A New Keynesian SVAR model of the Australian economy

Economic Modelling 28 (2011) 157–168

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Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d

A New Keynesian SVAR model of the Australian economy ☆ Shawn Chen-Yu Leu ⁎ School of Economics and Finance, La Trobe University, Victoria 3086, Australia

a r t i c l e

i n f o

Article history: Accepted 26 September 2010 JEL classification: C32 C51 E52 E58

a b s t r a c t We estimate an SVAR model for the Australian economy based on an open economy New Keynesian model that accounts for the forward-looking behaviour exhibited by economic agents. Deep structural parameters are identified by placing exclusion restrictions on the VAR residuals and the covariance matrix. Dynamic responses show no price and exchange rate puzzles and indicate that the Reserve Bank of Australia (RBA) stabilises output fluctuations in the short run while maintaining a medium-run inflation target since 1984. Aggregate demand shocks are found to be driven by external demands. The RBA exercises caution in responding to aggregate supply shocks. © 2010 Elsevier B.V. All rights reserved.

Keywords: SVAR model New Keynesian Rational expectations Impulse response function Empirical puzzles

1. Introduction Since the seminal work of Sims (1980), structural vector autoregression (SVAR) models have received immense attention mainly because of the ability to simulate dynamic responses of macroeconomic variables to particular structural shocks. Generally SVAR models are identified with a set of restrictions that are broadly consistent with economic theory. The identifying assumptions are then checked against sensible dynamic responses (e.g. Hall, 1995). In recent Australian literature, Brischetto and Voss (1999) adopted the contemporaneous structural relationships proposed by Kim and Roubini (2000). Huh (1999) based the identifying assumptions on a static Mundell–Fleming model with impositions of short-run and long-run restrictions. Dungey and Pagan (2000, 2009) developed a block-recursive structural model with eleven variables. This article presents a New Keynesian SVAR model of the Australian economy where the identification scheme is based on a small open economy New Keynesian model that specifies the interactions between the exogenous structural shocks and the forward-looking behaviour exhibited by economic agents. We use the estimated model

☆ I would like to thank Mardi Dungey, Viv Hall, Glenn Otto, Adrian Pagan, Jeff Sheen, Jim Thomson, Graeme Wells; the conference and seminar participants at the ANU, IMF, La Trobe, Sydney, and UWA for very helpful comments. I also benefited greatly from the comments and suggestions of four anonymous referees. ⁎ Tel.: + 61 3 94791731; fax: + 61 3 94791654. E-mail address: [email protected]. 0264-9993/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2010.09.015

to simulate dynamic responses of the output gap, inflation, exchange rate, and interest rate to four structural shocks—monetary policy, risk premium, aggregate demand, and aggregate supply shocks. The New Keynesian approach has received much attention recently due to its emphasis on the behaviour of intertemporally optimising agents and the incorporation of nominal rigidities. Aggregate relationships used in the SVAR framework are derived from dynamic general equilibrium models, where the central bank and private agents are assumed to be rational and forward-looking. The structural model is consisted of a dynamic aggregate demand (IS) equation based on representative agent utility maximisation in a small open economy setting, an aggregate supply (AS) equation or New Keynesian Phillips curve (NKPC) based on Calvo's (1983) staggered price model, the uncovered interest rate parity, and a forward-looking monetary policy rule. We set up an SVAR model by appending the contemporaneous structure motivated by the New Keynesian model with unrestricted short-run dynamics. The central bank and private agents are assumed to have the same information set in forming future expectations. To identify the SVAR model under rational expectations, we estimate ‘deep’ structural parameters using the methodology proposed by Keating (1990). Deep structural parameters come from utility functions and technological constraints of economic agents in the economy. Their identification is desirable because they are invariant to shifts in policy and hence the result is not subject to the Lucas critique. Taking advantage of the feature offered by the SVAR methodology, deep structural parameters in this model are identified by imposing restrictions on the VAR residuals and the covariance matrix, while leaving the lag dynamics unrestricted. Dhrymes and Thomakos (1998)

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employed a similar procedure for imposing exclusion restrictions on a small open economy model.1 Their study differs from this article in three respects: the open economy structural model is not based on intertemporal optimisation; the method for solving rational expectations is different; and no exclusion restrictions are imposed on the exogenous variables. To estimate our New Keynesian SVAR model's parameters, we use maximum likelihood with Australian data over the period 1984Q1 to 2009Q4. Our parameter estimates are comparable with other singleequation studies, while our results are obtained from full-system estimation, which has the advantage of allowing for interactions between consumers, firms, and the central bank in the economy. The coefficient estimates suggest that inflation dynamics in Australia are backward-looking, which is consistent with the finding by Gruen et al. (1999). The estimated monetary policy rule indicates that the Reserve Bank of Australia (RBA) has been stabilising inflation and output fluctuations since 1984. We simulate dynamic responses of the macroeconomic variables subject to a positive monetary policy shock. In the short run, a monetary tightening has significant contractionary effects on the output gap and inflation. The relatively higher domestic interest rate pressures the exchange rate to appreciate. Exchange rate depreciation follows in the ensuing periods and leads to overshooting. After reaching its peak of depreciation, the exchange rate continuously appreciates and approaches its medium-run value. This is in contrast to the persistent appreciation documented by Eichenbaum and Evans (1995) and Grilli and Roubini (1995). The dynamics exhibit no price and exchange rate puzzles. The impulse response functions for a positive risk premium shock highlight the indirect role in which the exchange rate has in the adjustment process. Given the shock, the exchange rate depreciates upon impact, and the central bank tightens quickly and decisively to stabilise output and inflation fluctuations. Even though the nominal exchange rate is not an explicit consideration in the monetary policy rule, large exchange rate fluctuations may have adverse effects indirectly on real output through the expenditure-switching effect and inflation through the pass-through effect. A positive aggregate demand shock leads to higher output and inflation. The central bank raises the interest rate immediately and maintains the tightening measure for about 10 quarters before easing the policy stance to return output and inflation back to their mediumrun values. The relationship between an aggregate demand shock and the exchange rate depends on the source of the shock—domestic demand or external demand. Our impulse response function shows that the exchange rate appreciates for 2 quarters suggesting that the aggregate demand shock is associated with increased external demand. A rise in the demand for Australian exports increases foreign demand for Australian dollar that leads to the exchange rate appreciation, hence the result suggests that export shocks have been the more dominant factor in recent years. In the face of an adverse aggregate supply (or positive inflation) shock, there is contraction in output but a rise in inflation at impact, which demonstrates a policy dilemma that awaits policymakers. The impulse response function suggests that the central bank cautiously delays policy action at the impact of the shock. In the short run, the central bank gradually raises the nominal interest rate in response to the high and sustained inflation rate. However, the nominal rate rises at a slower pace than inflation and therefore the real interest rate falls to correct the negative output gap. Consistent with the uncovered interest parity, the exchange rate appreciates in the short run followed by future expected depreciation. In the medium run the central bank

