A univariate analysis

59. A univariate analysis of inflation dynamics is used to assess inflation persistence both in relative and absolute terms. First, a simple regression of monthly seasonally adjusted consumer price inflation on its lag and on a linear trend is estimated, as in equation (1), where ${\pi }_t^m=\frac{P_t}{P_{t-1}}-1$ and P_t is the seasonally adjusted consumer price index (CPI) in month t:¹⁶

A higher value of β indicates stronger inflation persistence. The estimate of β can be used to compute an estimate of the half-life of a unit shock to inflation. The half-life measures the length of time needed to halve the magnitude of the original shock and is obtained using the formula in equation (2):

To allow for time variation in the degree of persistence, the half-life is estimated recursively using rolling samples of 60 monthly observations from January 1994 to March 2005. The procedure is also repeated using CPI inflation data for Poland and the Czech Republic.¹⁷ The results are displayed in Figure 2, where the horizontal axis indicates the end of the regression window.

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Inflation Persistence in Hungary, Poland, and the Czech Republic, 1999-2005

(Estimates of the half-life of a unit shock, months, in percent)

Citation: IMF Staff Country Reports 2005, 215; 10.5089/9781451818024.002.A003

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60. The results in Figure 2 suggest that CPI inflation persistence in Hungary is small in absolute terms and lower than in Poland. The estimated half-life of a unit shock to CPI inflation in Hungary is only about one month and has declined somewhat since 1999. As Figure 2 suggests, CPI inflation in Hungary is also less persistent than in Poland, where the estimated half life has been in the 1.5–2.5 month range since 2000. In the Czech Republic, inflation inertia appears to be even lower than in Hungary, with a half life of less than one month. For further comparison, Celasun, Gelos, and Prati (2003) apply a similar method to Turkish CPI data and obtain a half-life of about one month in Turkey over the 1999 to 2002 period.¹⁸

The relative importance of backward- versus forward-looking behavior

61. The second approach assesses the relative importance of backward- and forward-looking behavior by estimating a multivariate regression that nests both hypotheses. The distinction between backward- and forward-looking behavior is important from a policy point of view because the output costs of a disinflation are, other things equal, higher with backward-looking behavior. In this section, after describing the empirical model, survey inflation forecasts are used to assess the degree of forward-looking pricing behavior in Hungary. The results suggest that expectations of future inflation play a much more important role than past inflation in explaining current inflation dynamics.

The empirical model

62. In the model, inflation depends linearly on the previous period’s inflation rate, on the one-period-ahead expected inflation rate, and on the current marginal cost.¹⁹ The empirical model thus nests the possibility of both backward- and forward-looking price-setting behavior, as in Galí and Gertler (1999), and is a modification of the Calvo (1983) New Keynesian Phillips Curve in which all agents are forward looking. The inflation process is described by

The dependent variable, π_t, is the 12-month inflation rate at the end of a given month, E_tπ_t+1 is expected inflation for the following 12 months, and lagged inflation refers to the period between 12 and 24 months ago. Real marginal cost, mc_t, is the 12-month average over the past 12 months. Since a typical firm in a small open economy is likely to use imported intermediate goods and domestic labor as inputs in production, real marginal cost, mc_t, is proxied with a combination of the real effective exchange rate (the ratio of the trade share-weighted average of foreign consumer price levels to the domestic price level, which is a proxy of the real cost of imported inputs), and domestic real unit labor costs (both in deviation from trend).²⁰ An increase the real exchange rate therefore signals a depreciation. The estimated equation is thus:

where REER is the detrended real effected exchange rate and RULC is the detrended real unit labor cost. The degree of inflation inertia is governed by the parameter (1-α). The higher is the share of backward-looking price setters, the larger is the weight (1-α) on the lagged inflation term.²¹

63. Inflation expectations are measured using actual surveys of inflation forecasts made by professional forecasters. The forecasts are collected by Reuters on a monthly basis since 1997, for the end of the current year and of the following year. A 12-month-ahead expected inflation measure can then be obtained by taking the weighted average of the forecasts for the current and following year. In December, for instance, the one-year-ahead inflation forecast is simply the forecast for the next year. In January, a weight of eleven-twelfths is attached to the forecast of the current year, and one-twelfth to the forecast of the next year, and so on.

