RMSTEs and their decomposition

Table 10.2 shows the results from a series of counterfactual model simulations. For each interest rate rule we show the bias, standard deviation, and RMSTE measured relative to a baseline scenario. The baseline is the results we obtain for the variables from a model simulation where the interest rate is kept equal to actual sample values.[107]

Flexible and strict rules The least volatile development in interest rates is seen to follow from the strict targeting rule (ST). The sharp rise in output growth in 1997 is reflected in the volatility of the interest rates implied by the flexible rule (FLX) and the smoothing rule (SM). The FLX rule puts three times more weight on inflation than on output growth. Table 10.2 shows that the FLX rule gives a slightly more expansive monetary policy compared with the baseline over the period 1995(1)-2000(4): a lower interest rate and weaker exchange rate give rise to somewhat higher output growth (relative bias greater than one) and higher inflation growth (relative bias less than one). The explanation is that while average output growth in the baseline scenario is higher than the target growth of 2.5%, average headline and underlying inflation is lower. Thus the relative bias from a more expansionary monetary policy will become larger than one for output growth (moving output growth further away from the target) and smaller than one for inflation (moving inflation closer to the target). The relative variability of underlying inflation and output growth is 11% lower than in the baseline, while interest rates and exchange rates show greater variability.

The strict targeting rule ST leads to less variability in interest rates since the weight on output growth is reduced to zero. The exchange rate is somewhat weaker. This contributes to reducing the bias in underlying inflation compared to the FLX scenario.

Smoothing Giving the lagged interest rate in the (smoothing) rule SM a positive weight ur = 0.75, gives rise to a considerably more expansionary mon­etary policy. This reduces the bias for underlying inflation and gives a negative bias for headline inflation, which means that inflation on average is above the target of 2.5% in the SM scenario.

Open economy rules The RX rule puts some weight on the real exchange rate, vrt, such that a weaker real exchange rate leads to a tightening of monetary policy. In addition to its direct contractionary effect, the increase in interest rates also partly counteracts the weakening of the exchange rate and dampen the expansionary effects initially working through the exchange rate channel. In our simulation the RX scenario leads on average to a less expansionary monetary policy than the baseline scenario, and a relative bias larger than one for headline as well as underlying inflation. The exchange rate is more stable exchange rate (less variability in vt) at a cost of higher variability in interest rate changes.

interest rate rules we maintain these add factors over the simulation period. Thus, we isolate the partial effect from changing the interest rate rule while maintaining a meaningful com­parison with the historical sample values. In the counterfactual simulation we also make the usual assumption that the models’ parameters are invariant to the proposed changes in the interest rate rule across the period from 1995(1) to 2000(4).

Table 10.2

Counterfactual simulations 1995(1)-2000(4)

Simstart 1995(1), evaluation over 1995(1)-2000(4)

Д4Pt

A4put

A4Vt

ut

Д4 crt

vt

ДRSt

RSt

Policy rule

Target/

trigger

0.025

0.025

0.025

0.040

0.050

0

0

0.06

Baseline

Mean

0.023

0.019

0.027

0.032

0.074

0.013

0.000

0.055

(no rule)

bias

-0.002

-0.006

0.002

-0.008

0.024

0.013

0.000

-0.005

sdev

0.006

0.005

0.023

0.009

0.023

0.017

0.007

0.013

RMSTE

0.007

0.008

0.023

0.012

0.033

0.022

0.007

0.014

Flexible rule

Mean

0.023

0.019

0.028

0.032

0.075

0.016

-0.001

0.052

FLX

Rel. bias

0.94

0.99

1.24

1.03

1.03

1.19

-2.13

1.63

Rel. sdev

1.06

0.89

0.83

0.95

1.02

1.35

1.86

0.76

Rel.

RMSTE

1.05

0.95

0.83

0.99

1.03

1.30

1.86

0.91

Strict rule

Mean

0.024

0.020

0.027

0.032

0.076

0.017

0.000

0.052

ST

Rel. bias

0.80

0.95

1.21

1.04

1.06

1.28

-0.72

1.78

Rel. sdev

1.01

0.90

0.91

0.95

0.96

1.22

0.76

0.52

Rel.

RMSTE

0.99

0.93

0.91

0.99

1.01

1.25

0.76

0.78

Smoothing

Mean

0.025

0.021

0.028

0.031

0.081

0.028

-0.001

0.042

rule SM

Rel. bias

0.04

0.75

1.63

1.14

1.26

2.08

-3.70

3.88

Rel. sdev

1.02

0.88

0.83

0.93

1.12

1.38

1.46

1.12

Rel.

RMSTE

0.99

0.81

0.84

1.03

1.19

1.68

1.47

1.69

Real exchange

Mean

0.023

0.019

0.027

0.032

0.074

0.014

0.000

0.054

rate RX

Rel. bias

1.05

1.02

1.13

1.01

1.00

1.05

-1.61

1.24

Rel. sdev

1.06

0.92

0.85

0.97

1.02

1.20

2.13

0.87

Rel.

