Testing Wagner’s law versus the Keynesian hypothesis for GCC countries

By

Salah A. Nusair and Dennis O. Olson

Department of Economics and Finance

Gulf University for Science and Technology

West Mishref, Kuwait

Abstract

This paper examines the relationship between real GDP and real government spending for the

six Gulf Cooperation Council (GCC) countries to determine whether Wagner’s law or the

Keynesian hypothesis holds. A battery of linear and nonlinear Granger causality tests are

performed on annual data in both the time and frequency domains. Symmetric linear causality

tests support Wagner’s law for four of six GCC countries, while weak evidence for the

Keynesian model is found in two countries. In contrast, asymmetric nonlinear causality tests

provide support for Wagner’s law in five countries and for the Keynesian hypothesis across

all six GCC countries.

Keywords: GCC countries; Wagner’s law, Keynesian hypothesis; frequency domain

causality; asymmetric causality

JEL classification: C22; C23; H72; E62

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Testing Wagner’s law versus the Keynesian hypothesis for GCC countries

1. Introduction

When examining the role of the public sector in the economy, Wagner (1883) observed

that a wealthier populous demands more government goods and services, leading to an ever-

increasing level of state activity. Rather than finding an optimal size for the public sector in

the economy, he devised Wagner’s law from the experience in Europe which indicated that

government spending as a proportion of real income increases over time as national income

rises. In contrast to Wagner’s law, the Keynesian view of macroeconomics suggests that

increases in government spending (g) increase real GDP ( y). Given that the two primary

theories about the role of public sector in the economy are somewhat contradictory and lead

to different policy implications, a rather substantial body of literature has developed that

empirically tests the validity of both Wagner’s Law and the Keynesian hypothesis across a

variety of countries and over many different time periods.

A strict interpretation of Wagner’s law, as set forth in articles such as Narayan, Nielsen,

and Smyth (2008) or Narayan, Rath, and Narayan (2012), states that that the share of public

expenditures in national income rises as income rises. This form of Wagner’s law requires an

income elasticity for government spending that is greater than unity and suggests that

increases in real GDP lead to larger than proportional increases in public expenditures.

However, a weaker or less restrictive form of the law, as stated by Samudram, Nair, and

Vaithilingam (2009, p. 698), posits that “causality runs from economic growth to government

expenditure. This causality-based formulation of Wagner’s law only requires a positive

income elasticity and causation running from y to g. It implies that higher national income

leads to higher government expenditures, but it does not mean that governments spending

leads to economic growth. Conversely, the Keynesian view is that causality runs from g to y.

Such results, as shown in Iyare and Lorde (2004), suggest that fiscal policy through public

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expenditures can be instrumental in causing future income growth and economic

development.

A number of studies, such as Abizadeh and Gray (1985), Akitoby, Clement, and

Inchauste (2006) and Wu, Tang, and Lin (2010), suggest that Wagner’s law is more likely to

hold for the richer, developed countries rather than for poorer and developing nations.

Similarly, Wu, Tang, and Lin (2010) in a sample of 182 countries, and by Bayrak and Esen

(2014) in a study of 27 developed OECD countries, report that the Keynesian hypothesis is

more likely to hold for the developed and wealthier nations. In contrast, Narayan, Rath, and

Narayan (2102) find greater evidence of bi-directional Granger causality for low income

Indian states than for higher income states. Also, in a study of 23 OECD countries over the

period 1970 – 2006, Lamartina and Zaghini (2008) find stronger support for Wagner’s law

among the poorer countries of the sample. They argue that poorer countries have been

increasing government spending to catch up to the richer countries in terms of development

Based on the literature above, it is not clear whether Wagner’s law is more likely to hold

for developed or developing countries, but the general consensus is that both Wagner’s law

and the Keynesian hypotheses may be more applicable for developed nations. Due to the

increase in public sector spending in recent years, one region where the relationship between

g and y may be particularly important is for the six countries of the Gulf Cooperation

Council (GCC)--Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emirates

(UAE). Analysis is further complicated, however, because the GCC region has characteristics

of both developed and developing countries. It is now a wealthy, developed region, but prior

to the boom in oil exports in the 1970s, the GCC was certainly a developing area. Hence, the

expected causality relationship between g and y for the GCC is unclear.

The purpose of this paper is, therefore, to examine the relationship between government

spending and real GDP in the GCC countries. We empirically test for the validity of

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Wagner’s law versus the Keynesian hypothesis using various forms of linear and nonlinear

causality tests in both the time and frequency domains. As noted in Peacock and Scott (2000)

and Magazzino (2012), the possibilities for Granger causality may be divided into four

groups of hypotheses: (1) Wagner’s law involves causality from y to g , (2) the Keynesian

hypothesis requires causality from g to y , (3) the neutrality hypothesis is no causality, while

(4) the feedback hypothesis is one of bi-directional causality between y and g. Although

some studies require unidirectional causality to support either Wagner’s law or the Keynesian

hypothesis, we adopt the broader interpretation that bidirectional causality is evidence for

both Wagner’s law and the Keynesian hypothesis.

In addition to performing the now standard tests for linear causality in the time domain,

we consider nonlinearities and extend our analysis to the frequency domain to determine the

direction and strength of causality relationships at different frequencies (short-run and long-

run). In particular, we employ the frequency domain causality tests of Breitung and

Candelon (2006) and the asymmetric causality test in the frequency domain proposed by

Bahmani-Oskooee et al. (2016). The latter test extends the Hatemi-J (2012) asymmetric

causality test from the time to the frequency domain and differentiates between the impact of

positive and negative shocks. Although frequency domain causality analysis has been

adopted to examine a variety of topics, such as the predictive power of stock prices [Croux

and Reusens (2013)], to the best of our knowledge, this is the first study to test for Wagner’s

law versus the Keynesian hypothesis in the frequency domain using either linear or

asymmetric nonlinear causality analysis.

The paper is organized as follows. Section 2 provides a brief literature review

summarizing the multitude of studies that have examined Wagner’s law and the competing

hypotheses. Section 3 describes the data and some of the characteristics of the GCC region.

Section 4 discusses causality testing procedures with an emphasis on frequency domain

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analysis and nonlinear asymmetric causality tests. Section 5 presents the empirical results,

while Section 6 summarizes the study and suggests some policy implications.

2. Literature Review

A vast literature has developed testing the relationship between national income and

government spending across many nations over many different time periods. Researchers

have adopted a variety of techniques and have reported mixed and even contradictory results

regarding the applicability of both Wagner’s law and the Keynesian hypothesis. Magazzino

(2012) provides a nice summary of studies that have supported each of the four theories

describing the possible causal relationships between y and g: the neutrality hypothesis,

Wagner’s law, the Keynesian hypothesis, and the feedback hypothesis. Additionally, some

rather comprehensive literature reviews focusing primarily on Wagner’s law are provided by

Durevall and Henrekson (2011) and Babatunde (2011). Given the rather comprehensive

nature of these reviews, only a brief summary of the literature is presented below.

Broad support for the strong-form of Wagner’s law is generally found for only a few

countries and for limited time periods. For example, Narayan, Prasad, and Singh (2008) find

strong evidence that Wagner’s law held for the Fiji Islands over the years 1976-2002. They

reported an income elasticity of about 1.4 for government spending, but they also reported

short-run causality running from g to y, as predicted by the Keynesian hypothesis. Thornton

(1999) used data for six European countries to find evidence for Wagner’s law during the

1800s. Durevall and Henrekson (2011) also examined a long period of European history and

noted that while Wagner’s law holds during the periods 1860 – 1913 and 1920 – 1975, it was

largely irrelevant in other years before and after these periods.

