Policy reaction function

14. The study focuses on the period from the end of 1991 to the end of 1998 both because of data availability and because this is the period during which an explicit inflation targeting framework was adopted.⁹ Monthly data on 12-month inflation, 12-month inflation expectations, industrial production index, industrial employment index, money growth, and credit growth are used in the study.¹⁰ Trend industrial production and employment are estimated by the H-P filter; the deviation of actual production and employment from this trend is defined as the output gap and employment gap, respectively.¹¹

15. Augmented Dickey-Fuller tests on all the variables with a constant and a trend term indicate that except for inflation, all other variables are stationary. Further tests of inflation without the trend term show that the unit root hypothesis can be rejected at the 10 percent significance level. Given the low power of the standard unit root test, the evidence supports the hypothesis of the stationarity of the data.

16. Following Clarida, Gali and Gertler (1998a, 1998b), a monetary policy reaction function is estimated for Israel using the following variables: inflation, inflation expectation, and GDP and employment gaps. Generalized Method of Moment (GMM) estimators are estimated.¹² Specifically, the model is of the following form:

where i^*_t is the policy interest rate (discount rate) set by the BoI, π_t+k denotes inflation in period t+k, y_t+1 denotes the output gap or employment gap at time t+1. E is the expected value operator, and Ω_t is the information set at time t. The equilibrium nominal interest rate is denoted by α.

The implied real interest rate rule is then:

where $\overline{\alpha }=\alpha -{\pi }^{*}$ is the equilibrium real interest rate. This real interest rule implies that the response of the real interest rate to changes in expected inflation depends on whether β is greater or less than one.

However, given that the interest rate is likely affected by factors other than those included in the monetary policy reaction function derived in (1), and as the central bankers want to keep a relatively smooth path of interest rate, the following is assumed to be the actual interest rate process:¹³

which assumes a partial adjustment of the deviation of interest rate from its target level. The error term embeds other shocks and factors that influence the interest rate.

Combining the policy rule with the partial adjustment in interest rate, we obtain the following interest rate reaction function:

where ${\omega }_t=-(1-\rho )[\beta ({\pi }_{t+k}-E\left[{\pi }_{t+k}\right|{\mathrm{\Omega }}_t\left]\right)+\gamma (y_{t+1}-E\left[y_{t+1}\right|{\mathrm{\Omega }}_t\left]\right)]+{∊}_t$. It is a linear combination of the forecasting errors of inflation and output and the shock from equation 3. By construction, w_t is orthogonal to any variable in the information set at time t, i.e., there is no correlation between the error term and variables in the information set. In equation 4, the inflation target π^* is not included into the constant term because in Israel the inflation target changes from year to year. Therefore, the yearly target was subtracted from the inflation series as indicated by the model.¹⁴ A variant of equation (4) is obtained by replacing the expected inflation at time t+k with the inflation expectation measure ${\tilde{\pi }}_{t+k}$ derived from the capital markets:

In equation(5), ${\omega }_t=-(1-\rho )[\beta ({\tilde{\pi }}_{t+k}-E\left[{\pi }_{t+k}\right|{\mathrm{\Omega }}_t])+\gamma (y_{t+1}-E\left[y_{t+1}\right|{\mathrm{\Omega }}_t])]+{∊}_t$. Thus ω_t is the linear combination of the forecasting error of the capital market based inflation expectation measure from the expected inflation based on rational expectation, the output forecasting error, and the error from equation (3). Assuming that the market is efficient in pricing in all information, the first term in cot should be close to zero. Thus, ω_t should also be orthogonal to the information at time t.

17. We estimated the monetary policy reaction function in three different ways. First, we estimate a Taylor type of backward-looking rule based on current inflation and expected oneperiod-ahead output or employment. Second, a forward-looking reaction function of the form of equation (4) is estimated with the 12–month lead inflation and with the output or employment one period ahead. Third, the measure of inflation expectation is used as in equation (5). Implicitly we assume a shorter forecasting horizon for real variables. Here the forecasting horizon for inflation is 12 months ahead, while that for the output is one month ahead.¹⁵ According to the Augmented Dickey-Fuller test both the inflation and the inflation expectation measure are trend-stationary, so they are detrended before the estimation.¹⁶ The instrument sets include the lagged output or employment, lagged inflation or inflation expectation, lagged money growth and credit growth and lagged interest rates, up to 3 lags. As there are more instruments than the parameters, the over–identifying test is performed and none of the models is rejected at the conventional significance level.¹⁷ The following table presents the estimation results, t-statistics in parenthesis.

