This paper uses a recent panel method of Russell and Banerjee (2008) to estimate the new Keynesian Phillips curve for Australia. Our estimates show that while the hybrid new Keynesian Phillips curve and backward looking conventional Phillips curve are well determined, estimates of the Phillips curve with the pure forward looking expectations are unsatisfactory.Panel data estimates, new Keynesian Phillips curve, Australia and Unit roots in the rate of inflation.

Esposito, Piero

Paradiso, Antonio

Rao, B. Bhaskara

English

Research Papers in Economics

3/3/11 
Non-Stationary Inflation and Panel Estimates of the 
 New Keynesian Phillips Curve for Australia 
 
B. Bhaskara Rao 
raob123@bigpond.com 
School of Economics and Finance, University of Western Sydney, Sydney (Australia) 
 
Antonio Paradiso 
anto_paradiso@hotmail.com 
Department of Economics, University of Rome La Sapienza, Rome (Italy) 
 
Piero Esposito 
pieroesp@gmail.com, p.esposito@sssup.it  
Sant’Anna School of Advanced Studies, Pisa (Italy), Centro Europa Ricerche (CER) 
 
Abstract 
This paper uses a recent panel method of Russell and Banerjee (2008) to estimate the new 
Keynesian Phillips curve for Australia. Our estimates show that while the hybrid new Keynesian 
Phillips curve and backward looking conventional  Phillips curve are well determined, estimates of 
the Phillips curve with the pure forward looking expectations are unsatisfactory. 
 
Keywords: Panel data estimates, new Keynesian Phillips curve, Australia and Unit roots in the rate 
of inflation. 
 
JEL: C2, C12, E3. 
 
 
 
 
  
1. Introduction 
One branch of the Phillips curve (PC) literature recognizes that a stationary inflation rate is 
inconsistent with the theoretical and empirical properties of the inflation for the past fifty years; see 
Henry and Shiedls (2003) and Russell and Banerjee (2008). Therefore, four methods are used to 
overcome non-stationarity in inflation. Following Gali and Gertler (1999), many have used the 
difference between inflation and its sample mean as the dependent variable. King and Watson 
(1994), Stock and Watson (2007), and Ireland (2007) have differenced the data. Cogley and 
Sbordone (2008) have used the gap between inflation and its smooth time varying mean. Russell 
and Banerjee (2008) take the view that inflation could be nonstationary because monetary 
authorities respond to shocks by making discrete changes to inflation targets. Therefore, inflation 
may be stationary with structural breaks for shifting means.  
These alternative approaches may give different results on the relative importance of the 
forward and backward looking expectations of inflation and the trade off in the long run. This has 
policy implications because if backward looking expectations are more important, deflationary 
policies to reduce inflation will be costly. In a Monte Carlo study Russell et. al., (2010) found that 
the Gali and Gertler and Cogley and Sbordone methods overestimate the coefficient of forward 
looking expectations, but such biases are less in their shifting means approach. Therefore, this paper 
uses their panel data method, with shifting means, to estimate three formulations of PC for 
Australia: Backward looking PC, forward looking PC, and hybrid PC. 
Section 2 presents specifications and describes the Russell and Banerjee method. Section 3 
uses the Bai and Perron (2003) break tests to identify inflation regimes. Section 4 presents empirical 
results and Section 5 concludes. 
2. Specification and Estimation 
2.1 Specification 
The specifications can be presented in terms of restrictions to the hybrid PC (Gali and Gertler 
(1999)): 
 
(1) 
11
2                 (0, )     
t b t f t t y t t
t
Ey
N
      

    
  
where  rate of inflation (measured as year-on-year percentage change),  t E expected rate of 
inflation based on information in period tand  y a measure of the forcing variable, e.g., real 
marginal cost and output gap etc. Although US empirical studies use alternative measures for  , y in  
Australian works unemployment rate or its deviation from the natural rate (u – u
*) is popular. 
The purely backward looking adaptive expectations PC model of Friedman and Phelps (F-P) 
assumes  0 f   and  1 b   . The New Keynesian (NK) PC is based on the microeconomic 
foundations and implies that optimizing firms use rational and purely forward looking expectations 
of inflation in their product pricing decisions. Therefore, NKPC implies that  1 f   and  0 b   . 
Finally, the hybrid PC of Gali and Gertler assumes that  1 fb   . 
2.2 Estimation Method 
Unit root tests show that the rate of inflation is an integrated variable and unemployment rate too
1. 
Following the influential work by Gali and Gertler (1999) many studies have used the deviation of 
the rate of inflation from its sample mean as their inflation measure, believing that this is a 
stationary variable. This relationship is then estimated with a classical instrumental variable 
method. However, de-trending inflation with its sample mean may not make it stationary. 
Therefore, estimation with any classical method would give spurious results. 
  In the introduction we discussed various alternatives to transform inflation rate into a 
stationary variable. Since the scope of this paper is limited, we  explain only the Russell and 
Banerjee (2008) method because it is promising. They assume that inflation is stationary with 
shifting means. Based on this assumption, they use the Bai and Perron (2003) break tests to identify 
breaks in the mean rate of inflation so that the mean rate of inflation is constant in each inflation 
regime. If these tests show five structural breaks there will be six regimes to form six cross section 
units. Finally, Russell and Banerjee use the fixed effects panel data method to estimate the three 
versions of PC viz., F-P, hybrid, NK. 
                                                             