Samudram, Nair, and Vaithilingam (2009) report bi-directional causality between y and g

for administration and health expenditures in Malaysia for the period 1970-2004. In contrast,

Narayan, Nielsen, and Smyth (2008) found only limited support for the weak-form version of

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Wagner’s law in the poorer or less developed regions of central and western China and no

evidence for Wagner’s law in the more developed Eastern regions of the country. Wu, Tang,

and Lin (2010) examine a panel of 182 countries for the period 1950 – 2004 and report bi-

directional causality between g and y for high income countries, but that neither Wagner’s

law nor the Keynesian hypothesis seems relevant for low income countries. In contrast to the

results across countries, Narayan, Rath, and Narayan (2012) find stronger bi-directional

causality between y and g for low-income Indian states relative to high-income states over

the period 1986 – 2009. Although their results support both Wagner’s law and the Keynesian

hypothesis, it is surprising that the relationship is stronger for the lower income states.

Magazzino, Giolli, and Mele (2015) find evidence for the weak-form of Wagner’s law for 27

European countries for the years 1980 – 2013. However, only three countries in their sample

displayed bi-directional causality and support for the Keynesian hypothesis.

As noted by Henrekson (1993), results prior to the 1990s may be questionable because

they did not test for stationarity, nor adopt the cointegration and causality procedures that

have now become standard in the economics literature. Nevertheless, more recent studies that

adopt cointegration and causality tests still produce conflicting conclusions. For example,

Kolluri, Panik, and Wahab (2000) found that Wagner’s law generally held for the G7

countries, but when extending this research to 30 OECD countries, Wahab (2004) found little

evidence for Wagner’s law. Abizadeh and Gray (1985) suggest that Wagner’s law may be

more applicable for richer, rather than poorer countries, given their results across 55 countries

for the years 1963-1979. Also, Akitoby, Clement, and Inchauste (2006) and Wu, Tang, and

Lin (2010) have made similar arguments, but Lamartina and Zaghini (2008) arrive at the

opposite conclusion based on 1970 - 2006 data for 23 OECD countries. They show that

Wagner’s law holds for the poorer countries that are now playing catching up to the richer

countries by making proportionately larger government expenditures. In a study of an oil

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dependent economy that may be relevant for the GCC, Iniguez-Montiel (2010) finds

unidirectional causality from national income to government spending in Mexico for the

years 1950 – 1999, thereby supporting Wagner’s law, but not the Keynesian hypothesis.

The limited number of studies for the GCC region also provide conflicting results. For

example, Burney (2002) finds little evidence for either Wagner’s law or for the Keynesian

hypothesis in Kuwait for the years 1969 – 1995. In contrast, Ageli (2013) confirms that both

the causality-based and the strict interpretation of Wagner’s law apply to Saudi Arabia for the

years 1970 - 2012. His analysis also supports the Keynesian hypothesis in Saudi Arabia for

the same time period. In a study of the whole GCC region, Al-Faris (2002) finds strong

support for Wagner’s law for the years 1970 – 1997, but no causality-based evidence for the

Keynesian hypothesis. Although Henrekson (1993) has argued that conclusions from tests of

Wagner’s law prior to the 1990s are not robust because they have not examined stationarity,

the three studies for the GCC region examine stationarity, adopt cointegration techniques, and

still produce seemingly contradictory results. Differences in results across the GCC could be

due to different time periods considered or different countries analyzed. To make analysis

more uniform across studies, Giolli, and Mele (2015) suggest adopting a panel approach to

testing Wagner’s law. Another possible reason for differences across seemingly similar

studies could be due to neglected nonlinearities in some time series. For example, Singh

(2012) has shown that linear models for economic growth in OECD countries are rejected in

favor of various Smooth Transition Autoregressive (STAR) models in logarithmic or

exponential form, while Cavicchioli and Pistoresi (2016) examine Wagner’s law using a

different form of nonlinearity test based on threshold cointegration analysis. They suggest

that other forms of nonlinearities should be investigated when testing Wagner’s law. In this

vein, Hatemi-J (2012) has developed an asymmetric nonlinear Granger causality test based

on sums of positive versus negative shocks to the two variables. In our framework, there are

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four categories of possible causal relationships between annual changes in g and y. Annual

changes in both variables could be positive, both could be negative, g could be positive and y

negative, or the annual change in g could be negative and the change in y positive.

Nonlinearities would be important if causal relationships were different between the four

categories. Finally, both linear and nonlinear Granger causality in the traditional time domain

represent a single, one-shot test statistic that is assumed to be valid for the entire timeframe of

the data set. An alternative form of causality testing in the frequency domain has been

developed by Breitung and Candelon (2006) and more recently extended to nonlinear

causality by Bahmani-Oskooee et al. (2016). Frequency domain analysis permits researchers

to disentangle short-run from long-run predictability and to identify the direction and strength

of causal relationships over a range of data frequencies.

3. Data

The empirical examination of the causal relationship between government expenditures

and GDP is carried out using annual data extracted from the World Bank Development

Indicators (WDI) database. The data includes real government expenditures (g), real GDP ( y),

real per capita government expenditures ( pcg), and real per capita GDP ( pcy). The data are

available for the following years for the six GCC countries: Bahrain (1975-2014), Kuwait

(1995-2014)1, Qatar (1980-2014), Oman (1972-2014), Saudi Arabia (1968-2014), and UAE

(1975-2014).

The GCC economies are dominated by the oil industry and they receive the bulk of both

government and private sector income from the oil sector. The countries are rather

homogeneous in terms of the compositions of their populations and the structure of their

economies, although Bahrain is not an oil exporting nation. Nevertheless, the region has

changed considerably in the last 20 years and is still undergoing rapid economic development

1 The reason for starting the sample for Kuwait from 1995 is due to missing government spending and price data for the period 1990 – 1994, which is the period corresponding to the Iraqi invasion of Kuwait and the war that followed.

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and income growth. The population has exploded in the last 20 years and the age distribution

has changed dramatically. The GCC has one of the youngest average aged populations of any

area in the world and this could mean more pressure to increase government spending in the

GCC versus other regions. Even though income has risen steadily over the past twenty years,

this period has seen considerable shocks to the economy, such as the Global Financial Crisis

and a major decline in oil prices in 2014-2016. For these reasons, policy makers in the region

should be particularly interested in the relationship between government spending and GDP.

Figure 1 and Table 1 show the trends in real GDP and real government expenditures in

the GCC countries. In particular, Figure 1 plots real GDP and real government expenditures

for the years 1975 – 2014, and Table 1 presents five-year averages of the growth rates of real

GDP, real government expenditures, per-capita real GDP, per-capita real government

expenditures, and government expenditures as a percentage of GDP. A few observations are

worth mentioning for the GCC region. First, growth rates of real GDP have decreased from

9.56% over the period 1975-1979 to 4.79% over the period 2009-2014. Second, the growth

rates of real government expenditures have decreased from 15.94% over the period 1975-

1979 to 5.65% over the period 2009-2014. Third, the growth rate of per-capita real GDP has

decreased from 1.81% over the period 1975-1979 to 0.07% over the period 2009-2014.

Fourth, the growth rate of per-capita real government expenditures has decreased from 8.19%

over the period 1975-1979 to 0.92% over the period 2009-2014. Fifth, while government

expenditures as a percentage of GDP have increased from 18.38% over the period 1975-1979

to 28.60% over the period 1985-1989, they decreased to 15.70% over the period 2009-2014.

