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Hungary: Selected Issues

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International Monetary Fund
Published Date:
May 1999
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II. Are There Leading Indicators of Inflation in Hungary?1

A. Introduction

13. This chapter investigates the leading indicator properties of macroeconomic aggregates for inflation in Hungary.

14. The investigation uses nonstructural VAR systems. These make no assumptions regarding the structure of the economic model underlying inflation, and simply identify patterns in the data. In this respect, the approach contrasts with that in Chapter III, which attempts to model inflation explicitly.

15. Three principal methods are employed to identify the leading indicator properties for inflation of the aggregates under consideration: bivariate Granger causality tests, bivariate variance decompositions, and bivariate impulse–response functions. The results of these tests provide the basis for the estimation of an unrestricted multivariate VAR model of inflation.

16. Section B discusses the measures of inflation used in the study. Section C presents empirical results for the period 1992:1 to 1998:5. Section D contains a simple multivariate VAR model with an evaluation of parameter stability and forecasting properties. Section E offers concluding remarks.

B. Construction of Inflation Measures

17. The first task is to consider which measure of inflation to seek leading indicators for.

18. Clearly, the consumer prices index (CPI) should be included because of the prominent place it holds in the monetary framework. But it is not necessarily a good measure of inflation. Several factors affecting the CPI do not reflect the stance of financial policies, such as administrative price and relative price adjustments, but these show up in the CPI. These factors may account for the highly skewed and kurtotic cross–sectional distribution of the rate of change in the CPI,2 which implies that the headline inflation rate is vulnerable to changes in a few key components.

19. The concept of “core” inflation has been developed in response to these issues.3 Such measures essentially attempt to remove temporary price shocks from conventional inflation measures, but some also attempt to extract the impact effects of changes in indirect taxes. In the transition context, procedures to do this have generally been applied to the CPI excluding administered prices. This approach is adopted here. A number of methods of defining the “core” of the nonadministered price indices have been used, two of which have been adopted in this paper. The first follows Bryan, Cecchetti and Wiggins (1997), building a “trimmed mean” measure of market–determined inflation. Thus, the tails of the cross–sectional distribution of the consumer price index excluding administered prices, are trimmed and the central portion of the distribution is reweighted. The second measure is constructed by removing its more volatile components such as food, fresh vegetables, and motor fuels. (See Appendix I for details of the construction of these measures).

20. Thus, four inflation measures are defined and presented in (Figure 1).

Figure 1.Inflation Values, 1992–98

  • (i) Headline CPI.

  • (ii) CPI excluding fresh food, vegetables, motor fuels, and regulated prices (mcore),

  • (iii) Nonregulated CPI, excluding 10 percent of each tail in the distritution (mt20),

  • (iv) Weighted median of nonregulated CPI (mmed).

21. Note that 15 of the 160 CPI categories are under administrative control, so the indices excluding them consist of 145 series. In what follows, the market determined series is referred to as CPI(145). The authorities report an index for nonadministered prices which is slightly different from that constructed here. This is mainly because changes to indirect taxes have also been excluded from the authorities’ nonregulated price index, whereas such changes remain included in the CPI(145), for reasons of simplicity. As can be seen in Figure 1, the various core inflation measures are generally below headline CPI inflation and are less volatile.

22. Descriptive statistics for the measures of inflation investigated here are reported in (Table 1). The headline CPI displays the highest standard deviation, while the core of nonregulated CPI has the lowest standard deviation. The Ljung–Box statistic cannot reject the null hypothesis that there is no autocorrelation up to lag 24, which can be interpreted as a sign -of strong persistence and possibly of a unit root process. The trimmed mean (mt20), weighted median (mmed), and headline CPI (mcpi) exhibit strong kurtosis and skewness, while the core of nonadministered prices displays moderate kurtosis.

