INFLATION TARGETING IN A SMALL OPEN ECONOMY
Nargis Bharucha and Christopher Kent
Research Discussion Paper
9807
July 1998
Economic Research Department
Reserve Bank of Australia
We would like to thank Philip Lowe, Lars Svensson and David Gruen for helpful
suggestions. We are extremely grateful to Luci Ellis for training us in the use of
Mathematica 3.0. Any remaining errors are ours. The views expressed are those of
the authors and should not be attributed to the Reserve Bank of Australia.
Abstract
This paper investigates the merits of aggregate inflation targeting compared with
non-traded inflation targeting using a model of a small open economy producing
traded and non-traded goods. An important innovation of our approach is that we
isolate the effects of exchange rate, supply and demand shocks by analysing the
conditional variance of macroeconomic variables. We show that monetary policy
should be more activist in response to exchange rate shocks for a flexible aggregate
inflation target than for a flexible non-traded inflation target. However, in response
to demand and supply shocks monetary policy is more activist for a flexible
non-traded inflation target. The result is robust to the inclusion of forward-looking
expectations, gradual exchange rate pass-through, and discretionary policy. In order
to avoid excessive volatility in product and financial markets, it may be preferable to
target inflation over a medium-term horizon.
JEL Classification Numbers: C61, E52, E58, F41
Keywords: inflation targets, open economy, non-traded inflation,
forward-looking variables, conditional variance
i
Table of Contents
1. Introduction 1
2. Inflation Targeting in an Open Economy 3
3. Non-traded and Traded Inflation - Some Empirical Evidence 5
4. Theoretical Model 10
4.1 The Model 10
4.2 Baseline Model Specification - Model A 15
4.3 State-space Form and Solution 16
5. Results for Model A 18
6. Extensions to the Basic Model 23
6.1 Forward-looking Inflation Expectations 24
6.2 Gradual Exchange Rate Pass-through 25
6.3 Discretionary Solution 26
7. Conclusion 27
Appendix A: Data 29
Appendix B: State-space Forms 31
B.1 State-space Form for Model A 31
B.2 State-space Form for Model B 31
B.3 State-space Form for Model C 32
Appendix C: Further Results 34
References 40
ii
INFLATION TARGETING IN A SMALL OPEN ECONOMY
Nargis Bharucha and Christopher Kent
1. Introduction
The practice of inflation targeting is becoming increasingly popular amongst central
banks. Countries that currently have some form of inflation target include Australia,
Canada, Finland, New Zealand, Spain, Sweden and the United Kingdom. The
Reserve Bank of Australia (RBA) officially adopted an inflation target in 1993 with
the stated objective of keeping underlying inflation between 2 and 3 per cent, on
average, over the course of the business cycle (Grenville 1997).
The merits of inflation targeting are well documented in the literature.1 Inflation
targeting is said to impose discipline on central banks, promote policy transparency,
and foster the credibility of the central bank. This serves to anchor private agents'
inflation expectations, and can help to resolve the time inconsistency problems
associated with monetary policy. For these reasons the central bank may be able to
reduce inflation with less cost in terms of forgone output. In practice, inflation
targets are accompanied by concern for output stability and perhaps interest-rate
smoothing - in other words, the target is said to be flexible rather than strict. Strict
inflation targeting may require large adjustments to the policy instrument. This is
likely to induce extra volatility in output and interest rates, which can promote
uncertainty and damage credibility. Flexible inflation targeting allows the central
bank to maintain low, and relatively stable inflation, while promoting stability in
product and financial markets.
Earlier work on inflation targeting was based on a closed economy framework
where the central bank adjusts its policy instrument (usually the short-term nominal
interest rate), to impact upon demand which in turn affects inflation.2 More recent
work by Svensson (1998) and Ball (1998) focuses on inflation targeting in an open
economy, emphasising the importance of the exchange rate. Movements in the
exchange rate occur in response to changes in interest rates, but also for speculative
reasons. Changes in both interest rates, and the exchange rate, affect inflation
indirectly via a lagged effect on demand. However, changes in the exchange rate
also have a direct effect on the price of traded goods, and thus on aggregate
inflation. Also, changes in the exchange rate may affect inflation expectations
directly.
