The Interest Rate MP Reaction Function

The Taylor Rule

The forward looking specifications of the monetary policy rules is estimated using the Generalised Methods of Moments (GMM) based on CGG (1998, 2000). The backward looking (contemporaneous) specification is estimated using the Ordinary Least Square (OLS) approach. The GMM is employed to estimate the unknown parameters in the forward looking monetary policy rules described by Equation (2.20). The forward looking horizon for expected inflation is four quarters. Given that the instruments are correlated with the endogenous variables and uncorrelated with the error term, GMM estimators are strongly consistent and asymptotically normal.

Accordingly, the policy targets and instruments used are as follows: lags of monetary policy nominal rate, monetary base rate, inflation gap, the output gap, the exchange rate and the nominal income. The J-statistics tests the validity of the over-identifying restrictions for the GMM estimations. The monetary policy RFs are estimated for three UK policy regimes. Policy regime I represents the monetary and shadow/explicit exchange rate targeting regimes that covers from 1962Q1 to 1992Q4. Following the shift to the inflation-targeting regime in October 1992, policy regime II represents the inflation-targeting regime with RPI and CPI. This regime is presented as policy regime II for the period from 1993Q1 to 2007Q2.

The selection of these sample periods is based on the two major monetary policy frameworks in the UK with respect to its conduct and the time horizon in the regime shift (from a monetary targeting to an exchange rate then towards inflation targeting regimes). This period ends around the start of the GFC, 2007Q2. Policy regime III represents the period known as the GFC followed by recession and recovery (2007Q3 to 2014Q4). The separation of the policy regimes is tested as a break point using the Zivot and Andrews SB algorithm based on T=15% observation trimming and are significant at 5% level. The analysis estimates the Taylor’s rule reaction function using OLS-BL, for backward looking and the GMM for forward looking reaction functions. The results, reported in Table 2.4, show that the Taylor type reaction function based on Equation (2.20) had a significant operational feasibility for the non-inflation targeting I) and the inflation targeting regimes (PR-II and PR-(PR-III). The most important common element of policy behaviour in inflation targeting regimes is instrument smoothing with statistically significant coefficients (as in English et al., 2003) of lagged policy rates. Rudebusch and Svensson (1999) argue that gradualism in policy is the characteristic of inflation targeting countries. The statistical significance of the inflation gap coefficient in both backward and forward looking RFs is expected, given the success in disinflationary process in inflation targeting economies. The estimates are in good contrast to

52

simulation estimates of Taylor rules using data from 1962 to 2014. Particularly, the estimates before the GFC are in line with the plausible explanation that highlights a shift in the UK monetary policy reflecting a lesser emphasis on inflation. This is also consistent with the movement in interest rates for a long period of time and the austerity measures from early 2008 to early 2009. This occurs when inflation was above the target 2% level.

Comparing PR-III with PR-I and PR-II, the response of inflation in PR-II is higher which satisfies the Taylor principle. Turning to output gap, the response is also higher in the inflation pre-2007 period. The annual change in exchange rate is more relevant in the pre-inflation targeting period than the inflation targeting and post-crisis periods. This outcome is consistent with the UK monetary policy structure where exchange rate was a policy target during the pre-inflation targeting period.

The significant change in the lagged policy rate is more prominent during the pre-inflation targeting and post 2007 period, unlike Martin and Milas (2013) where their study failed to find significant changes in the equilibrium nominal interest rate or the degree of interest rate smoothing.

Additionally, the study by Martin and Milas did not account for the pre-inflation targeting period so its completeness is questionable.

Table 2.4 Estimates of the Taylor Rule Type of the UK Interest Rate RFs

Policy Regime I Policy Regime II Policy Regime III

1962Q1-1992Q4 1993Q1-2007Q2 2007Q3– 2014Q4

Notes: numbers in parentheses are standard errors. OLS-BL and the GMM-FL, values inside parenthesis refer to level of significance at 10% (*), 5% (**) and 1% (***). The values are determined using autocorrelation consistent standard errors and Jackknife heteroscedasticity, GMM Generalised Method of Moments. The J-statistics tests the validity of the over-identifications for the GMM estimations. All the estimated OLS/GMM models include a constant term. The dependent variable is 𝑅𝑡. The break point given as the p-value of the Zivot-Andrews breakpoint test. The p-value is reported from the maximum LR F-statistic using 0.15 observation trimming, based on Hansen (2001) method. The estimated breakpoint is reported where the test statistic is significant at 0.05. The statistics for the validity of instruments has a 𝜒² distribution with 21 degrees of freedom (25 instruments for 4 parameters) and takes the value of 31, 17.4 and 9.6 respectively for each samples, and does not reject the null at 𝜒_0.05² (21) = 32.671.

Source: author’s calculations.

