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ISSN 1561-2422 MODELLING CORE INFLATION IN UKRAINE IN 2003-2012 Natalia Novikova, Dmitry Volkov Working paper No 12/12E This project (No R105792) was supported by the Economics Education and Research Consortium and funded by GDN All opinions expressed here are those of the authors and not those of the EERC, GDN and Government of Sweden Research dissemination by the EERC may include views on policy, but the EERC itself takes no institutional policy positions 1 Abstract High volatility of Ukrainian inflation can partially be explained by large share of food and energy. The structure of Ukrainian CPI basket makes it difficult to distinguish between the underlining and temporary changes in inflation, which complicates the reaction of monetary policy. In this study we consider different measures of consumer price growth and examine moving to core inflation as an intermediate target for NBU monetary policy. We employ VEC framework to explore the difference between reaction of headline and core inflation to macro fundamentals in 2003-2012. Two approaches - exclusion-based method and trimmed mean – are used to construct alternative core indices. Although our estimation results do not allow making unambiguous choice of the inflation target for monetary policy in Ukraine, they suggest that core inflation should be monitored and used in communicating monetary policy decisions. We found that both headline and core inflation have high degree of persistence, fit well within the mark-up model, and that exchange rate pass-through is high in both cases. Meanwhile, core indices could help distinguish shocks coming from regulated prices and nominal wages. Key words: inflation modelling, Ukraine, mark-up, core inflation, monetary policy JEL Code: E31, E41, E52 Authors Natalia Novikova, Lecturer and Research fellow, National Research University Higher School of Economics, tel: +74957729590 *26128, email: [email protected] Dmitry Volkov, MSc, Imperial College London, UK, email: [email protected] Acknowledgements We would like to thank Gary Krueger, Elina Ribakova, Olga Ponomarenko, Robert Kirchner and the participants of the EERC Research Workshops for providing valuable advice. 2 Contents 1. Introduction .................................................................................................................................4 2. The evolution of inflation in Ukraine in 2003-2012 ...................................................................6 3. Determinants of price growth and inflation models ....................................................................7 4. The choice of core inflation measures.......................................................................................11 5. Data............................................................................................................................................15 6. Estimation results ......................................................................................................................17 7. Discussion of the results and policy implications .....................................................................23 Appendix 1. Major trends in inflation in Ukraine in 2002 - 2011.................................................26 Appendix 2. Structure of CPI basket in Ukraine, %......................................................................30 Appendix 3. Previous studies on headline inflation in Ukraine ....................................................31 Appendix 4. Core inflation indices................................................................................................32 Appendix 5. Data...........................................................................................................................34 Appendix 6. Impulse response functions and variance decomposition.........................................36 References .....................................................................................................................................38 3 1. Introduction Swings of Ukrainian consumer price inflation reached thirty percentage points over the last decade. Annual inflation accelerated from zero in 2002 to 31% in the middle of 2008, and fell to negative zone in the middle of 2012. High volatility is one of the features of Ukrainian inflation, which can partially be explained by high share of food and energy - together they account for about 60% of the CPI basket. The structure of Ukrainian CPI basket makes it difficult to distinguish between the underlining and temporary changes in inflation, which complicates the reaction of monetary policy. High variability of price movements and large share of items subject to external shocks can result in bias towards higher inflation. When developments in inflation are strongly influenced by a small number of large changes in a few CPI components, the risk exists that the aggregate measure of inflation deviates significantly from the underlining trend (Ball and Mankiw (1994), Pujol and Giffiths (1998)). Given that monetary policy affects inflation with a lag, reacting to changes of headline inflation could lead to larger output volatility. Therefore, in order to provide adequate monetary response policymakers need to distinguish between the acceleration of inflation due to, for example, indexation of stateregulated prices and second-round effects of such changes or changes in inflation due to factors under the influence of the monetary policy. Core inflation indices excluding most volatile and administratively controlled items of the consumer basket could be used as a measure of general inflationary pressure in the economy. And therefore core measured are sometimes viewed as a more appropriate indicator of inflation for the purpose of monetary policy. Core inflation indicators can also be used to explain policy decisions to the public and minimize risks of sharp changes in inflation expectations in response to temporary price shocks. In 2008 the National bank of Ukraine (NBU) started publishing core inflation excluding utilities and unprocessed food; however the headline inflation of about 5% in the medium term 4 remained an ultimate goal of the monetary policy as stated in the Memorandum of economic and financial policy. In this study we consider different measures of consumer price growth and examine if moving to core inflation as an intermediate target is beneficial to monetary policy in Ukraine. Two approaches - exclusion-based method and trimmed mean – are employed to construct alternative core indices and analyse the underlining inflation in 2003-2012. We employ VAR/VEC framework to explore the difference in reaction to macro fundamentals between headline and core inflation and to test if using core indicators can improve monetary policy over headline inflation. Although our estimation results do not allow making unambiguous choice of the inflation target for monetary policy in Ukraine, they suggest that core inflation should be monitored and used in communicating monetary policy decisions. In line with earlier studies, we found that headline inflation has high degree of