In this paper, we develop a model of a small open economy with traded and
non-traded sectors. We investigate the implications of aggregate inflation targeting
compared with targeting inflation of non-traded goods and services. Our model
provides a description of an open economy which takes the world price of traded
goods as given. In contrast to previous work, we distinguish between the
consequences of different types of shocks by presenting variances of key
macroeconomic variables, conditional on the type of shock hitting the economy.
The implications of inflation targeting in a small open economy are not as clear as in
the case of a closed economy. For example, consider a shock that causes a
persistent depreciation of the exchange rate which is not justified by fundamentals
(such as a fall in the terms of trade). The immediate result is higher inflation in the
traded goods sector. There will also be some inflationary pressure in the non-traded
sector. Targeting aggregate inflation may involve substantial adjustment of the
interest rate and subsequent volatility in output. One way of avoiding such an
extreme outcome may be to target non-traded inflation. This would require less
adjustment of the interest rate, and hence, less variability in output and non-traded
inflation, at the cost of greater variability in the exchange rate and aggregate
inflation. However, targeting non-traded inflation may produce undesirable
outcomes when the economy is subject to shocks other than to the exchange rate.
For example, in response to demand shocks, or shocks to non-traded inflation, a
central bank with a non-traded inflation target is likely to restore equilibrium
rapidly. This occurs through large adjustments in the interest rate, at the cost of
greater volatility in the exchange rate and aggregate inflation.
The paper is structured as follows. Section 2 provides a brief review of the literature
and discusses issues associated with inflation targeting in an open economy. We
maintain that in the context of a small open economy there is a fundamental
distinction between aggregate inflation and inflation in the non-traded sector.
Section 3 presents empirical evidence that aggregate inflation behaves differently to
non-traded inflation. Against this background, Section 4 presents a theoretical
model of a small open economy with traded and non-traded sectors, and a forward-
looking exchange rate. The model is used to compare aggregate versus non-traded
inflation targeting. Simulation results are presented in Section 5 for the simplest
version of the model with backward-looking inflation expectations. Section 6
presents some extensions to the basic model, including forward-looking inflation
expectations, gradual exchange rate pass-through and discretionary policy. Section 7
summarises the main findings of the paper.
2. Inflation Targeting in an Open Economy
Standard theoretical analysis of inflation targeting is based on a closed economy
model. Aggregate demand depends negatively on the lag of the real interest rate.
Aggregate supply is represented by a Phillips curve where inflation equals its
expectation plus some adjustment for inflationary pressure associated with the
output gap. The output gap is assumed to have a positive impact on inflation, often
with a one-period lag. Thus a change in the interest rate is transmitted to inflation
with a two-period lag via output.
Given the control lag with which policy affects inflation, the central bank must
adopt a procedure known as inflation forecast targeting (Svensson 1996). In the
simplest models, under strict inflation targeting, policy is set based on a two-period
ahead forecast of inflation so as to move towards the target within the minimum
control lag. However, under flexible inflation targeting the inflation forecast horizon
is longer than the minimum control lag, depending on the nature of the central
bank's preferences. These preferences are reflected in an objective function that
penalises deviations of inflation from target, and possibly deviations of output from
potential, and may also reflect some preference for interest-rate smoothing.
Recent contributions by Svensson (1998) and Ball (1998) extend models of inflation
targeting to an open-economy setting. This requires explicit consideration of both
the demand and exchange rate channels of monetary policy.
Ball (1998) includes the indirect effect of exchange rates on inflation via the output
gap, as well as the direct effect of the exchange rate on the domestic price of
imported intermediate inputs. The direct effect implies that the central bank can
target inflation with a one-period lag. Thus movements in the exchange rate have
strong implications for the setting of interest rates.3 Ball shows that an economy
subject to exchange rate fluctuations will be forced to make frequent adjustments to
the interest rate in order to achieve a strict inflation target. This will generate
volatility in output which may be unacceptable to the monetary authority. To avoid
excessive variability in the economy, Ball suggests targeting a refined measure of
inflation which abstracts from the direct, but temporary effects of changes in the
exchange rate.