64. As Figure 3 suggests, expectations track the actual realized inflation rates closely. Figure 3 presents a graph of actual inflation over the last 12 months against one-year-ahead forecasts made 12 months before. An important question is whether the survey expectations contain information about future inflation that is not contained in past inflation. To answer this question, actual inflation is regressed on the forecast made one year earlier and on the inflation rate on year earlier. The results (not shown) suggest that survey expectations have statistically significant forecasting power for future inflation, even after controlling for the inflation rates of recent history. In this sense, the survey expectations are forward-looking.²²

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Hungary: Current Inflation and Forecasts Made One Year Earlier, 1997-2005

(In percent)

Citation: IMF Staff Country Reports 2005, 215; 10.5089/9781451818024.002.A003

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Results

65. Table 1 displays the estimates of equation (4) based on three estimation approaches. The first column displays the results obtained using ordinary least squares (OLS). The second column reports results obtained using instrumental variables (IV). The IV regression addresses the possible endogeneity of real exchange rate and average real unit labor costs to the unobservable disturbance to inflation in the current period. The instruments are the 12-month lagged inflation rate, expected one-year-ahead inflation, and 12-month lags of the real exchange rate and of the real unit labor costs. The final column reports results obtained using the same instrumental variables but with an alternative measure of expected inflation: actual future inflation. Actual future inflation is often used as a proxy for expected inflation in the literature, although it implicitly imparts greater forecast accuracy to agents than may seem plausible.²³

Table 1.

Hungary: Estimates of Forward - Versus Backward-Looking Behavior ^1/

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

Table 1.

Hungary: Estimates of Forward - Versus Backward-Looking Behavior ^1/

Estimation Technique	OLS	IV	IV
Measure of expectations	Survey expectations	Survey expectations	Actual future inflation
Expected future inflation	0.71	0.74	0.61
	(0.07)	(0.08)	(0.14)
Lagged inflation	0.29	0.26	0.39
	(0.07)	(0.08)	(0.14)
Real exchange rate gap	0.23	0.24	0.15
	(0.08)	(0.08)	(0.10)
Real unit labor costs gap	0.05	0.05	0.04
	(0.26)	(0.33)	(0.49)
P-value of test: α = 0.5	0.004	0.008	0.415
R 2	0.92	0.85	0.67

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

View Table

Table 1.

Hungary: Estimates of Forward - Versus Backward-Looking Behavior ^1/

Estimation Technique	OLS	IV	IV
Measure of expectations	Survey expectations	Survey expectations	Actual future inflation
Expected future inflation	0.71	0.74	0.61
	(0.07)	(0.08)	(0.14)
Lagged inflation	0.29	0.26	0.39
	(0.07)	(0.08)	(0.14)
Real exchange rate gap	0.23	0.24	0.15
	(0.08)	(0.08)	(0.10)
Real unit labor costs gap	0.05	0.05	0.04
	(0.26)	(0.33)	(0.49)
P-value of test: α = 0.5	0.004	0.008	0.415
R 2	0.92	0.85	0.67

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

66. In all three cases, expected future inflation plays a larger role than lagged inflation in determining current inflation. The point estimate of α, the weight on future expected inflation is larger than one-half in all three cases. In the first two columns, the weight is significantly larger than one-half at the 1 percent level, as shown by the p-values in the second-to-last row. The finding of forward-looking behavior is intuitive given the very limited extent of price and wage indexation to past inflation in Hungary. The finding of a substantial forward-looking component in inflation is also consistent with the findings of Celasun, Gelos and Prati (2004) who estimate a very similar model using data on ten emerging markets.²⁴ Finally, the results are robust to excluding the admittedly imprecise real marginal cost proxies from the equation. A regression of actual inflation on past inflation and expected inflation yields an even larger weight on expected inflation.

