Economies of Scale, Information and
Fiscal Decentralization
By
LEONARDO LETELIER S.
Institute of Public Affairs
University of Chile
JOSÉ LUIS SAEZ LOZANO
Department of Economics
University of Granada
Abstract
The study makes a contribution in two basic areas. Firstly, it sets up model which combines efficiency as well
as political economy aspects in trying to explain the degree of fiscal decentralization. Whilst this hinges upon
previous contributions on the subject matter, it innovates in making explicit the benefits from better informed
politicians and policy makers which decentralization brings about and the potential cost push effect on public
services and public goods steaming from decentralization. Keeping exogenous factors aside, the model
predicts that economic growth will lead to more fiscal decentralization as long as these benefits in information
(Von Hayek effect) are higher than the cost effect (Scale Effect). Such a conclusion is compatible with the
hypothesis that only some specific functions of government will become more decentralized as income per
capita grows, whereas others will stay the same or even get more centralized. Secondly, by using a panel of
64 countries this paper tests a comprehensive set of hypotheses about the causes of Fiscal Decentralization.
Among other findings, evidence is provided that shows s a negative impact of urbanization on the degree of
fiscal decentralization. Furthermore, the effect of income per capita is stronger for high-income countries. In
contrast to the case of fiscal decentralization being measured as the share of the sub national government’s
expenditure over that of the general government, the use of functional measurements of fiscal decentralization
shows that income per capita has a negative effect on health decentralization. While urbanization has a
negative impact on the fiscal decentralization of health and education, it has a positive effect on the share of
housing expenditures being made by sub national governments.
I.
INTRODUCTION.
Fiscal Decentralization (FD) has turned into one of the most rapidly expanding areas of
academia interest in public finance. Whilst some general historical episodes may in part
explain this phenomenon, it becomes apparent that a number of clearly identifiable factors
are likely to be responsible for the significant differences in the degree of decentralization
we may observe across countries and over time. Fiscal Decentralization has become one of
the most widely discussed aspects of the modernization of the State. In spite that various
world level historical episodes may be identified to be responsible for the acceleration of
this process over recent years, there is still the lack of a more systematic economically
based explanation as to why some countries – and even specific areas within these
countries- have experience a faster evolution as far as FD is concerned. One the one hand,
countries is likely to have idiosyncratic characteristics that explain this. On the other, the
wide variety of services that may be subject to more decentralization exhibit specific
characteristics which could make them more – or less- appropriate to become further
decentralized.
This paper builds on two previous contributions to explain FD. One is a theoretical and
empirical paper by Panizza (1999), which provides a coherent theoretical explanation on
why countries differ in their degrees of FD. A second empirical reference is the recent
contribution by Letelier (2005). This examines empirically a comprehensive range of
factors that explain FD. Whilst this second paper suggests that interesting differences may
arise when decentralization is examined for specific areas of government, this is not
formally explained in a theoretical model. This present paper takes advantage of the
empirical evidence provided by that previous research in order to set up a theoretical
explanation about the causes of FD in different functional areas of the State. The model
being proposed combines a leviathan type of government with a set of characteristics of
specific government’s functions. In particular, it differentiates the potential gains on
information at the disposal of local officers and politicians (“von Hayek effect”) from the
disadvantages in economies of scale arising from a more decentralized structure of
government. The model is tested for the cases of health, education and housing by using a
panel of 64 countries.
The remaining of this paper is organized as follows. Section I discusses the existing
hypothesis about the origins of FD. Section II briefly describes the existing theoretical
literature on the causes of decentralization. A new theoretical model is presented in section
III and section IV provides the empirical analysis.
II. THE EXISTING THEORETICAL LITERATURE.
There is no unique and well-accepted theory to be tested regarding the identification of
causes for FD to vary across countries and over time. What we do find instead is a number
of hypotheses that provide some economic rationale to the effects that specific variables
may have on FD. There is, however, consensus that some broad basic elements can be
singled out. As in any optimization process, the social welfare function in each country
must take into consideration a number of restrictions. The basic question refers to which
40
variables determine the social welfare function, and which can be accounted for as the
relevant restrictions.
In so far as the median voter demonstrates his/her demand for the amount and basic
characteristics of local public goods, policy makers and politicians act accordingly. The
literature stresses that voters’ preferences will be shaped by numerous idiosyncratic
characteristics. Demographic, social, and ethnic features can be mentioned among others.
Restrictions are also numerous but of a different kind. They rank from cost considerations
to the more obvious fact that the political framework of the country at stake may not permit
median voters to express themselves freely.
The potential link between the quality of public goods and FD rests on a number of well
known theoretical arguments. We will hypothesize that two of them are the most relevant
ones. One stresses the advantages in terms of better information being available to local
bureaucrats and politicians (Von Hayek 1945). Since they are closer to local needs and
demands, they are more likely to decide correctly on the type of public goods and services
to be provided. Although a wide range of other quality improving implications from
decentralization may be identified (Letelier 2004), they can be assumed to be close relatives
to what it will be called Von Hayek’s effect (VHE). One explicitly accounted for in this
research is that put forward by Panizza (1999). By taking advantage of its agenda-setting
condition, the government is supposed to take the lead in deciding the level of fiscal
centralization. This depends upon the national median voter’s preferences regarding the
type and level of government expenditures. Since the government obtains rents from
staying in office, there will be a hedge between the median voter’s demand for government,
and the government’s optimum. As the median voter’s income rises, it also raises the
median voter’s demand for spending. However, the median voter will avoid the realization
of government’s rents by forcing more decentralization, which diminishes the power of
government to administer the budget.
However trendy, DF has numerous detractors. Among others there is the point about
whether individuals make their decisions about migration on the basis of the current
performance of the particular jurisdiction they belong, the likely coordination problem
across tiers of government, the lack of qualified personnel and the cost push effect from a
smaller scale of operation. In short, decentralization may lead to more expensive public
goods (Prud’homme, R. 1995). Since only rich countries can afford decentralization, we
can expect that generally, lower income countries will be more centralized.
We hypothesize that costs and benefits from decentralization being mentioned above
generally miss a fundamental aspect of the problem at stake. This is the fact that State
functions exhibit specific characteristics as far as decentralization is concerned
(Osterkamp and Eller 2003). By taking Panizzas’ model on centralization, this present
paper innovates in building a model that explicitly acknowledges differences across types
of public goods, both in terms of the information benefits (VHE) as well as regarding the
cost increasing effect of delivering public services by smaller units.
40
III.
A NEW MODEL.
III.1
THE GENERAL CONTEXT.
An interesting step ahead in modeling of the causes of fiscal decentralization is the work by
Panizza (1999). His paper confronts the median voter with a rent seeker Leviathan type of
government, which is assumed to define the agenda thereby the optimum degree of
“centralization” (θ) is achieved. Such an optimum results from the combination between an
exogenously given median voter structure of preferences and the level of government
expenditure being made. The institutional framework in which this process takes place is
represented by the depth of the democratic system (ϕ), which is also exogenous. The less
democratic the political system is, the more likely will be that the current government could
take advantage of centralization as a way to get Ricardian rents while it stays in power.
Whilst the above mentioned model captures the fundamentals of the subject matter, it may
be improved in at least two aspects. In the first place it seems very unlikely that θ is entirely
under the control of the central government. A more realistic approach should accept that
centralization is in strongly determined by factors exogenous to the incumbent government.
Two of such a factors may be identified in the light of the existing empirical evidence.
These characteristics may be explicitly integrated into the model by turning θ into a
function that depends on two types of variables. The second aspect worth considering is the
fact that the median voter’s demand of a particular public good could differ depending on a
set of specific characteristics. On the one hand the median voter will assign value to the fact
that decentralization deteriorates the quality of some public goods. On the other, he will
also consider that the cost of public goods will get higher the less decentralized the delivery
of these goods is. In this regard we should expect that the national median will be able to
accept more centralization the more sensitive to economies of scales is the particular public
good being considered and the more spillovers are likely to be produced by the local
provision of that good.
III.2
THE VOTER “i”.