Table 1.Hungary: Descriptive Statistics—Inflation Measures
Core of nonregulated CPI (Mcore)Median of CPI 145 (mmed)20 Percent Trim of CPI 145 (Mr20)Headline CPI (mcpi)
Mean0.01290.01410.01460.0169
Standard Deviation0.004020.004240.0046530.0123
Skewness-0.131.5041.9671.54
Kurtosis4.657.39910.846.7818
Jarque–Bera10.23102.99279.3687.46
(p–value)0.006000
Ljung Box Q–stat36.04682.38257.6881.94
(p–value)0.054000
Note: All variables are in log first differences. A normal distribution has a skewness of zero and a kurtosis of three.
Note: All variables are in log first differences. A normal distribution has a skewness of zero and a kurtosis of three.

C. Empirical Results

23. The list of indicator candidates Table 2 draws from standard literature on inflation indicators, as most analyses conclude that inflation in transition countries can be explained in terms of standard macroeconomic theory (Sahay and Vegh, 1995; Cottarelli et al. (1998a); Moghadam (1998); Cooray, Mecagni, and Offerdal (1996). Monthly data are used, for 1992:1 to 1998:5.4 Indicator candidates are tested for predictive content on target variables using Granger causality tests, impulse responses, and variance decompositions. The Granger causality tests provide information of statistical forecasting properties of the variables tested; the variance decompositions measure the proportion of the variance of inflation that is explained by the variance of the indicator variable; and the impulse responses can be useful in assessing the time horizon properties of the indicator variables. The estimated bivariate VAR equations are of the following form:

Table 2.Hungary: Indicator Variables
Exchange RatesFinancialFiscalReal VariablesMonetary AggregatesImport VariablesWages
Real effective exchange rate based on cpi (reercpi)Net Domestic Assets of Banking System (fnda)Budget balance of Central Government (percent of nominal GDP) (bbal)Retail sales (ars)Broad Money (fmb)Import Prices in dollars (Ppi6$)Total Industry Wages (Imegrs)
Nominal effective exchange rate (neer)Net Domestic Credit (fdc)Stock market Index (bux)Currency outside banks (fmbcur)Mirror import values from the EU in dollars (mireu)1Unit labor costs (hulc)
Forint per deutsch mark (ftperdm)Deposit interest rates more than one year (fidmy)Industrial production (aip)M2-real (m2real)Mirror import from the World (mirw)2
Forint per dollar (ftperdo)Treasury bill rate (tb90)Unemployment rate (unemp)M2 (m2)
Real effective exchange rate based on ppi (reerppi)Call money interest rate (cmon)Producer price index (ppi)
Real effective exchange rate based on ulc (reerule)Deposit interest rates of less than one year (fid 12m)

Mirror import trade values are those reported by Hungary’s trade partners as their exports to Hungary. The need for these data arises from several changes in Hungary’s import series, including the treatment of trade passing through Hungary’s free trade zone. Hungary’s trade data were also used, with inconclusive results, possibly due to these changes.

Mirror imports from the rest of the world is available only for 1992:1–1997:12. However, mirror imports from the European Union is constructed for 1992:1–1998:4.

Note: All inflation variables are seasonally adjusted. Of the indicator variables, industrial production (aip), retail sales turnover (ars), total industry wages (lmegrs), unit labor costs (hulc), monetary aggregates, unemployment and producer price index (ppi) are seasonally adjusted. Interest rates, stock market index, and exchange rates are not seasonally adjusted. The interest rates are transformed to backwards-looking ‘real’ interest rates by subtracting the 12-month inflation rate from the nominal rates.

Mirror import trade values are those reported by Hungary’s trade partners as their exports to Hungary. The need for these data arises from several changes in Hungary’s import series, including the treatment of trade passing through Hungary’s free trade zone. Hungary’s trade data were also used, with inconclusive results, possibly due to these changes.

Mirror imports from the rest of the world is available only for 1992:1–1997:12. However, mirror imports from the European Union is constructed for 1992:1–1998:4.

Note: All inflation variables are seasonally adjusted. Of the indicator variables, industrial production (aip), retail sales turnover (ars), total industry wages (lmegrs), unit labor costs (hulc), monetary aggregates, unemployment and producer price index (ppi) are seasonally adjusted. Interest rates, stock market index, and exchange rates are not seasonally adjusted. The interest rates are transformed to backwards-looking ‘real’ interest rates by subtracting the 12-month inflation rate from the nominal rates.

where L is the lag operator. X is the set of inflation measures described above. Y is the set of indicator variables.