persistence and fits well with the mark-up model. Core CPI was found to have similar to headline drivers. However our estimates confirmed that shocks coming from regulated changes in state-regulated relative prices (such as utilities) have little effect on the core inflation and therefore core indices could help distinguish these shocks. Also core inflation appeared to react faster to growth in nominal wages, and in this case could be used as a forward-looking indicator. The paper is structured as follows. We start with an overview of major trends in the Ukrainian inflation over the last decade. Section 2 discusses the determinants of inflation in emerging market economies and provides an overview of econometric approaches to modeling and forecasting inflation. It also takes a closer look at particular features of the Ukrainian inflationary process revealed by previous research. The choice of core inflation indicators is described in Section 3. Sections 4 and 5 provide data description and summary of estimation results. We conclude with policy implications in Section 6. 5 2. The evolution of inflation in Ukraine in 2003-2012 Ukrainian consumer price inflation fluctuated from zero to 30% since early 2000s (Figures A1-A2), and in most of periods stayed above the level of peer countries. Consumer prices decelerated sharply in 2001–2002 as a result of tight monetary policy and structural reforms in the previous years (Aslund (2009)). But inflation returned to the upward trend in 2003-2008 driven by pick up of the economic activity, credit growth and unfavorable shocks to energy and food prices (Table А1). In addition to that liberalization of the banking sector in 2004-2006 helped acceleration of the money supply to 60-70%YoY or three times faster than growth in nominal spending. In 2007-2008 nominal GDP growth accelerated to around 30% with average real growth of household consumption of about 12% pa. On this background Ukraine faced major commodity price shocks in 2005-2010: the price of natural gas imported by Ukraine more than doubled over the period 2005-2007 and then increased by another 30% in 2009-2011. In addition to that, in the beginning of 2007 and in the end of 2010 food prices have risen along with global food prices, the effect of which was magnified in Ukraine by a contraction of agriculture production due to unfavorable climatic conditions. While inflation was gradually accelerating in 2003-2008 the NBU continued to peg UAH/USD exchange rate and was smoothing hryvnia appreciation during that period. From the end of 2001 till mid-2008 the cumulative appreciation of the nominal effective exchange rate (NEER) reached about 20%. Accumulation of FX reserves was the major contributor to base money growth over that period (Figure A3). Consumer price growth increased sharply during 2008 and peaked at just below 30% as a result of growing inflation expectations, worries of hryvnia depreciation and fall in money demand. The financial crises led to sharp drop in export volumes and capital inflow, which resulted in slump of the economy and widening output gap. In 2009 GDP and private consumption fell more than 15% in real terms. Bank lending activity stalled and broad money growth turned negative. As a result despite sharp hryvnia depreciation inflation declined fast and 6 stood at around 12% in the end of 2009. At the same time as a part of bank recapitalization program the holdings of government bonds by NBU started to grow rapidly and became the major source of money base growth. In 2008 the National Bank of Ukraine started to publish core inflation indicator, which excludes raw food, energy and administratively regulated prices and covers about 55% of the CPI (see Appendix 2 for detailed structure of the Ukrainian CPI). According to this measure average core inflation in 2009 was above the growth of headline CPI (19.4%YoY and 15.9%YoY), probably suggesting the need for tighter monetary policy. A few external shocks kept the CPI inflation close to 10% in 2010 – spike in the global food prices, as well as hikes in gas tariffs and excise taxes. Disinflation continued once the effect of these shocks was absorbed and the central bank started to tighten monetary policy. Headline CPI inflation in Ukraine has decelerated to less than 5%YoY in 2011 and fell below zero in 1H 2012 as tight monetary policy was supported by lack of adjustment in administrative tariffs and falling global food prices. Meanwhile core inflation appeared to be more resistant and remained close to 8% in 2011 and 3-4% in the mid of 2012. 3. Determinants of price growth and inflation models The scope of traditional approaches used for modelling inflation processes is dominated by three major theories. The mark-up theory assumes that prices are set as the sum of the cost of all production inputs and a fixed mark-up which covers fixed costs and profits. The set of items to include into the mark-up is rather flexible with the intention to capture all the causality channels influencing the price level — exchange rate, labour costs, import prices, energy costs. According to the monetary theory, the change in monetary aggregate is the only factor determining the rate of inflation. In addition to the direct effect of the increase in monetary aggregate, monetary theory predicts that it is the excess supply of money that accelerates inflation. To model the “excess” supply one needs to estimate money demand and money supply simultaneously. The resulting “monetary overhang” is usually incorporated into the inflation 7 equation. Phillips curve models explain the inflation rate in the short run, or over the course of the business cycle, as being determined by three main variables—economic activity in the economy (e.g. output gap or unemployment), When there is a negative output gap (or a high unemployment rate), there is downward pressure on prices (and wage demands are lower), then the inflation-rate tends to fall. While conventional determinants of inflation, such as the output gap, excess money supply and labor costs were shown to have significant influence on consumer price growth in emerging markets (Mohanty and Klau (1999)), a few features of inflationary process should be considered in modelling inflation in such economies. First, inflation inertia is a key feature of inflationary process. It could be a result of backward-looking inflation expectations, indexation of wages or adjustment of relative prices (Rossi (2005)). Moriyama (2011) also looked at the role of fiscal dominance and output volatility in inflation persistence. Second, the exchange rate pass through is usually higher in emerging market economies than in advanced economies. While some studies showed that inflation could be lower under pegged exchange rate regimes (Ghosh et all (1997)), Mann (1986) argued that low exchange rate volatility likely to result in higher exchange rate pass through, as importers would prefer to alter prices rather than to adjust profit margins in case of rare changes in the exchange rate. On the other hand, analysis by McCarty (1999) also implied that lack of competitiveness could be associated with higher response of prices to changes in the exchange rate probably because in less competitive environment importers face little pressure to adjust profit margins. Third, changes in relative prices - particularly those arising from large supply shocks, or adjustment of the administrated prices are an important factor of inflation in many emerging market economies (Cotarelli, Griffiths and Maghadam (1998)). Relative price adjustments can drive inflation irrespective of whether these are accompanied by money supply growth. At that the size of the overall impact of the shock depends on the importance of the sector for the overall consumer inflation (Fisher (1981)). 