Variable G in this case may be defined as a combination of n different public goods. The
effect of consuming public good xh by individual “i” will be inversely related to distance
between i’s preferences and the median voters’, which is defined by Panizza (1999) as
α[θlim + (1-θ)lij]. Parameter α represents the degree of diversity in the spectrum of
preferences among voters, θ is the degree of centralization, lim is the distance of individual i
from the national median and lij is the distance between individual i and the local median
voter. Note that Panizza assumes that the degree of decentralization is the same regardless
of the public good we are dealing with. An alternative interpretation is that both α as well
as θ represent a sort of average for all public goods, being this assumption compatible with
an aggregate analysis of decentralization.
The model being presented innovates in three basic aspects. In the first please it makes
explicit acknowledgement of the fact that not all public goods and services should be
subject to the same treatment as far as decentralization is concerned. In one extreme we
have the cases of genuinely national public goods as it is the case of national defense and
40
international relations, in which the median voter will certainly favor a rather centralized
provision. At the opposite extreme, although public functions as street improvement and
maintenance, garbage collection, local public infrastructure and the like will be usually
performed by decentralized levels of government, they are likely to exhibit a more
heterogeneous structure of State provision across countries.
A second innovation is the integration of cost factors related to the degree of
decentralization (Faguet, 2001). It is assumed that some public goods have technological
characteristics which turn them relatively more costly when they are provided by sub
national governments. This might be the case of tax collection or the provision of social
oriented public programs in which the central authorities have a cost advantage in their
administration.
As far as relative prices are concerned, the private good will be defined as a numerare.
Concerning public good prices, they are assumed to depend on the so called Scale Effect
parameter (ηh) This captures the cost saving effect of centralization. In the case that ηh= 0,
the price for each unit of public good will equal p*. We will call ph the unit price of the
specific public good named “h”. If θh < 1, ph will correspond to the waited average of the
centralized and non decentralized components of that public good. It follows that the price
being paid for the public good xh will be an inversed function of the degree of centralization
and the corresponding scale economies involved in the provision of that particular good. It
will be assumed that all jurisdictions have the same number of tax payers, so that no
reference is made to the effect of population itself in the unit price per unit of public good.
This leads to the following definition of ph:
p
h
⎡ P* ⎤
⎢
⎥
= θ ⎢ h ⎥ + (1 − θ ) P* = P*τ
h 1+ η
h
h
⎢
h⎥
⎣
⎦
;
⎡
θη ⎤
τ = ⎢1 − 1 +h ηh ⎥ ; τ < 0 , τ
⎢
⎣
⎥
h⎦
η
θ
<
0
(1)
In case θh = 1 and/or ηh = 0, it follows that p h = Ph* . Given that the marginal utility from
xh depends on the quantity as much as on the quality of it, a coefficient called πh will be
introduced to capture the probability that xh posses exactly those characteristics being
demanded by individual “i”, so that πh = πh[θh] and π h' < 0 . A maximum quality will be
achieved when πh = 1. In the opposite case, a very low quality leads to πh = 0. It will be
assumed that the specific knowledge on the median voters’ needs being held by the
current government is inversely related to the degree of centralization. Assuming that
there are n different public goods and a single private good, every voter will express his
demand on n+ 1 options, of which n are public goods and the remaining one is a private
good (it will be called “n+1”). Formally, this amounts to saying that every voter should
decide on his personal demand for every available option such as that;
x1 ≥ 0,L, xh ≥ 0,L xn ≥ 0, xn+1 ≥ 0 , where x1 ,L, xn represent the demands for every
public good and xn +1 is the demand for the private good. Individual prices are
represented by p1 > 0,L, ph > 0,L, pn > 0 for the n public goods and pn+1 = 1 for the
private good. Every voter solves the following problem, ∀ u : Ω ⊂ ℜ → ℜ and:
n+1
Ω = {(x , L , x , x
1
n
n+1
)∈ ℜ
n+1
x ,L , x , x ∈ ℜ }
1
n
n+1
40
Max u = ∏ xhπ δ x β
n
h
h
n+1
h =1
n
y = xn+1 + ∑ phxh
s/t
(2)
h =1
The solution for the generic public good xh and the private good xn+1 for voter “i” is the
following:
xhi =
πδ y
h hi i
pξ
x
(3A)
n + 1. i
h i
Where ξ i = β +
∑π δ
n
j=1
j
hi
=
βy
i i
ξ
(3B)
i
. and δhi = 1-αh[θh lim + (1- θh)lij]..Note that for a given level of
income, factors that determine demand for xhi are just three. One is the sensitivity of voter’s
“i” utility with regard to his distance from the median voter (δh). The second one is the
quality of xhi (πh) and the third one is the price of that public good. Such a price depends on
the technological characteristics of that particular good (ηh), and the degree of
centralization involved (θh).
III.3
THE NATIONAL MEDIAN VOTER.
Assuming that all individuals settled down at the local jurisdiction are located on the basis
of their preferences (Tiebout, 1956), and that space localization may be represented as a
continuum of symmetrically distributed jurisdictions around the median voter, Panizza
(1999) shows that the median voter will chose a national level of “x” such that
x m = μy m /(μ + β) and μ = 1-α[θ(S/4)+(1-θ)(S/4J)], where 1-μ may be interpreted as the
“ideological distance relative to the center”, S is the country’s territory and J is the number
of jurisdictions. Following Panizza [θ(S/4)+(1-θ)(S/4J)] must be interpreted as a “weighted
average of the median distance from the national median and the jurisdiction median”.
In the context so defined only a perfectly representative democracy is assumed to capture
the median voter’s preferences. On behalf of the median voter, the government decides the
degree of decentralization by setting the agenda through which it will push for as much
centralization as possible. As long as the political system becomes less democratic, the
opportunistic side of government will predominate as a result of centralization being a more
rent generating policy. The national median voter’s problem may be presented as follows:
Max: Um = Gmxmβ , Gm =
n
∏x
h =1
πhμhm
hm
(4)
40
∑p π
n
s/t
ym = xn+1 +
h =1
h
hm
The solution to (4) will be:
xhm =
π h μhmym
phξ m
x n+1.m =
for public good “h” (h ≤ n)
β ym
ξm
Where ξ m = β +
for private good n+1.
∑π μ
n
h =1
h
and . μhm = 1 − α⎡⎢θh 4 + (1 − θh ) 4J ⎤⎥
S
hm
S
⎣
⎦
Sub index “m” stands for “median voter”. Results in (4) only differ from (3) in the term
μhm , which corresponds to the expression δhi for the generic voter “i”.
III.4
THE GOVERNMENT´S PROBLEM.
The Central Government’s optimum.
Since government is assumed to know this median voter’s rationale, it will choose the
optimum level of decentralization by solving the following problem:
Max U
gov
= φU
+
m
(1 − φ)θ'G
θ
θ Lθ ⎤⎥
3
n⎦
; G' = ⎡⎢ p x
px
p x L p x ⎤⎥
2 2m
3 3m
n nm ⎦
⎣ 1 1m
m
θ' = ⎡⎢ θ
⎣
1
2
(5)
Under the assumption that n = 1, πh = 1, θh = θ and ph = p ∀h, the maximization of (5)
with respect to θ leads to the confirmation of Panizza’s results. Centralization will be
lower; i) the more the degree of differentiation in people’s preferences (α), ii) the more
democratic the country is (ϕ), iii) the higher the income per head and iv) the larger the
country’s territory (S). In the case at stake there will be a specific ph and θh for every
different public good, n > 1 and πh , ph ≤ 0. Assuming that n=2, it can be shown that
government’s optimum θh for h=1 will be the solution to (Appendix 1):
∂U gov
π2μ2 β
π1μ1 β
π1μ1 π2μ2
= ϕ x2 x3 A1 + x1 x3 A2 + x1 x2 A3 + (1 − ϕ) (p1x1 + θ1p1 A4 + θ1x1 A5 ) + (θ2 p2 A6 + θ2x2 A7 ) = 0
∂θ1
[
]
A1 =
∂x1
∂θ1
>
0
<
A4 =
∂x1
∂θ1
<
π1μ1
>
0
A2 =
∂x2
∂θ1
A5 =
∂p1
∂θ1
[
]
A3 =
∂x3
∂θ1
> 0
A6 =
∂x2
∂θ1
> 0
(6)
β
π2μ2
> 0
< 0
A7 =
∂p2
=0
∂θ1
40
It can be stated that two effects will be involved in the government’s optimum degree of
centralization on x1. Formally, this amounts to saying that θ = θ [π , p , ε] , where θ stands
for the government’s optimum. On the one hand, a more decentralized delivery of this
public good will improve its quality. This will be labeled the Von Hayek Effect (VHE) and
it will be captured by π 'h . The extent to which this will affect government’s welfare
positively depends on the strength on democracy (ϕ) and the degree to which a lower θ
expands government’s expenditures. On the other, a lower θ raises the price of xh, which
further reduces demand for x1.This will be called the Scale Effect (SE). Needless to say, the
above mentioned effects will have the opposite impact on xh≠1.We may expect that public
goods which can be easily substituted either by other public goods or by similar private
goods are less likely to be excessively centralized.