The post-crisis period signifies a clear demarcation from the inflation-targeting regime. Table 2.4 also presents the post-crisis OLS-BL and GMM-FL estimates of the Taylor empirical model using quarterly data from 2007 to 2014. Martin and Milas (2013) data includes only from 2007 to 2010

53

which is marked as a recession period so their data could be misleading as it covers only a short period of time. The response of inflation and output gap in this period is only significant at 10%

level of sig. in both the backward and forward looking RFs. Martin and Milas (2013) also find insignificant inflation response to the nominal interest rate. There is a sharp decline in the output gap as compared to PR-I and PR-II. This result is consistent with Martin and Milas (2004, 2013) and Mihailov (2006). The inflation gap coefficients are significant rating from 5% to 10%. 𝛿_𝑇𝑅 >

0, the coefficient of the exchange rate deviations, implies that the monetary authority leans against the wind. Furthermore, the results in PR-II and III in OLS-BL, with regards to inflation gap and output gap confirm that the UK monetary authority leans against the wind during the inflation targeting and post-crisis periods. The non-inflation targeting regime (PR-I) shows no evidence of this monetary behaviour. The results in Table 2.4 also show that PR-I estimates (coefficients) are statistically significant for exchange rate and lagged policy rate. This implies that the period is known as a non-inflation targeting regime that exchange rates and lagged interest rates were in operation. Although the UK monetary policy did not peg lagged interest rate as a policy target, the outcome suggests that the monetary authorities implicitly tracking lagged interest rate to stabilise the real economic activity and adjust the nominal policy rate.

0 4 8 12 16

65 70 75 80 85 90 95 00 05 10

The UK Inflation Gap

Monetary Polic y Rate in the UK

Source: author’s analysis.

Figure 2.7 Monetary Policy Interest Rate and Inflation Gap in the UK

The set of instruments for the GMM estimates of the TRRF include a constant, 1–6^th, 9^th and 12^th lags (as in Hansen, 2001) of the interest rate, the inflation gap, the output gap, and exchange rate gap. The statistics for the validity of instruments has a 𝜒² distribution with 21 degrees of freedom (25 instruments for 4 parameters). The reported J statistics are the minimised values of the objective function so it gets the appropriate test statistics, the J stat values are multiplied by the number of observations in each policy regime. The test statistics takes the value of 28.3, 14 and 8.4, respectively for PR-I, II and III, so do not reject the null of validity of instruments (𝜒_0.05² (21) = 32.671), hence, the over-identifying (OI) restrictions of the set of instruments cannot be rejected

54

for all selected periods and the entire series of the MP rules. Overall, the Taylor rule is rather successful in explaining the UK monetary policy in the pre and post-inflation targeting period.

The GMM estimates presented in Table 2.4, consistently confirm that the coefficient on the inflation gap is statistically significant (𝛽 < 0 FL in PR-I & II; 𝛽 > 0 BL for PR-I, II and III; FL for PR-III).

It also holds true to the output gap except in PR-I and II. Figure 2.7 displays the actual path of the monetary policy interest rate and the inflation gap, showing a close relationship during the three policy regimes. The negative coefficients represent opposite relationship with the rate of change of the monetary policy rate. This is correctly represented in the inflation gap in PR-I as the inflation is declining while the monetary policy rate increases. The period 1970s and 80s is known as a high inflation period. The sign of point estimates represents in a manner of inflation targeting, although inflation-targeting regime began in October 1992, with a break date identified at 1992Q4, which is a cut-off point for this regime. The monetary authority was implicitly considering the inflation dynamics while base money and exchange rate were known to be the monetary policy targets in the pre-1992 period. The impact of money supply was assumed neutral in the long-run. The exchange rate reaction coefficient (𝛿_𝑇𝑅) is statistically significant in both FL and BL TMRF in PR-I (FL and BL), PR-II (FL) and PR-III (FL). The coefficient carries a negative sign during the non-inflation targeting regime (both BL and FL), PR II (BL) and the expected positive sign in PR-II (BL) and PR-III (both BL and FL). The positive output gap coefficient indicates that the central bank increases the interest rate while actual output is above potential output. A positive inflation gap also indicates the average inflation deviations from target inflation (𝛽 > 0).

There is a strong and statistically significant negative reaction to output gap in TMP RF during PR-I (non-inflation targeting regime). The monetary policy also responded to the exchange rate during policy regime I. It shows significant and strong negative coefficient. The reason for this might be due to the monetary authority’s implementation of the exchange rate band regime (targeting regime) until October 1992. The UK monetary policy responded significantly to inflation gap, output gap and exchange rate gap during PR-I. During PR-II, the monetary policy displays significant reaction to inflation gap, output gap and exchange rate gap in the BL and FL reaction functions during PR-II except to the exchange rate gap. The financial crisis and recovery period (PR-PR-III) display weak response to inflation gap both in BL and FL reaction functions, but significantly to output gap (BL), exchange rate gap (BL) and to monetary policy instrument smoothing both in BL and FL functions.