1 The main aim of their article is to examine the empirical appropriateness of forward-looking and backward-looking expectations.

unwinds its previous tightening measures as output and inflation adjust back to equilibrium in the medium run. This article is organised as follows: Section 2 lays out the New Keynesian specification of a small open economy. In Section 3 we discuss the rational expectations identification scheme. Section 4 describes the Australian data used in estimation and presents the empirical results. First we show the preliminary diagnostic tests of the underlying VAR. Second, the structural estimates and the fit of predicted variable values to actual values are examined. Third we look at the impulse response functions and report the forecast error variance decomposition. We close this section with a brief comparison of the results from the full sample period to those from the period up to the beginning of the global financial crisis (or the pre-GFC sample). Section 5 concludes. 2. A New Keynesian SVAR model We describe a small open economy New Keynesian model that is consistent with the underlying behaviour of intertemporally optimising agents. The aggregate relationships that form the contemporaneous part of the SVAR model are derived from dynamic general equilibrium setting, where agents are assumed to be rational and forward-looking. 2.1. IS equation The output gap is described by an open economy IS equation that is derived from the representative household maximisation problem in a small open economy setting (e.g. see the aggregate demand specification by McCallum and Nelson, 1999, 2000):  
 x * xt = α 0 + Et xt + 1 −α 1 it −Et πt + 1 + α 2 st + pt −pt + εt

ð1Þ

where xt is the output gap, it is the nominal short-term interest rate, πt is the inflation rate, st is the exchange rate expressed as the domestic currency cost of one unit of foreign currency, pt is the general price level, asterisk denotes foreign variables, and Et is expectation conditional on the information set available to economic agents at time t. Eq. (1) represents the aggregate demand side of a small open economy where εtx is interpreted as an aggregate demand shock. Its main difference from the traditional IS curve is the dependence of current output on the level of future expected output (Etxt + 1) through the effects of expected future marginal utility of consumption balancing current marginal utility. Current output rises when future output is expected to be higher because individuals desire to achieve a balanced consumption portfolio. Individuals anticipate a higher level of consumption next period due to higher expected output, which induces consumers to spend more today to smooth out the consumption path. The real interest rate effect, (it − Etπt + 1), on current output is negative, reflecting the intertemporal substitution of consumption. A rise in the value of the real exchange rate (st + p*t − pt), i.e. a real depreciation of the home currency, is expected to raise current output through the expenditure-switching effect. 2.2. AS equation The main theme in the New Keynesian model regarding price adjustment is to combine nominal rigidities and the optimising behaviour of firms which produce forward-looking inflationary dynamics. The New Keynesian Phillips curve derived from Calvo's (1983) staggered nominal price setting model with an exogenous aggregate supply shock, επt , is given by: πt = β0 + β1 Et πt

π

+ 1

+ β2 xt + εt

ð2Þ

S.C.-Y. Leu / Economic Modelling 28 (2011) 157–168

In each period, a fraction of the monopolistically competitive firms is allowed to adjust their price (but they may choose not to do so) according to a constant probability (1 − ω). Hence the expected interval between price adjustments is 1 / (1 − ω) and probability ω measures the degree of price rigidity in the economy. Firms maximise the expected discount value of current and future profits to obtain the optimal pricing decision. Those firms that can (and choose) to reset their price in the current period know that the new price will remain unchanged for the duration of 1 / (1 − ω). Therefore firms are concerned with future inflation because it may be unable to adjust the price for some periods in the future. As a result, current inflation depends on future expected inflation and β1 b 1 is the firm's subjective discount factor. This is a key difference to the standard Phillips curve where expected current inflation, Et − 1πt, enters the equation instead. 2.3. Uncovered interest parity A standard feature in most small open economy models is the inclusion of the uncovered interest parity condition to describe the nominal exchange rate:   s * st = Et st + 1 − it −it + ε t

ð3Þ

where the time-varying risk premium shock εts reflects temporary departures from the interest parity condition.

159

rational expectations models yield restrictions across equations arising from the assumption of rational expectations and the structure embedded in the optimisation problem. These cross-equation restrictions identify the structural parameters in the model.2 Alternatively, SVAR models typically consist of a contemporaneous system of broadly defined behavioural relationships with unrestricted short-run lag dynamics. Instead of using lag restrictions to identify structural parameters, this article adapts the rational expectations identification scheme of Keating (1990) to a New Keynesian open economy which takes full advantage of the features in an SVAR model. The contemporaneous structural model described by (1)-(4) is converted into a corresponding representation that is composed of structural disturbances and reduced-form innovations. Economic agents form future expectations using observable innovations that result from the dynamic structure of the economy. Therefore, the identification of deep parameters comes from the VAR residuals and restrictions on the covariance matrix of the structural disturbances. 3.2. SVAR identification incorporating rational expectations 3.2.1. A closed economy New Keynesian model We begin the demonstration of how to identify an SVAR model under rational expectations with a closed economy version of the New Keynesian model (e.g. see Clarida et al., 1999)3:
 x xt = α 0 + Et xt + 1 −α 1 it −Et πt + 1 + εt

2.4. A forward-looking monetary policy rule

πt = β0 + β1 Et π t

We close the model with the inclusion of a forward-looking monetary policy rule:

 it = γ 0 + πt + γ 1 Et πt

 it = γ0 + π t + γ1 Et πt

+ 1 −π

T



i

+ γ 2 xt + εt

ð4Þ

where πT is the target inflation rate and εti represents the monetary policy shock. The specification follows closely the forward-looking rule discussed by Clarida et al. (1998, 1999, 2000). The central bank is assumed to respond to expected future inflation deviations from its target value and contemporaneous output deviations from its trend value. When there is a positive inflation and/or output deviation from their respective target values, Eq. (4) calls for the central bank to adjust the nominal interest rate more than one-forone so that the real interest rate (it − πt) rises sufficiently to close the positive gap. Therefore a priori γ1, γ2 N 0 if the central bank pursues a stabilisation policy with respect to movements in inflation and output. 3. Econometric methodology 3.1. Rational expectations econometrics