Svensson (1998) presents an open-economy model where goods are either imported,
or domestically produced. He assumes that the economy is small in the market for
imported goods, but not in the world market for its own output. This justifies the
distinction between CPI-inflation targeting, and targeting inflation of domestically
produced goods. Strict CPI-inflation targeting relies on the direct exchange rate
channel to stabilise inflation at a short horizon, and thus introduces substantial
fluctuation in other variables. For this reason, Svensson recommends flexible
CPI-inflation targeting which stabilises inflation and output at a longer horizon.
small
The appropriate distinction for a open economy is that between aggregate
inflation and inflation in the non-traded sector.4 Domestically produced goods are of
two broad classes, traded or non-traded, the prices of which are determined by
different factors. Traded goods prices are determined in world markets and
converted into domestic currency prices at the prevailing exchange rate; non-traded
goods prices are in large part determined by domestic conditions.
In this paper we present a model of a small open economy with a traded and
non-traded sector. The exchange rate is forward looking and responds instantly to
shocks and unexpected changes in the path of the policy instrument. Inflation in the
traded sector is determined by changes in the exchange rate. Given the interaction
between the interest rate and the exchange rate, monetary policy can impact upon
the traded component of aggregate inflation rapidly due to the direct effect of the
exchange rate. Non-traded inflation is affected indirectly via demand, and directly
by the effect of policy on inflation expectations, and on the exchange rate.
3
This is of relevance to the construction of a Monetary Conditions Index (MCI), and is
discussed by Ball (1998).
4
For an early discussion of the distinction between traded and non-traded goods see
Salter (1959) and Swan (1960). Interestingly, Swan considers a small open-economy model in
which policy-makers are concerned about internal price stability, making this early work
relevant to the discussion of inflation targeting. See also Pitchford (1993).
Overlaying our representation of the economy is the central bank's loss function
which embodies preferences over inflation, output stability, and interest-rate
smoothing. An aggregate inflation target may induce excessive volatility in the
interest rate to offset exchange rate shocks. A non-traded inflation target may induce
excessive volatility in the exchange rate when policy is adjusted to offset supply or
demand shocks. Under such circumstances it may be appropriate to adopt a more
flexible aggregate inflation target over a longer forecast horizon.
3. Non-traded and Traded Inflation - Some Empirical Evidence
We maintain throughout the paper that aggregate and non-traded inflation follow
fundamentally different processes. This is confirmed by our analysis of Australian
data. Dwyer, Kent and Pease (1994) have shown that the domestic currency price of
traded goods depends on the world price and the exchange rate. This implies that
the exchange rate plays a significant role in the determination of aggregate inflation,
as we confirm below. In contrast, we show that the price of non-traded goods is
determined primarily by domestic conditions, namely unit labour costs.
For the purpose of empirical estimation we construct measures of both the aggregate
and non-traded underlying CPI for the Australian economy.5 Disaggregated price
series are used to construct measures of the underlying CPI for the traded and
non-traded sectors. Price series are associated with either traded or non-traded
sectors according to the classification scheme in Dwyer (1992). A sector is
classified as traded if at least 10 per cent of production in that sector is exported or
directly import competing. Remaining sectors are used to construct a measure of the
non-traded CPI; further details are provided in Appendix A.6
Figure 1 shows our measures of underlying CPI inflation for both traded and
non-traded goods and services. The published series for aggregate underlying CPI
inflation is also shown.
Figure 1: Underlying CPI
Percentage change over four quarters
% %
Non-traded
12 12
10 10
8 8
Aggregate
6 6
4 4
Traded
2 2
0 0
-2 -2
1981 1983 1985 1987 1989 1991 1993 1995 1997
There are three episodes during the 1980s and 1990s for which traded and
non-traded inflation behave somewhat differently.7 The first episode is that of the
early 1980s wage-push during which non-traded inflation reached almost
14 per cent, while traded inflation remained steady at around 9 per cent. The second
episode coincides with the strong depreciation of the Australian dollar in 1985/86.
