This paper examines the existence of the mean-reverting behavior of the consumption-income ratio from a panel of 24 OECD countries through the application of the series-specific SURADF panel unit root test. The results show that the consumption-income ratios in 22 OECD countries exhibit mean-reverting behavior. Furthermore, the half-life of the consumption-income ratio for these 22 OECD countries is between 0.28 to 3.48 years. This implies that policy shocks in industrialized economies are not likely to have permanent effects on the consumption-income ratio.Mean reversion; Consumption-income ratio; SURADF; Half-life

Lan-Hsun Wang

Mao-Lung Huang

Shu-Yi Liao

English

Research Papers in Economics

     
 
 
  
  
Volume 31, Issue 1 
  
Mean-reverting behavior of consumption-income ratio in OECD countries: 
evidence from SURADF panel unit root tests 
  
 
 
Shu-Yi Liao  
Department of Applied Economics, National Chung Hsing University, Taiwan 
Mao-Lung Huang  
Department of Applied Economics, National Chung 
Hsing University, Taiwan 
Lan-Hsun Wang  
Bachelor''''s Degree Program of Hotel Management, 
Tainan University of Technology, Taiwan
Abstract 
This paper examines the existence of the mean-reverting behavior of the consumption-income ratio from a panel of 24 
OECD countries through the application of the series-specific SURADF panel unit root test. The results show that the 
consumption-income ratios in 22 OECD countries exhibit mean-reverting behavior. Furthermore, the half-life of the 
consumption-income ratio for these 22 OECD countries is between 0.28 to 3.48 years. This implies that policy shocks 
in industrialized economies are not likely to have permanent effects on the consumption-income ratio.
The authors are grateful to an anonymous referee and the editor of the Economics Bulletin for helpful comments. 
Citation: Shu-Yi Liao and Mao-Lung Huang and Lan-Hsun Wang, (2011) ''Mean-reverting behavior of consumption-income ratio in OECD 
countries: evidence from SURADF panel unit root tests'', Economics Bulletin, Vol. 31 no.1 pp. 679-686. 
Submitted: Feb 23 2010.   Published: February 25, 2011. 
 
