Kenya: Selected Issues and Statistical Appendix
Author: International Monetary Fund
Publication Date:
19 Apr 2002
eISBN:
9781451821062
Language:
English
Keywords:
ISCR; CR; Kenya; inflation rate; CPI; price; bank; overall CPI; inflation outlook; CPI component; food price; Kenyan CPI; Consumer price indexes; Consumer prices; Food prices; concept views core inflation
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This Selected Issues paper and Statistical Appendix addresses the question of how to interpret recent developments in the Kenyan consumer price index (CPI) properly to assess the current inflation pressure and extract signals about possible future CPI inflation trends. The paper discusses why Kenya’s exports have performed poorly over the past five years in spite of a more liberalized trade and exchange rate regime. The analysis shows that Kenya faces both price and nonprice constraints on export performance.

Abstract

This Selected Issues paper and Statistical Appendix addresses the question of how to interpret recent developments in the Kenyan consumer price index (CPI) properly to assess the current inflation pressure and extract signals about possible future CPI inflation trends. The paper discusses why Kenya’s exports have performed poorly over the past five years in spite of a more liberalized trade and exchange rate regime. The analysis shows that Kenya faces both price and nonprice constraints on export performance.

II. Inflation in Kenya—Signal Extraction for Policy Purposes1

A. Introduction

9. This section addresses the question of how to interpret properly recent developments in the Kenyan consumer price index (CPI), so as to assess current inflationary pressures and extract signals about possible future CPI inflation trends. Expectations are formed, in part, on the perceived current situation. Monetary policy, moreover, influences inflation with a lag that can be significant. This makes it important to detect early signals in the data about possible changes in future inflation trends. Similarly, proper fiscal policy requires accurate revenue and expenditure forecasts, which, again depend, in part on accurate price (and volume) forecasts for key national accounts variables.

10. Moreover, failure of the key inflation rates monitored and published properly to reflect the current situation can cause market distortions, as well as complications for monetary and fiscal policy formulations. In 2001, the key inflation rates monitored and published in Kenya—the annual average2 and 12-month3 rates of change in the overall and “underlying”4 CPI—did not adequately indicate that consumer prices in fact had been falling since November 2000. During most of 2001, those rates continued to show strong positive inflation. Consequently, the 2001/02 budget (July-June) was based on an assumption of an average annual increase in consumer prices of 5 percent (equal to the CBK’s internal inflation target, and significantly higher than the actual outturn of 0.8 percent). Lower-than-projected inflation resulted in an overprojection of growth in nominal GDP and budget revenues. The 2001/02 budget projected revenues to be about K Sh 11 billion (1.2 percent of GDP) higher than are now expected for the year.

11. This section is organized as follows: Subsection B provides a summary of key aspects of the development of consumer prices, as measured by the current Kenyan CPI, during the last two years; Subsection C discusses briefly the properties of growth rates over different time-horizons and trend-cycle5 estimates from the perspective of extracting signals about possible future inflation trends; Subsection D addresses the current Kenyan measure of underlying inflation; and Subsection E offers conclusions. These issues are further elaborated in three annexes. Annex I elaborates on the properties of various growth rates. Annex II briefly discusses the signal extraction properties of standard univariate seasonal adjustment and trend-cycle estimation techniques, and relates the trend-cycle filters to the growth rates discussed in Subsection C and Annex I. Finally, Annex III provides a brief survey of the literature on the concept and measurement of core inflation.

12. The following main points are made:

  • The 12-month growth rate can be seriously misleading for some purposes and the annual average rate even more so. The 12-month rate is sensitive to one-off shocks and shows the current development with a delay of approximately five-six months. This delay in reflecting the current inflation pressure was the reason why the published Kenyan overall inflation rates continued to show strong positive inflation while prices were actually falling.

  • Simple trend extrapolations of the index level, but not of the growth rates, can provide relatively robust projections of the annual average and 12-month growth rates several months ahead, because past developments account for a large part of the future changes in these rates.

  • Evidence from other countries suggests that exclusion-based core inflation measures—such as the current Kenyan measure of underlying inflation, which exclude food and rent from the overall CPI—often perform poorly.

  • Although evidence suggests that some other measures of core inflation may perform better, these measures cannot be applied to Kenyan data because the Kenyan CPI is not prepared at a sufficiently detailed level.

  • When monitoring and publishing inflation data in Kenya, more attention should be given to one-month and three-month growth rates in the data, and less to the 12-month and annual average growth rates. More attention should also be given to the detailed CPI components.

B. Key Features of Consumer Price Inflation in Kenya, 2000–01

13. The 12-month rate of change in the CPI fell from 7.5 percent in December 2000 to - 3.1 percent in December 2001, and the annual average inflation rate declined from 6.2 percent in 2000 to 0.8 percent in 2001. Following the drought in early 2000, a sharp increase in prices of several nonfood groups (particularly fuel and power) and a more moderate increase in food prices caused overall CPI inflation to rise. Food prices have been falling since July 2000, and the overall CPI has been falling since November 2000 (Figure 1). Between February and November 2000, the overall CPI increased by 6.3 percent,6 or at an annualized average rate of 8.9 percent, while it fell by 3.2 percent, or at an annualized average rate of 2.9 percent, between November 2000 and December 2001.7

Figure 1.
Figure 1.