The depreciation led to a rapid increase in traded inflation to rates above non-traded
inflation, which had also increased, but to a lesser extent. Towards the end of this
episode, non-traded inflation turned down almost a year before traded inflation. The
third episode begins in 1995 when non-traded inflation increased against the
background of strong domestic conditions, while the exchange rate appreciation
reduced traded inflation.
Figure 2 compares underlying CPI inflation of traded goods and services with
import price inflation.8 The volatility of import price inflation reflects rapid and
complete first stage pass-through of the exchange rate to the price of imports
(Dwyer, Kent and Pease 1994). In contrast, our measure of CPI inflation in the
traded sector is less volatile. This is because our measure is based on final retail
prices, and therefore, it incorporates a sizeable non-traded component due to the
costs of bringing goods to market (Dwyer and Lam 1994). What we loosely refer to
as traded inflation in our theoretical model, is in reality closer to import price
inflation. While our measure of CPI inflation in the traded sector is not directly
comparable with our theoretical definition, non-traded CPI inflation is consistent
with our model. For this reason we focus our empirical analysis on the distinction
between aggregate and non-traded CPI inflation.9
Following de Brouwer and Ericsson (1995), we adopt an error-correction
framework in our estimation of Australian inflation. The model assumes a long-run
relationship between the underlying CPI, unit labour costs and import prices. The
mark-up of retail prices over the cost of production is determined in the short run by
the output gap (see Appendix A for a further discussion). We estimate a model for
both aggregate and non-traded inflation from September 1979 to December 1997.
Results for parsimonious specifications are shown in Table 1, and indicate that a
rise in unit labour costs and/or import prices will increase both measures of the CPI.
8
The price of imports is equal to the free on board price of merchandise imports (excluding oil,
computers and 'lumpy' items such as aircraft).
9
In some respects it may appear to be more appropriate to distinguish between import price
inflation and domestic inflation, rather than traded and non-traded inflation (Svensson 1998;
Ball 1998). However, a small open economy takes the prices of both imports and exports as
given, with the prices of domestically produced import substitutes also being closely linked to
world markets. To the extent that export goods are consumed domestically, their prices will
also be determined by world markets. A large proportion of Australian exports are either
resource or rural based, and therefore are not directly relevant to measures of consumer price
inflation. Also, Dwyer, Kent and Pease (1994) showed that prices of manufactured exports are
determined according to a world market for manufactured goods, and therefore should move
closely with the price of imports (which are themselves largely manufactures).
Figure 2: Import Prices
Percentage change over four quarters
% %
20 20
15 15
Traded prices
10 10
5 5
0 0
-5 -5
Import prices
-10 -10
-15 -15
1981 1983 1985 1987 1989 1991 1993 1995 1997
An increase in output above potential implies inflationary pressure. The significance
of the coefficients on the lagged level of underlying CPI indicates that cointegration
exists.10 Homogeneity is not rejected in either model.11
Estimated long-run elasticities for aggregate and non-traded CPIs are shaded in
Table 1. Import prices, and hence, the exchange rate, have a greater effect on the
aggregate CPI with a long-run elasticity of 0.40. Unit labour costs have a greater
effect on the non-traded CPI, with a long-run elasticity of 0.81, compared with 0.24
for import prices.12
10
Augmented Dickey-Fuller tests suggest that these variables are integrated of order one and that
at least one cointegrating relationship exists. We do not present these results, however, similar
findings are reported in de Brouwer and Ericsson (1995).
11
We may expect that homogeneity should be rejected in this model if there is greater
productivity growth in the traded sector relative to the non-traded sector. One way to address
this problem would be to include a linear time trend to capture any productivity differential.
Including a linear time trend did not alter our main findings.
