Price Dynamics, Forecastability and Policy Implication of Core and Headline Inflation

Transcription

1 Price Dynamics, Forecastability and Policy Implication of Core and Headline Inflation Kanit Kuevibulvanich This Version: December 3, 213 Abstract This paper investigates the implication between core and headline inflation in three aspects. First, using time series analysis and the data from selected inflation-targeting countries, I empirically investigate the use of core inflation as the forecasting measure of headline inflation. Although theories suggest the use of core inflation in forecasting total inflation as it represents the persistent components of the price level, the results from data suggest otherwise and I find that core inflation is not necessarily a good forecasting measure in all countries. Second, I find the pass-through effect from total price level to core prices, suggesting the transmission from transitory components to persistent components of the price level. The results are not only seen in data from developing countries, but also in advanced economies. Third, I analyze the role of core inflation as inflation target using baseline New Keynesian model with sticky-price and flexible-price sectors. Although my result confirms the theoretical findings from previous literature that core inflation targeting is the optimal monetary policy, the welfare loss resulting from the use of headline inflation as the target is small. A slight deviation in inflation expectation and inflation learning is introduced and results in headline inflation targeting being the optimal policy instead. Keyword: Monetary Policy, Inflation Targeting, Core Inflation, Headline Inflation JEL Classification: C2, E31, E2, E8 1 Introduction Since the introduction of inflation targeting in the 199s, most modern inflation-targeting central bankers initially observed core inflation for their conducts of monetary policy. Headline inflation, which measures the broad price level, includes the volatile and transitory components, such as food and energy. However, core inflation excludes such and represents the persistent components of inflation. Using baseline New Kanit Kuevibulvanich Department of Economics, University of Wisconsin-Madison (kuevibulvani@wisc.edu). Submitted Field Paper. 1

2 Table 1: List of inflation targeting countries in the analysis, summary of inflation targets and roles of core measure of price level IT Current Target Role of Core Country Adopted (212 and/or 213) Measure Canada 1991 Headline CPI, 2.% ± 1 pp Operational guide Chile 1991 Headline CPI, 3.% ± 1 pp Communication Colombia 1999 Headline CPI, 2.-4.% Communication Czech 1998 Headline CPI, 2.% ± 1 pp Communication Eurozone 1998* Headline CPI, 2.% - Iceland 21 Headline CPI, 2.% ± 1. pp Communication Israel 1992 Headline CPI, 1.-3.% Communication Japan 21 Headline CPI, 2.% Communication South Korea 1998 Headline CPI, 3.% ± 1 pp Communication, previous target until 26 Mexico 1999 Headline CPI, 3.% ± 1 pp Communication Poland 1998 Headline CPI, 2.% ± 1 pp Communication Switzerland 2 Headline CPI, 2.% Communication Thailand 2 Core CPI,.-3.% Target UK 1992 Headline CPI, 2.% Retail price index as target until 24 USA 212 Headline PCE, 2.% Communication Source: McCauley (27), Hammond (212) and information obtained from websites and inflation reports of various central banks. Note: * denotes inflation targeting is adhoc according to the European Central Bank, denotes inflation targeting is expected according to the Bank of Japan. Keynesian macroeconomic model, Aoki (21) concludes that targeting core inflation, calculated from the sticky-price sector, rather than headline inflation is the optimal monetary policy. Thereby, there is no tradeoff between stabilizing aggregate output gap and core inflation. Mankiw and Reis (23) propose a method in choosing a price index for a central bank that corresponds to the business cycle as the market basket might not fit the purposes of monetary policy. It is also argued that, in the U.S. data, the central bank should construct a price index that weighs on the level of nominal wages. However, Table 1 shows that all central banks have adopted the use of headline inflation as their indicators and targets, allowing core inflation as communication and forecasting measures only. As an example, The Bank of England has revised its inflation target to headline inflation in 24. The Bank of Thailand had considered in 212, though postponed, the use of headline inflation. Hammond (212) and various central bankers claim the use of headline inflation promotes the credibility and effectiveness of monetary policy communication and anchoring of inflation expectation in the long run. Furthermore, various literature disputes the use of core inflation as inefficient measures. Gelos and Ustyugova (212) find that commodity price shocks have stronger and lasting effects on inflation of developing countries than advanced economies and there exists a pass-through of commodity price shocks to core inflation. Anand and Prasad (21) suggest the headline, particularly food expenditure, inflation targeting in emerging markets due to the fact that credit-constrained consumers, with high expenditure share in food, are insensitive to interest 2

3 rates. In emerging Asian economies, this is also supported by Rhee and Lee (213) due to low monetary policy credibility, high fiscal intervention and pass-through of commodity prices to core prices. Wiseiolek and Kosior (21) question the measurement and relevance of core inflation in monetary policy conduct in Central European countries, particularly, threats from food and energy price shocks discredit the validity of core inflation. Nonetheless, selecting the price indices proves to be the problematic issue. King (24), the governor of The Bank of England at the time, admits that CPI does not include the potentially noisy and volatile real estate prices, but The Bank of England continues to monitor house prices, and convergence in measurement gaps from transitioning between targets are questionable. McCauley (27) considers the core inflation targeting policy of The Bank of Thailand and finds that the alternative measurement core prime core price index including the transportation sector would not perform in a satisfactory manner either. One of the ultimate goals in selecting components to be included in the price level is to efficiently forecast total inflation. Surprisingly, core inflation, as theoretically seen as less-volatile persistent component and representing inflation trend and pressure, does not always perform well in predicting future inflation. Experimenting with excluding components in price level through different model specification, Detmeister (212) argues that traditional core CPI excluding food and energy performs worse than other underlying inflation measures. Based on forecasting error measure, Crone et al. (213) find in U.S. data that CPI less food and energy, albeit a more volatile measure, outperforms total CPI in out-of-sample prediction, but CPI less energy performs worse. However, total PCE outperforms core PCE in predicting total PCE. Hence, core inflation is not necessarily the best predictor of total inflation. This paper first aims to empirically examine in reduced-form and provide the stylized facts on the price level dynamics and causality aspect between core and headline inflation using Granger (1969) causality test. The forecastability of core inflation in predicting headline inflation is inferred from the causality test from core to headline prices. The causality specification from headline to core prices is also examined in the commodity price pass-through investigation, similar to the survey in Asia by Rhee and Lee (213). The main questions from the time series exercises are the following. Do the shocks in volatile and transitory components of price level transmit into persistent and stable components? Is core inflation a good predictor for headline inflation for all countries? Selected inflation targeting countries with different characteristics and degrees of economic advancement are analyzed. The second half of this paper follows closely to the New Keynesian model with sticky-price and flexible-price sectors outlined by Aoki (21). The attention is then drawn to the monetary policy implication between core and headline inflation. The welfare from each monetary policy is analyzed. Although core inflation targeting is the optimal monetary policy, central bankers are targeting headline inflation owing to its effectiveness in communication; hence, there exists 3