     1.  Introduction 
The mean-reverting behavior of the consumption-income ratio, or the average 
propensity to consume (APC), has been a controversial issue in macroeconomics. On 
the theoretical side, there are two conflicting theoretical hypotheses about the 
mean-reverting behavior of the consumption-income ratio. The relative income 
hypothesis, the permanent income hypothesis, the life cycle hypothesis, and the habit 
persistent model all support that the consumption-income ratio will converge to a 
constant value in the long run. Unlike the above-mentioned point of view, the 
Keynesian absolute income hypothesis, the Marxian underconsumption theory, and 
Deaton’s (1977) involuntary savings theory all consider that the consumption-income 
ratio does not come back to the equilibrium in the long run instead. 
Whether the consumption-income ratio exhibits mean-reverting behavior or not has 
important implications to the modeling and understanding of consumption functions, 
savings behavior, business cycles, and economic policy. For example, a nonstationary 
consumption-income ratio implies that policy shocks will have permanent effects on 
individual’s consumption and savings behavior. To investigate the integrated nature of 
consumption-income ratio, most previous studies, which utilized either single unit 
root tests or panel unit root tests, support the hypothesis of nonstationary 
consumption-income ratio (e.g., Drobny and Hall, 1989; Hall and Patterson, 1992; 
Horioka, 1997; Sarantis and Stewart, 1999; Tsionas and Christopoulos, 2002; Cook, 
2002, 2003). Only a few studies provide the opposite results (e.g., King et al., 1991; 
Cook, 2005; Romero-Ávila, 2009).   
The use of panel unit tests mentioned above is motivated by the advantage of 
increased statistical power over that of conventional single unit tests. However, the 
empirical testing results may differ due to the heterogeneity across the panel members. 
In addition, a common feature of the panel unit root tests is that the rejection of the 
null hypothesis of a unit root in all panel members only indicates at least one panel 
member is stationary. No information is provided about how many panel members are 
stationary. Furthermore, the presence of a unit root in all panel members is not likely 
in practice, the imposition of uniformity across the panel under the null hypothesis 
greatly lower the power of panel data analysis.   
To allow for heterogeneous serial correlations across panel members and increase 
the power of panel data analysis, we adopted the series specific panel unit root test of 
Breuer  et al. (SURADF test) to test for the mean-reverting behavior of the 
consumption-income ratio for the panel of 24 OECD countries. SURADF test is based 
on the estimation of the augmented Dickey-Fuller statistics using seeming unrelated regressions. SURADF is used to test individual unit root within the panel members. 
We also report the convergent speed (half-life) of the consumption-income ratios for 
stationary members of the panel in this paper. It is found that the consumption-income 
ratios in 22 OECD countries exhibit mean-reverting behavior. Furthermore, the 
half-life of the consumption-income ratio for these 22 OECD countries ranges from 
0.28 to 3.48 years. 
The remainder of this paper is organized as follows: SURADF unit root test and 
half-life estimation are briefly described in section 2. The empirical results are 
presented in section 3 while section 4 concludes the paper. 
2.  SURADF panel unit root test and half-life estimation 
Following Breuer et al. (2002), the SURADF test is based on the system of ADF 
equations. The ADF regression for a sample of N (i = 1,2,…,N) countries observed 
over T time periods (t = 1,2,…,T) can be represented as: 
t n
p
j
j t n j n n t n n n t n
t
p
j
j t j t t
t
p
j
j t j t t
Y t Y Y
Y t Y Y
Y t Y Y
,
1
, , 1 , ,
, 2
1
, 2 , 2 2 1 , 2 2 2 , 2
, 1
1
, 1   , 1 1 1 , 1 1 1 , 1
ε δ γ β α
ε δ γ β α
ε δ γ β α
+ Δ + + + = Δ
+ Δ + + + = Δ
+ Δ + + + = Δ
∑
∑
∑
=
− −
=
− −
=
− −
M
                           ( 1 )  
where  ( 1 − = i i ) ρ β  and i ρ  is the autoregressive coefficient for country i. The 
system (1) is estimated by the SUR procedure. To test null and alternative hypotheses 
separately for each panel member within a SUR framework, N null and alternative 
hypotheses are tested individually: 
0 :    H ; 0 :
0 :    H ; 0 :
0 :     H ; 0 :
N
A 0
2
2
A 2
2
0
1
1
A 1
1
0
< =
< =
< =
N N
N H
H
H
β β
β β
β β
M
                                            ( 2 )  
with test statistics computed from SUR estimates of the system (1). The critical values 
are generated through Monte Carlo simulations because the test statistics from the 
SUR model have nonstandard distributions. Therefore, the computed critical values 
will be specific to panel composition. In the Monte Carlo simulations, the lagged 
differences and the covariances matrix were obtained from the SUR estimation on the actual consumption-income ratio data. The SURADF test statistic for each of the 24 
OECD countries was computed as the t-statistic calculated individually for the 
coefficient on the lagged level. To obtain critical values, the simulations were 
replicated 10,000 times and the critical values of 1%, 5%, and 10% are tailored to 
each of the 24 OECD countries.   
The series-specific SURADF panel unit root test has several advantages. First, this 
test produces efficient estimators over the single-equation unit root tests by exploiting 
the information from cross-equation residual covariance and allowing for 
autoregressive process. Second, the estimation allows for heterogeneity in lag 
structure across the panel members. Third, the test allows identification of how many 
and which members of the panel contain a unit root. Forth, the test also allows us to 
calculate the convergent speed of the consumption-income ratios for stationary 
members of the panel
1.  
3.  Empirical results 
Annual data of consumption and income over the period 1970-2006 for 24 OECD 
countries were obtained from OECD.Stat Extracts (Source OECD).
2 Before applying 
SURADF panel unit root test, we first used single-equation unit root tests to examine 
the null hypothesis of a unit root in each series. As shown in Table 1, the null 
hypothesis of non-stationary consumption-income ratio is rejected in only 6 
countries – Finland, Italy, New Zealand, Portugal, Sweden, and United States. Then 
we applied Levin et al. (2002, LLC test) and Im et al. (2003, IPS test) panel unit root 
test methods to examine the null hypothesis that all series contain a unit root. As 
reported in Table 2, the null hypothesis of non-stationary are rejected at conventional 
significant levels for the full panel in both LLC and IPS tests. This finding implies 
that there maybe a mixture of stationary and nonstationary processes in the panel 
under the alternative hypothesis. 
According to Sarno and Taylor (1998), panel unit root tests are meaningful when 
the single-equation unit root tests fail to reject the non-stationary null hypothesis. To 
resolve the ambiguous results described above, we applied SURADF panel unit root 
test to further exploit the information in the error covariances. With more powerful 
                                                 