Sixth, although the growth rates of real GDP and real government expenditures for the

individual countries seem to be different, overall, both variables do appear to move together

across all countries. Seventh, although the individual GCC countries have achieved

remarkably high growth rates in their real GDPs, especially over the period 2005-2009 due to

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rising oil prices, growth rates have declined over the period 2010-2014, as oil prices

decreased. The growth rates of real government expenditures, on the other hand, have

increased over the period 2005-2009 and continued to increase (in all the countries, except

Qatar) over the period 2010-2014, despite the decrease in oil prices. This is possibly due to

governments’ commitments to completing projects and providing social subsidies to their

citizens. The last observation concerns the low and negative growth rates of per-capita real

GDP and per-capita government expenditures--suggesting that the populations of the GCC

countries have been increasing at a faster rate than real GDP and government expenditures.

[INSERT FIGURE 1 HERE]

[INSERT TABLE 1 HERE]

4. Methodology

To capture the causal relationship between government expenditures and economic

growth, causality tests can be applied to the models below. One popular approach to

investigate the causal relationship between two variables is the Granger (1969) non-causality

test. According to this approach, a variable x is said to Granger cause the variable y, if y can

be better predicted from past values of both x and y than from past values of y alone. Despite

its popularity, one drawback of this approach is that it is based on the time domain that

produces a single, one-shot Granger causality test statistic for the interaction among variables

for the entire relationship (Bahmani-Oskooee et al., 2016). However, as noted by Granger

(1969), the direction and/or strength of Granger causality may vary over different frequencies

-short-run and long-run (Lemmens et al., 2008). Therefore, in this paper we employ the

frequency domain Granger causality test developed by Breitung and Candelon (2006) to

disentangle short-run from long-run predictability. The Breitung and Candelon (2006) test is

based on the work of Geweke (1982) and Hosoya (1991, who proposed measures of causality

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in the frequency domain. In particular, Breitung and Candelon (2006) consider a finite-order

VAR representation of order p

Θ ( L )( y t

x t )=(Θ11(L)Θ21( L)

Θ12(L)Θ22(L))( y t

x t )=(ε1 t

ε2 t)(1)

where Θ ( L )=I−Θ1 L−…−Θp Lp is a 2 ×2 lag polynomial of order p; Θifor i=1 ,…, p is a

2 ×2 coefficient matrix associated with lag i; and I is a 2 ×2identity matrix. The error vector

ε t=( ε1 t ε2 t )' is white noise with E (ε t )=0 and a positive-definite covariance matrix Σ=E (ε1 t ε 2t' )

. Assuming that the system in (1) is stationary, the moving-average (MA) representation of the

system is

( y t

x t)=Φ(L)ξt=(Φ11(L)Φ21(L)

Φ12(L)Φ22(L))(ξ1 t

ξ2 t)(2)where Φ ( L )=Θ (L)−1 Ψ−1, with Ψ being the lower triangular matrix of the Cholesky

decomposition Ψ ' Ψ =Σ−1, such that E (ξt ξ t' )=I and ξ t=Ψ εt. Then, the spectral density of y t

can be expressed as

f y ( ω)= 12 π {|Φ11 (e

−iω)|2+|Φ12(e−iω)|2} (3)

The measure of causality in the frequency domain suggested by Geweke (1982) and

Hosoya (1991) is then defined as

M x⇒ y (ω )=log [1+|Φ12(e

−iω)|2

|Φ12(e−iω)|2 ](4)

Testing the null hypothesis of no Granger causality from x to y in (4) is equivalent to

testing M x⇒ y (ω )=0, that is, when |Φ12(e−iω)|=0. In this case, we say that x does not Granger

cause y at frequency ω. Breitung and Candelon (2006) propose a new and simple approach to

test the null hypothesis of non-Granger causality using Φ12 ( L )=−ψ22Θ12(L)

|Θ(L)|, where ψ22 is the

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lower diagonal element of Ψ−1 and |Θ(L)| is the determinant of Θ(L). It follows that x does

not Granger cause y at frequency ω if 2

|Θ12(e−iω)|=|∑k=1

p

Θ12 ,k cos (kω )−∑k=1

p

Θ12 ,k sin (kω )i|=0(5)

where Θ12 ,k is the (1, 2)-element of Θk. Then, a necessary and sufficient set of conditions for

no Granger causality at the frequency ω is

∑k =1

p

Θ12 , k cos ( kω)=0 (6)

∑k =1

p

Θ12 , k sin (kω )=0 (7)

Breitung and Candelon (2006) specify the following VAR( p) model for y

y t=∑k=1

p

Θ11, k y t−k+∑k=1

p

Θ12, k x t−k+ϵ t(8)

The null hypothesis of no Granger causality y (ω)=0 at frequency ω is then tested by

employing a standard F-test for the linear restrictions (6) and (7). The F-test is distributed as

F (2 ,T−2 p) for ω∈(0 , π ), where 2 is the number of restrictions, T is the number of

observations used to estimate the VAR( p) model of order p.

This frequency domain Granger causality test assumes symmetrical casual effects; that is,

positive and negative shocks have the same impact in absolute terms (Hatemi-J, 2012). As

argued by Hatemi-J (2012), this assumption may be too restrictive since there are ample

studies and evidence documenting asymmetric response of different economic variables, such

as the response of economic activity to rising and falling oil prices, or the response of the trade

balance account to currency appreciations and depreciation. To this end, Hatemi-J (2012)

extends the Granger (1969) causality test to allow for asymmetric causal effects by

differentiating between positive and negative shocks. In particular, Hatemi-J (2012) introduces

2 For more details and discussion, the reader is referred to the original paper of Breitung and Candelon (2006).

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asymmetric causal effects by constructing the cumulative sums of positive and negative

shocks for two integrated variables y t and x t that follow the following data generating process

y t= y t−1+υ1 t= y10+∑i=1

t

υ1 i(9)

x t=xt−1+υ2 t=x10+∑i=1

t

υ2 i(10)

where y10 and x10 are the initial values of y t and x t, t=1 , …,T , and υ1i and υ2 i are white noise

disturbance error terms. Then, positive and negative shocks are defined as: υ1i+¿=max (υ1 i ,0)¿,

υ2 i+¿=max (υ2 i ,0)¿, υ1i

−¿=min (υ1i ,0 )¿, υ2 i−¿=min (υ2i ,0 )¿. Therefore, we can express υ1i=υ1 i

+¿+υ1 i−¿ ¿¿ and υ2 i=υ2i

+¿+ υ2 i−¿ ¿¿

. Then, it follows that

y t= y t−1+υ1 t= y10+∑i=1

t

υ1 i

+¿+∑i=1

t

υ1 i−¿(11)¿

¿

x t=xt−1+υ2 t=x10+∑i=1

t

υ2 i+¿+∑

i=1

t

υ2 i−¿(12)¿¿

The partial sums of positive and negative shocks are then defined as y t

+¿=∑i=1

t

υ1i+¿ ¿¿, y t

−¿=∑i=1

t

υ1i−¿ ¿¿,

x t

+¿=∑i=1

t

υ2i+¿ ¿¿, and x t

−¿=∑i=1

t

υ2i−¿ ¿¿. This produces four combinations of positive and negative shocks: ¿,

¿, ¿, and ¿. Then, Hatemi-J (2012) develops a test for identifying the causal relationship

between these positive and negative shocks employing a VAR model of order p. However,

this test, as argued by Bahmani-Oskooee et al. (2016), provides a single, one-shot test statistic

in the time domain and assumed valid at all points in the frequency distribution. To allow for

the possibility that the strength and/or direction of the Granger causality may vary over

different frequencies, Bahmani-Oskooee et al. (2016) extend the Hatemi-J (2012) asymmetric