4 welfare cost of using richer information of headline inflation. The question to be addressed is under the baseline model, what is the welfare loss resulting from the use of headline inflation? Furthermore, given the sub-optimal policies are implemented, can the outcome from the benchmark policy be equivalently replicated? A deviation from the baseline model is also presented in the flavors of inflation learning, where households form incorrect or adaptive expectation of inflation. The welfare is evaluated in the model with variation in inflation expectation and optimal policy is addressed. The paper is structured as follows: Section 2 implements the Granger causality tests with classic test statistics and presents the time series results. Relevant discussions on prediction and pass-through of inflation measures are also detailed in Section 2. Section 3 analyzes the New Keynesian model by Aoki (21) in terms of welfare under each monetary policy, welfare loss in using headline inflation, policy equivalence, and inflation learning. Section 4 concludes and provides the future directions of the author. 2 Time Series Analysis In this section, the forecastability and the pass-through effect of commodities and aggregate prices are empirically analyzed using the data from 1 selected inflation-targeting countries. Forecastability of core inflation is associated with the Granger causality from core inflation to headline inflation. The pass-through effect of commodities and aggregate prices to fundamental core prices is associated with the Granger causality from headline inflation to core inflation. This section analyzes the research question in a non-structural reduced-form fashion. The data and methodology used are first outlined. The results and discussions, in which, no policy implication is drawn, follow. 2.1 Data and Methodology This section relies heavily on the specification of Granger causality test. In line with Crone et al. (213) on the use of core inflation as the predictor of headline inflation, one may associate the regression model of the Granger causality test from core inflation to headline inflation. This is due to the fact that Crone et al. (213) also includes both core and headline CPI in the models used to evaluate forecasting of headline inflation. Furthermore, as Rhee and Lee (213) shows the pass-through from commodity components in headline price level towards core price level, there may also exist causality from changes in the price level of transitory components to the persistent components. Hence, with similar regression model as Rhee and Lee (213), one should be able to associate Granger causality from headline inflation to core inflation to investigate the pass-through effect of aggregate price level to the fundamental price level. 4

5 As an empirical investigation, I consider 14 countries and Eurozone, in which central banks have, either explicitly or normatively, implemented inflation targeting regime on or before the early 2s. However, some countries included will have implemented inflation targeting in the near future. Certain attributes of discretionary targeting countries are explained in the next paragraph. To capture both seasonal and cyclical effects, the inflation data used in the following analysis are constructed from the percentage change in monthly price indices (CPIs) using both year-on-year and annualized month-on-month calculation. Although the year-onyear percentage change is defined as π t = (CPI t CPI t 12 ) /CPI t 12 and annualized month-on-month percentage change is π t = (CPI t /CPI t 1 ) However, in line with the log-linearization method implemented in New Keynesian models, the log-percentage change is analyzed, where the percentage changes are defined as π t = ln (CPI t /CPI t 12 ) and π t = 12 ln (CPI t /CPI t 1 ), respectively. The definition of price indices for each country is standardized as per Aoki (21) for conceptual purposes of our analysis. Core CPIs are price indices that exclude the prices of food and energy, while headline CPIs are price indices which include every item in consumer basket. However, the weights of each component are determined by the responsible agencies in each country. The analyses on price dynamics whether there exists causality between volatile and persistent components are conducted on the direction from headline CPIs to core CPIs. The communication channel of inflation targeting is evaluated on the direction from core CPIs to headline CPIs, which is theoretically ideal in inflation targeting and policy communication. The scope of analysis is confined from January 2 to the currently available data, June or July 213, to isolate the effect of non-commodity economic crises during the early and the late 199s. This gives observations of each price index for each country. Table 2 details the list of countries and the respective data sources by the responsible agencies. Table 1 also summarizes the list of inflation targeting countries selected in this analysis, the respective targets, and roles of core CPI. In this paper, all countries are currently targeting headline CPI, with the exception of the Bank of Thailand, which has adopted inflation targeting and used core CPI as the target since 2. In the attempt to eradicate deflation, the Bank of Japan is expected to meet the inflation target of 2% on headline CPI by 21. The US Federal Reserve announced that it explicitly sets the inflation target of 2% on the headline personal consumption expenditures (PCE) price index. The European Central Bank has not mandated a precise prescription of its target; however, it defines price stability as a symmetric band on the year-on-year inflation of 2%, calculated from harmonized index of consumption prices. Note that New Zealand, the pioneer of inflation targeting, and Australia are excluded from this analysis as they do not publish monthly CPI, rather, quarterly. The decision to only include countries which have implemented inflation targeting on or before 21 allows for the enriched data of countries with long experience of inflation targeting. The plots of inflation data from each country in this analysis are presented in Appendix A. It can be observed

