expenditure over that of the general government, the use of functional ... arise when decentralization is examined for specific areas of government, this is not.
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
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
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
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
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
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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