E¢ cient monetary policy frontier for Iceland
A report to taskforce on reviewing Iceland’s monetaryand currency policies
Marías Halldór Gestsson
May 2018

1Introduction

A central bank conducting monetary policy faces a trade-o¤ between in‡ationand output ‡uctuations - less in‡ation ‡uctuations come at the cost of more
output ‡uctuations (and vice versa). An e¢ cient monetary policy frontier gives
the pairs of in‡ation and output gap ‡uctuations that give the smallest possible
in‡ation ‡uctuations for given output gap ‡uctuations (or the smallest possible
output gap ‡uctuations for given in‡ation ‡uctuation) given the structure of
the economy.
In this paper, we present e¢ cient monetary policy frontiers for Iceland. The
aim is to (i) analyse whether and how the frontier for Iceland has changed during
the past two decades, (ii) compare frontiers for Iceland using di¤erent measuresof in‡ation and (iii) compare the frontier for Iceland with the frontier for a
foreign economy.
An e¢ cient monetary policy frontier is based on an estimated macroeconomic model for the economy which is used to calculate the optimal monetary
policy rules that maximizes a welfare objective for the economy. The modelis then simulated using the optimal policy rules giving the pairs of standard
deviations of output gap and in‡ation that make up the frontier.
The paper is organized as follows: The macroeconomic model and its estimation is discussed in chapter 2 and the calculation of the optimal policy rules isdiscussed in chapter 3. The results are presented in chapter 4, which concludes
the paper.

12The model and estimation

We use a model and estimation techniques similar to the ones in Hunt (2006).
The macroeconomic model can be described by the following equations:y^t=^t 1 +1yyt+1 )2 Et (^t=

1 Et ( 4;t+4 ) + (1^t 1 +3r^t + "y;t5yit=^t 1 + 3 zt + " ;t2y"z;trt
t+Et (zt+1 ) + (1) zt 144^t ] + "i;t
1 it 1 + (11 ) [rt + 4;t + 2 (Et ( 4;t+4 )T ) + 3yy^t=^t 1 +1yt=

1 Et4;t+4+ (11)it=

1 it 1 + (11)rt +zt=1)^t 1 +4z4;t 1 +rt

2 Et^t 1 + "y;t3ry^t+14;t 1 +^t 1 + " ;t2y4;t +Et

24;t+4T+^t3y+ "i;twhere y^ (^y ) is the domestic (foreign) output gap, which is the di¤erence between
output and equilibrium output, r^ (^r ) is the domestic (foreign) real interest rategap, which is the di¤erence between domestic (foreign) real interest rates r (r )and domestic (foreign) equilibrium real interest rates r (r ), z^ is the domestic
real exchange rate gap, which is the di¤erence between the real exchange rate(z) and equilibrium real exchange rate1 , ( ) is domestic (foreign) annulized
quarterly in‡ation, 4 ( 4 ) is a four period moving average of domestic (foreign) annualized quarterly in‡ation, z = z z 1 , is domestic equilibriumrisk premium, i (i ) is domestic nominal interest rate, T ( T ) is the domestic(foreign) in‡ation target rate, Et () is an expectations operator given the available information at time t, "y , " , "z , "i , "y , " and "i are shocks, which are
all modelled as (stationary) AR (1) processes except "z , which is modelled as awhite noise process. Finally, 1 , 2 , 3 , 4 , 5 , 1 , 2 , 3 , , 1 , 2 , 3 , 1 ,2 , 3 , 1 , 2 , 1 , 2 and 3 are estimated parameters.
The …rst four equations represent the domestic economy and the last three
the foreign or the "rest of the world" economy. The …rst and …fth equations
describe aggregate demand (modi…ed Euler equations), the second and sixthdescribe aggregate supply (modi…ed Philips curves) and the fourth and seventh
are monetary policy equations (modi…ed Taylor rules). The third equation gives
development of the real exchange rate in for the domestic economy (a modi…ed
real interest rate parity equation).
The model is estimated for Iceland for two periods, i.e. 2001-2007 and 20102017, and using two measures of domestic in‡ation, i.e. consumer price index(CPI) in‡ation and harmonized CPI (HCPI) in‡ation - a total of four models
are therefore estimated for Iceland. The model is also estimated for the United
Kingdom (UK) for the two periods using CPI in‡ation.
When estimating the models for Iceland, trade-weighted averages of foreign
output gap, in‡ation, equilibrium real interest rates and in‡ation are used for
1 The real exchange rate is here de…ned such that an increase in z gives a depreciation of
the real exchange rate.