*
*
'
'
*
h
h
h
h
h
h
h
Proposition 1. In trying to set up the optimum degree of decentralization, the
central government will assign different degrees of centralization for different
public goods. The government’s optimum will differ across public goods, all
of them being (potentially) different from each other regarding their quality
sensitivity to decentralization (VHE), and the cost increasing effect of
decentralization (SE).
Separate mention deserves the effect of a change of θ on the weighted average of the
h
median distance from the national median and the jurisdiction median ( ∂μ ∂θ < 0 ). More
1
1
centralization lowers the median voter’s welfare as long as the number of jurisdictions is
higher than one (J > 1) (Appendix 1). This has two separate implications. One is the direct
impact on the median welfare, which is unambiguously welfare worsening for the non
opportunistic component of government (ϕ). The other one is the effect on government’s
expenditure as a whole induced by a lower demand on xh – and thereby- a higher demand
on xh≠1 , all of which is being filtered by the non democratic component of government’s
behaviour (1-ϕ). As opposed to both VHE and SE, the nature o this effect will equally
affect all public goods.
Proposition 2: As opposed to VHE and SE, the degree of centralization will
equally affect all public goods the weighted average of the median distance
from the national median and the jurisdiction median. Although more
centralization will unambiguously worsen the median voter’s welfare in this
regard, the central government will weight this against the chance of shifting
public goods demands toward other forms of public expenditures. That is to say:
∂μ1
∂θ1
=
∂μh
∂θh
∀h and
.
∂μ1
∂θh
= 0 ∀h ≠1 .
40
III.5
EXOGENOUS FACTORS IN THE DEGREE OF CENTRALIZATION.
Four exogenous factors will be considered to be relevant in determining the value of
∂U gov
∂θh
.
They are the median income voter’s income (y), the degree of heterogeneity in preferences
(α), the extension of the national territory (S) and the strength and depth of democratic
institutions (φ). The effect of the median voter’s income on the marginal utility of
centralization will tell us about the likely impact of growth on the country’s centralization
on a particular public good. It can be shown that for a generic public good xh (APENDIX 2)
for the case of h=1 and n=2), this has an ambiguous sign ∂ (U gov θ 1 ) ∂y
>
0 . The net
<
effect depends on the sign of ρ 2 = μhπ h' − (π h μh p h ) ph' which stands for the difference between
the price efficiency impact of centralization (SE) and the quality effect (VHE). As long as
this derivative is negative, it means that income lowers the government’s net benefit from
centralization. :If we look at APENDIX 2, it becomes clear that the net effect of S on θh
depends on the sign of (1/4J)-α. In a fully homogenous country (α = 0), ∂ (U gov θ h ) ∂S > 0 .
The opposite will occur as long as (1/4J) < α. This can be explained by saying that the
larger the territory the larger the weighted average of the median distance from the national
median and the jurisdiction median for public good h. Finally, the impact of a more
heterogeneous range of preferences (α.) is unambiguously negative on the government’s
marginal benefit from centralization.
IV
EMPIRICAL ANALYSIS.
The data:
The most common source for measuring FD is the Government Financial Statistics (GFS)
publication by the International Monetary Fund. Nevertheless, given that such a source
does not provide information on the tax-rate setting authority of sub-national
governments, some argue that the GFS-based proxy to FD is potentially misleading (Bahl,
1999). A recently published data base on FD for the OECD countries further divides tax
and grants between those under sub-national governments’ control and those regarded as
mere tax sharing arrangements. Although Ebel and Yilmaz (2003) show some evidence in
favor of using such a data set, two considerations should be made. One is that the data set
covers a relatively small group of countries for which these measurements are made for
only one year, which severely limits statistical analysis. The second is that, even if the GFS
figures might give an incorrect measurement of the degree of FD, there is no evidence of a
systematic measurement error across countries. Should that error be non-systematic, which
is most likely to occur, regression results will not be affected as long as the sample is large
enough. Although this study takes advantage of a panel in which numerous countries and
various years are combined, it maintains the standard use of the GFS figures on fiscal data.
Related data come from the World Development Indicators (1999), the United Nations
Statistical Year Book (1997), Sachs and Warner (1997), and The World Fact Book (1987).
40
The information on FD covers a sample of 64 countries for which data on local and/or state
governments is provided in the IMF Government Finance Statistics.
Methological Aspects
Regression analysis is done using an unbalanced panel of 64 countries for the (general)
government, and a subset of this panel in the cases of the functional expenditures. Yearly
frequency data are used between 1973 and 1997. A separate estimate is conducted for
three-year average data, which is meant to capture the long-term effects of the variables
being considered.
The basic model may be summarized as:
FDti = α + β1 X ti + β2 Zi + β3Qi + μti ,
(1)
where FD stands for Fiscal Decentralization, X accounts for the set of time-varying
variables that affect FD, Z captures country-specific characteristics for which only one
observation per country is available, and Q accounts for the country’s institutional factors.
Those variables included in X are income per capita (GDPCAP), population density
(DENSPOP), military expenditures as a share of central government expenditures
(MILGOV), trade orientation measured as the share of exports plus imports on the GDP
(TRADE), grants as a share of sub-national governments’ total revenues (GRG) and the
share of the urban population as a proxy of urbanization (URBAN). The social
heterogeneity indexes GINI, ETHNIC, and HI form the vector Z; see the Appendix for
details. There is only one observation on these last three variables for each country, and
some of the countries in the sample are not represented. The vector Q includes two
institutional variables: a dummy for constitutional federations (CSTAT), and a dummy for
non-democratic countries (PSTAT).
The estimation procedure follows a methodology proposed by Reilly and Witt (1996),
which consists of estimating the model in two separate stages. In the first stage, a fixed
effect panel data estimation is conducted with the set of explanatory variables for which a
significant variation is likely to be observed over time, all of which are grouped in vector
Xti (equation (2) below). In the second stage, the estimated country fixed effects from
∧
equation 2 (vector α ∗ ) are regressed on Z and Q together (equation (3) below):
FDti =αi∗ + β1∗ X ti + μti∗
∧
αi∗ = δ + β 2∗Zi + β3∗ Qi + ε i∗
(2)
(3)
Relative to a single stage estimation of equation (1), this procedure saves degrees of
freedom at each separate stage, and it avoids the potential for collinearity in equation (1)
arising from the fixed effect country dummies and the set of time invariant variables
included in vectors Z and Q.
40
In order to address the issue of likely different behavior between high and low income
countries, three sets of estimations of equation 1 are performed. All of them are repeated
for the two general indexes of Fiscal Decentralization (EFD and RFD). The first one takes
data from the 32 richer countries in the sample (according to the GDPCAP), while the
second is for the 32 low-income countries only. The third estimation uses the whole
sample. In this last case the estimation is repeated for annual and three-year average data.
The General Government Definition of FD
The first estimation results are in Table1. With the exception of MILGOV and GRG, all the
variables are expressed in natural logarithms (L). The potential endogenously of grants was
considered by performing a Hausman test on regression Model 4, and no statistical
evidence of endogenously was found. Time effects of regressions are removed, and the
equation is re-estimated whenever these effects are statistically non-significant.