Granger causality test from time domain (single, one-shot test statistic) into frequency domain

Granger causality test that is based on Breitung and Candelon (2006). To illustrate their test,

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Bahmani-Oskooee et al. (2016) consider the following finite-order VAR representation of

order p for the combination ¿

Θ ( L )¿

where Θ ( L )=I−Θ1 L−…−Θp Lp is a 2 ×2 lag polynomial of order p; and Θifor i=1 ,…, p is

a 2×2 coefficient matrix associated with lag i; I is a 2×2identity matrix. The error vector

ϱ t=(ϱ1 t ϱ2 t )' is white noise with E (ϱ t )=0 and positive-definite covariance matrix Σ=E (ϱ1t ϱ2 t' )

. Under the assumption that the system in (13) is stationary, then the moving-average (MA)

representation of the system is

¿

where Φ ( L )=Θ (L)−1 Ψ−1, with Ψ being the lower triangular matrix of the Cholesky

decomposition Ψ ' Ψ =Σ−1, such that E (ξt ξ t' )=I and ξ t=Ψ ϱt . Then, the spectral density of y t

can be expressed as

fy+¿ (ω )= 1

2 π {|Φ11(e− iω)|2+|Φ12(e− iω)|2}¿ (15)

The measure of causality in the frequency domain suggested by Geweke (1982) and

Hosoya (1991) is then defined as

Mx

+¿⇒ y+¿ ( ω)=log [1+|Φ 12( e−iω)|2

|Φ 12( e−iω)|2 ]( 16)¿

¿

The null hypothesis of no Granger causality from x+¿¿ to y+¿¿ in (16) involves testing

M X⇒Y (ω)=0, that is, when |Φ12(e−iω)|=0. In this case, we say that x+¿¿ does not Granger

cause y+¿¿ at frequency ω. Following Breitung and Candelon (2006), the null hypothesis of

non-Granger causality is tested using Φ12 ( L )=−ψ22Θ12(L)

|Θ(L)|, where ψ22 is the lower diagonal

element of Ψ−1 and |Θ(L)| is the determinant of Θ(L). It follows that x+¿¿ does not Granger

cause y+¿¿ at frequency ω if 3

3 For more details and discussion, the reader is referred to the original paper of Bahmani-Oskooee et al. (2016).

14

|Θ12(e−iω)|=|∑k=1

p

Θ12 ,k cos (kω )−∑k=1

p

Θ12 ,k sin (kω )i|=0(17)

where Θ12 ,k is the (1,2)-element of Θk. Then, a necessary and sufficient set of conditions for no

Granger causality at the frequency ω is

∑k =1

p

Θ12 , k cos ( kω)=0 (18)

∑k =1

p

Θ12 , k sin (kω )=0 (19)

Then, and following Breitung and Candelon (2006), Bahmani-Oskooee et al. (2016) specify

the following VAR( p) model for y t+¿¿

y t

+¿=∑k=1

p

Θ11 , k yt −k

+¿+∑k=1

p

Θ12 , kx t−k

+¿+ϵ t(20) ¿¿¿

The null hypothesis of no Granger causality M X⇒Y (ω)=0 at frequency ω is then tested by

employing a standard F-test for the linear restrictions (6) and (7). The F-test is distributed as

F (2 ,T−2 p) for ω∈(0 , π ), where 2 is the number of restrictions, T is the number of

observations used to estimate the VAR( p) model of order p.

In addition, we employ the panel causality test developed by Dumitrescu and Hurlin

(2012). The advantage of this test is it that accounts for cross-sectional dependence and

heterogeneity across individuals, or countries. They consider the following linear model

y i ,t=α i+∑j=1

J

ψ ij y i ,t− j+∑

j=1

J

φ ij xi , t− j+εi ,t (21)

where J is the lag order and assumed to be same for all cross-section units of the panel. The

autoregressive parameters (ψ¿¿ i j)¿ and the regression coefficients slopes (φ ¿¿ i j)¿ are

allowed to differ across groups. Dumitrescu and Hurlin (2012) propose an average Wald

statistic to test the null hypothesis of no causality for any of the cross-section units

(H 0 :φi=0∀ i=1 , …, N ), against the alternative that the causality occurs for at least one

subgroup of the panel (H 1 :φi=0∀i=1 ,…, N1 ;φi ≠0 ∀i=N 1+1 , N1+2 ,… , N ). The authors

15

define the average Wald statistic asWHT , NHnc = 1

N ∑i=1

N

W i ,T , where W i , T is the individual Wald

statistic for ith cross-section unit.

5. Empirical Results

In this section, we test for Granger causality between real GDP ( y ) and real government

expenditures (g), and between per-capita real GDP ( pcy) and per-capita real government

expenditures ( pcg). We perform both time domain and frequency domain causality tests. In

addition, we allow for asymmetries in the causal relationship between the variables. As a

preliminary step, we examine the order of integration of the variables to ascertain their

stationarity since the causality tests require stationarity of the variables. To this end, we apply

the augmented Dickey-Fuller (ADF) and the augmented Dickey-Fuller generalized least

squares (ADF-GLS) unit root tests. The results reported in Panel A of Table 2 suggest that the

variables are stationary across all six GCC countries in their first difference. Some tests

indicate that the variables are non-stationary in levels, but other tests suggest stationarity. For

example, the ADF test suggests that the variable g is stationary for the UAE, but the ADF-

GLS test suggests non-stationarity. Moving to panel data for the GCC region, three different

panel unit root tests (Breitung, Fisher, and IPS tests) were employed to ascertain the order of

integration of the variables with the results reported in Panel B of Table 2. Again, the unit root

tests in levels provide conflicting results about stationarity, but all variables are stationary in

first differences. This conflict about stationarity in levels could be due to lack of power in the

tests, so we proceed under the more conservative assumption that the variables are non-

stationary. Therefore, in the analysis that follows, we take the first differences for the variables

to get stationarity.

[INSERT TABLE 2 HERE]

5.1 Time domain tests for linear causality

16

First, we examine linear causality in the time domain for the variables g and y, as well as

for pcg and pcy. Results are presented in Table 3 for three different types of tests. Panel A of

Table 3 shows results for the standard Granger non-causality tests. The null hypothesis that y

does not cause g and that pcy does not cause pcg is rejected for three of six countries. Thus,

Wagner’s law is supported by evidence from Oman, Saudi Arabia, and the UAE. However,

the Keynesian hypothesis is supported in only one case. That is, g essentially causes y only in

Saudi Arabia.

A potential problem with using standard Granger causality tests arises when some

variables are stationary in levels and others in first difference. Hence, Toda and Yamamoto

(1996) modified the Wald test statistic to avoid the necessity of testing for the order of

integration and cointegration. The Toda-Yamamoto test for causality, as presented in Panel B

of Table 3, is implemented on the levels of the variables and is valid for stationary,

cointegrated, or for combinations of stationary and cointegrated variables. Since the results in

Panels A and B are similar, the choice to first difference all variables does not seem to

significantly impact the outcome of the causality tests. Nevertheless, there are some

differences between panels. Wagner’s law receives some support in Oman and the UAE, but

not for Saudi Arabia. Support for the Keynesian hypothesis only comes from the UAE.

