The Mandarin Model of Growth
Wei Xiong
y
September 2019
Abstract
This paper expands a standard growth model to analyze the roles played by
the government system in the Chinese economy, with a particular focus to include
the agency problem between the central and local governments. The economic
tournament among local governors creates career incentives for them to develop
local economies. The powerful incentives also lead to short-termist behaviors,
which explain a series of challenges that confront the Chinese economy, such as
overleverage through shadow banking and unreliable economic statistics.
I am grateful to Jianjun Miao, Yingyi Qian, Tao Zha, Li-An Zhou and seminar participants at the 2018
Hong Kong-Shenzhen Summer Finance Conference, the 2018 NBER Chinese Economy Meeting, the 2018
SAIF Symposium on Frontiers of Macroeconomics, the 2019 IMF Conference, Princeton, SWUFE and UIBE
for helpful discussions and comments, to Lunyang Huang and Chang Liu for able research assistance, and in
particular to M ichael Song for highly constructive suggestions.
y
After four decades of rapid growth, the Chinese economy has slowed down in the recent
years with a wide range of concerns about China’s …nancial stability.
1
To systematically
analyze these concerns requires an economic framework that accounts for China’s unique
economic structure. Despite that China’s highly successful economic reforms in the past
forty years have made it the second largest economy in the world, its economic structure
and policy making processes are still distinctively di¤erent from a typical western economy,
such as the U.S. These di¤erences dictate that China faces di¤erent risks and its p olicy
makers may adopt di¤erent policy responses to potential risks. This paper aims to expand
a standard macroeconomic framework to account for some of the di¤erences.
A large strand of the literature emphasizes that career incentives created by the economic
tournament among regional government o¢ cials as a key mechanism to explain China’s rapid
economic growth, e.g., Qian and Roland (1998), Maskin, Qian and Xu (2000), Blanchard
and Shleifer (2001), and Li and Zhou (2005). As nicely summarized by Xu (2011) and
Qian (2017), China has a complex government system with the central government working
along with regional governments at several levels: province, city, county, and township.
Regional governments are major players in China’s economic development. First, regional
governments carry out over 70% of …scal spending in China, and they are responsible for
developing economic institutions and infrastructure at the regional levels, such as opening up
new markets and constructing roads, highways, and airports. Second, despite their autonomy
in economic and …scal issues, regional government leaders are appointed by the central
government, rather than being elected by the local electorate. To incentivize regional leaders,
the central government has established a tournament among o¢ cials across regions at the
same level, promoting those achieving fast economic growth and penalizing those with poor
performance. The powerful incentives may lead to not only rapid growth but also short-
termist behaviors of regional governors, which have profound implications about China’s
…nancial stability. A key ongoing concern is related to China’s leverage rising to an alarming
level in recent years. As recognized by Bai, Hsieh and Song (2016) and Chen, He and Liu
(2017), this leverage boom was primarily driven by China’s local governments.
This paper develops an economic framework to analyze a range of short-termist behaviors
induced by the powerful incentives of regional governors. Speci…cally, my framework expands
the growth model of Barro (1990) to incorporate this institutional structure of China’s gov-
1
See Song and Xiong (2018) for a review of these concerns .
1
ernment system. As described in Section 1, the model considers an open economy with a
number of regions. In each region, the representative …rm has a Cobb-Douglas production
function with three factors: labor, capital, and local infrastructure. The …rm hires labor
from local households at a competitive wage and rents capital at a given interest rate from
an open capital market. By creating more infrastructure in the region, the local govern-
ment can boost the productivity of the local …rm. Infrastructure investment thus serves
the key channel for the local government to directly stimulate the local economy. However,
the local government faces a tradeo¤ in allocating its …scal budget into local infrastructure
and consumption by government employees. As the local government do es not internalize
household consumption, it has a tendency to underinvest in infrastructure relative to the
…rst-best benchmark, in which a social planner makes the infrastructure investment decision
to maximize the social welfare of not only government employees but also the households.
This underinvestment problem re‡ects a key agency problem between the central and local
governments, which motivates the central government to establish the economic tournament
among regional governors.
I introduce the economic tournament in Section 2. The central government uses the
output from all regions at the end of each period to jointly assess the ability and determine
career advancement of all regional governors. As more investment on infrastructure improves
regional output, the tournament generates an implicit incentive for each governor to invest in
infrastructure through the “signal-jamming mechanism”coined by Holmstrolm (1982), due
to the inability of the central government to fully separate the contribution of a governor’s
ability and infrastructure investment to the regional output. This incentive serves as a
powerful mechanism to drive China’s economic growth, as discussed above.
More interestingly, the powerful incentives induced by the tournament may also lead local
governments to engage in short-termist behaviors, which help to explain various challenges
that currently confront the Chinese economy. First, despite its advanced information tech-
nology, China still lacks reliable statistics about its economy. As discussed by Chen et al.
(2018), the sum of China’s provincial GDP has been routinely higher than the national GDP
by a substantial amount— around 5 percent— since 2004. This enormous discrepancy cannot
simply be attributed to measurement errors. Instead, it is deeply rooted in the government
bureaucracy, as regional governments can in‡uence regional statistics bureaus, which report
regional economic statistics. In Section 3, I extend the model to capture this phenomenon
2
by making the central government reliant on regional governors to report regional output,
which is, in turn, used to evaluate their performance and to determine the region’s tax
transfer to the central government. Consequently, career concerns motivate each regional
governor to overreport regional output, at the expense of a higher tax transfer to the central
government. This mechanism is similar in spirit to overreporting of earnings by executives
of publicly listed …rms, e.g., Stein (1989).
The tournament among regional governors also helps to explain the rising leverage across
China. To address this issue, I further expand the model in Section 4 to allow each regional
government to use debt …nancing to expand its …scal budget. The regional governor faces an
intertemporal tradeo¤ in using more debt to …nance more infrastructure investment. On one
hand, by taking advantage of a high growth rate of regional productivity, debt bene…ts the
households (a social motive) and boosts the governor’s personal career (a private motive).
On the other hand, it requires a higher debt payment in the next p eriod. While a certain
level of debt is socially bene…cial when the local productivity growth rate is su¢ ciently high,
my model also shows that a governor’s career concerns can lead to overinvestment by using
excessive leverage.
My model also o¤ers an intricate mechanism of spillover of excessive leverage from one
region to other regions. Under the assumption of rational expectations, the central govern-
ment is able to fully anticipate short-termist behaviors of each regional government, such
as output overreporting and excessive use of leverage, and thus insulate the relative per-
formance evaluations of other governors from such behaviors. By adopting a more realistic
assumption that the central government can only realize local governments’short-termist
behaviors with a delay, as consistent with China’s gradualistic approach to economic reform,
Section 5 shows that short-termist behaviors of one governor adversely a¤ect the relative
performance evaluation of other governors, which, in turn, leads to a rat race between the
governors in using leverage.
Overall, this “Mandarin” model is de…ned by two key features of the Chinese economy.
First, the government takes a central role in driving the economy through its active invest-
ment in infrastructure, which can be interpreted more broadly as measures and policies by
the government to stimulate economic development. Second, agency problems in the gov-
ernment system can lead to a rich set of phenomena— not just economic growth propelled
by the tournament among regional governors, but also short-termist behaviors of regional
3
governors that directly a¤ect China’s economic and …nancial stability.
Section 6 provides several stylized facts. In particular, by using local government leverage
reported by the national audit of the Ministry of Finance and provincial GDP overreporting
estimated by Chen et al. (2018), I show that across provinces, there is a positive relation-
ship between GDP overreporting and local government leverage. This curious relationship
suggests that these two types of short-termist behaviors might be driven by the same force,
lending support to a key notion of my model that career incentives lead regional governors
to pursue both GDP overreporting and excessive leverage.
My work builds on the literature that studies China’s institutional reform. Qian and
Roland (1998) model the competition among local governments for mobile production factors
(such as capital and labor) and the central government’s resource allocation, albeit not lo cal
o¢ cials’career incentives, and show that the competition helps harden local governments’
soft budget constraints. Lau, Qian and Roland (2000) analyze the optimality of the dual-
track reform approach adopted by China in allowing private …rms to coexist and compete
with state …rms. The work of Maskin, Qian and Xu (2000) is particularly close to mine as it
justi…es the e¤ectiveness of the tournament competition in motivating local o¢ cials. There
is also substantial empirical evidence showing that local economic performance, such as GDP
growth, is signi…cantly correlated with career incentives of local o¢ cials, e.g., Li and Zhou
(2005) and Yu, Zhou and Zhu (2016). Building on these insights, my model embeds local
governors’career incentives into a macroeconomic framework and expands this literature by
highlighting various short-termist behaviors induced by such incentives.
This unique focus also di¤erentiates my model from other work analyzing China’s macro-
economy. Brandt and Zhu (2000) highlight the government’s commitment to support em-
ployment in ine¢ cient state …rms through money creation as a key driver of in‡ationary
pressure in China. Song, Storesletten and Zilibotti (2011) develop a macroeconomic model
for how …nancial frictions cause banks to favor state …rms and discriminate against more
e¢ cient private …rms, leading to a puzzling observation of a fast-growing country exporting
capital to other countries. Li, Liu and Wang (2015) develop a general equilibrium model to
show how state …rms, despite being less e¢ cient, managed to earn more pro…ts than private
…rms by monopolizing upstream industries and extracting rent from more liberalized down-
stream industries. Hsieh and Klenow (2010) measure misallocation of capital and labor in
China. Young (2003) and Zhu (2012) provide growth accounting of China. Hsieh and Song
4
(2015) analyze the transformation of state …rms during China’s economic reform. Chere-
mukhin et al. (2017) use a neoclassical two-sector growth model with wedges to analyze
growth in China’s pre-reform years in 1953–1978.
1 The Basic Setting
I consider an economy with M regions and in…nitely many periods t = 0; 1; 2::: In each region,
I employ a standard setting of Barro (1990) with infrastructure as public goods provided by
the regional government. In region i (i = 1; :::; M), the local output is determined by the
production of a representative …rm:
Y
it
= A
it
K
it
L
1
it
G
1
it
;
where A
it
is the local productivity, K
it
is the capital used for production, L
it
is the local
labor input. The parameters 2 (0; 1) and 1 are the output shares of capital and
labor, respectively. In this section, I simply assume that the local pro ductivity A
it
in one
region is identically and independently distributed over time, without imposing any structure
on the productivities across regions. From the next section on, I will specify a particular
structure with the local productivity determined by the local governor’s ability and a common
productivity shock that a¤ects the productivities of all regions, in order to analyze the local
governors’career incentives.
The third factor G
it
is infrastructure created by the local government. It serves as a
public good that boosts the local productivity. One may interpret G
it
as electricity, roads,
bridges, ports, and highways.
2
One may also broadly interpret G
it
as other measures and
policies taken by the government to support and stimulate the lo cal market and economy.
As I will show, the …rm chooses capital and labor based on the level of local infrastructure.
