# Dress-up Contest: A Dark Side of Fiscal Decentralization

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Dress-up Contest: A Dark Side of Fiscal Decentralization Ruixin Wang∗ Wendun Wang† June 7, 2013 Abstract: This paper models a “dress-up contest” (competition for better images) between governments caused by ﬁscal decentralization, and investigates how this contest aﬀects social welfare. We show that yardstick competition (due to ﬁscal decentralization) enforces local governments to allocate more resources on the more visible public goods (such as cash assistance) than less visible ones (such as vendor payment), and thus starts a dress-up contest. The distortion of resource allocation causes a structural bias of public expenditure and further hurts social welfare. To empirically verify our theoretical model, we employ U.S. state-level data from 1992 to 2008, and estimate the panel data model using various econometric approaches. The empirical results provide strong evidence that ﬁscal decentralization can cause distortion in the use of public expenditure due to dress-up contest. We also ﬁnd that decentralization increases the regional poverty rate due to the distortion. JEL Classiﬁcation: D72, H75, H77 Keywords: Fiscal decentralization; Yardstick competition; Dress-up contest; Functional coeﬃcient model ∗ CentER, Tilburg University, The Netherlands. E-mail: r.wang 4@tilburguniversity.edu † CentER, Tilburg University, The Netherlands. E-mail: wangwendun@gmail.com 1

1 Introduction During the last three decades, ﬁscal decentralization and local government reform has been at the center stage of policy experiments, not just in countries with a traditional tendency of decentralizing like United States, but also in a large number of developing and transition economies, such as Africa, Asia, and Latin America (The World Bank, 1999). Fiscal decentralization, as a process to disperse the right of decision-making in public expenditure from central to local governments, is widely believed to be an eﬀective tool for improving the performance of public expenditure. One of the major transmission channels, documented by a burgeoning literature, is yardstick competition, through which ﬁscal decentralization regulates the behavior of Leviathan government (Besley and Case, 1995; Belleﬂamme and Hindriks, 2005; Besley and Smart, 2007; Bordignon et al., 2004); see Lockwood (2005) for a recent review. In contrast to various beneﬁts of ﬁscal decentralization discussed in the literature, this paper studies a dark side of ﬁscal decentralization. We argue that under asymmetric information, yardstick competition of capability between local governments (due to ﬁscal decentralization) turns into a competition for a better image, that is a “dress-up contest”. This is because voters with limited information cannot observe the politicians’ capability, but infer the capability from the outcome of the public service provided by politicians. It thus motivates politicians to allocate more resources on the public goods that can better demonstrate their capability. The dress-up contest can lead to structural bias in public expenditure, which may further result in a distortion of social welfare. This paper has three main contributions. First, we propose and model a dress-up con- test between local governments, caused by ﬁscal decentralization. We borrow the idea of Rogoﬀ (1990) and Mani and Mukand (2007), and introduce the visibility concept in a two-politician model. Public goods are “invisible” if their outcomes cannot well reﬂect the politicians’ capability, either because they are diﬃcult to observe or because they are determined by other factors out of the government’s control. Mani and Mukand (2007) showed that a government tends to spend more on the visible project than on the invisible project, since voters infer its capability from the visible project. This is referred to as a visibility eﬀect. We extend their model by introducing yardstick competition between two politicians. Using a two-stage game, we show that the yardstick competition between two politicians motivates them to start a dress-up contest. In order to win more support in an election, they allocate more resources (public expenditure and eﬀorts) on the more visible goods, since these goods are more eﬃcient at showing oﬀ their capability and establishing better images, given a binding ﬁscal budget constraint. In this sense, the yardstick com- 2

petition between local governments turns into a competition for a better image, and ﬁscal decentralization can intensify such a dress-up contest. Our model is related with the tax competition model (see for example Janeba and Peters (1999); Cai and Treisman (2005); Zissimos and Wooders (2008)), but our conclusion is rather diﬀerent. In the literature of tax competition, the mobility of capital motivates governments to promote public service. Using a similar framework, we show that the mobility of information may not always be good, because it can distort the structure of public expenditure and cause a welfare loss. Second, we contribute to the discussion of the role of the media in aggravating the “dress-up contest”. In practice, the media play a vital role in an election, since they can inﬂuence a wide range of voters and they have a large eﬀect on the election outcomes to a large extent; see for example Chiang and Knight (2011). On one hand, media supervision may improve political transparency and governance; on the other hand, media capture and media bias can also have a negative eﬀect on the election (DellaVigna and Kaplan, 2007; Durante and Knight, 2012; Gentzkow, 2006); see Prat and Strömberg (2011) for a thorough review. To capture the crucial role of media in an election, we introduce media in our two- politician model, and build up a bridge between two streams of literature: media capture and visibility eﬀect. We model the media as a ﬁrm which makes a proﬁt from supporting a politician, while the cost depends on the authenticity of its reports and the voters’ amount of information. We argue that the information externality caused by yardstick competition can inﬂuence the voters’ belief, either directly or indirectly by aﬀecting media behavior. If the media make false reports of one politician, they will lose reputation and proﬁt less from their readers (Gentzkow and Shapiro, 2006). Hence, media slants to support a politician with a better image, who is believed by the majority to be more capable. We show that media’s behavior enforces politicians to establish a better image by allocating more resources on the more visible projects than on the less visible ones. This can be a negative role of media, since it aggravates the dress-up contest when there exists yardstick competition, which further leads to structural bias in public expenditure and possible social welfare loss. Finally, we provide strong empirical evidence of public expenditure distortion in visible and invisible goods, and we also ﬁnd that such a distortion caused by ﬁscal decentral- ization can result in a social welfare loss. To the best of our knowledge, although the visibility eﬀect has been theoretically established, no research has empirically veriﬁed such an eﬀect, possibly due to the diﬃculties of ﬁnding good empirical proxies. In this paper, we investigate the ﬁscal decentralization eﬀect on the regional poverty rate, an important aspect of social welfare. We propose to use cash assistance to the poor as a proxy for the more visible project, and vendor payment as a proxy for the less visible project. Using 3