8 Forth, instability of money demand is also a common feature of economies in transition as institutional reforms, development of the financial sector, emergence of new types of financial assets affect money-price relationship (Jonas and Mishkin (2003)). In this case inflation forecasting based on money growth and monetary policy relying solely on targeting money supply become ineffective. Vector autoregressive models and factor models are two competitive econometric approaches that are most often used to analyse the effect of the abovementioned factors and to build inflation forecasts. Under VAR/VEC framework inflation and major macroeconomic factors are treated as endogenous variables being functions of the lagged values of all endogenous variables and exogenous variables in some cases. In VEC it is also expected that non-stationary expected to converge to some co-integrating relationship in the long run. The deviation from the long-run equilibrium is corrected gradually through a series of partial shortrun adjustments. The forecast is derived as a one-step ahead forecast. Factor models are based on the assumption that the behaviour of most macroeconomic variables can be well described by several unobservable factors, which are often interpreted as the driving factors in the economy (Stock & Watson (1998)). An approximate dynamic factor model serves as the statistical framework for the estimation of the indexes and construction of the forecasts. In factor models the forecast at moment t+h determined directly on the basis of information available in period t. While the use of wide range of indicators could help to improve the accuracy of forecasts derived from factor models as compared to VAR (Stock & Watson (2002), Kotlowski (2008), Cristadoro et all (2008)), VAR/VEC models provide good framework for analyses of interrelations between different variables as well as to look at different causality channels. Previous studies on Ukraine considered headline inflation in 1993-2008 under VAR/VEC framework (Lissovolik (2003), Leheyda (2005), and Kirchner, Weber and Giucci (2008), Siliverstov and Bilan (2005)) or as a part of cross country studies (Korhonen and Wachtel (2005)), Agayev (2009) and Cotarelli, Griffiths and Maghadam (1998)). They showed that Ukrainian inflation had large degree of persistence and was well described by the mark-up 9 model. Rossi (2005) also showed that Ukraine, together with Russia, Poland and Romania, had the highest inflation persistence among the CEE countries in 2002-2005. Nominal wages and exchange rate were found to have strong effect on inflation (summary of pass-through coefficients are provided in Appendix 3). However the difference between earlier studies lies in the choice of specific indicators to estimate the effect of macroeconomic factors on inflation. Lissovolik(2003) in the mark-up for Ukraine included the wages, exchange rate and paid services as a proxy for administered prices. Kirchner, Weber and Giucci (2008), Siliverstov and Bilan (2005) also used nominal wages but included commodity price index as a measure of energy costs. Meanwhile introduction of unit labour costs instead of nominal wages in the mark-up equation is also common (De Brouwer and Ericsson (1998) in the case of Australia, Oomes and Ohnsorge (2005) in the case of Russia) and allows taking into account change in productivity. Exchange rate pass-through coefficients, while being large compared to other economies, differ significantly depending on the period of analysis and the measure of the exchange rate – hryvnia’s exchange rates vis-à-vis US dollar and Euro, and nominal effective exchange rate, expected rate of devaluation. Studies on of the link between inflation and the growth of monetary aggregates came to varying conclusions depending on the period under consideration. Ukrainian inflation did not confirm the presence except. Lissovolik (2003) stated that the relationship existed during hyperinflation in 1993-1996, but no long-term relationship between money and inflation could be identified in 1996-2002. However, he noted that the linkage similar to the one observed in 1993-1996 could re-established later. No evidence was found that the excess money supply affects inflation was found by Leheyda (2005). At the same time, Kirchner, Weber, Giucci (2008), who analyzed headline inflation in 1999-2008, found that both M1 and M3 have significant impact on inflation with a lag of about 4-6 month. Output gap model in the case of Ukraine was tested by Kirchner, Weber and Giucci (2008), who found cointegration relationship between inflation and unemployment and revealed strong negative effect of unemployment on inflation. 10 In this study we would like to explore the influence of macroeconomic factors on both headline and core inflation. Similar to previous researches we employ VAR/VEC framework which allows taking into account different causality channels and interrelations between macroeconomic variables. We focus on the mark-up model and assume that in the long-run the level of inflation is defined by the equation below: Inflation = f(growth of labor costs, depreciation of the exchange rate, inflation of utilities/energy prices, mark-up), (1) where depreciation of the exchange rate is used as a proxy for inflation of imported goods and the growth of utilities index is a proxy for internal state regulated energy and utilities costs. In the short run, consumer price growth could also be growth affected by the exogenous shocks, for example monetary shocks (excess money supply) or shocks coming from commodity prices (like food and energy) that are determined on the global markets and have little influence from the local inflation. We would like to test whether there is significant difference in the reaction of headline and core inflation measured to various shocks. Lower dependence on regulated prices or exogenous shocks, as well as stronger/shorter links from monetary aggregates would support the idea of using core inflation as an intermediate target for monetary policy. The choice of core inflation indicator is discussed below. Description of alternative indicator tested as macroeconomic factors is provided in Section 5. 