Kenya: Overall CPI and Main Components (Indies, January 1999=100)

Citation: IMF Staff Country Reports 2002, 084; 10.5089/9781451821062.002.A002

Sources: Kenyan authorities; and Fund staff calculations.

14. This development in the CPI has been accompanied by strong short-term nonseasonal volatility8 (Table 1) and significant changes in relative prices (Fig. 1 right panel), which makes it difficult to gauge the underlying trend in inflation. Strong short-term volatility may be characteristic of price behavior in Kenya, but it may also reflect measurement problems. Of the subindices, only the food component shows any clearly identifiable (though moderate) seasonality.

Table 1.

Kenya: Short-Term Volatility in the CPI, 1995-2001

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15. The published key 12-month inflation rates fail to adequately indicate the steady fall in consumer prices since November 2000. During most of 2001, the published overall and underlying inflation rates continued to show strong positive inflation (Tables 2 and 3). The 12-month rate of change in the overall index averaged 2.6 percent for the November 2000 to September 2001 period, and dropped to 0.2 percent as late as June 2001, before turning negative in August 2001. Similarly, the 12-month rate of change in the authorities’ measure of underlying inflation stayed at around 7 percent for the first three quarters of 2001 before dropping to 2.4 percent in September 2001.

Table 2.

Kenya: Developments In the Overall CPI, January 1999-December 2001

(In percent, unless otherwise indicated)

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Source: Kenyan authorities and Fund staff calculations.
Table 3.

Kenya: Developments In the Underlying CPI,1 January 2000-December 2001

(In percent unless otherwise indicated)

article image
Sources: Kenyan authorities; and Fund staff estimates and calculations.

Equal to the overall CPI excluding rent and food.

From the X- 12-ARIMA seasonal adjustment program. Automatic selection of 9-term Henderson filter and adjustment for level shift in September 2000.

C. Growth Rates and Signal Extraction

16. In the absence of seasonally adjusted data and trend-cycle estimates,9 it is common practice in most countries to focus presentation of inflation data on 12-month rates of change and not on 1-month rates of change. The 12-month growth rates often provide a convenient summary of developments over the last 12 months. However, the 2000–01 developments in the Kenyan CPI (see Table 2) provide an extreme example of how 12-month and annual average growth rates can be misleading. Neither rate shows the current inflationary pressure, because both are backward looking, and thus neither provides timely signals about potential future trends in the series. One-month rates of change in nonseasonally adjusted data, however, may contain too much noise. Three-month growth rates in seasonally adjusted data, which lag the current development by one month, may provide a better balance between timeliness and noise than the 1-month and 12-month growth rates. One-month growth rates in the trend-cycle estimates computed by standard seasonal adjustment packages might provide an even better balance.

17. The 12-month growth rate represents the 1-month rate cumulated over the last 12 months. It is also, as shown in Annex I, equivalent to the (geometric) average one-month rate at an annualized rate for the last 12 months. Similarly, the annual average rate is approximately equal to the average 12-month rate for the last 12 months. And, as an average of the last 12 1-month rates, the 12-month rate represents a basic estimate of the trend growth five-six months earlier. Various versions of centered moving averages are commonly used as trend filters (see Annex I and Annex II). Consequently, the 12-month rate lags the current trend development by five-six months, which can be misleading. It may suggest, for example, that inflationary pressure is still rising when, in fact, prices have been falling for several months. The annual average rate constitutes a much longer trend filter and consequently lags the current trend development by even more than the 12-month rate.

18. Simple moving-average filters are sensitive to one-off shocks and other outliers. As can be seen from Table 3 below (bolded data), an especially large (small) change in one month will cause the 12-month growth rate to stay high (low) for the next 12 months. The table shows how the very strong increase in the index between August and September 2000 of 5.0 percent10 caused the published underlying (12-month) inflation rate to stay high for the next 12 months.

19. For the same reason, growth rates based on nonsmoothed data are subject to base effects, which, particularly for growth rates over longer horizons, may cause confusion. This base effect can be clearly seen in Table 3 (bolded data), where the drop in the 12-month rate from 7.2 percent in August 2001 to 2.6 percent in September 2001 is entirely caused by the dropping out of the 12-month average of the sharp increase in the index between August and September 2000 (the index actually increased by 0.3 percent between August and September 2001). As a rule, period-to-period changes in the 12-month rate reflect both the 1-month change for the current month of the current year and the 1-month change for the same month of the previous year.

20. Several authors11 have argued that 3-month growth rates, preferably based on seasonally adjusted data, may provide a better balance between timeliness and noise than the 1-month and 12-month growth rates (see Annex I). The 3-month growth rate lags the current development by only one month and, as illustrated in Annex I, provides a reasonably close approximation of trend-cycle estimates based on the shorter versions of the moving-average filters applied by the most widely used seasonal adjustment packages. As explained in Annex II, the trend-cycle estimates obtained by using these packages, however, offer several advantages over simple 3-month and 12-month growth rates for assessing the current inflationary pressure.

21. Trend-filter smoothing can help highlight the underlying trend in the data. It can, however, suppress or blur key signals in the data, such as the precise magnitude, duration and timing of the effect of exchange rate, monetary, or supply shocks on the series. As can be seen from Table 3, this is particularly the case if 3-month and 12-month growth rates, or other nonintervention trend filters,12 are used for smoothing the data.