U.S. state level data from 1992 to 2008, we ﬁnd that ﬁscal decentralization causes a public expenditure ﬂow from the more visible project to the less visible ones. This result provides evidence of the visibility eﬀect, and also conﬁrms our theoretical ﬁndings that ﬁscal decen- tralization can cause a dress-up contest between local governments. To capture how such distortion of public expenditure aﬀects poverty, we use a functional coeﬃcient approach, and estimate a pooled panel and a panel with a ﬁxed eﬀect. This approach allows us to capture the possible nonlinear interaction between cash-vendor-payment ratio, welfare ex- penditure, and poverty. We ﬁnd that the distortion of public expenditure, measured by the cash-vendor-payment ratio, can largely weaken the eﬀect of welfare expenditure on poverty reduction, and such inﬂuence appears to be nonlinear. Considering the possible endogene- ity of welfare expenditure, we propose to use public expenditure on health and hospital as an instrumental variable of welfare expenditure. Our analysis shows that this instrument is valid theoretically and statistically. We thus empirically verify our theoretical ﬁndings, and provide empirical evidence of a dark side of ﬁscal decentralization. The remainder of the paper is organized as follows. In the next section we formally model the causes and eﬀects of a dress-up contest in the presence of ﬁscal decentralization. In Section 3 provides empirical evidence of a dress-up contest, and Sections 4 and 5 analyze the decentralization eﬀect on social welfare. Section 6 summarizes and concludes. 2 The basic model The basic model aims to illustrate how yardstick competition (dress-up contest), which is introduced by ﬁscal decentralization, can aﬀect politicians’ resource allocation over two types of public goods, the more visible goods and the less visible one. Since voters can only infer politicians’ capability from the outcome of public service, politicians tend to establish a better image to win more votes. The media eﬀect on election strengthens politicians’ motivation of establishing a good image. However, overemphasis on image building can cause an eﬃciency loss of welfare expenditure, and further hurt social welfare. In this section, we ﬁrst derive the equilibrium of a two-stage game, and then analyze the comparative statics, i.e. the impact of ﬁscal decentralization on this equilibrium. 2.1 Politicians Assume there are two incumbent politicians A and B from two local governments, respec- tively, and there exists yardstick competition between them. In particular, they compete with respective challengers to win the local election of their own region, but their chal- 4

lengers can be cheap talkers. Due to the possible cheap talker, voters not only compare the incumbent with his challengers, but more importantly with the other incumbent in the neighboring jurisdiction; see Besley and Case (1995); Bordignon et al. (2003); Revelli (2006) for the empirical evidence of yardstick competition. To win a future election, politi- cians have to allocate their limited resources and show higher capability to voters. The expected utility function of each politician is E (Ui ) = Rηi − Pi Si − Ci (e1i , . . . , eJi ) i ∈ {A, B}, ∑J s.t. Ii = eji . (1) j=1 In this utility function, R is the return of winning the election with R = 0 when one fails, and ηi is the probability of winning the local election for politician i. To win the election, each politician has to buy the support of media at price Pi , and the cost of such media capture depends on the share of media supporting him Si and price Pi . Meanwhile, a politician needs to provide evidence of his capability (such as public service) at the cost C to make media endorsement convincing. Note that C depends on the public expenditure on J public services, and expenditure on jth public service is denoted by ej,i . We shall assume the ﬁrst and second order derives of the cost function satisfy C ′ (e) > 0 and C ′′ (e) > 0. The optimal problem is subject to a budget constraint that total public expenditure over all public services is bounded by Ii . This setup is in the similar essence of the tax competition model; see for example Janeba and Peters (1999), Cai and Treisman (2005), and Zissimos and Wooders (2008). 2.2 Voters We assume there are two types of voters, the well-informed voters with proportion k and ill- informed ones with proportion 1 − k. Well-informed voters not only observe the outcomes of public projects in the local jurisdiction, but also in the neighboring. Thus they are able to make their voting decision by comparing candidates with the politicians from other jurisdictions. On the contrary, the ill-informed voters only observe the outcomes of public projects oﬀered by the local incumbent, but they do not have access to the information of politicians from other jurisdictions. Therefore, ill-informed voters’ voting decisions are largely based on the the information provided by media. This results in (1 − k)Si share of voters, among all ill-informed voters, that support politician i. We then obtain the share of votes for politician i as ηi = kΦi + (1 − k)Si i ∈ {A, B}, (2) 5

where Φi is the inferred capability of politician i based on the outcomes of public projects they provide. This share can also be interpreted as a probability of a “representative voter” to support politician i. Equation (2) suggests that the probability of politician i to win the election is determined by the assessment of their capability and the endorsement of media. Note that ηA + ηB is not necessary to be unity, because politician A and B are only involved in yardstick competition rather than a direct competition for the same position. This implies that even if ηA < ηB , politician A could still beat his challenger (a possible cheap talker) and win the election. 2.3 Media Each media, as a ﬁrm, maximizes its proﬁt by choosing to support one politician, given the oﬀered price and politician’s performance. The expected proﬁt function of media is E (πi ) = s k[ρi (−N ) + (1 − ρi )M ] +s (1 − k)M . Pi + |{z} (3) |{z} | {z } | {z } politician repu. well-info. voters ill-info. voters Three components of the proﬁt are speciﬁed in the proﬁt function, namely the proﬁt from government, from readers/voters, and from advertisement. First, each media provides endorsement or propaganda for a politician, and receives revenue Pi from politician i. Sec- ond, media make proﬁt from readers/voters, e.g. newspaper sale, and voters with diﬀerent amount of information contribute to this part of proﬁt diﬀerently. Well-informed voters are able to compare the information provided by some media with their own information. If they ﬁnd two sources of information are not consistent, they choose not to buy the products of this media. This media thus have a proﬁt loss due to false endorsement, and we denote such loss by −L. If the media’s endorsement is in line with the information of well-informed voters, then it makes proﬁt from these voters which we denote by M . Since endorsement has to be made before the outcome of public service is realized, media can on- ly choose politician to support according to the expectation of Φi , denoted by Ωi := E(Φi ) for i = {A, B}. Media can make false endorsement if they choose to support politician i but Φi < Φ−i , and we denote the probability of making false endorsement for politician i as ρi := Pr (Φi < Φ−i ). Under appropriate conditions1 , Pr (Φi < Φ−i ) is negatively correlated with Ωi . Without loss of generality, we assume that 1 Pr (Φi < Φ−i ) = 0 < θ < 1. (4) Ωθi 1 For example, Φi and Φ−i has the same variance. 6