12
We also investigated the stability of these models by estimating over a rolling fixed window of
60 observations beginning in September 1974. There was a gradual increase in the importance
of import prices and a decrease in the importance of unit labour costs in explaining inflation,
Table 1: Aggregate and Non-traded Underlying Inflation 1979:Q3 - 1997:Q4
Aggregate CPI inflation Non-traded CPI inflation
Constant 0.016*** -0.009
(0.009) (0.019)
Lagged aggregate/non-traded CPI -0.075* -0.081*
(log level) (0.015) (0.015)
Lagged unit labour costs 0.043* 0.066*
(log level) (0.013) (0.018)
Lagged import prices 0.030* 0.020*
(log level) (0.006) (0.005)
Aggregate CPI inflation % change (lag 2) 0.234*
(0.086)
Unit labour costs % change (lag 0) 0.201*
(0.047)
(lag 3) -0.151*
(0.046)
(lag 4) 0.075***
(0.040)
Import prices (landed) % change (lag 2) 0.017
(0.011)
(lag 3) 0.017***
(0.010)
Output gap (lag 1) 0.106*
(0.033)
(lag 2) -0.099***
(0.050)
(lag 3) 0.134* 0.087*
(0.034) (0.022)
Long-run elasticity - Unit labour costs 0.579* 0.810*
(0.091) (0.097)
- Import prices 0.399* 0.244*
(0.068) (0.079)
Linear homogeneity {0.442} {0.311}
R-bar squared 0.917 0.851
LM test - 4th order autocorrelation {0.642} {0.331}
Notes: Numbers in parentheses () are standard errors. Numbers in braces {} are p-values.
*, ** and *** represent significance at the 1%, 5% and 10% levels respectively.
consistent with increased openness of the economy. However, these models exhibit instability
for sample periods beginning in the early 1980s, particularly in the case of aggregate inflation.
The source of this instability is difficult to discern.
In summary, our empirical results are consistent with the premise that aggregate
inflation and non-traded inflation follow distinct processes. The exchange rate has a
greater impact on aggregate inflation through its determination of traded goods
prices, while prices in the non-traded sector depend more on domestic conditions.
4. Theoretical Model
In this section of the paper we present a stylised model of a small open economy
with a traded and non-traded sector. Our goal is to investigate the behaviour of key
variables when targeting aggregate inflation as opposed to non-traded inflation.
4.1 The Model
We assume that traded and non-traded goods are produced and consumed in the
domestic economy. The structure of the economy is described by five reduced form
equations and three identities. An additional equation describes the central bank's
objective function. The solution to the model is the path of the policy instrument, in
this case the nominal interest rate, which minimises the objective function subject to
the structure of the economy. (All variables are expressed as deviations from their
long-run means and all coefficients are greater than, or equal to, zero.13)
Traded inflation
We assume that the country is small (that is, a price taker on world markets) and
that there is no non-traded component in the final price of traded goods. For
simplicity we assume that the world price of traded goods is constant and that
pass-through is complete and instantaneous. Hence:
T
= (1)
πt ∆te
T
where is the inflation rate of traded goods, e is the log of the nominal exchange
π
rate (defined as the number of units of local currency per unit of foreign currency),
and ∆ is the first difference operator. In Section 6.2 of the paper we consider an
extension to the model which allows for more gradual pass-through of the exchange
rate.
Non-traded inflation (Phillips Curve)
The centre-piece of the model is an extension of the standard Phillips curve for
non-traded inflation.14 Our reduced form specification is amenable to various
assumptions regarding expectations and price formation:
N N
** y e e (2)
π = π + α + β ∆ + β ∆ + ε
t t - 1 1 t - 1 2 t - 2 t
N
where is the inflation rate of non-traded goods and services, is expected
π π **
inflation (defined below), y is the output gap applicable to the non-traded sector,
N
and is an independently and identically distributed (i.i.d.) shock to non-traded
ε
2
inflation, normally distributed with mean zero, and variance σ . Hereafter we refer
N
loosely to this as a supply shock, by which we mean any shock which causes a
contemporaneous and unexpected change in non-traded inflation.
The term ** represents a general form of inflation expectations. There are two
π
avenues for consideration. First, expectations could be backward looking, forward
looking, or some combination of both. This specification may directly capture the
way in which agents form expectations.15 Alternatively, it may reflect the existence
of overlapping contracts (Taylor 1980). Second, we examine two special cases,
where ** is the expectation of either non-traded inflation or aggregate inflation.16
π
Whereas firms care about the real product wage, workers care about the real
consumption wage. More generally, there will be some bargaining between workers
14
Although we discuss our specification of the non-traded Phillips curve, it is beyond the scope
of this paper to derive it formally.