ð5Þ

π

+ 1

+ β 2 xt + ε t + 1 −π

T



ð6Þ i

+ γ 2 xt + ε t

ð7Þ

The identification scheme is based on converting the contemporaneous structural system into an innovations representation that consists of structural disturbances and VAR innovations, by subtracting from each variable the expectation at time t − 1 of that variable conditioned on all available past information:
 x ε t = ðxt −Et−1 xt Þ− Et xt + 1 −Et−1 xt + 1 + α 1 ðit −Et−1 it Þ
  x
−α 1 Et πt + 1 −Et−1 πt + 1 = et − Et xt + 1 −Et−1 xt + 1
 + α 1 eit −α 1 Et πt + 1 −Et−1 πt + 1
 επt = ðπt −Et−1 π t Þ−β1 Et π t + 1 −Et−1 πt + 1 −β2 ðxt −Et−1 xt Þ
 = eπt −β1 Et πt + 1 −Et−1 πt + 1 −β2 etx

ð8Þ

ð9Þ


 i ε t = ðit −Et−1 it Þ−ðπt −Et−1 πt Þ−γ1 Et πt + 1 −Et−1 πt + 1 −γ2 ðxt −Et−1 xt Þ
 i π x = et −et −γ1 Et πt + 1 −Et−1 πt + 1 −γ2 et

ð10Þ The Lucas critique undermines traditional procedures for econometric policy evaluation that did not allow expectations to adjust to policy shifts. When the government announces policy changes, economic agents update their expectations in anticipation of the new environment they face, which are embedded in the structural model. Since changes in expectations about the future affect current economic behaviour, the estimated structural relations are poor guides for policy evaluation under the new regime. Hence one should estimate structurally stable, deep parameters which have the advantage of being invariant to shifts in policy. One response is to estimate a structural rational expectations model. Private agents' optimising behaviour is combined with the complete knowledge of the structural parameters of the economy and the underlying stochastic forcing processes. Solutions to the dynamic

where (xt − Et − 1xt), (πt − Et − 1πt), and (it − Et − 1it) are the current values of the output gap, inflation, and the interest rate VAR innovations, respectively. In (8)-(10), each structural disturbance is additionally related to one or both of the expectations revision processes of the output

2 In structural rational expectations models, the cross-equation restrictions typically result in over-identification. 3 By adding a real exchange rate term in Eq. (5) and the uncovered interest rate parity equation to the closed economy model, we return to the open economy New Keynesian model discussed in Section 2. This first step helps to facilitate explanations on how the identification scheme is adapted for an open economy model.

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gap and inflation, i.e. (Etxt + 1 − Et − 1xt + 1) and (Etπt + 1 − Et − 1πt + 1). To calculate these two terms we first write the reduced-form VAR in stacked form4: ð11Þ

Yt = AYt−1 + Q et or equivalently 2

3 2 yt A1 6 yt−1 7 6 In 6 7 6 6 yt−2 7 = 6 0n 6 7 6 4 5 4 ⋮ ⋮ yt−q + 1 0n

A2 0n In

… … 0n

…

0n

32 3 2 3 yt−1 … Aq In 7 6 7 6 0n 7 y … 0n 76 t−2 7 6 7 6 7 6 7 … 0n 7 76 yt−3 7 + 6 0n 7et ⋱ ⋮ 54 ⋮ 5 4 ⋮ 5 yt−q 0n In 0n

⋱ ⋱

ð12Þ

where q denotes the lag order of endogenous variables, In and 0n are (n × n) identity and zero matrices respectively, and n = 3 is the number of endogenous variables. The j-step conditional expectation of (11) is j

Et Yt + j = ðAÞ Yt

ð13Þ

Two vectors of length nq are created to locate the forecasted variables: r′x = ð1; 0; 0; …; 0Þ for the output gap r′π = ð0; 1; 0; …; 0Þ for inflation

ð14Þ

The expected future values of the output gap and inflation one period ahead, j = 1, are derived by premultiplying (13) by the vectors defined in (14):

Hence the expectations revision processes are the differences between (15) and its own expected value at time t − 1, which by using (11), are Et xt + 1 −Et−1 xt + 1 = r′x AðYt −Et−1 Yt Þ = r′x AQ et

Inserting (16) into the system of VAR innovations described by (8)-(10) yields:   x x i ε t = et −r′x AQ et + α 1 et −r′π AQ et x

εt = et −β1 r′π AQ et −β2 et π

ð20Þ ð21Þ

 s s
i εt = et − Et st + 1 −Et−1 st + 1 + et

ð22Þ


 i i π x εt = et −et −γ1 Et πt + 1 −Et−1 πt + 1 −γ 2 et

ð23Þ

where the domestic price innovation is equal to domestic inflation innovation over 400.5 Economic agents are required to update their future expectations on the output gap, inflation, and the exchange rate, i.e., (Etxt + 1 − Et − 1xt + 1), (Etπt + 1 −Et − 1πt + 1) and (Etst + 1 − Et − 1st + 1). In the closed economy model all observable innovations contribute to the revision of future expectations. Since the exogenous variable innovations are subsumed within the innovations representation in (20)-(23), we can effectively calculate the expectations revision processes through the VAR stacked form (11), Yt = AYt−1 + Q et . With n =4, the following vectors of length nq are created:

x

ε t = et −et −γ1 r′π AQ et −γ2 et

r′π = ð0; 1; 0; …; 0Þ for inflation

ð24Þ

r′s = ð0; 0; 1; …; 0Þ for the exchange rate The expectations revision processes are defined as:


= r′π AQ et

i




 π π x εt = et −β1 Et πt + 1 −Et−1 πt + 1 −β2 et

ð16Þ

Et πt + 1 −Et−1 πt + 1 = r′π AðYt −Et−1 Yt Þ

i

+ 1 −Et−1 π t + 1

r′x = ð1; 0; 0; …; 0Þ for the output gap

Et πt + 1 = r′π AYt

π


x x
i ε t = et − Et xt + 1 −Et−1 xt + 1 + α 1 et −α 1 Et π t   s π −α 2 et −et = 400

ð15Þ

Et xt + 1 = r′x AYt

π

3.2.2. An open economy New Keynesian model We first convert the contemporaneous structural equations of the open economy New Keynesian model represented by (1)-(4) in terms of structural disturbances and VAR innovations. In the process of conversion, innovations to the exogenous variables (i.e. foreign prices and the foreign interest rate) become factors inside the system of VAR innovations to the four endogenous variables. Therefore we can write the following innovations representation that contains only endogenous variable innovations:

 Et xt + 1 −Et−1 xt + 1 = r′x AQ et
 Et πt + 1 −Et−1 πt + 1 = r′π AQ et
 Et st + 1 −Et−1 st + 1 = r′s AQ et

ð25Þ

ð17Þ

Apply the definitions in (25) we can write the open economy model in terms of the following innovations system:

ð18Þ

    x x i s π ε t = et −r′x AQ et + α 1 et −r′π AQ et −α2 et −et = 400

ð19Þ

where the forward-looking behaviour embedded in (17)-(19) suggests non-linear restrictions across the coefficients of each contemporaneous structural equation. Economic agents, i.e. consumers, firms, and the central bank, are assumed to incorporate all relevant innovations in forecasting future expected values of endogenous variables.