Unlike well-informed voters, ill-informed voters are “ignorant” and have no preference on media. Therefore, they randomly choose products of media, and contribute M to media’s proﬁt. Finally, the proﬁt includes other sources that rely on media’s reputation, e.g. advertisement. This part of proﬁt is closely related with the proﬁt from readers/voters, because more readers/voters are typically associated with more advertisement. Therefore, it is plausible to assume that this part of proﬁt (e.g. advertisement proﬁt) is proportional to the proﬁt from voters. If we denote s as a measure of reputation, then s enters media’s proﬁt function as a coeﬃcient of the proﬁt from voters. Assuming s follows a standard uniform distribution, then a value between [0, 1] uniquely identiﬁes a media. By plugging Equation (4) into Equation (3), we can rewrite media’s expected proﬁt function as sk (M + N ) E(πi ) = Pi + sM − . (5) Ωθ 2.4 Assessing politicians’ capability To model the dress-up contest, we consider two types of public goods, the more visible goods a and the less visible one b. According to Mani and Mukand (2007), some public goods are less visible if it is harder to assess government competence based on its observed outcome. Politicians need to allocate their limited resources across these two types of goods from which voters can infer their capability. Following Mani and Mukand (2007), we assume the production function of each good zj,i = τi + ej,i + ϵj,i j ∈ {a, b}, i ∈ {A, B}, (6) where zj,i is observed output of public goods j provided by politician i, τi is politician i’s capability, ej,i is the politician i’s expenditure or eﬀort allocated on goods j, and ϵj,i ∼ ( 2 ) N 0, σj,i capturing the exogenous stochastic factors. Public goods a being more visible 2 2 than b implies that there is more noise in the outcome of b than that of a, i.e. σa, i < σb, i . Mani and Mukand (2007) provided two reasons for the diﬀerences in visibility. First, outcomes of some public goods are intrinsically harder to directly observe or measure (e.g. short term outcomes are typically more visible than those in the long term); Second, some public goods are more “complex” in the sense that their outcomes are aﬀected by a vatiety of factors apart from government competence. For example, the quantity and quality of education is not fully determined by the work of government, but also the teachers, parents, and peers. For simplicity and without loss of generality, politicians are assumed to have the same τ and and ϵj . Voters can observe the outcome of the public goods z as well as the expenditure e. A politician’s capability τ is unobserved, but voters have common knowledge of its prior 7

distribution τi ∼ N (τ , στ2 ) for i ∈ {A, B}. Voters (with rational expectations) can use the observed outcome zi := {za,i , zb,i } and public expenditure e∗i := {e∗a,i , e∗b,i } to update their priors of politicians’ capability, that is from τ to (zj,i − e∗j,i ) with associated variance σj,i 2 . According to Mani and Mukand (2007), the mean posterior assessment of the politician’s capability can be obtained by [ ( ) ( )] ∗ ∗ h τ τ + h a z a,i − e + h b z b,i − e Φi = E (τi | zi , e∗i ) = a,i b,i , hτ + ha + hb where hτ = 1/στ2 and hj = 1/σj2 (j = a, b) the precision of the prior and two realizations, respectively. For politicians, according to his utility function (1), his optimal decision is based on the expectation of E (τi | zi , e⋆i ) over the entire distribution of possible output zi , that is [ ( ) ( )] ∗ ∗ h τ τ + h a τ + e a, i − e + h b τ + eb,i − e Ωi = Ezi [E (τi | zi , e∗i )] = a,i b, i . hτ + ha + hb As for media, since they have to make endorsement at the beginning of election campaign (before Φi is realized), they choose the politician to support also based on the expected mean posterior assessment ΩA = EzA [E (τA | zA , e∗A )] , and ΩB = EzB [E (τB | zB , e∗B )] . 2.5 Two-stage game We employ a two-stage game. In the ﬁrst stage, two politicians non-cooperatively and simultaneously choose public expenditure on project a and b, respectively. In the second stage, given the observed public expenditure, politician A and B choose the price of media capture PA and PB , respectively. Both stages are pure-strategy games. This order of events reﬂects the idea that the price of media capture can be changed relatively easily once the level of public expenditure has been determined, while a change in public expenditure would be more costly. Afterwards, the media choose to support one politician (A or B) given the price and the inferred capability. We shall use the backward induction to derive our results. The time line of the game is as follow. First, politicians choose the expenditure on two types of public goods. Then, they decide the price for media capture. Next, media choose one politician to support and make their endorsement before voting starts. As the last step, given the outcome and expenditure of public projects, well-informed voters choose to support politician i with higher inferred capability Φi . Diﬀerently, ill-informed voters make their decision based on media’s endorsement. After voting, politicians’ payoﬀs are then realized. 8

2.5.1 Media strategy Media’s choice is based on their proﬁt function (3) and the expected mean posterior assess- ment of politicians’ capability. To describe the media’s behavior in the election, we ﬁrst compute the position of the marginal media ŝ that make no diﬀerence between supporting politician A and B, that is πs,A = πs,B . This leads to indiﬀerence marginal media PA − PB ŝ = (7) k(M + N )Ψ where Ψ := 1/ΩθA − 1/ΩθB . This threshold value ŝ also determines the share of media to support A and B. Simple calculation gives that media with s < ŝ will choose to support A, while those with s > ŝ will support B, that is SA = ŝ and SB = 1 − ŝ. Plugging ŝ into (1), we can obtain the expected returns of politician A and B, respectively, as [ ] b A ) = R kΩA + (1 − k) (PA − PB ) (PA − PB ) E(U − PA − CA (ea,A ), (8) k(M + N )Ψ k(M + N )Ψ and [ ( )] [ ] b PA − PB (PA − PB ) E(UB ) = R kΩB + (1 − k) 1 − − PB 1− − CB (ea, B ) . (9) k (M + N ) Ψ k (M + N ) Ψ We note from Equation (7) that ŝ is not deﬁned in two special cases: ea,A = ea,B or k = 0. In the ﬁrst case with ea,A = ea,B , performance of two politicians are exactly homogeneous given the same budget constraint, and thus media’s strategies are completely determined by PA and PB . In the second case when k = 0, no media cares about the performance of politicians. Both cases can be analyzed by Bertrand price game, where politicians simply compete over the price. Therefore, these two cases are of less interest in this paper, and we mainly examine the case k ̸= 0 and ea,A ̸= ea,B . Without loss of generality, we shall assume ea, A < ea, B in the following analysis, and symmetric conclusions can be easily obtained in the other scenario. 2.5.2 Stage 2: Competition of price In the second stage, politicians decide the price of media capture for given value of public expenditure determined in the ﬁrst stage. Therefore, the best response of politician A is to maximize UA against a strategy of politician B, and vice verse. By solving the ﬁrst order conditions, we can obtain the equilibrium price k (M + N ) Ψ 2k (M + N ) Ψ PA∗ = R (1 − k) − , PB∗ = R (1 − k) − , (10) 3 3 9