22. Simple trend extrapolations of the index level can provide relatively robust projections of the annual average and 12-month growth rates several months ahead. Because the 12-month rate is equivalent to the geometric average monthly inflation rate at an annualized rate for the last 12 months, past developments account for a large part of the near-term changes in the rate. For instance, in a 1-month ahead forecast of the 12-month rate, the past 11 1-month rates will account for eleven-twelfths, and the next month’s 1-month rate one-twelfth, of the next month’s 12-month rate.

23. Extrapolating highly seasonal series requires that the seasonal variation in the 1-month growth rate be taken into account as well. Annex U explains how trend extrapolations based on seasonally adjusted and trend-cycle data can overcome this problem. The method described will give similar forecasts to those obtained based on ARTMA13 modeling of the time series, as long as no major change in the underlying trend is assumed. It is, however, simpler to use and allows for incorporating into the forecasts assumed changes in the underlying trend. ARIMA models are well suited for projecting repeated patterns in the series but not for forecasting changes in the underlying trend in the series.

D. Core Inflation Measures14

24. The term “core inflation” enjoys widespread use, but more than one definition of core inflation is used in the literature.15 In general, core inflation tends to be defined in terms of the particular method used to construct a practical measure, for instance, the CPI excluding certain items, rather than in terms of what the measure is trying to capture. The Kenyan core inflation measure is constructed as the overall CPI excluding rent and food.

25. Nonetheless, according to Roger (1998), most efforts to measure core inflation can be seen as trying to extract signals from the measured CPI about possible future inflation trends by quantifying one of two broad concepts. One concept views core inflation as the persistent component of the CPI, that is, the measured CPI inflation rate excluding the effect of any transient shocks. The second concept views core inflation as the generalized component of the CPI, that is, the measured CPI inflation rate excluding the effect of relative price shocks. This generalized component may, or may not, be persistent.16 In both views, core inflation is generally assumed to be associated with expectations and demand pressure components of the measured inflation rate, and to exclude the first-round impact of any supply shocks. The impact of expectations and demand pressure on inflation is generally assumed to be persistent, influence all prices evenly, and largely a monetary phenomenon, while the impact of supply shocks on inflation is assumed to be transient and influence particular prices.

26. The Kenyan, exclusion-based core inflation measure represents one of several approaches to measure the general component of the CPI. Alternative measures of the general component include volatility-adjusted measures; specific adjustment measures; and the use of robust, or limited-influence estimators, such as the median and various weighted trimmed means.17 Unfortunately, these alternative measures cannot be applied to Kenyan data because the Kenyan CPI is not prepared at a sufficiently detailed level. The overall CPI is also a measure of the general component of the CPI, but the stochastic approach to index numbers, as well as empirical studies, suggests that it may not be the most robust and efficient estimate of the general component (see Annex III).

27. Measures of core inflation need to satisfy four key criteria if they are to help detect possible future CPI inflation trends. They need to be (i) timely; (ii) not subject to any significant revisions; (iii) closely associated with the overall CPI in the long run; and (iv) forward looking, that is, leading indicators for the overall CPI, and not the other way around.18 The latter criterion should also imply that the core measures should be less volatile than the overall CPI. In addition, the core measures should be easier to model than the overall CPI. Finally, the core measures would need to be readily understood by the public and externally verifiable, if they also are to help explain monetary policy decisions.

28. Evidence from other countries suggests that exclusion-based core inflation measures—such as the current Kenyan measure—often perform poorly, while measures based on trimmed means may help improve the signal-to-noise ratio in the data (see Annex III). The exclusion-based measures may offer little reduction in volatility and a significant loss of signal, sometimes to the degree that they become lagging and not leading indicators of the overall index.

29. Exclusion-based measures constructed at a highly aggregate level, such as the Kenyan measure, may perform particularly poorly.19 Constructing these measures at a highly aggregate level creates the danger of excluding detailed components that may be among the least volatile elements of the series, while increasing the effective weight of some highly volatile components. The Kenyan underlying inflation measure is constructed on a highly aggregated level by excluding two of the ten main components. Furthermore, as is evident from Table 1 above, the two components excluded (food and rent) are among those that show the least short-term volatility. This, suggests that the Kenyan underlying inflation measure may be a poor indicator of the short- to medium-term inflation outlook.

30. The Kenyan measure of underlying inflation may, nonetheless, be a useful indicator of the longer-term developments in the price level and thus the longer-term inflation outlook. From Figure 2 below, it appears that

Figure 2.
Figure 2.

Kenya: Main CPI Components, 1990-2001 (Indices, January 1999=100)

Citation: IMF Staff Country Reports 2002, 084; 10.5089/9781451821062.002.A002

Sources: Kenyan authorities; and Fund staff calculations.

  • the underlying index in the long run is relatively unbiased compared with the overall CPI;

  • food prices, most likely affected by drought, have caused the overall CPI to increase faster than the underlying index for sustained periods over the past decade;

  • subsequent falls in food prices cause the overall CPI to decline for periods of significant duration; and

  • the level of the overall CPI tends to revert to the level of the underlying index in the long run.

Non-exclusion-based measures may not properly filter out these large semitransient swings, at least not if they occur gradually.

31. From Figure 2 it appears also that the current deviation between the overall CPI and the underlying index may differ from the past episodes. Currently, the overall index is lower than the underlying index. In contrast to the previous episodes, the current fall does not appear to be characterized by food prices’ reverting to their “natural” level after a preceding sharp increase. The sharp decline in food prices, however, has likely bottomed out, and the high energy prices may finally start coming down following the strong decline in world oil prices during 2001. The fundamental reforms of Kenya’s trade regime that have taken place over the past ten years are likely to have reduced the impact of droughts on food prices, and thus altered relationship between the overall CPI and the underlying index.

