In the contemporary literature of macroeconomics, the mainstream frameworks for policy evaluation have recognised the significance of price rigidities, emerging from the micro-level pricing behaviour of firms, to explain the short- and medium-run effects of monetary policy interventions (Gali 2002, 2008; Woodford 2003). With the progress of analytical techniques, a strand of theoretical literature on price stickiness has been shaped (Rotemberg 1982; Calvo 1983; Taylor 1999). Over the years, researchers have identified the role of price rigidity and subsequently, the price setting mechanism of the firms in the dynamic interactions between inflation and output, and the conduct of monetary policy in the economy.

Given the significant policy implications of the micro-level price setting behaviour, it was much needed to find the empirical evidence for the theoretical conjecture of price rigidity. Starting from the work of Klenow and Bils (2004), several studies are carried out across different countries in order to evaluate the degree of price stickiness from different perspectives. Following this stream of literature, we present a set of stylised facts on the frequency, size and distribution of price changes in the context of Indian economy, from the aggregate Consumer Price Index for Industrial Workers (CPI-IW) and its major components.

Various statistical measures and tests are used to explore (i) the degree of price rigidities across the different sectors, (ii) synchronisation between the frequency and size of price changes, and (iii) the behavioural patterns of the price setting mechanism. The results of our analyses will be useful to target appropriate inflation indicator, estimate the real effects of monetary transmission with sectoral pass-through, and design the optimal monetary policy in a multi-sector environment.

**Macro Implications of Micro Pricing **

Nominal rigidity in the goods market, alternatively known as price stickiness, implies the nature of price not to adjust immediately in response to the changes in market conditions (Hall and Yates 1998). The role of price rigidity for generating the short-run real effect of monetary policy works in the following way. When all prices in the market change simultaneously in response to a nominal shock, the relative prices will remain unaffected and hence, the real side of the economy remains unaltered. However, if the market prices are staggered, all the prices will not adjust immediately after a policy shock. This sluggish adjustment entails to the short-run movements of the relative prices, causes reallocation of resources and generates the output effects as observed in the data. Such nominal rigidity, which emerges from the price setting behaviour of firms, needs to be assessed in order to understand the microeconomic mechanisms of firm-level pricing.

Theoretically, it is well established that the degree of price stickiness determines the responsiveness of inflation to changes in the real marginal cost of production, and subsequently, pins down the inflation and output gap nexus. It is also shown in the literature that the analysis of welfare loss function of the central banks due to macroeconomic volatilities critically depends on the degree of nominal friction prevailing in the economy. In addition to theoretical relevance, there are several practical implications for the empirical assessments of price stickiness both at the aggregated and disaggregated level of Consumer Price Index (CPI).

First, the persistence of inflation is largely governed by the degree of price stickiness. Second, the empirically observed hump-shaped response of the macroeconomic variables to monetary policy shocks hinges on the degree of price rigidity. Third, the estimate of price stickiness directly affects the design of optimal monetary policy for an economy. Fourth, measurements of price stickiness based on aggregate-level data and micro-level data often lead to disagreement regarding the magnitude of nominal friction, which is critically important for policy formulation. Finally, disaggregated analysis of price stickiness across the sectors or industries needs to be addressed in order to recognise the policy dilemma of the policymakers when targeting CPI inflation, based on the measurement of headline vis-à-vis core inflation.

In view of these crucial implications, we examine the quantitative and qualitative features of nominal rigidity and price setting behaviour of the producers across sectors, using the CPI-IW.

**Stylised Facts of Price Changes**

Empirical evidence on price stickiness is available for the advanced and emerging economies both at the aggregate level as well as firm-level or sector-level data. It is observed that the degree of price stickiness and price setting behaviour are substantially heterogeneous across the countries and the sectors (Dhyne et al 2006). For example, the frequency of price change in the euro area is found to be lower than that in the United States’ (US) economy. Again, prices in the US economy change less frequently than those in high-inflation developing countries like Brazil, Chile, Mexico, and Slovakia (Klenow and Malin 2010). Works done by Morandé and Tejada (2008) on Latin America, and Kovanen (2006) on Sierra Leone provide evidence on the sectoral heterogeneity of price stickiness. Motivated by these cross-country variations and sectoral heterogeneities of nominal stickiness, our article aims to explore price rigidity for the Indian economy from CPI-IW monthly data.