4 Constants and deterministic variables are ignored since they do not affect expectations revisions.

π

π

s

s

i

i

x

εt = et −β1 r′π AQ et −β2 et

ð27Þ

i

εt = et −r′s AQ et + et π

ð26Þ

ð28Þ x

εt = et −et −γ1 r′π AQ et −γ 2 et

ð29Þ

5 Because quarterly inflation is calculated on an annualised basis, so the connection between inflation and prices is πt = 400(pt − pt− 1). The inflation innovation is derived by subtracting Et− 1πt away from πt, i.e., πt − Et− 1πt = 400(pt − Et− 1 pt), and therefore we obtain ept = eπt /400.

S.C.-Y. Leu / Economic Modelling 28 (2011) 157–168 Table 1 Reduced-form diagnostics. Diagnostic Tests

161

Table 2 Contemporaneous structural estimates.

Equations xt

πt

st

it

Serial correlation F(1,73)

2.83 (0.10)

2.40 (0.13)

0.86 (0.36)

2.26 (0.14)

ARCH F(1,98)

0.00 (0.96)

0.79 (0.38)

1.62 (0.21)

14.2 (0.00)

Normality χ2(2)

4.88 (0.09)

4.87 (0.09)

1.18 (0.56)

162 (0.00)

Functional form F(1,73)

0.89 (0.35)

6.16 (0.02)

3.78 (0.06)

2.41 (0.13)

Adjusted R2

0.72

0.99

0.87

0.97

Notes: P-values are in parentheses. The diagnostic tests are: (1) an F-test with the null of no serial correlation, which is based on regression of residuals on initial regressors and lagged residuals; (2) an F-test for no ARCH effects that is based on regression of squared residuals on lagged squared residuals. The F-test is a modified Lagrange multiplier (LM) test; (3) the Jarque–Bera normality test; and (4) Ramsey's RESET test using the square of the fitted value. It tests the null of no mis-specification.

α1

α2

β1

β2

γ1

γ2

0.07 (0.09)

3.14 (0.00)

0.08 (0.63)

0.38 (0.03)

2.84 (0.00)

2.75 (0.01)

Note: P-values are in parentheses.

potential output is obtained applying the Hodrick–Prescott (HP) filter on the Australian real GDP. The output gap is then computed as the difference between the logarithm of real GDP and its HP trend.6 We use the year-ended weighted median measure of inflation provided by the RBA as the domestic inflation rate. For the interest rate, we use the 11 a.m. call rate of the interbank market or the cash rate, which is representative of the policy stance of the RBA. The last domestic variable is the $A/$US bilateral exchange rate. Two foreign variables that enter the model are the U.S. CPI and the federal funds rate. These data series are presented in the Data Appendix.

4.1. Diagnostics of the reduced-form VAR 3.3. Estimating SVAR model with rational expectations identification restriction We write the dynamic open economy structural model in matrix form: Γ0 yt = Γ1 yt−1 + … + Γq yt−q + Λ0 zt + Λ1 zt−1 + … + Λk zt−k + εt ; εt ∼ð0; DÞ

ð30Þ where yt = ðxt ; πt ; st ; it Þ′ is the vector of endogenous variables and   zt = pt ; i*t ′ is the vector of exogenous variables, Γi and Λj are coefficient matrices for the endogenous and exogenous variables with
′ lag order q and k respectively, the vector εt = εxt ; επt ; εst ; εit contains the structural disturbances, 0 is a (4 × 1) vector of zeros, and D is a (4 × 4) diagonal variance–covariance matrix. Premultiply (30) by Γ−1 0 yields the reduced-form VAR: yt = A1 yt−1 + … + Aq yt−q + B0 zt + B1 zt−1 + … + Bk zt−k + et ; et ∼ð0; ΩÞ

ð31Þ −1 1 −1 where Ai = Γ− 0 Γi, i = 1,..., q, Bj = Γ0 Λj, j = 0, 1, …, k, et = Γ0 εt , and −1 − 1′ Ω = Γ0 DΓ0 . The estimation proceeds in two steps. Step 1 involves estimating the reduced-form VAR specified by (31). Parameter estimates contained in A and the rational expectations restrictions dictated by (26)-(29) are imposed on Γ0; further exclusion restrictions placed on the contemporaneous exogenous variables are in Λ0. The lagged dynamics are unrestricted and we estimate the structural system (30) using FIML with the assumption of normality in the structural disturbances. The structural parameters are obtained by maximising the following log-likelihood function: T

L= ∑

t =1

 n 1 1 −1 −1 −1 − lnð2πÞ− ln Γ0 DΓ0 ′ − ε′t D εt 2 2 2

j

j

ð32Þ

and the asymptotic standard errors are obtained as the inverse of the Hessian matrix. 4. Data and empirical results The New Keynesian SVAR model is estimated with Australian quarterly data from 1984Q1 to 2009Q4. For the output gap,

Estimation of SVAR models is preceded by performing a battery of diagnostic tests to check the statistical adequacy of the reduced form (Spanos, 1990). The lag orders of the endogenous and exogenous variables are allowed to be different. Keating (2000) termed this approach ‘asymmetric VAR’ which permits greater flexibility in specifying the dynamics. The dynamic structure used for estimation is four lags of the endogenous variables and two lags of the exogenous variables.7 Additionally, a constant and three seasonal dummies are included in each endogenous variable equation.8 The results of the diagnostic tests on the reduced-form VAR(4,2) are reported in Table 1. These residual diagnostic tests cannot reject the null hypotheses of no serial correlation, normality, and the absence of ARCH effects at the 5% significance level, except for non-normality and ARCH effect in the interest rate equation. We also perform the Ramsey RESET test on all four endogenous equations, where the null of no mis-specification is not rejected at 5% (1% for the inflation equation). When these test results are assessed together, there is general support for the statistical adequacy of the model. Additionally the adjusted R2 statistics show reasonably high goodness of fit.