The effect of GDPCAP is clearly positive and significant for the high-income sub-sample
and for the whole sample. The fact that low-income countries are statistically responsive to
income suggests the likelihood of some kind of threshold in the responsiveness of FD with
respect to income (Wasylenko 1987). Although GDPCAP is just below significance in the
three-year average sample (Model 5), it keeps the same sign and roughly the same value as
the other estimations.
Urbanization has a systematically negative effect on FD, which is clearly stronger among
low-income countries. As stated above, the reason probably lies in the fact that very often
low-income countries have only one or two large cities, from which most public affairs are
overseen. Although the political economy of such a phenomena might be difficult to
identify in statistical terms, this sheds light upon the fact that some Latin American
countries are very centralized and that they have a large proportion of their populations
living in few very large cities.
MILGOV has the expected sign, as does grants (GRG). In this last case, transfers do appear
to have an impact on sub-national governments’ expenditures. It must be noted, however,
that in most countries an important proportion of these grants is categorical. The impact of
population (DENSPOP) is unambiguously positive, and this effect appears to be stronger
among low-income countries. Once again, a feasible explanation is that there is a threshold
in terms of GDPCAP, after which the effect of population becomes more evident. Effective
FD might be feasible as long as a minimum number of taxpayers can afford the cost of
some local public goods.
As for the revenue definition of FD (RFD), results in Table 2 tend to confirm the same
hypotheses that were previously tested for EFD. The only difference between this set of
estimations and the ones reported for EFD is the absence of GRG in the regressions.
Although a direct causality might be expected from grants onto expenditures, this
relationship is not theoretically clear when it comes to grants. It is certainly worth noting
from Table 3 that both the magnitude and the sign of the estimated coefficients are
reasonably stable in the three sets of estimations. Interestingly, LURBAN appears to be
40
significant for the low-income countries only, which confirms the result achieved when
using the expenditure definition of FD in Table 1. Although LTRADE has the anticipated
sign in all the parsimonious estimations for each sample (Models 2, 4, and 8), it only
becomes significant when the whole sample is used (Model 8). Note that the t-ratios are
higher for low-income countries.
The second stage of the regression analysis is shown in Table 3. Two basic points can be
made. The first is that none of the diversity indexes appears to explain EFD or RFD,
although it should be noted that many of the countries in the regressions reported in Table 1
and 2 do not have information on these diversity indexes, so that the sample becomes
considerably smaller. The second point is that, as expected, federal and democratic
countries appear to be more decentralized.
A relevant question is the extent to which decentralization can be autonomously induced by
the political authority. One interpretation of these results argues that the government may
spur decentralization indirectly through the impact of public policies on income per capita,
urbanization, military expenditures and population density. Moreover, as long as the
political authority can determine the amount of grants being given to sub-national
governments, the regression analysis suggests that this is a direct channel to decentralize.
Alternatively, it can be assumed that all of the variables considered in the regressions are
exogenous to the government in office. If this were the case, the natural evolution of these
variables over time would change the preferences of the median voter, forcing the