The CPI-IW data is provided by the Labour Bureau. The data set spans from January (M01) 2006 to October (M10) 2016, covering the group- and subgroup-level observations. We classify the price indices of CPI-IW data into two groups, namely food and non-food, which are composed by the respective subgroup items. The rationales behind the choice of CPI-IW indicator are as follows.

First, the CPI-IW data (with 2001 as base year) provides much longer data set on consumer price indices compared to other relevant indicators like CPI-combined (where 2012 is the base year). The commodity-wise price index data of CPI-combined indicator, provided by the Central Statistics Office (CSO) and used for inflation targeting by the Reserve Bank of India, are available from M01, 2011. Hence, the choice of CPI-combined indicator would entail to loss of information by 60 data points for each group- and subgroup-level of commodities. Given the fact that the behavioural pattern of micro-level price setting is fundamentally a structural characteristic of the underlying economy and the price stickiness is treated as the deep parameter in the macroeconomic models, one needs to exploit as many observations as possible to draw inferences for the empirical analysis.^{1}

Second, we also check if CPI-IW can be considered as a reliable proxy indicator for economy-wide CPI similar to the CPI-combined indicator. Based on the measure of correlation coefficient, we find a strong coherence between the inflation series computed from CPI-combined and CPI-IW for general index, group-level indices (food and therefore, non-food by construction) and subgroup level of commodities.^{2} All these together justify the selection of CPI-IW data for our analysis.

The analysis runs in two layers. At the outset, we look into the frequency and size of price changes of the group- and subgroup-level items. Then, we examine the behavioural pattern of price adjustment across the various items of the respective groups. Following the relevant literature, we use some of the statistical measures and analytical tools for our purpose. These approaches reveal the conduct of micro-level pricing for a representative group of commodities.

**Frequency of price change: **We examine the degree of price stickiness from the group level CPI-IW data, which shows a considerable heterogeneity in the price setting behaviour across the sectors within the economy. Using the method of Indirect Frequency Approach, frequency of price change is evaluated for each sector and subsequently, we come up with the following observations.^{3}

First, the food sector features a higher frequency of price change compared to the non-food sector (88% versus 63% probability of price change in a month’s time). There exists a modest variation in the intra-sectoral frequency of price change. Almost half of the items of the food sector (pulses; protein items like meat, fish and eggs; vegetable and fruits, and spices) experiences price change in a month’s time with a probability of 90% or more. For another half of food sector items, like cereals, milk, edible oil, and other foods, the probability comes down within the range of 80% to 90%.

In contrast to the food items, the non-food sector shows a lower probability of price change, which hovers around 69%, excluding the housing component. The sector of housing service shows a significantly lower frequency of price change with the probability of 16%. The probability of price change in the education sector also lies in a lower tier (50%). Medical and clothing items share comparable frequency of price change, such as 62% and 67%, respectively. Fuel and light, transport and communications, and personal care closely resemble in their frequencies of price changes, which lie between 70% and 74%.

Following the frequency of price change, the duration of price spell (in months) for the food and non-food sectors is computed and plotted in **Figures 1a and 1b**, respectively. Given the observations from the frequencies of price changes, duration of the price spells is computed and plotted. These plots show the shortest duration of a price spell for the food product, as opposed to other groups, such as education and housing, which are subject to a very low frequency of price changes. Overall, the range of price spells across the industries is 5.4 months indicating the presence of sizeable price dispersion in the face of an exogenous shock.

