Institutional design, political competition and spillovers

Journal Pre-proof Institutional design, political competition and spillovers Marco Alderighi, Christophe Feder PII:

S0166-0462(18)30230-8

DOI:

https://doi.org/10.1016/j.regsciurbeco.2019.103505

Reference:

REGEC 103505

To appear in:

Regional Science and Urban Economics

Received Date: 19 June 2018 Revised Date:

10 December 2019

Accepted Date: 31 December 2019

Please cite this article as: Alderighi, M., Feder, C., Institutional design, political competition and spillovers, Regional Science and Urban Economics (2020), doi: https://doi.org/10.1016/ j.regsciurbeco.2019.103505. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

Institutional design, political competition and spillovers* Marco Alderighi§

Christophe Feder

Universit`a della Valle d’Aosta, Italy

Universit`a della Valle d’Aosta, Italy

Universit`a Bocconi, Milano, Italy

BRICK, Collegio Carlo Alberto, Italy

Abstract We establish a link between the best system of government and the strength of inter-state spillovers within a model of political competition with self-interested parties. We show the superiority of the unitary system when: inter-state spillovers are strong; the ego rents of local parties are high; and the system of government is chosen under a veil of ignorance. JEL classification: H11, D72, H41, H70, H77. Keywords: Institutional design; Voting; Self-interested politicians; Allocation of power; Federalism.

*

The authors would like to thank the editor and the two referees for their useful comments. The usual disclaimer

applies. § Corresponding author. Universit`a della Valle d’Aosta, Grand Chemin 75/77, Saint Christophe 11020, Italy; and GREEN, Universit`a Bocconi, Roentgen 1, 20136 Milan, Italy; telephone +39 0165 066 723; fax: +39 0165 066 748. E-mail: [email protected].

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1

Introduction

Changes in institutional design are not so unusual, and may have significant impacts on the prosperity of nations (North, 1990). When talking about institutional design, there are at least two central aspects to be taken into account: firstly, how much power is in the hands of the central and the local governments; and secondly, how the allocation of power is put into practice (Lijphart, 2012). Most constitutions contain a variety of rules on the allocation of power, which limit, but do not exclude, the possibility of modifications (Kessler et al., 2009). Referenda and legislative voting are two such possibilities. While the former is largely analyzed in the literature (Cr´emer and Palfrey, 1996; Lockwood, 2002, 2004), the latter is less considered (Hatfield and Padr`o i Miquel, 2012). In order to fill the gap, we develop a model of political competition with probabilistic voting, where a country is formed by two interconnected states; politicians are self-interested; and they gain utility from winning elections and from ego rents, which they receive from having power at their government level. The power associated with each level of government is given by the share of locally-produced public goods (LPPGs) under the control of that government. The probability of winning elections is positively affected by the parties’ ability to match the citizens’ preferences. The need to assign power at different government levels comes from the existence of inter-state spillovers. We compare the performance of two systems of government: the unitary system, where the decision on the allocation of power between levels is made by the central government; and the federal system, where this decision is in the hands of the local governments. We find that, without inter-state spillovers, it is optimal to allocate all the power to the local governments, and when the provision of LPPGs in one state has positive spillovers to the other, it is better to assign some power to the central government, which better accounts for state interdependencies (Oates, 1972; Redoano and Scharf, 2004). We show that, when spillover effects are positive and vary among different LPPGs, there is always an optimal allocation of power, which maximizes the welfare and,

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therefore, the probability of winning the election. However, since politicians also care about ego rents coming from the parliamentary office, in which all parties are involved, there is a trade-off between enlarging the power at their government level and increasing the probability of winning the election. Moving away from the optimal level to improve the political power of the parliament and of the executive branch, a party thereby reduces its chances to form a government (winning the election) but increases the returns from sitting in the parliament (ego rents). In our setup, as far as parties are either altruistic or they only care about winning elections, institutional design does not affect the outcome: both government systems yield the same allocation of power and the same welfare. Indeed, ex-ante homogeneous within-state preferences imply that maximizing the welfare of a representative citizen is optimal both for winning the elections and for overall welfare. On the contrary, with self-interested parties, the federal system brings too much decentralization, whereas the unitary system is conducive to excessive centralization. A main result of the paper is that higher welfare levels are reached under the system of government in which a deviation from the first-best allocation leads to a larger welfare loss. This conclusion emerges because, when there is the risk of high welfare losses due to a wrong allocation of power, citizens are very likely to modify their electoral preference by switching (in a two-party election) from one party to the other, and therefore a deviation of parties from the first-best allocation is more severely punished. This fact, therefore, reduces the incentive of parties to modify their electoral promises in their own interest. In sum, larger losses force parties to stay close to the social optimum in order not to significantly reduce their likelihood of winning the election. Moreover, we also show that the intensity of welfare losses caused by departing from the firstbest allocation depends on the interplay between the strength of spillovers and the allocation of power. When there are weak spillovers, larger losses occur when there is excessive decentralization, while, when there are strong spillovers, larger losses emerge with excessive centralization. Indeed, when it is socially optimal to allocate most of the power to one level of government, any further allocation of power is likely to produce high losses, since the public goods left under the control of

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the other level are those that cannot be easily managed otherwise. Based on these results, we present a new explanation for the general preference for a federal system when states are weakly interconnected. Indeed, our results follow this stream of reasoning. The federal system entitles local governments to choose the allocation of power. When spillovers are weak, the local government is the one that can cause larger losses. Consequently, the federal system of government emerges as the better one. Although this conclusion is well known in the literature, the above explanation differs from the usual one. In our case, the result is driven by the self-interested behavior of parties, while the standard explanation is based on the fact that the federal system leads to greater decentralization than the unitary one (Inman and Rubinfeld, 1997). Similar reasoning can be applied to show that the unitary system is preferred with strong spillovers. Finally, our theoretical analysis pointed out a peculiarity of institutional design and, in particular, it shows that, when the strength of spillovers and the level of the heterogeneity are unknown, in most cases the unitary system performs better than the federal one. Thus, under a veil of ignorance, the unitary system should be preferred, especially when inter-state spillovers and inter-state heterogeneity are sufficiently strong. To the best of our knowledge, our paper is the first that compares the allocation of power between unitary and federal systems of government in voting in the legislature. Moreover, our paper differs from most of the existing political economy models on fiscal decentralization because it assumes that politicians are office-motivated, i.e. they receive utility from holding office, and an extra-utility comes from the allocation of local public goods at their government level. The rest of the paper is organized as follows. Section 2 reviews the literature. Section 3 presents the model, and Section 4 studies the impact of different systems of government on the allocation of power and on welfare. Section 5 concludes. All the proofs are given in Appendix A. Appendix B provides some technical details on the electoral procedure. Finally, Appendix C shows that the results are robust to different specifications.