and these lead to the maximized expected utility b A )∗ = RkΩA + k(M + N )Ψ − CA , E(U b B )∗ = RkΩB + 4k(M + N )Ψ − CB (11) E(U 9 9 2.5.3 Stage 1: Competition for better image In this stage, based on the equilibrium price in (10), politicians decide the allocation of ea, A and ea, B to achieve high mean posterior assessments of their capabilities (better images) and a higher probability of winning election. We ﬁrst look at the strategy of politician A. His optimization problem is given by ( ) b ∗ k(M + N ) 1 1 E(UA ) = RkΩA + − − CA (ea,A ) 9 ΩθA (ea,A ) ΩθB (ea,B ) s.t. IA = ea, A + eb, A The ﬁrst order condition gives [ ( )1+θ ] ( ) ∂ Ê(UA )∗ kθ(M + N ) 1 ha ′ = Rk − − CA (ea,A ) − λ = 0, (12) ∂ea,A 9 ΩA (ea,A ) hτ + ha + hb where λA is a Lagrangian multiplier. Since we have assumed a binding budget constraint, λ must not be nonzero, and the optimal expenditure e∗a,A is the solution to (12). Similarly, the ﬁrst order condition for politician B is [ ( )1+θ ] ( ) b B )∗ ∂ E(U 4kθ(M + N ) 1 ha ′ = Rk − − CB (ea,B ) − λB = 0, (13) ∂ea,B 9 ΩB (ea,B ) hτ + ha + hb and the best strategy e∗a,B is the solution to (13). 2.6 Eﬀect of ﬁscal decentralization Based on the analysis above, we can examine how ﬁscal decentralization aﬀects politician- s’ behavior, that is their public expenditure on two types of goods ea,i and eb,i . Fiscal decentralization can be regarded as a trigger of yardstick competition, which strengthens information externality, and voters have more knowledge to compare politicians’ capabili- ty. This thus increases the proportion of well-informed voters, that is large k, and further forces media to care more about their reputation. A larger proportion of well-informed vot- ers and more careful media both motivate politicians to show a better image to the public, and may cause a dress-up contest. Therefore, we analyze eﬀect of ﬁscal decentralization by investigating how an increase in k aﬀects the equilibrium. 10

b B )∗ /∂ea,B . Note that we always have We ﬁrst look at politician B. Deﬁne FB := ∂ E(U ( ( )1+θ ) ( ) ∂FB (·) 4θ(M + N ) 1 ha = R+ > 0, ∂k 9 ΩB (ea,B ) hτ + ha + hb and [ ( )2+θ ] ( )2 ∂FB (·) 4kθ(θ + 1)(M + N ) 1 ha =− − CB′′ (ea,B ) < 0. ∂ea,B 9 ΩB (ea,B ) hτ + ha + hb Therefore, by using the implicit function theorem, we can obtain ( ) ( ) ∂e∗a,B ∂FB ∂FB =− / > 0. (14) ∂k ∂k ∂ea,B This shows that as k increases, politician B spend more on the more visible public goods. Given the binding budget constraint, the expenditure on the less visible public goods is thus shrinks as k increases. We then study the behavior of politician A. In the case of ea,A < ea,B , the behavior of politician A is slightly complicate than B. Politician A’s optimal expenditure on the more visible goods does not always increases as k rises. This can be seen from ( ( )1+θ ) ( ) ∂FA (·) θ(M + N ) 1 ha = R− · , ∂k 9 ΩA (ea,A ) hτ + ha + hb and [ ( )2+θ ] ( )2 ∂FA (·) kθ (θ + 1) (M + N ) 1 ha = − CA′′ (ea,A ) ∂ea,A 9 ΩA (ea,A ) hτ + ha + hb = Q − CA′′ (ea,A ). If R is large enough so that ∂FA /∂k > 0 and ∂FA /∂ea,A < 0, then we have ∂e∗a,A /∂k > 0. This means that if the revenue of wining a election is particularly high and the “cost” of spending on visible goods is convex2 , then politician A still chooses to participate the dress-up contest. To sum up, our model shows that when k increases (more well-informed voters and more careful media), politicians tend to put more eﬀorts on establishing a good image. Given ( ) 2 The “cost” refers to GC := CA (ea, A ) − k/9(M + N ) 1/ΩθA − 1/ΩθB . We regard GC as a generalized cost function of public expenditure on good a, because the ﬁrst order derive of GC with respective to ea,A is always negative. Thus, a convex generalized cost function implies negative ∂FA /∂ea,A , the second order derive of GC. 11

a binding ﬁscal budget constraint, the more visible goods are more eﬃcient at showing oﬀ their capability and establishing a good image. This explains why the expenditure on the more visible goods increases in the process of ﬁscal decentralization. However, overemphasis on the visible goods can lead to a structure bias of public expenditure, and thus hurt social welfare. This implies that politicians competition for better images may have a negative eﬀect on social welfare, and we shall empirically investigate these theoretical ﬁndings in the following sections. 3 Evidence of a dress-up contest Our empirical analysis has two goals. The ﬁrst is to provide evidence of the association between ﬁscal decentralization and a dress-up contest. Second, we ask how a dress-up contest aﬀects poverty, an important aspect of social welfare. We address the ﬁrst issue in this section, and the second in the following two sections. We use U.S. state level data, and our sample covers 48 states excluding Alaska and Hawaii with the time span from 1992 to 2008. A key issue is how to determine the more visible public goods and the less visible ones. It is diﬃcult to ﬁnd a strictly visible public good in the real world because most public goods are determined by a number of factors out of the government’s control, and their outcomes are diﬃcult to observe or measure. In our analysis regarding poverty, we take cash assistance as a relatively more visible public project and vendor payment as a less visible one. Cash assistance directly improves residents’ disposable income, and further reduces poverty. Hence, its outcome, i.e. poverty reduction, can be observed in the short term, and this outcome largely depends on government’s expenditure of this service, less aﬀected by other factors out of the government’s control. On the contrary, vendor payment is given to private purveyors for medical care, burials, and other commodities. Its outcome depends on a large number of factors out of government’s control, such as the performance of other institutes, and also the outcome may be observed in a longer period of time. Therefore, it is reasonable to regard cash assistance as relatively more visible, while vendor payment as less visible. We provide various evidence to show the existence of a dress-up contest. Since it is diﬃcult to exactly identify all transmission channels, we use evidence from various aspects to rule out possible alternative explanations. 12