**Size of price change: **In the context of micro-level pricing behaviour, a common finding in the literature is that size of price changes, on an average, is large in the emerging markets (Barros et al 2009; Konieczny and Skrzypacz 2005).^{4} This prompts us to examine the size of price changes at the group- and subgroup-levels along with the frequency of price changes. We find that the size of price change varies across the product groups moderately (Figures 2a and 2b).

For the food sector, the monthly average size of price change is 0.79%, while it is around 0.55% for the non-food sector. However, based on the difference between mean and median within each group, we find more pronounced dispersion (nearly twice greater) in the size of price change for the non-food sector than the food sector. It is also noticed that irrespective of group, monthly average and median price changes are highly correlated with the frequency of price change. The correlation coefficient between frequency and mean (median) size of price change values 0.55 (0.70) and it is statistically significant.

This finding indicates the synchronisation in the price changes, that is, the response of prices to exogenous disturbances or shocks, which can potentially alter the desired price of the firms. The positive association between the frequency and size of price changes is in line with the prediction of menu-cost models of price adjustment, which suggests that inflation is higher in the markets where price changes are more frequent (Barro 1972; Taylor 1999).

Overall, the CPI-IW in India features a high frequency of price changes. This can be attributed to the level and variability of inflation, frequency and size of cost and demand shocks, market structure and the degree of competition. While this high frequency of price changes fits well with the evidence from other emerging market economies, it stands in contrast to the findings from the advanced countries available in the literature.

Vermeulen et al (2007) and Peneva (2009) argue that goods with higher labour intensity are associated with less frequent price changes. But, the evidence from CPI-IW data indicates this may not be true for India. In general, labour intensity is expected to be higher in the food sector compared to the non-food sector. Nevertheless, we find a higher frequency of price changes for the food sector.

**Idiosyncratic shocks and price changes:** In the course of our empirical analysis, we have envisaged the role of sector-specific idiosyncratic shocks on the frequency of price changes. Due to the impact of high magnitude adverse shocks, producers are often unable to cope with their cost condition and pass on the burden to the buyers of the market by resetting their prices. Such effect of shocks comes out through the volatility of price change. Internalising this volatility component in the Indirect Frequency Approach, we re-examine the frequency of price change across the sectors of the CPI-IW.

We observe a substantial reduction in the frequency of price change for both food and non-food sectors (**Figures 3a and 3b**). For the food sector, the average (median) frequency of price change declines from 88% (89%) to 25% (25%). For the non-food sector, the average (median) frequency of price change goes down from 62% (69%) to 20% (17%). This result emphasises the role of sector-specific shocks, which would affect the price adjustment of the firms in the respective sector. Moreover, it shows that in case of any aggregative or common shocks, such as shocks to total factor productivity or policy shocks, the probability of price change may not be largely different between the food and non-food sectors.

**Time versus State Dependence of Price Setting **

Along with the frequency and size of price change, the nature of the price setting mechanism has also important implications for the monetary policy transmission in the economy. Price setting behaviour of the producers can be either time-dependent (TD) or state-dependent (SD). In a staggered pricing environment, if the timing of price changes by an individual firm is exogenous, price setting mechanism is TD. In a TD set-up, a firm can adjust the price at a fixed interval of time (Taylor 1980, 1999) or randomly (Calvo 1983). In the literature, two types of exogenous staggering price changes are available, namely Taylor-type and Calvo-type price settings. In both cases, it is assumed that the fraction of firms adjusting their prices each period is constant (Klenow and Kryvtsov 2008).

In contrast to TD models, under SD type pricing mechanism, firms endogenously choose the timing of price changes depending on the costs associated with price changes, alternatively known as the menu costs. In this set-up, firms choose to change prices if a specific event occurs and they gain by doing so (Klenow and Kryvtsov 2008; Morandé and Tejada 2008). In other words, the timing and the magnitude of the firms’ price changes depend on the state of the economy given the fixed menu costs (Dotsey et al 1999; Klenow and Kryvtsov 2008; Morandé and Tejada 2008).