6 The HP filter is a univariate detrending algorithm that extracts the potential output component by minimising a particular loss function. The smoothness of the HP stochastic trend depends on the input value of an ad-hoc smoothness parameter. For quarterly data Hodrick and Prescott (1997) recommended setting the smoothness parameter to 1600, which we follow in this article. Although the shortcomings of the HP filter are well documented in the literature, i.e. smoothing weight sensitivity and end-point problem, it is nevertheless a widely used methodology to obtain a measure of the output gap. 7 Given the quarterly data and its relatively small sample size, the upper bound was initially set at 4 lags for both the endogenous and exogenous variables. However, the interest rate equation in VAR(4,4) failed to reject the null of no serial correlation. We therefore tested down the order of exogenous variable lags to seek a more parsimonious specification. Using the likelihood ratio test where the null is VAR(4,4) against the alternative of VAR(4,2), the test statistic is χ2(16) = 29.91 with p-value = 0.02, hence the test rejects the null in support of the alternative hypothesis. 8 The inclusion of the seasonal dummies intends to deal with potential seasonal effects as we use seasonally unadjusted data (e.g. Australian real GDP). An alternative way is to specify a 5-lag dynamic structure which contains a year's worth of lags plus one extra lag to pick up any seasonal variation. Using the likelihood ratio test for the null of VAR(5,2) against the alternative of VAR(4,2), the test statistic χ2(16) = 30.08 with p-value = 0.02 rejects the null in favour of the alternative.

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Output Gap

Exchange Rate

0.03

0.7

0.02

0.6 0.5

ln

%

0.01 0.00

0.4 0.3

-0.01

0.2

-0.02

0.1

-0.03

0.0 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 actual value

10

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

fitted value

actual value

Inflation Rate

Interest Rate

20.0

9

fitted value

17.5

8 15.0

6

%

%

7 5

12.5 10.0

4

7.5

3

5.0

2 1

2.5 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 actual value

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

fitted value

actual value

fitted value

Fig. 1. Data vs. in-sample predicted values.

4.2. Contemporaneous parameter estimates The estimated contemporaneous parameters in (26)-(29) are shown in Table 2.9 Apart from β1, the parameter estimates are correctly signed and statistically significant at 5% (10% for α1). From the IS equation, α1 and α2 indicate that a lower real interest rate and a real exchange rate depreciation raise the output gap and aggregate demand. For the AS equation, β1 captures the extent of inflationary dynamics driven by forward-looking firms operating in a Calvo's sticky price environment. Our estimate of β1 is not statistically significant from zero which implies that inflation expectations in Australia are mainly backward-looking. This is consistent with Gruen et al. (1999). Two other studies that come to similar conclusions are Fuhrer and Moore (1995) who found that an NKPC with purely forward-looking dynamics inadequately accounts for the degree of inflation persistence in the post-war U.S. data, and Fuhrer (1997) confirmed that the presence of the forward-looking component in explaining inflation is not required empirically. The usefulness of lagged variables is demonstrated by Roberts (2001) who argued that additional lags are necessary to represent the simple autoregressive rules of thumb that agents use to forecast inflation. In agreement with studies that examine a forward-looking Phillips curve, such as Jondeau and Le Bihan (2005), our estimate of β2 suggests that the output gap is an important forcing variable for the Australian inflation dynamics.

9 To identify the structural parameters, there are 8 over-identifying restrictions. The likelihood ratio (LR) test yields a statistic of 29.78. This statistic is asymptotically distributed as a χ2-variate with 8 degrees of freedom and the 5% critical value is 15.51. The test result rejects the null hypothesis that the restricted (structural) model comes from the same asymptotic distribution of the unrestricted (reduced-form) model. Cho and Moreno (2006) and Garratt et al. (2003) showed that asymptotic tests such as the LR test can be severely biased in small samples. Hence we conduct a non-parametric bootstrapping exercise of 1000 simulations to obtain the small sample critical value that takes into account the dimensions of the model and the relatively small sample of data. The simulated 5% critical value is 33.46 indicating that the LR test adjusted for small sample does not reject the over-identifying restrictions implied by the economic theory.

Parameter estimates from the interest rate rule suggest that the RBA implemented policy measures to stabilise inflation and output fluctuations. The estimated coefficient of γ1 N 1 suggests that the short-term nominal interest rate adjusts more than one-for-one to inflation movements to effect a change in the real interest rate and hence the Taylor principle holds. Actual and predicted values of the endogenous variables are presented in Fig. 1. The graphs show that in-sample fitted values of the estimated structural equations track the actual data well. 4.3. Impulse response functions Impulse response functions with 95% confidence interval for the four structural shocks: monetary policy, risk premium, aggregate demand, and aggregate supply shocks are reported in Figs. 2–5.10, 11 Each structural shock is of one standard deviation with their size shown in Table 3. In many cases, the confidence intervals indicate that the dynamic responses are statistically significant (not including 0) in the short run (within the first year of the initial shock). All responses show mean-reversion which reflects the stationary properties of the structural model. 4.3.1. Monetary policy shock In Fig. 2, the effect of an unexpected monetary tightening leads to a decrease in the output gap and inflation, and the exchange rate appreciates upon impact. Hence the identification scheme generates no ‘price and exchange rate puzzles’. In the short run, the interest rate is lowered to offset the contractionary impact created by the initial policy tightening. The expansionary effects from subsequent monetary easing gradually stabilise output and inflation fluctuations in the medium run.

10 The computation of the confidence intervals is based on the bootstrapping procedure of Runkle (1987) with 5000 simulations. 11 Setting β1 = 0 does not change the impulse response function results qualitatively and in many cases the results are very similar quantitatively.

S.C.-Y. Leu / Economic Modelling 28 (2011) 157–168

Response of Output Gap to monetary policy shock

Response of Exchange Rate to monetary policy shock

0.07

2.0

0.00

1.5

-0.07

1.0

-0.14

0.5

%

%

163

-0.21

0.0

-0.28

-0.5

-0.35

-1.0 -1.5

-0.42 0

5

10

15

20

25

30

35

40

0

5

10

number of quarters

Response of Inflation to monetary policy shock

20

25

30

35

40

Response of Interest Rate to monetary policy shock

-0.00

0.3

-0.05

0.2 0.1

-0.10

-0.0

%

-0.15

%

15

number of quarters

-0.20

-0.1 -0.2

-0.25

-0.3

-0.30

-0.4

-0.35

-0.5 -0.6

-0.40 0

5

10

15

20

25

30

35

40

0

5

10

number of quarters

15

20

25

30

35

40

number of quarters

Fig. 2. Impulse response functions to a one-standard-deviation monetary policy shock.