government to decentralize. In this context, decentralization can be seen as an endogenous
process that responds to political demands. Nevertheless, results in Table 4 show that only
between 7 percent and 27 percent of the residuals obtained in stage one are explained by the
econometric analysis. A natural next step would therefore be to examine the pattern of
residuals and the share of their variation left unexplained by the regressions. The next
section performs this analysis.
V.
CONCLUDING REMARKS
In general, the results achieved with the general government definition of fiscal
decentralization confirm some previous findings. In particular, positive effects using a
broad definition of FD are found for the cases of income, population density, and
government grants. As opposed to previous studies, urbanization has a negative effect.
Constitutional federations and democratic governments exhibit a higher degree of FD.
Neither population diversity nor income distribution has a significant impact.
Interesting differences arise when closer examination is made of the two generic definitions
of FD (EFD and RFD) and the estimation of the model for two separate samples (high- and
low-income countries). First, the effect of income is stronger for high-income countries,
which suggests the existence of a threshold above which a higher income leads to more FD.
Another difference concerns urbanization, which is significant for low-income countries
only. When it comes to the revenue definition of FD (RFD), population density is only
significant in high-income countries.
40
As opposed to the general government definition of FD, specific public goods can be said
to differ in two aspects. One is the potential for information benefits from decentralization
(VHE) and the second is the cost increasing effect of it.(SE). Both in the cases of housing
and health, the fact that income has a negative impact on decentralization reveals that cost
effect predominates. The opposite occurs in education, in which the positive sign of income
reveals that information benefits are more important.
40
APPENDIX 1
Government’s optimum degree of centralization
The Optimization of Government:
∂Ugov
= γ 1 + γ 2 π'1 + γ 3 p'1 = 0
∂θ1
γ 1 = ϕ(x2π2μ2x3β σ11 + x1π1μ1x3β σ21 + x1π1μ1x2π2μ2σ31 ) + (1−ϕ )(p1x + θ1σ41 + θ2 p2σ61 )
γ 2 = ϕ(x2π2μ2x3β σ12 +1π1μ1 x3β σ22 + x1π1μ1x2π2μ2σ32 ) + (1−ϕ )(θ1σ42 + θ2 p2σ62 )
γ 3 = ϕx2π2μ2x3β σ13p'1 + (1−ϕ )(θ1σ43 + θ2x)
∂U
= ϕ[x x A + x x A + x x A ] + (1 − ϕ)[(p x + θ p A + θ x A ) + (θ p A + θ x A )] = 0
∂θ
π2μ2
β
2
3
gov
1
π1μ1
β
1
3
2
π1μ1
π2μ2
1
2
3
1
1
1
1
4
1
1
5
2
2
6
2
2
7
A1.1
1
∂x
∂(lnx )⎤ >
′
⎡
= x ⎢(π μ ) (ln x ) + π μ
0
∂θ
∂θ ⎥⎦ <
⎣
yp ⎛ π μ ⎞ ⎛
Sα
∂x
(1 − J )⎞⎟ > 0
A =
=− x
⎜
⎟ ⎜μ π + π
x ⎝ pξ ⎠ ⎝
4J
∂θ
⎠
A=
π 1 μ1
π 1 μ1
1
1
1
1
1
1
1
1
1
1
1
2
π2 μ 2
π 2 μ2
2
2
2
1
2
2
1
A =
3
'
2
2
∂x
∂θ
β
3
1
1
1
2
βy ∂ξ
= − ξ ∂θ = − ξ ⎡⎢μ π + π 4J (1 − J )⎤⎥ > 0
⎣
⎦
βy
2
Sα
'
2
1
1
1
1
⎛ yπ Sα(1 - J ) yμ
∂x
π μ y ⎛ Sα(1 - J)
⎞⎞ >
= ⎜⎜
π−
+
+ ξp ⎟ ⎟⎟
⎜p
p
ξ
4J
p
ξ
4J
∂θ
(
)
p
ξ
⎠⎠ <
⎝
⎝
∂p
A =
= p ≤ 0
∂θ
A =
1
1
1
4
'
1
5
'
1
1
2
1
1
1
1
1
6
'
∂x
π μy ⎛
⎛ ∂μ
=−
∂θ
(p ξ ) p ⎜⎜⎝ μπ + π ⎜⎝ ∂θ
2
7
2
'
2
2
1
A =
0
1
1
A =
1
1
2
2
11
1
1
1
⎞⎞
⎟ ⎟⎟ > 0 ;
⎠⎠
∂μ Sα(1 − J )
=
4J
∂θ
1
1
∂p
=0
∂θ
2
1
Identification of Von Hayek and scale effects:
Substituting A1 to A6 into A2.1, the general expression for
∂U gov
∂θ1
∂U gov
∂θ1
can be rewritten as:
= ϕ [x 2π2μ2 x 3β (σ 11 + σ 12 π '1 + σ 13 p1' ) + x 1π1μ1 x 3β (σ 21 + σ 22 π '1 ) + x 1π1μ1 x 2π2μ2 (σ 31 + σ 32 π '1 )]
+ (1 − ϕ )[(p1 x 1 + θ1 (σ 41 + σ 42 π '1 + σ 43 p1' ) + θ1 x 1 p'1 ) + (θ 2 p 2 (σ 61 + σ 62 π '1 ))] = 0
A1.2
By grouping similar terms,. A1.2 can be written as:
40
⎡⎛ Sα
1 y
(1 − J )⎞⎟(lnx1 ) + μ1 π 1
σ 11 = x1π1 μ1 ⎢⎜ π 1
4J
x
⎝
⎠
1 p1ξ
⎣⎢
⎛ Sα
π1 μ1
⎜ π1
⎜ 4J (1 − J ) − p ξ
1
⎝
⎡
1 yμ1
1 y
σ 12 = x1π1μ1 ⎢(lnx1 )μ1 + π 1 μ1
- μ1 π 1
x
p
ξ
x
1
1
1 p1ξ
⎣⎢
⎤
⎛ π1 μ1 ⎞
⎜⎜
⎟⎟ p1 μ1 ⎥
⎝ p1ξ ⎠
⎦⎥
⎛ ⎡ Sα
⎞ ⎞⎤
(1 − J )⎤⎥ ⎟⎟ ⎟⎟⎥
⎜⎜ p1 ⎢ π 1
⎦ ⎠ ⎠⎦⎥
⎝ ⎣ 4J
⎡
1 y π1 μ1 ⎤
σ 13 = − ⎢ x1π1 μ1 μ1 π 1
⎥
x1 p1ξ p1 ⎦
⎣
⎡ βy