The pattern of monetary policy transmission to the real side of the economy differs distinctively under TD- and SD-type pricing mechanisms. Monetary policy shocks are found to have stronger and persistent effect on real output in the TD models compared to the SD models (Klenow and Kryvtsov 2008; Gertler and Leahy 2008). Given the policy trade-off between inflation and output gap for stabilisation, the policymakers would face a greater cost of disinflation under the TD-type price setting mechanism than the SD-type pricing behaviour (Guimaraes et al 2014). From the perspective of monetary policy transmission in an economy, therefore, it is important to identify empirically the nature of price adjustment mechanism of the aggregate as well as sectoral prices in the country.

The TD versus SD of price adjustments have direct implications for the number of modes in the distribution of price changes (Cavallo and Rigobon 2011). Under the TD price adjustment process, distribution of price changes internalises the distribution of cost changes to some extent. As cost changes tend to have unimodal distribution in a low inflation environment, one would expect to find the unimodal distribution of price changes under the TD type adjustment mechanism.

On the other hand, under the SD price adjustment process, a small deviation from the optimal price is less costly than the menu cost. As a result, in a low inflation environment, the distribution of price changes tends to have a bimodal distribution around 0% with a positive and a negative mode (Cavallo and Rigobon 2011). Hence, the estimation of mode from the distributions of price changes using modality tests facilitates to identify the underlying price setting mechanism of the firms.

**Modality tests of price changes:** In our analysis, we estimate the number of modes in the distribution of changes in aggregate CPI-IW and its major components using the Hartigan Dip test (Hartigan and Hartigan 1985) and the Silverman test (Silverman 1981). **Table 1** (p 39) shows the summary statistics of price changes in CPI-IW and its major components.

In Hartigan’s test, the Dip statistic is calculated to measure the deviation of an empirical distribution from the best fitting unimodal distribution. The Dip statistic is zero when the empirical distribution is unimodal. When the empirical distribution is multimodal, the cumulative distribution has multiple regions of convexity and concavity. In that case, the empirical distribution function stretches until it takes the shape of a unimodal distribution. The larger the stretch needed, larger will be the departure from unimodality and subsequently, larger will be the value of the Dip statistic. Hence, in Hartigan’s test, positive Dip values provide evidence to reject the null hypothesis of unimodality.^{5}

Silverman’s Bandwidth test is a non-parametric test that uses the kernel smoothing technique to determine the most probable number of modes in an empirical distribution.^{6} Under this test, the null hypothesis that the true density “*f*” possesses at most “*k*” modes is tested against the alternative hypothesis that “*f*” has more than “*k*” modes. For the null hypothesis of *k* modes, the test statistic is the critical bandwidth, that is, minimum smoothing required for the smoothed kernel density to have at most *k* modes. Large values of critical bandwidth are evidence against the null hypothesis because a larger degree of smoothing is needed to eliminate additional modes in the density estimate.

The statistical significance of critical bandwidth is evaluated using the bootstrap method. For each bootstrap sample, the minimum bandwidth required to have at most *k* modes is computed and the probability of it exceeding the critical bandwidth estimated from the data is calculated. This probability provides the significance of the test statistics. The resulting probability is equivalent to the share of bootstraps that have more than *k* modes when evaluated at the critical bandwidth. The test is performed sequentially starting with critical number of mode k = 1, 2, … M, until the probability value is sufficiently low so that we cannot reject the null that the underlying density possesses at most *M* modes.^{7}

Results of the modality tests are reported in **Table 2**. The results show that both the tests find that pulses and products, vegetables and fruits, meat, fish and eggs, and oil and fats are unimodal, implying that these four groups are subject to TD price adjustment process. On the other hand, cereals and products, other food group, pan, supari and intoxicants; fuel and light; clothing; and the aggregate and the components of miscellaneous group are detected to have more than one mode by both the tests. Among these cases of multiple modes, cereals and products, other food group; transport and communications; personal care and effects; and the aggregate miscellaneous group are found to be bimodal by the Silverman test.

