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Local Direct Elections, Local Information and Meritocratic Selection1
Yu Wang and Renfu Luo
Job Market Paper
(September 29, 2019)
Abstract
This paper studies the relationship and mechanism between local direct elections in rural China and meritocratic selection. Our theoretical model upon Bayesian framework demonstrates that local direct elections facilitate the fulfillment of the meritocratic selection both for village leaders and for village party secretaries. As local direct elections empower the selection for village leaders to village residents, who naturally communicate of more times with village leader candidates than township officials, the representative village resident infers candidates’ virtue and capacity of higher accuracy and precision. Therefore, the introduction of local direct elections improves village leaders’ mean values of composite virtue-and-capacity and reduces their variances of composite virtue-and-capacity. Further, since village leaders are the major candidates for village party secretaries, village party secretaries’ mean values of composite virtue-and-capacity are also improved. Using quality of village roads, we find supportive empirical evidence for our theoretical demonstrations. Keywords: Local Direct Election, Local Information, Meritocratic Selection
���������������������������������������� ����1 Wang: Department of Applied Economics, University of Minnesota (email: [email protected]); Luo:
China Center for Agricultural Policies, Peking University (email: [email protected]). We thank Marc
Bellemare, Loren Brandt, Jay Coggins, Paul Glewwe, John Freeman and Sean Sylvia for valuable
comments and suggestions. All errors are authors.
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“When the Grand course was pursued, a public and common spirit ruled all under the sky; they chose men of talents, virtue, and ability; their words were sincere, and what they cultivated was harmony.” – Confucius (450 B.C., translated by James Legge [1885]), Li Chi: Book of Rites “The aim of every political constitution, is or ought to be, first to obtain for rulers men who possess most wisdom to discern, and most virtue to pursue, the common good of society.” – Hamilton, Madison and Jay (1788 [2008]), The Federalist Papers
I. Introduction
Meritocratic selection is pursued all over the world, both ancient and modern
times. Dating back to around 500 B.C., Chinese politicians and philosophers
raised that those who governed should be selected by merit rather than inherited
status (Sienkewicz, 2003). As the concept of pursuing meritocracy spread to
Europe and the U.S., it was favored by philosophers (Kazin et al., 2010) and
claimed in political statements (Hamilton, Maddison and Jay, 2008).
China has evolved a series of top-down political selection schemes, of which
the mechanism emphasizes the assessment, recommend and promotion for
politicians upon their virtue and capacity, aiming at meritocratic selection. In
around 134 B.C., the assessment & recommend system targeting noble families
was established (Qian, 2012). By enlarging the enfranchisement, the civil exam
system targeting scholars was developed in around 605 A.D., prevailed for over
1000 years, and has greatly influenced political selection schemes in China and
other countries (Elman, 2013; Bai and Jia, 2016; Bell, 2016).
Unlike top-down schemes in China, electoral system, the bottom-up political
selection scheme, was established in ancient Western regimes and prevailed
gradually. Since around 508 B.C., Athenian democracy was established; by
enlarging the enfranchisement, the electoral system has evolved to modern
representative democracy (Loeper, 2017). The mechanism of election
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emphasizes the incentives for politicians upon their behaviors, aiming at the ex
post accountability (Laffont, 2000; Besley, 2005).
The introduction of local direct elections to Chinese top-down political
selection system enables us to identify the relationship and mechanism between
local direct elections and meritocratic selection. We build up a theoretical model,
demonstrating that local direct elections in rural China, by providing local
information on village leader candidates’ virtue and capacity, facilitate the
fulfillment of meritocratic selection for village leaders. Even if the political
selection scheme for village party secretaries remains top-down, local direct
elections for village leaders also facilitate the fulfillment of meritocratic
selection for village party secretaries. Using quality of over 550 village roads,
our empirical evidence supports our theoretical predictions2.
Unlike previous studies regarding elections basically as ex post incentives for
politicians and using the game theory framework3, our model uses the Bayesian
framework to explain how local direct elections, by providing local information,
facilitate the fulfillment of meritocratic selection for village leaders. The
introduction of local direct elections empowers the selection for village leaders
to village residents from township officials. Village residents naturally
communicate with village leader candidates of more times than township
officials, implying village residents’ advantage in local information on
candidates (Ghatak, 1999; Bell, 2016). Therefore, the representative village
resident infers village leader candidates’ virtue and capacity of higher accuracy
and precision than the representative township official. Our theoretical model
���������������������������������������� ����2 Our theoretical findings are empirically supported by this paper and Wong et al., (2017), which also
provides motivations for this paper’s theoretical reasoning.�3 See Laffont (2000) and Besley (2006) for theoretical demonstrations, Ferraz and Finan (2011) and De
Janvry et al. (2012) for empirical evidence and Bell (2016) for demonstrations in political science.
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proves, with the inference of higher accuracy, that in a representative village,
the mean value of the elected village leader’s composite virtue-and-capacity (a
weighted average of virtue and capacity) exceeds that of the appointed village
leader’s. It also proves, with the inference of higher precision, that the variance
of the elected village leader’s composite virtue-and-capacity is smaller that of
the appointed village leader’s. These theoretical findings are in line with Hayek
(1945) and Chan (2013) that assessment and decisions must be left to people
with advantages in local information.
Due to the local information on village leader candidates’ virtue and capacity
that local direct elections provide in selecting village leaders, our model
demonstrates that local direct elections further facilitates the fulfillment of
meritocratic selection for village party secretaries. Village leaders are major
candidates of village party secretaries (O'brien and Li, 2000), and the
performance-based promotion for them as village party secretaries is both the
ex post assessment and the ex ante selection for village party secretaries. Our
model shows that because the mean value of the elected village leader’s
composite virtue-and-capacity exceeds that of the appointed one’s, the elected
village leader’s promotion likelihood surpasses the appointed one’s. It further
shows that the introduction of local direct elections raises the village party
secretary’s composite virtue-and-capacity. Therefore, the performance-based
promotion for village party secretaries not only holds village leaders
accountable, integrated with local direct elections that provide local information,
it is also endowed with meritocratic selection.
The rest of this paper is organized as follows: Section II introduces the
institutional backgrounds. Section III develops the theory. Section IV discusses
the empirical strategies and presents the empirical results. Section V concludes.
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II. Local Governance in Rural China
� � The Chinese village administrative organizations consist of village
committees, the de facto government entities at the village level, chaired by
village leaders, and the village-leveled leadership of the Chinese Communist
Party (CCP) named village party branches, chaired by village party secretaries.
Village party branches supervise village committees, and thus village party
secretaries are higher than village leaders in Chinese bureaucratic hierarchy,
stipulated by the “Organic Law of the Village Committees (OLVC)” (National
People’s Congress of China, 1998) and the “Working Regulation on the Rural
Grassroots Organizations of Chinese Communist Party (WRRGOCCP)”
(Central Committee of the Chinese Communist Party, 1999). Village leaders’
major responsibility is providing village public infrastructure and service,
developing the local economy, and improve village residents’ income (OLVC,
1998; Martinez-Bravo et al., 2011); yet village party secretaries’ duty in
developing the local economy is approving village leaders’ plans and
monitoring the implementation (WRRGOCCP, 1999; Oi and Rozelle, 2000).
The selection scheme for village leaders has transited from appointments by
township officials to local direct elections by village residents. The introduction
of local direct elections in rural China has experienced a gradual process4
(Martinez-Bravo et al., 2014). Until 2010, most villages in rural China have
���������������������������������������� ����4 In 1998, the National People’s Congress of China passed the revised “Organic Law of the Village
Committees (OLVC)”, introducing local direct elections for village leaders in rural China, which brought
elections for village leaders with open nomination, competitive election (O’Brien and Han, 2009). After
the national legislation in 1998, each province in China, in the following years, introduced its own
“Provincial Measures for Implementing the Organic Law of Village Committees” to provide further
instructions on the implementation of local direct elections (O’Brien and Zhao, 2011). Counties and
townships then followed suit (Wong et al., 2017).
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introduced local direct elections (Padró i Miquel et al., 2015; Wong et al., 2017).
Both appointments and local direct elections emphasize meritocratic selection,
requiring that village leader candidates be law-abiding, of moral integrity and
be intrinsically willing to serve village residents; and be of some diploma and
administrative capacity (OLVC, 1998). Village leader candidates are then
selected by village residents or township officials for village leaders with the
likelihood of being selected positively associated with their virtue and capacity
(Bell, 2016; Tang, 2016), rooted in the concept and practice of meritocratic
selection in Chinese history (Zhang, 2012).
Village party secretaries are appointed by township officials, which also
emphasizes meritocratic selection regarding village party secretary candidates’
virtue and capacity. WRRGOCCP (1999) and its following versions, regulated
the procedures of selecting village party secretaries and stipulated the decisive
role of township officials in this selection5. This working regulation requires
that village party secretaries be qualified in professional knowledge and
working skills, be responsive to village residents’ needs and demands, and be
intrinsically motived to serve village residents. Village leaders are the major
candidates for village party secretaries (O'brien and Li, 2000).
III. Theory
Our theoretical model upon Bayesian framework discusses how the
introduction of local direct elections to a representative village facilitates the
���������������������������������������� ����5 Township party officials basically have the following ways to select for village party secretaries. (1)
Village party secretaries are directly appointed by township party officials. (2) Village party branch
committee members are firstly elected by village party members, then village party secretaries are
appointed by township party officials or elected among those committee members and finally approved
by township party officials. (3) Village party secretary candidates are firstly nominated by township party
officials, then elected village party members to serve as village party secretaries.
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fulfillment of the meritocratic selection both for the village leader and for the
village party secretary6.
A. Inferences with Village Leader Candidates
In this section, we use the Bayesian framework to discuss the inference of
village leader candidates’ virtue and capacity in a representative village. We find
that because the representative village resident naturally communicates with
village leader candidates of more times than the representative township official
does, the representative village resident infers village leader candidates’ virtue
and capacity of higher accuracy and precision.