The dynamic behaviour of the exchange rate complies with the prediction of the interest parity condition. As the monetary tightening generates a favourable interest rate differential to the home country,

the exchange rate appreciates in the short run and then finds itself on a gradual depreciating trajectory, which overshoots to reach a peak before returning to its medium-run value. Our result is

Response of Output Gap to risk premium shock

Response of Exchange Rate to risk premium shock

0.20

0.50

0.15

0.25 0.00

0.10

-0.25

%

%

0.05 -0.00

-0.50 -0.75

-0.05

-1.00

-0.10

-1.25

-0.15

-1.50 -1.75

-0.20 0

5

10

15

20

25

30

35

40

0

5

10

number of quarters

15

20

25

30

35

40

number of quarters

Response of Inflation to risk premium shock

Response of Interest Rate to risk premium shock 0.75

0.25 0.20

0.50

0.15

%

%

0.10 0.05

0.25

0.00 0.00

-0.05 -0.10 -0.15

-0.25 0

5

10

15

20

25

number of quarters

30

35

40

0

5

10

15

20

25

number of quarters

Fig. 3. Impulse response functions to a one-standard-deviation risk premium shock.

30

35

40

164

S.C.-Y. Leu / Economic Modelling 28 (2011) 157–168

Response of Output Gap to aggregate demand shock

Response of Exchange Rate to aggregate demand shock 1

0.10

0

0.05

-1

-0.00

-2

%

%

0.15

-0.05

-3

-0.10

-4

-0.15

-5

-0.20

-6 0

5

10

15

20

25

30

35

40

0

5

10

number of quarters

15

20

25

30

35

40

number of quarters

Response of Inflation to aggregate demand shock

Response of Interest Rate to aggregate demand shock

0.15

0.3

0.10 0.2 0.05 0.1

%

%

-0.00 -0.05

0.0

-0.10 -0.1 -0.15 -0.2

-0.20 0

5

10

15

20

25

30

35

40

0

5

10

number of quarters

15

20

25

30

35

40

number of quarters

Fig. 4. Impulse response functions to a one-standard-deviation aggregate demand shock.

in contrast to the finding by Eichenbaum and Evans (1995) and Grilli and Roubini (1995) that a positive interest rate differential in favour of domestic assets is associated with persistent appreciation

of the domestic currency up to 2 years after the initial impact. Their dynamic responses of the exchange rate are thus consistent with the contractionary effect a negative interest rate shock produces

Response of Output Gap to aggregate supply shock

Response of Exchange Rate to aggregate supply shock

0.18

1.0

0.12

0.5

0.06

0.0 -0.5

-0.06

%

%

0.00

-1.0

-0.12 -1.5

-0.18 -0.24

-2.0

-0.30

-2.5

-0.36

-3.0 0

5

10

15

20

25

30

35

40

0

5

10

number of quarters

Response of Inflation to aggregate supply shock

20

25

30

35

40

Response of Interest Rate to aggregate supply shock

0.45

0.6

0.40

0.5

0.35

0.4

0.30

0.3

0.25

%

%

15

number of quarters

0.2

0.20 0.1

0.15

0.0

0.10

-0.1

0.05 0.00

-0.2 0

5

10

15

20

25

number of quarters

30

35

40

0

5

10

15

20

25

number of quarters

Fig. 5. Impulse response functions to a one-standard-deviation aggregate supply shock.

30

35

40

S.C.-Y. Leu / Economic Modelling 28 (2011) 157–168 Table 3 Size of one-standard-deviation shocks. Monetary policy

Risk premium

Aggregate demand

Aggregate supply

0.24%

0.40%

0.02%

0.14%

in SVAR analysis without the incorporation of forward-looking behaviour. 4.3.2. Risk premium shock A positive shock to the risk premium associated with holding Australian dollar leads to exchange rate appreciation. The output gap and inflation also rise upon impact as shown in Fig. 3. The central bank increases the interest rate immediately to counter the inflationary pressure and the policy remains contractionary in the short run. Even though the exchange rate is not an explicit consideration in the interest rate rule, Taylor (2001) argued that the exchange rate affects output through the expenditure-switching effect and inflation through the pass-through effect. Inspecting the aggregate demand and aggregate supply relationships, an unexpected exchange rate depreciation raises the output gap in the IS equation, which in turn leads inflation to rise through the Phillips curve. Hence monetary policy is tightened to reduce the level of economic activity and inflation, in the process, the rise in the interest rate also reverses the path of the exchange rate movements. In the medium run, the central bank cuts the interest rate to inflate the economy and boost output with the aid of depreciating exchange rate. 4.3.3. Aggregate demand shock In Fig. 4, output and inflation increase when an unexpected positive aggregate demand shock hits the economy. In response to these movements, the central bank increases the interest rate. The exchange rate appreciates for 2 quarters following the exogenous shock and adds deflationary pressure to the economy which leads to a contraction in output after the initial expansion.12 From quarter 2, the exchange rate starts to depreciate which helps to expand output and push up inflation. The dynamic responses of the interest rate suggest that the central bank maintains a relatively tight policy stance in the short run before reversing to reduce the negative output gap. In the medium run, the interest rate is returned to its neutral value, corresponding with inflation converging to its target value. The exchange rate response to the aggregate demand shock depends on whether the shock is related to domestic demand or external demand. An increase in consumption, for example, would be associated with an increased level of imports and a depreciation of the exchange rate. An increase in investment might have similar effect, unless favourable investment conditions induced matching capital inflows. On the other hand, an increase in demand by the foreign country (the U.S.) for Australian exports—which leads to an increased demand by the foreign country for Australian dollar to purchase Australian goods—would cause an appreciation of the exchange rate. Thus the dynamic responses of the exchange rate suggest that export shocks have been the more dominant factor in recent years. 4.3.4. Aggregate supply shock Consider an exogenous positive inflation shock, which can be thought of as an adverse aggregate supply shock which forces firms to raise prices. Fig. 5 shows that such a shock generates lower output and higher inflation at impact. The opposite movements of output

12 This is consistent with the results of Fisher (1996) who investigated movements in the Australian nominal and real exchange rates.