1 The results are available upon request by authors.  
3. Empirical Results 
Our data are from 1967Q1 to 2010Q3. Definitions and sources of data are in the appendix.
2 The 
natural rate of unemployment (
* u ) is estimated by smoothing the unemployment rate with Hodrick-
Prescott filter. Following Gali and Gertler (1999) the actual rate of inflation, one period ahead, is 
used for the expected rate of inflation.  
3.1 Bai-Perron Breakpoint Test 
The estimated model is: 
(2)  1 t k t       
where    is the inflation rate  and   1 k    is a series of k+1 constants that estimate the mean rate of 
inflation in each of k+1 inflation regimes and   t   is a random error. The model uses a trimming 
rate of 10 per cent of the sample and is estimated using quarterly data for the period 1967Q1 to 
2010Q3. The graph and the table of estimated regimes are reported below.  
Figure 1  
Inflation Rate and the Regime Specific Mean Inflation 
-5
0
5
10
15
20
25
1
9
6
7
Q
1
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4
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Q
1
 
                      ---- Actual rate of inflation and ____ mean rate of inflation. 
 
 
                                                             
2 This period is selected on the ready availability of reliable data on the unemployment rate. Table 1 
 Estimated Inflation Regimes with the Bai-Perron Break Tests 
Regime  Dates of Regimes  Mean inflation  Mean Natural 
unemployment 
Rate 
1  1967Q1 – 
1972Q2 
4.7  1.9 
2  1972Q3 – 
1977Q1 
13.7  3.7 
3  1977Q2 – 
1983Q2 
9.8  6.6 
4  1983Q3 – 
1990Q2 
6.9  7.9 
5  1990Q3 – 
1999Q3 
1.4  8.6 
6  1999Q4 – 
2010Q3 
3.7  5.5 
 
3.2 Empirical Results 
The three specifications of the PC are estimated with fixed effects and the results are in Table 2. In 
F-P all the coefficients have the expected signs and are statistically significant. The Wald test on  
b  rejects the null that  1. b    Estimates of the hybrid PC are good. All the coefficients have the 
expected signs and are statistically significant. The Wald test confirms the hypothesis that 
1 fb   . The NK PC performs poorly. The coefficient of the forcing variable has the wrong 
positive sign and the coefficient of forward expectations is significantly higher than an expected 
value of unity.   
Table 2 
Fixed Effects Estimates of the PC for Australia (GMM) 
*
11 () t b t f t t u t t E u u               
  (1) 
F-P 
(2) 
Hybrid 
(3) 
NK 
   1.507*** 
[0.465] 
0.469 
[0.539] 
-2.462* 
[1.287] 
b    0.715*** 
[0.073] 
0.516*** 
[0.077] 
- 
f   
- 
0.381*** 
[0.116] 
1.488*** 
[0.254] 
u    -0.527*** 
[0.154] 
-0.281* 
[0.162] 
0.483 
[0.340] 
Centered
2 R   0.92  0.96  0.83 
Hansen test  2.80  3.30  3.37 
Under ID test  27.00***  10.37*  11.54*** 
Weak ID test  56.86***  3.56*  5.34** 
AR(1)  0.44  0.14  0.49 
AR(2)  0.45  0.24  0.96 
Wald test (p-
value) 
0.10E
-3  0.23  - 
* Significant at 10%; ** significant at 5%; *** significant at 1%. AR(1) and 
AR(2) are the p-values from the Arellano and Bond test for serial correlation. 
Hansen is the test for over-identifying restrictions, Weak ID and Under ID are 
the weak identification and under-identification tests (Kleibergen-Paap rk test 
LM and Wald statistic). 
 
Instruments used: F-P = lags 2 and 3 of inflation, lags 1 and 2 of unemployment, 
lags 1 and 2 of the cyclical component of oil price; 
 
Instruments used: Hybrid = lags 2 and 3 of inflation, lags 1 and 2 of 
unemployment, lags from 1 to 3 of the cyclical component of oil price; 
 
Instruments used: NK= lags 2 of inflation, lags 1 and 2 of unemployment, lags 
from 1 to 3 of the cyclical component of oil price. 
 4. Conclusions 
In this paper we applied the Russell and Banerjee (2008) panel data method of estimating three 
specifications of the PC for Australia. The cross section units are based on the breaks in the mean 
rate of inflation. We found that estimates of the  pure backward looking and hybrid versions give 
good results and the micro-founded NKPC performs poorly. In the hybrid model the restriction that 
the coefficient of backward and forward looking expectations sum to one is accepted.  Therefore, 
the long run Phillips curve is vertical in Australia. The hybrid PC also indicates that backward 
looking expectations are relatively more important than forward looking expectations for product 
pricing decisions. Therefore, deflationary policies to reduce inflation are costly. However, these 
conclusions have the usual limitations and need further analysis with improved methods of 
estimation.   
     Data Appendix 
  Data Source. Sample 1967Q1 – 2010Q3 
Variable  Definition  Source 
   GDP deflator Inflation (year-on-year percentage 
changes). 
OECD Statistical 
database. 
u   Unemployment rate.  OECD Statistical 
database. 
* u   Natural unemployment rate obtained through a 
Hodrick-Prescott filter technique of u. 
Our calculation. 
oil  Cyclical component of natural log of oil price 
(US$/barrel) obtained with Hodrick-Prescott filter. 
Dow Jones & 
Company. 
  
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Inflation dynamics: A structural econometric analysis,

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The long-run Phillips curve and non-stationary inflation,

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Why has U.S. inflation become harder to forecast?,

Non-stationary inflation and panel estimates of the n ew Keynesian Phillips curve for Australia

Non-stationary inflation and panel estimates of the n ew Keynesian Phillips curve for Australia

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