G
it
thus serves as a direct channel for government investment to drive the economy. After
accounting for …rms’ capital and labor choices, the regional economy displays a constant
return with respect to G
it
; a feature that resembles the endogenous growth model of Romer
(1986).
2
Bai and Qian (2010) provide a detailed account of China’s development of infrastructure in three sec-
tors: electricity, highways, and railways. Zhang and Barnett (2014) show that infrastructure investment
contributed to nearly 15% of China’s GDP in 2008–2012.
5
1.1 Firms and Households
In each period, the representative …rm in region i …rst observes the current period produc-
tivity A
it
and then hires capital and labor to maximize its pro…t:
max
fK
it
;L
it
g
A
it
K
it
L
1
it
G
1
it
it
L
it
RK
it
;
where
it
is the competitive wage and R is the rental rate of capital, which is equal to the
interest rate. Throughout the paper, I assume that each region has small open economy so
that the …rm in each region can rent capital from the global capital market at an exoge-
nously given interest rate R: Suppose that labor is not mobile and each region has a …xed
labor supply L
it
= 1. Then, the …rst-order condition implies that the competitive wage is
determined by the marginal product of labor:
it
= (1 ) A
it
K
it
G
1
it
: (1)
Equating the marginal product of capital with the rental rate of capital gives the …rm’s
optimal capital:
K
it
=
A
it
R
1=(1)
G
it
; (2)
which depends on the …rm’s productivity, the capital rental rate, and the local infrastructure.
By substituting L
it
and K
it
back to the output and market wage, I have
Y
it
=
R
=(1)
A
1=(1)
it
G
it
: (3)
The …rm’s optimal capital choice and output are both proportional to local infrastructure
G
it
; which is developed by the local government. Thus, by developing local infrastructure,
the local government can directly stimulate …rms to expand their capital investment and raise
the labor wage.
3
Furthermore, the production technology of the local economy is essentially
an AK technology with respect to infrastructure stock G
it
.
In each region, there are overlapping generations of households, as in Diamond (1965).
Each generation of households lives for two periods, and each individual born at t has
identical preferences represented by
ln(C
t
it
) + ln(C
t
it+1
);
3
Allowing labor to be mobile across regions would further amplify the tournament competition among
the regional governors as their infrastructure investment may also attract labor from other regions.
6
where C
t
it
and C
t
it+1
represent consumption chosen by the individual across his lifetime at
t and t + 1. The parameter 2 (0; 1) is the individual’s time discount rate for the next
period’s consumption. This OLG speci…cation with logarithmic utility simpli…es household
decisions, but is inconsequential to our key insight.
Each individual supplies one unit of labor when he is young, i.e., L
it
= 1, at a competitive
wage and divides his wage income between consumption C
t
it
and savings S
t
it
:
C
t
it
+ S
t
it
(1 )
it
L
it
;
where
it
is the competitive wage and is the tax rate on both labor and capital income.
The savings are invested in the capital market at the constant gross interest rate R > 1 for
the next p eriod’s consumption:
C
t
it+1
= (1 ) RS
t
it
:
The standard result for log utility implies that the individual consumes a …xed fraction of
his labor income in the current period and saves the rest for the next perio d:
C
t
it
=
1
1 +
(1 ) (1 )
it
L
it
=
1
1 +
(1 ) (1 )
R
=(1)
A
1=(1)
it
G
it
;
C
t
it+1
=
1 +
R (1 ) (1 )
2
R
=(1)
A
1=(1)
it
G
it
:
1.2 Local Government
I assume that the country adopts a system of …scal federalism. Speci…cally, the local govern-
ment of each region collects tax and uses the tax revenue for developing local infrastructure
and funding its own consumption. For simplicity, this paper ignores the …scal spending of
the central government, as well as other policy interventions of the central government in
the economy.
Tax is collected from labor and capital income at a rate of : Thus, the local government’s
tax revenue in period t is (
it
L
it
+ RK
it
) = Y
it
; which contributes to its budget at the
end of perio d t:
W
it
= Y
it
+ (1
G
) G
it
; (4)
with
G
2 [0; 1] as the depreciation rate of infrastructure and (1
G
) G
it
as the infrastruc-
ture stock after depreciation. As the government employs a large number of employees, a
7
fraction of this budget has to be spent for the bene…t of government employees. Thus, the
local governor needs to allocate the budget between infrastructure for the following p eriod
G
it+1
and consumption by government employees E
G
it
> 0 in the current period:
G
it+1
+ E
G
it
= W
it
: (5)
For simplicity, I ignore other types of government spending. Note that E
G
it
bene…ts govern-
ment employees,
4
but does not directly serve the households. In contrast, the infrastructure
G
it+1
serves the welfare of both government employees and households as it increases the
productivity of the local economy. This budget allocation of the local government between
infrastructure investment and consumption of government employees serves as the key agency
problem in our model.
5
I assume that the local government aims to maximize the following Bellman equation:
V (G
it
; A
it
) = max
G
it+1
E
t
ln
C
t
it
+ ln(C
t1
it
)
+ ln (W
it
G
it+1
) + V (G
it+1
; A
it+1
)
;
(6)
subject to the budget constraint in (5). In this speci…cation, the local government assigns
a weight of 2 [0; 1] to the consumptions of the households and a weight of > 0 to
the consumption of government employee. For comparison, we assume that in the …rst-
best benchmark, which we analyze in the next subsection, household consumption carries a
weight of 1. The expectation operation E
t
[] represents the conditional expectation at time
t after the current-period productivity A
it
and output Y
it
are observed. The government
uses the same discount rate as households. The value function V () captures the welfare
of the households and the government employees from period t onwards, with both G
it
and
A
it
as the state variables to capture the infrastructure level and productivity shock for the
current period. In choosing the current period consumption E
G
it
, the local government faces a
dynamic tradeo¤ as a higher level of E
G
it
reduces the infrastructure level and thus the output
in the following period.
6
4
Note that the government consumption may also include corruption and embezzlement in the government
system.
5
An alternative setting is to introduce an e¤ort choice by the local government, which would also induce
an agency problem between the central and local governments. I prefer the agency problem induced by the
budget allo cation because it allows me to introduce leverage as an additional choice to the local government,
which I will examine later.
6
While the households live for two periods, I assume that the government lives forever in order to highlight
the notion that the bureacracy aims to maximize the welfare of government employees, as opposed to the
social welfare.
8
Note the following remarks on the setting: First, in this section, the government cannot
borrow or save and must spend its budget in each period on either infrastructure investment
or government consumption. I relax this restriction in Sections 4 and 5 by allowing the
government to use debt. Second, the government’s investment decision at time t determines
the level of infrastructure at t + 1. This feature is realistic as infrastructure usually takes
time to build. Third, throughout the paper, I assume that the local government faces a hard
budget constraint and cannot lobby for any additional budget or bailout from the central
government.
7
Fourth, I ignore the multiple layers of subnational governments in China to
focus on the potential distortions induced by the agency problem in one layer.
8
Finally, this
paper simply assumes that the local government can carry out its infrastructure investment,
without introducing state owned enterprises, which are often responsible for infrastructure
investment in practice.
As the governor is constrained from borrowing or saving, he faces an intertemporal trade-
o¤ in allocating his current-period budget on either infrastructure investment or government
consumption. If he allocates more to infrastructure investment (i.e., a higher G
it+1
), the
local output and tax revenue in the next period are higher, trading o¤ less current-period
government consumption. This dynamic tradeo¤serves as the key mechanism throughout the
paper for discussing the career incentives and short-termist behaviors of the local government.
By directly solving the Bellman equation, Proposition 1 summarizes the governor’s optimal
investment rule.
Proposition 1 In each period, the local government allocates a fraction of its budget to local
infrastructure:
G
it+1
=
1
(1 )
+
[Y
it
+ (1
G
) G
it
] :
This simple setting captures a mixed economic structure— the local government drives the
regional economy by building up local infrastructure, while local …rms make capital and labor
choices in response to the government’s infrastructure investment. Thus, by investing more
into local infrastructure, the local government can stimulate more investments from local
…rms. One may broadly interpret infrastructure in this model as including not only physical
7
See Qian and Roland (1998) for a thorough analysis of how …scal competition among local governments
under factor mobility can harden their soft budget constraints.
8
See Li et al. (2017) for a model that speci…cally analyzes distortions in a multi-layered tournament-
based organization. Their analysis illustrates a top-down ampli…cation of economic growth targets along the
jurisdiction levels.
9
infrastructure, such as roads and ports, but also intangible infrastructure such as policies
and systems that local governments develop to improve the local economic and business
environment. Proposition 1 highlights a tension in the infrastructure development. The
fraction the local government assigns its budget to infrastructure
1
(1)
+
is increasing
with but decreasing with . The intuition is simple. As the local government puts a greater
weight on household consumption, it allocates more budget to infrastructure. On the other
hand, a greater weight on consumption of government employees leads to a lower budget
to infrastructure.
1.3 The First-Best Benchmark
Since the local government’s infrastructure choice does not fully account for the welfare of
the households, it may not b e socially optimal. For comparison, I now analyze the …rst-best
benchmark. Speci…cally, I consider a social planner, who aims to maximize the welfare of
the households in addition to that of the government employees. In each period, I let the
social planner, rather than the local government, make the infrastructure decision. Then,
given the infrastructure level, the representative …rm makes its capital and labor choices, as
in the main setting. That is, at time t; the …rm chooses its capital after observing the local
government’s infrastructure choice G
it
and the local productivity A
it
as given in (2), and
o¤ers a competitive wage, as given in (1), so that L
it
= 1: Consequently, the output is given
by (3).
The social planner allocates the aggregate social budget in the local economy
W
planner
it
= Y
it
+ (1
G
) G
it
to the young generation consumption C
t
it
, to the old generation consumption C
t1
it
, to the
government consumption E
G
it
, and to infrastructure G
it+1
:
W
planner
it
= C
t
it
+ C
t1
it
+ E
G
it
+ G
it+1
(7)
to maximize
V
W
planner
it
= max
C
t
it
;C
t1
it
;E
G
it
;G
it+1
E
t
h
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ V
W
planner
it+1
i
; (8)
subject to the budget constraint in (7). Di¤erent from the objective of the local government,
the planner assigns a weight of 1 to household consumption, rather than .
The following proposition states the result from solving the planner’s Bellman equation:
10
Proposition 2 In the …rst-best benchmark, the social planner allocates a …xed fraction of
the aggregate social budget to infrastructure:
G
it+1
= [Y
it
+ (1
G
) G
it
] :
A comparison of Propositions 1 and 2 shows that the local government underinvests
in infrastructure relative to the …rst-best level if is su¢ ciently small. As & 0, the
local budget to infrastructure goes to G
it+1
= [Y
it
+ (1
G
) G
it
], which is strictly lower
than the …rst-best level. This is because the local government does not fully internalize the
consumption of the households in its infrastructure choice. This underinvestment re‡ects a
fundamental agency problem between the central and local governments.