Estimating the Persistence of Household Inflation Expectations

67. The third approach analyzes the degree of persistence in household expectations. This approach complements the second by analyzing what determines expectations of future inflation and how quickly typical consumers absorb information about the inflation outlook. The importance of household inflation expectations arises from their influence on wage aspirations, and on consumption and savings decisions. The degree of inertia in household expectations, therefore, also influences the persistence of inflation shocks and the costs of disinflation. The model’s estimates suggest that, although household expectations are “sticky,” they are less persistent than in the United States.

68. The methodology used in this approach draws on the Carroll (2003) model, in which households’ views derive from news reports of the views of professional forecasters, which represent the most up-to-date predictions of future inflation. The model is based on the assumption that consumers update information sporadically rather than instantaneously. Each period, a fraction α of consumers update their inflation forecasts using the most up-to-date (professional) inflation forecasts published in the news media. The remaining (1-α) fraction of consumers’ views about future inflation are based on outdated information collected in the past.

69. This model implies the following specification for observed household inflation expectations.²⁵ Household expectations for the next year are a weighted average of the current up-to-date (professional) inflation forecast and last period’s measured inflation expectations:

where H_t(π_{t, t+12}) is the mean measured household (H) expectation of 12-month inflation in period t+12, made in period t; H_t-1(π_{t-1, t+11}) is the mean measured household expectation of 12-month inflation in period t+11 made in period t-1; and P_t(π_{t, t+12}) is the professional (P) forecast of 12-month inflation in period t+12.

70. Estimating equation (4) requires a source of professional inflation expectations, and of household inflation expectations. For consumer expectations, the European Commission (EC) publishes a survey on consumer expectations in Hungary, the GKI survey, on a monthly frequency, going back to 1993. Unfortunately, however, the EC survey does not ask households to name a specific figure for the future inflation rate. Rather, households are asked whether, compared with the previous 12 months, they expect prices over the next 12 months to (i) rise more rapidly, (ii) rise at the same rate, (iii) rise at a slower rate, (iv) stay about the same, or (v) fall.²⁶ The survey is then summarized by a “balance statistic,” an index that rises when agents expect inflation to accelerate over the coming year. This index can then be converted into a forecast of the change in the inflation rate by using the predicted value from a regression of the actual change in inflation on the predicted change.²⁷ Thus, the regression

is estimated, where ${\overline{\pi }}_{t-12,t}$ is the average (year-on-year) inflation rate over the next 12 months, that is, $\stackrel{-}{{\pi }_{t-12,t}}\text{=}\frac{1}{12}\underset{i=0}{\overset{11}{\mathrm{\Sigma }}}{\pi }_{t-i}$ , and GKI_t is the balance statistic for future inflation based on the survey made in month t. The fitted values from equation (5) are then deployed to construct the quantitative household expectation series, H_t(π_{t, t+12}).²⁸ Professional inflation forecasts for average inflation have been available from the Reuters poll since 1997.

71. Table 2 presents the estimates of the household expectations model and suggests that, in a given month, about 20 percent of households access the latest available inflation forecast. The estimate is robust to three alternative specifications (Table 2). For comparison, in the United States, the proportion is about 8 percent (Carroll, 2003). The findings presented here therefore suggest that, although Hungarian household expectations are “sticky” and do not all adjust instantly, Hungarian consumers do receive information about inflation more frequently than do consumers in the United States. This finding is intuitive. In a country with higher and more variable inflation, inflation is likely to affect households more and feature more prominently in the news media than in a country with low and stable inflation, such as the United States. The second row of Table 2 shows that the model’s hypothesis that the coefficients on professional and household expectations sum to one on the right-hand side of Equation (4) has a p-value of 18 percent. The data, therefore, fail to reject the model’s unit sum assumption. The final row of Table 2 reports that the results are robust to including a constant and a lagged inflation term in the model. Both additional terms are small and statistically insignificant at the 10 percent level.