1. Setup: Our theory discusses a representative village, in which all adult
village residents are potential village leader candidates. Each one has two
personal characteristics: virtue and capacity, both are assumed to be
independent and identically distributed over [0, 1] with both means of 0.57.
After the local direct election is introduced to this representative village, a
pool of village leader candidates, subset of all the potential candidates,
competes for being elected as the village leader by village residents. Before this
introduction, a pool of village leader candidates competes for being appointed
as the village leader by township officials. Village leader candidates’ virtue is
denoted as &', with &' ∈ 0,1 , and their capacity is denoted as )', with )' ∈
���������������������������������������� ����6 According to our survey data, around 86% (1718 out of 2000) interviewed village residents replied that
local direct elections were implemented law-abidingly, in which no corruption or conspiracy exists. 7 Village residents’ virtue and capacity are both assumed to be bounded, because (1) the number of
residents in a village is usually small (Liu et al., 2009; Martinez-Bravo et al. 2014), and (2) their
socioeconomic characteristics, thinking patterns and behaviors, tend to be homogenous, due to the
homogenous socioeconomic, cultural and institutional constraints, as well as the long-term, generation-
by-generation interactions (Bell, 2016). For simplicity, we assume village residents’ virtue and capacity
are both bounded at [0, 1].
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0,1 , where * = {1,2, … } . In the following analysis, we discuss the
representative village resident instead of village residents, by assuming
homogenous perception among village residents over village leader candidates’
virtue and capacity, as well as the representative township official instead of
township officials, by assuming homogenous perception among township
officials over village leader candidates’ virtue and capacity.
2. Bayesian Inferences: Neither the representative village resident nor
township official observes each village leader candidate’s virtue or capacity. To
infer village leader candidates’ virtue and capacity, the representative village
resident or township official, by naturally communicating with each candidate,
obtains 0'12 , a series of observations of village leader candidate *’s virtue, in
the times of 3 = 1,… , 4567 and 1,… , 4899, respectively. 4567 represents the
ultimate times of natural communication between the representative village
resident and each village leader candidate, right before the representative village
resident makes the decision on which candidate to elect as the village leader.
4899 represents the ultimate times of natural communication between the
representative township official and each village leader candidate, right before
the representative township official makes the decision on which candidate to
appoint as the village leader. 0'12 is specified as,
(1) 0'12�&' + ;'1
where ;'1 is the series of random shocks in observing virtue. Similarly, the
representative village resident or township official, by naturally communicating
with each village leader candidate, obtains 0'1< , a series of observations of
village leader candidate * ’s capacity, in the times of 3 = 1,… , 4567 and
1,… , 4899, respectively. 0'1< is specified as,
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(2) 0'1<�)' + ='1
where ='1 is the series of random shocks in observing capacity.
Natural communication is defined to be the daily communication in work,
living or other circumstances, in which communicators behaves naturally and
artlessly (Bell, 2016). In addition, this communication induces no illegal
outcomes in village affairs management, like conspiracy or rent-seeking (Baker
and Faulkner, 1993), Since such communication happens in large number of
times and in various situations, communicators can hardly, and thus be basically
unwilling to, behave strategically to hide their real personally characteristics.
Therefore, it is acceptable to assume that first, the times of natural
communication are sufficiently large; second, the series of observations on
virtue or on capacity is normally distributed.
ASSUMPTION 1 (Natural communication and observations on virtue and
capacity): The representative village resident or township official communicates
with village leader candidates naturally, thus we have ;'1~?(0, ABCD ) and
='1~?(0, AFGD ) , and for a long time, thus we have 4567 and 4899 both
sufficiently large.
With ;'1~?(0, ABCD ),='1~?(0, AFG
D ), (1) and (2), we have 0'12~?(&', ABCD ),
and 0'1<~?()', AFGD ).
Before natural communication, both the representative village resident and
township official simply hold their prior perceptions over each village leader
candidate’s virtue and capacity. Assumption 2 discusses the distributions of
their prior perceptions.
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ASSUMPTION 2 (Prior distribution on village leader candidates’ virtue and
capacity): The representative village resident or township official’s prior
perceptions on village leader candidate *’s virtue are identically distributed as
? &'7, A2H
D , truncated at 0,1 , where &'7 ∈ [0, 1]. Their prior perceptions on
village leader candidate *’s capacity are identically distributed as ? )'7, A<H
D ,
truncated at 0,1 , where )'7 ∈ [0, 1]. &'7 and )'7, the prior means, and A2HD
and A<HD , the prior variance, are known to the representative village resident or
township official.
As both virtue and capacity are assumed to be bounded at [0, 1], and the
representative village resident or township official have long-term natural
communication with each village leader candidate, the representative village
resident or township official’s prior perception on each village leader
candidate’s virtue or capacity is truncated at 0,1 .
With the prior perception on virtue, and each time of natural communication,
the representative village resident or township official obtain the posteriorly
inferred perception of village leader candidates’ virtue. According to the Bayes’
Rule, such a posterior perception is obtained by iteration, such that the inferred
perception of virtue in period 3 is contingent on a previously inferred virtue,
the inferred perception virtue in period 3 − 1, and a posteriorly updated virtue,
the observation of virtue in in period 3.
Now we introduce deriving the density kernel of the posterior distribution of
village leader candidate * ’s virtue. The representative village resident or
township official hold identical prior perception on village leader candidate *’s
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virtue, of which the density kernel of her prior distribution is J &' . After
naturally communicating with village leader candidate * for the first time, the
representative village resident or township official updates the density kernel of
the posterior distribution of her virtue as,
(3) K &' Ω'M2 = J &' ∙ O &'; Ω'M2
This posterior distribution in period 3 = 1 is also the previous distribution in
period 3 = 2. After the natural communication in period 3 = 2, the updated
density kernel of posterior distribution is
(4) K &' 0'M2 , 0'D2 = J &' ∙ O &'; 0'M2 ∙ O &'; 0'D
2
= J &' O &'; 0'M2 ∙ O &'; 0'D
2
Repeating this iteration, after ultimately 4 times of natural communication
between the representative village resident or township official and village
leader candidate *, the density kernel of posterior distribution of village leader
candidate *’s virtue (See Appendix A.1) becomes
(5) K &' 0'M2 ∙∙∙ 0'R2 = J &' ∙ [O &'; 0'M2 …O &'; 0'R
2 ]
∝ TUK{− M
D
M
V 2W(&' − X &' )D }
where the posterior mean of village leader candidate *’s virtue is,
(6) X &' =YZC[
YZC[ \RYCH
[ &'7 +
RYCH[
YZC[ \RYCH
[ &'
and the posterior variance of village leader candidate *’s virtue is,
(7) ] &' =YCH[ YZC
[
YZC[ \RYCH
[
Given different ultimate times of natural communication, the representative
village resident in election or the representative township official in
appointment obtains the posterior mean of village leader candidate *’s virtue as,
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(8) X567(899) &' =YZC[
YZC[ \RYCH
[ &'7 +
RYCH[
YZC[ \RYCH
[ &', where 4 = 4567or4899
and obtains the posterior variance of village leader candidate *’s virtue as,
(9) ]567(899) &' =YCH[ YZC
[
YZC[ \RYCH
[ , where 4 = 4567`a4899
Following similar Bayesian inference, the density kernel of posterior
distribution of village leader candidate *’s capacity is (See Appendix A.2)
(10) K )' 0'M< ∙∙∙ 0'R
< = J )' ∙ [O )'; 0'M< …O )'; 0'R
< ]
∝ TUK{− M
D
M
V <W()' − X )' )D }
where the posterior mean of village leader candidate *’s capacity is,
(11) X )' =YbG[
YbG[ \RYGH
[ )'7 +
RYGH[
YbG[ \RYGH
[ )'
and the posterior variance of village leader candidate *’s capacity is,
(12) ] )' =YGH[ Y
bG[
YbG[ \RYGH
[
Therefore, the representative village resident or township official’s posterior
mean of village leader candidate *’s capacity is,
(13) X567(899) )' =YbG[
YbG[ \RYGH
[ )'7 +
RYGH[
YbG[ \RYGH
[ )' where 4 = 4567, 4899
and their posterior variance of village leader candidate *’s capacity is,
(14) ]567(899) )' =YGH[ Y
bG[
YbG[ \RYGH
[ where 4 = 4567, 4899
Proposition 1 discusses how accumulating times of natural communication
improve the inference of village leader candidates’ virtue and capacity.
PROPOSITION 1: As the times of the representative village resident or
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township official’s natural communication with village leader candidates
accumulate, the inference of each village leader candidate’s virtue and capacity
is improve in the following aspects:
(a) The Inference Precision increases with the times of natural communication,
shown by the deceasing posterior variance of virtue (or capacity) with the
ultimate times of natural communication.
(b) The Inference Accuracy increases with the times of natural communication,
shown by the decreasing scaled ratio of the difference between the posterior
mean of virtue (or capacity) and the real value of virtue (or capacity) over the
difference between the prior mean of virtue (or capacity) and the real value of
virtue (or capacity) with the ultimate times of natural communication.
(c) The Marginal Inference Accuracy decreases with the times of natural
communication, shown by the increasing marginal scaled ratio of the difference
between the posterior mean of virtue (or capacity) and the real value of virtue
(or capacity) over the difference between the prior mean of virtue (or capacity)
and the real value of virtue (or capacity) with the ultimate times of natural
communication.