165

and inflation demonstrate the policy response dilemma that usually occupies the policymakers when faced with an aggregate supply shock. In our case, the estimated monetary policy response at the impact of the shock is a very small reduction in the interest rate (0.4 basis points). However, this may be interpreted as caution (or delayed action) exercised by policymakers at the outset to monitor the progression of the shock. In the short run, the central bank gradually raises the interest rate in response to sustained higher inflation rates. However, as the nominal interest rate rises at a slower rate than inflation, this has the effect of lowering the real interest rate to stimulate the economy and raise output. Given the foreign nominal interest rate, uncovered interest parity implies short-run exchange rate appreciation followed by expected future depreciation, as reflected in the dynamic responses of the exchange rate. The interest rate response peaks at quarter 10 before the central bank gradually unwinds it back to the neutral level in response to fluctuations in output and inflation in the medium run. 4.4. Variance decomposition An assessment of the relative importance of the four structural shocks at various horizons can be gained by examining the proportion of the forecast error variance which is accounted for by each of the shocks and reported in Table 4. For the output gap, the aggregate supply shock is the major contributor to explaining its variability. This shock accounts for around 53% of the forecast error variance at short horizons and 33% at long horizons. Monetary policy shocks rank second in its relative contribution. At the 1 quarter horizon, it accounts for around 47% of the forecast error variance and increases to 53% in the medium run. As in the study by Huh (1999), the aggregate demand shock does not play a significant role in influencing output even in the short run. In the case of inflation, the monetary policy shock explains most of the short-run forecast error variance followed by the aggregate supply

Table 4 Forecast error variance decomposition. Series

Output gap

Inflation

Exchange rate

Interest rate

Number of quarters

Structural shocks MP

RP

AD

AS

1 4 8 12 20 40 1 4 8 12 20 40 1 4 8 12 20 40 1 4 8 12 20 40

46.60 64.34 57.33 53.59 52.98 52.95 57.86 47.38 50.71 46.10 40.04 38.66 4.54 1.45 1.19 3.20 11.74 15.02 15.16 5.93 25.21 26.70 23.15 22.39

0.08 2.04 7.43 9.62 10.17 10.21 0.78 13.74 8.61 6.14 4.90 4.53 0.90 2.11 4.79 6.99 5.99 4.74 71.76 85.98 59.91 43.19 37.04 34.97

0.17 1.35 1.40 2.94 3.39 3.39 0.09 1.37 1.17 0.82 0.73 0.85 93.49 92.80 88.60 81.00 61.62 48.41 7.46 5.90 3.27 2.52 2.97 2.72

53.14 32.27 33.84 33.84 33.46 33.46 41.27 37.52 39.52 46.94 54.33 55.95 1.07 3.64 5.42 8.82 20.64 31.84 5.62 2.19 11.61 27.59 36.84 39.93

Notes: MP denotes the monetary policy shock; RP denotes the risk premium shock; AD denotes the aggregate demand shock; and AS denotes the aggregate supply shock.

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Table 5 Contemporaneous structural estimates (pre-GFC sample). α1

α2

β1

β2

γ1

γ2

0.21 (0.00)

3.88 (0.00)

0.01 (0.95)

0.42 (0.01)

3.55 (0.00)

3.38 (0.00)

Note: P-values are in parentheses.

shock in the second place. Both explain around 58% and 41% of the variability in the short run respectively. While the influence from monetary policy declines to 39%, aggregate supply shocks increase its explanatory power to 56% at the 40 quarter horizon. There is a modest rise in contribution from the risk premium shock. An examination of the exchange rate movements shows that the aggregate demand shock is the most important factor that accounts for between 93% and 48% of forecast error variance in the exchange rate at all horizons. Over time, contributions from other sources steadily increase. At quarter 40, the second most contribution comes from the aggregate supply shock at 32% followed by the monetary policy shock which accounts for 15% of the forecast error variance. This is consistent with Fisher (1996) that real shocks are the major determinant of movements in the Australian nominal exchange rate. Finally, the risk premium shock explains 72% and 86% of the interest rate variability at the horizons of 1 and 4 quarters respectively. As the forecast horizon increases, the aggregate supply shock becomes increasingly important in its contribution. At the 40 quarter horizon, the aggregate supply shock overtakes as the most important explanatory factor with 40%, the risk premium shock becomes second at 35%, and followed by the monetary policy shock explaining 23% of the interest rate variability.13 4.5. Comparison with the pre-GFC period Australia has been enjoying strong and robust economic growth in particular fuelled by external demand for resources from Asia recently. However, the financial turmoil that began in late 2007 and peaked in September 2008 in the U.S. spread quickly beyond its borders and led to perhaps the most severe global financial and real crisis since the Great Depression. Australia has not been immune from this experience. We compare the estimation result from the full sample period (that ends in 2009Q4) to the preGFC period (that ends in 2007Q4) to see if (1) the results are relatively robust over time; and (2) there are changes to policy stance of the central bank. The estimated coefficients for the preGFC sample are reported in Table 5. Comparing with the coefficients from the full sample, we observe that the real interest rate effect in the IS curve is stronger. Interestingly, the coefficient estimates from the monetary policy rule suggest that the RBA responded to inflation and output fluctuations relatively more aggressively in the pre-GFC period. This reflects the strong economic conditions in Australia prior to the global financial meltdown and the level of intensity in which the RBA was prepared to adjust the policy rate in response to domestic economic developments. During 2008– 2009, the world economy went into recession. Given the severity of the slowdown, major developed economies recognised the need to implement stimulus measures in packages that go beyond just cutting interest rates, i.e. including fiscal expansion and bank deposit

13 A substantial role played by risk premium shocks in explaining interest rate variations on short-run horizons was also found by Liu (2007), who presented an SVAR model identified by sign restriction for the Australian economy. Over the longerrun horizons, our variance decomposition results for the interest rate are similar to those by Buncic and Melecky (2008).