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2

Literature review

The seminal paper of Oates (1972) poses a new question in the fiscal federalism debate: when a country is formed by heterogeneous states, is it better to decentralize or centralize the provision of public goods? Most of the following papers in the field, and even those including a political economy approach, confirm the initial finding that there exists an inter-state spillover threshold, which determines the preferred way to provide public goods. For values below this threshold, decentralization is better than centralization, and the opposite holds when values are above it (Besley and Coate, 2003; Hindriks and Lockwood, 2009; Feidler and Staal, 2012). Around the 2000s, an additional research question began to gain ground: when a country is formed by heterogeneous states, how does the institutional design affect the allocation of power and, eventually, the performance of a country? Some authors only consider single aspects of the institutional design: Lockwood (2002) and Loeper (2013) study the referendum in a unitary system of government; and Panizza (1999) and Lorz and Willmann (2013) analyze the voting in the legislature in a unitary system. Other authors, indeed, investigate the effects of different forms of voting (voting in legislature vs voting by referendum) or of alternative systems of government (federal vs unitary systems). In particular, Redoano and Scharf (2004) study centralization decisions using different forms of voting. They find that voting in the legislature leads to a higher centralization than voting by referendum. Lorz and Willman (2005) obtain a similar result in a model with a continuum of local public goods. Rota Graziosi (2009) endogenizes the choice of voting system (full delegation, partial delegation, no delegation, or voting by referendum) showing that voting by referendum is not an outcome of the game, even when it is Pareto-superior to other voting systems. Moreover, Cr´emer and Palfrey (1996) and Lockwood (2004) compare two systems of government in the case of vote by referendum. Cr´emer and Palfrey (1996) demonstrates what is called the ‘principle of aggregation’: when the number of states is large, the federal system leads to less decentralization than the unitary one. Lockwood (2004) shows that there are benefits from centralization

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when there are economies of scale in the provision of public goods. The author also generalizes the principle of aggregation when preferences are single-peaked, while the previous results are based on the assumption that extreme voters prefer decentralization. Other papers consider: the allocation of power by private citizens or by the public sector (Aghion et al., 2004; Hayo and Voigt, 2013); the relationship between the size of a country and the allocation of power among different levels of government (Alesina et al., 2005; Lorz and Willmann, 2013); and different taxation regimes (Brueckner, 2004; 2009; Ortu˜no-Ort´ın and Sempere, 2006; Hindriks and Lockwood, 2009; Hatfield and Padr`o i Miquel, 2012; Borge et al., 2014; Bellofatto and Besfamille, 2018). Although these papers share some assumptions with our model, they do not explicitly focus on the effects of the self-interested behavior of parties on welfare, which is indeed a major goal of our analysis.

3 3.1

The model State welfare and locally provided public goods

A country is formed by two interconnected states. Policy choices concern the decision on the intensity of a continuum of LPPGs offered in each of the two states, gaj , where j = 1, 2 refers to the state; and a ∈ Ω ≡ [0, 1] is an index ordering LPPGs on the strength of inter-state spillovers, which are given by (Wilson and Janeba, 2005; Lorz and Willmann, 2005; Hatfield and Padr´o i Miquel, 2012): k (a) = κa(1−θ)/θ ,

(1)

with θ, κ ∈ [0, 1]. κ is an overall measure of the size of spillovers; θ measures how similar is the strength of spillovers among different public goods and is inversely related to , the elasticity of k(a) with respect to a: θ = (1 + )−1 . For θ = 1 ( = 0), all LPPGs produce the same (maximum)

6

spillovers; for θ < 1 ( > 0), the smaller a and the lower the spillovers.1 Note that (1) implies that inter-state spillovers are symmetric and equal in size across states. 2 ; the public budget-balancing condition Production costs are quadratic, i.e. Caj = C (gaj ) = gaj

holds in each state; LPPGs are entirely financed by a non-distortionary local tax, τj ; and transfers from one state to the other are not permitted (Redoano and Scharf, 2004):2 Z

1 2 gaj da = τj .

(2)

0

The utility that a citizen living in j = 1, 2 receives from consuming the LPPG a is uaj = γaj (gaj + k (a) ga,−j ), where γaj measures the appeal of the LPPG a for citizens living in j; and gaj and ga,−j are the intensity of the LPPG a offered, respectively, in the state where (s)he lives, namely j, and in the other state, namely −j. We assume that γaj ∈ (0, ∞), with average γ¯ = 1 and variance σ 2 ∈ (0, ∞); and that all γaj are independent and identically distributed random variables. Differences between the two states originate from heterogeneity in the citizens’ preferences for LPPG items. Citizens living in j also receive utility from the consumption of a bundle of private goods, xj . Therefore, their utility is:3 Z Uj =

1

γaj (gaj + k (a) ga,−j ) da + xj .

(3)

0

The mass of citizens in each state is normalized to 1, and their income is I > τj . From citizen budget constraint, xj + τj = I, and using (2) and (3), the indirect utility function of a citizen living 1

We thank an anonymous referee for suggesting this interpretation. In sub-section 4.1, we provide a complementary interpretation of θ by showing that it is positively related to the average strength of spillovers. 2 In general, different taxation systems can induce distortionary effects (Besley and Coate, 2003; Hindriks and Lockwood, 2009). This issue is relevant, for example, when the central government can choose different levels of LPPGs among states (Lockwood, 2005). In our setup, however, as we discuss in sub-sections 3.3 and 3.5, governments choose the intensity of LPPGs optimally, since this choice maximizes their likelihood of winning the elections (citizens are able to identify the effects of spending decisions on taxes, and, therefore, they will punish the party, which chooses a distortionary LPPG rule). 3 Quasi-linear utility functions have the property that the demand for a set of goods is independent of income (usually called the numeraire) since the marginal utility of income is constant and equal to 1. Therefore, the optimal intensity of any LPPG is reached when its decreasing marginal utility reaches 1.

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in j, as well as of welfare in state j, is: Z Uj =

1

 2 γaj (gaj + k (a) ga,−j ) − gaj da + I.

(4)

0

3.2

Institutional design

The country has three governments: one central government and two local governments. The governments have different power and roles, depending on whether there is a unitary (U ) or a federal (F ) system. In the unitary system, the central government plays a major role. It chooses the allocation of power, i.e. the set of LPPGs, which will be managed by the local governments, Ad ⊂ Ω, and those which will be kept under its own control, Ac ≡ Ω \ Ad . In the federal system, vice versa, the two local governments have a major role since they choose the allocation of power between the c ∈ Ac , two levels. In both systems, every gaj ∈ Ω is assigned either to the central government, gaj d ∈ Ad . or to a local government, gaj

The central government and the local governments have different information sets and views: the central government, being less informed, takes into account the welfare of the whole country and, therefore, it considers inter-state spillovers; the local governments, however, take into consideration only the utility of citizens living in their own states, and they can base their decisions on state-specific needs (Oates, 1972; Besley and Coate, 2003). A reasonable allocation of power between the central and the local governments is to assign control over those LPPGs with weaker spillovers to the local governments and control over those with stronger spillovers to the central one. More formally, the allocation of power consists of choosing the level of autonomy, a ˆ, which creates two sets of LPPGs: Ad = [0, a ˆi ) provided at the local level; and Ac ≡ Ω \ Ai = [ˆ ai , 1] managed at the central level (see: Appendix B.1).