Panel C of Table 3 shows the results from the panel causality test developed by

Dumitrescu and Hurlin (2012). It allows coefficients to vary over cross-sectional units, but

requires stationarity. We therefore apply the test on the first differences of the variables to the

unbalanced panel of the six GCC countries, as a whole. The null hypothesis of Granger non-

causality from y to g is rejected at the 1% level and the null hypothesis of non-causality from

pcy to pcg is rejected at the 10% level. The evidence suggests that Wagner’s law is valid for

the GCC, as a whole. In contrast, there is no evidence of significant causality running from g

to y or from pcg to pc y. Hence, the Keynesian hypothesis does not appear to be supported

17

using time domain panel causality tests, nor does it receive much support among the various

GCC countries individually using time domain causality tests. To summarize, time domain

tests generally support Wagner’s law for the GCC and suggest that government expenditures

are influenced by national income. There is only limited evidence for causality running from

government spending to income for either Saudi Arabia or the UAE, depending upon which

test is used in Panel A or B. Without moving to the frequency domain or without considering

nonlinear asymmetric models, the implication would be that there is only a limited role that

fiscal policy could play in GCC regional economic development. Nevertheless, we have found

differences in causality relationships between g and y across rather similar countries in the

same region. Our analysis is consistent with Burney’s (2002) rejection of Wagner’s law for

Kuwait and for the years 1969 – 1995 and Ageli’s (2013) support for both Wagner’s law and

the Keynesian hypothesis in Saudi Arabia for the years 1970 – 2012.

[INSERT TABLE 3 HERE]

5.2 Frequency domain tests for linear causality

A shortcoming of causality tests in the time domain, as previously discussed, is that such

analysis only produces a single snapshot over an entire period of the interaction between g and

y. This relationship may vary in strength, or even in direction over the short-run versus the

long-run (Lemmens et al., 2008). The frequency domain Granger causality test developed by

Breitung and Candelon (2006) allows us to disentangle short-run from long-run predictability

and see how causality varies over different frequencies. Figure 2 presents the results for the

six GCC countries for (symmetric) linear causality tests in the frequency domain, maintaining

the assumption implicit in all of our previous analysis that increases in g or y would have the

same impact as decreases in the same variables. The results are consistent with our previous

analysis based on the time domain. Once again, there is no support for the Keynesian

hypothesis, but some evidence for Wagner’s law in Oman, Saudi Arabia, and the UAE.

18

Focusing on Oman, the Wald statistic is significant at the 10% level for frequencies ω∈(0 , π ).

In term of years (T ), since T=2π /ω, it means that Wagner’s law holds only in the long run,

for periods of about 6 years or greater. For the UAE and Saudi Arabia, Wagner’s law seems to

hold for periods of about 8 to 10 years or longer. For all three of these countries, there is no

significant causality at high frequencies—meaning no support for Wagner’s law in the short-

run. Hence, short-run, or temporary annual fluctuations in real GDP and government

expenditures do not have significant long-run consequences.

[INSERT FIGURE 2 HERE]

5.3 Time domain tests for symmetric nonlinear causality

While analysis in the frequency domain provides some insights about short-run versus

long-run impacts not easily seen with time domain analysis, another issue is whether the

causal relationships between g and y could be nonlinear in nature. We now consider

nonlinearities that can be represented by symmetric logistic and exponential smooth transition

autoregressive (LSTAR and ESTAR) models, as considered in a different contest by Singh

(2012). In general, nonlinearities are significant for all four variables (g, y, pcg, and pcy)

across most countries, and for the whole GCC.4 Results, reported in Table 4, are similar to

those from linear time domain analysis, but greater support for both Wagner’s law and the

Keynesian hypothesis is found by considering these nonlinearities. Evidence for Wagner’s law

is found for four countries—Oman, Qatar, Saudi Arabia, and the UAE. The LSTAR

framework is more appropriate for Oman, Qatar, and the UAE, while the ESTAR model better

models the causal relationships for Saudi Arabia. Some evidence for the Keynesian model is

found for both Saudi Arabia and for the UAE and in more instances than for the linear case. In

general, most causal relationships are greater using one lag for the adjustment process, but in a

few instances, two lags give slighter strong results.

4 The null hypothesis of linearity was rejected in favor of the alternative of non-linearity in most of the cases with mixed evidence of ESTAR and LSTAR types of non-linearities. All unreported results are available upon request.

19

We also tested for panel causality following the Dumitrescu and Hurlin (2012) procedures.

These panel causality tests indicate that Wagner’s law is valid for the whole GCC, while the

Keynesian hypothesis is not supported. Since results are similar to those presented above they

are not presented in a separate table.

[INSERT TABLE 4 HERE]

5.4 Frequency domain tests for asymmetric nonlinear causality

Analysis of causality in the time domain has been extended to the asymmetric nonlinear

case by Hatemi-J (2012). He constructs partial sums of positive and negative shocks for each

pair of causal variables because the response of various economic variables to positive shocks

may be different than the response to negative shocks. For any pair of variables there are four

possible categories of responses. However, we are interested in the two cases that could be

consistent with either the Keynesian hypothesis or Wagner’s law. That is, we will only

examine positive changes in both g and y (or in pcg and pcy), and negative changes in both g

and y (or in pcg and pcy). The other two cases involving a positive change in one variable

and a negative change in the other would involve testing some other theory, such as smoothing

of government expenditures in response to changes in income, or some rather inexplicable

anti-Keynesian hypothesis where GDP reacts negatively to changes in government spending.

This asymmetric analysis has been extended to the frequency domain by Bahmani-

Oskooee et al. (2016). We apply that basic framework to each of the six GCC countries to

examine the two cases involving positive g and positive y (one for causality from y to g to

test Wagner’s law and the other case involving causality from g to y to test the Keynesian

hypothesis. We also test for causality involving the two positive cases for pcg and pcy. Then

we examine negative shocks to both variables. Hence for each country, we examine eight

possible asymmetric causality relationships. Time domain results lead to the same conclusions

20

as those from the frequency domain. So since a graphical analysis gives more complete

picture, we only present frequency domain results below.

Asymmetric nonlinear frequency domain tests are performed using the GRETL software

and the results for each of the six GCC countries are presented in Figure 3. The evidence for

both Wagner’s law and for the Keynesian hypothesis are much stronger than for linear

causality, as shown in Figure 3. Also the impact of moving from nonlinear symmetric analysis

in Table 4 to the asymmetric nonlinear case in Figure 3 is substantial. To summarize, the

results in Figure 3, provide some evidence for Wagner’s law in five of six countries and some

support for the Keynesian hypothesis across all six GCC countries. For the 24 graphs

involving country-specific tests for Wagner’s law, it is supported in ten instances, while the 24

graphs presenting country-specific tests for the Keynesian hypothesis indicate support in 12 of

24 cases. Causal relationships are generally, but not always, stronger for totals rather than for

per capita public expenditures and national income. Support for both theories is divided nearly

equally across the instances of positive shocks and negative shocks, but in some countries the

support comes primarily from negative shocks and in other countries it is from positive

income shocks. For some countries, the causality is short-run and in others it is long-run. To

summarize, asymmetric causality tests support both Wagner’s law and the Keynesian

hypothesis across the GCC region, but the evidence is moderate and not overwhelming. In

about half of the cases, neither hypothesis is supported. So, even in the asymmetric case, the

neutrality hypothesis receives about as much support as either Wagner’s law or the Keynesian

hypothesis.