3.1 Fiscal decentralization eﬀect on public expenditure structure We ﬁrst consider a direct test for the causal eﬀect of ﬁscal decentralization on a dress- up contest. To outline our empirical strategy, we introduce some preliminary notations. Assume politicians in the state-level government spend 1/vS of state expenditure on visible projects, while local-level politicians spend 1/vL of local expenditure on these projects. Since yardstick competition is more ﬁerce in a local election than in a state election, we have vS > vL ≥ 1. If we denote Γ as total (state + local) public expenditure, and denote D as the degree of ﬁscal decentralization, then the total expenditure on the more visible project (cash assistance) and total expenditure on the less visible project (vendor payments) are given, respectively, by ( ) ( ) Γ 1 1 D D−1 Cash = + ΓD − , and Vendor = Γ − Cash = Γ 1 − + . vS vL vS vL vS The ratio of Cash over Vendor (hereafter CV ratio) then follows vL + D(vS − vL ) RCV = . vL (vS − 1) − D(vS − vL ) Note that RCV is a monotonically increasing function of the degree of ﬁscal decentraliza- tion, i.e. ∂RCV vS vL (vS − vL ) = > 0. (15) ∂D [(vS − 1)vL − D(vS − vL )]2 Therefore, as the degree of ﬁscal decentralization increases, total expenditure on cash and the ratio of total cash expenditure over total vendor payment expenditure both increase. Inequality (15) thus allows us to empirically test the direct association between decentral- ization and a dress-up contest. To test this direct association, we consider the reduced form model RCVit = αi + κ0 + κ1 Dit + κ2 TWEit + εit , (16) where subscript ‘it’ denotes observation of i-th state (i = 1, . . . , N ) at year t (t = 1, . . . , T ), αi is the individual-speciﬁc eﬀect. D represents the degree of ﬁscal decentralization, and we measure it by Local public expenditure D := , Total public expenditure where the local expenditure includes expenditure of county, city, and town governments, and total expenditure is the expenditure of state and local governments; TWE is the total (state + local) welfare expenditure. Fixed eﬀect estimation results3 are given in 3 Preliminary analysis suggests the ﬁxed eﬀect model is more appropriate than the random eﬀect model. 13

column (1) of Table 1. It shows that a larger degree of decentralization is associated with a larger ratio of cash over vendor payment, and the correlation is strong and robust. In column (2) and (3), we replace the contemporary ﬁscal decentralization D by its ﬁrst and second order lagged value DL1 and DL2 , respectively, to capture the causal eﬀect, since a ﬁscal decentralization policy may take eﬀect after a time. We see that using lagged values of ﬁscal decentralization gives a more positive and also more signiﬁcant estimate, conﬁrming the causal relationship between decentralization and the CV ratio. Table 1: Decentralization eﬀect on the CV ratio (1) (2) (3) (4) D 0.4849 (2.43) DL1 0.5018 (2.67) DL2 0.4888 (3.06) DCT 2.3915 (2.77) TWE −0.2464 −0.2539 −0.2270 −0.2760 (−9.78) (−10.26) (−10.06) (−5.68) CONST 0.2430 0.2484 0.2233 0.2532 (7.83) (8.40) (8.58) (6.86) As a robustness check, we recompute the ﬁscal decentralization ratio using the local expenditure that only covers expenditure of city and town governments (without county- level governments), and we denote this ratio as DCT . Since the yardstick competition between local governments at the city and town level is supposed to be more intense than between county-level governments, we expect to observe stronger association between a dress-up contest and ﬁscal decentralization when using the public expenditure of city and town level, i.e. a more signiﬁcant and positive estimated coeﬃcient κ1 . The results in column (4) indeed report a more signiﬁcant eﬀect of ﬁscal decentralization on the CV ratio, in line with our expectation and also showing the robustness of this ﬁnding. 3.2 The role of yardstick competition Since yardstick competition plays a crucial role in the theoretical model, to further examine the mechanism, we introduce yardstick competition in our empirical analysis. Considering the fact that ﬁscal decentralization distorts the structure of public expenditure through 14

the channel of yardstick competition, we should expect that if yardstick competition gets ﬁercer, then the distortion should be intensiﬁed. To see this more formally, suppose the local level yardstick competition is intensiﬁed, i.e. smaller vL , then we have RCV increases, because ∂RCV DvS2 =− < 0. ∂vL [(vS − 1)vL − D(vS − vL )]2 This implies that given the same degree of decentralization, if yardstick competition for local election is ﬁercer in one state than in the other, then politicians in the former state have more incentive to invest on visible projects. Put it diﬀerently, the degree of yardstick competition can aﬀect the impact of ﬁscal decentralization on the structure of public ex- penditure. This mechanism can be empirically captured by an interaction term of yardstick competition and ﬁscal decentralization. Thus we consider the model RCVit = αi + κ0 + κ1 Dit + κ2 COMPit + κ3 Dit × COMPit + κ4 TWEit + εit , (17) where COMP is a measure of yardstick competition. Estimating (17) allows us to identify the mechanism described in Section 2, at least to some extent. Yardstick competition is a diﬃcult concept to measure, and to our best knowledge there is no satisfactory measures in the literature. We propose two measures for yardstick competition from the perspectives of comparability of jurisdictions and competitiveness of local governments. First, we consider the comparability of jurisdictions. This is mo- tivated by the argument of Bodenstein and Ursprung (2005) that yardstick competition “emerges when the performance of governments in various jurisdictions becomes suﬃcient- ly comparable so that the voters can alleviate the agency problem by making meaningful comparisons between jurisdictions”; see also Besley and Case (1995). In U.S., most con- gressional districts consist of several local governments that share similar political and economic situations, such as similar political interests, voters’ preference, et al. Hence, we expect that the yardstick competition between local governments within one congression- al district is stronger than that outside the district. This implies that the congressional district demarcates the political boundaries of yardstick competition. If a district contains more local governments, then the yardstick competition in this district is more intense because each local government has more comparable rivals. Thus motivated, we propose to measure yardstick competition by The number of local governments COMPr := . The number of congressional districts This ratio is unaﬀected if we control for a state’s land size or population since we divide both nominator and denominator by the land size or population at the same time. 15