6 Table 2: List of inflation targeting countries in the analysis and the sources of data used Country Base Data Source Canada 22 Statistics Canada Chile 29 National Statistical Institute of Chile Colombia 28 The National Central Bank of Colombia Czech 2 Czech Statistical Office Eurozone* 2 Eurostat and OECD Statistics Iceland 1997 Statistics Iceland Israel 26 Central Bureau of Statistitics of Israel Japan 2 Statistics Bureau, Ministry of Internal Affairs and Communications, Japan South Korea 21 Statistics Korea Mexico 21 Bank of Mexico Poland 26 Eurostat Switzerland 2 Federal Statistical Office, Switzerland Thailand 211 Bureau of Trade and Economic Indices, Ministry of Commerce, Thailand UK 2 Office for National Statistics, United Kingdom USA 1984 Bureau of Labor Statistics, USA Note: * The harmonized consumer price indices are sourced and used in both core and headline measures for Eurozone, defined as 17 countries participating in Euro currency. in all data sets that, annualized month-on-month calculation provides a highly amplified effect of monthly price level fluctuation, resulting from seasonal effect. Furthermore, under year-on-year calculation, the less volatile core inflation loses track with headline inflation during the energy price rally in in all countries, except Iceland. In other words, removing seasonality effect, core inflation exhibits relatively slow, and of less magnitude, price adjustment despite the flexible energy price shock. However, during the same period with month-on-month data, it can be observed that core inflation tends to lose track with headline inflation, i.e. the large variation between core and headline inflation, in less developed economies. To analyze the dynamics and causality of price levels over the course of inflation targeting regime, I split all sample periods into three sets full samples, before and after the energy crisis. I define the break point as January 27, which marks the start of energy price rally. Granger causality test is implemented using classic F-statistics. The optimal lag length specification for the test chosen by Akaike (1974), Bayesian (Schwarz, 1978) and Hannan-Quinn (1979) Information Criterion are all presented to guide the optimal specification. To elaborate the causality break, the Chow (196) structural break test is also presented as guidelines in each of the two break-point cases, January 27 and January 28, with the optimal lag length specification chosen by each criterion on full samples. All test statistics used are detailed in Appendix B. The results of causality tests are presented in the next section. 2.2 Results Using full samples of year-on-year inflation calculation, Table 3- summarize the results by countries from 6

7 Table 3: Conclusion from Granger causality tests, classified by countries, using year-on-year inflation data and optimal lag length selected by Akaike Information Criterion Headline Granger causes Core Full Sample Yes No Colombia, South Korea Yes Chile, Iceland, Israel Switzerland, UK Core Granger causes Headline Canada, Czech, Eurozone No Thailand, USA Japan, Mexico, Poland Headline Granger causes Core Jan - Dec 6 Yes No Yes Israel, Switzerland, USA South Korea Canada, Colombia, Czech Core Granger causes Headline No Chile Eurozone, Iceland, Japan Mexico, Poland, Thailand, UK Headline Granger causes Core Jan 7 - Jun 13 Yes No Yes - Canada, Eurozone, UK Chile, Colombia, Czech Core Granger causes Headline No Japan, Poland, Thailand Iceland, Israel, South Korea Mexico, Switzerland, USA Granger causality test between core and headline inflation with the optimal lag length selected by Akaike, Hannan-Quinn, and Bayesian information criterion, respectively. Table 6-8 summarize the results using annualized month-on-month calculation in the same order of information criterion used. In all analysis, the maximum lag length analyzed is 24 months, corresponding to the lag in the transmission mechanism of monetary policy. In each table, the samples are also analyzed by splitting into two periods, January 2 to December 26, and January 27 to June/July 213. The conclusion from Granger causality tests is inferred at % significance level. Enthused readers may inquire the p-value of the Granger causality tests, and the relevant Chow structural break tests, in Table of Appendix C. Section 2.3 and 2.4 offer analyses based on year-on-year and annualized month-on-month inflation data, respectively. 2.3 Analysis on -on- Inflation Data Lag Length Selected by Akaike and Hannan-Quinn Information Criterion It can be observed in general that both Akaike and Hannan-Quinn information criterion similarly select longer lag length as the optimal specification. This corresponds to the theorized lag in response of monetary policy. Note that longer lag length specification may also suggest more persistence or wider fluctuation from shock. From the results jointly inferred from Table 3 and 4, there exists a statistically causality from headline 7

8 Table 4: Conclusion from Granger causality tests, classified by countries, using year-on-year inflation data and optimal lag length selected by Hannan-Quinn Information Criterion Headline Granger causes Core Full Sample Yes No Yes Chile, Iceland Colombia, Israel South Korea, UK Core Granger causes Headline Canada, Czech, Eurozone No Thailand, USA Japan, Mexico, Poland Switzerland Headline Granger causes Core Jan - Dec 6 Yes No Yes Israel, USA South Korea, Switzerland Canada, Colombia, Czech Core Granger causes Headline No Chile Eurozone, Iceland, Japan Mexico, Poland, Thailand, UK Headline Granger causes Core Jan 7 - Jun 13 Yes No Yes - Canada, Eurozone, UK Chile, Colombia, Czech Core Granger causes Headline No Japan, Poland, Thailand Iceland, Israel, South Korea Mexico, Switzerland, USA Table : Conclusion from Granger causality tests, classified by countries, using year-on-year inflation data and optimal lag length selected by Bayesian Information Criterion Headline Granger causes Core Full Sample Yes No Yes Chile, Israel, Thailand Mexico Core Granger causes Headline Colombia, Czech, Iceland Canada, Eurozone No Japan, Poland, USA South Korea, Switzerland, UK Headline Granger causes Core Jan - Dec 6 Yes No Yes Israel, Thailand, USA South Korea Canada, Colombia, Czech Core Granger causes Headline No Chile, Japan, Poland Eurozone, Iceland, Mexico Switzerland, UK Headline Granger causes Core Jan 7 - Jun 13 Yes No Yes - Canada, Eurozone, UK Chile, Colombia, Czech Core Granger causes Headline No Japan, Poland, Thailand Iceland, Israel, South Korea Mexico, Switzerland, USA 8