15
It may be that price setting by firms follows a partial adjustment process as in Svensson (1998).
For a discussion of how this can be incorporated into our model see Section 6.1.
16
Taylor (1980) assumes that wages are the only source of nominal rigidity, while Calvo (1983)
assumes that all nominal rigidities are in product markets. Svensson (1998) provides a
structural aggregate supply equation for domestically produced goods based on nominal
rigidities in product markets. We assume that when setting prices, non-traded firms have no
regard for the relative price of non-traded to traded goods. However, this relative price does
have a delayed impact through its effect on aggregate demand for non-traded goods.
and firms, and π ** might be some combination of expected aggregate inflation and
expected non-traded inflation.
Increases in the non-traded output gap cause higher non-traded inflation.
Finally, non-traded inflation may also depend on the cost of traded intermediate
inputs. Firms in the non-traded sector are assumed to purchase traded intermediate
inputs in advance of production. This effect is captured by the inclusion of lagged
changes in the exchange rate.
Aggregate inflation identity
Aggregate consumer price inflation, π , depends on the long-run share of traded
goods in consumption, η :17
N
(3)
π ≡ ηπ + (1 - η ) π , η ∈ [0,1]
t Tt t
Non-traded output gap
The non-traded output gap is equal to (log) demand for the non-traded good, less
(log) potential output of the non-traded good. For simplicity we assume that
potential output in both sectors is fixed. Output in the short run is determined by the
level of demand. Given that all series are demeaned, the non-traded output gap is
equivalent to the demand for non-traded goods which depends on lags of both the
real interest rate and the relative price of non-traded goods:
y y r q q (4)
= μ - φ - γ - γ + ε , μ ∈ [0,1)
t t - 1 t - 1 1 t - 1 2 t - 2 yt
where r is the real interest rate, q is the relative price of non-traded to traded
y
goods, and ε is an i.i.d. shock to demand for non-traded goods, normally
distributed with mean zero, and variance σ 2. For ease of exposition we refer to this
y
as a demand shock. The parameter μ captures the degree of persistence in demand.
This specification implies that it takes two periods for interest rate changes to have
an effect on non-traded inflation via the demand channel. In addition, an increase in
the relative price of non-traded goods is assumed to reduce demand in the
non-traded sector, albeit with a lag. This mechanism drives the model towards
long-run equilibrium in which the relative price of non-traded goods is unchanged.18
The relevance of the non-traded output gap is justified by assuming that (at least in
the medium term) factors of production are specific to each sector of the economy.
Hence, only demand in the non-traded sector will have an impact on non-traded
inflation. Alternatively we could develop a model where the focus is on aggregate
demand. In this case there would be no role for the relative price of non-traded
goods in determining aggregate demand. However, to close this model, we would
need to include a role for the relative price of non-traded goods directly in the
Phillips curve for non-traded inflation.19
Nominal exchange rate
We assume Uncovered Interest Parity (UIP) which implies:
∆ e = i - i - ρ (5)
t t + 1 t ft t
f
where i is the domestic nominal interest rate, i is the foreign interest rate
(assumed to be zero for simplicity), ρ is a risk premium, and represents the
t ∆te +1
expectation at t of the nominal depreciation between t and t +1.
Shocks to the exchange rate are an important focus of our paper. We model these
shocks as changes in the risk premium which can exhibit persistence. This allows us
to focus on shocks that are speculative in nature, rather than driven by fundamentals
(such as the terms of trade).
Relative price identity
The relative price of the non-traded good is:
N
q ≡ p - p (6)
t t Tt
where pN and pT are the (log) price levels of non-traded and traded goods
respectively.
Real interest rate identity
r i -π * (7)
t ≡t
where π * is the expectation of aggregate inflation (consistent with the form of
expectations in π **).