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3.3

Political competition

Government formations are guaranteed by central and local elections. In each type of election, there are two non-ideologically-oriented parties in competition. During the electoral campaign, parties present a binding electoral promise concerning how they will choose the intensity of the LPPGs that they would manage;4 and, the allocation of power they would set, when their level of government is entitled to this choice. For the sake of clarity, the parties are called the left-wing party and the right-wing party. We use L (l) to refer to the central (local) representatives of the left-wing party, and R (r) to refer to the central (local) representatives of the right-wing party. Politicians cannot switch from one party to the other, and, more importantly, they cannot move inside the same party from one government level to the other. Thus, there is horizontal competition between the left-wing and the right-wing parties, and vertical competition between the central and the local parties (Salmon, 2002). The two levels of government differ in nature since, in the production stage, local politicians receive information at state level, i.e. they know γaj , while central politicians only retain coarse information on state preferences, i.e. they only know γ¯ and σ 2 . However, the utility of the central politicians is affected by the behavior of citizens in the overall country, and they can fully account for inter-state spillovers. Thus, there is a trade-off between having tailored decisions that fit local specificities and coordinated decisions that internalize spillovers (Oates, 1972; Lorz and Willmann, 2005). We suppose that politicians are self-interested, and receive utility from winning elections, and from holding power at their government level, i.e. from ego rents. The first factor (winning the elections) induces parties to optimally choose the intensity of the LPPGs; and to correctly allocate power between the two levels of government. The second factor (ego rents) induces parties to assign too much power to their own level of government. 4

Because (local) parties receive additional information during the production stage in the electoral promise they cannot indicate the intensity of the LPPGs based on state contingencies, but they commit to a production rule which accounts for it.

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In order to avoid unnecessary complexities, we assume that the parties pledge that the LPPGs they would have to manage should be chosen optimally (e.g. they commit themselves to follow the optimal production rule described in Section 3.5). Indeed, this choice dominates any other because it produces larger expected utility for the parties, for any possible allocation of power. Given this background and the fact that the central and the local governments are involved alternatively in the decision on the allocation of power, the utility of the local and the central parties is now described for, respectively, the federal and unitary systems. In the unitary system, the (expected) utility function of central party i = L, R is:
Vi = Πi + Λ 1 − a ˆU ,

(5)

where Πi is the probability that party i wins the election; Λ is the marginal utility of power; 1 − a ˆU is the expected power assigned to the central government, with a ˆ U = Πi a ˆi + (1 − Πi )ˆ a−i ; and a ˆi and a ˆ−i are, respectively, the levels of autonomy proposed by party i and −i in their electoral promises. Moreover, the probability of winning the elections is affected by some unpredictable and uncontrolled factors (e.g. rumors, gossip, scandals, or errors of voting), as well as by the parties’ ability to match the citizens’ preferences. We then assume that Πi = Pr (Uj (ˆ ai ) > Uj (ˆ a−i ) + ∆) and depends on the relative appeal of the electoral promises Uj (ˆ ai ) − Uj (ˆ a−i ) , and on a random component ∆, which is uniformly distributed on the interval [−Ψ, Ψ] (Persson and Tabellini, 2002). The couple (Λ, Ψ) constitutes the electoral context in which the central election is played. Note that (5) implies that the party, which has lost the election still has some utility from being in the parliament, albeit as a minority group. The utility of the loser, as well as that of the winner, is increasing in the power of the level of government, because the larger the set of LPPGs included in their level of government, the higher the prestige, the larger the resources, etc. (Strom, 1990; Trebbi et al., 2008). This specification reflects the idea that: (a) both parties stay in the parliament and then ego rents are positively affected by the power of the parliament; (b) the winning party has

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an additional prize since it holds more seats in the parliament and it is in government. In Appendix C, we show that our results do not substantially differ if we assume that the winner takes all, i.e. the winning party holds all seats in the parliament and it is in government. In the federal system, the winning parties choose the level of local power, a ˆF , through a bargaining process. That is, a ˆF = B(ˆ aW ˆW 1 ,a 2 ), where B is a bargaining function (the details are presented in sub-section 3.6 and Appendix B.2), and a ˆW j is the winning promise in state j = 1, 2. We assume that the (expected) utility function of the local party i = l, r in state j is: vij = πij + λˆ aF ,

(6)

where a ˆF is the power of the local governments, which comes from the negotiation between the winning parties of the local elections; λ is the marginal utility of power; and πij = Pr(Uj (B(ˆ aij , a ˆW −j )) > Uj (B(ˆ a−i,j , a ˆW −j )) + δj ) is the probability that party i wins the election in state j, which depends on the relative appeal of the outcome of the electoral promise Uj (B(ˆ aij , a ˆW a−i,j , a ˆW −j ))−Uj (B(ˆ −j )), and on a random component δj , which is uncorrelated between states, i.e. Cov (δj , δ−j ) = 0, and uniformly distributed on the interval [−ψ, ψ], ψ > 0. The couple (λ, ψ) constitutes the electoral context in which local elections are played. The previous comments also apply to (6). Different streams of literature offer various interpretations for (5) and (6). A first view is that politicians are self-interested (Brennan and Buchanan, 1980; Caplan, 2001a). A second view, proposed by Dixit and Londregan (1998) and empirically analyzed by Caplan (2001b), is that politicians have two interests: a utilitarian one (winning the election) and an ideological one (reaching a certain allocation of power).

3.4

Timing of the game

We analyze two different versions of a similar game: one for the unitary system and the other for the federal system. In the unitary system of government, the electoral promise of the central party

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includes a binding proposal on the allocation of power between the two levels of government and an LPPG rule, which describes how the intensity of LPPGs will be chosen at the central level. The electoral promise of the local party contains the rule it is going to follow for those LPPGs which it will manage if it wins the election. Vice versa, in the federal system, the electoral promise of the local party comprises the allocation of power between the two levels of government and the LPPG rule it will use to select the intensity of LPPGs which it intends to manage at the local level. The electoral promise of the central party is the LPPG rule that it will adopt whether or not it wins the election. The timing of the game is as follows: • t = 0 – Nature determines ∆, δj , and γaj , which are unknown to the parties. • t = 1 – Central parties L and R simultaneously announce their binding electoral promise. Moreover, local parties l and r of the two states simultaneously and independently announce their electoral promises. The electoral promise at both levels of elections includes an LPPG rule. Moreover, in the unitary system, central parties also present their allocation of power, a ˆi , with i = L, R. In the federal system, however, the allocation of power is presented by local parties l and r: a ˆij , with i = l, r and j = 1, 2. • t = 2 – Citizens of the two states, on the basis of the electoral promises, δi , δ−i , and ∆, choose their preferred party. The party which receives the larger number of votes wins the election; and the level of local power a ˆ is set in accordance with the winning promise. In the case of a tie, the winner is randomly chosen. In the case of a federal system the level of local power is the result of a bargaining process between the winning parties (see: sub-section 3.5 and Appendix B). • t = 3 – Nature reveals γaj to the local governments, but not to the central government. Local and central governments optimally choose the intensity of LPPGs based on their rules and on their information set. 12

Since, depending on the system of government, local or central parties alternatively choose the allocation of power, it is not necessary to specify the order of local or central elections, as the outcome of each game remains unaffected. Note that politicians at the local level know the preference term γaj when setting LPPG levels, but not when deciding about centralization, while those at the central level do not receive information throughout the game. This hypothesis reflects the emergence of unforeseeable events during the parliamentary term, which can be more promptly identified and managed by the local rather than the central governments. We solve the model backwards to characterize perfect Bayesian equilibria.