Proof: (a) The first-order derivative of ] &' with respect to 4 is
(15) c[V 2W ]
cR=
dYCHe YZC
[
(YZC[ \RYCH
[ )[< 0
Similarly, the first-order derivative of ] )' with respect to 4 is
(16) c[V <W ]
cR=
dYGHe Y
bG[
(YbG[ \RYGH
[ )[< 0
(b) The scaled ratio of the difference between the posterior mean of virtue
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and the real value of virtue over the difference between the prior mean of virtue
and the real value of virtue is
(17) g 2W d2W2WHd2W
=YZC[
YZC[ \1YCH
[ = V 2WYCH[
Therefore, we have
(18) c[h CW iCWCWHiCW
]
cR= M
YCH[c[V 2W ]
cR< 0
Similarly, the scaled ratio of the difference between the posterior mean of
capacity and the real value of capacity over the difference between the prior
mean of capacity and the real value of capacity is
(19) g <W d<W<WHd<W
=YbG[
YbG[ \RYGH
[ = V <WYGH[
Therefore, we have
(20) c[h GW iGWGWHiGW
]
cR= M
YGH[cV <WcR
< 0
(c) The second-order derivative of ] &' with respect to 4 is
(21) c[V 2WcR[
�DYCH
j YZC[
(YZC[ \RYCH
[ )k> 0
Therefore, the second-order derivative of g 2W d2W2WHd2W
with respect to 4, which
is the marginal scaled ratio of the difference between the posterior mean of
virtue and the real value of virtue over the difference between the prior mean of
virtue and the real value of virtue, is
(22) c[[
h CW iCWCWHiCW
]
cR[= M
YCH[c[V 2WcR[
> 0
Similarly, the second-order derivative of ] )' with respect to 4 is
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(23) c[V <WcR[
�DYGH
j YbG[
(YbG[ \RYGH
[ )k> 0
Therefore, the second-order derivative of g <W d<W<WHd<W
with respect to 4, which
is the marginal scaled ratio of the difference between the posterior mean of
capacity and the real value of capacity over the difference between the prior
mean of capacity and the real value of capacity, is
(24) c[[
h GW iGWGWHiGW
]
cR[= M
YGH[c[V <WcR[
> 0 ∎
Figure 1 shows that as the times of the representative village resident or
township official’s natural communication with village leader candidates
accumulate, (a) the band widths for the squared roots of posterior variances
decease, reflecting the increasing inference precision; (b) the difference
between the posterior mean of virtue (or capacity) and the real value of virtue
(or capacity) decreases, reflecting the increasing inference accuracy; and (c) the
curves of the posterior means are concave in ascending updates and convex in
descending updates, reflecting the decreasing marginal inference accuracy.
The implication of the improved inference precision and accuracy is that each
time of natural communication brings local information on village leader
candidates’ virtue and capacity, and such local information improves the
inference of village leader candidates’ virtue and capacity on precision and
accuracy. For the marginal inference accuracy, the implication is that as the
times of natural communication accumulate, the increment of local information
�Figure 1 is about here��
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for inferring village leader candidates’ virtue and capacity diminishes.
3. Institutional Comparison (Inference Accuracy and Precision): To
compare the inference precision and accuracy after and before introducing local
direct elections, we have an assumption regarding 4567 and 4899 , the
representative village resident’s and the representative township official’s
ultimate times of natural communication with each village leader candidate.
ASSUMPTION 3: 4567 > 4899
Assumption 3 indicates that the representative village resident naturally
communicates with village leader candidates of more times than the
representative township official. The reason is that village leader candidates are
also residents in this representative village, who have long-time and frequent
natural communication with other village residents in various situations (Bell,
2016). For instance, village leader candidates and other village residents usually
know each other since they were very young. As they grow up and live in the
village, they have long-term and frequent communication at school, in
production or commercial activities, and in everyday lives. On the contrary,
village leader candidates have less chances of natural communication with
township officials. The reasons could be that village leader candidates usually
communicate with township officials when dealing with village public affairs
or their private affairs involved with township administration; in addition,
township officials are often posted among different towns.
Given that 4567 > 4899 , we compare the inference precision and the
inference accuracy of each village leader candidate’s virtue and capacity after
and before introducing local direct elections:
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(a) The representative village resident infers village leader candidates’ virtue
and capacity of higher precision before electing one of them as the village leader,
compared to the representative township official does before appointing one of
them as the village leader.
(b) The representative village resident infers village leader candidates’ virtue
and capacity of higher accuracy before electing one of them as the village leader,
compared to the representative township official does before appointing one of
them as the village leader.
As is shown in Figure 1, the band width representing the squared root of the
posterior variance of village leader candidates’ virtue or capacity in election is
smaller than that in appointment, implying the representative village resident’
higher inference precision. The difference between the posterior mean of village
leader candidates’ virtue or capacity and its real value in election is smaller than
that in appointment, implying the implying the representative village resident’
higher inference accuracy.
To sum up, the representative village resident, due to her more times of
natural communication with village leader candidates, have more local
information on village leader candidates’ virtue and capacity than the
representative township official. Therefore, as local direct elections empower
the selection for the village leader to the representative village resident from the
representative township official, village leader candidates’ virtue and capacity
are both inferred of higher precision and accuracy.
B. Selection for Village Leaders
This section discusses how local direct elections, by providing local
information on village leader candidates’ virtue and capacity, facilitate the
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fulfillment of meritocratic selection for village leaders. Specifically, local direct
elections, by providing the inference of higher accuracy on village leader
candidates’ virtue and capacity, improve the mean value of the village leader’s
composite virtue-and-capacity in a representative village. In addition, by
providing the inference of higher precision on village leader candidates’ virtue
and capacity, local direct elections also reduce the variance of the village
leader’s composite virtue-and-capacity in a representative village.
1. Setup: The representative village resident and township official both
would select the village leader candidate with the highest composite virtue-and-
capacity as the village leader. Our theory defines composite virtue-and-capacity
as a weighted average of virtue and capacity, such that n&' + (1 − n))' , of
village leader candidate * , where n represents the weight that the
representative village resident and township official put on village leader
candidates’ virtue, in other words, the preference spectrum over virtue and
capacity, and n ∈ [0, 1].
Mean Value of Composite Virtue-and-Capacity To obtain the composite
virtue-and-capacity of the elected (or appointed) village leader in a
representative village, we calculate the mean value of composite virtue-and-
capacity of all village leader candidates in a representative village that has
already (or has not) introduced the local direct election. To calculate the mean
value of composite virtue-and-capacity of all village leader candidates, we
calculate a weighted average of all village leader candidates’ composite virtue-
and-capacity with weight o', the likelihood that village leader candidate * is
elected or appointed. o' has the following properties:
(a) o' is contingent on village leader candidate * ’s composite virtue-and-
capacity.
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(b) o' ∈ [0, 1], thus its value represents the likelihood of electing or appointing
village leader candidate * as the village leader.
(c) o' is positively associated with village leader candidate *’s virtue and her
capacity, which reflects positive screening of the election and appointment for
village leaders (Dal Bó et al., 2017) upon candidates’ virtue and their capacity.
Specifically, c8Wc2W
> 0 and c8Wc<W
> 0.
To satisfy these three properties, for simplicity and without losing generality,
we use a weighted average of village leader candidate *’s posterior mean of
virtue and her posterior mean of capacity as her likelihood to be elected or
appointed as the village leader, with weight n, the preference spectrum over
virtue and capacity. In the light of Alesina and Tabellini (2007), village leader
candidate *’s likelihood to be elected or appointed that we use here can be
regarded as a reward. This reward is a product of the village leader’s constant
payoff standardized to 1 with village leader candidate * ’s likelihood to be
elected or appointed.
Therefore, the likelihood that village leader candidate * is elected or
appointed takes the form that
(25)� � o' = nX &' + 1 − n X )'
� � � � � � � = n[V 2WYCH[ &'
7 + (1 − V 2WYCH[ )&'] + (1 − n)[
V <WYGH[ )'
7 + (1 − V <WYGH[ ))']�
where ] &' ≡YCH[ YZC
[
YZC[ \RYCH
[ , ] )' ≡YGH[ Y
bG[
YbG[ \RYGH
[ .
As is discussed in Section III.A., ] &' and ] )' measure the inference
precision. As the times of natural communication rise, ] &' and ] )'
decreases and thus o' tends to be the composite virtue-and-capacity. Therefore,
when 4 = 4567 , ] &' = ]567 &' and ] )' = ]567 )' , then we have
o' = o'567, the likelihood that village leader candidate * is elected; when 4 =
� 20
4899 , ] &' = ]899 &' and ] )' = ]899 )' , then we have o' = o'899 ,
the likelihood that village leader candidate * is appointed.
To calculate the weighted average of all village leader candidates’ composite
virtue-and-capacity with weight o' , since o'Mq r&'
Mq r)' < 1, that is, the
sum of weights are smaller than 1, we should have [n&' + (1 −Mq
Mq
n))'] o'r&' r)' , the weighted average of all village leader candidates’
composite virtue-and-capacity, divided by o'Mq r&'
Mq r)' , in order to
standardize the weights. As a result, the mean value of the composite virtue-
and-capacity of the elected (or appointed) village leaders is,
(26 ) n& + 1 − n ) st,567 899 = u567 899 n&' + 1 − n )'
=v2W\ Mdv <W 8W
wxH(yzz){| }2W
{| }<W
8WwxH(yzz){
| }2W{| }<W
�
where the likelihood that village leader candidate * is elected, or appointed, is
(27)� � o'567 899 = nX567 899 &' + 1 − n X567 899 )'
� � � � � � � � � � � � � � = nVwxH yzz 2W
YCH[ &'
7 + 1 −VwxH yzz 2W
YCH[ &' �
� � � � � � � � � � � � � � � � � � +(1 − n)[VwxH(yzz) <W
YGH[ )'
7 + (1 −VwxH(yzz) <W
YGH[ ))']�
where ]567(899) &' ≡YCH[ YZC
[
YZC[ \RwxH(yzz)YCH
[ , ]567(899) )' ≡YGH[ Y
bG[
YbG[ \RwxH(yzz)YGH
[ .
Therefore, it shows that what distinguishes the elected village leader’s and the
appointed village leader’s mean values of the composite virtue-and-capacity in
a representative village is the representative village resident’s and the
representative township official’s different times of natural communication with
village leader candidates.
Variance of Composite Virtue-and-Capacity We could also obtain the
variance of composite virtue-and-capacity of the elected (or appointed) village
� 21
leader in a representative village, by calculating the variance of composite
virtue-and-capacity of all village leader candidates in a representative village
that has already (or has not) introduced the local direct election. By the
definition of variance, the variance of composite virtue-and-capacity of of the
elected (or appointed) village leader in a representative village is,
(28) ~�ast,567(899) n& + 1 − n ) = ~�a567 899 n&' + 1 − n )'
= u567(899) n&' + 1 − n )' D − u567(899)Dn&' + 1 − n )'
This measures to what extent the elected (or appointed) village leader’s
composite virtue-and-capacity varies. Similar to the mean value, it shows that
what distinguishes the elected village leader’s and the appointed village leader’s
variances of the composite virtue-and-capacity in a representative village is also
the representative village resident’s and township official’s different times of
natural communication with village leader candidates.
� � 2. Institutional Comparison (Meritocratic Selection for Village Leaders):
Proposition 2 compares the mean value of the elected village leader’s composite
virtue-and-capacity with that of the appointed village leader.
PROPOSITION 2: The elected village leader’s virtue or capacity exceeds the
appointed village leader’s in a representative village. Specifically, we have
(29) [n& + 1 − n )]st,567 > [n& + 1 − n )]st,899
where [n& + 1 − n )]st,567 = u567 n&' + 1 − n )' , [n& + 1 −
n )]st,899 = u899(n&' + (1 − n))').
Followed are specific cases:
Case 1: When n = 1, that is, the representative village resident or township
official only considers village leader candidates’ virtue.
Case 2: When n = 0, that is, the representative village resident or township
� 22
official only considers village leader candidates’ capacity.
Case 3: When n = M
D, that is, the representative village resident or township
official considers village leader candidates’ virtue and capacity with equal
weights.
Case 4: When n ∈ (MD, 1) , that is, the representative village resident or
township official emphasizes more on virtue. This is contingent on )'7 ∈ [0.5, 1],
that is, the prior mean of each village leader candidate’s capacity is above the
mean of the real values of all potential village leader candidates’ capacity.
Case 5: When n ∈ (0, MD) , that is, the representative village resident or
township emphasizes more on capacity. This is contingent on &'7 ∈ [0.5, 1],
that is, the prior mean of each village leader candidate’s capacity is above the
mean of the real values of all potential village leader candidates’ capacity.
Proof: See Appendix B.1. ∎
The assumption that Case 4 is contingent on is from requirements by OLVC
that village leader candidates satisfy a series of personal characteristics
regarding capacity, such as some diploma or management experience, thus the
mean of the representative village resident’s or township official’s prior
perceptions for village leader candidates’ capacity is larger than or equal to 0.5,
the mean of all village residents’ capacity.
Similarly, the implication assumption that Case 5 is contingent on is from
requirements by OLVC that village leader candidates satisfy a series of personal
characteristics regarding virtue, such as no criminal record or some affiliation
to the CPC, thus the mean of the representative village resident’s or township
official’s prior perceptions for village leader candidates’ virtue is larger than or
� 23
equal to 0.5, the mean of all village residents’ virtue.
Proposition 3 compares the variance of the elected village leader’s composite
virtue-and-capacity with that of the appointed village leader.
PROPOSITION 3: The variance of the elected village leader’s composite
virtue-and-capacity is smaller than the variance of the appointed village
leader’s in a representative village. Specifically, we have
(30) ~�ast,567 n& + 1 − n ) < ~�ast,899 n& + 1 − n )
whatever the value at [0, 1] that n take. It’s denoted that ~�ast,567 n& +
1 − n ) = ~�a567 n&' + 1 − n )' , and that ~�ast,899 n& + 1 −
n ) = ~�a899 n&' + 1 − n )' .
Proof: See Appendix B.2. ∎
In sum, after introducing the local direct election to a representative village,
the village leader’s composite virtue-and-capacity’s mean value increases while
its variance decreases. This implies that by providing local information on
village leader candidates’ virtue and capacity, local direct elections facilitate the
fulfillment of meritocratic selection for village leaders.
�
C. Selection for Village Party Secretaries
This section demonstrates that local direct elections, by providing local
information on village leader candidates’ virtue and capacity, also facilitates the
fulfillment of meritocratic selection for village party secretaries. Specifically,
local direct elections raise the mean value of composite virtue-and-capacity of
village leaders, who are also the main candidates of village party secretaries,
thus elected village leaders are more likely to be promoted, based on their
� 24
performance, as village party secretaries than appointed village leaders. As a
result, the village party secretary’s composite virtue-and-capacity is raised.
1. The Performance-based Promotion for Village Party Secretaries: In a
representative village, village party secretary candidates are usually members
of the village party committee. Similar to the selection for the village leader
discussed above, the representative township official, by naturally
communicating with village party secretary candidates, infers their composite
virtue-and-capacity and appoint the highest one as the village party secretary.
The village leader, also a member of the village party committee, is a special
and the major candidate of village party secretary (O'brien and Li, 2000). Since
the village leader is the major policymaker in the village, her performance in
village economic development is a key signal of her composite virtue-and-
capacity. By observing the village leader’s performance, the representative
township official infers the village leader’s composite virtue-and-capacity and
is likely to promote her as the village party secretary (WRRGOCCP, 1999).
Without losing generality, it is assumed that the village leader’s performance is
a strictly increasing function of her composite virtue-and-capacity, in lights of
Jones and Olken (2005), Besley et al. (2011), Yao and Zhang (2015) and Bloom
et al. (2015). Specifically,
(31) Ç = ℱ[(n& + 1 − n ))st] + Ñ
where Ç represents the village leader’s performance, (n& + 1 − n ))st
represents her composite virtue-and-capacity, and Ñ represents the random
error, where Ñ~?(0, AÖD). ℱ[∙] is strictly increasing in (n& + 1 − n ))st.
The likelihood to appoint the village leader as the village party secretary is
specified as
(32) Ü = á (n& + 1 − n ))st|Ç
� 25
which is, similar to Section III.B., the posterior mean of composite virtue-and-
capacity of the village leader by observing her performance.
To specify (32), the posterior mean of composite virtue-and-capacity, similar
to Section III.A., we first assume the representative township official’s prior
perception on the village leader’s, either elected or appointed, composite virtue-
and-capacity distributed as
ASSUMPTION 4 (Prior distribution on the village leader’s virtue and capacity):
The representative township official’s prior perception on the village leader’s
virtue is distributed as ? &â, A2äD , truncated at 0,1 , where &â ∈ [0, 1]. Her
prior perception on the village leader’s capacity is distributed as ? )â, A<äD ,
truncated at 0,1 , where )â ∈ [0, 1]. &â and )â, the prior means, and A2äD
and A<äD , the prior variances, are known to the representative township official.
The prior distribution of village party secretary candidate ã ’s composite
virtue-and-capacity is thus a normal distribution ? nD&â + (1 − n)D)â, A2äD +
A<äD , truncated at 0,1 , according to the convolution formula. Using the
similar Bayesian framework as in Section III.A., the posterior mean of the
composite virtue-and-capacity of the village leader is (See Appendix C),
(33) á (n& + 1 − n ))st|Ç
= 1 − å nD&â + (1 − n)D)â + åℱ (n& + 1 − n ))st
where n ∈ (0,1), å ≡YCä[ \YGä
[
YCä[ \YGä
[ \Yç[.
2. Institutional Comparison (Meritocratic Selection for Village Party
Secretaries): In this part we first compare the elected village leader’s and the
� 26
appointed village leader’s likelihood to be promoted as the village party
secretary, in a representative village. Then we compare the village party
secretary’s composite virtue-and-capacity before and after introducing the local
direct election.
Before comparing the likelihood to be promoted as the village party secretary
in a performance-based promotion, we need another assumption:
ASSUMPTION 5: The introduction of local direct elections only influences
village leaders’ composite virtue-and-capacity, not other village party secretary
candidates’ composite virtue-and-capacity.
With Assumption 5, we have the following proposition:
PROPOSITION 4: (The Elected Village Leader’s Higher Promotion
Likelihood): In a representative village with the performance-based promotion
for the village party secretary, the elected village leader, due to her higher
composite virtue-and-capacity, has higher likelihood to be promoted as the
village party secretary, compared to the appointed village leader.
Proof: Section III.B. has shown that in a representative village, the elected
village leader’s composite virtue-and-capacity exceeds the appointed village
leader’s, that is, [n& + 1 − n )]st,567 > [n& + 1 − n )]st,899.
Based on (31), we know that
(34) ℱ [n& + 1 − n )]st,567 > ℱ [n& + 1 − n )]st,899
Following (33), the likelihood of the elected (or appointed) village leader to
be promoted as the village party secretary is specified as
� 27
(35) Ü567(899) = á (n& + 1 − n ))st|Ç567(899)
= 1 − å nD&â + (1 − n)D)â + åℱ[[n& + 1 − n )]st,567(899)]
where n ∈ (0,1), å ≡YCä[ \YGä
[
YCä[ \YGä
[ \Yç[.
According to (34), we know that Ü567 > Ü899. ∎
Proposition 4 shows that because what underlies the village leader’s
promotion likelihood is her composite virtue-and-capacity revealed through her
performance, and the elected village leader’s mean value of composite virtue-
and-capacity exceeds the appointed one’s, thus the elected village leader’s
promotion likelihood surpasses the appointed one’s.
� � By comparing, in a representative village, the elected and appointed village
leader’s promotion likelihood, we have
(36) Ü567 899 = åΓè + åℱ [[n& + 1 − n )]st,899
+ 1 − å nD&â + (1 − n)D)â
where Γ ≡ ℱ [[n& + 1 − n )]st,567 − ℱ[[n& + 1 − n )]st,899 , è ≡
è{= 1, *êTëTí3Tr;= 0, *ê�KK`*ì3Tr} is the indicator, å ≡YCä[ \YGä
[
YCä[ \YGä
[ \Yç[.
åℱ [[n& + 1 − n )]st,899 is named as the performance-based promotion
premium, implying the appointed village leader’s promotion likelihood as the
village party secretary explained by her performance observed. This shows that
the performance-based promotion scheme is an ex post assessment for the
village leader, because it incentivizes politicians and holds them accountable,
as is discussed in previous studies (Dewatripont et al., 1999; Alesina and
Tabellini, 2007).
åΓè is named as the local information increment, implying the elected
village leader’s promotion likelihood increment, compared to the appointed
� 28
village leader, as the village party secretary, which is explained by the elected
village leader’s performance observed. This shows that integrated with local
direct elections, the performance-based promotion scheme is also an ex ante
meritocratic selection for the village leader. Local direct elections provide local
information on village leader candidates’ virtue and capacity and upon which
raise the composite virtue-and-capacity of the village leader. Therefore, in a
performance-based promotion scheme, the elected village leader with her
higher composite virtue-and-capacity, has an increment of the likelihood to be
promoted as the village party secretary, compared to the appointed one.
We further provide a Corollary of Proposition 4 showing how local direct
elections facilitate the fulfillment of meritocratic selection for the village party
secretary. Suppose there are two village party secretary candidates: the village
leader and a representative other candidate. The elected (or appointed) village
leader’s composite virtue-and-capacity is [n& + 1 − n )]st,567(899) and her
promotion likelihood is Ü567 899 . The representative other candidate’s
composite virtue-and-capacity is [n& + 1 − n )]î1ï7ñ and her promotion
likelihood is assumed to be 1 − Ü567 899 . According to Assumption 5,
[n& + 1 − n )]î1ï7ñ is uncorrelated with whether introducing the local direct
election or not. Therefore, we have,
COROLLARY (Meritocratic Selection for Village Party Secretaries): After
introducing the local direct election to a representative village, the village party
secretary’s composite virtue-and-capacity is raised. Specifically, we have
(37) [n& + 1 − n )]sóg,567 > [n& + 1 − n )]sóg,899
Proof: we know that
� 29
(38) n& + 1 − n ) sóg,567
= n& + 1 − n ) st,567Ü567 + n& + 1 − n ) î1ï7ñ 1 − Ü567
= Ü567 n& + 1 − n ) st,567 − n& + 1 − n ) î1ï7ñ
+ n& + 1 − n ) î1ï7ñ
and that
(39) n& + 1 − n ) sóg,899
= n& + 1 − n ) st,899Ü899 + n& + 1 − n ) î1ï7ñ 1 − Ü899
= Ü899 n& + 1 − n ) st,899 − n& + 1 − n ) î1ï7ñ
+ n& + 1 − n ) î1ï7ñ
Since Proposition 2 implies that [n& + 1 − n )]st,567 > [n& + 1 −
n )]st,899 and Proposition 4 implies that Ü567 > Ü899, we know that
(40) n& + 1 − n ) sóg,567 > n& + 1 − n ) sóg,899 ∎
D. Summary
This section demonstrates that local direct elections, by providing local
information on village leader candidates’ virtue and capacity, facilitate the
fulfillment of meritocratic selection both for village leaders and for village party
secretaries, yet in different ways.
Local direct elections facilitate the fulfillment of meritocratic selection for
village leaders directly, by providing the local information on village leader
candidates and through which improving the screening effects. Specifically,
after local direct elections empower the selection for village leaders, who have
more times of natural communication with village leader candidates than
township officials, village leader candidates’ virtue and capacity are posteriorly
inferred of better screening effects, that is, of higher precision and accuracy. As
a result, the mean values of village leaders’ composite virtue-and-capacity rises
� 30
while the variances of that drops. With the preference spectrum over virtue and
capacity, our theory apply for a continuum of scenarios of selection for leader
from the purely virtue-oriented to the purely capacity-oriented.
On the contrary, local direct elections facilitate the fulfillment of meritocratic
selection for village party secretaries indirectly, by providing the local
information on village leader candidates and through which improving the
candidate pool. Specifically, since village leaders are the main candidates for
village party secretaries, and the mean values of village leaders’ composite
virtue-and-capacity rises,
IV. Empirical Evidence
In this section, we first introduce the sampling method and data. Then we
introduce the empirical evidence supporting the meritocratic selection for
village leaders in rural China. Finally, we introduce the empirical evidence
supporting the meritocratic selection for village party secretaries in rural China.
A. Sampling and Data
The sampling and data used in this paper are the same as used in Wong et al.
(2017). The 101 sampled villages representing five major agro-ecological zones
in China were surveyed three times (in 2005, 2008 and 2012). We obtain
detailed information in these 101 villages on village public goods, local
governance and local socio-economic conditions, which ranges from 1995 to
2012 and contains five office terms (approximately three years per term).
In these 101 villages, we obtain reliable and comprehensive project quality
measures of 563 village roads in total. To ensure the measure precision, the field
team worked with professional civil engineers and the transportation
departments of local governments, before field surveys, to develop a standard
� 31
and scientific village road quality evaluating scheme. A series of measures was
also taken to avoid enumerator-specific subjectiveness on village road projects8.
By adding up all partial quality scores, the comprehensive village road quality
score (0-100 points) for these 563 village roads is obtained.
We consider project quality of village roads influenced both by village leaders’
virtue and by their capacity; therefore, it reflects village leaders’ composite
virtue-and-capacity. The reason is that it is village leaders’ capacity that
influences the investment of village public road projects (Martinez-Bravo et al.,
2011); yet making good use of the investment and transforming it to the quality
require village leaders’ virtue, including, but not limited to, responsibility and
intrinsic motives to serve local people (Tian et al., 2013).
B. Evidence of the Meritocratic Selection for Village Leaders
The data used in this section is the “road-construction year” panel data set
used in Wong et al. (2017). Our data use the mean value of village road quality
to represent the mean value of village leaders’ composite virtue-and-capacity,
and uses the variance of village road quality to represent the variance of village
leaders’ composite virtue-and-capacity. The mean value of village road quality
by elected village leaders is 80.27, while that by appointed village leaders is
60.18. On the contrary, the variance of village road quality by elected village
leaders is 123.29 while that by appointed village leaders is 195.07. Figure 2
shows histograms of village road quality by either elected or appointed village
leader, and illustrates similar results as above. In a word, local direct elections
���������������������������������������� ����8 For details on avoiding measurement errors in project quality of village roads, see Wong et al. (2017).
�Figure 2 is about here��
� 32
facilitate the fulfillment of meritocratic selection for village leaders.
Wong et al. (2017) also provides econometric estimation results as evidence
for elected village leaders’ higher mean value of composite virtue-and-capacity
than appointed village leaders’. The econometric specification is
(41) òë3ôöñõ = úq + úMáëTöõ + +ùöñõû + üö + †õ + °ö1
where òë3ôö¢ is the quality of village road a built starting in year of £ in
village §. áëTöõ is a dummy variable whether the village leader who built the
road starting in year of £ in village § was elected directly by local village
residents. ùöñõ represents controlling variables, üö is the village dummy and
†õ is the road project starting year dummy. °ö1 is the random error,
The estimation results in Wong et al. (2017), show that after introducing local
direct elections, the village road quality is increased on average. Since village
leaders’ composite virtue-and-capacity underlies the village road quality, these
estimation results imply elected village leaders’ higher mean value of composite
virtue-and-capacity than appointed village leaders’.
C. Evidence of the Meritocratic Selection for Village Party Secretaries
The meritocratic selection for village party secretaries can be empirically
testified, according to Section III.C., by comparing, in a representative village,
the association between elected village leaders’ performance with their
likelihood to be promoted as village party secretaries, and that association of
appointed village leaders. Based on (36), the specification is
(42) Üö1 = úq + úMáëTö1 + úDoòë3ôö1 + ú•áëTö1 ∙ oòë3ôö1
+¶ö1ß + üö + ®1 + ©ö1
where Üö1 is a dummy variable whether the village leader is promoted as the
� 33
village party secretary as her tenure ends. In village §, if the village leader
would be promoted as the village party secretary as her village leader tenure
ends in year 3, the value of Üö1 of this observation is 1; otherwise it is 0. áëTö1
is a dummy variable whether this village leader was elected directly by local
village residents. oòë3ôö1 is the average project quality of village roads in this
village leader’s tenure.
¶ö1 represents the controlling variables, that is, the characteristics of village
§, of the village leader, and of the party secretary incumbent in the village
leader’s tenure-ending year 3. We control for population and per capita income
in the village, village leaders’ age and years of schooling, and party secretary
incumbents’ age. In addition, üö and ®1 represents the village fixed effects
and the tenure-ending year fixed effects, respectively. ©ö1 is the random error.
Different from the “road-construction year” panel data set used in Section
III.B., this section uses the “village-tenure” panel data set. Since partial village
leaders hold the position for more than one term, in each village, we regard the
village leader’s whole tenure (one or more terms) as one observation. Therefore,
a village-tenure panel data set is obtained, where the tenure is marked with the
village leader’s tenure-ending year. On average, there are 4-5 village leaders in
each of the 101 villages from 1995 to 2012. Therefore, our village-tenure panel
data set contains 455 observations, in which the average project quality of
village roads in each village leader’s tenure is also calculated.
Online Appendix Table 1 presents the summary statistics of variables used in
our study. Table 1 presents the estimation results of our specifications. Column
�Table 1 is about here��
� 34
1 shows that úM is significantly positive. This result is consistent with our
Proposition 4 that the elected village leader in a representative village receives
higher promotion likelihood.
The result in Column 2 of Table 1 shows that úD is significantly positive, in
other words, the average project quality of village roads observed by township
officials has statistical evidence to contribute to appointed village leaders’
average promotion likelihood. This result is consistent with our theoretical
prediction of the performance-based promotion premium, in other words,
úDoòë3ôö1 matches åℱ [[n& + 1 − n )]st,899 in (36).
The result in Column 2 of Table 1 also shows that ú• is significantly positive,
that is, the average project quality of village roads contributes, statistically, to
elected village leaders’ average promotion likelihood to a larger extent than to
appointed village leaders’. This result is consistent with our theoretical
prediction of local information increment, in other words, ú•áëTö1 ∙ oòë3ôö1
matches åΓè in (36).
V. Concluding Remarks
Two major issues in political economy, both concerns information asymmetry,
are political selection that may suffer from adverse selection and political
incentive that could suffer from moral hazards. In addressing moral hazards,
accumulating studies have been conducted, either by deciphering existing
schemes or by designing new mechanisms, to discuss the fulfillment of
accountability of politicians (Laffont, 2000; Besley, 2006). Addressing adverse
selection, however, appears commonly in literature regarding, for instance, job
market signaling (Spence, 1973) and product advertisement (Milgrom and
Roberts, 1986), yet seldom in political selection literature. Both types of issues,
� 35
in existing studies, are basically discussed under the game theory framework.
In lights of local information (Hayek, 1945), we discover new ways to
address adverse selection in political selection with the Bayesian framework.
We demonstrate that local direct elections facilitate the fulfillment of
meritocratic selection for village leaders directly, by providing the local
information on village leader candidates and through which improving the
screening effects. This demonstration is empirically supported9.
We further demonstrate theoretically and empirically that integrating local
information with ex post incentives facilitates addressing adverse selection and
moral hazards in political selection, endowing the performance-based
promotion with meritocratic selection. Specifically, local direct elections
facilitate the fulfillment of meritocratic selection for village party secretaries
indirectly, by providing the local information on village leader candidates and
through which improving the candidate pool.
Several limitations and extensions are important to note. First, although
assumption in our model that political selections in rural China law-abiding
could partially deviate from facts, our theoretical predictions on meritocratic
selection for village leaders and for village party secretaries are supported
empirically. Second, it’s a strong assumption that the election or appointment
likelihood for village leaders equal to village leader a weighted average of
village leader candidates’ posterior virtue and posterior capacity, and some
further discussion is in need to relax this assumption. Third, although it is
interesting to discuss whether the meritocratic selection for village leaders
���������������������������������������� ����9 Given the previously discussed assumption that politicians’ performance is an increasing function of
their composite virtue-and-capacity, our demonstration is empirically supported by studies regarding the
impacts of local direct elections on village public investment (Luo et al., 2007; Martinez-Bravo et al.,
2014), and studies regarding that on quality of village public infrastructure (Wong et al. 2017).
� 36
facilitates by local direct elections leads to an equilibrium in which village
leaders, village residents and township officials all obtain optimized payoffs,
due to limited spaces, it is not discussed in this paper.
� 37
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� 41
FIGURE 1: INFERENCE ACCURARY AND PRECISION WITH NATURAL COMMUNICATION TIMES
� 42
�
���
FIGURE 2: HISTOGRAM OF ROAD QUALITY BY ELECTION OR APPOINTMENT
05
10
40 60 80 100 40 60 80 100Source: Authors' survey Source: Authors' survey
Roads built by appointed leaders Roads built by elected leaders
Perc
ent o
f villa
ge ro
ad p
roje
cts
Road quality scoresGraphs by institution
� 43
Online Appendix Table 1: Summary statistics of sample village road projects and sample villages
N Mean S.D. Min Max
Explained variables
Village leader promoted as party secretary as her tenure ends (Y=1; N=0) 455 0.248 0.433 0 1
Main explanatory variable
Village leader elected (Y=1; N=0) 455 0.547 0.498 0 1
Average comprehensive road quality scores of all village road projects in the village leader’s tenure 226 71.353 16.123 26.75 98.9
Village leader characteristics
Age 455 50.147 4.775 36 63
Years of Schooling 455 9.435 2.459 5 16
Party secretary incumbent characteristics
Age 455 53.668 5.642 41 68
Village characteristics
Village population (in 1,000 persons) 455 1.912 1.387 0.16 6.60
Village per capita income (in 1,000 yuan) 455 3.455 1.887 0.30 10.15
Data source: Authors’ survey
� 44
Table 1: FE estimates of the impacts of village election and village road project quality on village leaders’ promotion likelihood as village party secretaries
Explained variable: Village leader promoted as village party secretary (Y=1; N=0)
(1) (2)
Village leader elected
(Y=1; N=0)
0.160***
(0.061)
-0.034
(0.058)
Average comprehensive road quality scores of all village road projects in
the village leader’s tenure (0-100)
0.0019**
(0.0010)
Village leader elected × Average comprehensive road quality scores of
all village road projects in the village leader’s tenure (0-100)
0.0030**
(0.0012)
Village characteristics Y Y
Village leader characteristics Y Y
Party secretary incumbent characteristics Y Y
Village FE & Tenure-ending year FE Y Y
N 455 455
R2 0.06 0.16
Data source: Authors’ survey
Note: All models control for characteristics of villages, village leaders and party secretary incumbents, and village fixed effects and tenure-ending year fixed effects. Village characteristics include village population and village per
capita income. Village leaders’ characteristics include age and years of schooling. Party secretary incumbents’ characteristics include age. Linear probability models are used in this table. Robust standard errors, clustered at the
village level, are reported in parentheses. ***, **, and * indicate statistical significance from zero at the 1, 5, and 10 percent levels.
� 45
Online Appendix for Local Direct Elections, Local Information and Meritocratic
Selection
A. Posterior Distributions of Virtue and Capacity
A.1 Virtue: In the light of Koop et al. (2007), we derive the density kernel of the
posterior distribution of virtue, such that
(A1) ! "# $%&' = ) "# ∙ [, "#; .#/0 …, "#; .#2
0 … , "#; .#30 ]]
where the vector $%&' is [.#/0 ….#20 ….#30 ].
First, we derive ) "# , the density kernel of the prior distribution of virtue. Since
the prior distribution is a normal distribution truncated at [0, 1], we have
(A2) ) "# = ) "# 0 ≤ "# ≤ 1, "#9)
=<
=>?@ A[
>BC>B?
=>?@ ]
D 0B EF0BF/,0B?)
=GHI>?
@ C<@∙9JK
C >BC>B? @
@=>?@
D 0B EF0BF/,0B?)
∝9JK{
C >BC>B? @
@=>?@ }
D 0B EF0BF/,0B?)
where O "# 0 ≤ "# ≤ 1, "#9) = P(
/R0B?
I>?@ ) − P(
R0B?
I>?@ ) represents the likelihood that "#
is at [0, 1], contingent on "#9.
Second, we derive the joint density of $%&' as a likelihood function that
(A3) , "#; $%&' = 2UVW>G R
<@ ∙ XY!
R ZB[>R0B
@
GI\>@
32]/
= 2UVW>G R
^@ ∙ XY! −
ZB[>R0B
@
GI\>@
32]/
∝ XY! −ZB[>R0B
@
GI\>@
32]/
∝ XY! −ZB[>RZ_
>`Z_>R0B
@
GI\>@
32]/
∝ XY! −/
GI\>@ [ .#2
0 − .a0 G32]/ + .a0 − "# G3
2]/ + 2 .#20 − .a0 .a0 − "#3
2]/
where .a0 =/
3.#203
2]/ . Because .#20 − Ωa0 G3
2]/ , the second-order moment, is a
� 46
constant, 2 .#20 − Ωa0 .a0 − "#3
2]/ = 2 .a0 − "# .#20 − Ωa03
2]/ = 0, we have
(A4) , "#; $%&' ∝ XY! −Z_>R0B
@
GI\>@
32]/ ∝ XY! −d
Z_>R0B
@
GI\>@
Thirdly, by Bayes’ rule, the density kernel of posterior distribution of virtue is
(A5) , "#; $%&' ) "# ∝
9JK R3e_>C>B
@
@=\>@ fgh
C >BC>B? @
@=>?@
D 0B EF0BF/,0B?)
∝9JK R
^
=\>@
e_>C>B
@
@9JK R
<
=>?@
>BC>B? @
@
D 0B EF0BF/,0B?)
∝R<@9JK
^
=\>@ Z_
>R0B@`
<
=>?@ 0BR0B
? @
D 0B EF0BF/,0B?)
∝^
=\>@ Z_
>@RG0BZ_>`0B
@ `<
=>?@ 0B
@RG0B?0B`0B
?@
D 0B EF0BF/,0B?)
∝^
=\>@ `
<
=>?@ 0B
@RG<
=>?@ 0B
?`^
=\>@ Z_
> 0B`^
=\>@ Z_
>@`<
=>?@ 0B
?@
D 0B EF0BF/,0B?)
∝
<
=\>@ =>?
@
=\>@ i^=>?
@
0B@RG
=\>@ =
>?@
=\>@ i^=>?
@<
=>?@ >B
?i^
=\>@ e_
>
=\>@ =>?
@
=\>@ i^=>?
@
0B`^
=\>@ Z_
>@`<
=>?@ 0B
?@
D 0B EF0BF/,0B?)
(A5) is positively associated with
<
=\>@ =>?
@
=\>@ i^=>?
@
0B@RG
=\>@ =
>?@
=\>@ i^=>?
@<
=>?@ >B
?i^
=\>@ e_
>
=\>@ =>?
@
=\>@ i^=>?
@
0B
D 0B EF0BF/,0B?)
after
dropping the constants uncorrelated with "#. Then we have
(A6) , "#; $%&' ) "# ∝
9JK R<@[
<
=\>@ =>?
@
=\>@ i^=>?
@
[0BR{=\>@ =
>?@
=\>@ i^=>?
@<
=>?@ 0B
?`^
=\>@ Z_
> }]@]
D 0B EF0BF/,0B?)
where O "# 0 ≤ "# ≤ 1, "#9) = P(
/R0B?
I>?@ ) − P(
R0B?
I>?@ ). Therefore, this density kernel is
still of a truncated normal distribution, in which the posterior variance of virtue is
(A7) j "# =I\>@ I>?
@
I\>@ `3I>?
@
and the posterior mean of virtue is
(A8) k "# = j "#/
I>?@ "#
9 +3
I\>@ .a0 =
I\>@
I\>@ `3I>?
@ "#9 +
3I>?@
I\>@ `3I>?
@ .a0
� 47
Since .#20~m("#, VW>G ), and d = dno9 dpKK → +∞, we have
(A9) .a0 =/
3.#203
2]/ = s .#20 = "#
thus the posterior mean of virtue is
(A10) k "# =I\>@
I\>@ `3I>?
@ "#9 +
3I>?@
I\>@ `3I>?
@ "#
A.2 Capacity: Similar to virtue, we derive the density kernel of the posterior
distribution of virtue, such that
(A11) ! t# $%&u = ) t# ∙ [, t#; .#/
v …, t#; .#2v … , t#; .#3
v ]]
where the vector $%&u is [.#/v ….#2v ….#3v ].
First, we derive ) t# , the density kernel of the prior distribution of capacity. Since
the prior distribution is a normal distribution truncated at [0, 1], we have
(A12) ) t# = ) t# 0 ≤ t# ≤ 1, t#9)
∝9JK{
C wBCwB? @
@=w?@ }
D vB EFvBF/,vB?)
where O t# 0 ≤ t# ≤ 1, t#9) = P(
/RvB?
Iw?@ ) − P(
RvB?
Iw?@ ) represents the likelihood that t#
is at [0, 1], contingent on t#9.
Second, we derive the joint density of $%&u as a likelihood function that
(A13) , t#; $%&u = 2UVxw
G R<@ ∙ XY!
R ZB[wRvB
@
GIyw@
32]/
∝ XY! −ZB[wRZ_
w`Z_wRvB
@
GIyw@
32]/
∝ XY! R/
GIyw@ [ .#2
v − .avG3
2]/ + .av − t#G3
2]/ + 2 .#2v − .av .av − t#3
2]/
where .av =/
3.#2v3
2]/ . Because .#2v − .av
G32]/ , the second-order moment, is a
constant, 2 .#2v − .av .av − t#3
2]/ = 2 .av − t# .#2v − .av3
2]/ = 0, we have
(A14) , t#; $%&u ∝ XY! −
Z_wRvB
@
GIyw@
32]/ ∝ XY! −d
Z_wRvB
@
GIyw@
� 48
Thirdly, by Bayes’ rule, the density kernel of posterior distribution of capacity is
(A15) , t#; $%&u ) t# ∝
9JK R3e_wCwB
@
@=yw@ fgh
C wBCwB? @
@=>?@
D vB EFvBF/,vB?)
∝9JK R
^
=yw@
e_wCwB
@
@9JK R
<
=w?@
wBCwB? @
@
D vB EFvBF/,vB?)
∝R<@9JK
^
=yw@ Z_
wRvB@`
<
=w?@ vBRvB
? @
D vB EFvBF/,vB?)
∝
^
=yw@ Z_
w@RGvBZ_
w`vB@ `
<
=w?@ vB
@RGvB?vB`vB
?@
D vB EFvBF/,vB?)
∝
^
=yw@ `
<
=w?@ vB
@RG<
=w?@ vB
?`^
=yw@ Z_
w vB`^
=yw@ Z_
w@`
<
=w?@ vB
?@
D vB EFvBF/,vB?)
∝
<
=yw@ =w?
@
=yw@ i^=w?
@
vB@RG
=yw@ =
w?@
=yw@ i^=w?
@<
=w?@ wB
?i^
=yw@ e_
w
=yw@ =w?
@
=yw@ i^=w?
@
vB`^
=yw@ Z_
w@`
<
=w?@ vB
?@
D vB EFvBF/,vB?)
(A15) is positively associated with /=yw@ =w?
@
=yw@ i^=w?
@
t#G − 2
=yw@ =
w?@
=yw@ i^=w?
@<
=w?@ vB
?`^
=yw@ Z_
w
=yw@ =w?
@
=yw@ i^=w?
@
t# after
dropping the constants uncorrelated with t#. Then we have
(A16) , t#; $%&u ) t# ∝
9JK R<@[
<
=yw@ =w?
@
=yw@ i^=w?
@
[vBR{=yw@ =
w?@
=yw@ i^=w?
@<
=w?@ vB
?`^
=yw@ Z_
w }]@]
D vB EFvBF/,vB?)
where O t# 0 ≤ t# ≤ 1, t#9) = P(
/RvB?
Iw?@ ) − P(
RvB?
Iw?@ ). Therefore, this density kernel is
still of a truncated normal distribution, in which the posterior variance of capacity is
(A17) j t# =Iyw@ Iw?
@
Iyw@ `3Iw?
@
and the posterior mean of capacity is
(A18) k t# = j t#/
Iw?@ t#
9 +3
Iyw@ .av =
Iyw@
Iyw@ `3Iw?
@ t#9 +
3Iw?@
Iyw@ `3Iw?
@ .av
Since .#2v~m(t#, VxwG ), and d = dno9 dpKK → +∞, we have
� 49
(A19) .av =/
3.#2v3
2]/ = s .#2v = t#
thus the posterior mean of capacity is
(A20) k t# =Iyw@
Iyw@ `3Iw?
@ t#9 +
3Iw?@
Iyw@ `3Iw?
@ t#
B. Comparing Elected and Appointed Village Leaders’ Mean Values and
Variances of Composite Virtue-and-Capacity
B.1 Mean Values: We compare, in a representative village, the elected and the
appointed village leader’s mean values of composite virtue-and-capacity. Specifically,
we compare
(B1) {no9(|"# + (1 − |)t#) =}0B` /R} vB pB
~�?<Ä Å0B
<Ä ÅvB
pB~�?<
Ä Å0B<Ä ÅvB
and
(B2) {pKK(|"# + (1 − |)t#) =}0B` /R} vB pB
ÇÉÉ<Ä Å0B
<Ä ÅvB
pBÇÉÉ<
Ä Å0B<Ä ÅvB
and we know that
(B3) Ñ#no9 pKK = |kno9 pKK "# + 1 − | kno9 pKK t#
where
(B4) kno9 pKK "# =Ö~�? ÇÉÉ 0B
I>?@ "#
9 + 1 −Ö~�? ÇÉÉ 0B
I>?@ "#
=I\>@
I\>@ `3~�?(ÇÉÉ)I>?
@ "#9 +
3~�?(ÇÉÉ)I>?@
I\>@ `3~�?(ÇÉÉ)I>?
@ "#
(B5) kno9 pKK t# =Ö~�? ÇÉÉ vB
Iw?@ t#
9 + 1 −Ö~�? ÇÉÉ vB
Iw?@ t#
=Iyw@
Iyw@ `3~�?(ÇÉÉ)Iw?
@ t#9 +
3~�?(ÇÉÉ)Iw?@
Iyw@ `3~�?(ÇÉÉ)Iw?
@ t#
Since dno9 > dpKK, comparing the elected and appointed village leader’s composite
virtue-and-capacity is equivalent to having
(B6) á Y à , â à =}0B` /R} vB }ä 0B ` /R} ä vB Å0B ÅvB
<Ä
<Ä
}ä~�? 0B ` /R} ä~�? vB Å0B ÅvB<Ä
<Ä
where k "# = 1 − Y "#9 + Y"# , Y ≡
I>?@ 2
Iå>@ `I>?
@ 2; k t# = 1 − â t#
9 + ât# , â ≡
Iw?@ 2
Iyw@ `Iw?
@ 2. à = dno9çédpKK. Then we need to prove that
� 50
(B7) èêè2=
èê
èJ∙èJ
è2+
èê
èë∙èë
è2> 0
It is easy to prove that èJè2> 0, and èë
è2> 0, so we only need to prove that èê
èJ≥ 0
and èêèë≥ 0.
Firstly, simplify the numerator of (B6) as
|"# + 1 − | t# | 1 − Y "#9 + Y"# + 1 − | 1 − â t#
9 + ât# ì"# ìt#/
E
/
E
=|G"# 1 − Y "#
9 + Y"# + 1 − | Gt# 1 − â t#9 + ât#
+| 1 − | "# 1 − â t#9 + ât# + | 1 − | t# 1 − Y "#
9 + Y"#ì"# ìt#
/
E
/
E
where
(B8) |G"# 1 − Y "#9 + Y"# = |G 1 − Y "#
9"#ì"# ìt#/E
/E
+ |GY"#Gì"# ìt#
/E
/E
= /
G|G 1 − Y "#
9 +/
î|GY
(B9) 1 − | 1 − â t#9 + ât#
= 1 − | G 1 − â t#9t#ì"# ìt#
/E
/E
+ 1 − | Gât#Gì"# ìt#
/E
/E
= /
G1 − | G 1 − â t#
9 +/
î1 − | Gâ
(B10) | 1 − | "# 1 − â t#9 + ât#
= | 1 − | "# 1 − â t#9ì"# ìt#
/E
/E
+ | 1 − | "#ât#ì"# ìt#/E
/E
= /
G| 1 − | 1 − â t#
9 +/
ï| 1 − | â
(B11) | 1 − | t# 1 − Y "#9 + Y"#
= | 1 − | 1 − Y "#9t#ì"# ìt#
/E
/E
+ | 1 − | Y"#t#ì"# ìt#/E
/E
= /
G| 1 − | 1 − Y "#
9 +/
ï| 1 − | Y
Therefore, (B6)’s numerator becomes:
(B12) /G| 1 − Y "#
9 +/
G1 − | 1 − â t#
9 +/
/G| | + 3 Y +
/
/G| − 4 | − 1 â
Secondly, simplify the denominator of (B6)
(B13) | 1 − Y "#9 + Y"# + 1 − | 1 − â t#
9 + ât# ì"# ìt#/E
/E
= | 1 − Y "#9 ì"# ìt#
/E
/E
+ |Y"# ì"# ìt#/E
/E
� 51
+ 1 − | 1 − â t#9 ì"# ìt#
/E
/E
+ 1 − | ât# ì"# ìt#/E
/E
= | 1 − Y "#9 +
/
G|Y + 1 − | 1 − â t#
9 +/
G1 − | â
Accordingly, (B6) becomes
(B14) á Y à , â à =<@} /RJ 0B
?`<@/R} /Rë vB
?`<<@} }`î J`
<<@
}Rï }R/ ë
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
where (B14)’s numerator’s first-order derivative with respect to Y is −/
G|"#
9 +
/
/G| | + 3 , (B14)’s denominator’s first-order derivative with respect to Y is
−|"#9 +
/
G|.
Then we could derive that
(B15) èêèJ=
<<@}ò0B
?`<<@} /R} @ë0B
?`<<@}@ /R} /Rë vB
?`<@ô} /R} G}R/ ë
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
@
=<<@}ò0B
?`<<@}@ /R} /Rë vB
?`<@ô} /R} ë G} /R0B
? `G0B?R/
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
@
To ensure èêèJ≥ 0, we need to have, as is shown in the first step of (B15), 2| − 1 ≥
0, that is, 1 ≥ | ≥/
G, or | = 0. However, when 0 < | <
/
G, we need to reorganize the
numerator items in (B15), as is shown in the second step of (B15), that when we have
2| 1 − "#9 + 2"#
9 − 1 ≥ 2| 1 − "#9 ≥ 0, that is, "#9 ≥
/
G, then we have èê
èJ≥ 0. In
a word, èêèJ≥ 0 when 1 ≥ | ≥
/
G, or | = 0, or both 0 < | <
/
G and "#9 ≥
/
G.
Now we discuss èêèë
. (B14)’s numerator’s first-order derivative with respect to â is
= −/
G1 − | ∙ t#
9 +/
/G| − 4 | − 1 , (B14)’s denominator’s first-order derivative
with respect to â is − 1 − | ∙ t#9 +
/
G1 − | .
Then we could derive that
(B16) èêèë=
<<@}@ /R} JvB
?`<<@
/R} òvB?`
<<@} /R} @ /RJ 0B
?`<@ô} /R} J /RG}
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
@
� 52
=<<@
/R} òvB?`
<<@} /R} @ /RJ 0B
?`<@ô} /R} J /RG}`G}∙vB
?
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
@
To ensure èêèë≥ 0, we need to have, as is shown in the first step of (B16), 1 − 2| ≥
0, that is, 0 ≤ | ≤/
G, or | = 1. However, when /
G< | < 1, we need to reorganize the
numerator items in (B16), as is shown in the second step of (B16), that when we have
1 − 2| + 2| ∙ t#9 ≥ 1 − 2| + õ ≥ 0, that is, t#9 ≥
/
G, then we have èê
èë≥ 0. In a word,
èê
èë≥ 0 when 0 ≤ | ≤
/
G, or | = 1, or both /
G< | < 1 and t#9 ≥
/
G.
By proving èêèJ≥ 0 and èê
èë≥ 0, we prove that èê
è2> 0. As dno9 > dpKK, we know
that {no9 |"# + 1 − | t# > {pKK(|"# + (1 − |)t#).
In sum, when | = 0, 1,/
G, we have {no9 |"# + 1 − | t# > {pKK(|"# + (1 −
|)t#) . When 0 < | </
G, by assuming that "#9 ≥
/
G, we have {no9 |"# + 1 −
| t# > {pKK(|"# + (1 − |)t#) . When /G< | < 1 , by assuming that t#9 ≥
/
G, we
have {no9 |"# + 1 − | t# > {pKK(|"# + (1 − |)t#).
B.2 Variances: We then compare, in a representative village, the elected and
appointed village leader’s variances of composite virtue-and-capacity. We know that
(B17) úùéno9 pKK |"# + 1 − | t#
= {no9(pKK) |"# + 1 − | t# G − {no9(pKK)G|"# + 1 − | t#
We first define û(Y à , â(à)) ≡ {no9(pKK) |"# + 1 − | t# G , and we have
(B18) û Y à , â à =}0B` /R} vB
@ }ä 0B ` /R} ä vB Å0BÅvB<Ä
<Ä
}ä 0B ` /R} ä vB Å0BÅvB<Ä
<Ä
where k "# = 1 − Y "#9 + Y"#, k t# = 1 − â t#
9 + ât#, Y ≡I>?@ 2
Iü>@ `I>?
@ 2, and â ≡
Iw?@ 2
Iyw@ `Iw?
@ 2.
First, we simplify the numerator of û ∙ as
(B19) |G"#G + 1 − | Gt#
G + 2| 1 − | "#t# ∙| 1 − Y "#
9 + Y"# + 1 − | 1 − â t#9 + ât# ì"#ìt#
/E
/E
� 53
=|î"#
G 1 − Y "#9 + Y"# + |G 1 − | "#
G 1 − â t#9 + ât#
+| 1 − | Gt#G 1 − Y "#
9 + Y"# + 1 − | ît#G 1 − â t#
9 + ât#+2|G 1 − | "#t# 1 − Y "#
9 + Y"# + 2| 1 − | G"#t# 1 − â t#9 + ât#
ì"#ìt#/
E
/
E
where
(B20) |î"#G 1 − Y "#9 + Y"# =
/
î|î 1 − Y "#
9 +/
ï|îY
(B21) |G 1 − | "#G 1 − â t#
9 + ât# =/
î|G 1 − | 1 − â t#
9 +/
†|G 1 − | â
(B22) | 1 − | Gt#G 1 − Y "#
9 + Y"# =/
î| 1 − | G 1 − Y "#
9 +/
†| 1 − | GY
(B23) 1 − | ît#G 1 − â t#
9 + ât# =/
î1 − | î 1 − â t#
9 +/
ï1 − | îâ
(B24) 2|G 1 − | "#t# 1 − Y "#9 + Y"# =
/
G|G 1 − | 1 − Y "#
9 +/
î|G 1 − | Y
(B25) 2| 1 − | G"#t# 1 − â t#9 + ât# =
/
G| 1 − | G 1 − â t#
9 +/
î| 1 − | Gâ
The numerator of û ∙ becomes /†| |G − | + 2 1 − Y "#
9 +/
†1 − | |G − | +
2 1 − â t#9 +
/
/G| |G + 2 Y +
/
/G1 − | |G − 2| + 3 â. Therefore, we have
(B26) û ∙ =<°} }@R}`G /RJ 0B
?`<°/R} }@R}`G /Rë vB
?`<<@} }@`G J`
<<@
/R} }@RG}`î ë
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
Then we define á Y à , â à ≡ {no9(pKK) |"# + 1 − | t# , and we know that
á Y à , â à =<@} /RJ 0B
?`<@/R} /Rë vB
?`<<@} }`î J`
<<@
}Rï }R/ ë
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
from (B14).
From (B17) we know that
(B27) 袣§ ∙
è2=
è• ∙
è2− 2á ∙ ∙
èê ∙
è2
It is known that á ∙ > 0,èê ∙
è2> 0. We then need to derive è• ∙
è2=
è• ∙
èJ∙èJ
è2+
è• ∙
èë∙
èë
è2. It is known that èJ
è2> 0,
èë
è2> 0, therefore, we
(B28) è• ∙
èJ=
<<@}ò0B
?`<<@} /R} @ë0B
?`<<@}@ /R} /Rë vB
?`<@ô} /R} G}R/ ë
[ /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë]@
(B29) è• ∙
èë=
<<@}@ /R} JvB
?`<<@
/R} òvB?`
<<@} /R} @ /RJ 0B
?`<@ô} /R} /RG} J
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
@
Thus, è• ∙
è2=
<<@}ò0B
?`<<@} /R} @ë0B
?`<<@}@ /R} /Rë vB
?`<@ô} /R} G}R/ ë
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
@ ∙èJ
è2
� 54
+<<@}@ /R} JvB
?`<<@
/R} òvB?`
<<@} /R} @ /RJ 0B
?`<@ô} /R} /RG} J
} /RJ 0B?` /R} /Rë vB
?`<@}J`
<@/R} ë
@ ∙èë
è2
It is easy to find that è• ∙
è2=
èê ∙
è2. In addition, from (B14) we could derive that
á ∙ >/
G, as twice the numerator of á ∙ is larger than the denominator of á ∙ . As a
result, we can derive from (B27) that 袣§ ∙
è2=
è• ∙
è2− 2á ∙ ∙
èê ∙
è2< 0. As dno9 >
dpKK, we know that úùéno9 |"# + 1 − | t# < úùépKK |"# + 1 − | t# .
C. Promotion Likelihood as the Village Party Secretary
We know that for the village leader’s composite virtue-and-capacity, the distribution
of the representative township official’s prior perception is m |G"¶ + (1 −
|)Gt¶, V0ßG + Vvß
G . After an update by observing her performance O = ℱ[(|" +
1 − | t)¢©] + ™, we can obtain the posterior distribution of village party secretary
candidate ´’s composite virtue-and-capacity. For simplicity, denote that U¶ ≡ |G"¶ +
(1 − |)Gt¶, U¢© ≡ (|" + 1 − | t)¢© and V¶G ≡ V0ßG + Vvß
G .
First, we derive ) U¢© , the density kernel of the prior distribution of composite
virtue-and-capacity. Since the prior distribution is a normal distribution truncated at
[0, 1], we have
(C1) ) U¢© = ) U¢© 0 ≤ U¢© ≤ 1, U¶)
∝9JK{
C ¨≠ÆC¨ß@
@=ß@ }
D H≠Æ EFH≠ÆF/,0B?)
where O U¢© 0 ≤ U¢© ≤ 1, U¶) = P(/RHß
Iß@ ) − P(
RHß
Iß@ ) represents the likelihood that
U¢© is at [0, 1], contingent on U¶.
Second, we derive the density of O as a likelihood function that
(C2) , U¢©; O ∝ XY! −dℱ[H≠Æ]RH≠Æ
@
GIØ@
Thirdly, by Bayes’ rule, the density kernel of posterior distribution of the village
leader’s composite virtue-and-capacity is
� 55
(C3) , U¢©; O ) U¢© ∝
9JK R<@[
<
=Ø@=ß
@
=Ø@i=ß
@
[H≠ÆR{=Ø@=ß
@
=Ø@i=ß
@<
=ß@H
ß`ℱ[¨≠Æ]
=Ø@ }]@]
D H≠Æ EFH≠ÆF/,Hß)
Therefore, this density kernel is still of a truncated normal distribution, in which
the posterior mean of the village leader’s composite virtue-and-capacity, which is also
her likelihood of being promoted as the village party secretary, is
(C4) s U¢©|O =IØ@Iß@
IØ@`Iß
@/
Iß@ U
¶ +ℱ[H≠Æ]
IØ@ =
IØ@
IØ@`Iß
@ U¶ +
Iß@
IØ@`Iß
@ ℱ[U¢©]