32. It should be possible to improve the Kenyan underlying inflation measure if the CPI were to be prepared at a more detailed level. Several improvements can be envisaged. First, the information content of all core measures discussed above can be improved by using seasonally adjusted data for those series that show seasonal variations. Second, for exclusion-based measures, the information content should be improved by making sure that only the detailed subcomponents that show the largest short-term nonseasonal volatility, as well as those food subcomponents responsible for the large semitransient swings, are excluded. Third, the signal-to-noise ratio in the data may be improved by use of the trimmed-mean method. Finally, it may be possible to combine exclusion and trimmed-mean methods: first, those food subcomponents responsible for the above-mentioned large semitransient swings could be excluded, and then for each period, a fixed proportion of the remaining items at each end of the distribution of price changes could be zero-weighted.

E. Conclusion

33. There is no “best measure of inflation.” Different measures provide different perspectives on the inflation process. The key inflation rates monitored and published in Kenya, however, failed to adequately indicate that prices were falling during 2001.

34. Consequently, when monitoring and publishing inflation data in Kenya the authorities should give more attention to 1-month and 3-month growth rates in the data, and less to the 12-month and annual average growth rates. More attention should also be given to the detailed CPI components. Experience from other countries has shown that the key information for predicting future inflation may sometimes be found in the tails of the price change distribution, and thus be excluded from trimmed-mean based core measures. Therefore, monitoring the detailed component series, and not only aggregate measures, often proves to be critical. In addition, it would be useful to start compiling and publishing seasonally adjusted and trend-cycle estimates in Kenya using one of the standard seasonal adjustment packages.

35. Finally, the discussion suggests that one should be careful in labeling particular measures as the “underlying”—or “core”—inflation rate because those labels may promise more than the measures can deliver. Evidence from other countries suggests that exclusion-based core inflation measures—such as the current Kenyan measure of underlying inflation—often perform poorly.

ANNEX I: Growth Rates and Signal Extraction

36. The 12-month growth rate represents the cumulative rate of change from the same month in the previous year or, put differently, the 1-month rate cumulated over the last 12 months:

(XtXt−12−1)⋅100=(Xt−11Xt−12⋅Xt−10Xt−11⋅…XtXt−1−1)⋅100⁢,(1)

where Xt is the value of the index in period t

37. It follows that the 12-month growth rate also is equivalent to the geometric average monthly inflation rate for the last 12 months at an annualized rate: the geometric average for the last 12 months is

r¯t=((XtXt−12)112−1)⋅100=((Xt−11Xt−12⋅Xt−10Xt−11⋅…XtXt−1)112−1)⋅100⁢ ;⁢    (2)⁢

at an annualized rate is

arr=[(1+rt¯100)12−1]⋅100=[((XtXt−12)112)12−1]⋅100⋅     (3)

38. The 12-month rate lagged five-six months provides a close approximation of the basic centered 2×12 moving-average trend filte20 used in the first iteration of the X-11, X-11-ARIMA, and X-12-ARIMA seasonal adjustment packages. It provides, however, only a rough approximation of the final trend estimates obtained by these programs, which use the more responsive Henderson moving-average filters.21 This is particularly the case if the trend is relatively unstable, outliers are present, and, consequently, the seasonal adjustment program chooses shorter version of the Henderson filter.

39. As illustrated in Figure 3 below, centered 3-month growth rates provide a reasonable close approximation of trend-cycle estimates based on the shorter versions of the Henderson moving-average filters.22

Figure 3.
Figure 3.

Kenya: the Trend-Cycle Component and Approximations to the Trend-Cycle Component of the Overall CPI, January 1999-December 2001 (Annualized percentage change)

Citation: IMF Staff Country Reports 2002, 084; 10.5089/9781451821062.002.A002

Sources: Kenyan authorities; and Fund staff calculations.

ANNEX II Seasonal Adjustment and Estimation of Trend-Cycles

40. Seasonal adjustment means using analytical techniques to identify the main components of the time series—the three main ones being the trend-cycle component, the seasonal component, and the irregular component, each of which may be made up of several subcomponents. The purpose is to provide a better understanding of the behavior of the time series and help forecast the series. In seasonally adjusted data, the impact of the regular within-year seasonal pattern, the influences of moving holidays, and the number of working/trading days and the weekday composition in each period (the trading-day effect) are removed. By removing the repeated impact of these effects, seasonally adjusted data highlight the underlying trends and short-run movements (including any irregular movements) in the series. Seasonal adjustment is not a smoothing technique, and, if the impact of irregular events is strong, seasonally adjusted data may not represent a smooth series.

41. In trend-cycle estimates, the impact of irregular events in addition to seasonal variations is removed. Adjusting a series for seasonal variations removes the identifiable, regularly repeated influences on the series but not the impact of any irregular events. To further highlight the underlying trend-cycle, most standard seasonal adjustment packages provide a smoothed trend line running through the seasonally adjusted data (representing a combined estimate of the underlying long-term trend and the business-cycle movements in the series).