3.5

Local public goods

We now consider the last stage of the game. As already mentioned in sub-section 3.3, we have assumed that, conditional on their information set, governments choose the intensity of LPPGs in order to maximize welfare since it increases the likelihood of winning the election, leaving the other components of their utility unaffected. Furthermore, we have also mentioned that the allocation of power between levels of government involves a trade-off between better information on citizens’ preferences at the local level and better coordination of policies at the central level. We therefore assume that, in the production stage, each local government knows precisely state-specific citizens’ preferences, but it only accounts for the welfare of its own state, while the central government only knows the distribution of the citizens’ preferences, but it maximizes the welfare of the country as a whole. d , the local government j considers Under these premises, in order to find the optimal LPPG, gaj

the difference between the benefit, uaj , and the cost, Caj , solving the following problem: 2 max γaj (gaj + k (a) g˜a,−j ) − gaj , gaj

13

where g˜a,−j is the expectation of local government j on ga,−j . Because of the additivity form of d is independent of expectation formation, and is given by: uaj , the optimal intensity of LPPG gaj

d gaj =

γaj . 2

(7)

c and g c , the central government considers the Indeed, in order to find the optimal LPPGs, ga1 a2

difference between the overall benefits and the overall costs solving the following problem:

max

ga1 ,ga2

X


2 E γaj (gaj + k (a) ga,−j ) − gaj ,

j=1,2

and, remembering that γaj is a random variable with mean 1 and variance σ 2 , we derive the optimal intensity of the LPPGs: c gaj =

1 + k (a) , 2

for j = 1, 2.

(8)

Since the central government has no precise information on state-specific citizens’ preferences, c = gc = LPPGs supplied in both states with the same spillover index a have the same intensity: ga1 a2

gac (Lockwood, 2002; Besley and Coate, 2003; Feld et al., 2007; Hindriks and Lockwood, 2009). Moreover, the stronger the spillovers, the larger is the intensity chosen by the central government. c > E(g d ) for any a. Thus, By comparing (7) and (8), knowing that E(γaj ) = 1, it follows that gaj aj

because the central government accounts for spillovers, it wants to provide, on average, a larger intensity of LPPGs.

3.6

Allocation of power in federal and unitary systems

In this sub-section we discuss how power is allocated between the central and the local levels of government in the unitary and the federal systems. This analysis is preceded by a study of the firstbest outcome. To simplify the discussion, we focus only on interior solutions, which emerge with 14

the following parameter restrictions: 4ΛΨ < σ 2 < κ2 − 4λψ.

(9)

In the first stage of the game, politicians (still) do not have exact information on citizens’ pref2 ) = 1 + σ 2 and E(γ γ erences. Knowing that E(γaj aj a,−j ) = 1 and using (7) and (8), equation (4)

can be expressed to account for the dependence of welfare on the level of local power, a ˆ ∈ [0, 1], which gives: Z Uj (ˆ a) = 0

a ˆ

 Z
1 1 1 1 2 (1 + k (a))2 da + I, 1 + σ + k (a) da + 4 2 4 aˆ

(10)

where expectations are taken over γaj . Simple computations show that the utility function is concave in a ˆ. Benchmark. Before considering how the different systems of government affect the allocation of power (and eventually reduce the welfare), we study the first-best (or benchmark) level of local power a ˆB , i.e. the level which yields to the maximum overall welfare to the country, provided that central and local parties choose the LPPG intensities optimally on the basis of their respective information. Since the two states are ex-ante identical, the overall welfare is simply given by: 2Uj (ˆ a) = Uj (ˆ a) + U−j (ˆ a). Using (10), the unique first-best level of local power is: a ˆB =

σ  κ

θ 1−θ

.

(11)

Unitary system. We now consider the case in which the central government is entitled to allocate power. Being self-interested, central parties want to centralize power. However, in order to increase their odds of winning the election, the two parties will transfer some power to the local governments. From sub-section 3.3, and remembering that ∆ is uniformly distributed on the interval

15

[−Ψ, Ψ], the probability of party i winning is given by (Persson and Tabellini, 2002):

Πi =

1 11 + [Uj (ˆ ai ) − Uj (ˆ a−i )] , 2 2Ψ

(12)

where a ˆi and a ˆ−i are the electoral promises of party i and −i, respectively. From (5) the utility function of party i can be written as:

Vi (ˆ ai |ˆ a−i ) = Λ (1 − a ˆi ) + Πi + (1 − Πi ) Λ (ˆ ai − a ˆ−i ) .

(13)

From (13), the utility of central party i can be interpreted as the sum of three components: the utility coming from the electoral promise a ˆi , Λ (1 − a ˆi ); the utility of winning the election, Πi ; and the utility coming from having a different level of local power, a ˆi − a ˆ−i when losing the election, (1 − Πi ) Λ (ˆ ai − a ˆ−i ). Equalizing the first derivative of (13) to zero, we obtain the response function of party i to the electoral promise of party −i. Proceeding in a similar way, we can find the response function of party −i, and, from this, the level of local power chosen by both parties in the unitary system. Thanks to symmetry, in equilibrium the two parties will offer the same electoral promise.5 Lemma 1 formally presents the result: Lemma 1 When the system of government is unitary, the level of local power emerging from the
central election, a ˆU , satisfies Uj0 a ˆU = ΛΨ, and is:  θ  p 1−θ 1 2 σ − 4ΛΨ . a ˆ = κ U

(14)

Lemma 1 suggests the following considerations. First, there is an insufficient delegation of power to the local governments, i.e. a ˆU < a ˆB . Second, from (14), it immediately follows that the larger the product ΛΨ, the lower is a ˆU . Thus, an increase in uncertainty and/or in the marginal utility of power yields smaller decentralization. Third, and relatedly, as the result depends on the product 5

We limit our analysis to symmetric solutions for both unitary and federal systems.

16

ΛΨ, there are different levels of Λ and Ψ, from which we can expect a similar decentralization. Federal system. We finally consider when local governments are entitled to set the level of local power a ˆF . Also in this case, local parties would tend to retain power at their government level, but, in order to increase their odds of winning the political competition, they will promise to transfer some power to the central government. The federal system has some complications that are not present in the unitary system. In particular, because there are now two winning electoral promises, the emerging level of local power is the result of a negotiation between the two local governments, i.e. a ˆF = B(ˆ aW ˆW ˆW 1 ,a 2 ), where B is a bargaining function, and a j is the winning proposal in state j = 1, 2. The way in which the negotiation process is articulated affects the electoral promises, as well as the citizens’ decision. Indeed, citizens of one state will choose the electoral promise which, in combination with the expected outcome of the electoral competition in the other state, yields their highest welfare. We assume that the result of the bargaining process is simply the average proposal: a ˆF = B(ˆ aW ˆW 1 ,a 2 )=

a ˆW ˆW 1 +a 2 . 2

(15)

The result presented in (15) can be derived as a solution of a Nash bargaining game (Lorz and Willmann, 2005; 2013; Feder, 2018) or of a Baron-Ferejohn bargaining game (Baron and Ferejohn, 1989; Lockwood, 2002; 2004) between the winning parties (see: Appendix B.2). From sub-section 3.3 and using (15), the probability of party i winning is:      1 1 W 1 1 W 1 11 ˜ ˜ Uj a ˆij + a ˆ − Uj a ˆ−i,j + a ˆ , πij = + 2 2ψ 2 2 −j 2 2 −j

(16)

˜

where a ˆW −j is the expectation in state j on the outcome of the election in −j. Moreover, noting that ˜

a ˆF = 0.5 (πij a ˆi + (1 − πij ) a ˆ−i ) + 0.5ˆ aW −j , the utility function of party i is:  vij (ˆ aij |ˆ a−i,j ) =

  1 1  W ˜ 1 + λ (ˆ aij − a ˆ−i.j ) πij + λ a ˆ−j + a ˆ−i,j , 2 2

17

(17)

where πij is given by (16). Finally, from the maximization of (17) with respect to a ˆij , we obtain the response function of party i to the promise of party −i in state j. Having information on the distribution of γaj and being ˜

rational, it implies that citizens in j will correctly anticipate the outcome in −j, i.e. a ˆW ˆW −j = a −j . Proceeding in a similar way, we can find the response function of party −i in state j, and, from this, the level of local power chosen in state j. After performing similar computations for state −j, and thanks to (15), we find the level of local power chosen in the federal system. Lemma 2 formally presents the result. Lemma 2 When the system of government is federal, the level of local power chosen by local
governments, a ˆF , satisfies Uj0 a ˆF = −λψ and is:  θ  p 1−θ 1 2 σ + 4λψ a ˆ = . κ F

(18)

Note that in this case, there is an insufficient delegation of power to the central government, i.e. a ˆF > a ˆB .