2

foreign or variables. When estimating the models for UK, data on these variables
for the Euro Area are used as a proxy for foreign variables.
The models are estimated using Bayesian estimation techniques available inthe computer program Dynare (see Dynare) using quarterly data for 2001-2007(second quarter 2001 - fourth quarter 2007) and 2010-2017 (…rst quarter 2010 third quarter 2017).
All data used in estimating the models for Iceland was obtained from theCentral Bank of Iceland’s QMM database (see QMM) except for data on domestic HCPI, which was obtained from Statistics Iceland (see Statistics Iceland).
Data on foreign output gap was calculated by the author as deviations in foreign
gross domestic product (GDP) from trend using the Hodrick-Prescott (HP) …lter. Data on equilibrium foreign real interest rates was calculated by the author
as HP-trend for the foreign real interest rates using the HP-…lter.
The data used in estimating the model for UK was obtained from the International Monetary Fund (data on domestic and foreign CPI) (see IMF), OECD(data on domestic and foreign GDP and nominal interest rates) (see OECD),
the Bank for International Settlements (data on domestic real exchange rate)(see BIS). Data on domestic and foreign output gap and equilibrium real interest
rates were calculated by the author using HP-…lter.

3

Optimal policy

Given the estmated parameters of the model ( 1 , 2 , 3 , 4 , 5 , 1 , 2 , 3 ,, 1 , 2 , 3 , 1 , 2 , 1 , 2 and 3 ), the estimated parameters of the AR (1)processes for the shocks as well as the estimated standard deviations of theshocks, the optimal policy parameters ( 1 , 2 , 3 ) are chosen such that thefollowing loss function is minimized:
L=1 hX2T ) + (1( tt=0) y^t2i

conditional on 1 2 [0; 1] where 2 (0; 1) gives the relative weight assigned toin‡ation ‡uctuations in the loss function. According to the function, loss (welfare) is increasing (decreasing) in both in‡ation and output gap ‡uctutations.
The policy parameters are chosen and the model is simulated for each value of= 0:1; 0:2; ::::0:9 giving the pairs of standard deviations of in‡ation and output
gap that make up the e¢ cient monetary policy frontier.
The e¢ cient monetary policy frontier is constructed for each of the six estimated macroeconomic model discussed above.

4

Results

The resulting e¢ cient monetary policy frontiers are given in the following …gure:3

Figure 1. E¢ cient monetary policy frontiers

The whole lines show the frontiers for 2010-2017 while the dotted lines show
the frontiers for 2001-2007. The frontiers for UK are blue, the frontiers for
Iceland using CPI in‡ation are black and red where HCPI in‡ation is used.
A few conclusions can be drawn from the …gure:
The frontiers for the UK lie closer to the origin than the frontiers for
Iceland indicating that the structure of the Icelandic economy is such that
it faces worse options in terms of in‡ation and output gap ‡uctuations in
conducting monetary policy than the UK.
The frontiers using CPI in‡ation for Iceland has moved closer to the origin
between the two periods implying better options in terms of in‡ation andoutput gap ‡uctuations in conduction monetary policy in 2010-2017 thanin 2001-2007.
The frontier using HCPI in‡ation in Iceland lies closer to the origin than
the frontier using CPI in‡ation in 2001-2007 but further from the origin
in 2010-2017. It is therefore inconclusive whether using HCPI in‡ation
instead of CPI in‡ation as a measure of in‡ation in the economy improves
the policy options in terms of in‡ation and output gap ‡uctuations in
conduction monetary policy in Iceland.

4References[1] BIS: www.bis.org[2] Dynare: www.dynare.org[3] IMF: www.imf.org[4] Hunt, B. (2006), Simple e¢ cient policy rules and in‡ation control in Iceland,
Central Bank of Iceland’s Working Paper No. 30.
[5] OECD: www.oecd.org[6] QMM: https://www.sedlabanki.is/library/Skraarsafn/Peningamal/2018/Februar2018/QMM_Gagnagrunnur_(.xlsx)_7_februar_2018.xlsx[7] Statistics Iceland: www.statice.is5