Table 2.

Estimates of Monetary Policy Reaction Function

Table 2.

Estimates of Monetary Policy Reaction Function

	Current Inflation		12-Month Lead Inflation		Inflation Expectation
	Output	Employment	Output	Employment	Output	Employment
α	13.48	9.89	14.13	10.75	13.65	13.55
	(31.3)	(3.47)	(19.8)	(5.88)	(60.3)	(40.7)
β	0.28	0.10	1.41	1.71	0.68	0.68
	(3.97)	(0.39)	(3.17)	(1.88)	(9.32)	(6.06)
γ	0.03	-1.71	-0.34	-1.48	0.26	-1.22
	(0.15)	(-0.51)	(-0.79)	(-0.51)	(1.43)	(-1.48)
ρ	0.84	0.93	0.68	0.90	0.64	0.65
	(18.2)	(18.6)	(5.48)	(17.68)	(17.91)	(13.8)

View Table

Table 2.

Estimates of Monetary Policy Reaction Function

	Current Inflation		12-Month Lead Inflation		Inflation Expectation
	Output	Employment	Output	Employment	Output	Employment
α	13.48	9.89	14.13	10.75	13.65	13.55
	(31.3)	(3.47)	(19.8)	(5.88)	(60.3)	(40.7)
β	0.28	0.10	1.41	1.71	0.68	0.68
	(3.97)	(0.39)	(3.17)	(1.88)	(9.32)	(6.06)
γ	0.03	-1.71	-0.34	-1.48	0.26	-1.22
	(0.15)	(-0.51)	(-0.79)	(-0.51)	(1.43)	(-1.48)
ρ	0.84	0.93	0.68	0.90	0.64	0.65
	(18.2)	(18.6)	(5.48)	(17.68)	(17.91)	(13.8)

18. First, all the models suggest that the interest rate series is highly auto-regressive, the interest rate-smoothing coefficient p is highly significant in most cases and below one. Second, the coefficient γ has the wrong sign in most cases, when the expected output is above the trend then the interest rate will be raised, but when the future employment is strong then the interest rate will be cut. But γ is never significant at any conventional significance level, suggesting that the Central Bank of Israel has consistently adopted a pure inflation targeting strategy during the sample period. This finding would appear to be consistent with the stated objective of the BoI of bringing inflation down over this period to the level close to that in industrial countries. Lastly, coefficient α, which should proximate the average interest rate during the sample period, is highly significant. The highly significant policy reaction coefficient β warrants more discussion below.

19. We can see that β remains well below one when the current realized inflation is used in the reaction function and when the 12-month inflation expectation measure is used.¹⁸ This indicates that the central bank does not raise discount rate one to one to the deviations of inflation from its targeted level. So when there is a surge in past inflation or inflation expectation, the real interest rate based on these inflation measures will decline even after the interest rate increase. However, the picture is quite different when the reaction function was estimated with 12-month ahead actual inflation, which exploits the relation between the ex post 12-month inflation and ex ante policy action. In this case, the β coefficient is well above one and statistically significant.¹⁹ We interpret this result as indicating that even though ex ante the central bank did not appear to raise the interest rate more than proportionately to preempt inflation, the ex post inflation performance suggests that the increase was more than enough to compensate the inflation shock 12 months later. This is entirely consistent with the fact that the inflation expectation measure tends to overstate the actual inflation, as discussed in Section B. One implication of this finding would appear to be that a decision based on this overstated measure ex ante may lead to aggressive inflation reduction ex post.

20. To summarize, our estimates seem to confirm the view of the BoI itself (Leiderman (1999, 2000), BoI (1999)) that the BoI is pursuing a pure inflation targeting regime. Moreover, to the extent that there is reliance on the inflation expectation measure derived from the capital markets, the findings by Bernanke and Woodford (1998) would apply. They showed that a central bank policy reaction rule with pure inflation targeting on a non–structural inflation expectation measure could lead to indeterminacy in the rational expectation equilibrium outcomes and very likely, to excess volatility in the policy variable and macroeconomic outcome. However, as Leiderman (2000) notes, the monetary policy reaction of the BoI at times has been quite rapid to departure of inflation from targeted levels. He argues that in an economy where there is uncertainty about the persistence of inflation shocks and only partial credibility of monetary policy, aggressive policy responses to deviation of inflation can be more effective than gradual policy actions in bringing inflation back to target. Hence, what appears to be “excess volatility” can in fact be an appropriate policy response.²⁰