⎤
Sα
(1 − J )⎥
σ 31 = − ⎢ 2 π 1
4J
⎣⎢ ξ
⎦⎥
⎡ βy ⎤
σ 32 = − ⎢ 2 μ1 ⎥
⎢⎣ ξ
⎥⎦
⎛ yπ Sα (1 - J ) π 1 μ 1 y
Sα (1 - J) ⎞
⎟
σ 41 = ⎜⎜ 1
−
p1
2
p
ξ
4J
4J ⎟⎠
(
)
p
ξ
1
⎝ 1
σ 42 = −
π 1 μ1 y
(p ξ )
2
1
σ 43 = −
π 1 μ1 y
(p ξ )
2
1
σ =−
61
π μy
(p ξ )
2
2
2
2
σ =−
62
π μy
(p ξ )
2
2
2
⎛ ∂μ ⎞
pπ⎜
⎟
⎝ ∂θ ⎠
1
2
1
1
pμ
2
1
2
40
APENDIX 3
Exogenous factors on Centralization
The Median Voter’s income (y):
Let us write
∂U gov
∂θ1
U gov
∂θ 1
as follows:
= φ[B1 + B2 + B3 ] + (1 − φ)[B4 + B5 ] = 0
Th
B1 = x
π 2 μ2
2
x A1
β
3
B2 = x
π1μ1
1
∂
us, we have to solve for
•
B3 = x
x A2
β
3
π 1 μ1
1
x
π 2 μ2
2
A3
B4 = p1x1 + θ1 p1 A4 + θ1x1 A5
U gov
∂θ 1
∂y
⎡ ∂B
⎡ ∂B1 ∂B2 ∂B3 ⎤
∂B ⎤
+
+
+ (1 − φ)⎢ 4 + 5 ⎥ = 0 ,
⎥
∂y
∂y ⎦
∂y ⎦
⎣ ∂y
⎣ ∂y
= φ⎢
in which:
∂B1
∂x β
∂A
∂x π 2 μ 2
= x 2π 2 μ2 x 3β 1 + x 2π 2 μ 2 A1 3 + x 3β A1 2
∂y
∂y
∂y
∂y
⎡
y
A1 = x1π1μ1 ⎢ A13 (lnx 1 ) + μ1 π 1
x 1 p1 ξ 1
⎣⎢
⎛
⎞ > ⎤
πμ
⎜⎜ π1 ρ1 A11 + ρ 2 − 1 1 ( p1 μ1 A12 )⎟⎟
0⎥
p1ξ
⎝
⎠ < ⎥⎦
⎛ ∂lnx1 ⎞
⎟
∂⎜⎜
∂θ1 ⎟⎠ 1 1
∂A1
⎝
[π1 ρ1 A11 + ρ 2 ]× 1 − ηyx1
=
=
∂y
∂y
x1 p1ξ
[
ρ1 = 1 −
A11 =
0
Sα
(1 − J ) < 0
4J
β
= x 1π 1μ1 x 3β
<
⎛
⎞
πμ
ρ2 = ⎜⎜ μ1 A12 − 1 1 A14 ⎟⎟
p
1
⎝
⎠
A13 = μ1 π '1 + π 1 A11 < 0 A14 = p1' < 0
∂x 3β ⎡ β ⎤
=
y β −1 > 0
∂y ⎢⎣ ξ ⎥⎦
∂B2
∂y
>
]
π 1 μ1
>0
ξ
A12 = π1' < 0
y ∂x1
>0
ηyx1 =
x1 ∂y
•
B5 = θ2 p2 A6 + θ2x2 A7
∂x2π 2 μ 2
∂y
= π 2 μ2 xπ 2 μ 2
1
>0
y
∂x β
∂A2
∂x π 1μ 1
+ x1π 1μ 1 A2 3 + x 3β A2 1
∂y
∂y
∂y
∂A2
=
∂y
∂
∂x2π2 μ2
2
⎛ π 2 μ2 ⎞
∂θ1
π 2 μ2
⎟⎟ × 1 − ηyx1
= − x2 p2 A11 ⎜⎜
∂y
⎝ p2 ξ ⎠
[
]
>
0
<
40
∂x3β
β
= β x3β −1
∂y
ξ
∂B 3
∂y
•
= x1π1μ1 x2π 2 μ 2
>0
1
∂x1π 1μ1
>0
= π 1 μ1 x π 1μ1
∂y
y
∂A3
∂x π 2 μ 2
∂x π 1μ 1
+ x1π 1μ 1 A3 2
+ x2π 2 μ 2 A3 1
∂y
∂y
∂y
xβ
∂A3
β Sα
∂y
(1 − J ) > 0
=− 2
=
ξ 4J
∂y
∂y
∂
⎛ ∂A5
∂B4
∂x
∂A4
∂x ⎞
= p1 1 + θ1 p1
+ θ1 ⎜⎜ x 1
+ A5 1 ⎟⎟
∂y
∂y
∂y
y
∂
∂y ⎠
⎝
•
⎛ ∂x ⎞
∂⎜⎜ 1 ⎟⎟
>
∂θ
∂A4
1
[π1 ρ1 A11 + ρ2 ]
= ⎝ 1⎠ =
0
<
∂y
∂y
p1ξ
∂x 1
∂y
=
π 1 μ1
p1ξ
∂A
=0
∂y
5
∂B5
∂A
∂A
∂x
= θ 2 p 2 6 + θ 2 x 2 7 + θ 2 A7 2
∂y
∂y
∂y
∂y
•
∂A6
=
∂y
∂
∂x 2
π μ
∂θ1
= − 2 22 p 2 A13 > 0
(p2ξ )
y
∂A
=0
∂y
7
The surface of the country(S):
∂
•
U gov
∂θ 1
∂S
∂B ⎤
∂B1 ∂B2 ∂B3 ⎤
⎡ ∂B
+
+
+ (1 − φ)⎢ 4 + 5 ⎥ = 0
⎥
∂S
∂S ⎦
∂S ⎦
⎣ ∂S
⎣ ∂S
= φ ⎡⎢
∂x β
∂A
∂x π 2 μ 2
∂B1
= x 2π 2μ2 x 3β 1 + x2π 2 μ 2 A1 3 + x3β A1 2
∂S
∂S
∂S
∂S
∂A1 ∂a11 ∂a12
+
=
∂S
∂S
∂S
40
∂ a 11
∂ lnx 1 ⎞ ⎛ Sα
⎛ ∂ x π1 μ 1
⎛ Sα
(1 − J ) + μ 1 π 1' ⎞⎟⎛⎜
(1 − J ) + μ 1 π 1' ⎞⎟ (ln x 1 )⎜⎜ 1
= x 1π1μ1 ⎜ π 1
⎟ + ⎜ π1
∂S
⎠
⎝ 4J
⎠ ⎝ ∂ S ⎠ ⎝ 4J
⎝ ∂S
⎛π α
⎛ ∂μ
+ x 1π1μ1 (ln x 1 )⎜⎜ 1 (1 − J ) + π 1' ⎜ 1
⎝ ∂S
⎝ 4J
⎞
⎟⎟
⎠
⎞⎞
⎟ ⎟⎟
⎠⎠
⎛ Sα
⎞⎛ ∂x π1μ1 ⎞
π μ p π Sα
∂a12
(1 − J ) + μ1π 1' − 1 1 ⎛⎜ 1 1 + ξp1' ⎞⎟ ⎟⎟⎜⎜ 1 ⎟⎟
= y ⎜⎜ π 1
p1 ξ ⎝ 4J
∂S
⎠ ⎠⎝ ∂S ⎠
⎝ 4J
⎛π α
∂ξ ⎞⎤ ⎞
⎛ pπ α
⎞⎛ ∂x ⎞
⎛ ∂μ ⎞ ⎡⎛ p π Sα
+ x1π1μ1 ⎜⎜ 1 (1 − J ) + π 1' ⎜ 1 ⎟ − ⎢⎜ 1 1 + ξp1' ⎟⎜ 1 ⎟ + x1 ⎜ 1 1 + p1'
⎟ ⎟
∂S ⎠⎥⎦ ⎟⎠
⎝ 4J
⎠⎝ ∂S ⎠
⎝ ∂S ⎠ ⎣⎝ 4J
⎝ 4J
•
∂B2
∂S
= x1π1μ1 x 3β
∂x β
∂A2
∂x π 1μ1
+ x1π 1μ1 A2 3 + x3β A2 1
∂S
∂S
∂S
⎡⎛
⎛π μ
∂A2
Sα
(1 − J )⎞⎟⎜⎜ 2 2
= − ⎢⎜ μ1 π '1 + π 1
∂S
4J
⎠⎝ ξ
⎣⎢⎝
⎛ ∂x 2π2μ2
⎜⎜
⎝ ∂S
⎞ π2μ2 π 2 ⎛ ∂μ 2 ⎞ π2μ2 π 2 μ 2
⎟⎟ + x2
⎜
⎟ − x2
ξ ⎝ ∂S ⎠
ξ2
⎠
⎛ ∂ξ ⎞ ⎞⎟⎤
⎜ ⎟ ⎟⎥
⎝ ∂S ⎠ ⎠⎦⎥
⎡
⎤
π μ ⎛ ∂μ
α
(1 − J )⎞⎟⎥
− ⎢ x2π2μ2 2 2 ⎜ π '1 1 + π 1
ξ ⎝ ∂S
4J
⎠⎦
⎣
•
∂B3
∂S
= x 1π1μ1 x2π 2 μ 2
∂A3
∂x π 1μ 1
∂x π 2 μ 2
+ x 2π 2 μ 2 A3 1
+ x1π 1μ1 A3 2
∂S
∂S
∂S
⎡β ⎛
⎛ ⎛ ∂x β ⎞
∂A3
Sα
1 ∂ξ ⎞⎤
(1 − J )⎞⎟⎜⎜ ⎜⎜ 3 ⎟⎟ − x3β ⎛⎜ ⎞⎟ ⎟⎟⎥
= − ⎢ ⎜ μ1 π '1 + π 1
∂S
4J
ξ ⎝ ∂S ⎠ ⎠⎦⎥
⎠⎝ ⎝ ∂S ⎠
⎢⎣ ξ ⎝
⎡ β ⎛ ∂μ
⎤
α
(1 − J )⎞⎟⎥
− ⎢ x3β ⎜ π '1 1 + π 1
4J
∂S
⎠⎦
⎣ ξ⎝
•
∂x ⎞
∂A4
∂x
∂B4
⎛ ∂A5
+ θ1 ⎜ x 1
+ A5 1 ⎟
= p1 1 + θ1 p1
∂S ⎠
∂S
∂S
∂S
⎝ ∂S
∂x1
∂θ 1
yπ 1 α (1 - J ) ⎛
∂A4
1 ∂ξ ⎞ ⎛ yπ ' ⎛ ∂μ ⎞ yπ ' μ ∂ξ ⎞
⎜⎜ 1 − ⎛⎜ ⎞⎟ ⎟⎟ + ⎜⎜ 1 ⎜ 1 ⎟ − 1 21 ⎛⎜ ⎞⎟ ⎟⎟
=
=
∂S
ξ p1 4J ⎝
ξ ⎝ ∂S ⎠ ⎠ ⎝ p1 ξ ⎝ ∂S ⎠ p1 ξ ⎝ ∂S ⎠ ⎠
∂S
∂
⎛ 1 ⎛ Sα (1 - J)
1 ⎛ α (1 - J)
⎞⎛ ∂x ⎞
⎛ Sα (1 - J)
⎞ 1 ⎛ ∂ξ ⎞
⎛ ∂ξ ⎞ ⎞ ⎞
− ⎜⎜
+ ξp1' ⎟⎜ 1 ⎟ − x1 ⎜ p1
+ ξp1' ⎟ 2 ⎜ ⎟ + x1
+ p1' ⎜ ⎟ ⎟ ⎟⎟
⎜ p1
⎜ p1
∂
∂
4J
S
4J
S
4J
ξ
p
ξ
p
ξ
⎝
⎠
⎝
⎠
⎝
⎠
⎝ ∂S ⎠ ⎠ ⎠
⎝
⎠
1 ⎝
⎝ 1
40
•
∂A5
=0
∂S
•
∂B5
∂A6
∂x
∂A7
= θ2 p2
+ θ2x2
+ θ 2 A7 2
∂S
∂S
∂S
∂S
∂x
∂ 2
⎛ ∂μ ⎞ ⎞⎛ 1 ⎛ ∂x ⎞
∂A6
∂θ1 ⎛⎜ '
1 ⎛ ∂ξ ⎞ ⎞
=
− π 1 μ1 + π 1 ⎜⎜ 1 ⎟⎟ ⎟⎜⎜ ⎜ 2 ⎟ − x2 2 ⎜ ⎟ ⎟⎟