guarantees, to prop up confidence and support aggregate demand. Hence the monetary policy rule coefficients associated with the full sample may reflect the policy uncertainty that prevailed during this period. Inspecting the impulse response functions shown in Fig. 6, the basic story does not change between the two sample periods in a qualitative sense. Consistent with the larger monetary policy rule coefficients in the pre-GFC period, the dynamic responses of the interest rate to monetary policy, aggregate demand, and aggregate supply shocks are relatively more aggressive. As a result, fluctuations in output, inflation, and the exchange rate are more pronounced and they generally take longer to return to equilibrium in the medium run. 5. Conclusions We estimate a New Keynesian SVAR model of the Australian economy covering the period 1984 to 2009. The aggregate relationships imposed on the contemporaneous structure of the SVAR model are derived from an open economy New Keynesian model which features intertemporally optimising agents who are rational and forward-looking. Hence the identification of the SVAR model under rational expectations requires exclusion restrictions to be placed on the VAR residuals and the covariance matrix. The New Keynesian SVAR model is estimated by maximum likelihood that accounts for the full interactions between consumers, firms and the central bank. We then simulate dynamic responses of the macroeconomic variables to monetary policy, risk premium, aggregate demand, and aggregate supply shocks. Our parameter estimates are significant (but one) and correctly signed. From the dynamic IS curve, we find that a lower real interest rate and a depreciating real exchange rate raise the level of current output. The estimated coefficient of the subjective discount factor in the NKPC supports the notion that a large fraction of firms is backward-looking in setting prices. The output gap is found to be a significant and important forcing variable in driving the dynamics of Australian inflation. The estimated coefficients from the monetary policy rule suggest that the RBA adjusts nominal interest rates more than one-for-one so that real interest rates move sufficiently to stabilise deviations in inflation and output from their target values. Simulated dynamic responses show that a positive monetary policy shock has significant contractionary effects on output and inflation. The relatively higher domestic interest rate induces the exchange rate to appreciate on impact. Hence there is no sign of a price or exchange rate puzzle. In the event of a positive risk premium shock to domestic currency holding, the exchange rate depreciates and the central bank raises the interest rate in response to higher output and inflation. Even though the nominal exchange rate is not an explicit consideration in the monetary policy rule, large exchange rate fluctuations may have detrimental effects indirectly on the real output through the expenditure-switching effect and on inflation through the passthrough effect. When the economy experiences a positive aggregate demand shock, output and inflation rise and the central bank tightens policy accordingly. Interestingly, the exchange rate appreciates which suggests that the aggregate demand shock is associated with an increase in the external demand for Australian goods. An adverse aggregate supply shock presents a policy dilemma to the central bank as the economy experiences stagflation at impact. The impulse response functions suggest that the central bank does not rush into policy action at the beginning of the shock. Over time it gradually raises the nominal rate to counter the inflationary pressure but allow the real rate to fall which helps to correct the negative output gap.

Response of Output Gap to MP shock

Response of Output Gap to RP shock

Response of Output Gap to AD shock

0.10

0.2

0.02 0.05

%

% -0.05 -0.10

-0.4

-0.15

-0.3

10

15

20

25

30

35

40

0

5

10

15

20

25

30

35

40

0

5

10

number of quarters

Response of Inflation to MP shock

-0.00

-0.4

-0.12

number of quarters

Response of Inflation to RP shock

0.10

30

35

40

0

0.05 0.00

0.45

0.075

0.40

-0.05

5

10

15

20

25

30

35

40

5

10

number of quarters

20

25

30

35

40

0.05 5

10

15

20

25

30

35

40

0

Response of Exchange Rate to AD shock

0

0.0

-1.00 -1.25 0

5

10

15

20

25

30

35

40

-6 5

10

15

20

25

30

35

40

Response of Interest Rate to RP shock

-0.6 -0.8 20

25

number of quarters

30

35

40

15

20

25

30

35

40

0

0.7

0.5

0.25

0.6

0.2

-0.1

0.00

0.0

-0.2

-0.05

-0.1

25

number of quarters

30

35

40

30

35

40

0.2

0.0

20

25

0.3

0.05

15

20

0.4

0.15 0.10

10

15

0.5

0.20

5

10

Response of Interest Rate to AS shock

0.8

0.30

0

5

number of quarters

Response of Interest Rate to AD shock

0.35

0.1

15

10

0.6

%

%

-0.4

10

5

number of quarters

0.3

-0.2

5

-5 0

0.4

0

-4

-5

0.7

-0.0

40

%

-3

number of quarters

Response of Interest Rate to MP shock

35

-3

0

0.2

30

-4

number of quarters 0.4

25

-1

-0.75

-0.5

20

-2

-0.25 -0.50

0.5

15

-2

%

%

1.0

10

Response of Exchange Rate to AS shock

0

-1

0.00

1.5

5

number of quarters

0.25

2.0

40

0.25

number of quarters

0.50

35

0.10 0

Response of Exchange Rate to RP shock

0.75

2.5

30

0.15

number of quarters

Response of Exchange Rate to MP shock

3.0

15

25

0.20

-0.075 0

20

0.30

-0.050

-0.10 0

15

0.35

0.025

-0.025

-0.40

10

Response of Inflation to AS shock

0.50

0.100

0.000

-0.30 -0.35

5

number of quarters

0.050

%

%

-0.25

25

S.C.-Y. Leu / Economic Modelling 28 (2011) 157–168

0.15

-0.20

20

Response of Inflation to AD shock

0.125

-0.10 -0.15

15

number of quarters

0.20

-0.05

%

-0.2

%

5

-0.1

-0.08 -0.10

0

%

-0.04 -0.06

-0.2 -0.3

-0.0

%

%

0.00 -0.1

0.1

0.00 -0.02

%

0.1 -0.0

%

Response of Output Gap to AS shock 0.2

0.04

0.1

0

5

10

15

20

25

30

number of quarters

35

40

0

5

10

15

20

25

30

35

40

number of quarters

Fig. 6. Impulse response function comparison: full sample (black) and pre-GFC sample (blue).

167

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S.C.-Y. Leu / Economic Modelling 28 (2011) 157–168

Data Appendix

Australian Output Gap

$A/$US Exchange Rate

US Consumer Price Index

0.03

0.7

4.8

0.02

0.6

4.7 4.6

0.5

0.01

4.5

0.00

ln

ln

%

0.4

4.3

0.3 -0.01

4.2

0.2

4.1

-0.02

0.1

-0.03

0.0 1984 1987 1990 1993 1996 1999 2002 2005 2008

4.0 3.9 1984 1987 1990 1993 1996 1999 2002 2005 2008

Australian Inflation Rate

1984 1987 1990 1993 1996 1999 2002 2005 2008

Australian Cash Rate

10 9

US Federal Funds Rate

20.0

12

17.5

10

8 15.0

7

8

5

%

12.5

6

%

%

4.4

6

10.0

4

4

7.5

3 2

5.0

2 1

2.5 1984 1987 1990 1993 1996 1999 2002 2005 2008

0 1984 1987 1990 1993 1996 1999 2002 2005 2008

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