There are a few instances when the two tests have different views regarding the number of modes in the series. As an example, for the aggregate CPI-IW index, the null of unimodal distribution is rejected under the Dip test, whereas the Silverman test suggests that CPI-IW possesses a unimodal distribution. The similar situation arises in the milk and products category. On the contrary, the aggregate food group and housing are found to be unimodal by the Dip test, while the Silverman test suggests these series to have two modes. While the Dip test suggests that the group of condiments and spices has one mode, the Silverman’s Bandwidth test shows that this group is multimodal.

**Rec****onciling results of price adjustment:**** **The variation of the results across two tests can be due to the fact that in reality, price adjustment process of a commodity may not be uniquely TD or SD, but rather, a combination of the two (Woodford 2009; Alvarez et al 2010; Cavallo and Rigobon 2011). As a result, the shape of the distribution function of price changes depends on the relative importance of the two types of pricing mechanisms (Cavallo and Rigobon 2011).

For the series detected as unimodal by both tests and bimodal by the Silverman test, we further test for the relative importance of TD versus SD elements in pricing using the Bimodality Coefficient (BC) test. The BC is a measure of the proportion of bimodality after correcting for the finite sample bias. The value of BC ranges from 0 to 1, where a value greater than “5/9” or greater than 0.556 suggests bimodality. The results are reported in **Table 3**.

The series that are detected as unimodal by both the tests, namely pulses and products; vegetables and fruits; meat, fish, and eggs; and oil and fats, have a BC lower than the cut-off value of 0.556, implying that price adjustment mechanism is tD in these series. Hence, we expect to have persistent real effects of monetary shocks in these sectors. Surprisingly, all the series that are detected as bimodal by the Silverman test, except for housing, also show the value of BC less than the cut-off value 0.556, indicating the predominance of TD element in price setting mechanism in these sectors.

These series include cereals and products; other food group; the aggregate food group; fuel and light; clothing; the aggregate miscellaneous group; transport and communications; and personal care and effects. These sectors are also expected to generate more persistent real effects of monetary policy. The BC value for the housing sector is found to be 0.782, greater than the cut-off value, indicating that the price adjustment process is SD, unlike the other sectors. Intuitively, a small deviation from the optimal price facing moderate change in the demand condition of the housing sector is less costly than incurring the menu cost in this sector.

Some of the groups are found to have either more than two modes by the Silverman test or to be non-unimodal by the Dip test. The aggregate CPI-IW index; milk and products; condiments and spices; pan, supari, tobacco and intoxicants; medical care; education, recreation and amusement; and the other categories in the miscellaneous group fall into this class. Since testing for the proportion of unimodality versus bimodality is not applicable for these groups, we instead test whether each of these series consists of one multimodal component or is a combination of multiple distributions with different frequencies, so that it appears as a multimodal distribution.

To this end, we fit the Gaussian mixture model to the data by maximum likelihood through the expectation-maximisation (EM) algorithm. If a series is found to be a combination of multiple components, then we fit the data to a single component model. Next, a likelihood ratio (LR) test is performed to choose the model among the unrestricted multiple-component model and the restricted single-component model that best fits the data. The results are reported in **Table 4**.

The EM algorithm fits one component model to the aggregate CPI-IW series and the series on milk and products. Hence, we can infer that the distribution functions of Cpi-iw and the milk and products group consist of multiple modes indicating the prevalence of the SD element in the price adjustment mechanisms in these series. For the rest of the series, the LR test suggests rejection of the null that the data best fit to a single-component model. Therefore, the multiple modes in these series could be due to the fact that each series consists of multiple components of different frequencies. The existence of multiple modes in the distribution function in these series may not necessarily indicate the relative importance of the SD element in price setting mechanism in these series.