⎜
⎟
∂S
∂S
ξ ⎝ ∂S ⎠ ⎠
⎝ ∂θ1 ⎠ ⎠⎝ ξ ⎝ ∂S ⎠
⎝
−
(1 − J ) ⎞⎟
1 ⎛ ' ⎛ ∂μ1 ⎞
x2 ⎜⎜ π 1 ⎜
⎟ + π 1α
ξ ⎝ ⎝ ∂S ⎠
4J ⎟⎠
∂A7
=0
∂S
Other parial derivates:
⎡1
⎤ >
∂μh
= θh ⎢ − α ⎥
0
∂S
⎣ 4J
⎦ <
∂xh π 1 y ⎡ ⎡ 1
⎤ μ ⎛ ∂ξ ⎞⎤
=
− α ⎥ − h ⎜ ⎟⎥
θh
∂S p hξ ⎢⎣ ⎢⎣ 4 J
⎦ ξ ⎝ ∂S ⎠⎦
⎡
μ ⎛ ∂x ⎞⎤
∂xhμhπh
= x hμhπh π h ⎢lnx h + h ⎜ h ⎟⎥
∂S
x h ⎝ ∂S ⎠⎦
⎣
h= 1, 2
⎡1
⎤
∂ξ
= ( π 1 + π 2 )θ1 ⎢ − α ⎥
∂S
4J
⎣
⎦
βy ⎛ ∂ξ ⎞
∂x 3
=− 2 ⎜ ⎟
∂S
ξ ⎝ ∂S ⎠
Heterogeneity of preferentes (α):
∂
•
U gov
∂θ 1
∂α
∂B1 ∂B 2 ∂B 3 ⎤
⎡ ∂B 4 ∂B 5 ⎤
+
+
⎥ + (1 − φ)⎢ ∂α + ∂α ⎥ = 0
α
α
α
∂
∂
∂
⎦
⎣
⎦
⎣
= φ ⎡⎢
∂x β
∂B1
∂A
∂x π 2 μ 2
= x 2π 2μ2 x 3β 1 + x 2π 2 μ 2 A1 3 + x3β A1 2
∂α
∂α
∂α
∂α
∂A1 ∂a11 ∂a12
=
+
∂α
∂α
∂α
40
∂a11
∂lnx 1 ⎞ ⎛ Sα
⎛ ∂x π1μ1
⎛ Sα
(1 − J ) + μ1π 1' ⎞⎟⎛⎜
(1 − J ) + μ1π 1' ⎞⎟(ln x1 )⎜⎜ 1
= x1π1μ1 ⎜ π 1
⎟ + ⎜ π1
∂α
⎠
⎝ 4J
⎠⎝ ∂α ⎠ ⎝ 4J
⎝ ∂α
⎞
⎟⎟
⎠
⎛π α
⎛ ∂μ ⎞ ⎞
+ x1π1μ1 (ln x1 )⎜⎜ 1 (1 − J ) + π 1' ⎜ 1 ⎟ ⎟⎟
4J
⎝ ∂α ⎠ ⎠
⎝
⎞⎛ ∂x π1μ1
⎛ Sα
∂a 12
π μ p π Sα
(1 − J ) + μ 1 π 1' − 1 1 ⎛⎜ 1 1 + ξp 1' ⎞⎟ ⎟⎟⎜⎜ 1
= y ⎜⎜ π 1
∂S
p 1 ξ ⎝ 4J
⎠ ⎠⎝ ∂S
⎝ 4J
⎞
⎟⎟
⎠
⎛π α
∂ξ ⎞⎤ ⎞⎟
⎛ ∂μ ⎞ ⎡⎛ p π Sα
⎞⎛ ∂x ⎞
⎛pπ α
+ x 1π1μ1 ⎜⎜ 1 (1 − J ) + π 1' ⎜ 1 ⎟ − ⎢⎜ 1 1 + ξp 1' ⎟⎜ 1 ⎟ + x 1 ⎜ 1 1 + p 1'
⎟⎥
∂α ⎠⎦ ⎟⎠
⎝ ∂α ⎠ ⎣⎝ 4J
⎠⎝ ∂α ⎠
⎝ 4J
⎝ 4J
•
∂B2
∂α
= x1π1μ1 x 3β
∂x β
∂A2
∂x π 1μ1
+ x1π 1μ1 A2 3 + x3β A2 1
∂α
∂α
∂α
⎡⎛
⎛π μ
∂A2
Sα
(1 − J )⎞⎟⎜⎜ 2 2
= − ⎢⎜ μ1 π '1 + π 1
∂S
4J
⎠⎝ ξ
⎢⎣⎝
⎛ ∂x 2π2μ2
⎜⎜
⎝ ∂α
⎞ π2μ2 π 2 ⎛ ∂μ 2 ⎞ π2μ2 π 2 μ 2
⎟⎟ + x2
⎟ − x2
⎜
ξ ⎝ ∂α ⎠
ξ2
⎠
⎛ ∂ξ ⎞ ⎞⎟⎤
⎟ ⎥
⎜
⎝ ∂α ⎠ ⎟⎠⎥⎦
⎡
⎤
π μ ⎛ ∂μ
α
(1 − J )⎞⎟⎥
− ⎢ x2π2μ2 2 2 ⎜ π '1 1 + π 1
∂
ξ
S
4J
⎝
⎠⎦
⎣
•
∂B3
∂α
= x 1π1μ1 x2π 2 μ 2
∂A3
∂x π 2 μ 2
∂x π 1μ 1
+ x1π 1μ1 A3 2
+ x 2π 2 μ 2 A3 1
∂α
∂α
∂α
⎡β ⎛
⎛ ⎛ ∂x β ⎞
∂A3
Sα
1 ∂ξ ⎞⎤
(1 − J )⎞⎟⎜⎜ ⎜⎜ 3 ⎟⎟ − x3β ⎛⎜ ⎞⎟ ⎟⎟⎥
= − ⎢ ⎜ μ1 π '1 + π 1
4J
∂α
ξ ⎝ ∂α ⎠ ⎠⎥⎦
⎠⎝ ⎝ ∂α ⎠
⎢⎣ ξ ⎝
⎡ β ⎛ ∂μ
⎤
α
(1 − J )⎞⎟⎥
− ⎢ x3β ⎜ π '1 1 + π 1
4J
⎠⎦
⎣ ξ ⎝ ∂α
•
∂B4
∂x
∂A4
∂x ⎞
⎛ ∂A5
= p1 1 + θ1 p1
+ θ1 ⎜ x 1
+ A5 1 ⎟
∂α
∂α
∂α
∂α ⎠
⎝ ∂α
∂x1
1 ∂ξ ⎞ ⎞ ⎛ yπ1' ⎛ ∂μ1 ⎞ yπ1' μ1 ⎛ ∂ξ ⎞ ⎞
∂A4
∂θ1 yπ 1 α (1 - J ) ⎛
⎜⎜ 1 − ⎛⎜
=
=
⎜
⎟−
⎟⎟ + ⎜
⎜
⎟⎟
ξ p1 4J ⎝
ξ ⎝ ∂α ⎠ ⎟⎠ ⎜⎝ p1ξ ⎝ ∂α ⎠ p1ξ 2 ⎝ ∂α ⎠ ⎟⎠
∂α
∂α
∂
⎛ 1 ⎛ Sα (1 - J)
1 ⎛ α (1 - J)
⎛ ∂ξ ⎞ ⎞ ⎞⎟
⎞⎛ ∂x ⎞
⎛ Sα (1 - J)
⎞ 1 ⎛ ∂ξ ⎞
− ⎜⎜
+ ξp1' ⎟⎜ 1 ⎟ − x1 ⎜ p1
+ ξp1' ⎟ 2 ⎜
⎜⎜ p1
+ p1' ⎜
⎟ + x1
⎟ ⎟⎟
⎜ p1
4J
p
ξ
4J
p
ξ
4J
α
ξ
α
∂
∂
⎠⎝
⎠
⎝
⎠ ⎝
⎠
⎝ ∂α ⎠ ⎠ ⎟⎠
1 ⎝
⎝ 1 ⎝
•
∂A5
=0
∂α
40
•
∂B5
∂A6
∂A7
∂x
= θ2 p2
+ θ2x2
+ θ 2 A7 2
∂α
∂α
∂α
∂α
∂x 2
⎛ ∂μ ⎞ ⎞⎛ 1 ⎛ ∂x
∂A6
∂θ1 ⎛⎜ '
=
− π 1 μ1 + π 1 ⎜⎜ 1 ⎟⎟ ⎟⎜⎜ ⎜ 2
⎜
⎟
∂α
∂α
⎝ ∂θ1 ⎠ ⎠⎝ ξ ⎝ ∂α
⎝
∂
−
1 ⎛ ∂ξ ⎞ ⎞
⎞
⎟ − x2 2 ⎜
⎟ ⎟⎟
ξ
⎝ ∂α ⎠ ⎠
⎠
(1 − J ) ⎞⎟
1 ⎛ ' ⎛ ∂μ1 ⎞
x2 ⎜⎜ π 1 ⎜
⎟ + π 1α
ξ ⎝ ⎝ ∂α ⎠
4J ⎟⎠
∂A7
=0
∂α
Other parial derivates:
∂μ1
S ⎞
⎛ S
= − ⎜ θ1 + (1 − θ1 ) ⎟
4J ⎠
∂α
⎝ 4
⎡
μ ⎛ ∂x ⎞⎤
∂x1μ1π1
= x1μ1π1 π 1 ⎢lnx 1 + 1 ⎜ 1 ⎟⎥
∂α
x1 ⎝ ∂α ⎠⎦
⎣
∂x1 π 1 y ⎡⎛ ∂μ1 ⎞ μ 1 ⎛ ∂ξ ⎞⎤
=
⎟− ⎜
⎟⎥
⎢⎜
p1ξ ⎣⎝ ∂α ⎠ ξ ⎝ ∂α ⎠⎦
∂S
⎡
μ ⎛ ∂x
∂x2μ2π 2
= x2μ2π2 π 2 ⎢lnx 2 + 2 ⎜ 2
∂α
x2 ⎝ ∂α
⎣
∂μ 2
∂μ 1
∂ξ
+ π2
= π1
∂α
∂α
∂α
βy ⎛ ∂ξ ⎞
∂x 3
=− 2 ⎜
⎟
ξ ⎝ ∂α ⎠
∂α
⎞⎤
⎟⎥
⎠⎦
40
APPENDIX 3
Empirical Analysis
Table 1. Panel Data: General Government Expenditure Fiscal Decentralization
High Income
Countries
Model 1
Model 2
Constant
-0.547
(-0.392)
7.994
(3.784)**
LGDPCAP
0.185
(2.179)**
-0.082
(-0.626)
LURBAN
0.215
(0.779)
Model 5
5.043
(6.413)**
5.081
(5.425)**
0.011
(0.087)
0.154
(2.265)**
0.106
(1.565)
-2.50
(-7.301)**
-2.632
(-7.461)**
-1.404
(-8.194)**
-1.488
(-5.872)**
-0.008
(-2.845)**
-0.016
(-2.433)**
-0.020
(-2.45)**
-0.009
(-3.241)**
-0.005
(-1.01)
GRG
0.004
(4.737)**
0.005
(2.618)**
0.006
(2.578)**
0.005
(6.108)**
0.006
(4.953)**
LDENSPOP
0.309
(1.937)*
1.192
(2.164)**
1.387
(4.301)**
0.644
(4.060)**
0.823
(3.57)**
Area Fixed
Effect:
Df
Yes
30
1531.20**
Yes
32
678.65**
Yes
32
678.65**
Yes
62
2352.715**
Yes
62
1162.26**
Time Effect:
Df
Yes
25
14.135
NO
χ2
Yes
27
87.469**
Yes
27
44.871**
Yes
9
22.423**
Observations
Adj R2
546
0.957
292
0.914
292
0.919
837
0.949
318
0.972
χ2
Model 3
Whole Sample
Model 4
MILGOV
*
Low Income
Countries
Significant at 10%. * * Significant at 5%. t-statistics are in parentheses. Model 5 uses the three-year average sample.