4. The choice of core inflation measures Core inflation indices measuring general inflationary pressure in the economy are sometimes viewed as a more appropriate indicator of inflation for the purpose of monetary policy. Widely used definitions of core inflation consists of measures that exclude certain components on a period-by-period basis (exclusion based core inflation, trimmed mean methods) 11 and measures that downplay the more volatile components (variance-weighted core inflaiton)1. The choice of core inflation indicator is determined by a number of desired properties (Roger (1997), Wynne (1999)). Core inflation indicators should be (i) significantly less volatile than headline inflation; (ii) available on a timely basis; (iii) unbiased, in the sense that the difference between the historical average of headline and core measure should be small; and (iv) easily reproducible; (v) understandable by the public; (vii) not be subject to major revisions; (viii) be forward-looking, in the sense of helping to project inflation developments. To construct core inflation indices for the purpose of this study we employ two approaches - exclusion-based method and trimmed mean. These approaches were found to perform well on a wide range of criteria in the Ukrainian case (Moulin (2008) and Jakubiak et all (2005)). Since 2008 the National Bank of Ukraine officially publishes core inflation indicator, which excludes raw food, energy and administratively regulated prices and covers about 56% of the CPI. At the same time, studies for the US, Australia and Ukraine showed that trimmed mean measured core inflation indicators tend to be more consistent in terms of Granger causality and average inflation forecast. Our exclusion-based core inflation index (CORE) covers approximately 59% of the CPI basket. We applied approach similar to the one used by the NBU, and excluded items with administratively regulated prices (utilities, energy and petrol etc.) and unprocessed food (Appendix 4). Two measures of trimmed mean inflation were constructed using standard deviation and fixed weights approaches. The CPI index was split into 48 items with average weight of about 2%. According to standard deviation approach we excluded those items, which had monthly growth rates certain number of standard deviations above or below from the average across items in each month. Under fixed weight approach a certain percentage of weights from each tail of the distribution of monthly growth rates were dropped. In both cases the trimming parameters were allowed to be asymmetric. 1 For overview of approaches to measure core inflation see Silver (2006), and Bermingham (2006) 12 A set of core inflation indices were ranked using following criteria (Bryan and Checchetti (1994); Hogan et all (2001)): • deviation from the trend measured with root mean squared error (RMSE) and mean absolute deviation (MAD); • stability criteria, suggesting lower volatility for core inflation as compared to headline and measured by standard deviation. • and unbiasness with respect to the CPI, which requires that core inflation should be an unbiased predictor of headline inflation over 9-18 months2. We chose two trimmed mean measures of core inflation. One excluding items with monthly growth rates above (or below) 0.3 (0.4) standard deviations for each month (TRIMSD). And the second, based on fixed weights approach excluding 11% from the left tail and 14% from the right tail (TRIMFW). Figures A4-A5 (Appendix 1) and Table 3 below provide comparison of different inflation measures. Except for TRIMFW, core inflation measures appeared to provide worse estimate of the average inflation in 12-18 months than the headline. But our trimmed core inflation indices appear to provide a better indication of underlining inflation than the official NBU core measure. None of the year-over-year core inflation indicators (including the one used by the NBU) passed the unbiasedness test described above for headline inflation forecasts ranging from 6 to 18 month. However, the hypothesis of unbiasedness was confirmed for month-over-month inflation rates. 2 This could be tested by the following regression (Hogan et all (2001)): CPI t + h − CPI t = α + β (COREt − CPI t ) + ξt + h , where CPI t + h is the h-months ahead headline inflation, CPI t is current rate of headline inflation, and CORE t denotes current rate of core inflation. If α = 0 and β = 1 the current core inflation is an unbiased predictor of future headline inflation. 13 TABLE 3. Summary statistics for inflation measures (2004-2011) Inflation index, YoY Headline Weight, % of headline CPI* Mean Max Min Standard deviation Correlation with headline inflation Deviation from n-month centered moving average of headline inflation MAD RMSE N=8 12 18 8 12 18 100% 12.0 31.1 0.9 6.1 1.0 1.0 1.4 1.7 1.4 1.8 2.3 59% 10.9 27.3 0.3 6.1 0.93 2.2 2.4 2.7 2.8 3.0 3.4 Trimmed mean (standard deviation) 57% 11.4 27.6 1.1 5.6 0.95 1.6 1.8 2.2 2.5 Trimmed mean (fixed weights) 75% 12.1 28.0 1.5 5.7 0.94 0.9 2.2 1.8 2.7 NBU core** 56% 12.2 23.6 7.0 6.0 0.91 2.2 2.3 2.6 2.6 Exclusionbased (this study) 2.1 2.6 Source: authors’ calculations. *) Average across periods for trimmed mean measures. **) For 2008-2011 Granger tests of causality between core inflation measures and headline CPI also gave mixed results. We found that there is either bi-directional Granger causality between our core inflation measures and headline or causality from core to headline (as expected) depending on the time span and inclusion of producer price index (PPI). TABLE 4. Granger test summary (2 variable VAR, 12 lags, 2004M01—2012M03) from/to Exclusion based core inflation (this study) Trimmed mean (fixed weights) Trimmed mean (standard deviation) to YES NO YES from NO NO YES Headline CPI Lack of stability in causality between core and headline measures is consistent with historical patterns. This could indicate high speed of transmission of inflation expectations into core inflation or suggest there are second round effects to core from headline to exclusion-based 14 core inflation. Possible reasons: (1) too wide definition of core inflation; (2) high speed of transmission of inflation expectations into core inflation as a result of accommodative monetary policy, lack of confidence or flexible prices. Similar phenomenon (wrong/unstable Granger causality between core inflation measures based on exclusion method and headline inflation) was found in other countries as well (for example in the US, Turkey, Australia). In case of the US, Mehra and Reilly (2009) showed that the speed and direction of adjustment between core and headline inflation appear to depend on the monetary regime. They found that the gap between core and headline measures closed mainly through adjustment of core, when monetary policy was accommodating shocks to inflation. Unfortunately, due to the lack of long data series for Ukraine it is impossible to look at periods with different monetary regimes to check if Mehra’s hypothesis is true for Ukraine as well. 5. Data We use data series from Jan 2003 to March 2012 which allows us to get about 90-100 observations in terms of year-on-year growth rates. The list of variables and acronyms used in the estimation results tables, as well as summary of Augmented Dickey-Fuller test statistics are provided in Appendix 4. Inflation rates are calculated as year-on-year growth rates of the headline CPI index (CPI), Producer Price Index (PPI) and the core inflation indices (CORE, TRIMSD and TRIMFW) defined above. All YoY inflation series were found to be nonstationary and integrated of order 1. This result does not look unusual and is consistent with previous studies of inflation in Ukraine as well as other emerging markets (Mohanty and Klau (1998), Onsorger and Oomes (2005).) Month-over-months growth rates were found to be I(0) process, which again is consistent with other studies. However we stick to usage of YoY growth rates, which are consistent with the definition of the monetary policy target set by the National Bank of Ukraine, more appropriate indicator for long-term equations, and also allow avoiding introduction of additional variables to capture seasonality. 