In-sample forecast based on an alternative policy rule

21. This section follows Bernanke and Woodford (1998) to develop an alternative policy rule which is derived from a dynamic structural model. In their paper, they showed that a policy rule based on the past value of the interest rate itself, its expectation, observed values of output or unemployment and other macroeconomic variables, and the inflation measure will lead to an efficient equilibrium outcome. If we adopt a version of the sticky-price dynamic model used by many others in the literature, e.g., Taylor (1999) and Clarida, Gali and Gertler (1998), and linearize the equilibrium conditions along the steady state, we obtain the following interest rate policy rule which is very similar to the one proposed by Bernanke and Woodford (1998).

where m_t−1 and l_t−1 are the observed money growth and credit growth in last period, with other variables defined as above.

22. The alternative rule along with the estimated monetary policy rule as in equation (5) are also estimated using GMM with four lags of each of the variables in the model. The baseline estimation was done with data from the first month of 1992 to November 1995. This sub-sample was chosen to ensure sufficient observations in the estimation for accurate estimates, and at the same time to leave enough data for in-sample forecasts. Rolling regression is used to continuously update the estimation of the model whenever there is “new” information. One step ahead forecasts of the interest rate are obtained from the estimates of the model. Two measures of inflation are used in the forecasting, one is the current observed past 12–month inflation, the other is the current 12–month inflation expectation measure derived from the capital markets. The comparisons between the actual interest rate and the forecasted interest rates based on the alternative models is tabulated in Table 3, where:

	Alternative Model Eq. 6	Estimated Policy Rule Eq. 5
Actual Inflation	Prediction 1	Prediction 4
Inflation Expectation Measure	Prediction 2	Prediction 3

View Table

	Alternative Model Eq. 6	Estimated Policy Rule Eq. 5
Actual Inflation	Prediction 1	Prediction 4
Inflation Expectation Measure	Prediction 2	Prediction 3

The four in-sample forecasts and the actual interest rate series are also plotted together in Figure 2.

Forecasts of Interest Rate and Actual Interest Rate

Citation: IMF Staff Country Reports 2000, 062; 10.5089/9781451819502.002.A003

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Forecasts of Interest Rate and Actual Interest Rate

Citation: IMF Staff Country Reports 2000, 062; 10.5089/9781451819502.002.A003

• Download Figure
• Download figure as PowerPoint slide

Forecasts of Interest Rate and Actual Interest Rate

Citation: IMF Staff Country Reports 2000, 062; 10.5089/9781451819502.002.A003

• Download Figure
• Download figure as PowerPoint slide

Table 3.

In-Sample Forecasts of Interest Rate vs. the Actual Interest Rate

Table 3.

In-Sample Forecasts of Interest Rate vs. the Actual Interest Rate

	Prediction 1	Prediction 2	Prediction 3	Prediction 4	Actual Interest Rate
Mean	13.38	13.51	13.58	13.55	13.48
Median	13.43	13.60	13.56	13.60	13.50
Maximum	15.14	15.71	16.61	16.70	17.00
Minimum	11.20	11.22	10.56	10.34	9.50
Std. Dev.	1.01	1.16	1.44	1.49	1.71
Skewness	-0.37	-0.15	-0.11	-0.07	-0.36
Kurtosis	2.57	2.49	2.74	2.81	3.12
Observations	36	36	36	36	36

View Table

Table 3.

In-Sample Forecasts of Interest Rate vs. the Actual Interest Rate

	Prediction 1	Prediction 2	Prediction 3	Prediction 4	Actual Interest Rate
Mean	13.38	13.51	13.58	13.55	13.48
Median	13.43	13.60	13.56	13.60	13.50
Maximum	15.14	15.71	16.61	16.70	17.00
Minimum	11.20	11.22	10.56	10.34	9.50
Std. Dev.	1.01	1.16	1.44	1.49	1.71
Skewness	-0.37	-0.15	-0.11	-0.07	-0.36
Kurtosis	2.57	2.49	2.74	2.81	3.12
Observations	36	36	36	36	36

23. The statistics in table 2 indicate that the four forecasted interest rates all have lower standard deviations than the actual interest rate. Some statistical tests are performed to check if the differences are statistically significant. We cannot reject the null that the variances of the five series are equal, neither can we reject the null of equal variance among predictions based on the estimated monetary reaction function as in equation (5) and the interest rate. But the hypothesis of equal variance between the alternative model described by equation (6) and the actual interest rate is strongly rejected.²¹ The test results are reported in Table 3.