4

Preferred system of government

A major result of the previous section is that the parties’ self-interested behavior yields a distortionary allocation of power in the two systems of government. In order to choose the better system of government, it is necessary to identify which system produces lower losses. The following definition classifies welfare functions in a useful way. Let U (ˆ aB ) be the maximum achievable welfare corresponding to the first-best allocation, and U (ˆ aA ) be the welfare coming from the level of local power a ˆA ∈ [0, 1). Then, the welfare loss associated with the allocation a ˆA is: L(ˆ aA ) = U (ˆ aB ) − U (ˆ aA ).

18

(19)

We now consider three different situations, where the better system of government depends on: the intensity of inter-state spillovers; the electoral context; and both situations.

4.1

Intensity of inter-state spillovers

We initially assume that the electoral context is the same in both the central and the local elections, i.e. (Ψ, Λ) = (ψ, λ). Using the results presented in sub-section 3.6, the first-order condition is Uj0 (ˆ a) = ξ, and the allocation of power in the different systems of government is:  p  θ 1−θ 1 2 a ˆ= σ − 4ξ , κ

(20)

where ξ = 0 in the benchmark case; ξ = ΛΨ in the unitary system; and ξ = −λψ in the federal system. Thus, when the three solutions are interior, they satisfy: 0 < a ˆU ≤ a ˆB ≤ a ˆF < 1.6 Equation (1) implies that the strength of inter-state spillovers of different LPPGs, k(a), ranges in the interval [0, κ], with k 0 > 0, k(0) = 0, and k(1) = κ; and that the average strength of interR ¯ state spillovers, k(θ) = k(a(θ))da = κθ, is increasing in θ. Because of this positive functional dependency between k¯ and θ, we can interpret θ as a measure of the overall strength of spillovers. The following Proposition provides the preferred system of government when the type of election does not affect the electoral context. Proposition 1 Assume that (Ψ, Λ) = (ψ, λ) and (9) is satisfied. When there are weak (strong) spillovers, i.e. θ < 2/3 (θ > 2/3), the federal (unitary) system is the second-best solution; when θ = 2/3, the unitary and the federal systems provide the same welfare. Proposition 1 has a simple economic interpretation. Without inter-state spillover, it is optimal to allocate all the power to the local government. However, when LPPGs exhibit sufficiently high 6

Note that, when the parties are altruistic, we reached the first-best allocation of power in both systems of government. This result comes from our assumption about the moment at which information on state-specific shocks is unveiled to the parties. Indeed, during the elections, i.e. when the parties propose a ˆ and commit to a production rule, the information set is the same for both the central and the local parties, and therefore they reach the same solution.

19

inter-state spillovers, it is better that their control is assigned to the central government, which can better internalize these effects. By listing public goods from those with lower to those with higher spillovers, there is always an optimal allocation of power, which maximizes the welfare and, therefore, the probability of winning the election in both the unitary and the federal systems of government. However, politicians also care about power, i.e. gaining ego rents. Therefore, there is a trade-off between increasing the utility from ego rents and the probability of winning the election. Moving away from the optimal level to improve its power, a party reduces its chances of winning the election, but increases the returns from ego rents. In choosing their electoral promises, the parties face a trade-off between requiring larger political power and increasing their likelihood of winning the election. When a deviation from the first-best allocation can cause a large welfare loss, the parties stay close to the optimum in order not to greatly reduce their probability of winning the election, while, when it can cause a limited fall, the parties feel freer to deviate and increase their political power. In other words, when the parties’ self-interested behavior (i.e. deviations from the social optimum) is much more tolerated by citizens (i.e. a marginal change in the allocation induces a limited welfare loss), we observe a larger deviation, and, eventually, a larger fall in utility. Figure 1 provides a simple graphical representation of the impact of the two systems of government on the allocation of power. As expected, a ˆU < a ˆB < a ˆF . The upper panels describe the welfare function in levels, and the lower panels the corresponding first derivative. The colored areas indicate the welfare loss in the two systems of government. The spillovers are strong (θ > 2/3) in the left panels and weak (θ < 2/3) in the right ones. In the left panel, a marginal increase of the allocation of power from the first-best solution induces a lower welfare loss than a marginal reduction. Therefore, only a limited deviation from a ˆB can emerge before reaching the marginal welfare loss threshold, ΛΨ, while a more significant deviation can occur before reaching the other threshold, λψ. Consequently, when there are strong spillovers, the preferred system of government is the unitary one. An opposite reasoning can be applied to show that, when there are weak spillovers, the

20

Figure 1: Second-best allocation of power. The colored areas indicate the welfare loss in the two systems of government. Parameters: κ = 1; σ 2 = 1/2; λψ = ΛΨ = 1/10; θ = 9/12 (left panels); θ = 5/12 (right panels).

preferred system of government is the federal one. Proposition 1 says that, in order to minimize the inefficiency, it is better to choose the system of government that is potentially more damaging, henceforth inducing a smaller departure from the optimum: when spillovers are weak, local government is the system of government is that causing larger losses. Indeed, with weak spillovers most of the power is given to local governments, and any further allocation of power beyond the social optimum is likely to produce high losses, since, otherwise, goods under control of the other level are those that cannot be easily managed.

21

Consequently, the federal system emerges as the preferred one.7 On the contrary, the usual argument to identify the preferred system of government is based on the following syllogism (Inman and Rubinfeld, 1997): greater decentralization is preferred when spillovers are weak; a federal system yields greater decentralization; a federal system is preferred when spillovers are weak. Thus, this conclusion coincides with ours, but is based on a different argumentation, which does not consider parties’ self-interested behavior, the negative effects of it, and its interplay with spillovers.

4.2

Ego rents and the veil of ignorance

A quantitative analysis provides some interesting insights on the effects of spillovers and selfinterested behavior of parties on the pros and cons of the two systems of government. We first show that the two systems of government exhibit very different performances, and we argue that a unitary system should be preferred under the veil of ignorance, i.e. when information about the parameters of the model is vague and the decision maker cares about the worst case (Rawls, 1999, p. 118). Figure 2 presents the distortion in the allocation of power in the two levels of government as a function of the strength of spillovers (left panel), and the corresponding welfare losses (right panel) for a given electoral context (λψ = ΛΨ = 1/10).8 The left panel shows that the distortion in the allocation of power is not uniform over θ and between the systems of government. Indeed, it decreases near the right-hand corner. In other words, when spillovers are very strong/weak, the choice of the system of government is irrelevant. This result comes from the fact that, in extreme cases, the parties find themselves forced to choose a level of local power close to the first-best level, because a deviation causes such a high welfare loss that they will almost certainly lose the elections. Instead, larger welfare losses occur when θ assumes intermediate values in the unitary system, and 7

We have developed the argument in favor of the federal system, but a similar argument can be used in favor of the unitary one. 8 Other parameters are: κ = 1 and σ 2 = 1/2.