Next, we consider measuring yardstick competition by the competitiveness of local election, which is computed by the percentage of votes won by the leading party. We denote this measure as COMPc . The competitiveness of local election reﬂects the level of local yardstick competition, and the average level of competitiveness is a reasonable index to measure the yardstick competition within the state. Competitiveness is high if the leading party just win a small share, suggesting that either competing parties are well matched or none of the candidates can get support of most voters. In both cases, yardstick competition can be intense. Due to the lack of county-level data, we use congressional district level data. In the two-party system of U.S., congressional election is expected to be highly correlated to local (county, city or town) election, and thus the average level of congressional election competitiveness can be a proxy of the yardstick competition of local election in a state. To see how the decentralization eﬀect varies over diﬀerent levels of competitiveness, we ﬁrst rank all states according to its average competitiveness (average over time). Then, we estimate the ﬁscal decentralization eﬀect using two samples, states with most intensiﬁed competition and states with least intensiﬁed competition, respectively. Column (1)–(4) of Table 2 present the comparison between the two samples. It is clear that ﬁscal decen- tralization eﬀect on the CV ratio is much stronger and more signiﬁcant in the states with more intensiﬁed competition. Next, we examine the interaction eﬀect of competitiveness more formally by estimating the panel data model (17). Estimation results are given in column (5)–(8) of Table 2. We see that the interaction terms are strongly positive when using COMPr and strongly negative when using COMPc in models with contemporary and lagged decentralization. This again conﬁrms that more intense yardstick competition leads to stronger eﬀect of decentralization on the CV ratio. The signiﬁcance of level terms D and COMP diﬀers across the measurements of yardstick competition. COMP is sig- niﬁcant but D is not when we measure competition by COMPr ; on the contrary, D is signiﬁcant but COMP is not when competition is measured by COMPc . In the diﬀerence- in-diﬀerence model, the coeﬃcients of level terms only capture an “initial” eﬀect. Diﬀerent signiﬁcance levels suggest that COMPr and COMPc measure yardstick competition from diﬀerent perspectives. Since the size of the interaction term in column (5) and (6) is much larger than that in column (7) and (8), and also larger than the size of its level terms, we thus ﬁnd results using two measures generally consistent, namely that larger degree of ﬁscal decentralization and more intense yardstick competition are associated with higher CV ratio. To summarize, the above analysis shows that a large degree of ﬁscal decentralization is associated with an expenditure ﬂow from the more visible product (cash assistance) to the 16

Table 2: Interaction between decentralization, yardstick competition, and CV ratio Comp. top 15 Comp. bottom 15 Entire sample (1) (2) (3) (4) (5) (6) (7) (8) D 0.7432 0.5789 −0.0900 0.4929 0.0599 0.8393 (4.91) (2.52) (−0.40) (1.55) (0.39) (2.92) DL1 0.1178 0.9182 (0.79) (3.60) TWE −0.2923 −0.2769 −0.2804 −0.2195 −0.2636 −0.2668 −0.2457 −0.2536 (−8.00) (−4.94) (−8.76) (−6.50) (−11.90) (−12.39) (−10.24) (−10.64) √ √ COMPr −2.4494 −2.7143 (−3.56) (−4.01) √ √ COMPc −0.0004 −0.0004 (−0.66) (−0.56) D×COMPr 6.9800 (3.91) D×COMPc −0.0067 (−2.24) DL1 × COMPr 6.3943 (4.05) DL1 × COMPc −0.0081 (−3.05) CONST 0.2590 0.2591 0.3086 0.2328 0.3266 0.3335 0.2661 0.2722 (8.07) (3.68) (8.62) (8.74) (11.50) (12.54) (5.93) (5.90) Note: Column (1) and (2) use the sample of 15 states with the most ﬁerce competition, based on COMPr and COMPc , respectively; column (3) and (4) use the sample of 15 states with the least ﬁerce competition, based on COMPr and COMPc , respectively; column (5) and (6) use the entire sample of 48 states. 17

less visible product (vendor payment), and the association is even stronger in regions with more intense yardstick competition. This is because to achieve a better image and win more votes, politicians tend to allocate more resources on the more visible project. Such a dress-up contest is intensiﬁed by ﬁscal decentralization through the channel of yardstick competition. These empirical results thus provide evidence to our theoretical ﬁndings. 4 Fiscal decentralization eﬀect on poverty We have seen, from both theoretical and empirical perspectives, that ﬁscal decentralization can cause a dress-up contest which enforces governments to allocate more expenditure on the more visible public goods. In the following two sections, we investigate how such distortion of public expenditure inﬂuences social welfare. We focus on the eﬀect of ﬁscal decentralization on poverty rate, an important aspect of social welfare, and empirically identify the transmission mechanisms. For this purpose, we introduce additional three variables: poverty (p), unemployment rate (UNEM), and Gini index (GINI). Poverty is deﬁned by the share of people with income lower than the standard, and this standard diﬀers across states. More detailed description of the variables and their sources are given in the Appendix. Figure 1: Transmission channels from ﬁscal decentralization to poverty A - Cash B Vendor payment ? Fiscal decentralization C - Welfare expenditure -Poverty D 6 E We mainly focus on three channels from ﬁscal decentralization to poverty, which are sum- marized in Figure 1. First, according to the two-politician model in Section 2, ﬁscal decentralization can aﬀect poverty through the dress-up contest, that is an expenditure ﬂow from the less visible goods to the more visible goods (eﬀects A and B). Second, ﬁscal decentralization can also indirectly aﬀect poverty by aﬀecting the amount of welfare ex- penditure (eﬀect C and D). On one hand, ﬁscal decentralization may increase the amount 18

of welfare expenditure due to more administrative cost; on the other hand, it is likely that welfare expenditure shrinks after decentralization because mobility of the poor motivates governments to spend less on welfare to cut down the ﬁscal burden. There is no priori which eﬀect dominates, and we shall investigate this in our empirical study. Finally, in addition to the indirect eﬀects, ﬁscal decentralization can have impact on poverty through other channels besides welfare expenditure and a dress-up contest. Therefore, we also con- sider other connection between decentralization and poverty as eﬀect E. We point out that CV ratio does not directly inﬂuence the poverty, but indirectly by aﬀecting the welfare expenditure eﬀect on poverty (change the structure of welfare expenditure). That is why the arrow line of eﬀect B does not point at poverty, but at the eﬀect D. We use the dashed line for channel D since there is potential reverse causality between welfare expenditure and poverty, which we shall investigate using instrumental variables. 4.1 Standard panel data To provide empirical evidence of the transmission channels described in Figure 1, we ﬁrst identify each eﬀect A– E separately, and then jointly in the next section. First, we examine the transmission channel from ﬁscal decentralization to welfare expenditure, and then to poverty, namely the eﬀect C and D. To show the mediation of welfare expenditure, we estimate the following models TWEit = αi + θ0 + θ1 Dit + eit , (18) pit = αi + β0 + β1 Dit + β2 TWEit + β3 UNEMit + β4 GINIit + ϵit . (19) Model (18) captures the transmission eﬀect C, while (19) captures the direct eﬀect from decentralization to poverty (eﬀect E) and the indirect eﬀect through welfare expenditure (eﬀect D). Columns (1)–(5) of Table 3 present the standard ﬁxed eﬀect estimation results based on Equation (18) and (19). Column (1) shows that ﬁscal decentralization has strongly negative eﬀect on welfare expenditure. Column (2) replaces the contemporary value of F D by its ﬁrst order lagged value DL1 , and shows a similar result, conﬁrming that large degree of decentralization leads to less welfare expenditure. This suggests that the negative eﬀect of ﬁscal decentralization on welfare expenditure dominates in our case. In particular, since the poor are mobile, an increase of welfare expenditure in one jurisdiction attracts the poor to ﬂow in this region, which of course adds to burden of this jurisdiction but reduces the burden of others. Therefore, if most jurisdictions are free riders, then decentralization leads to a coordination failure and an ineﬃcient public goods provision. Column (3) shows 19