The risk premium
The risk premium is assumed to have some degree of persistence:
ρ
, [0,1) (8)
ρ = θ ρ + ε θ ∈
t t -1 t
ρ
where ε is an i.i.d. shock to the risk premium, normally distributed with mean
zero, and variance 2. For expositional purposes we refer to this as an exchange
σρ
rate shock.
The central bank's loss function
The central bank has a loss function which is generalised to incorporate preferences
for targeting aggregate or non-traded inflation, as well as preferences for output
stability and smoothing the path of interest rates:
where δ is the central bank's rate of time preference (0 < δ≤ 1 ), and ( )o is the
Et
expectations operator taken at time t. The coefficients and reflect the
μN
μπ
central bank's preferences for aggregate or non-traded inflation being at target (the
target is set to zero for simplicity). The coefficient represents a preference for
μy
maintaining output at potential.20 The coefficients and represent preferences
μi μ∆i
for interest rate stabilisation, and interest-rate smoothing respectively.21
4.2 Baseline Model Specification - Model A
The solution to the model is the path of the interest rate that minimises the loss
function subject to the constraints implied by the structure of the economy. First we
examine a very simple model with backward-looking inflation expectations and with
based on non-traded inflation. We refer to this as Model A:
π **
Model A
N N N
π = π + α y + β ∆ e + β ∆ e + ε (2A)
t t - 1 t - 1 1 t - 1 2 t - 2 t
r i (7A)
≡ - π
t t t
Parameters
We choose parameter values that are broadly consistent with Australian data, and
are comparable with those used by Haldane and Batini (1997), and Svensson
(1998). Parameter values are presented in Table C1 in Appendix C. We present two
sets of results, one where the central bank targets aggregate inflation, and one where
the central bank targets non-traded inflation.22
20
The non-traded output gap is equivalent to the aggregate output gap in our model. The traded
output gap is equal to zero because potential output is assumed fixed, and total demand (as
opposed to domestic demand) for the traded good is constant. The latter point is implicit in our
assumption of a constant price for traded goods in foreign currency terms.
21
We present results based on = 0 and ≥ 0 ; the interest rate jumps in response to a
i
μi μ∆
shock, but by less than in the case where > 0 and = 0.
i
μi μ∆
22
Consistent with the observed practice of inflation-targeting, we assume that the central bank
always places some weight on output stability and interest rate smoothing.
4.3 State-space Form and Solution
There is a standard technique for obtaining the solution to models with
forward-looking variables. This technique requires that the equations be expressed
in state-space form. Using the same notation as Svensson (1998), let denote a
Xt
vector of the predetermined variables and denote a vector of the forward-looking
xt
variables. The vector of shocks to the predetermined variables is represented by ,
vt
' '
and the vector of policy goal variables is denoted by . Finally, Z = ( X , x ) is the
Yt t t t
combined vector of predetermined variables and forward-looking variables:
'
N N
X , y , , , i , q , q
= π ρ π
t t t t t - 1 t - 1 t - 2 t - 1
( )
x q
=
t t )
'
ρ
N
ν = ε , ε , ε ,0, 0, 0, 0
t t yt t
(( )
'
N
Y = π , π , y , i , i - i
t t t t t t t - 1
( )
The vectors , , and are of length n = n n and
Xt xt Zt Yt n1, n2, 1+ 2 n3
respectively =7 = 1 and = 5 ). The state-space form is as follows:
(n1 ,n2 n3
ν
 t 1   t 1 
+ +
= AZ + Bi +
t t
xX 0
t t
 + 1   
Y = C Z + C i (10)
t Z t i t
'
= Y KY
t t t
where A is an n ×n matrix, B is an n ×1 vector, is an n ×n matrix, is an
CZ 3 Ci
× 1 vector, and K is an n n diagonal matrix, with the preference weights on
n3 3 ×3
the diagonal (see Appendix B for more details).
This dynamic optimisation problem is solved in Backus and Driffill (1986), and
applied in Svensson (1994, 1998). In models with forward-looking variables, the
form of the solution depends on whether the central bank can pre-commit to an
optimal policy rule. For now, we restrict our attention to the commitment solution
and consider the alternative discretionary solution in Section 6.3. The c