22

Figure 2: Departure from the first-best levels of local power (left panel) and welfare losses (right panel) as a function of inter-state spillovers. The dashed lines refer to the federal system and the continuous lines to the unitary system. C (g) = g 2 and k (a, θ) = κa(1−θ)/θ . Parameters: κ = 1; σ 2 = 1/2; λψ = ΛΨ = 1/10.

23

Figure 3: Preferred system of government in the worst case scenario.

medium to high values in the federal system. The same figure also shows that welfare losses caused by a wrong system of government are not symmetric. The worst outcome in the unitary system yields lower welfare losses than (the worst outcome) in the federal one. The maximum welfare loss caused by excessive centralization is smaller than that caused by excessive decentralization. Hence, if the choice of the system of government is taken under the veil of ignorance, a unitary system is the preferred choice. Finally, comparing the two curves of the right panel, it emerges that the gain from having one system of government with respect the other |L(aU ) − L(aF )| (the distance between the two curves) has nonlinear behavior. Moving from weak to strong spillovers, the gain is increasing and then decreasing. This implies that there are some ranges of spillovers where it is very important to be in the right system of government and others in which it is less relevant. Figure 3 extends the previous conclusions when federal and unitary systems of government have the same electoral context (λψ = ΛΨ). Without loss of generality, we normalize κ to 1. From (9), the set of admissible parameters is given by the colored area. For any electoral context (λψ) and any inter-state heterogeneity (σ 2 ), we have computed the maximum welfare loss in each of the two systems of government by moving θ in its whole interval, [0, 1]. Then, for each parameter set,

24

Figure 4: Electoral context and spillovers. Each curve represents the locus of points where citizens are indifferent to the two systems of government for a given parameter z ≡ ΛΨ + λψ. Parameters: κ = 1; σ 2 = 1/2; z = 0.01, 0.04, 0.08, 0.12.

we have chosen as the preferred system of government the one which induces the lower maximum welfare loss. The figure shows that both systems of government could be a second-best solution; and the unitary system is preferred to the federal one in a more extensive range of parameters. We, therefore, conclude that, under the veil of ignorance, the unitary system is more likely to be the preferred one. Until now, we have analyzed how the strength of spillovers determines the preferred system of government, provided that the electoral context is the same in the central and the local elections, i.e. (Ψ, Λ) = (ψ, λ). We now continue the analysis by removing this simplifying assumption. Moreover, Proposition 1 identifies the better system of government from the strength of spillovers. Figure 4 adds the distorting effects associated with different electoral contexts at the local and the central levels. Indeed, the horizontal axis measures the strength of spillovers, θ, and the vertical axis displays a relative measure of the potentially distorting effects of the electoral context at the central level:

25

ρ=

ΛΨ . ΛΨ + λψ

(21)

Each curve of the figure represents the locus of points where citizens are indifferent to the two systems of government for a given parameter z ≡ ΛΨ + λψ, where z = 0.01, 0.04, 0.08, 0.12. Points located above and below the curve describe, respectively, situations in which either the federal system or the unitary one is preferred to the other. By construction, for any z satisfying (9), when θ = 2/3, the indifference between the two systems of government occurs at ρ = 0.5, i.e. ΛΨ = λψ. Indeed, when citizens’ preferences for centralization and decentralization are symmetric, i.e. θ = 2/3, there emerges a special case, where the electoral context fully determines the preferred system of government. We find that the indifference curve has a similar shape and position for different parameter values. Figure 4 clearly shows that the preferred system of government depends on both the electoral context and the strength of the spillovers. For example, fixing an electoral context, say ρ = 0.55, the federal system is preferred when there are low-to-medium spillovers, while the unitary one is preferred for strong spillovers. It also emerges that the higher z is, the smaller is the parameter set where the federal system is preferable. Indeed, all things being equal, a larger z implies that the local distortion becomes larger in relative terms, and then the unitary system is preferable in a larger region of the parameter set. Moreover, strong asymmetries emerge when we compare the two systems of government. If ρ is smaller than approximately 0.435, then a unitary system is always preferred, regardless of the strength of spillovers; while, in order to get the same result for the federal system, we need ρ to be greater than approximately 0.941. This last argument reinforces the previous conclusion about the preference for the unitary system under the veil of ignorance. Indeed, the federal system may not only potentially cause larger welfare losses, but rapidly loses ground when the strength of spillovers increases.

26

5

Conclusions

In this paper, we have shown that, when parties are self-interested, it is necessary to choose the institutional design that allocates excessive power to the level of government that may cause higher marginal damage. In this way, citizens are less inclined to vote for an electoral promise which departs too much from the optimal allocation of power, and parties are obliged to stay close to the first-best. The economic features of the country (notably the strength of inter-state spillovers) and the political environment (the size of the ego rents) may, therefore, affect the optimal design. When inter-state spillovers are weak, the federal system is preferred since local parties want to deviate less than the central ones. This theoretical finding is in line with some major conclusions in the empirical literature (Biela et al., 2012): a federal system is preferred since it provides a larger decentralization than the unitary system, and it is recommended when inter-state spillovers are weak, in order to better account for state differences. Thus, this widely shared conclusion coincides with our own, although it is based on a different argumentation. Interestingly, our model implies that, under the federal system, there is greater decentralization than in the unitary one, but the preference for this system emerges because it yields a smaller departure from the first-best outcome than in the other case (and not because it yields larger decentralization). We also find that the loss of efficiency under the two systems of government is asymmetric, and a unitary system should be preferred when the ego rents of local parties are high, or when the institutional system is chosen under a veil of ignorance. When inter-state spillovers are high, the federal system tends to perform very poorly because of loss of coordination among states generates large welfare losses. Moreover, when inter-state spillovers are low to medium, the preferred system of government is mainly driven by the relative size of the ego rents of local and central parties, while when inter-state spillovers are high, the unitary system might be preferred, even if the ego rents of central parties are significantly larger than those of local ones. Finally, our findings point out that different aspects can concur with the definition of the optimal

27

system of government. Combining these results with the rapid change in technology, the economy and the political environment that we have recently observed from all around the world, it suggests that many key factors that affecting the performance of an institutional design have changed, or are going to change, and therefore it may be necessary for countries to update their constitutions to keep pace with the times. The analysis suggests that there are two main lines of intervention: first, a fine tuning of the allocation of competencies in the provision of public goods between central and federal governments, without major changes in the constitution. This emerges when the current system is still the preferred one; and, second, a major change in the constitution, when a switch to a different institutional system of government is required. This modification is much more difficult to achieve, although it could also be the most urgent and essential one, as it might lead to more significant welfare effects.