[INSERT FIGURE 3 HERE]

6. Conclusion

This paper has found moderate support for both Wagner’s law and for the Keynesian

hypothesis across the six countries of the GCC. The strength of causal relationships varies

21

across countries and by model specification, but the strongest support for both theories is

provided by asymmetric nonlinear causality analysis. Thus, we have found evidence that the

relationship between government spending and real income in the GCC is nonlinear and

asymmetric between positive and negative income shocks.

The differences between linear and nonlinear causality analysis may be summarized as

follows. Linear panel causality tests validate Wagner’s law across the whole GCC region, but

they do not confirm the Keynesian hypothesis. At the individual country level, support for

Wagner’s law comes primarily from Oman, Saudi Arabia and the UAE, while there is mild

support for the Keynesian hypothesis in Saudi Arabia and the UAE. Frequency domain

analysis indicates that linear causality in either direction occurs in the slowly fluctuating

components of the variables—meaning that causal relationship between government spending

and real GDP in either direction are stronger in the long-run than in the short-run. Nonlinear

symmetric causality tests based LSTAR and ESTAR representations of variables provide

slightly greater support for both Wagner’s law and the Keynesian hypothesis than linear

models. However, the evidence for both theories becomes more pronounced when adopting

asymmetric nonlinear causality tests. Support for the Keynesian hypothesis is found in each of

the six GCC countries and some evidence for Wagner’s law is found in five of the six GCC

countries. Since Wagner’s law hold in general across the GCC, the implication is that

government spending responds to changes in real income and that more public expenditures

will be demanded as regional income rises. Our finding of moderate support for the Keynesian

hypothesis means that there is some role for fiscal policy in guiding economic development

and increasing national income in the GCC region. It is noteworthy that the two countries

providing the greatest support for the Keynesian hypothesis--Saudi Arabia and the UAE—are

also the two countries that have embarked on the largest infrastructure and economic

development projects in the region.

22

Table 1: five-year averages for real government expenditures and real GDP

Country 1975-1979 1980-1984 1985-1989 1990-1994 1995-1999 2000-2004 2005-2009 2010-2014Bahrain

y g11.32 5.88 3.37 6.67 3.96 4.75 5.87 3.89

gg10.94 12.09 7.10 3.56 3.77 -1.23 3.88 6.15

pcyg5.04 2.44 0.04 4.02 0.87 0.12 -1.99 1.31

pcgg4.66 8.65 3.77 0.92 0.68 -5.86 -3.97 3.56

g/ y 14.50 16.50 24.60 22.60 20.40 16.80 12.80 14.70

Kuwaity g

N.A N.A N.A N.A 0.74 7.35 4.13 2.77

ggN.A N.A N.A N.A -3.93 1.30 2.69 3.69

pcygN.A N.A N.A N.A -2.38 4.22 -1.58 -2.52

pcggN.A N.A N.A N.A -6.91 -1.82 -3.01 -1.60

g/ y N.A N.A N.A N.A 28.70 22.60 15.10 16.60

Omany g

8.40 12.68 5.70 4.70 3.24 1.42 5.17 3.43

gg3.77 11.95 3.97 3.05 2.35 0.20 2.23 8.52

pcyg3.21 7.27 1.77 0.59 2.46 -0.48 2.76 -5.13

pcgg-1.43 6.54 0.03 -1.07 1.57 -1.71 -0.18 -0.03

g/ y 31.90 28.70 30.20 24.40 24.30 22.6 18.3 20.5

Qatary g

N.A 1.56 2.39 2.57 9.64 8.14 14.91 9.14

ggN.A 16.79 3.85 0.19 3.74 -5.36 18.50 6.98

pcygN.A -9.00 -3.72 1.23 6.80 3.15 -0.61 2.91

pcggN.A 6.23 -2.26 -1.51 0.90 -10.34 2.97 0.75

g/ y N.A 28.50 41.90 34.40 30.40 16.70 13.40 13.30

Saudi Arabiay g

5.47 -2.29 0.64 4.39 1.63 4.33 5.63 5.12

gg26.24 3.18 1.76 -2.04 2.56 2.12 5.03 8.91

pcyg-0.13 -8.43 -3.78 1.38 -0.88 1.45 3.02 2.73

23

pcgg20.64 -2.96 -2.66 -5.05 0.06 -0.76 2.42 6.52

g/ y 20.2 25.70 32.80 28.20 25.00 24.80 20.30 21.70

UAEy g

13.03 3.62 -1.51 5.78 4.63 6.33 3.00 4.41

gg22.80 11.56 1.20 2.34 2.28 1.56 7.16 -0.38

pcyg-0.90 -2.83 -7.32 0.42 -0.44 -0.09 -10.23 1.12

pcgg8.87 5.11 -4.62 -3.02 -2.72 -4.93 -6.07 -3.68

g/ y 6.90 11.10 13.50 11.20 10.00 8.50 6.90 7.40

All countriesy g 9.56 4.29 2.12 4.82 3.97 5.39 6.45 4.79gg 15.94 11.11 3.58 1.42 1.80 -0.24 6.58 5.65

pcyg 1.81 -2.11 -2.60 1.53 1.07 1.40 -1.44 0.07

pcgg 8.19 4.71 -1.15 -1.95 -1.07 -4.24 -1.31 0.92

g/ y 18.38 22.10 28.60 24.16 23.13 18.67 14.23 15.70

Authors’ calculations. N.A indicates not available. y g, gg, pc y g, and pc gg stand for the growth rates of real GDP, real government expenditures, per-capita real GDP, and per-capita real government expenditures. g/ y stands for government expenditures as a percentage of GDP.