42. Various well-established techniques are available for removing the seasonal patterns from the series. The most commonly used technique is the Census X-11/X-12 method, which is based on a series of centered moving-average filters.23

43. Seasonal adjustment and trend-cycle estimation using centered moving-average filters allow the seasonal pattern of the series to change over time and allow for a gradual update of the seasonal pattern. This results in a more correct identification of the seasonal effects influencing different parts of the series, but also implies that the final seasonally adjusted and trend-cycle values depend on both past and future values of the series. Thus, at the beginning and end, the series has to be either explicitly extended by use of backcasts and forecasts based on the pattern of the time series, or implicitly through the use of asymmetric filters. In either case, this leads to a constant revision of the most recent seasonally adjusted and the trend-cycle estimates as new observations replace the forecasts. These revisions to the seasonally adjusted and trend-cycle estimates, owing to new observations, are commonly referred to as the “wagging tail” problem, from which all major seasonal adjustment methods suffer. To avoid systematically biased estimates, the use of symmetric filters is required, and revisions are an unavoidable consequence.

44. The revision problem should not be exaggerated. Although seasonally adjusted data may be subject to nonnegligible revisions even after one to two years,24 these revisions will generally be small, particularly for series with a stable seasonal pattern. Furthermore, although estimates of the underlying trend-cycle component may be subject to large revisions at the first updates, they will—especially if based on the shorter versions of the Henderson trend filter—converge relatively quickly to their final values. Moreover, it is not possible to distinguish between an outlier and a change in the underlying trend-cycle from a single observation, unless a particular event generating an outlier is known to have occurred. In general, several observations are needed to verify the change in the trend-cycle indicated by the first observation.

45. Trend-cycle estimates obtained through seasonal adjustment offer several advantages over simple 3-month and 12-month growth rates for assessing the current inflationary pressure, particularly if these estimates are based on one of the newest seasonal adjustment packages. First, the estimates obtained should be more precise and robust, and less influenced ex post by disturbances from outliers through the following:

  • automatic selection of filter length based on degree of noise relative to trend-cyclical variations in the data—that is, the “noise-to-signal ratio”;25

  • automatic, as well as user-determined, outlier detection and adjustment;

  • automatic, as well as user determined, level shift detection and adjustment; and

  • user-determined adjustment for the effect of known irregular events.

46. Second, the estimates should be smoother and provide a clearer signal than the 3-month growth rates. Third, seasonal adjustment reduces the amount of short-term volatility and thus should allow for the use of shorter and more responsive filters. Assuming a stable seasonally adjusted series, estimates based on the 9-term weighted Henderson filter will be close to final within one-two months, while those based on the 3-term weighted Henderson filter will be close to final within two-three months because of the distribution of the weights in the filters. For this reason, the trend-cycle estimates should provide a quicker and more robust indication of turning points in the data than the 12-month growth rates.

47. Decomposing the series into its main components should help forecast the series. For instance, near-term forecasts of highly seasonal series may be best done simply by projecting the level of the trend-cycle component (e.g., by extrapolating using the most recent 1-month growth in the trend-cycle component) and multiplying (assuming a multiplicative seasonal model) the projected trend-cycle by a forecast of the seasonal factors.26 This procedure implicitly assumes that the future multiplicative irregular factors are equal to one (that is, equal to their by-definition average value), which is equivalent to assuming no future irregular impact on the series. This assumption is reasonable since it generally is not possible to forecast the irregular component. Similarly, the simplest and most robust near-term forecast of the level of non-seasonal series may be as equal to the projected level of the trend-cycle component.

ANNEX III Core Inflation

48. As discussed in Subsection D, most efforts to measure core inflation can be seen as trying to extract signals from the measured CPI about possible future inflation trends by quantifying either the persistent or the generalized component of the CPI. Core inflation defined as the persistent or generalized component of a selected measure of inflation (the CPI) should not be confused with the related, but somewhat different, issues of constructing “a general measure of inflation,” measuring “monetary inflation,” and measuring the “purchasing power of money,” which may all require inclusion of prices of a much broader group of products than those covered by the CPI. These measures may also require the use of different weighting procedures than those used for constructing the CPI. The CPI is not designed as a general measure of inflation, but as a measure of changes in the households’ cost of living. It is in practice, however, often used as a general measure of inflation. Core inflation defined as the persistent or generalized component of the CPI should also not be confused with the related, but different, issue of which price domain is controlled by monetary policy, or the normative issue of which price index inflation-targeting central banks should officially target. The term core inflation is, however, often used as if the CPI were a general measure of inflation.

49. Core inflation as persistent inflation can be associated with Milton Friedman’s (1963) definition of inflation as a “steady and sustained increase in the general price level,” according to Roger (1998). Friedman emphasizes the distinction “between a steady inflation, one that proceeds at a more or less constant rate, and an intermittent inflation, one that proceeds by fits and starts….” According to Friedman, the steady or persistent element of inflation will tend to be incorporated into expectations and thus, consistent with Quah and Vahey’s (1995) definition of core inflation, have no medium- to long-term impact on real output. The definition of core inflation as the persistent element is reflected in a common tendency to describe core inflation and trend27 inflation as essentially synonymous.