1 According to Andrews (1993), half-life (HL) can be defined as:
) ln(
) 5 . 0 ln(
HL
ρ
= , where ρ is the 
autoregressive coefficient of series i in AR(1) model ( t t t Y Y ε ρ + = −1 ). 
2 Consumption is measured by private final consumption expenditure at current prices, annual levels, 
S.A, while income is measured by gross domestic product at current prices, annual levels, S.A. Panel 
members include 24 OECD countries: Australia, Austria, Belgium, Canada, Denmark, Finland, France, 
Germany, Greece, Iceland, Italy, Japan, Korea, Luxembourg,  Mexico, Netherlands, New Zealand, 
Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom, and United States. test statistics over single-equation methods, SURADF test allows us to identify how 
many and which members of the panel contain a unit root. 
Table 1.  Single-equation  unit  root  test  results of consumption-income ratio 
Country Lag  Length  ADF 
（with intercept and trend terms） 
Australia  0 -2.1940 
Austria  0 -1.9993 
Belgium  0 -1.5861 
Canada  1 -2.4011 
Denmark  1 -3.0284 
Finland  1 -3.5052* 
France  0 -1.7757 
Germany  0 -2.2191 
Greece  0 -1.5141 
Iceland  0 -2.7026 
Italy  0 -3.2270* 
Japan  0 -2.5147 
Korea  0 -1.2790 
Luxembourg  0 -2.5547 
Mexico  0 -1.8017 
Netherlands  0 -1.2246 
New Zealand  2 -3.4846* 
Norway  0 -1.5683 
Portugal  1 -4.0177** 
Spain  2 -2.9284 
Sweden  1 -3.2978* 
Switzerland  0 -1.7863 
United Kingdom  0 -1.6443 
United States  0 -3.3874* 
Notes: (1) The null hypothesis of ADF is  Variable has a unit root.  : 0 H
(2) Asterisks (**,*) denote statistical significance at the 5%, 10% level, respectively. 
 