Unit root testing

24. Before Granger causality testing and application of bivariate VAR systems, the stationarity properties of the time series need to be determined. For this purpose the Phillips Perron (PP) and the augmented Dickey–Fuller (ADF) tests were used. The ADF could not reject the null hypothesis of a unit root for any of the series tested in levels except for deposit interest rates (fid12m, fidmy, fid1m), while the PP test rejected the null for industrial production (aip_sa), budget balance (bbal), unit labor costs (hulc), mirror import values (mireu, and mirw), real effective exchange rate based on unit labor cost (reerulc), and unemployment (unemp) in levels. The PP test in first differences rejects the null hypothesis of a unit root for all series tested, while the ADF test could not reject the null for deposit interest rates of more than a year (fidmy), three month treasury bills (tb90), net domestic assets (fnda_sa), M2, broad money (fmb_sa), producer price index (ppi_sa) as well as all the inflation variables.

25. The difference in results between the PP and the ADF may reflect the ability of the PP test to identify more complex error processes. The results are, however, sensitive to the lag length selected. Considering the need to impose a uniform order of integration and the low power of ADF tests, all variables have been treated as I(1).

Granger causality tests

26. This test identifies if movements in one variable tend to be followed by movements in another. A series of these tests was carried out for each indicator variable: first, a test on the first lag, then on the first two lags together, and so on up to eight lags. It would have been desirable to study longer lag lengths as well, but the loss of degrees of freedom becomes considerable, so a cutoff at eight lags was used. Recall, however, that the series used are seasonally adjusted. (Table 3) reports the groups of lags of each indicator variable which were significant leading indicators for the 12-month rate of change of the four price indices at the 10 percent level.

Table 3.Hungary: Summary of Granger Causality Test, Significance, 10 Percent Level
Indicator Targetmcoremcpimmedmt20
Industrial production (aip)
Retail sales (ars)
Budget balance (bbal)1-2 lags4-8 lags4-5, 8 lags
Stock market index (bux)3 lags
Call money (cmon)
Net domestic credit (fdc)
Deposit interest rate (fid 12m)7-8 lags
Deposit interest rate (fidmy)8 lags8 lags1 lag
Deposit interest rate (fitblm)
Treasury bill (tb90)2 lags
Broad money (fmb)1,5 lags
Money outside Banks (fmbcur)Hag1 lag
M2 Real (m2real)7 lags
M2 (m2)
Net domestic assets (fnda)1-2 lags1-2 lags
Forint per DM (ftperdm)2, 4-7 lags
Forint per Dollar (ftperdo)4-8 lags2, 4-8 lags2, 4-8 lags
Unit labor costs (hulc)
Gross wages industry (lmegrs)7 lags
Imports from EU (mireu)1-5 lags6-8 lags6-8 lags
Imports from world (mirw)1-3, 5-6 lags1-8 lags1-8 lags
Nominal effective exchange rate (neer)6 lags
Producer price index (ppi)1-7 lags1-7 lags2,7-8 lags2,7-8 lags
Import prices in dollars (ppi6$)4-8 lags3,4-8 lags4, 5-8 lags6-8 lags
Real effective exchange rate (reercpi)6-8 lags6 lags6 lags
Real effective exchange rate (reerppi)5-6 lags6 lags
Real effective exchange rate (reerulc)2 lags
Unemployment rate (unemp)6-7 lags
Note: The Table represents the lags which were significant on the 10 percent level. All series are in first differences.
Note: The Table represents the lags which were significant on the 10 percent level. All series are in first differences.

27. A wide variety of variables have some statistical predictive power for at least some of the measures of inflation. Those with predictive power across all the different core inflation measures include the following: producer prices (ppi), import prices (ppi6$), import values in dollars from EU (mireu), budget balance (bbal) and 12 months deposit interest rates (fidI2m). Of the exchange rates, real exchange rates based on cpi (reercpi) and the nominal forint per dollar exchange rate (ftperdo) help forecast future inflation for the core measures.

28. Some have predictive power for two of the core measures. These include net domestic assets (fnda) which shows weak signs of predictive content for median of CPI(145) (mmed) and trim of CPI(145) (mt20), and the mirror import values from the world (mirw).