50. Examples of approaches to measuring core inflation as the persistent component of the CPI includes univariate smoothing techniques and (multivariate) structural vector autoregressive (VAR) models. The simplest measures obtained by smoothing are the 3-month and 12-month growth rates, which, as discussed above, are simply averages of the 1-month inflation rate over the past 3 and 12 months, respectively. Other such measures include the trend-cycle estimates obtained through seasonal adjustment and trend measures obtained by using trend filters, such as the Hodrick-Prescott filter. The structural VAR approach (first presented in Quah and Vahey 1995) decomposes aggregate inflation into a measure of core inflation that is not associated with medium-or long-term changes in output volume and a residual element that is associated with persistent effects on output volume. The decomposition is based on an estimated structural VAR model, including the measured CPI growth rate and a measure of aggregated output volume, together with restrictions on the properties of disturbances to the system. Measures based on this approach may, depending on how the distinction between the short and medium term is drawn, include cyclical movements in inflation associated with excess demand pressures. The lack of monthly or quarterly GDP estimates prevents the structural VAR model approach from being applied to Kenyan data.

51. Core inflation as generalized inflation can be associated with, among others, Arthur Okun’s (1970) definition of inflation as “a condition of generally rising prices” and John Flemming’s (1976) as “the rate at which the general level of prices in [the] economy is changing,” according to Roger (1998). In this conception, relative price disturbances are regarded as “noise” blurring the more general or “underlying” evolution of prices. The notion that relative price movements driven by supply shocks may “distort” the aggregate inflation rate has been controversial for almost as long as aggregate price measures have existed (Roger, 1998). Basically, it is argued that, unless there is monetary accommodation, the quantity theory of money suggest that rises in some relative prices should be offset in terms of the impact on the aggregate price level by falls in other relative prices. If they are not, this must reflect genuine, core inflation. The argument assumes, however, a measure of monetary inflation covering all prices, however defined, and not a cost-of-living-based measure like the CPI, which covers consumer products only.

52. Examples of approaches to measuring core inflation as the general component of the CPI include exclusion-based measures, volatility-adjusted measures, specific adjustment measures, the use of robust, or limited-influence, estimators, such as the median and various trimmed means. Exclusion-based measures involve reweighting the CPI to exclude, or zero weight, particular items, such as fresh fruit and vegetables, petrol, and, sometimes, prices that are deemed to be largely determined by supply-side and nonmarket forces. This is probably the most common approach, but it is crude and ad hoc. Volatility-adjusted measures involve adjusting the CPI weights in inverse proportion to past volatility of the various price series. The historical pattern of relative volatility in prices is assumed to hold in the future-which may not be valid. Specific adjustment measures involve adjusting price movements to remove the effects of specific shocks that are judged to be essentially transient in character. The use of robust estimators involves down-weighting extreme price movements whenever they occur—without regard to the identity of the good or service involved. Most robust measures used in the core inflation context are based on weighted trimmed means, in which a fixed proportion of prices at each end of the distribution of price changes (i.e., the extreme price changes) are zero weighted for that period, and the mean or the remaining price changes recomputed. The lack of sufficiently detailed CPI components prevents the volatility-adjusted and robust estimator measures from being applied to Kenyan data.

53. The overall CPI is also a measure of the general component of the index, but practice and the stochastic approach to index numbers suggest that it may not be the most robust and efficient estimate of the general component. The stochastic approach to index numbers,28 which has gained renewed popularity in the core inflation literature, treats individual price changes as reflecting a generalized trend-the core inflation rate-plus relative price shocks, and possibly a constant rate of long-term changes in relative prices. The standard theory of statistical inference says that the arithmetic sample mean-that is, the measured inflation rate-is the best (most efficient) estimator of the true mean or core inflation rate if the distribution of price changes is normal (Gaussian). However, in almost every country and period over the entire history of price collection, the distribution of price movements has been characterized by high kurtosis29 and right skewness. Extensive simulation analysis in the 1970s indicated that the arithmetic mean is an extremely poor estimator of the central tendency for even quite small departures from Normality, and that the sample median or other forms of trimmed means30 may provide a better estimator of the true mean of the distribution in those circumstances. The use of asymmetric trimmed means may be required to avoid a systematic bias compared with the published aggregated CPI inflation rate, if the skewness appears to be significant and chronic.

54. Studies suggest that measures based on trimmed means may improve the signal-to-noise ratio, while other measures often perform poorly. Folkertsma and Hubrich (2001) in a study of measures based on structural VAR models of aggregate data from a group of European countries, find that none of the measures seemed “to yield core inflation estimates which are sufficiently accurate to be useful for monetary policy purposes.” One of the main shortcomings of measures based on structural VAR models is their instability—history tends to change each time a new observation is added. Marques, Neves, and Sarmento (2000), in a study on Portuguese data, find that the exclusion-based measure is a lagging, not leading, indicator of the overall CPI inflation rate, while the trimmed-mean and volatility-adjusted measures appear to be leading indicators of the CPI rate. Similarly, Vega and Wynne (2001), in a study on aggregate data for the euro area find, that trimmed-mean measures “may be a useful input to the monetary policy process” and find evidence that they outperform the alternative core measures. He finds also, however, that non of the measures does particularly well in forecasting CPI inflation. Cecchetti (1997) also finds, based on US data, that “the CPI excluding food and energy is an extremely poor measure of any underlying or core component of the CPI” and that it is not less volatile but often more volatile that the overall CPI. He also concludes that “limited-influence estimators are more efficient estimators of the central tendency of the price-change distribution than is the overall mean.” Aucremanne (2001), however, finds, based on Belgian data, that for the whole sample all core measures tested were lagging rather than leading the overall CPI. He attributes this surprising finding to the effects of the second positive oil price shock in 1979–82 and the negative oil price shock of 1985–86, which had a direct impact on the observed inflation and a significant but only indirect impact on the core measures through the second- and third-round effects. Aucremanne’s example shows that the key information for future inflation may sometimes be located in the tails of the distribution, and thus excluded from trimmed-mean based core measures. Therefore, monitoring the detailed component series, and not only aggregate measures, often proves to be critical. Also, it follows that the core measures should never be the only policy indicator.