24

Table 2: Unit root tests for the six GCC countries

Panel A:ADF test ADF-GLS test

Levels First difference

Levels First difference

Variable No trend Trend No trend No trend Trend No trend

Bahrain g -2.49(0) -2.26(0) -5.82(0)* 0.44(0) -1.48(0) -5.01(0)*

y -2.36(0) -6.25(0)** -5.93(0)* 1.55(1) -2.63(0) -2.20(0)**

pcg -2.11(0) -1.80(0) -5.32(0)* -1.04(0) -1.28(0) -4.86(0)*

pcy -3.29(0)** -2.52(0) -5.59(0)* -0.62(0) -1.61(0) -2.41(0)**

Kuwait g -1.98(0) -1.99(0) -4.01(1)* -1.64(0) -2.10(0) -3.89(0)*

y -1.77(0) -2.38(1) -4.07(0)* 0.01(1) -2.63(1) -2.92(0)*

pcg -2.12(0) -3.41(1)*** -3.35(3)** -1.50(0) -3.67(1)** -3.73(0)*

pcy -1.88(1) -1.70(1) -2.77(0)*** -0.62(0) -1.61(0) -2.41(0)*

Oman g -1.41(0) -2.24(0) -6.92(0)* 0.52(0) -1.87(0) -5.56(0)*

y -2.63(2)*** -1.59(2) -5.25(0)* -0.38(1) -2.42(1) -2.40(0)**

pcg -2.94(0)** -2.84(0) -7.71(0)* -2.01(0)** -2.56(0) -6.04(0)*

pcy -2.12(2) -0.49(2) -5.11(0)* -0.70(2) -2.86(1) -2.37(0)**

Qatar g -0.85(0) -1.75(0) -6.02(0)* 0.36(0) -1.70(0) -4.17(0)*

y 2.88(0)*** -1.44(0) -3.69(0)* -0.29(2) -1.46(2) -3.7590)*

pcg -1.52(0) -3.28(0)*** -6.93(0)* -1.54(0) -2.86(0) -4.71(0)*

pcy -0.40(0) -3.45(0)*** -3.88(0)* -0.50(0) -1.71(0) -3.87(0)*

Saudi Arabia g -2.54(0) -2.40(0) -7.27(0)* 0.26(0) -1.50(0) -7.21(0)*

y -1.92(1) -3.97(2)** -3.62(0)* -0.15(2) -2.50(1) -3.65(0)*

pcg -2.65(0)*** -2.45(0) -7.50(0)* -0.87(0) -1.67(0) -7.42(0)*

pcy -2.61(2)*** -2.85(2) -3.49(0)** -2.29(2)** -2.50(2) -3.52(0)*

UAE g -4.23(0)* -4.86(1)* -5.01(0)* -0.41(0) -2.08(0) -4.22(0)*

y -0.83(1) -2.76(1) -4.70(0)* 0.54(1) -2.52(1) -3.83(0)*

pcg -0.25(0) -3.37(0)*** -5.31(0)* -0.39(0) -1.98(0) -4.96(0)*

pcy -1.01(1) -2.44(1) -4.53(0)* -0.39(1) -2.52(1) -4.50(0)*

*, **, *** denotes rejection of the null hypothesis of a unit root at the 1%, 5% and 10% significance level. The number of lags in parentheses is selected by the minimum of Schwarz Information Criterion (SIC). The 10%, 5% and 1% critical values for the ADF test are -2.61, -2.94 and -3.61 for no trend, and -3.20, -3.53 and -4.22 for the trend model. The 10%, 5% and 1% critical values for the ADF-GLS test are -1.61, -1.95 and -2.63 for no trend, and -2.89, -3.19 and -3.7 for the trend model. g, y , pcg, and pcy stands for real government expenditure, real GDP, real per capita government expenditure, and real per capita GDP, respectively. All variables are in logarithmic forms.

Panel B:

Panel unit root tests for the GCC regionLevel First difference Breitung IPS ADF-F Breitung IPS ADF-F

Variable

Trend No trend Trend No trend Trend

g 0.70[0.758]

-2.01[0.022]**

-0.99[0.1162]

25.12[0.014]**

16.98[0.150]

-6.27[0.000]*

-11.85[0.000]*

131.05[0.000]*

y -0.53[0.701]

1.12[0.867]

-2.65[0.004]*

13.01[0.368]

34.54[0.001]*

-3.91[0.000]*

-8.35[0.000]*

85.51[0.000]*

pcg 0.09[0.534]

-1.13[0.129]

-2.01[0.022]**

18.05[0.114]

21.35[0.045]**

-6.68[0.000]*

-12.09[0.000]*

137.22[0.000]*

pcy 0.79 -1.02 -0.25 16.98 14.05 -4.45 -7.46 77.14

25

[0.784] [0.153] [0.401] [0.150] [0.298] [0.000]* [0.000]* [0.000]*

*, **, *** denotes rejection of the null hypothesis of a unit root at the 1%, 5% and 10% significance level. P-values in square brackets. Number of lags is selected by SIC.

Table 3: Time domain--Linear non-causality tests

Panel A: Granger non-causality tests

Null hypothesisy⇏ g g⇏ y pcy⇏ pcg pcg⇏ pcy

Country

k χ2 stat. χ2 stat. k χ2 stat. χ2 stat.

Bahrain 1 0.388[0.533]

0.129[0.720]

1 0.550[0.458]

1.654[0.199]

Kuwait 1 0.5067[0.4876]

0.154[0.694]

1 0.269[0.604]

0.018[0.893]

Oman 2 6.0856[0.048]**

0.290[0.865]

2 4.838[0.088]***

0.857[0.652]

Qatar 1 0.3410[0.559]

0.194[0.660]

1 0.208[0.649]

0.001[0.972]

Saudi Arabia

1 5.7549[0.016]**

3.046[0.081]***

1 4.893[0.027]**

2.649[0.104]

UAE 1 9.3778[0.002]*

1.176[0.278]

1 5.0506[0.025]**

1.540[0.215]

Panel B: Toda and Yamamoto non-causality tests

Null hypothesisy⇏ g g⇏ y pcy⇏ pcg pcg⇏ pcy

Country

k χ2 stat. χ2 stat. k χ2 stat. χ2 stat.

Bahrain 1 0.039[0.845]

0.0372[0.847]

1 0.014[0.906]

0.953[0.329]

Kuwait 1 1.728[0.189]

0.174[0.677]

1 0.115[0.735]

1.117[0.291]

Oman 1 5.299[0.021]**

0.538[0.463]

1 3.343[0.068]***

0.325[0.569]

Qatar 1 0.001[0.976]

0.009[0.923]

1 1.516[0.218]

0.479[0.489]

Saudi Arabia

1 1.934[0.164]

0.173[0.679]

2 3.562[0.169]

1.091[0.581]

UAE 1 2.504[0.114]

5.425[0.012]**

1 7.789[0.005]*

0.286[0.593]

Panel C: Pairwise Dumitrescu Hurlin panel non-causality tests (one lag)

Null hypothesisy⇏ g g⇏ y pcy⇏ pcg pcg⇏ pcyχ2 stat. χ2 stat. χ2 stat. χ2 stat.

GCC 3.363[0.005]*

0.792[0.671]

2.254[0.074]***

0.977[0.882]

26

*, **, and *** indicate significance at the 1, 5, and 10 percent significance levels. The number of lags (k ) in the VAR model is determined by SIC. p-values are square bracketed. y⇏ g means y does not Granger cause g. g⇏ y means g does not Granger cause y . Boldfacing is used to highlight any of the rejections of non-causality significant at the 10% level or greater that could be used to support either Wagner’s law or the Keynesian hypothesis.

Table 4: Time domain—Nonlinear non-causality tests Null hypothesis

y⇏ g g⇏ y pcy⇏ pcg pcg⇏ pcyESTAR LSTAR ESTAR LSTAR ESTAR LSTAR ESTAR LSTAR

Country m χ2 stat. χ2 stat. χ2 stat. χ2 stat. χ2 stat. χ2 stat. χ2 stat. χ2 stat.Bahrain 1 0.1317

[0.9405]0.7418[0.5348]

0.3929[0.7590]

0.6572[0.5846]

0.2721[0.8451]

0.1382[0.9365]

0.6629[0.5811]

0.5381[0.6595]

2 0.9569[0.4820]

0.8841[0.5316]

0.5694[0.7738]

0.5977[0.7520]

0.5027[0.8239]

0.4548[0.8584]

0.3675[0.9129]

0.3508[0.9227]

Kuwait 1 0.4482[0.7225]

0.9163[0.4583]

0.1827[0.9064]

0.2572[0.8551]

1.2795[0.3296]

0.5969[0.6301]

0.2023[0.8927]

0.0069[0.9991]

2 0.5009[0.8128]

0.7395[0.6469]

1.1930[0.3932]

1.1135[0.4189]

1.5951[0.2929]

0.3986[0.8728]

0.1850[0.9783]

0.2960[0.9369]

Oman 1 1.2478[0.3077]

2.3492[0.0898]***

0.7189[0.5476]

0.5030[0.6826]

1.0165[0.3975]

1.2697[0.2998]

0.3799[0.7681]

0.3570[0.7844]

2 0.7800[0.6092]

1.1551[0.3579]

0.6913[0.6786]

0.8109[0.5850]

0.8461[0.5591]

0.9361[0.4938]

1.0268[0.4340]

1.3251[0.2742]

Qatar 1 4.4305[0.0121]**

3.0899[0.0431]**

0.5241[0.6670]