Table 2.

Hungary: Estimates of Speed of Updating of Household Expectations ^1/

Estimating Equation: $H_t\left({\overline{\pi }}_{t,t+12}\right)\text{=}{\alpha }_0+{\alpha }_1{P}_t\left({\overline{\pi }}_{t,t+12}\right)+{\alpha }_2{H}_{t-1}\left({\overline{\pi }}_{t-1,t+11}\right)+{\alpha }_3{\overline{\pi }}_{t-13,t-1}+{\epsilon }_t$

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

Table 2.

Hungary: Estimates of Speed of Updating of Household Expectations ^1/

Estimating Equation: $H_t\left({\overline{\pi }}_{t,t+12}\right)\text{=}{\alpha }_0+{\alpha }_1{P}_t\left({\overline{\pi }}_{t,t+12}\right)+{\alpha }_2{H}_{t-1}\left({\overline{\pi }}_{t-1,t+11}\right)+{\alpha }_3{\overline{\pi }}_{t-13,t-1}+{\epsilon }_t$

Equation	α0	α1	α2	α3	R 2	DW	Test P-value
1		0.21	0.79		0.95	1.97	α1=0
		(0.05)	(0.05)				0.00
2		0.17	0.82		0.95	2.07	α1+α2=1
		(0.06)	(0.06)				0.18
3	0.23	0.23	0.82	-0.07	0.95	2.12	α3=0
	(0.19)	(0.09)	(0.05)	(0.05)			0.18

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

View Table

Table 2.

Hungary: Estimates of Speed of Updating of Household Expectations ^1/

Estimating Equation: $H_t\left({\overline{\pi }}_{t,t+12}\right)\text{=}{\alpha }_0+{\alpha }_1{P}_t\left({\overline{\pi }}_{t,t+12}\right)+{\alpha }_2{H}_{t-1}\left({\overline{\pi }}_{t-1,t+11}\right)+{\alpha }_3{\overline{\pi }}_{t-13,t-1}+{\epsilon }_t$

Equation	α0	α1	α2	α3	R 2	DW	Test P-value
1		0.21	0.79		0.95	1.97	α1=0
		(0.05)	(0.05)				0.00
2		0.17	0.82		0.95	2.07	α1+α2=1
		(0.06)	(0.06)				0.18
3	0.23	0.23	0.82	-0.07	0.95	2.12	α3=0
	(0.19)	(0.09)	(0.05)	(0.05)			0.18

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

Methodology

75. The estimated monetary policy reaction function used in this section is based on the standard approach in the monetary policy literature, as exemplified by Clarida, Galí, and Gertler (1998). The policy interest rate reacts to deviations of expected inflation and the exchange rate from their respective targets. Specifically, the desired interest rate, $i_t^{*}$, is determined by

where E_tπ_t+h is the forecast of inflation h months in the future made in month t, and ${\pi }_{t+h}^{*}$ the official inflation target h months in the future. Under IT, the central bank responds positively to a deviation of the inflation forecast from the target. In line with the literature, a forecasting horizon of h=12 months is assumed.³⁰ The term e_t denotes the (log) forint-euro nominal exchange rate (an increase signals a depreciation), and e^* represents the MNB’s implicit exchange rate target.³¹ e^* may differ from the central parity rate. Finally, the $\stackrel{-}{rr}$ term denotes the long-run equilibrium real interest rate.