Table 2.    LLC and IPS panel unit root tests results for consumption-income ratio 
LLC 
（with intercept and trend terms） 
IPS 
（with intercept and trend terms） 
-2.6221*** -1.9907** 
Stationary Stationary 
Notes: (1) The null hypothesis of LLC, IPS are  Variable has a unit root.    : 0 H
            (2) Asterisks (***,**) denote statistical significance at the 1%,5% level, respectively. As shown in Table 3, the null hypothesis of non-stationary consumption-income 
ratio is not rejected in only 2 countries ― Greece and Netherlands. This finding is in 
contrast with the results of single-equation unit root tests (see Table 1) that most 
consumption-income ratios are non-stationary. This is not surprising because the 
SURADF test produces more efficient estimators and more powerful test statistics 
than single-equation methods when the data to be analyzed are based on a limit time 
series dimension. In effect, Breuer et al. (2002) have shown that the SURADF test is 
28 to 65 percent more powerful than single-equation ADF test. 
On the other hand, the result of SURADF test is somewhat similar to the findings in 
Table 2 that not all countries of the panel contain a unit root. However, rejection of the 
null hypothesis in Table 2 does not provide us with the information about the exact 
mix of stationary and nonstationary series in the panel. With null and alternative 
hypotheses testing separately for each panel member in SURADF tests, we further 
identified that only 2 OECD countries (Greece and Netherlands) have nonstationary 
consumption–income ratios. The remaining 22 OECD countries all have stationary 
consumption–income ratios. As shown in the second column of Table 3, the half-life 
estimates of the consumption–income ratios for these 22 OECD countries range from 
0.28 to 3.48 years. The results imply that policy shocks in these OECD economies are 
not likely to have permanent effects on the consumption-income ratio.   
4.  Conclusions 
The inference drawn from the single-equation unit root test suggests that most 
series in the panel are nonstationary while the SURADF panel unit root test indicates 
22 out of 24 series are stationary. The findings from LLC, IPS, and SURADF panel 
unit tests reveal that single-equation unit root tests may lead to misleading inferences 
when the data to be analyzed are based on a limit time series dimension. Using 
SURADF panel unit tests, we further identified that the rejection of the null 
hypothesis of non-stationary consumption-income ratio in LLC and IPS tests is driven 
by most of the OECD countries within the panel. From a policy perspective, our 
half-life estimates suggest that policy shocks in most of the 24 OECD countries are 
not likely to have long-run effects on the consumption-income ratio. 
 
 
 
 
 
 
 Table 3.    SURADF panel unit root test results for consumption-income ratio 
Critical Value  Country  Half-Life 
(Year)  SURADF 
1% 5%  10% 
Australia  1.45 -4.7807**  -5.0546  -4.3580  -4.0174 
Austria  1.66 -5.4727***  -5.2588  -4.5951  -4.2067 
Belgium  3.15 -4.3847**  -4.8318  -4.1573  -3.7898 
Canada  1.39 -7.5496***  -5.7171  -4.9826  -4.5884 
Denmark  1.25 -10.2166*** -5.6557  -4.9254  -4.5280 
Finland  0.88 -9.8866***  -5.2553  -4.5486  -4.1490 
France  2.45 -6.4194***  -5.9396  5.2133  -4.8075 
Germany  2.00 -7.9785***  -6.6481  5.9306  -5.5182 
Greece  -- -3.0887  -5.0993  -4.3727  -3.9906 
Iceland  1.99 -4.2093*  -5.0100  -4.2697  -3.8966 
Italy  1.02 -6.0381***  -4.9619  -4.2203  -3.8400 
Japan  2.16 -5.5016**  -5.5484  -4.7604  -4.3693 
Korea  3.48 -3.8434*  -4.7515  -4.0828  -3.7172 
Luxembourg  1.79 -5.8628**  -5.8932  -5.1826  -4.7798 
Mexico  2.10 -4.6754***  -4.6660  -3.9771  -3.6226 
Netherlands  -- -3.2962  -5.1922  -4.4811  -4.0873 
New Zealand  0.28 -10.2501*** -6.0928  -5.3160  -4.9273 
Norway  1.97 -5.2241**  -5.9171  -5.1593  -4.7381 
Portugal  0.58 -16.8303*** -5.2095  -4.4843  -4.0959 
Spain  1.54 -5.5831***  -5.1529  -4.4194  -4.0315 
Sweden  0.82 -5.4460***  -4.9081  -4.1930  -3.8290 
Switzerland  1.95 -7.7264***  -5.9445  -5.2092  -4.8178 
United Kingdom  2.34 -4.7566**  -4.9878  -4.3070  -3.9569 
United States  0.86  -7.4469***  -4.8640 -4.2111 -3.8454 
Notes: (1) Critical values are calculated using Monte Carol simulations based on 37 observations for 
each series and 10,000 replications. 
      (2)  Asterisks  (***,  **,*)  denote  statistical significance at the 1%, 5%, 10% level, respectively. 
References 
Andrews, D.W.K. (1993) “Exactly median-unbiased estimation of first-order 
autoregressive /unit root models” Econometrica 61, 139–65. 
Breuer, J.B., R. McNown and M.S. Wallace (2002) “Series-specific unit root tests 
with panel data” Oxford Bulletin of Economics and Statistics 64, 527–46. 
Cook, S. (2002) “Asymmetric mean reversion in the consumption-income ratio: 
Evidence from OECD economics” Applied Econometrics and International Development (AEEADE) 2–2, 27–34. 
Cook, S. (2003) “The nonstationarity of the consumption-income ratio: evidence from 
the more powerful Dickey-Fuller tests” Applied Economics Letters 10, 393–5. 
Cook, S. (2005) “The stationary of consumption-income ratios: Evidence from 
minimum LM unit root testing” Economics Letters 89, 55–60. 
Deaton, A.S. (1977) “Involuntary saving through unanticipated inflation” American 
Economic Review 6, 899–910. 
Drobny, A and S.G. Hall (1989) “An investigation of the long-run properties of 
aggregate non-durable consumers’ expenditure in the United Kingdom” Economic 
Journal 99, 454–60. 
Hall, S.G and K.D. Paterson (1992) “A systems approach to the relationship between 
consumption and wealth” Applied Economics 24, 1165–71. 
Horioka, C.Y. (1997) “A cointegration analysis of the impact of the age structure of 
the population on the household saving ate in Japan” Review of Economics and 
Statistics 79, 511–516. 
Im, K.S., M.H. Pesaran and Y. Shin (2003) “Testing for unit roots in heterogeneous 
panels” Journal of Econometrics 115, 53–74. 
King, R.G., C.I. Plosser, J.H. Stock and M.W. Watson (1991) “Stochastic trends and 
economic fluctuations” American Economic Review 81, 819–40. 
Levin, A., C.F. Lin and C.S. Chu (2002) “Unit root tests in panel data: Asymptotic and 
finite-sample properties” Journal of Econometrics 108, 1–24. 
Romero-Ávila, D. (2009) “Are OECD consumption-income ratios stationary after 
all?” Economic Modelling 26, 107–117. 
Sarantis, N. and C. Stewart (1999) “Is the consumption-income ratio stationary? 
Evidence from panel unit root test” Economics Letters 64, 309–14. 
Sarno, L. and M.P. Taylor (1998) “Real exchange rates under the recent float: 
unequivocal evidence of mean revision” Economics Letters 60, 131–7. 
Tsionas, E. and D. Christopoulos (2002) “Non−Sationarity in the 
Consumption−Income Ratio: Further Evidence from Panel and Asymetric Unit Root 
Tests” Economics Bulletin 3 (12), 1−5. 
 