The central government cannot resolve this underinvestment problem by standard …s-
cal policies. First, as the central government controls taxation, it is tempting to use an
optimal tax rate to solve the underinvestment problem. Comparing Propositions 1 and 2
reveals that optimizing the tax rate cannot lead to the …rst-best outcome. Suppose that the
agency problem is severe with = 0, then G
it+1
= [Y
it
+ (1
G
) G
it
] : In this situation,
setting the tax rate to 100% could lead the local government to choose the …rst-best level
of infrastructure. However, this tax rate is clearly not feasible as it leaves nothing to the
households, and thus cannot be socially optimal.
Second, the central government may choose to subsidize infrastructure investment, for ex-
ample by providing loans at subsidized interest rates to local governments for infrastructure
projects. Such …scal subsidies are able to boost infrastructure investment. However, under-
investment in infrastructure is just one of many possible distortions caused by the agency
problems of local governments. Fiscal subsidies cannot remedy all of such distortions, such
as corruption. Thus, the central government needs to give local governors incentives to do
the right things in numerous decisions they make, which we discuss in the next section.
2 Career Incentives
Di¤erent from the typical federal government system in other countries, regional governors
in China are appointed by the central government rather than elected by a local electorate.
As eloquently summarized by Xu (2011) and Qian (2017), by giving local governments
large …scal independence and evaluating them based on a common set of criteria that weigh
heavily on local economic performance, regional governors are greatly incentivized to become
11
helping hands, rather than grabbing hands, in developing local economies. This economic
tournament is widely recognized as a key mechanism contributing to China’s rapid growth
over the past 40 years.
In typical western countries, career concerns of politicians who aim to win local elections
may also generate incentives to develop local economies. Such incentives vary across regions
depending on the preferences and interests of local electorates. For example, voters in one
region may care more about economic growth, thus leading to greater incentives for the
local politicians to develop local economy, while voters in another region may care more
about the environment, leading the local politicians to give lower priority to developing the
economy. Having the central government as the common evaluator of all regional governors
in China dictates that they all share the same career incentives and thus compete directly
with each other. Maskin, Qian and Xu (2000) argue that the relatively homogenous economic
structures across di¤erent regions in China also make this economic tournament an e¤ective
institutional arrangement.
To incorporate the tournament, I adopt the following speci…cation of the productivity of
region i:
A
it
= e
f
t
+a
it
+"
it
;
where f
t
N
f;
2
f
represents a countrywide common shock with Gaussian distribution
of mean
f and variance
2
f
, a
it
N (a
i
;
2
a
) represents the governor’s ability in developing
the local economy, which has Gaussian distribution of mean a
i
and variance
2
a
; and "
it
N (0;
2
"
) is an idiosyncratic noise component, again with Gaussian distribution of mean 0
and variance
2
"
. These components are independent of each other, and neither of them is
publicly observable. Furthermore, their distributions are common knowledge to all agents.
I assume that a new governor, randomly drawn from the distribution N (a
i
;
2
a
), is as-
signed to a region in each period. The governor works in the region for only one period
and is concerned about the central government’s perception of his ability after observing his
performance and his peers’performance. Speci…cally, suppose that a governor takes over
region i at the end of period t after Y
it
is realized, and chooses E
G
it
and G
it+1
. As the gov-
ernor’s ability a¤ects the local productivity at t + 1, the local output Y
it+1
provides useful
information about his ability when he is evaluated by the central government at t + 1. That
is, his performance is determined by
ba
it+1
= E
h
a
it+1
j fY
it+1
g
i=1;:::;M
i
:
12
By substituting in Y
it+1
from (3), I obtain a linear expression for the log output:
y
it+1
ln (Y
it+1
) = ln
R
=(1)
A
1=(1)
it+1
G
it+1
=
1
1
(f
t+1
+ a
it+1
+ "
it+1
) +
1
ln
R
+ ln (G
it+1
) : (9)
Thus, the local output ln (Y
it+1
) provides a useful signal about the governor’s ability a
it+1
.
As the governor can boost the local output by taking on more infrastructure investment, his
career incentives motivate him to invest more in infrastructure, overcoming the preference
for more government consumption. This implicit incentive to invest in local infrastructure
is in the spirit of Holmstrolm (1982) and Gibbons and Murphy (1992).
To analyze this mechanism, I assume that the central government cannot observe the
stock of local infrastructure (i.e., G
it+1
) and other input in local production. Instead, it
observes only the output level Y
it+1
. This assumption is realistic for several reasons. First, the
central government has to rely on lo cal statistics bureaus to report local statistics. As local
governments have strong in‡uences on local statistics bureaus, they have ample ‡exibility
to manage or even distort local statistics. Second, the National Bureau of Statistics devotes
a great deal of e¤ort to auditing and verifying regional output, as it is a key variable for
many policy decisions of the central government. As a result, it is harder to distort output
statistics than other factor statistics.
9
Motivated by these observations, I assume for the
rest of the paper that the central government can only use regional output to evaluate the
performance of local governors. Note that I will further modify the setting to examine
how lo cal governors may overreport regional output in Section 3 even though output is not
manipulatable in other sections.
Following Holmstrolm (1982), I assume that the central government has rational expecta-
tions and anticipates the local governor’s choice. That is, even though the central government
does not observe the local governor’s choice G
it+1
, it anticipates that the local governor will
choose G
it+1
equal to the equilibrium level G
it+1
. As a result, in interpreting the observed
output, the central government would simply deduct the anticipated level ln
G
it+1
from
9
One might still argue that it is easier to observe infrastructure than GDP. As argued by Pritchett (2000),
adding up investment may not be an accurate measure of actual installed capital because of cream-skimming
and corruption. For the same reason, the observed infrastructure may not represent quality of infrastructure
and thus cannot be used as a reliable measure of regional performance.
13
the observed log output y
it+1
; by constructing the following su¢ cient statistic:
z
it+1
(1 )
y
it+1
1
ln
R
+ ln
G
it+1
= f
t+1
+ a
it+1
+ "
it+1
+ (1 )
ln (G
it+1
) ln
G
it+1
: (10)
From the central government’s perspective in interpreting the information content of this
statistic, G
it+1
= G
it+1
and thus
z
it+1
= f
t+1
+ a
it+1
+ "
it+1
: (11)
Due to the common shock in each region’s productivity, the central government will use
the outputs from all regions to jointly infer each governor’s ability. This joint evaluation
leads to a tournament in which each governor’s performance is compared with that of other
governors. By directly applying the Bayes Theorem based on the composition of z
it+1
given
in (11), I obtain the following learning rule for the central government:
^a
it+1
= E
h
a
it+1
j fz
it+1
g
i=1;:::;M
i
= a
i
+
2
a
2
a
+
2
"
+ (M 1)
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
(z
it+1
z
it+1
)
2
a
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
X
j6=i
(z
jt+1
z
jt+1
) :
From the governor’s perspective, z
it+1
depends on his own choice G
it+1
in (10). As a
result, the governor can in‡uence the central government’s perception ^a
it+1
by choosing a
higher level of G
it+1
at time t. By substituting in z
it+1
from (10), I have
^a
it+1
a
i
(12)
=
2
a
2
a
+
2
"
+ (M 1)
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
f
t+1
f
+ (a
it+1
a
i
) + "
it+1
+ (1 )
ln G
it+1
ln G
it+1
2
a
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
X
j6=i
f
t+1
f
+ (a
jt+1
a
j
) + "
jt+1
+ (1 )
ln G
jt+1
ln G
jt+1
:
This expression shows that choosing a higher G
it+1
a¤ects the central government’s percep-
tion, because the central government cannot fully separate the local governor’s ability from
its infrastructure investment. This is the basic insight of the signal-jamming mechanism
coined by Holmstrolm (1982).
Under rational expectations, the central government rationally anticipate that each local
governor j chooses G
jt+1
= G
jt+1
. Consequently, the performance evaluation of governor i
14
in (12) is not a¤ected by the infrastructure investment choice of any other governor. That is,
each governor’s career concerns are insulated from other governors’behaviors, because the
central government is able to fully …lter out any e¤ect induced by other governors. In Section
5, I will relax this rational expectations assumption to consider a more realistic setting in
which the central government can only realize the infrastructure and debt choices of local
governments with a delay.
To capture the governor’s career incentives induced by the tournament, I introduce an
additional term into the local government’s Bellman equation previously speci…ed in (6):
V (G
it
; A
it
) = max
G
it+1
E
t
ln
C
t
it
+ ln(C
t1
it
)
+ ln (W
it
G
it+1
) (13)
+
i
(^a
it+1
a
i
) + V (G
it+1
; A
it+1
)g
where
i
(^a
it+1
a
i
) is the new term with
i
> 0 as the weight assigned to the governor’s
career incentives.
10
The budget constraint remains the same as in (5). In formulating this
Bellman equation, I implicitly assume that while the governor changes in each period, other
employees of the local government will remain. As these government employees care about
their future consumption, their internal bargaining with the governor in the bureaucracy will
ensure that the governor’s infrastructure choice accounts for their future welfare, as re‡ected
by the last term in the Bellman equation.
With the additional career concern term, the relevant terms in the governor’s objective
for choosing G
it+1
on the right-hand side of the Bellman equation (13) are
max
G
it+1
E
t
ln C
t
it
+ ln (W
it
G
it+1
) +
i
ln G
it+1
+ V (G
it+1
; A
it+1
)
where
i
=
2
a
2
a
+
2
"
+ (M 1)
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
(1 )
i
: (14)
These terms are almost the same as those from the Bellman equation in (6), except for the
additional term
i
ln G
it+1
, which addresses the governor’s career incentives. By solving the
Bellman equation, I obtain the optimal infrastructure as summarized in the next proposition:
Proposition 3 The governor’s career incentives lead to greater infrastructure investment:
G
it+1
=
1
(1 )
+
i
+
(Y
it
+ (1
G
) G
it
) :
10
One may micro-found this term by assuming that the central government randomly pairs each governor
with another governor and promotes the one with better perception. Linearizing the expected promotion
probability leads to the linear term speci…ed in the objective.
15
Proposition 3 shows that career incentives motivate the governor to choose a greater
level of infrastructure investment. In particular, a governor with a higher
i
coe¢ cient
invests more into infrastructure. Thus, the tournament helps to overcome the underinvest-
ment problem to infrastructure, as derived in Proposition 1. This simple insight provides a
key mechanism for China’s rapid growth, as recognized by the literature mentioned in the
introduction.
Career incentives for local governors had already existed in China’s government system
even during China’s Great Famine in 1959-1961. What make the incentives so much more
e¤ective in the recent years than before? To address this important question, one needs
to recognize the development of the market sector as a result of the economic reforms that
started in late 1970s. Before the economic reforms, China had a central-planning economy
with government o¢ cials managing every aspect of the economy at all levels. In this en-
vironment, the career incentives of local governors were not enough to overcome pervasive
frictions and incentive problems that confronted every part of the Chinese economy, such as
the incentive problems of workers. The economic reforms have greatly changed the structure
of the Chinese economy by letting a substantial fraction of the economy driven by market
forces. My model also captures this market sector through the representative …rm in each
region. With the …rms driven by market forces, these forces also guide local governors’ca-
reer incentives to improve infrastructure and other market conditions that would e¤ectively
boost local productivities. This integration of local governors’career incentives with market
forces did not exist before the economic reforms.