40
Table 2. Panel Data: General Government Revenue Fiscal Decentralization
High Income Countries
Model 1
Model 2
Model 4
-0.651
(-0.429)
4.713
(3.152)**
Model 5
Whole Sample
Model 6
Model 7
5.025
(3.260)
3.062
(3.792)**
Model 8
Model 9
Model 10
Constant
-2.471
(-1.354)
LGDPCAP
0.310
(2.584)**
0.216
(2.586)**
0.100
(0.99)
0.366
(3.548)**
0.423
(4.159)**
0.017
(0.157)
0.344
(4.925)**
0.359
(5.617)**
0.039
(0.591)
0.221
(3.095)**
LURBAN
-0.061
(-0.191)
-0.399
(-1.185)
0.458
(1.706)*
-0.840
(-2.974)**
-0.871
(-3.285)**
-1.772
(-6.207)**
-0.922
(-5.582)**
-0.997
(-5.973)**
-1.183
(-7.239)**
-1.21
(-4.839)**
LTRADE
0.078
(0.945)
-0.063
(-0.803)
0.031
(0.456)
-0.077
(-1.341)
-0.065
(-1.270)
-0.015
(-0.258)
-0.070
(-1.713)*
-0.073
(-1.750)*
0.022
(0.595)
-0.07
(-1.111)
LDENSPOP
0.594
(3.039)**
0.418
(2.517)**
0.300
(1.82)*
-0.429
(-1.062)
0.016
(0.059)
1.077
(2.653)**
0.154
(1.003)
0.253
(1.69)*
0.469
(3.190)**
0.398
(1.862)*
GRG
-0.017
(-19.361)**
5.694
(7.323)**
-0.008
(-5.464)**
-0.011
(-14.429)**
Area Fixed Effect:
Df
Yes
31
1398.32**
Yes
31
1398.32**
Yes
30
1577.76**
Yes
31
848.84**
Yes
31
848.84**
Yes
31
868.43**
Yes
63
2630.37**
Yes
63
2630.37**
Yes
62
2522.01**
Yes
63
1027.72**
Time Effect:
Df
NO
Yes
27
50.12**
Yes
25
21.026
NO
Yes
25
24.38
Yes
27
23.22
NO
Yes
27
25.56
NO
χ2
Yes
27
34.75
Observations
Adj R2
595
0.949
595
0.949
538
0.970
362
0.923
362
0.925
323
0.940
957
0.943
957
0.943
861
0.958
354
0.944
χ2
*
Low Income Countries
Model 3
Significant at 10%. * * Significant at 5%. Model 10 uses the the three-year average sample.
40
Table 3. Cross Section: General Government
Constant
Model 1
0.175
(0.276)
GINI
-0.003
(-0.187)
ETHNIC
-0.001
(-1.467)
Model 2
Model 3
0.08
(0.24)
-0.861
(-1.164)
Model 4
-0.271
(-1.470)
Model 5
-0.282
(-1.558)
Model 6
Model 7
Model 8
2.669
(10.58)**
2.814
(6.16)**
Model 9
2.789
(17.920)*
*
Model 10
2.640
(5.385)**
0.002
(0.205)
-0.011
(-1.46)
-0.002
(-0.436)
-0.002
(-0.387)
2.778
(18.123)**
0.001
(0.885)
HI
0.884
(2.011)**
0.956
(2.186)**
0.839
(2.122)**
0.803
(2.160)**
0.854
(2.33)**
0.765
(2.984)**
0.803
(2.717)**
0.645
(2.317)**
0.728
(2.592)**
0.766
(2.894)**
PSTATt
-1.713
(-5.378)**
-1.295
(-2.169)**
-0.825
(-1.067)
-1.017
(-1.381)
-1.630
(-3.14)**
-2.079
(-6.18)**
-0.96
(-1.809)*
-0.618
(-0.973)
-0.613
(-1.102)
-1.070
(-2.717)**
Observations
Adj. R2
Br-Pagan
37
0.118
8.142(4)
46
0.172
0.835(3)
61
0.10
3.612(3)
63
0.10
7.376(2)
64
0.20
0.383(2)
37
0.268
1.822(4)
46
0.17
1.180(4)
62
0.07
8.456(3)
64
0.10
6.398(2)
63
0.20
0.109(2)
CSTAT
* Significant at 10%., * * Significant at 5%. t-ratios are in parenthesss. Degrees of freedom are in parenthesis for the Br-Pagan test.
40
Table 4. Panel Data: EFD by Function
EDU1
EDU2
HEL1
HEL2
HOUS2
7.540
(4.892)**
LGDPCAP
0.304
(2.277)**
0.249
(3.018)**
-0.578
(-3.138)**
-0.520
(-2.772)**
-0.066
(-0.298)
0.336
(2.209)**
LURBAN
-1.593
(-5.912)**
-1.520
(-4.089)**
-0.931
(-2.571)**
-0.93
(-2.217)**
1.295
(2.928)**
1.329
(2.597)**
GRG
0.005
(3.019)**
0.005
(1.656)*
0.011
(3.906)**
0.008
(3.643)**
0.0001
(-0.067)
LDENSPOP
-0.030
(-0.107)
1.127
(2.982)**
1.055
(2.974)**
-2.495
(-5.462)**
-1.765
(-4.529)**
Area Fixed Effect:
Df
Yes
41
1239.92**
Yes
41
1232.44**
Yes
41
1311.06**
Yes
41
1311.06**
Yes
40
663.239**
Yes
41
804.32**
Time Effect:
Df
NO
Yes
24
24.41
NO
Yes
24
30.60
NO
χ2
Yes
24
20.363
Observations
Adj R2
407
0.956
408
0.956
385
0.964
385
0.965
400
0.849
486
0.864
χ2
7.322
(3.523)**
HOUS1
Constant.
9.000
(3.550)**
* Significant at 5%., * * Significant at 10%. t-statistics are in parentheses.
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