0.4779[0.7002]

1.0396[0.3915]

1.8316[0.1643]

1.0586[0.3836]

0.1650[0.9190]

2 3.4487[0.0129]**

2.3616[0.0566]***

0.5112[0.8158]

0.8114[0.5870]

1.6522[0.1756]

1.4865[0.2212]

0.5990[0.7498]

0.5182[0.8107]

Saudi Arabia

1 3.9898[0.0145]**

1.7626[0.1707]

3.0885[0.0385]**

3.0053[0.0415]**

1.9255[0.1419]

0.8507[0.4750]

2.5197[0.0725]**

2.8006[0.0529]***

2 3.8989[0.0034]*

0.9125[0.5091]

3.1322[0.0120]**

2.7331[0.0226]**

2.4650[0.0377]**

0.8705[0.5397]

4.1560[0.0022]*

4.5798[0.0012]*

UAE 1 1.5879[0.2122]

3.2857[0.0337]**

2.7258[0.0610]***

2.6494[0.0662]***

1.5189[0.2291]

2.4501[0.0809]***

2.0450[0.1280]

1.8817[0.1519]

2 0.5766[0.7683]

2.0660[0.0843]***

1.7798[0.1343]

1.3686[0.2560]

0.5226[0.8092]

2.0562[0.0828]***

1.7043[0.1519]

1.9799[0.0940]***

*, **, and *** indicate significance at the 1, 5, and 10 percent significance levels. m denotes the lag orders of the polynomial in the causing variable. p-values are square bracketed. Boldfacing is used to highlight any of the rejections of non-causality significant at the 10% level or greater that could be used to support either Wagner’s law or the Keynesian hypothesis.

27

Figure 1: evolution of GDP and government expenditures in the GCC countries

Sloid line is logarithm of real GDP and dotted line is logarithm of real government expenditures.

28

Figure 2: Frequency domain linear Granger causality tests

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: g - Cause variable: GDP

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: pcg - Cause variable: pcGDP

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: GDP - Cause variable: g

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: pcGDP - Cause variable: pcg

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: g - Cause variable: GDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: pcg - Cause variable: pcGDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: GDP - Cause variable: g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: pcGDP - Cause variable: pcg

29

Figure 2: Frequency domain linear Granger causality tests (continued)

3

3.5

4

4.5

5

5.5

6

6.5

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: g - Cause variable: GDP

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: pcg - Cause variable: pcGDP

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: GDP - Cause variable: g

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: pcGDP - Cause variable: pcg

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: g - Cause variable: GDP

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: pcg - Cause variable: pcGDP

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: GDP - Cause variable: g

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: pcGDP - Cause variable: pcg

30

Figure 2: Frequency domain linear Granger causality tests (continued)

0

1

2

3

4

5

6

7

8

9

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: g - Cause variable: GDP

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: pcg - Cause variable: pcGDP

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: GDP - Cause variable: g

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: pcGDP - Cause variable: pcg

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: g - Cause variable: GDP

3.6

3.8

4

4.2

4.4

4.6

4.8

5

5.2

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: pcg - Cause variable: pcGDP

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: GDP - Cause variable: g

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: pcGDP - Cause variable: pcg

31

Figure 3a: Frequency domain asymmetric nonlinear Granger causality tests (Bahrain)

Panel A: Testing Wagner’s law

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: positive g - Cause variable: positive GDP

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: negative g - Cause variable: negative GDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: positive pcg - Cause variable: positive pcGDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: negative pcg - Cause variable: negative pcGDP

Panel B: Testing the Keynesian hypothesis

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: positive GDP - Cause variable: positive g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: negative GDP - Cause variable: negative g

1

2

3

4

5

6

7

8

9

10

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: positive pcGDP - Cause variable: positive pcg

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Bahrain - Target variable: negative pcGDP - Cause variable: negative pcg

32

Figure 3b: Frequency domain asymmetric nonlinear Granger causality tests (Kuwait)

Panel A: Testing Wagner’s law

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: positive g - Cause variable: positive GDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: negative g - Cause variable: negative GDP

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: positive pcg - Cause variable: positive pcGDP

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: negative pcg - Cause variable: negative pcGDP

Panel B: Testing the Keynesian hypothesis

2

3

4

5

6

7

8

9

10

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: positive GDP - Cause variable: positive g

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: negative GDP - Cause variable: negative g

2

3

4

5

6

7

8

9

10

11

12

13

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: positive pcGDP - Cause variable: positive pcg

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Kuwait - Target variable: negative pcGDP - Cause variable: negative pcg

33

Figure 3c: Frequency domain asymmetric nonlinear Granger causality tests (Oman)

Panel A: Testing Wagner’s law

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: positive g - Cause variable: positive GDP

0

2

4

6

8

10

12

14

16

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: negative g - Cause variable: negative GDP

3.5

4

4.5

5

5.5

6

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: positive pcg - Cause variable: positive pcGDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: negative pcg - Cause variable: negative pcGDP

Panel B: Testing the Keynesian hypothesis

2.6

2.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: positive GDP - Cause variable: positive G

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6

6.2

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: negative GDP - Cause variable: negative G

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: positive pcGDP - Cause variable: positive pcG

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5 3frequency

Oman - Target variable: negative pcGDP - Cause variable: negative pcG

34

Figure 3d: Frequency domain asymmetric nonlinear Granger causality tests (Qatar)

Panel A: Testing Wagner’s law

4

6

8

10

12

14

16

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: positive g - Cause variable: positive GDP

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: negative g - Cause variable: negative GDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: positive pcg - Cause variable: positive pcGDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: negative pcg - Cause variable: negative pcGDP

Panel B: Testing the Keynesian hypothesis

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: positive GDP - Cause variable: positive g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: negative GDP - Cause variable: negative g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: positive pcGDP - Cause variable: positive pcg

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3frequency

Qatar - Target variable: negative pcGDP - Cause variable: negative pcg

35

Figure 3e: Frequency domain asymmetric nonlinear Granger causality tests (Saudi Arabia)

Panel A: Testing Wagner’s law

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: positive g - Cause variable: positive GDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: negative g - Cause variable: negative GDP

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: positive pcg - Cause variable: positive pcGDP

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: negative pcg - Cause variable: negative pcGDP

Panel B: Testing the Keynesian hypothesis

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: positive GDP - Cause variable: positive G

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: negative GDP - Cause variable: negative G

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: positive pcGDP - Cause variable: positive pcG

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

Saudi Arabia - Target variable: negative pcGDP - Cause variable: negative pcG

36

Figure 3f: Frequency domain asymmetric nonlinear Granger causality tests (UAE)

Panel A: Testing Wagner’s law

3

3.5

4

4.5

5

5.5

6

6.5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: positive g - Cause variable: positive GDP

4.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: negative g - Cause variable: negative GDP

3.5

4

4.5

5

5.5

6

6.5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: positive pcg - Cause variable: positive pcGDP

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: negative pcg - Cause variable: negative pcGDP

Panel B: Testing the Keynesian hypothesis

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: positive GDP - Cause variable: positive g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: negative GDP - Cause variable: negative g

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: positive pcGDP - Cause variable: positive pcg

4.5

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

0 0.5 1 1.5 2 2.5 3frequency

UAE - Target variable: negative pcGDP - Cause variable: negative pcg

37

+ is the test statistic. x is the 10 percent significance level. g is government expenditures, pcg is per-capita g, and pcGDP is per-capita GDP. All variables are in logs. Positive and negative stand for partial sum processes of positive and negative shocks. References

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