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Journal of Applied Sciences Research, 7(5): 562-565, 2011
ISSN 1819-544X
This is a refereed journal and all articles are professionally screened and reviewed
ORIGINAL ARTICLES
Does Armey Curve Exist in Pakistan and Iran Economies?
1
Hamidreza Vaziri, 2Younes Nademi, 3Abdol Aziz Paghe, 4Arash Nademi
1
Department
Department
3
Department
4
Department
2
of
of
of
of
Social Sciences, Islamic Azad University Branch of Ali Abad Katool, iran.
Economics, University of Ayatollah Boroojerdi, Boroojerd-iran.
Engineering, Islamic Azad University Branch of Ali Abad Katool, Iran.
Mathematics, Islamic Azad University Branch of Ilam, iran.
ABSTRACT
We apply the two-sector production function developed by Ram (1986) to estimate the threshold regression
model for Iran and Pakistan countries, concerning the effect of government size on economic growth. The final
government consumption divided by GDP is used to find out the threshold points. In addition, we adopt the
heteroskedasticity-consistent Lagrange multiplier (LM) of Hansen (1996) by using the bootstrapping method
to test the null hypothesis of the linear assumption versus nonlinear relationship between government size and
economic growth. Results indicate that the Armey Curve exists in Iran and Pakistan Economies.
Key words: Armey Curve, Government size, Economic growth, Threshold regression model.
Introduction
Armey (1995) popularized the existence of an optimal size of government as depicted by the Armey curve.
The Armey curve illustrates the existence of a government share of GDP that maximizes GDP growth.
The threshold government size is a point at which any rise in government spending lower than this value
will have positive effects, while more than that will have negative effects on economic growth. Figure (1)
represents the Armey curve and t* is the threshold value.
Fig. 1: Armey Curve.
The positive effects may be due to providing substructures, and public goods and the negative effects could
be due to the crowding-out effect of government monopolistic activities.
This paper modifies Ram (1986) two-sector production model in order to estimate the threshold government
size in Pakistan and Iran Economies. In addition, we adopt the heteroskedasticity-consistent Lagrange multiplier
(LM) of Hansen (1996) by using the bootstrapping method to test the null hypothesis of the linear assumption.
Corresponding Author: Hamidreza Vaziri, Department of Social Sciences, Islamic Azad University Branch of Ali
Abad Katool, iran.
E-mail: [email protected]
J. Appl. Sci. Res., 7(5): 562-565, 2011
563
Method:
We have used the Ram (1986) model as following:
Gt
It
Y t   0   1( )   2 g Lt   3g G t ( )  et
Yt
Yt
(1)
Regression (1) shows that the variables which affect economic growth ( Y ) include the investment rate ( 1 ),
Y
growth of labor force (
), and the multiplication effects of government expenditure growth (
) times
government size (G/Y). In addition, we identify the multiplication effects through the sign of β3. This indicates
that the government sector has a reciprocal effect on economic growth through two ways: one is the direct
contribution of the government sector and the other is the indirect effect through the non-government sector
(externality effect).
Regression (1) is a traditional linear economic growth model, but we alter the linear model into the two
regime TAR model of Hansen (1996, 2000). The model can be shown as follows:

Gt
It
Y t   10   11( )   12 g Lt   13g G t ( )  etif q t  
Yt
Yt


      ( I t )   g   g ( G t )  e if q  
20
21
22 Lt
23 G t
t t
Y t
Yt
Yt
(2)
Or as one nonlinear regression such as:

Gt 
It
Y t    10   11( )   12 g Lt   13g G t ( )  I  qt   
Yt
Yt 


G 
I
   20   21( t )   22 g   23 g ( t )  I  qt     et
Gt Y
Lt
Yt
t 

(3)
The threshold value γ can be found by estimating the regression (3) through finding the minimum Error
Sum of Squared in a re-order threshold variable. The threshold variable can be set by the exogenous variables
out of the theoretical model. For example, in this paper we set government size as the threshold variable. We
can also apply the statistic coming from the threshold variable. For instance, we adopt the heteroskedasticityconsistent Lagrange multiplier (LM) of Hansen (1996) to test the null hypothesis of the linear assumption.
Once the estimator can be found, we then start with the statistical test, but the test procedure of Eq. (3)
is different from the traditional test. Under the null hypothesis of no threshold effect, the threshold parameters
will be unidentified. This will cause the traditional test statistic in a large sample distribution to not belong
to the χ2 distribution, but rather to a non-standard and non-similar distribution which is affected by nuisance
parameters. This will cause the critical value of the distribution to not be estimated through simulation. In order
to overcome the difficulty, Hansen (1996) uses a statistic of his own large sample distribution function to
transfer and calculate the asymptotic p-value of a large sample. Under the null hypothesis, the distribution of
the p-value statistic is uniform, and this kind of transformation can be calculated through bootstrap. The null
hypothesis to test Eq. (3) is as follows:
H :
0
1i
  2i; i  1, 2,3.
(4)
If H0 is not rejected then the relationships between economic growth and the government size would be
the linear regression as the regression (1). This means there exists no threshold effect. Otherwise, if H0
hypothesis is rejected, it means that there exist different effects between the two regimes of δ1i and δ2i. The
F-test statistics is as follows:
J. Appl. Sci. Res., 7(5): 562-565, 2011
F
RSS  RSS ˆ 
ˆ
0
1
2
564
(5)
In which RSS0 and RSS1 are the residual sum of squares under the null hypothesis and the alternative,
respectively.
Data Description:
We have used the WDI 2008 annual data for 1960-2007 periods. The variables are: Total Labor Force (L),
Gross Capital Formation (K), General Government Final Expenditure1 (G), GDP2 and GDP Annual Growth.
Results:
This paper uses Hansen (1996, 2000) threshold regression model to study whether a non-linear Armey
curve exists in Iran and Pakistan economies. As Table 2 shows, we adopt Hansen (1996, 2000) advice to use
the bootstrapping model. While the threshold variable is “government consumption expenditure divided by
GDP”, we find that F-statistic is 7.99 and 10.95 for Iran and Pakistan respectively, which is significant at 1%
level and this means that the threshold exists in Iran and Pakistan economies.
Table 1: The Bootstrapping Method for Threshold Test.
Countries
Threshold
-----------------------------------Threshold value
p value
Iran
0.246
0.0
Pakistan
0.119
0.0
The impact ( gG)(GS) on growth
---------------------------------------------------------------------------------------------------#threshold
p-value
>threshold
p-value
63.57
0.0
-46.3
0.0
158.16
0.0
-12.27
0.0
As table 1 shows, while “General Government Final Expenditure divided by GDP” is the threshold
variable, The Armey curve exists in Iran and Pakistan economies.
Empirical results indicate that there is a nonlinear relationship between Government size and Economic
growth in Iran and Pakistan.
Conclusion:
Following the non-linear theory of Armey (1995) and Vedder and Gallaway (1998), we have tested the
presence of a non-linear Armey curve relationship between government size and economic growth in Iran and
Pakistan economies. Doing so, we have modified the Ram (1986) two-sector production model into a threshold
regression model and apply Hansen (1996, 2000) method using bootstrapping method to test the threshold
effect. The empirical results indicate that threshold effect exists between government size and economic growth
in Iran and Pakistan countries, while we use “General Government Final Expenditure divided by GDP” as the
threshold variable.
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