29. It is notable that the real variables such as industrial production (aip), stock market index (bux) and retail sales (ars) have generally no predictive power in the Granger causality sense. Likewise, gross wages (lmegrs), unit labor costs (hulc) and monetary aggregates such as m2real, and m2, display little predictive power. Broad money and currency outside banks, fmb and fmbcur, respectively, show some significance at very short lags for the trimmed core inflation variables. The unemployment rate (unemp) does not help forecast core inflation.

Variance decompositions

30. Variance decompositions illuminate the relative contribution of innovations in the variables in the VAR to the dependent variable. The procedure used for orthogonalizing the innovations is the Cholesky factorization. The variance decompositions were carried out with four lags for the forecast horizons of 1, 3, 6 and 12 months.

31. The results of bivariate variance decompositions largely reinforce the results obtained from the Granger causality tests. Based on the variance decompositions, it appears that the producer price index (ppi), and import prices (ppi6$) contain predictive content across all inflation measures. Budget balance (bbal) and stock market index (bux) also display predictive power.5

32. Exchange rates such as the real effective exchange rate based on CPI (reercpi) and nominal effective exchange rate (neer) have only moderate predictive power on the variance decomposition test. The forint per deutsch mark variable (ftperdm) is relatively strong for the nonregulated core variable (mcore), while weak for the others. Imports in dollars from the EU (mireu) is strong for the nonregulated core measure, while imports in dollars from the world (mirw) is strong for all variables except the core of nonregulated (mcore). The interest rates (fidmy and tb90) show moderate predictive power.6

33. The variance decompositions for wage measures (Imegrs), and industrial production (aip), retail sales (ars), unit labor costs (hulc) display little or no predictive content across different inflation measures. The behavior of the monetary aggregates (m2real, m2, fmb, and fmbcur) is erratic for the different inflation measures.

Impulse responses

34. The Granger causality tests and variance decompositions have yielded indicator candidates that have information in a statistical sense about future inflation. An examination of the impulse response functions illuminates the lag length between innovations in the candidatate variable, and inflation. The indicators that perform robustly in the impulse responses are generally the ones indicated by the Granger causality and variance decompositions.

35. The producer price index (ppi) appears to have information regarding future inflation peaking at 4–5 months, while the impact of import prices (ppi6$) is evident 4–9 months ahead with a peak at five months. Budget balance (bbal) contains information over a time period of 2–9 months with a peak at 5 months.

36. The impulse response functions of the various interest rate measures ((fid12m), (fidmy), (cmon), and (tb90)) are erratic. Moreover, the interest rate measures are positively associated with inflation.

37. The forint per deutsch mark (ftperdm) consistently generate a response between one and seven months with a peak at three months. The behavior of the import value variables is peculiar as import values from EU (mireu) have the right sign with a peak of impact two to four months ahead of time while the sign of the impulse response of imports from the world (mirw) is consistently negative.

38. The impulse responses of wages (lmegrs), unit labor costs (hulc), employment (unemp) and monetary aggregates (m2real, m3real, fmb, and fmbcur) as well as retail sales (ars) and stock market index (bux) fail to consistently generate a significant impulse response of the right sign.

Assessment

39. The indicators that emerge from the Granger Causality tests, variance decompositions and the impulse responses with significant indicator properties are the producer price index, import prices, budget deficit, and real and nominal exchange rates. Note that the unemployment rate, wages, and monetary aggregates have little predictive power. In addition, the impulse responses indicate relatively short lags between the innovations and inflation, all well less than one year, in some contrast to the perception of inertia in Hungarian inflation.

40. These results represent the statistical relationships emerging out of a VAR; they should not therefore be interpreted as necessarily suggesting causal relationships. Nevertheless, a number of observations may be made about the statistical results.

41. The fact that wages do not have leading indicator properties is particularly notable given the often expressed view of the importance of wage formation in inflation. Not even unit labor costs appear to have leading indicator properties, so productivity does not obviously account for the absence of a statistical link between nominal wage growth and subsequent inflation. Shocks to profit share may mask the link between wage pressures and inflation in the period covered by the data.