A cointegration analysis of the impact of the age structure of the population on the household saving ate in

A systems approach to the relationship between consumption and wealth”

An investigation of the long-run properties of aggregate non-durable consumers’ expenditure in the United Kingdom”

Are OECD consumption-income ratios stationary after all?”

Asymmetric mean reversion in the consumption-income ratio:

Exactly median-unbiased estimation of first-order autoregressive /unit root models”

Involuntary saving through unanticipated inflation”

Is the consumption-income ratio stationary? Evidence from panel unit root test”

Non−Sationarity in the Consumption−Income Ratio: Further Evidence from Panel and Asymetric Unit Root Tests”

Real exchange rates under the recent float: unequivocal evidence of mean revision”

Series-specific unit root tests with panel data”

Stochastic trends and economic fluctuations”

Testing for unit roots in heterogeneous panels”

The nonstationarity of the consumption-income ratio: evidence from the more powerful Dickey-Fuller tests”

The stationary of consumption-income ratios: Evidence from minimum LM unit root testing”

Unit root tests in panel data: Asymptotic and finite-sample properties”

Mean-reverting behavior of consumption-income ratio in OECD countries: evidence from SURADF panel unit root tests

http://www.accessecon.com/Pubs/EB/2011/Volume31/EB-11-V31-I1-P65.pdf

Mean-reverting behavior of consumption-income ratio in OECD countries: evidence from SURADF panel unit root tests

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics