Dress-up Contest: A Dark Side of Fiscal Decentralization

 
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.

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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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