28

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Appendix A - Proofs Proof of Lemma 1. Replacing (12) in (13) and computing the first-order derivative, we obtain:  −Λ

 1 11 11 0 + (Uj (ˆ ai ) − Uj (ˆ a−i )) + U (ˆ ai ) (1 − Λ (ˆ ai − a ˆ−i )) = 0. 2 2Ψ 2Ψ j 0

Limiting to symmetric solutions, a ˆi = a ˆ−i and then from Uj (ˆ ai ) =

1 4

  2(1−θ) 2 2 θ σ −κ a ˆi , the

result follows. Proof of Lemma 2. Replacing (16) in (17) and computing the first-order derivative, we obtain:  λ

   1 11 11 0 1 + [Uj (ˆ aij ) − Uj (ˆ a−i,j )] + U (ˆ aij ) 1 + λ (ˆ aij − a ˆ−i,j ) = 0. 2 2ψ 2ψ j 2 0

Limiting to symmetric solutions, a ˆij = a ˆi,−j and then from Uj (ˆ aij ) =

1 4

  2(1−θ) 2 2 θ σ −κ a ˆij ,

we obtain the result. Proof of Proposition 1. From (10), after some computations, we obtain:

∆Uj

= EUj a ˆ

U




θ − κ2 2−θ

F

− EUj a ˆ "




=σ

σ2 λψ −4 2 2 κ κ

2

"

2−θ  2(1−θ)

 θ  2  θ # λψ 2(1−θ) σ λψ 2(1−θ) σ2 −4 2 − +4 2 + κ2 κ κ2 κ  2  2−θ # σ λψ 2(1−θ) − +4 2 . κ2 κ

Rearranging the terms, it emerges that ∆Uj > 0 when (X − Y )Θ (X + ΘY ) − (X + Y )Θ (X − ΘY ) > 0, where X = σ 2 /κ2 , Y = 4λψ/κ2 , and Θ = 2 (1 − θ) /θ, with 0 < Y < X < 1 − Y < 1 and Θ ∈ [0, ∞). Replacing x = X/Y > 1, we obtain: (x − 1)Θ (x + Θ) − (x + 1)Θ (x − Θ) > 0. When x ≤ Θ, it follows that: ∆Uj > 0. When x > Θ, we have ∆Uj > 0, if:  Υ=

x−1 x+1

Θ

34

x+Θ > 1. x−Θ

Note that ∆Uj = 0 (i.e. Υ = 1) if Θ = 0 or Θ = 1 (i.e. θ r = 2/3). Moreover, since Υ and  −1 dΥ/dΘ are continuous in Θ ∈ (0, x), dΥ/dΘ = 0 only in Θ = 2 ln x−1 x + x2 ∈ (0, 1); x+1   2 x−1 and dΥ(0) dΘ = x + ln x+1 < 0, then, for Θ ∈ (0, 1), ∆Uj < 0; for Θ = 1, ∆Uj = 0; and for Θ ∈ (1, x), ∆Uj > 0. Therefore, for θ ∈ (0, 2/3), we have ∆Uj < 0; for θ = 2/3, ∆Uj = 0; and for θ ∈ (2/3, 1), we have ∆Uj > 0.

Appendix B - Technical details on electoral promises B.1

Form of the set of LPPGs

In the baseline model we have assumed that any electoral promise with a level of local power a ˆi splits the set of LPPGs indexed by ai ∈ Ω ≡ [0, 1) into two intervals: Ai ≡ [0, a ˆi ) indicating those LPPGs which are managed at the local level; and Aci ≡ Ω \ Ai ≡ [ˆ ai , 1) being those which are managed at the central level. We now assume that an electoral promise A is a Borelian set in [0, 1), S i.e. A = ∞ h=1 [rh , sh ), where [rh , sh ) are disjoint intervals with 0 ≤ rh < sh ≤ 1 and rh < rk , P∞ h < k (Billingsley, 1995). Let µ {A} = h=1 µ {[rh , sh )} be a measure of probability which n o defines the level of local power for any electoral promise Aˆi : a ˆi = µ Aˆi . Proposition B The (almost everywhere) optimal strategy for the political party i is to choose the set of LPPGs managed at the local level of the form Aˆi ≡ [0, a ˆi ). Proof We present the proof for the unitary system. A similar reasoning can be made for the federal system. We start by showing that, for any level of local power a ˆi , the probability of winning   the election, Πi , is maximized when Aˆi = [0, a ˆi ). Let Uj A˜−i be the welfare coming from a generic proposal A˜−i ∈ A. Then, from (12), it follows that, in order to maximize Πi , party i has to maximize welfare. According to the new formulation of an electoral promise, we can define the

35

welfare function (10) as: Z Uj (Ai ) = Ai



 Z
1 1 1 1 + σ 2 + k (a) da + (1 + k (a))2 da + I. 4 2 4 Aci

S Assume by contradiction that there exists an electoral promise A˜i = ∞ h=0 [rh , sh ) with mean o n o ˆi and µ A˜i ∩ Aˆci > 0, such that Uj (A˜i ) ≥ Uj (Aˆi ). Let r0 = s0 if 0 sures µ A˜i = a ∈ / A˜i . Choose a small θ > 0, such that θ < min {r1 − s0 , s1 − r1 }, and a new promise A¨i = A˜i ∪ [r1 − θ, r1 ) \ [r1 , r1 + θ). Then, the variation of utility induced by the new promise A¨i ,     Uj A¨i − Uj A˜i , is:   Z Z
1 1 1 2 2 (1 + k (a)) da − 1 + σ + k (a) da+ 4 [r1 ,r1 +θ) 2 [r1 ,r1 +θ) 4   Z Z
1 1 1 1 + σ 2 + k (a) da − (1 + k (a))2 da = + 2 4 [r1 −θ,r1 ) [r1 −θ,r1 ) 4
θ2 2 = κ − σ 2 > 0, 4 where the last inequality comes from (9). Therefore, Uj (A¨i ) > Uj (A˜i ), which contradicts. To complete the proof, we show that the equilibrium solution of the electoral competition game cannot admit strategies in which parties voluntarily want to lose the election, i.e. where at least one party wants to reduce their likelihood of winning, and, therefore, it chooses an electoral promise not in the form Aˆi = [0, a ˆi ). By contradiction, assume that (A˜i , A˜−i ) is an equilibrium in which at least one party i chooses an electoral promise that, for a given level of local power a ˆi , has a lower probability of winning the election. This is not an equilibrium because, if party i prefers its own level of local power, it would prefer to increase the probability of winning the election, and, if it prefers the level of local power of the other party, it can choose a promise which has the same level of local power as the other party and maximize its probability of winning.

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B.2

Bargaining process

In subsection 3.6 we assumed that the level of local power emerging in the federal system is given by the average of the two winning proposals described by (15). We now show that this result can be derived as a solution of a Nash bargaining game (Lorz and Willmann, 2005; 2013; Feder, 2018) or a Baron-Ferejohn bargaining game (Baron and Ferejohn, 1989; Lockwood, 2002; 2004). Nash bargaining game. Assume that in each state the winning party chooses a mediator with 2 the following utility function: mj (ˆ aF ) = M − (ˆ aF − a ˆW j ) if she completes the bargaining process,

and mj (ˆ aF ) = 0 if she does not obtain an agreement with the other mediator. For a sufficiently large
M , by solving the bargaining problem, maxaˆF mj (ˆ aF ) m−j (ˆ aF ) , we obtain three solutions: two minima and one maximum. The latter solution is the result presented in (15). Baron-Ferejohn legislative bargaining game. Assume that the two mediators have the same probability of being recognized as proposer, d ∈ [0, 1] is the discount factor, and (ˆ a1 , a ˆ2 ) = (0, 0) is the status quo. Both mediators have the same probability of being chosen at first; the game ends after two runs. If the mediator of state j is selected, her proposal is accepted by the mediator of state −j if a ˆ∗j > dˆ a∗−j ; otherwise, in the next step, the mediator of state −j will propose a ˆ∗−j ≥ 0, and mediator j will accept. In this setup, (15) is the outcome of the Baron-Ferejon game when the √ √ W √ ˆ / d), where a ˆW d and space of actions of the two parties is in the following interval: (ˆ aW d, a √ a ˆW / d are, respectively, the lower and the upper bounds of the interval, and a ˆW , the geometric mean of the two bounds, is the equilibrium outcome of the bargaining game. In this interval, the proposal of the first mediator is always accepted and, therefore, each proposal has a 50% chance of being accepted. This solution implies that the smaller the discount factor, the larger the space of actions under which the equilibrium holds. When d = 0, (15) becomes the solution of the game for all possible actions (ˆ a∗j , a ˆ∗−j ∈ [0, 1]), because any offer of the first mediator will be accepted. Interestingly, also when d = 1, (15) stands for all possible actions, since in this case, the second mediator always refuses the offer of the first one, and then her proposal will surely be accepted. For those actions 37

outside the proposed intervals, the solution of the game becomes very complex and we cannot guarantee that (15) is still the solution of the game.