9 inflation to core inflation, which implies pass-through from commodity price shock, in four countries Chile, Iceland, Thailand and the United States over the full samples. However, from the split sample analysis, only Japan, Poland, and Thailand possess such pass-through after the oil shock. Other countries do not show the causality from headline to core inflation. My finding partially supports the conclusion by Rhee and Lee (213) concerning the pass-through from commodity price shock to core price level in Asian countries: Thailand on full samples, Japan on the latter half of samples, and no pass-through in South Korea. Although in Rhee and Lee (213), the data in analysis from shows significant pass-through in Thailand, but not in Japan and South Korea. Furthermore, the causality tests also show such pass-through for other countries, including the United States, as well. On the other direction, Colombia, South Korea and UK exhibit statistically significant unidirectional causality from core inflation to headline inflation over the full samples. The characteristics of countries which possess different attributes of causality cannot be grouped by degree of economic advancement or length of time in which inflation targeting has been adopted. Note further that there are two countries Chile and Iceland which exhibit bidirectional causality of core and headline inflation over full samples, and the optimal lag length selection by both information criterion yield contradicting results for Israel and Switzerland Lag Length Selected by Bayesian Information Criterion Unlike Akaike and Hannan-Quinn information criterion discussed in Section 2.3.1, Bayesian information criterion selects shorter lag length as optimal specification using full samples. The shorter lag length specification also improves the degree of freedom. From the result in Table, nine out of fifteen countries exhibit causality from headline inflation to core inflation over full samples. Although there may exist pass-through of commodity price shock, combining with shorter lag length specification, this implies less persistence or fluctuation from such shock. However, with the restricted samples before and after oil price shock, Table shows the identical result as Section that Japan, Poland, and Thailand possess the pass-through from headline to core inflation after the oil shock with the longer lag length specifications. Similar results also hold for the other direction that, before the end of 26, there exists a unidirectional causality from core to headline inflation only in South Korea. Only four countries Chile, Israel, Mexico, and Thailand display the other direction of causality from core to headline inflation. 9

10 Table 6: Conclusion from Granger causality tests, classified by countries, using annualized month-on-month inflation data and optimal lag length selected by Akaike Information Criterion Headline Granger causes Core Full Sample Yes No Canada, Eurozone, Israel, Japan Yes Chile, Colombia, USA Core Granger causes Headline South Korea, Switzerland, UK No Iceland, Thailand Czech, Mexico, Poland Headline Granger causes Core Jan - Dec 6 Yes No Core Granger causes Headline Yes - - No UK All countries except UK Headline Granger causes Core Jan 7 - Jun 13 Yes No Core Granger causes Headline Yes - - No - All countries Table 7: Conclusion from Granger causality tests, classified by countries, using annualized month-on-month inflation data and optimal lag length selected by Hannan-Quinn Information Criterion Headline Granger causes Core Full Sample Yes No Canada, Colombia, Eurozone Core Granger causes Headline Yes USA Israel, Japan, South Korea Switzerland, UK No Chile, Thailand Czech, Iceland, Mexico, Poland Headline Granger causes Core Jan - Dec 6 Yes No Yes - - Core Granger causes Headline All countries except No Mexico, UK Mexico and UK Headline Granger causes Core Jan 7 - Jun 13 Yes No Core Granger causes Headline Yes - - No - All countries 1

11 Table 8: Conclusion from Granger causality tests, classified by countries, using annualized month-on-month inflation data and optimal lag length selected by Bayesian Information Criterion Headline Granger causes Core Full Sample Yes No Canada, Colombia, Czech Eurozone, South Korea Yes Israel, Japan, Mexico Switzerland, UK Core Granger causes Headline Chile, Iceland, Poland No - Thailand, USA Headline Granger causes Core Jan - Dec 6 Yes No Yes Mexico Czech, Iceland, Switzerland Chile, Poland, Thailand Canada, Colombia Core Granger causes Headline No UK Eurozone, Israel, Japan South Korea, USA Headline Granger causes Core Jan 7 - Jun 13 Yes No Yes - - Core Granger causes Headline No - All countries 2.4 Analysis on Month-on-Month Inflation Data Lag Length Selected by Akaike and Hannan-Quinn Information Criterion Similar to Section 2.3, the Akaike and Hannan-Quinn information criterion select longer lag length as optimal specification compared to Bayesian information criterion. From the results with full samples in Table 6 and 7, more countries exhibit causality from core to headline inflation, which is in addition to the existing list of countries which possess such causality with year-on-year inflation data. Although the joint results from both tables are inconsistent for Chile, Colombia, and Iceland, they show that countries with a higher degree of advancement tend to exhibit the unidirectional causality from core to headline inflation. However, from both information criterion, the bidirectional causality between the headline and core inflation is detected in the United States. In the split samples analysis, it is interesting to note that, both information criterion suggests no causality between core and headline inflation in all countries after the end of 26. This may imply that commodity price shock affects the forecastability from core inflation to headline inflation under higher volatility of month-on-month measurement Lag Length Selected by Bayesian Information Criterion The Bayesian information criterion chooses shorter lag length in both directions of tests as optimal specification using full samples. From the results in Table 8, most countries exhibit causality from core inflation to 11

12 headline inflation over full samples, although the list of countries is slightly different to the other two information criterion. However, with shorter lag length chosen, the causality tests also shows the other direction from headline to core inflation in many countries as well. This, along with the implication of seasonality from the month-on-month calculation, also suggests the pass-through from the transitory to persistent component as seasonal effect. An interesting note can be observed from the split sample analysis that there exists no causality between core and headline inflation after the end of 26; while there is at least one direction of causality with full samples. 2. Implication on Forecasting Inflation and Pass-through of Commodity Prices Based on the forecasting evaluation, Crone et al. (213) find that core inflation measure may not be the best predictor for total inflation, depending on forecasting horizon. Note however that Crone et al. (213) estimates the regression as per Blinder and Reis (2) specification, in which total inflation the regressand is calculated by annualized forecasted percentage change, while the regressor price indices are calculated by year-on-year percentage change, then the mean squared forecast error is obtained. The causality tests in this analysis use the same calculation method on both left and right-hand-side variables; however, I provide the result using both methods. Note however that, along with the indices of interest, Granger causality test involves nested models with lagged total inflation as independent variables as well; therefore, core inflation in Granger causality test cannot be viewed as sole predictor. Using year-on-year calculation and all information criterion discussed, as Granger causality tests do not support the causality from core to headline inflation in some countries, there is no concrete evidence suggesting that core inflation outperforms headline inflation in predicting inflation. Furthermore, including seasonal effect by means of annualized month-on-month calculation does not warrant such causality in all countries, but more countries admit such causality despite being more fluctuating and volatile. Hence, core inflation, as a candidate measure of underlying inflation, is not guaranteed as the best predictor for total inflation for every country. Furthermore, with sufficient degrees of freedom when the lag length specification is selected by Bayesian information criterion, I find that there are more countries which admit such conclusion that core inflation does not predict headline inflation after 26 the start of energy price rally. Comparing to the findings by Crone et al. (213) in the U.S. data, this paper provides similar result in the sense that, an alternative model with core and total inflation does not significantly perform better than baseline model solely with total inflation as the independent variable. This follows that fact that core inflation does not Granger cause headline inflation in both month-on-month and year-on-year U.S. inflation data. The findings of causality from headline inflation to core inflation in various countries also lend support to 12

13 Rhee and Lee (213). There exist pass-through effects from commodity prices to core prices in some Asian countries. Moreover, some advanced economies also possess such pass-through effects as well, particularly with the shorter lag length specification and year-on-year data. Such pass-through effects imply that there exists a transmission from commodity prices to underlying prices when there are shocks to the commodity prices, which may explain the inefficiency in using core inflation as a forecasting measure. 3 The New Keynesian Model and Welfare Cost of Information In this section, the policy implication between core and headline inflation is drawn using a New Keynesian model. The analysis and model are largely based on Aoki (21) literature with the contrast of the preference shock being absent. A brief summary of the model is outlined. The welfare cost of information is defined as the cost of using headline inflation, namely when noisy information of the transitory component of prices is used in the headline inflation. The welfare evaluation under baseline model is first presented, in which, the welfare cost of information on each policy is examined under rational expectation. A potential for variation in inflation expectation as discussed by Hammond (212) is investigated and the results are concluded. 3.1 Summary of Aoki (21) Model Aoki (21) constructs a New Keynesian model where households are divided into two sectors characterized by the market structure of the goods each produces. The two production sectors are the sector with sticky price adjustment (i = s), and the sector with flexible price adjustment (i = f ), in which, each sector is occupied by a unit mass of population. Sticky-price sector produces a continuum of differentiated goods which are sold in monopolistically competitive market and follows staggered price setting. Flexible-price sector produces a single type of standardized good which is sold in a perfectly competitive market, analogous to commodity-type goods of food and energy. Each type of households i = s and i = f lives forever and maximizes expected discounted sum of utility from consumption and production, E t= βt [ u ( C i t) v ( Ai,t y i t)], where u ( ) and v ( ) are utility from consumption and disutility from production, respectively. The supply shocks in each sector are given by A i,t = A s,t and A i,t = A f,t for stickyprice sector and flexible-price sector, respectively. The consumption of each household composes of both types of goods with γ [, 1] fraction in sticky-price good, C s,t, and 1 γ fraction in flexible-price good, ( ) γ ( ) C f,t, given by Ct i Cs,t = i C i 1 γ f,t γ 1 γ. The consumption of sticky-price good CS,t i is constructed from continuum z [, 1] of differentiated goods by CES aggregator with elasticity of substitution θ given by C i S,t = [ 1 ci t (z)(θ 1)/θ dz] θ/(θ 1). The aggregate price level is given bypt = (P s,t ) γ ( P f,t ) 1 γ. Under the 13