11
Career incentives not only motivate development of local infrastructure but also short-
termist behaviors. In the subsequent sections, I analyze such short-termist behaviors, which
are important for understanding various challenges currently faced by the Chinese economy.
12
11
While my model focuses on local governors’career incentives, it is useful to note that they might also be
driven by other incentives, such as corruption. To the extent that China’s recent anti-corruption campaign
has uncovered a large number of corrupted o¢ cials, one may infer that a certain fraction of the government
o¢ cials take payments from corruption. I would argue that the presence of corruption does not necessarily
invalidate the incentive mechanism highlighted by my model and, to the contrary, may reinforce it. To the
extent that a governor may be able to extract greater side payments from local …rms when th e …rms are
more productive, the side payments give another source of incentives that motivate the governor to invest
more to infrastructure. In fact, one can eas ily expand my framework to capture such incentives by adding
another utility term to the Bellman equation for the governor’s personal gain from side payments that are
proportional to local output.
12
Based on the local governor’s optimal infrastructure investment derived in Proposition 3, it is possible
for the central government to d esign an incentive program, i.e., a suitable coe¢ cient
i
, to fully impleme nt
the …rst-best investment level in Prop osition 2. The choice of
i
would need to adjust for the governor’s
career stage, as re‡ected by the prior variance regarding his ability, and the local economic structure, as
16
3 Output Overreporting
China has a multilayered structure for reporting economic statistics. The National Bureau of
Statistics (NBS) reports national statistics, while local statistics bureaus, which are subject
to strong in‡uence from local governments, report local statistics. Chen et al. (2018) and
Hortacsu, Liang and Zhou (2017) report that the sum of provincial GDP has been routinely
higher than the national GDP by an amout in the order of …ve percent of national GDP. This
substantial gap, which is also illustrated in Section 6, suggests that local statistics bureaus
in aggregate overreport provincial GDP. Furthermore, Chen et al. (2018) provide forensic
analysis of overreporting of provincial GDP and capital investment.
In this section, I analyze overreporting of regional output induced by the career concerns
of local governors. To examine this issue, I modify the model setting by assuming that
the central government does not directly observe the regional output in the current period.
Instead, each governor reports the output of his region to the central government. This gives
each governor the ‡exibility to overreport his performance. To discipline overreporting, the
central government takes away a fraction of the reported output as tax revenue to fund
central government spending. This assumption is consistent with the split tax arrangement
between the central government and local governments in China. Thus, from the perspective
of a regional governor, overreporting the local output comes at the cost of a larger tax transfer
to the central government.
Speci…cally, I assume that a governor is free to report Y
0
it
as the output of his region,
which may be di¤erent from the actual output Y
it
. Or equivalently, the governor may choose
to overreport the log output y
0
it
by an amount '
it
:
y
0
it
= y
it
+ '
it
:
With the actual olog utput given by (9), the reported log output is
y
0
it
=
1
1
(f
t
+ a
it
+ "
it
) +
1
ln
R
+ ln (G
it
) + '
it
:
In interpreting the reported output, the central government anticipates the governor to invest
re‡ected by the noise structure of the local output and the composition of the local tax revenue and the
infrastructure stock. One would also need to account for the short-termist behaviors induced by the career
incentives. It is not the objective of this paper to analyze this optimal design. Instead, I take the ince ntive
program as given and analyze its various e¤ects on the economy.
17
G
it
in infrastructure and overreport by '
it
and thus constructs the su¢ cient statistic:
z
0
it
(1 )
y
0
it
1
ln
R
+ ln (G
it
)
'
it
= f
t
+ a
it
+ "
it
+ (1 ) [ln (G
it
) ln (G
it
) + ('
it
'
it
)] :
Again, bear in mind that from the central government’s perspective ln (G
it
) = ln (G
it
) and
'
it
= '
it
in equilibrium, while from the governor’s perspective it controls both G
it
and '
it
.
Consequently, the central government follows the same learning rule as before:
^a
it+1
a
i
= E
h
a
it+1
j
z
0
it+1
i=1;:::;M
i
a
i
=
2
a
(
2
a
+
2
"
)
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
f
t+1
f
+
2
a
2
a
+
2
"
+ (M 1)
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
(a
it+1
a
i
) + "
it+1
+ (1 )
ln G
it+1
ln G
it+1
+ '
it+1
'
it+1
2
a
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
X
j6=i
(a
jt+1
a
j
) + "
jt+1
+ (1 )
ln G
jt+1
ln G
jt+1
+ '
jt+1
'
jt+1
:
Like before, the central government’s perception of the governor’s ability ^a
it+1
a
i
is tied
to his output overreporting '
it+1
'
it+1
. Even though the central government rationally
anticipates the governor to overreport by '
it+1
= '
it+1
and, consequently, the overreporting
does not a¤ect the central government’s perception in the equilibrium, the governor still has
to overreport by this amount, as overreporting less will lead to a worse perception. This is
again due to the signal jamming mechanism.
I further expand the tax system by assuming that the local government needs to transfer
part of its tax revenue to the central government at a rate of
c
< based on the reported
output level Y
0
it+1
. In other words, while the local government collects a tax of Y
it+1
based
on the actual output, it has to transfer a greater fraction of the tax revenue to the central
government if it chooses to overreport the output. Then, the residual tax revenue for the
local government is
T
it+1
= Y
it+1
c
Y
0
it+1
= Y
it+1
1
c
e
'
it+1
: (15)
A higher overreporting '
it+1
thus reduces the local budget for the following perio d.
18
I now revisit the governor’s Bellman equation:
V (G
it
; T
it
) = max
G
it+1
; '
it+1
E
t
[ ln ((1
G
) G
it
+ T
it
G
it+1
) +
i
(^a
it+1
a
i
) + V (G
it+1
; T
it+1
)] ;
subject to the next period budget in (15). To simplify the setting, I let = 0; i.e., the
governor assigns zero weight to household consumption for the remaining parts of the pa-
per. I also modify the state variables to fG
it
; T
it
g, which are informationally equivalent to
fG
it
; A
it
g.
13
The relevant terms in the governor’s objective for choosing G
it+1
and '
it+1
on
the right-hand side of the Bellman equation are
max
G
it+1
; '
it+1
ln ((1
G
) G
it
+ T
it
G
it+1
) +
i
ln (G
it+1
) +
i
'
it+1
'
it+1
+ E
t
h
V
G
it+1
; Y
it+1
1
c
e
'
it+1
i
:
The term
i
'
it+1
'
it+1
; with
i
given in (14), captures the governor’s incentive to boost
his career by overreporting the output, while the last term E
t
V
G
it+1
; Y
it+1
1
c
e
'
it+1
contains the cost of leaving a smaller …scal budget for the next period.
By solving this Bellman equation, the next proposition con…rms that the governor’s career
concern indeed leads to overreporting of the local output, and such overreporting increases
with his career incentive
i
and decreases with the central government tax rate
c
.
Proposition 4 The governor’s output overreporting is given by the following equation:
'
it+1
= ln
(1 )
i
c
(
i
+ )
ln
(
R
=(1)
E
t
"
A
1=(1)
it+1
1
G
+
1
c
e
'
it+1
R
=(1)
A
1=(1)
it+1
#)
;
which has a unique root between 0 and ln (=
c
) under the conditions (25) and (26) listed in
the Appendix. This root is increasing with
i
and decreasing with
c
.
This mechanism for regional governors to overreport output is similar in spirit to that
for earnings manipulation by publicly listed …rms, e.g., Stein (1989). As …rm managers
have incentives to boost their stock prices, the signal jamming mechanism causes them to
overreport …rm earnings, despite that investors rationally anticipate such overreporting and
deduct it from stock valuation. By con…rming this mechanism, Proposition 4 suggests that
13
With rational expectations, the central government fully anticipates the local governor’s overreporting.
As a result, even though the central government does not directly observe G
it
and T
it
, it can nevertheless
infer their values in each period and thus anticipate the governor’s optimal strategy. This feature is common
to the signal jamming models and greatly simpli…es the equilibrium analysis, relative to an alternative setting
in which the central government cannot fully infer the governor’s overreporting.
19
the lack of reliable economic statistics in China may not be random noise and instead could
be a systematic problem associated with China’s government bureaucracy. As far as I know,
the literature has not recognized this important aspect. Furthermore, Proposition 4 also
provides useful comparative statics that the overreporting of local output is increasing with
the local governor’s career incentives and decreasing with the lo cal government’s …scal cost
of overreporting.
In recent years, several Chinese provinces have publicly acknowledged their GDP over-
reporting in the past. For example, in early 2017, the provincial government of Jiaoning
revealed in its annual report submitted to its People’s Congress that it had systematically
over-reported Liaoning’s economic statistics in 2011-2014. In January 2018, the provincial
governments of both Inner Mongolia and Tianjing also confessed that they had also in‡ated
their economic statistics in the previous years. Such confessions were partly driven by large
shortfalls in their …scal budgets, as the confession relieved these provincial governments o¤
the additional …scal pressure induced by the overreporting, as consistent with the model.
14
The output overreporting by local governors may have another important economic con-
sequence by distorting the central government’s information set. In my current setting,
the central government fully anticipates the overreporting of the local governors due to the
assumption of rational expectations. Under more realistic settings, overreporting by local
governors may distort the expectations of the central government regarding the regional
economies, as well as the overall national economy. Such expectational distortions may
in turn reduce the e¢ ciency of the central government’s economic policies, which is a key
concern about China’s unreliable economic statistics.
15
14
For simplicity, I would leave it to future work to explicitly incorporate such public confess ion into the
model as a way to unwind previous overreporting. Interestingly, this kind of confession typically happens after
the previous governors lose their prominence as a result of corruption investigations or other misbehaviors.
Otherwise, such confession runs the political risk of o¤ending the previous governors, who might have and
may become national leaders.
15
This concern has been illustrated by the Great Famine of China in 1959–1961. Fan, Xiong and Zhou
(2016) …nd that during this period, overreporting of regional grain output by local governments led to greater
procurement of grain to the central government and more severe famine in the region. In particular, they
argue that the widely-spread overreporting of grain output, ind uce d by the Great Leap Forward, made the
central government unaware of the national famine, which explains the lack of any relief e¤ort by the central
government even at the peak of the famine in 1960. In contrast, China shipped a large quantity of grain
either as export or food aid to other countries at the time.