15 Two indicators of labor costs are considered: (1) YoY growth of nominal wages (WAGE) and (2) YoY growth of unit labor cost index (ULC, which is as a linear combination of year-on-year growth rates of the nominal wage (WAGE), industrial production index (IP), and the number of employed. Owing to data limitations number of employed is calculated using monthly data on unemployment rate and average annual number of employed. The growth of exchange rate is commonly used if there is no reliable data on inflation of imported goods. Two indicators are tested in this study hryvnia exchange rate vis-à-vis the US dollar (USD = hryvnias for 1 USD) and the nominal effective exchange rate (NEER). The use of USD/UAH exchange rate could be justified by significant dollarization of the Ukrainian economy and the fact that NBU uses it as a nominal anchor. At the same time, growing trade Europe and work migration between Europe/Russia and Ukraine suggest that Euro and Ruble should also be taken into account. Therefore NEER could appear to be relevant indicator (Korhonen and Wachtel (2005), Kirchner, Weber and Giucci (2008)). As a proxy for state regulated prices and energy costs we chose utilities index, being about 8% of the CPI basket. Utilities index includes such items like housing costs, water supply, gas, electricity and fuels other than petrol. Most of these prices are set/controlled at the state or local levels. Their indexation is often driven by political events and was not always linked to general inflation level. Output gap (GAP) is approximated using Hodrick-Prescott filter from monthly series of industrial production (seasonally adjusted using X12 procedure) as a percentage deviation from the trend (FIGURE 1). To deal with the end-sample bias which is an important drawback of the HP filtering (Canova (1998)) we exclude the last three observations from the sample if model specification uses GAP. Lack of long enough data series in emerging market economies sometime is overcome by taking into account the level of factor utilization (St-Amant and van Norden (1997); Oomes and Dynnikova (2006)). Here we ignore this adjustment given that HPfiltered series appeared to provide at least reasonable estimate. According to this measure economy looked significantly overheated in the beginning of 2008 and probably had negative 16 output gap in the beginning of 2005 and 2009 (Figure A6). Two monetary aggregates are tested – M1, which is supposed to be better controlled by the central bank, and M3 as a measure of broad money. These aggregates are used to estimate excess money supply (OVERHANG) as a residual from the long run money demand equation: = Intercept + α * LOG ( IP) − β * DEPOSIT LOG Monetary _ aggregate CPI (2), where IP is industrial production index used as a proxy for the level of economic activity and DEPOSITS is the interest rate on deposits. Tests confirmed the presence of the cointegrating equation. According to our estimates the deposit rate was found to have only marginal effect on money demand, growth in industrial output leads to 1.3-3% increase in real broad money (M3) and 1.2-2% increase in M1 depending on the period and model specification. We also consider two indicators of external prices – index of the world food prices (FOOD) and index of petroleum prices (OIL) calculated by the World bank 6. Estimation results Three sets of results are considered to explore the difference between reaction of headline and core inflation to macro fundamentals and to test the hypothesis that using core inflation can improve monetary policy over headline inflation. First, we examine Granger causality between different inflation measures and other macroeconomic variables. Second, we compare variance decomposition and impulse response functions of headline and core inflation from labor costs and the exchange rate. And finally, we provide a range of quantitative estimates of the passthrough coefficients. We start with examining Granger causality between different inflation measures and other macroeconomic factors (Table 5). Our estimates suggest that the exchange rate (NEER or USD) and labor costs (nominal wage or ULC) could be Granger causes of both headline inflation and core inflation. We could not reject hypothesis that inflation (independent of the measure) also could be a cause of the exchange rate. This is consistent with the theory that inflation 17 expectations could be a driver of the exchange rate. On the contrary, we found that wages have one-way effect on inflation. This could be explained by the fact that increases of minimal wage in Ukraine are set in the beginning of the fiscal year and take into account official inflation forecast, not the actual inflation rate. Utilities prices appear to affect only headline inflation and trimmed mean core inflation with fixed weights. That is what we aimed to achieve by constructing core indices. The link from inflation to growth in utilities prices was rejected, supporting the fact that utilities prices are subject to regulation. TABLE 5. Granger test summary (3-variable VAR, 12 lags, 2004M01—2012M03, P-values in []) to/from from Headline CPI Exclusion based core inflation (this study) Trimmed mean (fixed weights) Trimmed mean (standard deviation) YES YES YES YES [0.0064] [0.0351] [0.0036] [0.0262] NO NO NO NO [0.941] [0.4139] [0.7369] [0.8633] YES YES YES YES [0.0000] [0.0447] [0.0150] [0.0004] YES YES YES YES [0.0007] [0.0047] [0.0003] [0.0000] YES NO YES NO [0.0072] [0.1878] [0.0000] [0.0784] NO NO NO NO [0.1049] [0.5219] [0.6531] [0.5978] Wage to from Exchange rate to from Utilities to Granger tests for causality between our measure of output gap and inflation indicators gave mixed results. Most of the tests supported the hypothesis that output gap could be a Granger cause for consumer price inflation in a multivariable VAR if nominal wage was included, or showed bi-directional relationship in a two-variable VAR. The presence of link from gap to 18 inflation was rejected if unit labor costs were included instead of the nominal wage. This looks reasonable given that unit labor costs take into account productivity. Hypothesis that money supply could be a Granger cause of consumer price growth was rejected for all inflation indicators. To compare the reaction of headline and core inflation to labor costs and the exchange rate 3-variable VAR models were estimated for changes in nominal wage growth (DWAGE), exchange rate growth (DUSD) and inflation rates (Table 6 and Appendix 5). Analysis