42. The importance of real and nominal exchange rates and import prices is not surprising for a small open economy. And the role of the exchange rate in determining the producer price index (ppi) may account for the latter’s leading indicator properties. The fact that monetary aggregates fail to show any indicator properties may reflect the instability of money demand as a result of the transition.

43. Two interpretations of the positive association of interest rates with inflation seem possible. First, to the extent that sterilized intervention has been effective in the pre–and post–crawl eras, the positive association reflects that interest rates have not been raised early enough to nip incipient inflationary pressures in the bud, and vice versa. As a result, interest rates and inflation have risen and fallen together. Second, to the extent that sterilized intervention has not been effective, capital flows have failed to fully anticipate the inflationary pressures. The leading indicator properties of the budget deficit is notable, but is qualified to the extent that inflation also affects the balance though nominal interest payments.

D. Multivariate VAR Model of Inflation

44. Based on the preceding results, exploratory VAR models of the measures of core inflation have been constructed.7 The independent variables included in the VAR systems are nominal money, budget deficit, industrial production, nominal exchange rate, import prices, interest rates, and wages. On basis of the standard errors, r–squared, significance and forecasting properties of the different permutations, “tested down” models are selected. The final models include industrial production, producer price index, broad money and forint per deutsch mark rate as well as a dummy for the Jan. 1993 outlier (VAT shock).8 Only two lags are included and the result of the four–variable VAR(2) are summarized in (Table 4).

Table 4.Hungary: Summary Statistics of VAR Model
MCPIMCOREMMEDMT20
R–squared0.3405720.1340490.6721330.576731
Adj. R–squared0.232469-0.007910.6183850.507342
Sum sq. resids18.654057.3291853.8558476.26187
S.E. equation0.5529960.3466270.2514170.320396
Akaike AIC-53.2363-19.60523.516698-13.9393
Schwarz SC-52.8885-19.25733.864522-13.5915
Mean dependent1.6192531.3023521.418871.459257
S.D. dependent0.631210.3452650.4069880.456472

45. The indicator variables generally have the expected sign across the various target measures, but only lagged inflation (one and two lags), broad money (two lags) and the dummy are significant for all measures of core inflation. Of the various inflation measures, the median of CPI(145) (mmed) variable displays the highest r–squared value and the lowest standard error. The standard error is also highest for the model of headline inflation, MCPI, likely reflecting the role of administered and volatile prices.

46. The impulse responses of the VAR(2) model are presented in (Figure 2). The impulses are of the right sign and in the case of producer price index fairly persistent over the 12 month period. Though this could indicate that producer prices have information on inflation 12 months ahead, it could also indicate the presence of a unit root.

Figure 2.VAR Impulse Responses

47. The residuals from the VARs are generally well behaved. The residuals of the headline inflation measure (mcpi) fluctuate quite frequently outside the standard error bands, with spikes around September 1992, September 1993, March 1995, and May–June 1997. The residuals of the nonregulated core (mcore) are generally within the bands, save for a period in October–December 1992. The residuals of the median and trim of CPI (145) (mmed and mt20) are also mostly within the one standard error bands. The coefficients in the VARs were also reasonably stable as the data set was progressively increased.

48. Finally, the out–of–sample dynamic forecast errors are reported in Figure 3, with the system estimated up until 1997:7, and the obtained values are used to forecast the period 1997:7–1998:5. It is worth noting that the forecasts consistently overestimate the inflation out of sample, for all target variables (a pattern reported again in Chapter IV). This overestimation could be an indication of missing elements in the model, such as unanticipated productivity growth during 1998 or the boldness of the authorities’ inflation targets for that year. Of the different target variables, the median measure (mmed) consistently produces the best forecasts, while headline CPI produces the worst.9

Figure 3.Step Out of Sample Forecast Errors VAR(2)

E. Concluding Remarks

49. The empirical investigation has shown that there are macroeconomic variables that contain, in a statistical sense, information about future inflation. Producer prices, import prices, nominal and real exchange rates, and budget balance all seem to possess this information at various horizons. In most cases, these horizons were relatively short, always less than one year. Wages, unit labor cost and monetary aggregates did not exhibit leading indicator properties.