RMSTE

1.06

0.97

0.85

0.99

1.01

1.15

2.13

0.92

Unemployment

Mean

0.022

0.018

0.026

0.033

0.069

0.006

0.000

0.062

UR

Rel. bias

1.75

1.20

0.62

0.93

0.80

0.46

1.06

-0.34

Rel. sdev

0.97

0.75

0.90

0.91

0.87

1.17

0.93

0.80

Rel.

RMSTE

1.05

1.02

0.90

0.91

0.83

0.97

0.93

0.76

Wage growth

Mean

0.023

0.019

0.027

0.032

0.073

0.012

0.000

0.057

WF

Rel. bias

1.26

1.07

1.01

0.99

0.94

0.89

0.01

0.73

Rel. sdev

1.06

0.85

0.90

0.93

1.03

1.27

2.09

1.08

Rel.

RMSTE

1.07

0.98

0.90

0.96

0.99

1.15

2.09

1.05

Credit growth

Mean

0.023

0.019

0.027

0.032

0.073

0.012

0.000

0.056

CR

Rel. bias

1.19

1.05

0.94

1.00

0.96

0.94

-0.60

0.94

Rel. sdev

1.03

0.83

0.84

0.93

0.96

1.32

1.92

0.86

Rel.

1.05

0.96

0.84

0.96

0.96

1.19

1.92

0.87

RMSTE

Note: RMSTE and its decomposition in bias, standard deviations and RMSTE of the different interest rate rules, relative to the baseline scenario (with interest rates kept equal to actual sample values).

Real-time interest rate rules When the interest rate rule responds to changes in unemployment we observe an early contraction of monetary pol­icy compared with the FLX rule. This is due to the fact that in the model the unemployment rate follows Okun’s law when demand changes, and thus shows substantial persistence. Hence we observe a gradual tightening of mon­etary policy under the UR scenario over the simulation period as unemployment falls under the trigger level (of 4%) and on average we observe that this rule has the highest average interest rate level across all alternatives. This runs together with the lowest relative bias in output growth and unemployment and the highest relative bias in inflation. In the two alternative real-time rules the interest rate responds to wage growth A4wt (WF rule) and credit growth A4crt (CR rule), respectively. The WF rule gives rise to more volatile inter­est rates than the FLX rule and also to a slightly more contractive monetary policy over the simulation period. The observed volatility in inflation is, how­ever, at the same level as for the FLX rule. The credit growth based rule CR shares many of the characteristics observed for the flexible rule FLX, except that the interest rate is higher in particular towards the end of the simulation period.

Comparing the rules The main features of the counterfactual simula­tions can be seen in Figure 10.4. For each monetary policy rule the figure shows the deviations from the baseline scenario (with ‘exogenous’ short-term interest rates). Figure 10.4 shows that most of the rules give a more expansive monetary policy with lower interest rates in the first two years, compared with the base­line scenario. The initial easing averages around 2 percentage points (pp) and it is followed by a tightening of more than 3 pp. It is hard to evaluate details on the individual rules from the figure although we see that the smoothing rule SM appears to give rise to the most expansionary monetary policy over the simulation period.

When we evaluate the implications for inflation, output and unemployment, we see from Figure 10.4 that the SM scenario and the UR scenario form the boundaries of a corridor for the relative responses for each rule compared with the data. For inflation the width of this corridor is about plus/minus 0.5 pp relative to actual inflation. Output growth deviates from actual growth with about plus/minus 2 pp, and unemployment deviates from actual with about plus/minus 0.7pp. The width of the corridor would be considerably smaller if we take out the SM scenario. Note, however, that the parameters in the monetary policy rules were chosen to illustrate some main features of each rule, and are not necessarily optimising the rule.

It is also of interest to compare the counterfactual simulations with the actual data as shown in Figure 10.2. Output growth increases sharply during

1997 to levels above their assumed steady-state growth rate of 2.5%, and this is a driving force behind the tightening of monetary policy during 1997 and

1998 in the counterfactual simulations in Figure 10.4, where interest rates

image218

Figure 10.4. Counterfactual simulations 1995(1)-2000(4) for each of the
interest rate rules in Table 10.1. The variables are measured as deviations
from the baseline scenario

on average rise towards a peak level of 8%. Interestingly, as can be seen from Figure 10.3, there was a marked tightening of actual monetary policy, but this happened one year later when interest rates were increased sharply under the fixed exchange rate regime in an attempt to resist speculative attacks at the Norwegian krone. The actual monetary policy was eased later in 1998 and at this point we note in Figure 10.4 that there are consi­derable differences between the interest rates implied by the different interest rate rules. This motivates us to make a further assessments of the rules by turning to their implications for the variables in the monetary authorities’ loss function.

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