14 assumption of complete financial markets, perfect insurance against idiosyncratic shock and identical initial wealth, each household will choose identical consumption plans. Producers in the flexible-price sector are assumed to be price takers setting price equal to marginal cost of production. Producers in the sticky-price sector follow Calvo (1983) staggered price setting with fraction α (, 1) of producers unable to change their prices. Since the mass of population is 2, the market clearing conditions in each sector and total output are Y s,t = 2C s,t, Y f,t = 2C f,t and Y t = 2C t, respectively. Aggregate inflation rate and inflation rate in each sector are defined as Π t = P t /P t 1 and Π i,t = P i,t /P i,t 1, i = s, f, respectively. The headline inflation shall be referred to as Π t. The core inflation is Π s,t. The relative price of each sector is defined by x i,t = P i,t /P t, i = s, f. The utility functions are assumed as u (c) = c 1 σ / (1 σ) and v (y) = y 1+ω / (1 + ω). and The first-order conditions and finer details from the model are omitted from this summary; enthused reader may inquire from Aoki (21). However, the log-linearized system of equations and the specification of productivity shock are relevant to the simulation and analysis; they are presented in the following subsection. 3.2 Log-linearized Equations and the Welfare Function Aoki (21) log-linearizes the system of equations around the steady state with constant prices where all variables are written in percentage deviation from steady state values. The aggregate inflation can be decomposed into the weighted average of inflation in each sector as ˆΠ t = γ ˆΠ s,t + (1 γ) ˆΠ f,t Using the identities of relative price and price level that x s,t = may write the aggregate inflation as ( ) P s,t P s,t 1 P t 1 1 γ, P s,t 1 P t 1 P t and 1 = (x s,t ) γ x f,t one ˆΠ t = ˆΠ s,t + 1 γ γ ( ˆx f,t ˆx f,t 1 ) (1) The dynamic IS equation, where ˆR t is nominal interest rate, can be written as Ŷ = E t Ŷ t+1 σ ( ˆR t E t ˆΠ t+1 ) (2) 14

15 The output of each sector can be written as Ŷ s,t = Ŷ t + 1 γ γ ˆx f,t (3) Ŷ f,t = Ŷ t ˆx f,t (4) The supply equation and supply shock in the flexible-price sector are written as ˆx f,t = κ (Ŷt Ŷ n f,t ) () Ŷ n f,t = 1 + ω 1 σ 1 + ω 1  f,t (6) κ = ω 1 + σ ω 1 The supply equation and supply shock in the sticky-price sector are written as ˆΠ s,t = κ 1 (Ŷt Ŷs,t n ) + βet ˆΠ s,t γ γ κ 2 ˆx f,t (7) Ŷ n s,t = 1 + ω 1 σ 1 + ω 1 Âs,t (8) κ 1 = 1 α α κ 2 = 1 α α (1 αβ) ω 1 + σ θ/ω (1 αβ) ω θ/ω I assume that the productivity shocks in flexible-price and sticky-price sectors follow AR(1) processes of ( )  f,t = φ f  f,t 1 + ε f,t, ε f,t N, σ 2 f ( )  s,t = φ s  s,t 1 + ε s,t, ε s,t N, σs 2 (9) (1) Equations (1) through (1) form the system of equations used in the simulation. The optimal monetary policy maximizes the welfare in the form of ex-ante expected utility [ 1 ) W = E 2u (Y t /2) v (A s,t y s,t (z)) dz v (A ] f,t Y f,t By second-order Taylor approximation around steady state, Aoki (21) shows that the welfare function can 1

16 be written independently from the choice of monetary policy as W = 1 2 u Y (σ 1 + ω 1) { Var ( ) [ )] 2 } Ĝ t + E (Ĝt 1 ( 2 u Y ω 1 + 1) { ( ) [ ( )] } 2 Var ˆx f,t ˆx f,t + E ˆx f,t ˆx f,t 1 ( 2 γu Y θ 1 + ω 1) α {Var ( ) [ ( )] } 2 ˆΠ (1 α) 2 s,t + E ˆΠ s,t (11) where u and Y are steady state value of marginal utility of consumption and total output. The welfare function in (11) is expressed as the percentage of permanent decrease in consumption from steady state level of consumption. The aggregate output gap and the relationship between relative output and relative price are defined as Ĝ t = γ ( ) Ŷ t Ŷs,t) n + (1 γ) (Ŷt Ŷf n,t ) ˆx f,t = γκ (Ŷn s,t Ŷf n,t The welfare function in equation (11) implies that the stabilization of aggregate output gap, core inflation and the deviation of the relative price from its efficient value are relevant to social welfare. Furthermore, it is also shown that the welfare function can be written as W = λ 1 Var ( ˆΠ s,t βe t ˆΠ s,t+1 ) λ2 Var ( ˆΠ s,t ) λ3 [ E ( ˆΠ s,t )] 2 (12) where λ 1, λ 2 and λ 3 depend on parameters γ, ω, σ, α, θ, κ, κ 1 and steady state values of u and Y. Hence, the welfare function written as (12) implies that the theoretically maximum welfare is attained at W = when ˆΠ s,t = for all t, i.e. a policy in which core inflation is completely stabilized. 3.3 Methodology and Parameterization The parameters from the model as outlined in Section 3.1 and 3.2 are first calibrated with the quarterlyperiod model. The baseline evaluation is made on the assumption that households have the rational expectation of inflation. The vital point of departure in this analysis is the different consumption basket weight on food and energy (1 γ) between advanced and emerging economies. This owes to the fact that households in advanced and emerging economies have different expenditure shares on commodities. The comparison of welfare under complete stabilization policies is made using core inflation and headline inflation, ˆΠ s,t = and ˆΠ f,t = for all t, respectively. The monetary policy is then restricted to Taylor-type policy rules. The 16