76. An independent response to the exchange rate, after controlling for expected inflation, corresponds to a separate exchange rate objective. The literature identifies a number of possible reasons why a central bank may wish to respond to the exchange rate. In an open economy, movements in the exchange rate may carry important information about aggregate demand conditions that the central bank may wish to stabilize. Ball (2000) argues that monetary policy should react to exchange rate movements to offset the effects of the exchange rate on spending. Clarida, Galí, and Gertler (1998) find that in major industrialized countries the exchange rate played a role in setting monetary policy over the 1979–1994 period, but that its quantitative importance was small.³² However, having a separate exchange rate objective raises the possibility of a conflict between IT and the exchange rate regime.

77. In practice, central banks adjust policy rates gradually, so that the actual interest rate moves toward the desired policy rate. Reasons for wishing to adjust interest rates gradually in response to news include a possible loss of credibility following sudden policy reversals, as discussed in Clarida, Galí, and Gertler (1998). Accordingly, this process of gradual adjustment of the actual policy rate i_t toward the desired level, $i_t^{*}$, is modeled following the literature as

where ε_t denotes a mean-zero, serially uncorrelated policy shock. The empirical specification combines equations (6) and (7) from above and can be written as:

where α is a constant that comprises (i) the natural rate of interest, $\stackrel{-}{\mathrm{rr}}$, and, (ii) the implicit exchange rate target, $\alpha =\overline{rr}-\zeta e^{*}$.

78. The model is estimated using IV to address the possible endogeneity of the inflation forecast and of the exchange rate to the interest rate in the current period. The IV estimation is conducted following the two-stage-least squares procedure, using a standard set of instruments. The instruments are: six lags of policy rate, six lags of the inflation forecast, six lags of the log exchange rate, and a time trend.

Data

79. The sample of analysis is May 2001 to March 2005, that is, the period covering IT. The expected inflation term is measured using the Reuters survey of professional forecasters. Using actual inflation forecasts made in real time distinguishes this approach from much of the literature. The canonical approach is to measure expected inflation with actual future inflation. In addition, the explicit inflation targets for year’s end can be interpolated to provide a continuous series of 12-month-ahead inflation targets, ${\pi }_t^{*}$. The nominal exchange rate, e_t, is calculated as the period average of the (log) forint-euro market rate. The nominal interest rate, i_t, is the official MNB policy interest rate.³³

80. For robustness, the estimation is also conducted using an alternative, tax-adjusted measure of expected inflation. In early 2004, there was an increase in value-added and other indirect tax rates. The MNB announced that it would accommodate the first-round effects of the indirect tax shocks on prices (as described in the August 2003 Quarterly Report on Inflation). The estimated direct impact of changes in the taxes on the price level was estimated by MNB staff at 1 percent.³⁴ Accordingly, 1 percentage point is subtracted off the expected inflation rate for 2004.

81. Figure 6 suggests that the policy rate has responded positively to increases in the inflation forecast above target and to forint depreciations. The figure displays the policy rate along with the expected inflation gap and the exchange rate. The figure also suggests that the interest rate is more strongly correlated with the exchange rate than with the inflation gap, but formal analysis in the next subsection is required to test this hypothesis.

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Hungary: Interest Rate, Expected Inflation Gap, and Exchange Rate, May 2001-March 2005

Citation: IMF Staff Country Reports 2005, 215; 10.5089/9781451818024.002.A003

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Results

82. Estimates of the policy reaction function for the IT period suggest that the MNB has responded to both expected inflation and the exchange rate. As reported in Table 3, the response to the inflation gap is 1.48, in line with the IT responses of other central banks, as described, for instance in Clarida Galí, and Gertler (1998). The response is significant at the 10 percent level. However, when the tax-adjusted expected inflation measure is used, the inflation response is no longer statistically significant.

Table 3.

Estimates of the MNB Monetary Policy Reaction ^1/

Estimates of equation: $i_t=\mathrm{(}1-\rho )(\alpha +{\pi }_{t+12}^{*}+\beta (E_t{\pi }_{t+12}-{\pi }_{t+12}^{*})+\zeta e_t)+\rho i_{t-1}+{\epsilon }_t$

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

Table 3.