The results also show that the UK monetary authority has managed to keep the inflation gap relatively low during the non-IT, and IT periods, except some high inflationary instances. The instrument smoothing (lagged monetary policy rate) is significant in all sample periods for the Taylor-type reaction function.

55 2.8.2 The Monetary Base Policy Reaction Function The McCallum Rule

The original McCallum rule is a backward looking reaction function. The study estimates both the contemporaneous and forward looking versions of the monetary policy rules. The monetary base (Δ𝑏%) is the dependent variable to determine the response as stated by the rule. The income gap term, defined by McCallum as trend growth minus actual growth and defined by Taylor as an actual growth minus trend growth. The term is expected to have a positive coefficient. When actual income growth is declining relative to the trend growth, monetary policy is expected to be accommodative and base money expands. Table 2.5 reports OLS-BL and GMM-FL estimates for the MMPR with monetary base as the central bank’s policy variable, in Equation (2.21).

Similarly, the set of instruments for the GMM estimates of the MRRF includes a constant, 1–6^th, 9^th and 12^th lags (as in Hansen, 2001) of the monetary policy base, the nominal income gap, and the exchange rate gap. The statistics for the validity of instruments has a 𝜒² distribution with 22 degrees of freedom and takes the value of 31, 17.4 and 10.11, respectively for PR-I, II and III, so the null hypothesis for the validity of instruments is not rejected, (𝜒_0.05² (22) = 33.924) . The over-identifying restrictions of the set of instruments cannot be rejected for all selected periods and the entire series of the MRRF. According to the test statistics, the rule is successful in explaining the UK monetary policy in the pre-inflation targeting period. The estimates of monetary base reaction functions for the UK monetary policy rule, reported in Table 2.5, show that in the non-inflationary targeting period (1962Q1 to 1992Q4) an increase in the nominal income gap is met with a decrease in monetary base, which is expected. The estimated coefficients on the income gap in this period are not close to the value 0.5, employed by McCallum that was estimated for Japan and the U.S.

(McCallum, 2003). The period from 1993Q1 to 2007Q4, (inflation targeting to the start of GFC) follows the policy rule whereby an increase in the nominal income gap is met with an increase in monetary base, i.e. the central bank was leaning against the wind. The same is true during PR-III.

The nominal income gap coefficient has a positive sign in PR-II (both FL and BL) and PR-III (FL).

In the period 2007Q3 to 2014Q4, which refers to as the GFC and recovery, the McCallum type rule is not able to explain this policy regime and the policy does not seem to be the appropriate reaction function for the UK. The results, both the BL and FL reaction functions’ coefficients of the nominal income gap, show that the reaction was not in accordance to the value (0.5) suggested by McCallum. Furthermore, the lower value coefficients of the nominal income gap suggest that the central bank monetary policy target of the nominal income path has not been met with a strong movement in the monetary base (GMM instrument). If the reaction exceeds the McCallum proposed value, the strong movement of the income gap could have been the cause that destabilises the

56

economy. This has not been the case for the UK from 1962Q1 to 2014Q4. The most obvious example of an intermediate target in monetary policy is the rate of growth of the money supply.

This was attempted explicitly in the UK during the period known as the “Medium Term Financial Strategy (MTFS)” between 1981 and 1985 (BoE, 2009).

Table 2.5 Estimates of the McCallum Rule Type of the UK Interest Rate RFs

Policy Regime I Policy Regime II Policy Regime III

1962Q1-1992Q4 1993Q1-2007Q2 2007Q3– 2014Q4

Notes: numbers in parentheses are standard errors. OLS-BL and the GMM-FL, values inside parenthesis refer to level of significance at 10% (*), 5% (**) and 1% (***). The values are determined using autocorrelation consistent standard errors and Jackknife heteroscedasticity, GMM - Generalised Method of Moments. The dependent variable is the rate of change of the monetary base Δb(%).The estimated breakpoint is reported where the test statistic is significant at 0.05 level.

Source: author’s analysis.

At the outset of the strategy, a declining target range for money growth was published in the hope that this would bring down the rate of inflation. However, the scheme was abandoned in 1985 because the money supply proved impossible to control with sufficient precision and the rate of inflation fell sharply. As an intermediate target, the money supply seemed to tell us nothing useful (Bain and Howells, 2009). Instrument smoothing is significant in the estimates for the UK economy.

The reaction of base money to the exchange rate is less important during PR-I and II, both in BL and in FL reaction functions. In the case of the GMM estimates, only PR-III shows a statistically significant reaction to the exchange rate where the accommodative-exchange rate depreciations met with an increase in base money.