**Conclusions **

The degree of price stickiness is one of the determinants of responsiveness of current inflation to output gap in the New Keynesian Phillips curve equation. The higher is the stickiness in price changes, lower is the response of inflation to changes in the real-side activities. It then follows that the extent of price stickiness also determines the optimal weight assigned to inflation variation in the approximation of a representative consumer’s welfare loss that serves as a quantitative basis for choosing the optimal monetary policy rule from a set of alternative policy rules (Rotemberg and Woodford 1997). Higher the degree of price stickiness, higher weight is to be given on inflation variations to minimise the welfare loss. For effective implementation of monetary policy, it is essential to evaluate the frequency and duration of price changes at the disaggregated level as well. If these vary substantially across sectors, then the welfare loss might need to be evaluated in a multisectoral framework, with sectoral price stickiness determining the optimal weights assigned to the sectoral inflation variations.

A well-known dilemma that central banks often face is the choice between headline inflation, including food and core inflation as the target inflation indicator. Such a dilemma is even more profound for emerging economies where food constitutes a substantial share of the consumption basket. The general equilibrium model-based welfare analysis suggests that targeting broad CPI is welfare superior (Catão and Chang 2010;

Pesenti 2013; Anand and Prasad 2010; Soto 2003). In fact, the majority of the emerging economies practising inflation targeting (IT) monetary policy have chosen broad CPI as the underlying indicator for the inflation target. However, the choice of headline inflation is often criticised on the ground that setting a target by the central bank involves medium- to long-term inflation forecasting, which may be affected by large swings in the commodity prices. Hence core inflation, that is, the headline inflation net of volatile items such as food needs to be chosen as the target.

India has entered into the IT monetary policy regime in the recent past with overall CPI being the underlying indicator for the inflation target. In this context, our analysis provides a ground for incorporating food in the inflation target. Our analysis shows that when small price changes are ignored, food and non-food sector record more or less similar frequencies of price changes and the durations of price spells among the major subgroups of CPI-IW. These findings also conform to the observed high inflation persistence in the food sector in India in the recent past. Hence, excluding food group from the target inflation indicator, assuming rapid changes in price in this sector, may moderate the effectiveness of monetary policy. Overall, the results suggest that analysing the degree and pattern of price adjustment at the sectoral level is important for effective implementation of monetary policy.

**Notes**

1 For the purpose of Bayesian estimation of a fully specified structural macroeconomic model (New Keynesian DSGE framework) for Indian economy, Banerjee and Basu (2017) use CPI-IW data set to set the prior for Calvo-type price stickiness parameter.

2 We have checked the correlation coefficients between the year-on-year inflation series of the two indicators with respect to different levels of commodity groups over the common sample period of M01, 2012 to M10, 2016. All the correlation coefficients are positive and statistically significant at level of 5% except spices. Since the composition of the subgroup of “spices” is different between the two indicators, we find a low degree of association for them.

3 Following Kovanen (2006) and Morandé and Tejada (2008), we summarised the methodological details of indirect frequency approach. We define an indicator function (*I*_{it}) such that it takes value 1 if the price of an item (*p*_{it}) at date *t* does not change from the previous period, and takes zero otherwise. Using this indicator function over the sample period, we get the value of indicator across the sectors (as given by 1.1), from which we derive the implied duration (as specified in 1.2) of a price spell.

I_{it}= 1 if p_{it }≠ p_{it-1}; i = 1, 2, …, k (number of subgroups)

=0 if p_{it }= p_{it-1}; t = 1, 2, … n (number of periods)

^{“}^{i = 1, 2, …, k …(1.1)}

D_{i }= – “i = 1, 2, …, k …(1.2)

4 For example, in the United States CPI data, Klenow and Kryvtsov (2008) report a mean (median) absolute change in posted prices of 14% (11.5%), while regular price changes are smaller but still large with a mean (median) of 11% (10%). The average consumer price decrease (increase) is 10% (8%) in the Euro area (Dhyne et al 2006).

5 For further details, see Cavallo and Rigobon (2011).

6 For a given sample, it estimates kernel density *f *as a function of a smoothing parameter or bandwidth *h* and a Gaussian kernel function *K*.

7 For more details, see Silverman (1981); Cavallo and Rigobon (2011); Salgado-Ugarte et al (1997).

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