of impulse response functions (Appendix 5) showed little difference between headline and core inflation. The initial effect of currency depreciation comes within 2-3 months leading to acceleration of inflation. We also identified second-round effects of changes in the exchange rate within 5-7 months for headline and fixed-weights trimmed mean and exclusion-based core inflation. Acceleration of nominal wage growth leads to acceleration of inflation, and this effect peaks after about 3-4 months. Meanwhile, headline CPI seems to react to with a lag of about 2 months as compared to exclusion-based core inflation fixed-weights trimmed mean, which accelerate right after the increase in wage growth. According to variance decomposition analyses, both headline and core inflation have very high degree of persistence (Appendix 5). Error variance is mostly explained by its own shock: 65-80% depending on the model. Except for fixed weights trimmed mean about 20% of variance is explained by the exchange rate shock, while the power of wage shock appeared to be weaker, especially in the case of standard deviation trimmed mean. 19 TABLE 6. Impulse response functions (3-variable VAR, 12 lags, 2004M01—2012M03) From WAGE to inflation From USD to inflation Response of D(CPIY) to Cholesky One S.D. D(USDY) Innovation Response of D(CPIY) to Cholesky One S.D. D(WAGEY) Innovation .006 .006 .004 .004 .002 .002 .000 .000 -.002 -.002 -.004 -.004 1 2 3 4 5 6 7 8 9 10 1 2 Response of D(COREY) to Cholesky One S.D. D(WAGEY) Innovation 3 4 5 6 7 8 9 10 9 10 9 10 9 10 Response of D(COREY) to Cholesky One S.D. D(USDY) Innovation .006 .006 .005 .004 .004 .003 .002 .002 .000 .001 .000 -.002 -.001 -.004 -.002 1 2 3 4 5 6 7 8 9 10 1 2 Response of D(TRIMFWY) to Cholesky One S.D. D(WAGEY) Innovation 3 4 5 6 7 8 Response of D(TRIMFWY) to Cholesky One S.D. D(USDY) Innovation .005 .004 .004 .003 .003 .002 .002 .001 .001 .000 .000 -.001 -.001 -.002 -.002 -.003 -.003 1 2 3 4 5 6 7 8 9 10 1 2 Response of D(TRIMSDY) to Cholesky One S.D. D(WAGEY) Innovation 3 4 5 6 7 8 Response of D(TRIMSDY) to Cholesky One S.D. D(USDY) Innovation .004 .006 .005 .003 .004 .002 .003 .001 .002 .000 .001 .000 -.001 -.001 -.002 -.002 -.003 -.003 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 20 To estimate pass-through coefficients for each of the indicators of inflation we built VEC models, with individual equation taking the form below (CPI inflation equation is taken as an example): ∆CPI = Bec * (CPI t −1 − b1 * Labort −1 − b2 * USDt −1 −b3 * Utilitiest −1 − c) + + ∑ B1i ∆CPI t −i + ∑ B2i ∆Labort −i + ∑ B3i ∆USDt −i + ∑ B 4i ∆Utilities t −i + ∑ B mj ∆EXO t − j (2), where CPI, Labor, Utilities and USD (exchange rate) are treated as endogenous, while EXO denotes exogenous factors effecting inflation only in the short-run, and four equations of the system (i.e. ∆CPI , ∆Labor , ∆USD and ∆Utilities ) are estimated simultaneously. Vector of exogenous variables includes growth world commodity prices (FOOD, OIL) and monetary aggregates (M1, M3, and OVERHANG). We found that the long term level of headline CPI is driven by unit labor costs, the exchange rate and utility prices. The exchange rat pass-through appeared to be strong at about 0.35-0.4, suggesting that 10% devaluation of hryvnia would lead to increase in inflation rate by 3.5-4% in YoY terms (Table 7). This result appeared to be robust independent of the model specification and looks close to estimates in the earlier studies. Long-term pass-through coefficient for labor costs indicate that 10% increase in ULC leads to about 1.5-2pp increase in YoY inflation. The effect of UT is spread over time with long -run pass-through coefficient of about 0.15. Exogenous global food and energy prices appeared to be insignificant, as well as our measure of excess money. At the same time, M3 aggregate YoY growth was found to be significant, when added as exogenous variable with 6-7 months lag. TABLE 7. Long run pass-through effects for headline inflation Variable CPI: Long run pass-through coeffitients Basic mark-up model Mark-up model with utilities prices Mark-up model with exogenous money growth (M3) ULC 0.45 0.14 (0.19) 0.18 USD (NEER) 0.40 0.36 (0.35) 0.37 --- 0.15 (0.16) 0.14 UT 21 Similar models were applied to exclusion based and trimmed mean measures of core inflation. For exclusion-based core inflation (CORE) utilities and food prices were found to be insignificant in the long-run as well as in the short run. The long- run exchange rate pass-through was estimated at about 0.37-0.45. The increase in nominal wages translates into 0.44pp increases in core inflation rate. In contrast to headline inflation we could not confirm presence of cointegration between CORE and unit labor costs, however we found cointegrating equation between core inflation, nominal wage, exchange rate and our proxy of output gap. So the longrun equation was also modified to: CORE = Intercept+a*GAP+b*USD+c*WAGE. Introduction of output gap into the mark-up model can be justified as follows. Producers demand a higher markup over costs when the economy is overheated (since they are working close to full capacity) and can sacrifice part of it in order to stay in business during crisis. Meanwhile the economic theory does not provide clear prediction of mark-up behaviour over the cycle. There are empirical evidence of both counter-cyclicality (USA, South Africa) and procyclicality (UK, Canada) of mark-up behaviour. See Rotenberg and Woodford (1999) and Klien (2011) for a discussion and literature overview. Similar to the case of headline inflation, OVERHANG was found insignificant, but growth in monetary aggregates M1Y and M3Y appeared to affect the inflation dynamics with a lag of 3-6 months. TABLE 8. Long run pass-through effects for core inflation (exclusion-based method) CORE: Long run pass-through coeffitients Variable Basic mark-up model Mark-up model with GAP Mark-up model with exogenous money growth (M1) WAGE 0.42 0.45 0.44 USD 0.45 0.39 0.46 GAP --- 0.68 --- For core inflation measures based on trimmed mean approach mark-up model showed good fit as well. We also found that nominal wages work better than unit labor costs. At the 22 same time exchange rate pas-through (USD) appeared to be even stronger – close to 0.5. Utility and food prices were found insignificant. Money supply growth measures were significant with 4-6 months lag. TABLE 9. Long run pass-through effects for core inflation (trimmed mean) Variable TRIM (fixed weights) Mark-up model Mark-up model with with GAP exo money (M1) TRIM (standard deviation) Basic mark-up Mark-up model with model exo money (M3) WAGE 0.35 0.33 0.17 0.27 USD 0.51 0.48 0.50 0.57 GAP 1.35 1.21 --- --- 7. Discussion of the results and policy implications In this study we compare headline CPI with thee measures of core inflation and test if using core indicators can improve monetary policy over headline inflation. Although our estimation results do not allow making unambiguous choice of the inflation target for monetary policy in Ukraine, they suggest that core inflation should be monitored and used in communicating monetary policy decisions. On the one hand, we found that headline and core