55. The studies show that volatility-adjusted measures, while often showing the biggest reduction in volatility, often result in a disappointing loss of signal. These measures may often be biased compared with the overall CPI, and show poor out-of-sample performance unless the pattern of relative volatility in prices is stable.

References

  • Aucremanne, Luc, 2000, “The Use of Robust Estimators as Measures of Core Inflation,” Nederlandsche Bank Staff Report No. 61 (Amsterdam: Netherlandsche Bank).

    • Search Google Scholar
    • Export Citation

  • Blinder, Alan S., 1997, “Commentary,” Federal Reserve National bank of St. Louis Review (May/June), pp. 157 –60.

  • Bloem, Adriaan, Robert Dippelsman, and Nils O. Maehle, 2001, Quarterly National Accounts Manual: Concepts, Data Sources, and Compilation (Washington: IMF).

    • Search Google Scholar
    • Export Citation

  • Bowley, A. L., 1901, Elements of Statistics (Westminster London: P.S. King and Son).

  • Cecchetti, Stephen, 1997, “Measuring Short-Run Inflation for Central Bankers,” Federal Reserve Bank of St. Louis Review (May/June), pp. 143 –55.

    • Search Google Scholar
    • Export Citation

  • Diewert, W. Erwin, 1995, “On the Stochastic Approach to Index Numbers,” Department of Economics Discussion Paper No. 95–31 (Vancouver: University of British Columbia).

    • Search Google Scholar
    • Export Citation

  • Edgeworth, F. Y., 1887, “Measurement of Change in the Value of Money,” memorandum presented to the British Association for the Advancement of Science, reprinted in Papers Relating to Political Economy, Vol. 1, by F. Y. Edgeworth (New York: Burt Franklin, 1925), pp. 198 –297.

    • Search Google Scholar
    • Export Citation

  • Flemming, J. S., 1976, Inflation, (London: Oxford University Press).

  • Friedman, Milton, 1963, Inflation: Causes and Consequences (New York: Asia Publishing House).

  • Folkertsma, C. K., and K. Hubrich, 2001, “Performance of Core Inflation Measures,” Nederlandsche Bank Staff Report No. 63 (Amsterdam: Nederlandsche Bank).

    • Search Google Scholar
    • Export Citation

  • Jevons, W. S., 1863, A Serious Fall in the Value of Gold Ascertained and Its Social Effects Set Forth, reprinted in Investigation in Currency and Finance by W. S. Jevons (London: Macmillan, 1884), pp. 13 –150

    • Search Google Scholar
    • Export Citation

  • Keynes, J. M., 1930, A Treatise on Money (London: Macmillan).

  • Marques, Carlos R., Pedro D. Neves, and Luis M. Sarmento, 2000, “Evaluating Core Inflation Indicators,” Banco de Portugal Working Paper No. 3–00 (Lisbon: Banco de Portugal).

    • Search Google Scholar
    • Export Citation

  • Okun, Arthur, 1970, “Inflation: The Problems and Prospects Before Us,” in InflatiomThe Problems It Creates and the Policies It Requires ed. by Arthur Okun, Henry Fowler, and Milton Gilbert (New York: New York University Press, pp. 3 –53.

    • Search Google Scholar
    • Export Citation

  • Quah, Danny, and Shaun Vahey, 1995, “Measuring Core Inflation,” Economic Journal, Vol. 105 (September), pp. 1130 –44.

  • Roger, Scott, 1997, ”A Robust Measure of Core Inflation in New Zealand, 1949–96,” Reserve Bank of New Zealand Discussion Paper No. G97/7 (Wellington: Reserve Bank of New Zealand).

    • Search Google Scholar
    • Export Citation

  • _____, 1998, “Core Inflation: Concepts, Uses and Measurement,” Reserve Bank of New Zealand Discussion Paper No. G98/9, (Wellington: Reserve Bank of New Zealand). Also available from the RBNZ website www.rbnz.govt.nz)

    • Search Google Scholar
    • Export Citation

  • Taillon, Jacques, 1997, “Review of the Literature on Core Inflation,” Analytical Series No. 4, (Ottawa: Statistics Canada).

  • Vega, Juan and Mark Wynne, 2001, “An Evaluation of some Measures of Core Inflation for the Euro Area,” European Central Bank Working Paper No. 53 (Frankfurt: European Central Bank).

    • Search Google Scholar
    • Export Citation

  • Wynne Mark, 1999, “Core Inflation: A Review of Some Conceptual Issues,” European Central Bank Working Paper No. 5 (Frankfurt: European Central Bank). Also available from the ECB website www.ecb.int.

    • Search Google Scholar
    • Export Citation
1

Prepared by Nils Mzehle.

2

Defined as the percentage change in the average index value for the last 12 months over the average index value for the previous 12 months.

3

The 12-month rate of change is the rate of change from the same month in the previous year and is sometimes referred to as the “annual” rate of change or the “over-the-year” rate of change. In Kenya, the 12-month rate is called the month-on-month rate of change; a label that elsewhere is used exclusively for the rate of change from the previous month—the 1 -month rate of change.