Table 3: Estimation results of separate transmission channels (1) (2) (3) (4) (5) (6) (7) TWE TWE p p p p p D −1.1031 7.4507 5.4731 4.7246 3.3062 4.6255 (−3.58) (4.54) (3.49) (2.29) (1.54) (1.82) DL1 −1.0418 (−3.56) TWE −1.7927 −2.2731 −0.4419 −2.3902 (−3.38) (−3.57) (−0.72) (−3.48) GINI −0.1913 0.6650 (−0.08) (0.29) UNEM 0.5519 0.5784 (6.07) (5.78) RCV 4.5906 0.1824 (3.19) (0.13) CONST 0.7922 0.7796 12.037 13.457 10.960 12.142 10.518 (28.15) (27.82) (80.16) (30.95) (8.46) (22.83) (8.00) a signiﬁcant and positive overall eﬀect of ﬁscal decentralization on poverty, challenging the conventional viewpoint that ﬁscal decentralization has a positive impact on social welfare. This eﬀect is largely reduced (size and signiﬁcance) when including welfare expenditure (column (4)), but remains strong, and the coeﬃcient of welfare expenditure is signiﬁcantly negative. It suggests that part of ﬁscal decentralization eﬀect on poverty is explained by the intermediate transmission through welfare expenditure, and it provides evidence of strong eﬀect C and D. These eﬀects are robust when we include Gini coeﬃcient and unemployment (column (5)). To examine the eﬀect B, we ﬁrst add RCV as an explanatory variable in the poverty regression. Column (6) and (7) show that ﬁscal decentralization eﬀect remains strong and positive after controlling welfare expenditure and CV ratio, and this suggests the existence of eﬀect E. The strongly positive and robust eﬀect of ﬁscal decentralization again conﬁrms the negative eﬀect of ﬁscal decentralization on poverty reduction. The CV ratio is positively related with poverty, but this eﬀect becomes insigniﬁcant controlling unemployment and Gini index. It shows that the CV ratio can be positively related with poverty, but the delicate coeﬃcient suggests that the standard panel data model may not fully capture the eﬀect of CV ratio on poverty. Also, we see that including RCV can aﬀect the estimated coeﬃcient of WE, which suggests possible interactions between RCV and WE. In fact, the CV ratio inﬂuences poverty by interacting the eﬀect of welfare expenditure. Excessively 20

large (or small) proportion of cash over vendor payment harms the eﬃciency of welfare expenditure in poverty reduction, while an appropriate ratio can maximize the eﬀect of welfare expenditure. Therefore, the eﬀect B cannot be fully captured by the standard ﬁxed eﬀect model with RCV as a control variable, and more appropriate methods are required. 4.2 Endogeneity of welfare expenditure A potential issue is the endogeneity of welfare expenditure. The endogeneity is due to possible reverse causality between welfare expenditure and poverty; in particular, welfare expenditure can reduce poverty, while regions with a higher poverty rate are likely to have larger welfare expenditure. To reduce potential bias caused by reverse causality, we consider instrumental variable estimation. We propose to use public expenditure on health and/or hospital as the instrumental variable of welfare expenditure. Expenditure on health and hospital is highly correlated with welfare expenditure because factors such as citizens tastes for government services, the politicians attention on citizens’ wellbeing, and power of public sector unions can jointly inﬂuence the expenditure on welfare, health, and hospital. Besides, this instrument does not depends on poverty, and not aﬀect poverty via indirect routes other than welfare expenditure. Therefore, health and hospital expenditure satisﬁes the requirement of relevance and exogeneity, allowing for its possibility to be an appropriate instrumental variable. The choice of such instrument is also in the similar essence of Levitt (2002). We consider four choices of the instruments, expenditure on health (HE), expenditure on hospital (HO), expenditure on health and hospital (HH), and expenditure on health together with expenditure on hospital (HEO). In the ﬁrst three, the model is exactly iden- tiﬁed, and we estimate it using 2 stage least square (2SLS). In the last case, we estimate the overidentiﬁed model using generalized method of moment (GMM). Results are pre- sented in Table 4. We see that using the instrumental variable does not change our results. In particular, the estimated coeﬃcient of welfare expenditure using 2SLS/GMM remains signiﬁcantly negative, and has a slightly larger size (in absolute value) compared with the s- tandard ﬁxed eﬀect coeﬃcient estimate except in column (2). Estimates of other covariates are generally unaﬀected by using 2SLS as well. The ﬁrst-stage F statistic and its p-value show that the instruments are in general highly correlated with the endogenous variable. Even though, we see the single instrument HO is relatively weak compared with HE, and this explains the small absolute value of welfare expenditure coeﬃcient in column (2). In column (5) and (6), the rejection of Hansen’s J test suggests that the overidentiﬁed instruments satisfy the orthogonal conditions, and thus are valid instruments. 21