inflation have common drivers and have similar reaction to changes in nominal wages and the exchange rate. We also could not prove that using core inflation would improve medium term forecast of inflation. On the other hand, our estimates confirmed that shocks coming from regulated changes in relative prices (such as utilities) have little effect on core inflation and therefore core inflation could help to distinguish these shocks. Also core inflation appeared to react faster to growth in nominal wages, and in this case could be used as a forward-looking indicator. From this perspective, exclusion-based core inflation is preferable indicator. It provides more stable results across the tests as compared to trimmed mean measures, and is easily understandable by the public. At the same time, according to our analysis Ukrainian inflation process shares major features common to other emerging market economies and these properties have some policy 23 implications. First of all, both headline and core inflation have high degree of persistence, which implies significant role of inflationary expectations and high costs of disinflation. Therefore clear communication related to monetary policy, as well as transparent and predictable government policy on administrative price changes are needed to avoid undermining the NBU’s credibility if the inflation target is missed due to administrative price adjustments. Gradual and but reliable adjustment of state regulated prices and move to market-based indexation of administrated prices could mitigate the effect of changes in relative prices on inflation inertia. Even if it is not used as a monetary policy target, core inflation remains important part of policy formulation, communication and management of inflation expectations. We also found that the exchange rate is the key explanatory variable. Depending on the model the exchange rate pass-through was estimated at about 0.35-0.5 (10% devaluation of hryvnia leads to about 3.5-5pp increase in yoy inflation rate) in the long run. The coefficient looks high even compared to other emerging market economies. As we discussed in section 3, this could be a consequence of tightly managed exchange rate regime and/or high share of imports in the CPI basket. Given relatively high exchange rate pass-through, the exchange rate seems to be the most efficient tool of monetary policy in the short run. However, gradual move to more flexible exchange rate is required in order to reduce the effect of the external shocks on inflation in the future and to improve efficiency of other tools of monetary policy such as interest rates. The cost of labor appeared to have strong and relatively fast effect on both headline and core inflation. Therefore the central bank should avoid accomodative monetary policy, when there is exogenous shock to wages (e.g. increase in minimal wages before the elections in the excess of the average inflation level). As noted by Moriyama (2011) pro-cyclical monetary policy and lack of timely response to demand shocks could propagate larger fluctuations of output gap and higher inflation persistency. Here core inflation could be used to justify tightening of monetary policy before growing wages lead to acceleration of headline CPI. 24 Meanwhile, the relationships between money growth and different inflation measures require further research. The hypothesis that money growth could be a Granger cause of inflation, as well as the presence of cointegration between growth of money aggregates and inflation were rejected for all inflation measures. We found cointegrating relationship between money aggregates, headline inflation and industrial production, which could be interpreted as long-term money demand. However excess money appeared to have no effect on the CPI growth in the short run. On the other hand, we found that short run effect of changes in money supply have stronger and faster effect on core inflation (3-4 months) than on headline inflation (6-7 months) if money growth is treated as exogenous variable. These results could indicate instability of the money demand function and suggest that monetary aggregates should not be used as a policy target in Ukraine. Also, money velocity should be taken into account in order to identify inflation indicator that have closer links to monetary policy tools. 25 Appendix 1. Major trends in inflation in Ukraine in 2002 - 2011 TABLE A1. Ukraine key macroeconomic indicators in 2002-2011 Real GDP, % yoy Real consumption growth, % yoy Nominal wages, % yoy Broad money growth, %YoY Credit extension to private sector, % change Policy interest rate, %, eop Average UAH/US$, %YoY 9.6 5.2 NA 20.7 42.4 49.8 7.00 -0.8 18.4 9.1 9.5 9.4 23.0 46.5 64.9 7.00 0.1 9.0 29.1 8.6 12.1 8.7 27.7 31.8 32.2 9.00 -0.3 2005 13.5 27.9 7.2 3.0 14.0 36.5 54.1 63.6 9.50 -3.7 2006 9.1 23.3 6.9 7.4 12.2 29.4 34.3 69.8 8.50 -1.5 2007 12.8 32.5 6.4 7.6 13.1 29.7 51.7 73.7 8.00 0.0 2008 25.2 31.5 6.4 2.3 10.1 33.7 30.4 67.1 12.00 4.2 2009 15.9 -3.7 8.8 -14.7 -12.3 5.5 -5.3 2.8 10.25 48.0 2010 9.4 19.8 8.1 4.2 7.0 17.7 23.0 0.7 7.75 1.9 2011 8.0 21.6 7.9 5.2 15 17.5 16.4 8.9 7.75 0.4 CPI, % avg Nominal GDP, %YoY Unemployment, % of labour force 2002 0.0 10.6 2003 5.2 2004 26 FIGURE A1. Ukraine CPI inflation vs peers Average CPI, % YoY 30 25 20 15 10 5 Ukraine Kazakhstan Russia Czech Republic 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 0 Poland Sources: Haver, State statistical committee of Ukraine FIGURE A2. Highly volatile items account for more than 50% of the basket. 40 YoY, % 35 30 25 20 15 10 5 0 Headline CPI Food Utility Services Jan-12 Oct-11 Jul-11 Apr-11 Jan-11 Oct-10 Jul-10 Apr-10 Jan-10 Oct-09 Jul-09 Apr-09 Jan-09 -5 T ransport Sources: Haver, State statistical committee of Ukraine 27 FIGURE A3. Sources of base money growth 100% 80% 60% 40% 20% 0% -20% -40% Aug-03 Nov-03 Feb-04 May-04 Aug-04 Nov-04 Feb-05 May-05 Aug-05 Nov-05 Feb-06 May-06 Aug-06 Nov-06 Feb-07 May-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08 Nov-08 Feb-09 May-09 Aug-09 Nov-09 Feb-10 May-10 Aug-10 Nov-10 Feb-11 May-11 Aug-11 -60% Contribution to Money base growth, %YoY NFA Net claims on gov Claims on other residents OIN Monetary Base FIGURES A4-A5. Core and headline inflation in Ukraine in 2004-2011 35% 30% 25% 20% 15% 10% 5% Headline CPI Exclusion-based core inflation (CORE) Jul-11 Jan-11 Jul-10 Jan-10 Jul-09 Jan-09 Jul-08 Jan-08 Jul-07 Jan-07 Jul-06 Jan-06 Jul-05 Jan-05 Jul-04 Jan-04 Jul-03 Jan-03 0% NBU core inflation 28 35% 30% 25% 20% 15% 10% 5% Jul-11 Jan-11 Jul-10 Jan-10 Jul-09 Jan-09 Jul-08 Jan-08 Jul-07 Jan-07 Jul-06 Jan-06 Jul-05 Jan-05 Jul-04 Jan-04 Jul-03 Jan-03 0% Trimmed mean fixed weights (TRIMFW) Trimmed mean standard deviation (TRIMSD) Headline inflation (CPI) Sources: Haver, Authors’ estimates FIGURE A6. Output gap approximation base on HP-filtered seasonally adjusted IP GAP 20% 15% 10% 5% 0% -5% -10% -15% -20% 2011M07 2011M01 2010M07 2010M01 2009M07 2009M01 2008M07 2008M01 2007M07 2007M01 2006M07 2006M01 2005M07 2005M01 2004M07 2004M01 2003M07 2003M01 -25% Source: Authors’ estimates. 