20
4 Excessive Leverage
So far I have restricted regional governments from using any debt to leverage their …scal
budgets. This assumption is realistic for China in the period before 2008, as the central
government had strict rules against subnational governments’raising debt without its explicit
approval. However, the situation changed substantially after 2008, when the global …nancial
crisis prompted China to implement a massive economic stimulus of four trillion RMB. As
the stimulus was mostly …nanced by …scal budgets of local governments (rather than that
of the central government), and the stimulus required much more …nancing than what local
governments could a¤ord, the central government allowed local governments to establish the
“local government …nancing vehicle”(LGFV), which used explicit or implicit guarantees from
local governments to obtain bank loans to fund the stimulus projects, e.g., Bai, Hsieh and
Song (2016). After the stimulus program ended in 2010, the central government instructed
banks to discontinue lending to local governments. Facing pressure to roll over their maturing
loans, local governments moved their debt …nancing into shadow banking, as analyzed in
detail by Chen, He and Liu (2017), leading to even higher leverage. Zhang and Barnett
(2014) provide an estimate that debt …nancing (in the forms of both bank loans and shadow
banking debt) contributed to about two-thirds of infrastructure investment in China in 2008–
2012.
Debt gives a governor a greater capacity to invest in local infrastructure and thus may
exacerbate his short-termist behavior induced by career concerns. To address this issue, I
further extend the model setting. Speci…cally, I anchor on the setting from Section 2 (without
output overreporting and tax transfer to the central government), and allow each regional
government to use debt to …nance its infrastructure investment and spending. Speci…cally,
I assume that it can issue debt at a constant interest rate R: Then, its budget in period t
is its tax revenue from the previous period Y
it
plus the stock of infrastructure (1
G
) G
it
minus its debt due RD
it1
:
W
it
= Y
it
+ (1
G
) G
it
RD
it1
:
The governor can take new debt D
t
, in addition to W
it
; to fund the next-period infrastructure
G
it+1
and government consumption E
G
it
:
G
it+1
+ E
G
it
= W
it
+ D
it
: (16)
21
I modify the Bellman equation in (13) by letting = 0 for simplicity and by giving the
governor the additional debt choice in each period:
V (W
it
) = max
G
it+1
; D
it
ln (W
it
+ D
it
G
it+1
) +
i
ln G
it+1
ln G
it+1
(17)
+ E
t
[V ( Y
it+1
+ (1
G
) G
it+1
RD
it
)] ;
subject to the new budget constraint in (16).
16
It shall be clear that W
it
is su¢ cient to
capture the state of the regional economy at time t; despite the use of debt.
To facilitate the analysis, I scale the local government’s infrastructure in each period by
its budget:
g
it+1
=
G
it+1
W
it
;
and debt level by its infrastructure level:
d
it
=
D
it
G
it+1
:
d
it
can be directly interpreted as the fraction of infrastructure …nanced by debt. As I formally
derive in the Appendix, debt allows the governor to take on a higher level of infrastructure
relative to its current-perio d budget:
g
it+1
=
+
i
+
i
1
(1 d
it
)
:
A certain level of debt is socially bene…cial as it allows the regional government to expand
its budget to fully take advantage of high productivity in the current period. However, the
governor’s career concerns may induce excessive use of debt to …nance overinvestment at
the expense of a higher debt payment and thus a smaller budget in the next period. To
systematically examine this issue, I also examine the debt choice of a social planner who
aims to maximize the welfare of both the government and the households. Following the
setting in Section 1.3, the planner’s budget at time t is
W
planner
it
= Y
it
+ (1
G
) G
it
RD
it1
;
which also includes repayment of the local government debt from the previous period. The
planner can also use new debt to boost its current period budget:
C
t
it
+ C
t1
it
+ E
G
it
+ G
it+1
= W
planner
it
+ D
it
16
The logarithmic utility function ensures that the local governor will avoid any possibility of future
default. In this sense, my setting implicitly assumes that the local government has hard budget constraints,
i.e., it cannot run a Ponzi scheme by continuing to borrow more and more. Despite the absence of soft
budget constraints, my setting is nevertheless able to capture important short-termist behaviors of local
governments, such as excessive leverage and overinvestment.
22
to …nance infrastructure investment G
it+1
, together with the consumption of the two gener-
ations of households C
t
it
and C
t1
it
and the government consumption E
G
it
: Then, the planner’s
Bellman equation is given by
V
W
planner
it
= max
G
it+1
;C
t
it
;C
t1
it
;E
G
it
;D
it
E
t
h
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ V
W
planner
it+1
i
:
(18)
I directly solve the Bellman equation of both the governor in (17) and the planner in
(18). Interestingly, their debt choices are determined by a maximization problem with the
same structure except di¤erent coe¢ cients, as summarized in the following proposition:
Proposition 5 Both the governor and the social planner would choose a debt level of d
it
=
D
it
=G
it+1
in the interval [0; (1
G
)=R] ; based on the following maximization problem:
max
d
it
ln
1
1 d
it
+ E
t
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
; (19)
where the coe¢ cient is 1 for the planner and
1
i
+
i
+ 1 for the governor. If
E
t
"
R
R
=(1)
A
1=(1)
it+1
+ (1
G
)
#
< < E
t
"
R +
G
1
R
=(1)
A
1=(1)
it+1
#
;
there is an interior debt choice. The governor’s debt choice is always higher than the plan-
ner’s, and the governor’s debt choice is increasing with his career incentive parameter
i
.
This proposition shows that career concerns indeed lead the governor to take on excessive
debt, i.e., a debt level higher than the level chosen by the so cial planner. In cho osing the
debt level, both the governor and the planner face the same intertemporal tradeo¤— a higher
debt level boosts the current period’s output, as re‡ected by the …rst term in (19), at the
expense of a higher debt payment in the following p eriod, as re‡ected by the second term in
(19). The career concern causes the government to assign a greater weight to the …rst term,
leading to a higher debt choice.
To further illustrate the governor’s debt choice, Figure 1 depicts the debt choices of the
governor and the planner under a set of baseline parameter values:
= 0:2; = 1=3; R = 1:1;
G
= 0:05; = 0:9; = 1;
f = a = 0:05;
f
= 0:4;
a
= 0:4;
"
= 0:2;
i
= 1:
23
0 2 4 6 8 10
0.4
0.5
0.6
0.7
0.8
0.9
1.4 1.6 1.8 2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Figure 1: Leverage with Career Incentives and Expected Growth
The left panel depicts d
it
by varying
i
between 0 and 10. The governor’s debt choice
coincides with the planner’s choice when
i
= 0. As the governor’s career incentives rise with
i
, his debt choice also rises with
i
. The right panel depicts the debt choices of the governor
and the planner by varying the expected productivity growth E (A
i
). As expected, both debt
choices are increasing with E (A
i
), with the governor’s debt choice always higher than the
planner’s. Taken together, this section describes a mechanism for the local governor’s career
concerns to lead to overinvestment in infrastructure by using excessive leverage.
5 Leverage Spillover
Policy innovations and …nancial innovations can complicate the agency problem between the
central and local governments. In this section, I analyze a novel channel through which
innovations can cause short-termist leverage choices by one governor to spill over to other
governors.
The discussion of local governors’career concerns so far builds on the premise that the
central government fully anticipates each regional governor’s short-termist behaviors (such
as overreporting and excessive leverage) with rational expectations and, consequently, is
24
able to perfectly …lter the e¤ect of any short-termist behavior of one governor on the rel-
ative performance evaluation of other governors. This means that short-termist b ehaviors
do not spread across governors. Innovations may prevent the central government from fully
anticipating the short-termist behaviors of local governments. First, as part of the key grad-
ualistic approach adopted by China to reform its economy over the past 40 years, the central
government encouraged local o¢ cials to experiment with policy reforms and innovations at
the regional level and also to follow and imitate promising policy initiatives of other regions.
When a new policy initiative emerges, the central government often takes a passive mode of
simply observing its e¤ects before eventually determining whether to endorse or terminate
it. Xu (2011) gives an extensive review of this reform approach and argues that it has played
an important role in China’s institutional development. This reform approach implies that
the central government is, by design, slow to catch up with the policy innovations of local
governments.
Second, …nancial innovations further complicate the central government’s learning process
of new strategies and new games created by local governments. This is because …nancial
innovations provide new instruments and new arrangements for local governments to strate-
gically hide or reveal part of their …nancial transactions and …scal conditions to the central
government. For example, various shadow banking products, such as wealth management
products, allow banks to move regular bank loans made to local government …nancing vehi-
cles o¤ their own balance sheets. By doing so, banks are able to make at least some of these
loans o¤ the radar of the central government. While it is easy for the central government to
anticipate the incentives of local governments to pursue short-termist behaviors, the lack of
transparent statistics makes it di¢ cult for the central government to …gure out the speci…c
form and magnitude of such behaviors, when they are hidden behind complicated …nancial
arrangements.
If the central government does not fully anticipate the debt and investment levels taken by
each lo cal government, the tournament between the regional governors may take a di¤erent
form because short-termist behaviors by one governor can also motivate other governors to
pursue short-termist strategies, which in turn may feed back to the initial governor, leading
to a rat race among the governors. To formally address this issue, I suppose that the central
government faces a delay in updating its anticipation of each local governor’s investment:
25
G
it
= G
it1
, which is similar in nature to adaptive expectations.
17
Following the central
government’s learning of governor i in (12),
^a
it
a
i
=
f
t
f
+ (a
it
a
i
) + "
it
+ (1 ) (ln G
it
ln G
it1
)
0
X
j6=i
f
t
f
+ (a
jt
a
j
) + "
jt
+ (1 ) (ln G
jt
ln G
jt1
)
;
where
=
2
a
2
a
+
2
"
+ (M 1)
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
and
0
=
2
a
2
f
(
2
a
+
2
"
)
2
a
+
2
"
+ M
2
f
:
An immediate consequence of the central government’s adaptive expectations is that each
local governor’s career concerns are no longer immune from the investment and leverage
choices of other governors, as re‡ected by the summation term involving G
jt
in this formula.
In practice, the central government often directly compares the performance of a governor
with another governor in a region with similar economic conditions. Building on the linear
career incentive speci…ed in (17), I also add another quadratic term to the governor’s career
incentive:
V (W
it
) = max
G
it+1
; D
it
E
t
[ ln (W
it
+ D
it
G
it+1
) +
i
(^a
it+1
^a
i
0
t+1
) (20)
i
(^a
it+1
^a
i
0
t+1
)
2
+ V (W
it+1
)
;
with i
0
as the other governor paired with i and the budget constraint in (16). This quadratic
term gives an increasing incentive for governor i to catch up with the other governor i
0
.
As there are a large number of other governors, I suppose that i
0
is chosen to have the
same economic conditions: G
i
0
t
= G
it
and W
i
0
t
= W
it
. This pairing allows me to maintain
simplicity of the derivation without any loss of generality. I also make the setting symmetric
so that a
i
= a
j
= a and = = . Then, it follows that
^a
it+1
^a
i
0
t+1
= ( +
0
) [a
it+1
a
i
0
t+1
+ "
it+1
"
i
0
t+1
+ (1 ) (ln G
it+1
ln G
i
0
t+1
)] :
Consequently,
E
t
[
i
(^a
it+1
^a
i
0
t+1
)] =
i
( +
0
) (1 ) (ln G
it+1
ln G
i
0
t+1
) ;
and
E
t
i
(^a
it+1
^a
i
0
t+1
)
2
=
i
( +
0
)
2
(1 )
2
(ln G
it+1
ln G
i
0
t+1
)
2
+ const:
17
The speci…c form of how G
it
is updated is not particularly important. As long as it is delayed and
G
it
6= G
it
, the investment and leverage choices of one governor would interfere the relative performance
evaluation of other governors.