17 welfare, W, as outlined in (11) is evaluated under Taylor rules with different types of inflation measures, contemporaneity and forward-looking of inflation, and different weights on inflation and output gap, Ŷ t. Note that the welfare computed is presented with negative sign removed; thus, the percentage presented implies the permanent consumption decrease from steady state level of consumption. The welfare cost of information is defined as the percentage decrease in consumption equivalence compared to the steady state level of consumption as richer but noisier information of headline inflation is used to communicate to the public and adjust the monetary policy via Taylor rules. I then present variations in inflation expectation in the later subsection, in which households do not have the rational expectation of inflation. This inflation expectation is reflected in the model in equation (2), the Euler behavioral equation. With this deviation, the welfare function is discussed under different Taylor rules. The following parameters are selected to those commonly found in most of the business cycle and New Keynesian literature. They are held constant throughout the analysis between advanced and emerging economies. The discount factor is selected as β =.99, corresponding to the annualized real return on assets of 4 percent. The coefficient of risk aversion is chosen as σ = 2. The Frisch elasticity of labor supply is chosen as ω = 3. The elasticity of substitution between differentiated goods is selected as θ = 1. Anand and Prasad (21) conclude from micro-evidence and previous literature that the probability that sellers cannot change price is identical in both advanced and emerging economies; hence, it is chosen as α = 2/3. The steady state labor supply is chosen as.38 for hours of labor in both sectors of production. The expenditure shares of commodity goods are of the interest in this analysis. Following the calculation by Anand and Prasad (21) that the average shares of food expenditure in advanced and emerging economies are 1% and 4%, respectively. This is also supported by the findings of Harris et al. (29) that the U.S. household expenditure on energy accounts for about 7%. Hence, it is sensible to set γ =.9 and γ =. for advanced and emerging economies, respectively. The interest rate coefficients for Taylor rules in both advanced and emerging economies are assumed as ψ π = 1. and ψ y =./4, namely, the weights on inflation and quarterly output gap are 1. and./4, respectively. The autoregressive persistence parameters of productivity shocks in flexible-price sector and sticky-price sector are φ f =.2 and φ s =.9, respectively. The standard deviations of innovation in the flexible-price sector and sticky-price sector are σ f =.3 and σ s =.2, respectively. 3.4 Baseline Evaluation of Policies under Core and Headline Inflation Having parameterized the model, the welfare resulting from each type of monetary policies can be analyzed in the different settings of expenditure shares in the flexible-price sector. As a preliminary analysis, the 17

18 Table 9: Welfare computed from instrument policies in the baseline model Instrument Policy γ =.9 γ =. ˆΠ t =, for all t.4487%.3661% ˆΠ s,t =, for all t.%.% instrument policies are evaluated where monetary policymaker strictly adhere to complete stabilization of headline and core inflation, i.e. when the policies are ˆΠ t = and ˆΠ s,t =, for all t. Then various policies in the class of Taylor-type rules are analyzed. Welfare calculations under calibrated parameters and Taylor rules with fixed weights are presented. This section ends with the welfare equivalency analysis where, given the benchmark welfare of Taylor rule with only contemporaneous core inflation, the weight on inflation in each type of Taylor rule is obtained to equate the welfare to benchmark Taylor rule Instrument Policies Table 9 shows the welfare computed from the instrument policies of ˆΠ t = headline inflation targeting, and ˆΠ s,t = core inflation targeting under different consumption basket weights of γ =.9 advanced economies, and γ =. emerging economies. Note that under this regime, the monetary policy is to set inflation rate equal to zero in all period regardless of the output gap. It can be observed that, as theorized by the model, headline inflation targeting is welfare inferior to core inflation targeting in both cases of advanced and emerging economies. Since the welfare function admits only core inflation as shown in Section 3.2, it can be conjectured that strict core inflation targeting is the optimal policy. Although the welfare loss from using headline inflation as the target is small. Furthermore, simulation results in Table 1 also show that the outcome of strict core inflation targeting can be replicated using Taylor rule where core inflation is used as the measurement and sufficiently large coefficient on inflation rate is placed. Table 1: Welfare computed using contemporaneous Taylor rule with strict core inflation target in the baseline model ψ π (Taylor Rule: ˆR t = ψ π ˆΠ s,t + v t ) γ =.9 γ = %.66%.9%.1% 2.1%.3% 1.%.% Taylor Rule Policies in the Baseline Model Table 11 shows the welfare computed under the baseline model when the policies are Taylor rules with the 18

19 Table 11: Welfare computed from contemporaneous Taylor rules in the baseline model Taylor Rule (ψ π = 1., ψ y =./4) γ =.9 γ =. ˆR t = ψ π ˆΠ s,t (Benchmark).26%.66% ˆR t = ψ π ˆΠ t.616%.2424% ˆR t = ψ π ˆΠ t + ψ y Ŷ t.646%.3722% ˆR t = ψ π ˆΠ s,t + ψ y Ŷ t.444%.386% ˆR t = ψ π ˆΠ s,t + ψ y Ŷ s,t.483%.74% Table 12: Welfare computed from forward-looking Taylor rules in the baseline model Taylor Rule (ψ π = 1., ψ y =./4) γ =.9 γ =. ˆR t = ψ π ˆΠ s,t (Benchmark).26%.66% ˆR t = ψ π E t ˆΠ s,t+1.327%.78% ˆR t = ψ π E t ˆΠ t+1.627% 3.842% ˆR t = ψ π E t ˆΠ t+1 + ψ y Ŷ t.761% 1.833% ˆR t = ψ π E t ˆΠ s,t+1 + ψ y Ŷ t.288%.44% ˆR t = ψ π E t ˆΠ s,t+1 + ψ y Ŷ s,t.74%.796% ˆR t = ψ π E t ˆΠ t+1 + ψ y E t Ŷ t+1.724% 3.11% ˆR t = ψ π E t ˆΠ s,t+1 + ψ y E t Ŷ t+1.499%.423% ˆR t = ψ π E t ˆΠ s,t+1 + ψ y E t Ŷ s,t+1.38%.76% contemporaneous inflation rate. The coefficients in Taylor rules are parameterized as in Section 3.3 in all cases. The first two rows of Table 11 correspond to the Taylor rules where only inflation rates are measured, core and headline inflation, respectively. Within the last three rows of Table 11 where output gap is used, the first two rows are Taylor rules with total output gap added, the last row with core output gap added. It can be observed that, in each class of Taylor rules and regardless of the expenditure shares on the flexible-price goods, the consumption decrease is lower when core inflation is used as the measure in adjusting monetary policy. Hence, the welfare under core inflation targeting policy is higher. Furthermore, the last two rows of Table 11 also confirm the finding by Aoki (21) that aggregate output gap is the relevant policy variable, as the welfare when core output gap is used is lower than using total output gap. Table 12 shows identical welfare results when inflation rates in the Taylor rules are forward-looking that core inflation targeting provides higher welfare. However, note from the first two rows of Table 12 that, although using expected core inflation results in the highest welfare within the class of forward-looking Taylor rules, the welfare is still lower than the benchmark case of using the contemporaneous core inflation. In all analysis, however, it is shown that although the welfare under core inflation targeting is higher than headline inflation targeting in all cases, the difference in welfare when headline inflation is used as the target instead is minimal. Hence, it can be concluded that the welfare cost of information using headline inflation in communicating the policy is low. Having established the use of core inflation as the sole instrument in the benchmark Taylor rule under the 19