50. These findings do not necessarily indicate causal relations. Note, in particular, that none of the statistical tests distinguish between permanent and temporary shocks to the indicator variables. While this qualifies the results as indicative of structural relationships, this treatment does nevertheless mimic the practical problem often faced by policymakers, for whom it is not always possible to make the distinction in practice in the time available before a response is required. To this extent, variables with significant leading indicator properties according to these tests may be particularly helpful to policymakers, either because this distinction is not central in their case, or because there is leading indicator information even in “temporary” shocks to these variables.

51. The study also indicates the gains from constructing core inflation measures and, possibly, using them as the focus for monetary policy. In the context of a leading indicator study, the main case for them is that they are more predictable than the headline measure. In particular, of those considered here, the trimmed mean measure seems particularly predictable. Using the two trimmed core inflation measures, 20 percent trim and median of the cross–sectional rate of change distribution of the CPI, consistently yields lower standard errors as well as better dynamic forecasts than using the core inflation measure excluding volatile items and headline CPI. Of the two trimmed mean core variables, the median appears to possess the most attractive forecasting properties. However, there is no guarantee that using the median is the optimal trim. A suggested path for further research would be finding the optimal trim, as defined by Bryan, Cecchetti and Wiggins (1997), of the CPI cross–sectional rate of change distribution as a target variable. But whatever the technical advantages of a trimmed mean measure, it is complicated and, to that extent, less transparent than headline CPI. If, on these grounds, such a measure was not adopted as the principal inflation target, trimmed mean measures could still be useful for internal assessment by the monetary authorities.

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APPENDIX I: Construction of Core Inflation Measures: Trimmed Means

1. The motivation for constructing core inflation measures is that monetary policy ought to react to changes in underlying inflation and disregard temporary shocks. Changes in a few key components will give a distorted impression of the rate of inflation. Bryan and Cecchetti (1994) have shown how skewness in the cross–sectional distribution for high frequency data can cause significant noise in the CPI. One solution to the problem is to remove the distortionary influence of ‘outlier’ prices, i.e. remove the tails of the cross sectional distribution. Thus by eliminating temporary movements, we can identify permanent trends in inflation by looking at what is happening to the central portion of the distribution.

2. There are several ways to calculate core inflation.10 A common method is to remove certain volatile components of the CPI such as food and energy. Following the alternative approach of Bryan, Cecchetti and Wiggins (1997), a trimmed mean is constructed from the CPI(145) data set by discarding 10 percent of each tail in the distribution and then taking the average of the remaining data.11

3. More specifically, the observations, x, and their associated weights, w, are ordered. Then we define W as the cumulative weight from observation 1 to I, i.e. W=Σw. We then determine the central portion to be calculated by α/100<W<(1-α/100). This portion is called Iα. We compute the weighted trimmed mean as

4. The 20 percent trim is measured by averaging the central 80 percent of the price change distribution each month.

Prepared by Peter Doyle and Dan-Frederik Nyberg who was on a summer internship in European I Department, Central II Division on June 16-September 11, 1998.

There is no consensus regarding the definition of core inflation. Early attempts can be found in Eckstein (1981), and more recent examples in Bryan and Cecchetti (1993) and Bryan, Cecchetti and Wiggins (1997).

All variables are in logs, except for the interest rates and budget balance. The monthly inflation rates are calculated by taking the first difference of the logarithms.

Stock market index is strong except for core inflation measure, while the budget balance is weak for the nonregulated core (mcore) and headline inflation (mcpi).

The deposit interest rates 1–12 months (fidI2m) explains 15 percent of the variation for the nonregulated core variable.

See Bruno (1993) for a theoretical model.

The variable import prices (ppi6$) was originally included but had the wrong sign and was therefore excluded in favor of industrial production (aip). Various exchange rate measures, nominal and real, were considered, with the best results produced by forint per deutsch mark (ftperdm).

Bryan and Cecchetti (1994) find that the median measure produces superior forecasts of inflation in United States.

For additional approaches, see Roger (1997) and Quah and Vahay (1995).

For an overview of various trimmed mean measures, see Berkowitz (1998).

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