26
These two terms reveal that governor i’s career concerns are a¤ected not only by his own
infrastructure investment G
it+1
but also by the investment of his paired governor i
0
.
I again rescale each governor’s two choice variables as
g
it+1
=
G
it+1
W
it
and d
it
=
D
it
G
it+1
:
The following proposition summarizes the equilibrium between the two paired governors.
Proposition 6 Given the investment choice g
i
0
t+1
of governor i
0
, the investment choice g
it+1
of governor i is determined by the unique positive root of the following equation:
1
(1 d
it
) g
it+1
= 1 +
1
+
i
( +
0
) (1 )
i
( +
0
)
2
(1 )
2
(ln g
it+1
ln g
i
0
t+1
)
;
which implies g
it+1
as an increasing function of g
i
0
t+1
and d
it
. Governor i’s leverage choice
d
it
is then given by the following maximization problem:
max
d
it
ln [1 (1 d
it
) g
it+1
] +
i
( +
0
) (1 ) (ln g
it+1
ln g
i
0
t+1
)
i
( +
0
)
2
(1 )
2
(ln g
it+1
ln g
i
0
t+1
)
2
+
1
ln g
it+1
+ E
t
ln
R
1
A
1
1
it+1
+ (1
G
) Rd
it
;
which determines d
it
= d
i
(g
i
0
t+1
) ; and thus governor i’s investment response to governor i
0
:
g
it+1
= g
i
(g
i
0
t+1
) : (21)
Similarly, governor i
0
’s leverage choice is a function of governor i’s investment choice: d
i
0
t
=
d
i
0
(g
it+1
) ; which in turn determines governor i
0
’s investment response to governor i:
g
i
0
t+1
= g
i
0
(g
it+1
): (22)
Equations (21) and (22) jointly determine the equilibrium choices of the two governors.
Proposition 6 shows that the two governors’investment and debt choices are entangled.
To illustrate their interactions, I use a numerical example based on the following parameter
values:
= 0:2; = 1=3; R = 1:1;
G
= 0:05; = 0:9; = 1;
f = a = 0:05;
f
= 1;
a
= 1;
"
= 0:5:
27
0 1 2 3 4 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 1 2 3 4 5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Figure 2: Equilibrium Debt and Investment Choices
In addition, I choose the following incentive parameters for the two governors, denoted as 1
and 2:
1
=
2
= 2;
1
=
2
= 40:
Figure 2 illustrates the equilibrium. Because of the symmetric parameters chosen for the
two governors, they make symmetric investment and debt choices. The left panel depicts
each governor’s debt choice d
i
as a function of the other governor’s investment choice g
i
0
.
When g
i
0
is small, d
i
is zero. As g
i
0
rises, governor i chooses a higher leverage d
i
to …nance
greater infrastructure investment in his region. The right panel depicts the two governors’
investment choices with respect to each other. The dashed line represents the best investment
response g
2
of governor 2 to governor 1’s investment g
1
, while the solid line represents the best
investment response g
1
of governor 1 to governor 2’s investment g
2
. Both of these investment
response functions are increasing. The equilibrium lies at the intersection of these two lines.
To further highlight the interactions between the two governors’investment choices, I
increase the incentive parameter
2
of governor 2 from the initial value of 2 to 3: Figure 3
illustrates the changes in the equilibrium by plotting the investment response curves of both
governors 1 and 2. Point a in the plot is the initial equilibrium with g
1
= g
2
= 3:77: As
2
28
3.6 3.65 3.7 3.75 3.8 3.85 3.9 3.95 4
3.6
3.65
3.7
3.75
3.8
3.85
3.9
3.95
4
a
b
b
2
b
1
b
3
b
4
Figure 3: Rat-Race Dynamics
rises from 2 to 3, governor 2 becomes more aggressive in his investment and debt choices,
and his best response curve, shown by the dashed line, moves up. If governor 1’s investment
choice g
1
is kept at the initial value, governor 2’s investment choice will move up to point
b
1
, which is accompanied by a corresponding increase in his debt choice not shown in the
…gure. However, with g
2
increased, governor 1 would also respond to increase his investment
to a level given by point b
2
, which in turn stimulates governor 2 to increase his investment
level further to b
3
, and so on and so forth. This rat-race dynamic would eventually converge
and drive the equilibrium to point b, which has a substantially larger investment increase
for governor 2 than his initial increase if governor 1’s investment choice stays unchanged.
Through this rat race, the change in the career incentives of governor 2 also leads to a
substantial increase in the investment choice of governor 1:
6 Discussion
In this section, I summarize several stylized facts about local government leverage and GDP
overreporting across di¤erent provinces in China to illustrate empirical relevance of the
Mandarin model. A key insight of the model is that career concerns lead each local governor
29
Figure 4: Local government debt to GDP ratio in 2015
to not only use excessive leverage but also overreport regional output. Thus, one would
expect a positive correlation between local government leverage and overreporting of local
output. I illustrate such a positive correlation in the data.
Local government leverage As discussed earlier, the post-crisis stimulus led to a leverage
boom among local governments in China. Because local governments used LGFV to raise
debt from both banks and shadow banking, their debts were largely nontransparent to the
central government and the public. Based on the data released by the Ministry of Finance
(MoF) in 2015 (several years after the post-crisis stimulus program had ended) from its
national audit of the leverage of local governments, Figure 4 depicts the local government
debt-to-GDP ratio for all provinces (excluding Tibet due to its special economic status).
The average debt-to-GDP ratio is 27.5 percent. There is also substantial variation in this
ratio, with some western provinces, such as Guizhou and Qinghai, having a leverage ratio of
over 50%.
GDP overreporting Figure 5 depicts the gap between the sum of provincial GDP (re-
ported by provincial statistics bureaus) and the national GDP (reported by the National
Bureau of Statistics) divided by the national GDP for each year in 2001–2016. Since 2004,
the sum of provincial GDP has been regularly higher than the national GDP by about 5
30
Figure 5: Provincial GDP over-reporting
percent. One may argue that di¤erent provinces might have double-counted output made
by …rms with production across provincial borders. The …gure also shows the percentage
of provinces reporting a GDP growth rate higher than the national GDP growth rate. In
a given year, over 80 percent of the provinces reported a GDP growth rate higher than the
national growth rate, except in 2006 and 2007. Taken together, Figure 5 reveals a compelling
pattern that provincial governments in China in aggregate overreport their GDP.
18
Leverage versus GDP overreporting Chen et al. (2018) provide an estimate of each
province’s GDP overreporting for each year after 2004. Speci…cally, they compare the sum
of value-added of sectors as reported at the provincial level with the same sectors at the
national level. They …nd little discrepancy in these two numbers for large …rms, but large
discrepancies for small …rms as well as sectors in which these numbers are based on local
governments’administrative data. They reestimate provincial GDP using alternative data
sources, such as China Customs and microdata from national value-added tax invoices. They
assume that …nal consumption (at both the national and provincial levels) and net exports
(at the national level) are reliable. They correct provincial GDP mainly through adjusting
investment data.
18
Regional statistics bureaus revise their statistics from time to time, just like publicly listed …rms restate
their past e arnings. In 2017 and 2018, several provinces, including Inner Mongolia, Tianjin and Liaoning,
substantially revised their GDP statistics. Thus, the large fraction of provinces reporting growth rates higher
than the national growth rate may not lead to growing overstatement of GDP.
31
Figure 6: Provincial GDP overreporting versus local government leverage
Based on the provincial GDP overreporting estimated by Chen et al. (2018), Figure
6 provides a scatter plot of the ratio of provincial GDP overrep orting to GDP and lo cal
government debt-to-GDP ratio in 2015. Interestingly, western provinces such as Guizhou
and Qinghai show both higher leverage and greater GDP overreporting. Overall, there is
an evident positive relationship between GDP overreporting and local government leverage
with a t-statistic of 5.4. This signi…cant relationship reveals a strong connection between
these two types of short-termist behaviors of local governments. The literature has not
previously related them with each other. In light of my model, they may be driven by the
same force— the career incentives of local governors.
7 Conclusion
This paper develops the Mandarin model of growth to capture two key features of the Chinese
economy. First, the government takes a central role in driving the economy through its active
investment in infrastructure. Second, agency problems in the government system generate
a rich set of phenomena in the Chinese economy, including not only rapid economic growth
prop elled by the tournament among local governments but also their short-termist behaviors,
which directly a¤ect China’s economic and …nancial stability.
These features provide a useful foundation for more elaborate studies of the Chinese
32
economy. The behaviors of local governments are particularly important for China’s real
estate markets, a key source of concerns about China’s …nancial stability. As discussed in a
recent review by Liu and Xiong (2018), local governments have de facto control of local land
supply and heavily rely on the revenues from land sales to fund local …scal spending. During
the aforementioned leverage boom, local governments had regularly used land and future
land sale revenue as collateral to borrow from banks. Thus, a systematic analysis of China’s
real estate market would have to build on a framework that accounts for the incentives and
…scal status of local governments.
The behaviors of local governments are also central to the central government’s economic
policies. A curious observation is that China still uses a quantity-based, rather than the
seemingly more e¢ cient price-based, monetary policy framework, e.g., Chen, Ren and Zha
(2018). While it is tempting to attribute this observation to the underdevelopment of China’s
…nancial markets, a key reason is that a substantial fraction of the Chinese economy, includ-
ing local governments and state owned enterprises (whose managers are also government
o¢ cials and thus face the same career incentives as local government o¢ cials), is still not
su¢ ciently market driven. As these players are not particularly sensitive to price ‡uctua-
tions, it is di¢ cult to implement the typical price-based monetary policy framework. More
generally, their behaviors also a¤ect the implementation of many other policies of the central
government, such as …scal policies and industrial policies. Thus, analyzing China’s economic
policies would also require a framework that account for the behaviors of local governments.
My model provides a potentially useful framework for these purposes.