20 Table 13: Policy equivalence of contemporaneous Taylor rules to the benchmark of core inflation targeting in the baseline model γ =.9 γ =. Contemporaneous Taylor Rule (ψ y =./4) ˆR t = ψ π ˆΠ s,t + v t (Benchmark) ˆR t = ψ π ˆΠ t + v t Cannot match Cannot match ˆR t = ψ π ˆΠ t + ψ y Ŷ t + v t Cannot match Cannot match ˆR t = ψ π ˆΠ s,t + ψ y Ŷ t + v t ˆR t = ψ π ˆΠ s,t + ψ y Ŷ s,t + v t ψ π ψ π Table 14: Policy equivalence of forward-looking Taylor rules to the benchmark of core inflation targeting in the baseline model γ =.9 γ =. Forward-looking Taylor Rule (ψ y =./4) ˆR t = ψ π ˆΠ s,t + v t (Benchmark) ˆR t = ψ π E t ˆΠ s,t+1 + v t ˆR t = ψ π E t ˆΠ t+1 + v t Cannot match Cannot match ˆR t = ψ π E t ˆΠ t+1 + ψ y Ŷ t + v t Cannot match Cannot match ˆR t = ψ π E t ˆΠ s,t+1 + ψ y Ŷ t + v t ˆR t = ψ π E t ˆΠ s,t+1 + ψ y Ŷ s,t + v t ˆR t = ψ π E t ˆΠ t+1 + ψ y E t Ŷ t+1 + v t Cannot match Cannot match ˆR t = ψ π E t ˆΠ s,t+1 + ψ y E t Ŷ t+1 + v t ˆR t = ψ π E t ˆΠ s,t+1 + ψ y E t Ŷ s,t+1 + v t 4.6 ψ π ψ π baseline model, the analysis of Taylor rules continues with the question whether or not the welfare under benchmark Taylor rule could be replicated with other Taylor rules. Fixing the coefficient on output gap in Taylor rules at ψ y =./4, Table 13 and 14 report the coefficients on inflation rate required for other Taylor rules, contemporaneous and forward-looking, to achieve the same welfare as the benchmark rule. Note that the simulation cannot match the welfare from benchmark Taylor rule when headline inflation is used as the instrument; thus, no coefficient on inflation rate under headline inflation targeting can replicate the welfare of the benchmark case. In all cases of core inflation in the Taylor rules, it can be observed that, if the output gap is added as an instrument, the coefficient of inflation needs to be higher in order to match the welfare under benchmark rule. Hence, with output gap in the Taylor rule, the monetary policy must be more vigilant on core inflation. Note however that with forward-looking Taylor rules when expected core inflation is used as the instrument, the coefficient of inflation also needs to be higher as well. This implies that monetary policy must also be more vigilant on inflation when the expected inflation is used instead of 2

21 current inflation. 3. Variation in Inflation Expectation In this section, the inflation expectation in the intertemporal Euler equation is considered. Recall from dynamic IS equation in (2) given by Ŷ t = E t Ŷ t+1 σ ( ) ˆR t E t ˆΠ t+1 and note that inflation rate is written as the weighted average of inflation in sticky-price and flexible-price sectors ˆΠ t = γ ˆΠ s,t + (1 γ) ˆΠ f,t. It is assumed that households rationally and correctly expect the total inflation in the next period given current information, E t ˆΠ t+1. Hence, under correct expectation, the expected inflation can be written as E t ˆΠ t+1 = γe t ˆΠ s,t+1 + (1 γ) E t ˆΠ f,t+1. I consider two possible cases of variation where households incorrectly or adaptively form the expectation of inflation Incorrect Expectation of Inflation Since the inflation ˆΠ t composes of inflation from the sticky-price sector, ˆΠ s,t and from the flexible-price sector, ˆΠ f,t with the appropriate factors of γ and 1 γ according to consumption expenditures, respectively. In other words, inflation comes from two sources of non-commodity core inflation and commodity inflation from food and energy. Suppose households incorrectly perceive inflation so that households place λ [, 1] fraction of inflation arisen from commodity flexible prices and 1 λ from non-commodity sticky prices. Define the perceived inflation rate as ˆΠ p t = λ ˆΠ f,t + (1 λ) ˆΠ s,t, the incorrect expected inflation can be written as E t ˆΠ p t+1 = λe t ˆΠ f,t+1 + (1 λ) E t ˆΠ s,t+1 (13) Note that if λ = 1 γ, the perceived inflation is identical to actual inflation. Note that the dynamic IS equation with incorrect expectation of inflation as in (13) becomes Ŷ t = E t Ŷ t+1 σ ( ˆR t E t ˆΠ p t+1 ) (14) Equation (14) replaces (2) in the simulation; thus, households decision now depends on perceived expected inflation. However, the actual inflation rate still follows the definition of inflation. Furthermore, since the welfare function as outlined in (11) and (12) does not admit aggregate inflation rate, the welfare can be calculated using identical formulation. 21