Estimates of the MNB Monetary Policy Reaction ^1/

Estimates of equation: $i_t=\mathrm{(}1-\rho )(\alpha +{\pi }_{t+12}^{*}+\beta (E_t{\pi }_{t+12}-{\pi }_{t+12}^{*})+\zeta e_t)+\rho i_{t-1}+{\epsilon }_t$

Expected Inflation Measure	β	ζ	ρ	α	R 2	Test P-value
Total CPI	1.48	0.52	0.75	-2.86	0.87	ζ=0
	(0.85)	(0.26)	(0.08)	(1.42)		(0.047)
Tax-adjusted CPI	1.79	0.72	0.80	-3.91	0.86	ζ=0
	(1.39)	(0.26)	(0.06)	(1.42)		(0.008)

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

View Table

Table 3.

Estimates of the MNB Monetary Policy Reaction ^1/

Estimates of equation: $i_t=\mathrm{(}1-\rho )(\alpha +{\pi }_{t+12}^{*}+\beta (E_t{\pi }_{t+12}-{\pi }_{t+12}^{*})+\zeta e_t)+\rho i_{t-1}+{\epsilon }_t$

Expected Inflation Measure	β	ζ	ρ	α	R 2	Test P-value
Total CPI	1.48	0.52	0.75	-2.86	0.87	ζ=0
	(0.85)	(0.26)	(0.08)	(1.42)		(0.047)
Tax-adjusted CPI	1.79	0.72	0.80	-3.91	0.86	ζ=0
	(1.39)	(0.26)	(0.06)	(1.42)		(0.008)

^1/All standard errors are corrected for heteroscedasticity and serial correlation using a Newey-West procedure.

83. The response to the exchange rate is positive and significant at the 5 percent level, even after controlling for the inflation forecast. This result suggests that the MNB has, at times, responded to the exchange rate over and beyond the exchange rate’s predictive power for future inflation. This finding is intuitive, given the policy commitment to keep the exchange rate within the band. When the tax-adjusted expected inflation measure is used, the exchange rate response rises in both magnitude and statistical significance. The estimate of ρ=0.74 provides evidence of interest rate inertia, in line with estimates for other central banks. Finally, the high R² indicates that the model fits the interest rate data well.

84. A counterfactual simulation reveals that the policy rate would have been set more smoothly without the independent exchange rate response. The policy rate based solely on the IT component of the reaction function in equation (9) is denoted by $i_t^{IT}$:

Based on the estimated reaction function for the total CPI, the inflation response parameter is set to β=1.48. The equilibrium interest rate is set to $\stackrel{-}{rr,}$ = 4 percent. In line with the literature, this value is the mean of the exante real interest rate over the sample of analysis.³⁵ Figure 7 compares the interest rate based on solely on IT with the actual interest rate over the 2001–05 period. In late 2002 and early 2003, inflation was expected to meet or slightly overshoot its target, but the exchange rate had approached the strong edge of the band. As Figure 7 suggests, the MNB responded by cutting rates by 300 basis points between October 2002 and January 2003, to below the level that could be justified based on IT considerations. This 300-basis-point cut was subsequently fully reversed in June 2003. Then, in November 2003, an additional 300-basis-point hike raised rates well above the level that could be justified by IT considerations alone. Once again, it appears that this response was motivated by exchange rate movements. Starting in March 2004, policy interest rates were lowered gradually. By early 2005, interest rates had reached the levels that would be expected based on IT considerations. Figure 7 shows that these conclusions are robust to conducting the counterfactual simulation with the tax-adjusted inflation series.

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Hungary: Counterfactual - Interest Rate Based on IT Model, May 2001-March 2005

(In percent)

Citation: IMF Staff Country Reports 2005, 215; 10.5089/9781451818024.002.A003

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