A Appendix
A.1 Proof for Proposition 1
By substituting in the various consumption components in Bellman equation (6), I have
V (G
it
; A
it
) = max
G
it+1
E
t
ln
1
1 +
(1 ) (1 )
R
=(1)
A
1=(1)
it
G
it
(23)
+ ln
R
=(1)
A
1=(1)
it
G
it
+ (1
G
) G
it
G
it+1
+ V (G
it+1
; A
it+1
)
:
33
I conjecture that
V (G
it
; A
it
) = k
G
ln G
it
+ v (A
it
) + k
0
:
Then, the right hand side of Bellman equation (23) is
max
G
it+1
ln
1
1 +
(1 ) (1 )
R
=(1)
+
1
ln A
it
+ ln G
it
+ ln
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
G
it+1
+ k
G
ln G
it+1
+ E
t
[v (A
it+1
)] + k
0
= max
G
it+1
ln
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
G
it+1
+ k
G
ln G
it+1
+ ln
1
1 +
(1 ) (1 )
R
=(1)
+
1
ln A
it
+ ln G
it
+ E
t
[v (A
it+1
)] + k
0
:
The …rst-order condition for G
it+1
gives
h
R
=(1)
A
1=(1)
it
+ (1
G
)
i
G
it
G
it+1
=
k
G
G
it+1
;
which directly implies that
G
it+1
=
k
G
+ k
G
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
:
Then, the right-hand side of the Bellman equation becomes
ln
+ k
G
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
+k
G
ln
k
G
+ k
G
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
+ ln
1
1 +
(1 ) (1 )
R
=(1)
+
1
ln A
it
+ ln G
it
+ E
t
[v (A
it+1
)] + k
0
= ( + + k
G
) ln (G
it
) + ln
+ k
G
R
=(1)
A
1=(1)
it
+ (1
G
)
+k
G
ln
k
G
+ k
G
R
=(1)
A
1=(1)
it
+ (1
G
)
+ ln
1
1 +
(1 ) (1 )
R
=(1)
+
1
ln A
it
+ ln G
it
+ E
t
[v (A
it+1
)] + k
0
To equate this with the left-hand side, k
G
ln G
it
+ v (A
it
) + k
0
; I need
k
G
= + + k
G
) k
G
=
+
1
;
together with
v (A
it
) = ( + k
G
) ln
R
=(1)
A
1=(1)
it
+ (1
G
)
+
1
ln A
it
;
34
and
k
0
= ln
+ k
G
+ k
G
ln
k
G
+ k
G
+ E
t
[v (A
it+1
)] + k
0
which gives
k
0
=
1
1
ln
+ k
G
+ k
G
ln
k
G
+ k
G
+ E
t
[v (A
it+1
)]
:
A.2 Proof of Proposition 2
I have the following Bellman equation for the planner:
V
W
planner
it
= max
G
it+1
;C
t
it
;C
t1
it
;E
G
it
E
t
h
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ V
W
planner
it+1
i
subject to
C
t
it
+ C
t1
it
+ E
G
it
+ G
it+1
= W
planner
it
:
I again conjecture that
V (W ) = k
w
ln W + k
0
:
Then,
V
W
planner
it
= max
G
it+1
;C
t
it
;C
t1
it
;E
G
it
E
t
h
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ k
w
ln
W
planner
it+1
+ k
0
i
= max
G
it+1
;C
t
it
;C
t1
it
;E
G
it
E
t
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ k
w
ln (Y
it+1
+ (1
G
) G
it+1
) + k
0
= max
G
it+1
;C
t
it
;C
t1
it
;E
G
it
E
t
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ k
w
ln (G
it+1
)
+k
w
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
)
+ k
0
:
The …rst-order conditions with respect to G
it+1
; C
t
it
; C
t1
it
; E
G
it
give
1
C
t
it
=
1
C
t1
it
=
E
G
it
=
k
w
G
it+1
:
The budget constraint then implies that
C
t
it
= C
t1
it
=
1
2 + + k
w
W
planner
it
E
G
it
=
2 + + k
w
W
planner
it
G
it+1
=
k
w
2 + + k
w
W
planner
it
:
35
Furthermore, by equating the co e¢ cients of ln W
planner
it
on both sides of the Bellman equa-
tion, I have
k
w
= 2 + + k
w
) k
w
=
2 +
1
:
Thus, G
it+1
= W
planner
it
: The infrastructure level is determined by fraction of the social
wealth, rather than the budget of the local government. This is because the social planner
also internalizes the welfare of the households in addition to that of the government.
A.3 Proof of Proposition 3
I need to solve the following Bellman equation:
V (G
it
; A
it
) = max
G
it+1
ln
C
t
it
+ ln (W
it
G
it+1
) +
i
ln G
it+1
+ E
t
[V (G
it+1
; A
it+1
)] :
I again conjecture that
V (G; A) = k
G
ln G + v (A) :
Then, the governor’s objective on the right-hand side becomes
max
G
it+1
ln
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
G
it+1
+ (k
G
+
i
) ln G
it+1
+ ln
1
1 +
(1 ) (1 )
R
=(1)
+
1
ln A
it
+ ln G
it
+ E
t
[v (A
it+1
)] + k
0
:
The …rst-order condition for G
it+1
gives
G
it+1
=
k
G
+
i
+ k
G
+
i
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
:
Equating the two sides of the Bellman equation leads to
k
G
= + +
i
+ k
G
; ) k
G
=
+ +
i
1
:
Thus,
G
it+1
=
1
(1 )
+
i
+
R
=(1)
A
1=(1)
it
+ (1
G
)
G
it
:
A.4 Proof of Proposition 4
I now derive the Bellman equation:
V (G
it
; T
it
) = max
G
it+1
; '
it+1
ln ((1
G
) G
it
+ T
it
G
it+1
) +
i
ln (G
it+1
) +
i
'
it+1
'
it+1
+ E
t
h
V
G
it+1
; Y
it+1
1
c
e
'
it+1
i
:
36
I conjecture that
V (G; T ) = k
g
ln (G) + v (T=G) :
The …rst-order condition for G
it+1
gives that
i
+ k
g
G
it+1
=
(1
G
) G
it
+ T
it
G
it+1
;
which directly implies that
G
it+1
=
i
+ k
g
i
+ k
g
+
[T
it
+ (1
G
) G
it
] :
The …rst order condition for '
it+1
gives that
i
=
c
e
'
it+1
E
t
Y
it+1
G
it+1
v
0
T
it+1
G
it+1
;
which further implies that
'
it+1
= ln
2
4
i
c
E
t
h
Y
it+1
G
it+1
v
0
T
it+1
G
it+1
i
3
5
:
By substituting G
it+1
back to the Bellman equation, I have
k
g
ln (G
it
) + v (T
it
=G
it
)
= (
i
+ k
g
) ln (G
it+1
) + ln ((1
G
) G
it
+ T
it
) + ln
i
+ k
g
+
+
i
'
it+1
'
it+1
+ E
t
v
1
c
e
'
it+1
Y
it+1
G
it+1
= (
i
+ k
g
+ ) ln (G
it
) + (
i
+ k
g
+ ) ln (1
G
+ T
it
=G
it
)
+ (
i
+ k
g
+ ) ln
i
+ k
g
+
i
'
it+1
+ E
t
v
1
c
e
'
it+1
R
=(1)
A
1=(1)
it+1
:
Thus,
k
g
=
i
+ k
g
+ ) k
g
=
i
+
1
and
v (T
it
=G
it
) =
i
+
1
ln (1
G
+ T
it
=G
it
) + k
0
with
k
0
= E
t
v
1
c
e
'
it
R
=(1)
A
1=(1)
it+1
+ (
i
+ k
g
+ ) ln
i
+ k
g
+
i
'
it+1
:
37
By substituting v into '
it+1
; I obtain that
'
it+1
= ln
2
4
i
c
E
t
h
Y
it+1
G
it+1
v
0
T
it+1
G
it+1
i
3
5
= ln
2
6
6
4
(1 )
i
c
(
i
+ ) E
t
(
R
)
=(1)
A
1=(1)
it+1
1
G
+
(
1
c
e
'
it+1
)(
R
)
=(1)
A
1=(1)
it+1
3
7
7
5
= ln
(1 )
i
c
(
i
+ )
ln
(
R
=(1)
E
t
"
A
1=(1)
it+1
1
G
+
1
c
e
'
it+1
R
=(1)
A
1=(1)
it+1
#)
(24)
This equation has a unique root in the interval (0; ln ln
c
) under the following inequality
conditions:
ln
(1 )
i
c
(
i
+ )
ln
(
R
=(1)
E
t
"
A
1=(1)
it+1
1
G
+ (
c
)
R
=(1)
A
1=(1)
it+1
#)
> 0 (25)
and
ln
(1 )
i
c
(
i
+ )
ln
(
R
=(1)
E
t
"
A
1=(1)
it+1
1
G
#)
< 0: (26)
Note that the right-hand side of (24) is increasing with
i
and decreasing with
c
. The
Implicit Function Theorem thus implies that '
it+1
is increasing with
i
and decreasing with
c
:
A.5 Proof of Proposition 5
I …rst solve the governor’s Bellman equation in (17) by conjecturing that
V (W
it
) = k
w
ln W + k
0
and denoting d
it
=
D
it
G
it+1
. Then, the Bellman equation becomes
k
w
ln W
it
+ k
0
= max
G
it+1
; d
it
ln (W
it
(1 d
it
) G
it+1
) +
i
ln G
it+1
ln G
it+1
+k
w
E
t
[ln (Y
it+1
+ (1
G
) G
it+1
Rd
it
G
it+1
)] + k
0
= max
G
it+1
; d
it
ln (W
it
(1 d
it
) G
it+1
) + (
i
+ k
w
) ln G
it+1
i
ln G
it+1
+E
t
k
w
ln
(1
G
) +
R
=(1)
A
1=(1)
it+1
Rd
it
+ k
0
:
38
The …rst-order condition for G
it+1
gives that
k
w
+
i
G
it+1
=
(1 d
it
)
W
it
(1 d
it
) G
it+1
:
This condition implies that
G
it+1
=
k
w
+
i
+ k
w
+
i
W
it
(1 d
it
)
: (27)
Then, the Bellman equation becomes
k
w
ln W
it
+ k
0
= max
d
it
( +
i
+ k
w
) ln W
it
+ (
i
+ k
w
) ln
1
1 d
it
+ ln
+ k
w
+
i
+ (
i
+ k
w
) ln
k
w
+
i
+ k
w
+
i
i
ln G
it+1
+E
t
k
w
ln
(1
G
) +
R
=(1)
A
1=(1)
it+1
Rd
it
+ k
0
:
Equating the coe¢ cients of ln W
it
gives
k
w
= +
i
+ k
w
) k
w
=
+
i
1
:
The relevant terms for choosing d
it
are
max
d
it
(
i
+ k
w
) ln
1
1 d
it
+ E
t
k
w
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
= max
d
it
i
+
( +
i
)
1
ln
1
1 d
it
+
( +
i
)
1
E
t
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
_ max
d
it
1
i
+
i
+ 1
ln
1
1 d
it
+ E
t
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
(28)
I now analyze the debt choice of the social planner. I also conjecture that
V
W
planner
it
= k
w
ln
W
planner
it
+ k
0
:
Then, the planner’s Bellman equation in (18) becomes
V
W
planner
it
= max
G
it+1
;C
t
it
;C
t1
it
;E
G
it
;D
it
E
t
h
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ k
w
ln
W
planner
it+1
+ k
0
i
= max
G
it+1
;C
t
it
;C
t1
it
;E
G
it
;D
it
E
t
[ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ k
w
ln (G
it+1
)
+ k
w
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
+ k
0
];
39
where d
it
=
D
it
G
it+1
:
The Lagrange for the maximization problem on the right-hand side is
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ k
w
ln (G
it+1
)
+k
w
E
t
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
+ k
0
C
t
it
+ C
t1
it
+ E
G
it
+ G
it+1
W
planner
it
G
it+1
d
it
:
The …rst-order conditions imply
=
1
C
t
it
=
1
C
t1
it
=
E
G
it
=
k
w
G
it+1
(1 d
it
)
and
k
w
E
t
2
4
R
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
3
5
= G
it+1
:
The budget constraint implies
1
+
1
+
+
k
w
= W
planner
it
) =
2 + + k
w
W
planner
it
:
Then,
G
it+1
(1 d
it
) =
k
w
2 + + k
w
W
planner
it
and
C
t
it
= C
t1
it
=
1
2 + + k
w
W
planner
it
E
G
it
=
2 + + k
w
W
planner
it
:
Equating the coe¢ cients of ln W
it
on both sides of the Bellman equation again gives k
w
=
+
i
1
: Thus, the relevant terms in the planner’s choice of d
it
are
ln
C
t
it
+ ln(C
t1
it
) + ln E
G
it
+ k
w
ln (G
it+1
)
+k
w
E
t
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
+ k
0
/ ln
1
1 d
it
+ E
t
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
: (29)
It is interesting to note that the two terms in (28) for the governor’s debt choice are the
same as the two terms in (29) for the planner’s debt choice, except that the coe¢ cient of the
40
…rst term for the governor’s debt choice is larger than that for the planner’s choice. I thus
write the objectives of the governor and the planner in the following general form
max
d
it
ln
1
1 d
it
+ E
t
ln
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
;
where the coe¢ cient of the …rst term is 1 for the planner’s choice and
1
i
+
i
+ 1 for the
governor’s choice.
