First, the time-series properties of all the component price indices is examined using the conventional Augmented Dickey-Fuller and Phillip-Perron unit root tests. The tests have been conducted for a sequence of rolling subsamples with a given window size. The results from the unit root tests indicate that the null of unit root is rejected in the case of all the component price indices (in logarithmic form), implying that the time series of each variable follows the I(1) process.4

After verifying that each component price series contains a single unit root and thus integrated of same order, the cointegration test is carried out for estimating the total number of significant cointegrating vectors (r). The cointegration test is used for a sequence of rolling subsamples, each consisting of 30 observations.5 The results from the cointegration test indicate that a large variation is observed in the number of cointegrating relations (r) over a period of time.6 Next, the average inflation (πt) corresponding to each rolling subsample is calculated.

In Figure 1, the number of significant cointegrating relations (r) is plotted against the average rate of inflation rate (πt) during the corresponding period. It is evident that initially, the number of cointegrating relations increase as inflation falls up to a certain level, and con­sequently as inflation continues to fall further to lower levels, the number of cointegrating relation start decreasing. These results imply that the dispersion in relative prices is comparatively higher during the periods of both high as well as low inflation, indicating that it is the deviation of actual inflation from certain threshold rate that matters for relative price dispersion rather than inflation per se.7 Apparently, this threshold rate turns out to be around 5%.

To visualise this relationship more clearly, the time series of average inflation (with corresponding period’s cointegration relations) is arranged in ascending order. Then, the deviation of inflation from its threshold (ππ*) rate is calculated, considering π* = 5%. In Figure 2, the scatter plots of number cointegrating relations (r) is presented against the deviation of the average inflation rate from its threshold rate (ππ*). Here, the number of cointegrating relations (r) is measured along vertical axis, and the corresponding period’s inflation-deviation (ππ*) is measured on horizontal axis.

It is evident from Figure 2 that this scatter plot is of inverted U-shape and ­indicating that the number of significant cointegrating relations among component price indices is comparatively lesser during the periods when actual inflation departs significantly from its threshold rate in either direction. That is when a shock pushes the actual inflation farther away from its threshold in any direction, the relative prices get more dispersed over time. However, the dispersion of relative prices tends to decline as actual inflation approaches to the threshold rate. It is interesting to note that the maximum number of significant cointegration relationships is observed when the deviation of actual inflation (from 5% threshold rate) is zero; implying that the dispersion in relative prices is minimised when the long-term average inflation is stabilised around 5%.

To complement these findings, a piece­wise regression equation given below is estimated using the ordinary least squares (OLS) method:

rt = α1 + α2 (πtπ*) + α3(πtπ*)+ + et

where, αcaptures the impact of negative inflation-deviations (that is, when actual inflation πis lower than the threshold/target inflation π*) and α3 captures the impact of positive inflation-deviations on the measure of relative price dispersion (r). The results are given in Table 1.8 These results indicate that α2 = 0.58 and α3 = 0.58 with associated t-values 8.72 and -6.42, respectively, implying that both these coefficients are statistically significantly different from zero. This suggests that both larger positive and negative inflation-deviations result in lower r and thus high dispersion in relative prices over time.

These findings provide evidence in ­favour of the view the relationship bet­ween inflation and dispersion of relative prices is also of U-shaped profile as is the traditional inflation-relative price variability relationship documented in the ­recent literature. It is interesting to note that the proposal of 5% long-term inflation target is consistent with the threshold rates suggested by Rather et al (2014) and Senapati et al (2018). Although their argument is based on the minimisation of traditional measure of relative price variability, the threshold inflation rate proposed by them is same as here.9 This has a crucial implication that stabilising the inflation around 5% will not only minimise the dispersion of relative prices over time, but will also minimise the relative price variability in a given point of time.

Overall, the empirical findings provide evidence in favour of view that the dispersion of relative prices over time increases with increase in deviation of inflation from certain rate but not with the inflation rate per se. The more interesting inference that emerges from this empirical exercise is the presence of a certain threshold inflation rate corresponding to which the dispersion of relative prices is minimised, and this thre­shold turns out to be 5%. This estimate is consistent with the official threshold rate maintained by the Reserve Bank of ­India (RBI).

These findings highlight the significance of adopting an inflation targeting framework and having an appropriate and precise estimate of the target for conducting monetary policy. More precisely, in a credible inflation targeting framework, the monetary authorities will be more efficient in stabilising the actual/realised inflation rate around its target level in the short run; which in turn will result in minimum distortions in the relative price structure of the economy. Further, stabilising long-term inflation at the target level will help the central banks delink the expectations from the realised inflation in the short run. This ­underlines the role and signi­ficance of inflation-target oriented monetary ­actions in anchoring the expec­tations in forward looking inflation-expectation settings.

Concluding Remarks

This study examines the impact of inflation on dispersion of relative prices using a cointegration framework. The evidence from rolling samples indicate that the dispersion of relative price increases in response to the increase in the deviation of inflation from a certain threshold rate in either direction but not with inflation per se, as is traditionally believ­ed. The crucial inference that emerges from the empirical findings is the presence of 5% threshold inflation rate corresponding to which the dispersion of relative prices is minimised. It is interesting to note that this estimate is consistent with the official threshold/target rate maintained by the RBI. This finding has crucial implication for monetary policy that stabilising the long-run inflation rate around 5% will not only reduce other welfare costs, but it will also ­minimise the inflation-induced distortions in the relative price structure of the economy.

Notes

1 Number of empirical studies from both developing and developed countries demonstrate that a significant proportion of variability in relative prices is generated mainly due to inflation (Ram 1990Rather et al 2014).

2 Note that in a cointegration framework a large (small) number of common stochastic trends in the system of component price indices implies wider (lesser) relative price dispersion over time.

3 For more details on the method of Johansen cointegration test, see Rather et al (2018).

4 The results are not present here.

5 The rolling windows of different size were considered as well.

6 Detailed results from the cointegration tests can be obtained from the author.

7 The results were also obtained for rolling windows of different size. However, a change in window size does not change the inferences significantly.

8 The variables were normalised to common scale and then the regression equation was estimated.

9 Both Rather et al (2014) and Senapati et al (2018) used variance of cross-sectional price changes as a measure of relative price variability.

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Updated On : 20th Oct, 2020

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