Table 4: Results of poverty regression: IV estimation (1) (2) (3) (4) (5) (6) Instrument HE HO HH HH HEO HEO D 3.5819 5.1961 4.4651 4.6046 4.0719 4.5837 (1.90) (2.56) (2.44) (2.44) (2.50) (2.54) TWE −3.5619 −1.7413 −2.5657 −3.2093 −2.9985 −3.5670 (−2.87) (−1.14) (−2.25) (−1.73) (−3.05) (−2.06) GINI 0.9078 −0.6449 0.0582 0.7794 0.4733 0.7590 (0.35) (−0.24) (0.02) (0.31) (0.18) (0.30) UNEM 0.5360 0.5585 0.5483 0.5943 0.5424 0.6001 (8.75) (9.01) (9.03) (7.79) (9.12) (7.64) RCV −0.9291 −1.4686 (−0.33) (−0.55) First-stage F -stat. 122.13 75.64 146.95 76.61 80.98 38.27 p-value of ﬁrst-stage F -test 0.00 0.00 0.00 0.00 0.00 0.00 p-value of Hansen’s J-test 0.24 0.24 Note: The dependent variable in all models is poverty. Column (1)– (4) are 2SLS, and column (5) and (6) are GMM. Using 2SLS to estimate column (5) and (6) leads to consistent results. To conclude, results from separate estimation of each channel show that eﬀects A– E indeed exist. Fiscal decentralization can have an impact on poverty through shrinking the welfare expenditure, and more interestingly, through the CV ratio. However, we also note that the interaction between poverty and cash-vendor-payment (eﬀect B) cannot be fully captured by the standard panel data model, and more thorough studies are then required. 5 Joint estimation using functional coeﬃcient model The above analysis speciﬁes each channel separately, and shows each eﬀect is strong and signiﬁcant. However, it is not yet clear whether these channels are jointly strong and how is their relative importance. For example, it is possible that the transmission channel through CV ratio (eﬀect A and B) is individually signiﬁcant, but plays a minor role when we control the channel through welfare expenditure. Also, the standard ﬁxed eﬀect model considered in the previous section cannot capture the interaction between the CV ratio, welfare expenditure, and poverty. A frequently-used method to capture the interaction 22

eﬀect is diﬀerence-in-diﬀerence estimation ∑ 2 pit = αi + β0 + β1 Dit + β2 TWEit + β4 RCVit + β5 TWEit × RCVit + γk xit,k + ϵit , (20) k=1 where xit = (GINIit , UNEMit ). We argue that this approach does not work here for two reasons. First, since RCV is inﬂuenced by D, the interaction term TWE × RCV can be highly correlated with the level terms even if all variables are centered to remove multi- collinearity, and therefore the estimated coeﬃcient of interaction term can be ineﬃcient. Second, the interaction term can only provides a positive or negative (linear) interaction eﬀect, and this eﬀect is the same for all CV ratio levels. However, it is possible that the welfare expenditure eﬀect on poverty depends nonlinearly on the CV ratio; in particular, both extremely large and small values of the CV ratio reﬂect the distortion of welfare expenditure, and such a distortion can weaken its eﬀect on poverty reduction. Therefore, welfare expenditure eﬀect is expected to be a nonlinear function of the CV ratio (roughly U-shape). This nonlinear relationship cannot be captured by Equation (20). Indeed, estimates of Equation (20) show that β̂5 is not signiﬁcant. 5.1 Standard functional coeﬃcient model In order to investigate the relative importance of each channel and capture a possibly nonlinear relationship between the CV ratio and poverty, we consider the functional coef- ﬁcient model in which slope coeﬃcients are allowed to vary over a common variable. We ﬁrst consider a standard functional coeﬃcient model pit = δ0 + δ1 Dit + δ2 TWEit + δ3 GINIit + δ4 UNEMit + ηit , (21) where the slope coeﬃcient δk (k = 0, 1, . . . , 4) is a continuous function of the CV ratio. The same variables D, TWE, GINI, and UNEM appear in Equation (21) as in Equation (19), except that DINC is not included to avoid possible multi-collinearity between TWE and DINC. Our robustness check suggests that including DINC does not change the shape of the curves, but just widens the conﬁdence bands. One advantage of a functional coeﬃcient model is that it allows regressors to be correlated with the smoothing variable RCV, and thus avoids the multi-collinearity problem in (20). Moreover, it provides information on how the eﬀect of welfare expenditure varies (possibly nonlinearly) across diﬀerent values of the CV ratio. The model also allows us to rule out other possible transmission channels from the CV ratio to poverty, at least to some extent, if other functional coeﬃcients (δ1 , δ3 , and δ4 ) do not vary over RCV or show no clear trends. For the moment, we consider a 23

standard functional model without individual-speciﬁc eﬀect αi (pool estimation), and the estimated coeﬃcients are consistent if αi is assumed to be uncorrelated with regressors. We shall allow correlation between αi and regressors, and estimate a ﬁxed eﬀect functional coeﬃcient model in the next subsection. The parameters in this model are estimated by local linear estimation (Fan and Gijbels 1996; see also Cai et al. 2000). Thus we specify δk = δCk + δSk (RCV − u0 ) (k = 0, 1, . . . , 4) (22) where min(RCV) ≤ u0 ≤ max(RCV). The parameters (δCk , δSk ) are estimated by mini- mizing the following object function as ( )2 ∑∑ ∑ 4 min pit − {δCk + δSk (RCVit − u0 )}xitk Kh (RCVit − u0 ), δCk ,δSk i t k=0 where xitk is the k-th regressor, and Kh (·) := h−1 K(·/h) with bandwidth h and kernel function K(·). Various data-driven methods could be employed for selecting bandwidth, for example cross-validation (Fan et al., 2003). Here we choose the bandwidth by minimizing the averaged mean square error following Cai et al. (2000). Figure 2 shows the slope parameters changing as a function of the CV ratio. The solid line plots the coeﬃcient estimate, and the dashed lines are ±2 × bootstrap standard errors (calculated with 200 replications). We see a rough ‘U-shape’ of welfare expenditure eﬀect on poverty (upper-left subﬁgure). The eﬀect is signiﬁcantly negative when cash assistance only takes a relatively small proportion, and it becomes even stronger (more negative) as the ratio increases until around 0.2. However, when the ratio is more than 0.3, increasing cash proportion largely weakens the welfare expenditure eﬀect on poverty reduction with wide conﬁdence bands. The eﬀect even becomes weakly positive when the ratio is particularly high. The nonlinear behavior shows that the deviation of the CV ratio from its optimal value, especially overlarge ratio, can largely weakens the poverty reduction eﬀect by welfare expenditure, and this provides an evidence of eﬃciency loss caused by overemphasis of visible products. For the ﬁscal decentralization eﬀect on poverty (upper- right subﬁgure), it is signiﬁcantly positive at a large interval of the CV ratio (from around 0.1 to 0.4), and less signiﬁcant for larger values of the ratio. The estimated functional coeﬃcients of welfare expenditure and ﬁscal decentralization conﬁrm the results in the standard ﬁxed eﬀect model that the indirect channel (eﬀect C and D) is strong, other channels also matter for poverty (eﬀect E), but the evidence to direct eﬀect (A and B) is not so clear. Besides, we also see that the curves of decentralization, unemployment, 24

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