Appendix C - An alternative parties’ utility function Throughout the paper, it was assumed that the utility function of parties is separable into the probability of winning the election and the power assigned to their level of government. In this Appendix we show that our conclusions also hold in the case of multiplicative utility functions. In order to do this, in what follows, (5) and (6) are replaced, respectively, by:9

Vi = Πi (1 + Λ (1 − ai )) , !! aij + aW −j . vij = πij 1 + λ 2

(C.1) (C.2)

This new specification has some differences in terms of the parties’ evaluation of the electoral result, as well as of the role of competing electoral promises in the expected utility function of parties. First, with this new utility function, the winning party takes all, i.e. the politicians receive a positive utility from the power assigned to the local government only if they are in government. Second, the electoral promise proposed by the opponent party only affects the probability of winning, but not the ego rents that politicians receive. Contrary to previous cases, we are not able to find a closed form for the second-best solution in the unitary and federal systems. However, we are able to provide the analogues of Proposition 1 and of Figures 2 and 4. Proposition C Assuming that (Ψ, Λ) = (ψ, λ) and σ < κ, then there is a θ¯ ∈ (0, 1) such that,
when θ < θ¯ θ > θ¯ , the federal (unitary) system is the second-best solution. 9

We thank an anonymous referee, who suggested using the following specification.

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Figure C.1: Departure from the first-best levels of local power after an increase of θ when κ2 = 2σ 2 .



¯ if it exists, is such that Uj a Proof By continuity, θ, ˆ U = Uj a ˆF . Using (C.1) and (C.2), and computing the first-order conditions with respect to the level of autonomy, we obtain the response function of the central and the local parties.

1 0 U ψ j

  1 1 0 U (ˆ ai ) (1 + Λ (1 − a ˆi )) − Λ 1 + (Uj (ˆ ai ) − Uj (ˆ a−i )) = 0, Ψ j Ψ ! ! ! !! a ˆij + a ˆW a ˆij + a ˆW a ˆij + a ˆW a−ij + a ˆW λ −j −j −j −j 1+λ +λ+ Uj − Uj = 0. 2 2 ψ 2 2

From symmetry, in equilibrium a ˆL = a ˆR and a ˆlj = a ˆrj for j = 1, 2. Therefore, a ˆU and a ˆF are implicitly defined by the following equilibrium conditions: U0 a ˆU


= Φ a ˆU ,

U0 a ˆF = φ a ˆF ,


(C.3) (C.4)

where: U 0 (a) =

2−2θ σ2 ΨΛ ψλ − κ2 a θ ; Φ (a) = ; φ (a) = − . 4 1 + Λ (1 − a) 1 + λa

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(C.5)

Figure C.1 provides a graphical proof of the Proposition C when κ2 = 2σ 2 . As we will show below, such a parameter choice corresponds to the case in which the threshold θ¯ = 2/3.10 The three solid curves refer to the case in which θ = 2/3, and therefore U 0 (a) is linear and crosses the horizontal axis in a ˆB = 1/2.11 The other two functions Φ (a) and φ (a) are increasing in a and symmetric with respect to the point a ˆB . Moreover, Φ (0) =

ΨΛ 1+Λ ,

φ (0) = −ψλ, Φ (1) = ΨΛ,

ψλ and φ (1) = − 1+λ . Equilibrium solutions a ˆU , a ˆB , and a ˆF are obtained from the intersection of

U 0 (a) with Φ (a), the horizontal axis, and φ (a), respectively. By construction, the triangular area a ˆU a ˆB T corresponds to the welfare loss L(ˆ aU ) and, similarly, the area a ˆF a ˆB t to the welfare loss L(ˆ aF ). Symmetry implies that L(ˆ aU ) = L(ˆ aF ), i.e. θ¯ = 2/3. Consider now the graph for θ > 2/3. Φ (a) and φ (a) remain unchanged and, from (C.5), it emerges that the U 0 (a) curve shifts down and becomes convex. Now the new equilibrium solutions are in a ˆ0U , a ˆ0B , and a ˆ0F , and welfare losses L(ˆ a0U ) and L(ˆ a0F ) are given by a ˆ0U a ˆ0B T 0 and a ˆ0F a ˆ0B t0 , ˆ0U is respectively. We claim that L(ˆ aU ) < L(ˆ aF ) for the following reasons. First, the segment T 0 a ˆ0F because the equilibrium solutions have moved left. Second, thanks to the previous shorter than t0 a argument, and because U 0 (a) has a decreasing slope, also a ˆ0U a ˆ0B is shorter than a ˆ0B a ˆ0F . Finally, the first area is a concave set, while the other area is a convex one. Thus, for θ > θ¯ the unitary system is preferred. A similar argument can be used to show that for θ < θ¯ the federal system is preferred. Before concluding we also present the analogues of Figures 2-4. Also in this case the results displayed by Figures C.2-C.4 do not significantly differ from those contained in the original figures.

10

Simulations confirm that the result holds for the whole parameter set which guarantees the existence of internal solutions, i.e. when σ < κ. 11 With a little abuse of notation, points on the horizontal axis are labeled by the x-coordinate.

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Figure C.2: Departure from the first-best levels of local power (left panel) and welfare losses (right panel) as a function of inter-state spillovers. The dashed lines refer to the federal system and the continuous lines to the unitary system. C (g) = g 2 and k (a, θ) = κa(1−θ)/θ . Parameters: κ = 1; σ 2 = 1/2; λψ = ΛΨ = 1/10.

Figure C.3: Less distortive system of government in the worst case scenario.

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Figure C.4: Electoral context and spillovers. Each curve represents the locus of points where citizens are indifferent to the two systems of government for a given parameter z ≡ ΛΨ + λψ. Parameters: κ = 1; σ 2 = 1/2; z = 0.01, 0.04, 0.08, 0.12.

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Highlights


We study unitary vs federal systems within a model of political competition
Parties face a trade-off between their power and winning the election
The unitary system is better if interstate spillovers and local ego rents are high
The unitary system is better in the worst-case scenario
Excessive (de)centralization leads to larger losses if spillovers are (weak) strong

CRediT author statement Marco Alderighi: Conceptualization, Methodology, Software, Formal analysis, WritingOriginal draft preparation, Writing- Reviewing and Editing. Christophe Feder: Conceptualization, Methodology, Software, Formal analysis, WritingOriginal draft preparation, Writing- Reviewing and Editing.

Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.