29 Appendix 2. Structure of CPI basket in Ukraine, % Source: National bank of Ukraine 30 Appendix 3. Previous studies on headline inflation in Ukraine TABLE A1. Estimated coefficients in the long-run inflation model (headline CPI) Study / period Leheyda (2005) Lissovolik (2003) 1997-2003 1993-2002 Kirchner, Weber, Giucci (2008) 1999-2008 0.33-0.34 (1993-2002) 0.45 (1996-2002) 0.25-0.45 (1993-2002) Wage growth 0.28 0.32 (1996-2002) *Coefficients in the restricted model, where the sum of the coefficients in the eq. (3) is set to equal 1. Administered prices (paid services) 0.34 TABLE A2. Estimates of the exchange rate pass-through effect on inflation (headline CPI). Study / period Leheyda (2005) Lissovolik (2003) 1997-2003 1996-2002 0.11-0.17 (1993-2002) 0.08 (1996-2002) US dollar Euro Korhonen and Wachtel (2005) 1999-2004 Kirchner, Weber, Giucci (2008) 1999-2008 0.63-0.64 0.24-0.28 0.3-0.5 NEER(IMF) 0.41 *Coefficients in the restricted model, where the sum of the coefficients in the eq. (3) is set to equal 1. TABLE A3. Comparison of estimated coefficients in the long-run money demand equation. Study / period Kirchner, Weber, Giucci (2008) 1999-2008 M3 M1 Lissovolik (2003) 1996-2002 M3 Leheyda (2005) 1997-2003 M2 0.94* Output level 1.71* 1.17* 1.3-1.6 Deposit rate (lending rate for KWG) -0.012* -0.017* -0.02—0.03 *Mean the coefficient was found to be significant. 31 Appendix 4. Exclusion-based core inflation index Exclusion-based methods are built on the idea of removing certain categories of goods or services from the index. While NBU’s components are not explicitly described, we apply similar approach to build core inflation index for the period from 2002-2011 using publicly available data on the weights and dynamic of particular items in the CPI basket. Our core inflation index covers approximately 59% of the CPI basket. Exact replication of the NBU core inflation index is also problematic due to the differences in classification of the CPI basket given by COICOP (post 2007) and by national methodology (2003-2006). Weights of the excluded items (utilities, transportation, fruits and vegetables and some other raw food) replicate the weights of the categories in the headline CPI. Weights for the period of 2003-2006 were constant (national methodology). Weights for 2007-2010 change in the middle of each year. The smoothening technique employed by the State statistical committee to deal with the transitory points was not available to the public. The weights of certain excluded components varied over the period 20062010. The most remarkable changes occurred to 1) utilities: their contribution to CPI basket was building up from 2006(6.6%) to 2009(8.11%) but dropped below 2006 weight in 2010 (6.5%). 2) sugar weight reduced almost twofold (from 2.2% in 2006 to 1.24% in 2010) 3) petrol weight increased 1.5 times in 2009-2010. TABLE A4. Weights of selected items excluded from core inflation index, % Utilities Fruit Vegetables Sugar Petrol Bread Butter Milk Rail 2003 6.6 3.1 5.1 2.2 0.7 3.9 1.3 4.2 0.2 2004 6.6 3.1 5.1 2.2 0.7 3.9 1.3 4.2 0.2 2005 6.6 3.1 5.1 2.2 0.7 3.9 1.3 4.2 0.2 2006 6.6 3.1 5.1 2.2 0.7 3.9 1.3 4.2 0.2 2007 7.31 3.15 5.04 2.28 0.88 5.03 1.25 3.16 0.24 2008 8.11 3.48 4.88 1.47 0.99 4.81 1.26 3.34 0.24 2009 8.11 3.48 4.88 1.47 1.38 4.64 1.26 3.33 0.23 2010 6.5 3.49 4.79 1.24 1.57 4.81 1.25 3.34 0.27 32 TABLE A5. Headline and exclusion based core (this study) consumer price inflation in Ukraine. Item Weight Headline CPI 100% Exclusion - based core CPI (this study) 59% Non-core CPI, including - Water, electricity & gas 7.5% - Unprocessed food 24% - Other items 9.5% Source: Author’s estimates. Note: Weights here are averages. Given for indicative purposes 33 Appendix 5. Data TABLE A6. List of variables and notations Variable Description Measurement Source CORE Exclusion based core CPI YoY %YoY Authors' calculations based on Ukstat data CPI Inflation YoY %YoY Ukrstat PPI YoY PPI growth %YoY Ukrstat IP Industrial production ULC Unit labor cost %YoY Calculations based on Ukrstat data TRIMSD Trimmed mean core CPI, based on standard deviation Trimmed mean core CPI, based on fixed weights UAH/USD exchange rate %YoY %YoY Authors' calculations based on Ukstat data Authors' calculations based on Ukstat data NBU TRIMFW USD Ukrstat %YoY NEER Hryvnia Nominal effective Exchange Rate (increase means depreciation) Index Haver, Authors' calculations NEERY NEER 12 months change %YoY Haver, Authors' calculations UWAGE Average Wage/Industrial Output, %YoY Average depreciation of Hryvnia against Euro and Ruble, YoY %YoY Ukrstat %YoY Calculations based on NBU data Index Ukrstat BM /CPI Utilities price index (component of CPI) Utilities price index (component of CPI) Real Broad Money DEPOSIT Average deposit rate M1Y BASKET UT UTY %YoY Index NBU, Authors' calculations % NBU M1 growth %YoY NBU M3Y Broad Money(M3) growth %YoY NBU OVERHANG DEPOSIT Resudials from the long-run equation of money demand Average deposit rate FOOD World Food Price Index Index Haver, World Bank FOODY World Food Price Index %YoY Haver, World Bank GAP Approximated using HodrickPrescott filter from monthly series of industrial production (seasonally adjusted using X12 procedure) Authors' calculations % Percentage deviation from the trend NBU Haver, Authors' calculations 34 TABLE A7. ADF test statistics and [P-Value]. H0: series has unit root Series Lag length (selected by Schwarz criterion) 1 Intercept Intercept and Trend -2.12 [0.2382] -1.86 [0.6666] 0 -5.20 [0.0000] -5.47 [0.0001] CORE (exclusion-based core inflation) D(CORE) 1 -2.58 [0.0996] -2.43 [0.3622] 0 -5.44 [0.0000] -5.55 [0.0001] TRIMFW (trimmed, fixed weights) D(TRIMFW) 1 -2.68 [0.0807] -2.50 [0.3256] 0 -3.93 [0.0026] -4.04 [0.0101] TRIMSD (trimmed, standard deviation) D(TRIMSD) 2 -2.50 [0.1194] -2.29 [0.4345] 0 -5.31 [0.0000] -5.43 [0.0001] USD 2 -2.23 [0.1972] -2.24 [0.4604] D(USD) 1 -6.76 [0.0000] -6.73 [0.0000] WAGE 0 -1.82 [0.3676] -2.29 [0.4337] D(WAGE) 0 -10.19 [0.0000] -10.14 [0.0000] ULC 1 -2.28 [0.1792] -2.28 [0.4418] D(ULC) 0 -8.31 [0.0000] -8.28 [0.0000] GAP 0 -2.13 [0.2339] -2.12 [0.5300] D(GAP) 0 -9.79 [0.0000] -9.76 [0.0000] M3Y 5 -2.01 [0.2806] D(M3Y) 4 -3.08 [0.0306] CPI (headline inflation) D(CPI) 35 Appendix 6. Impulse response functions and variance decomposition TABLE A8. Impulse response functions (3-variable VAR, 12 lags, 2004M01—2012M03) From inflation to WAGE From inflation to USD Response of D(USDY) to Cholesky One S.D. D(CPIY) Innovation Response of D(WAGEY) to Cholesky One S.D. D(CPIY) Innovation .012 .025 .020 .008 .015 .004 .010 .000 .005 .000 -.004 -.005 -.008 -.010 -.012 -.015 1 2 3 4 5 6 7 8 9 1 10 2 Response of D(USDY) to Cholesky One S.D. D(COREY) Innovation 3 4 5 6 7 8 9 10 9 10 9 10 9 10 Response of D(WAGEY) to Cholesky One S.D. D(COREY) Innovation .012 .025 .020 .008 .015 .010 .004 .005 .000 .000 -.005 -.004 -.010 -.008 -.015 1 2 3 4 5 6 7 8 9 1 10 2 3 4 5 6 7 8 Response of D(WAGEY) to Cholesky One S.D. D(TRIMFWY) Innovation Response of D(USDY) to Cholesky One S.D. D(TRIMFWY) Innovation .012 .03 .008 .02 .004 .01 .000 .00 -.004 -.01 -.008 -.012 -.02 1 2 3 4 5 6 7 8 9 1 10 2 3 4 5 6 7 8 Response of D(WAGEY) to Cholesky One S.D. D(TRIMSDY) Innovation Response of D(USDY) to Cholesky One S.D. 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