24. The results seem to suggest that the alternative model does produce smoother interest rate reactions to shocks in the economy, and the difference is statistically significant. While the estimated monetary policy rule as in equation (5) generates a smaller variance in interest rate forecasts than that of the actual interest rate, the difference is not significant. Using the actual observed inflation in the two forecasting models also generates statistically different interest rate forecasts. These results provide evidence in favor of the view that an alternative policy rule as specified in equation (6) does produce a smoother interest rate outcome than a pure inflation targeting rule, especially if the targeted inflation forecast is not generated from a structural model.

25. The finding that the alternative monetary policy rule produces a smoother policy reaction is consistent with the result from Bernanke and Woodford (1998). When a structural model is used in formulating inflation forecast and based on which policy response is then generated, the additional information contained in the structural forecast helps to smooth the policy reaction. However, a smoother policy reaction to shocks may not coincide with an optimal policy reaction to shocks. Given the inherent tradeoff between the variability in output and in inflation, the conduct of monetary policy must balance the costs and benefits of departure of inflation and output from their target levels. To evaluate whether the alternative policy reaction rule in equation (6) is “better” than the estimated one as in equation (5), one has to compare the tradeoff between the variability of output and inflation implied by these two rules, termed the efficiency frontier of policy reaction functions. For any given level of inflation variability, the reaction function that leads to the lowest output variability on the efficiency frontier is considered a “better” policy reaction function. There is a body of research in this area, as demonstrated by the work of Clark, Laxton and Rose (1997) and more comprehensively, Black, Macklem and Rose (1998), Drew and Hunt (1999) and Taylor (1999). This line of work is beyond the scope of this paper, but provides an interesting line of investigation for future analysis of alternative reaction functions.

Table 4.

Test of Equal Variance Among the Interest Rate Predictions From the Alternative Model and the Actual Interest Rater²²

Table 4.

Test of Equal Variance Among the Interest Rate Predictions From the Alternative Model and the Actual Interest Rater²²

Method	Degree of freedom	Statistic Value	Probability
Bartlett	2	10.6	0.00
Leven	(2,105)	3.09	0.05
Brown–Forsythe	(2,105)	3.07	0.05
Test of equal variance among the predictions from the estimated model and the interest rate
Method	Degree of freedom	Statistic Value	Probability
Bartlett	2	1.18	0.55
Leven	(2,105)	0.34	0.71
Brown-Forsythe	(2,105)	0.34	0.71
Test of a variance between the two predictions based on the actual inflation
Method	Degree of freedom	Statistic Value	Probability
F-test	(35,35)	2.18	0.02
Bartlett	1	5.12	0.02
Leven	(1,70)	2.88	0.09
Brown-Forsythe	(1,79)	2.88	0.09
Test of a variance between the two predictions based on the actual inflation
Method	Degree of freedom	Statistic Value	Probability
F-test	(35,35)	1.51	0.22
Bartlett	1	1.46	0.22
Leven	(1,70)	0.74	0.39
Brown Forsythe	(1,70)	0.76	0.38

View Table

Table 4.

Test of Equal Variance Among the Interest Rate Predictions From the Alternative Model and the Actual Interest Rater²²

Method	Degree of freedom	Statistic Value	Probability
Bartlett	2	10.6	0.00
Leven	(2,105)	3.09	0.05
Brown–Forsythe	(2,105)	3.07	0.05
Test of equal variance among the predictions from the estimated model and the interest rate
Method	Degree of freedom	Statistic Value	Probability
Bartlett	2	1.18	0.55
Leven	(2,105)	0.34	0.71
Brown-Forsythe	(2,105)	0.34	0.71
Test of a variance between the two predictions based on the actual inflation
Method	Degree of freedom	Statistic Value	Probability
F-test	(35,35)	2.18	0.02
Bartlett	1	5.12	0.02
Leven	(1,70)	2.88	0.09
Brown-Forsythe	(1,79)	2.88	0.09
Test of a variance between the two predictions based on the actual inflation
Method	Degree of freedom	Statistic Value	Probability
F-test	(35,35)	1.51	0.22
Bartlett	1	1.46	0.22
Leven	(1,70)	0.74	0.39
Brown Forsythe	(1,70)	0.76	0.38