The …rst-order condition of the debt choice is
1
1 d
it
| {z }
f
1
(d
it
)
E
t
"
R
R
=(1)
A
1=(1)
it+1
+ (1
G
) Rd
it
#
| {z }
f
2
(d
it
)
= 0:
Due to the logarithmic utility for all agents in the model, neither the governor nor the
planner would engage in any possibility of default. Thus, they would both choose debt
d
it
2
0;
1
G
R
so that their budgets would never turn negative. Note that both f
1
(d) and
f
2
(d) are positive and increasing. The following conditions ensure an interior solution to
this …rst-order condition:
f
1
(0) > f
2
(0) and f
1
1
G
R
< f
2
1
G
R
;
which are equivalent to
> E
t
"
R
R
=(1)
A
1=(1)
it+1
+ (1
G
)
#
and < E
t
"
R +
G
1
R
=(1)
A
1=(1)
it+1
#
:
As the coe¢ cient is larger for the governor’s decision, the governor’s debt choice is
higher in order to satisfy the …rst-order condition. Furthermore, the governor’s choice is
increasing with and thus with the governor’s career incentive coe¢ cient
i
.
A.6 Proof of Proposition 6
To solve the Bellman equation speci…ed in (20), I again assume V (W
it
) = k
w
ln (W
it
) + k
0
;
as suggested by the derivation in the previous section. Then, by substituting in E
G
it
=
W
it
+ D
it
G
it+1
and rescaling the choice variables as
g
it+1
=
G
it+1
W
it
and d
it
=
D
it
G
it+1
;
41
I have
max
g
it+1
; d
it
ln W
it
+ ln [1 (1 d
it
) g
it+1
] +
i
( +
0
) (1 ) (ln g
it+1
ln g
i
0
t+1
)
i
( +
0
)
2
(1 )
2
(ln g
it+1
ln g
i
0
t+1
)
2
+ k
w
ln W
it
+ ln g
it+1
+ E
t
ln
R
1
A
1
1
it+1
+ (1
G
) Rd
it
+ k
0
:
The …rst-order condition for g
it+1
gives
(1 d
it
)
1 (1 d
it
) g
it+1
=
h
k
w
+
i
( +
0
) (1 )
i
( +
0
)
2
(1 )
2
(ln g
it+1
ln g
i
0
t+1
)
i
1
g
it+1
;
which in turn gives
1
(1 d
it
) g
it+1
= 1 +
k
w
+
i
( +
0
) (1 )
i
( +
0
)
2
(1 )
2
(ln g
it+1
ln g
i
0
t+1
)
;
(30)
which has a unique root for g
it+1
in (0; 1) ; for a given d
it
. This root is increasing with b oth
g
i
0
t+1
and d
it
.
Equating the coe¢ cients of ln W
it
on both sides gives
k
w
= + k
w
) k
w
=
1
:
Then, the leverage choice is determined by
max
d
it
ln [1 (1 d
it
) g
it+1
] +
i
( +
0
) (1 ) (ln g
it+1
ln g
i
0
t+1
)
i
( +
0
)
2
(1 )
2
(ln g
it+1
ln g
i
0
t+1
)
2
+k
w
ln g
it+1
+ E
t
ln
R
1
A
1
1
it+1
+ (1
G
) Rd
it
;
where g
it+1
(d
it
; g
i
0
t+1
) is given by (30). This optimization problem leads to an optimal choice
d
it
= d
it
(g
i
0
t+1
) :
Symmetrically, I have
d
i
0
t
= d
i
0
t
(g
it+1
) :
These two equations jointly determine the two governors’debt choices and lead to rat-race
dynamics.
References
42
Bai, Chong-En, Chang-Tai Hsieh, and Zheng Song (2016), The long shadow of China’s
…scal expansion, Brookings Papers on Economic Activity, Fall, 129–165.
Bai, Chong-En and Yingyi Qian (2010), Infrastructure development in China: The cases of
electricity, highways, and railways, Journal of Comparative Economics 38, 34–51.
Barro, Robert (1990), Government spending in a simple model of endogeneous growth,
Journal of Political Economy 98(5, Part 2), S103–S125.
Blanchard, Olivier and Andrei Shleifer (2001), Federalism with and without political cen-
tralization: China versus Russia, IMF Sta¤ Papers 48, 171–179.
Brandt, Loren and Xiaodong Zhu (2000), Redistribution in a decentralized economy: Growth
and in‡ation in China under reform, Journal of Political Economy 108, 422–439.
Chen, Xilu, Wei Chen, Chang-Tai Hsieh, and Zheng Song (2018), A forensic examination
of China’s national accounts, Brookings Papers on Economic Activity, forthcoming.
Chen, Kaiji, Jue Ren, and Tao Zha (2018), The nexus of monetary policy and shadow
banking in China, American Economic Review 108(12), 3891–3936.
Chen, Zhuo, Zhiguo He, and Chun Liu (2017), The …nancing of local government in China:
Stimulus loan wanes and shadow banking waxes, Working paper, University of Chicago.
Cheremukhin, Anton, Mikhail Golosov, Sergei Guriev, and Aleh Tsyvinski (2017), The
economy of People’s Republic of China from 1953, Working paper.
Diamond, Peter (1965), National debt in a neoclassical growth model, American Economic
Review 55(5), 1126–1150.
Fan, Ziying, Wei Xiong, and Li-An Zhou (2016), Information distortion in hierarchical
organizations: A study of China’s Great Famine, Working paper, Princeton University.
Gibbons, Robert, and Kevin J. Murphy (1992), Optimal incentive contracts in the presence
of career concerns: Theory and evidence, Journal of Political Economy 100(3): 468–
505.
Holmstrom, Bengt (1982), Managerial incentive problems: A dynamic perspective, in Es-
says in Economics and Management in Honor of Lars Wahlbeck, Helsinki: Swedish
School of Economics.
Hortacsu, Ali, Shushu Liang, and Li-An Zhou (2017), Chinese local o¢ cials and GDP data
manipulation: Evidence from night lights data, Working paper, University of Chicago
and Peking University.
43
Hsieh, Chang-Tai, and Peter Klenow (2009), Misallocation and manufacturing TFP in
China and India, Quaterly Journal of Economics 124, 1403–1448.
Hsieh, Chang-Tai, and Zheng Michael Song (2015), Grasp the large, let go of the small: The
transformation of the state sector in China, Brookings Papers on Economic Activity,
Spring, 295–366.
Lau, Lawrence J., Yingyi Qian, and Gerard Roland (2000), Reform without losers: An in-
terpretation of China’s dual-track approach to transition, Journal of Political Economy
108, 120–143.
Li, Hongbin and Li-An Zhou (2005), Political turnover and economic performance: The
incentive role of personnel control in China, Journal of Public Economics 89(9–10),
1743–1762.
Li, Xi, Xuewen Liu and Yong Wang (2015), A model of China’s state capitalism, Working
paper, HKUST.
Li, Xing, Chong Liu, Xi Weng, and Li-An Zhou (2017), Target setting in tournaments:
Theory and evidence from China, Working paper, Peking University.
Liu, Chang and Wei Xiong (2018), China’s real estate market, Handbook chapter, in The
Handbook of China’s Financial System, edited by Marlene Amstad, Guofeng Sun and
Wei Xiong, Princeton University Press, forthcoming.
Maskin, Eric, Yingyi Qian, and Chenggang Xu (2000), Incentives, information, and orga-
nizational form, Review of Economic Studies 67(2), 359–378.
Pritchett, Lant (2000), The tyranny of concepts: CUDIE (cumulated, depreciated, invest-
ment e¤ort) is not capital, Journal of Economic Growth 5(4): 361–384.
Qian, Yingyi and Gerard Roland (1998), Federalism and the soft budget constraint, Amer-
ican Economic Review 88, 1143–1162.
Qian, Yingyi (2017), How Reform Worked in China, MIT Press.
Song, Zheng, Kjetil Storesletten, and Fabrizio Zilibotti (2011), Growing like China, Amer-
ican Economic Review 101(1), 196–233.
Song, Zheng and Wei Xiong (2018), Risks in China’s …nancial system, Annual Review of
Financial Economics, forthcoming.
Stein, Jeremy (1989), E¢ cient capital markets, ine¢ cient …rms: A model of myopic corpo-
rate b ehavior, Quarterly Journal of Economics, 104(4), 655–669.
44
Xu, Chenggang (2011), The fundamental institutions of China’s reforms and development,
Journal of Economic Literature 49(4), 1076–1151.
Young, Alwyn (2003), Gold into base metals: Productivity growth in the People’s Republic
of China during the reform period, Journal of Political Economy 111, 1220–1261.
Yu, Jihai, Li-An Zhoub and Guozhong Zhu (2016), Strategic interaction in political compe-
tition: Evidence from spatial e¤ects across Chinese cities, Regional Science and Urban
Economics 57, 23–37.
Zhang, Yuanyan Sophia and Steven Barnett (2014), Fiscal vulnerabilities and risks from
local government …nance in China, Working paper, IMF.
Zhu, Xiaodong (2012), Understanding China’s economic growth: Past, present and future,
Journal of Economic Perspectives 26, 103–124.
45