4

The authorities’ underlying index is equal to the overall CPI excluding rent and food, and represents only 35 percent of the CPI basket. The rent component has for the latest years been imputed by assuming that it follows the rest of the CPI.

5

The trend-cycle is the combined long-term trend and the business-cycle movements in the data.

6

During the same period, nonfood prices increased by 10.0 percent, while food prices increased by 3.7 percent.

7

During the same period, nonfood prices increased by 2.0 percent, while food prices fell by 6.9 percent.

8

Seasonal variations does not cause problems because it can be identified and removed using standard seasonal adjustment tools.

9

Publication of seasonally adjusted CPI data is becoming more common. Many statistical agencies, however, are still reluctant to publish seasonally adjusted CPI data because these data typically are subject to revisions.

10

Caused by an 11.8 percent increase in fuel and power prices.

11

See, among others, Blinder (1997) and Cecchetti (1997).

12

That is, without temporary removal of any level shifts or outliers in the series before smoothing the series. X-12-ARIMA provides options for temporarily removing such effects. In the trend-cycle estimate in Table 3, a level shift in September 2000 was temporarily removed before smoothing the series.

13

Autoregressive moving average.

14

In Kenya referred to as “underlying inflation.”

15

See, among others, Taillon (1997), Roger (1998), and Wynne (1999) for an extensive discussion of the concept and measurement of core inflation.

16

Examples of generalized but transient shocks to the CPI inflation rate include changes in sales or value added taxes, as well as exchange rate and money supply shocks.

17

In weighted trimmed mean measures, a fixed proportion of the price changes at each end of the distribution (i.e,. the extreme price changes) are zeroweighted for that period, and the mean or the remaining price changes recomputed.

18

See Marques, Neves, and Sarmento (2000) for an extensive discussion of these issues.

19

See Roger (1997).

20

A 2 × 12 moving average is a 2-term moving average of a 12-term moving average: X¯t2x12=1/24(X¯t1x12+X¯t+11x12)=1/24⁢   Xt−6+1/12⁢  Xt−5+….+1/12Xt+….+1/12⁢ Xt+5+1/24⁢ Xt+6.

21

A Henderson moving average is a special type of weighted moving average in which the weights are constructed to produce the smoothest possible trend-cycle estimate. In X-l 1 and X-l 1-ARIMA, for monthly series, Henderson filters with lengths of 7, 9, and 13 months could be automatically chosen or determined by the user. In X-12-ARIMA, the users can specify Henderson filters of any odd-number length.

22

The three center months obtain 67 percent of the weights in the 13-term Henderson filter.

23

For an introduction to seasonal adjustment and trend-cycle estimation, and to the X-l 2-ARIMA package, see Chapter VIII of Bloem, Dippelsman, and Maehle (2001).

24

The seasonal factors will be final after two years with the default 5-term (3 × 3) moving average seasonal filter (as long as any pre adjustments for calendar effects and outliers are not revised later on).

25

In each iteration, a 13-term Henderson filter is used to temporarily decompose the seasonally adjusted series into a trend-cycle and an irregular component. From these components the noise-to-signal ratio is estimated as R^=I¯/C¯, where C¯ is the sample mean of the absolute change in the estimated trend based on the 13-term Henderson filter |T^t−T^t−1| and Ī is the sample mean of the absolute change in the corresponding irregular component |I^t−I^t−1|. In the final iteration, a 9-term Henderson filter will be used if R^≤1.0, a 13-term Henderson filter if 1.0<R^<3.5, and a 23-term Henderson filter if R^≥3.5.

26

Most standard seasonal adjustment packages, including X-12-ARTMA, provide one-year-ahead forecasts of the seasonal factors.

27

Often meaning the long-run trend, as distinct from the trend-cycle in Annex II.

28

The stochastic approach to index numbers originates according to Diewert (1995), with Jevons (1863), Edgeworth (1887), and Bowley (1901), and was driven by the quantity theory of money. It has been controversial for most of this time, however. Diewert (1995), following up on earlier critiques of the stochastic approach by Keynes (1930), asserts that the basic assumptions underlying the stochastic approach contradict well-established empirical facts.

29

Distributions with a high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have long or heavy tails, compared with the normal distribution.

30

The median represent the 50 percent trimmed mean.

Same Series

Other IMF Content

Other Publishers

Cover IMF Staff Country Reports
Kenya: Selected Issues and Statistical Appendix
Author: International Monetary Fund
Volume/Issue:
Volume 2002: Issue 084
Publisher:
International Monetary Fund
ISBN:
9781451821062
ISSN:
1934-7685
Pages:
159
DOI:
https://doi.org/10.5089/9781451821062.002
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    Kenya: Overall CPI and Main Components (Indies, January 1999=100)

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    Kenya: Main CPI Components, 1990-2001 (Indices, January 1999=100)

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    Kenya: the Trend-Cycle Component and Approximations to the Trend-Cycle Component of the Overall CPI, January 1999-December 2001 (Annualized percentage change)

Kenya: Overall CPI and Main Components (Indies, January 1999=100)

Kenya: Main CPI Components, 1990-2001 (Indices, January 1999=100)

Kenya: the Trend-Cycle Component and Approximations to the Trend-Cycle Component of the Overall CPI, January 1999-December 2001 (Annualized percentage change)