Taxation under Autocracy: Theory and Evidence from Late Imperial

Taxation under Autocracy:
Theory and Evidence from Late Imperial China
Qiang Chen
School of Economics, Shandong University
Jinan, China
[email protected]
Yijiang Wang
CK Graduate School of Business
Beijing, China
[email protected]
Chun-Lei Yang
RCHSS, Academia Sinica
Taipei, Taiwan
[email protected]
Abstract: We model a game to show that the taxation level in an autocracy reflects
the state’s coercive power relative to people’s capacity for violence. The model also
specifies the mechanisms through which various factors affect relative state power.
The model predicts that taxation level increases with state coercion level, efficiency of
coercion technology, cost of rebelling, and likely labor incomes. Data from late
imperial China are used to test the hypotheses, and the findings are entirely consistent
with the predictions of the theory.
JEL: D74; H20; N45; O11
Key words: Taxation; Autocracy; State power; Rebellion; Imperial China

Qiang Chen is grateful for financial support from Shandong University Independent Innovation
Fund (FW12043), and Shandong University Humanities and Social Sciences Major Research
Project “Western Cliometrics and Its Applications in China” (12RWZD12). Chun-lei Yang
appreciates funding by National Science Council of Taiwan (NSC 101-2410-H-001-001-MY2).
1 1. Introduction
Taxation impacts the welfare of billions of people living in autocracies. It is a core
issue of the political economics of development.1 In this paper, we study a question
of great theoretical and practical importance: What determines the taxation level in an
autocracy?
To answer the question, we first model a game between a ruler and people who
pay taxes on their work incomes. We then use a unique set of data from late imperial
China to test the hypotheses derived from the model. The model shows that taxation
level is determined jointly with relative state power, i.e., the balance between state
coercion and the capacity of the people for violent tax rebellions. The model identifies
factors affecting relative state power and specifies a mechanism through which they
determine taxation level, generating testable hypotheses. The empirical findings are
entirely consistent with the predictions of the theory.
There is no doubt that taxation in an autocracy is determined by complex factors.
Any effort to explain it must confront two challenges: it must identify at least the
main factors; and it must specify the mechanisms through which they affect taxation.
Our model accomplishes the task by capturing the essence of taxation: it is a process
by which the state uses coercion to extract revenue from society, and people can either
pay or rebel against taxes. In our model the net-revenue maximizing ruler can
strategically spend resources to enhance state coercive power (as in Besley and
1
North et al. (2009) refer to non-democracies as “natural states” emphasizing that they are the
dominant political system of the world, both historically and contemporarily. Acemoglu and
Robinson (2006) offer an excellent study of distributive politics centering on taxation.
2 Persson, 2011a, b). The spending is a cost that needs to be justified by tax revenue.
Our analysis shed lights on the interplay between state power and taxation, based on
the cost-and-benefit calculus of the ruler’s spending on state coercion.
Specifically, we find that the upper limit of taxation is a function of the state’s
coercive power, i.e., how much a state can maximally tax depends on how effectively
it can deter people’s potential for violent tax rebellions. It follows that any factor
affecting relative state power also affects taxation. Among these factors are violence
factors such as the odds of a rebellion’s success, coercion technology and costs of
violence; and income factors such as wages and the ruler’s benefits from non-tax
sources.
This work belongs to the political economics of development and benefits from
many previous works. The model is adapted from Wang (2012), which builds on the
landmark contributions of Acemoglu and Robinson (2006), North et al. (2009) and
Besley and Persson (2011a, b) on distributive politics. Balance in violence is central
in Acemoglu and Robinson (2006) to the transition to democracy, and in Besley and
Persson’s (2011b) on the clustering of institutions. It is also central in Barzel (2002),
North et al. (2009) and Acemoglu et al. (2013) to the relationship among the elites,
and in Aoki (2014) to a three-party taxation game with a middleman between the ruler
and the peasants as taxpayers. The main contribution of the present work to the
literature is twofold: it adopts a model of relative state power to explain taxation
levels in an autocracy and derives testable hypotheses from the model; and it uses a
unique data set to test the hypotheses.
3 This work is also closely related to those studying the predatory behaviors of the
state (see Shleifer and Vishny 2008, North et al. 2009, and Wang 2012, for reviews).
Our contribution to this literature is to observe that violence is a two-way threat, and
taxpayers’ capacity for violence sets a limit to taxation. We show how the threat of
violence changes the ruler’s behavior. The logic is exactly the same as that of entry
games studied by Milgrom and Roberts (1982).
The empirical part of our work, in which we use a unique data set from late
imperial China to test the hypotheses derived from the model, is closely related to Sng
(2014), who explains the regional variations in land taxation in late imperial China
through the lens of agency cost and predicts lower taxes in prefectures more distant
from Beijing. In contrast, our theory predicts lower taxes in prefectures where state
coercion is less effective, e.g., prefectures that are more distant from the state’s major
military bases. It is also worth emphasizing that, although both works explain
variations in taxation levels across prefectures within an autocracy, our theory can
also apply to international variations, i.e., it can explain variations in taxation levels
across countries. Our empirical findings also cast doubt on Fukuyama (2011)'s
contention that emperors in imperial China may best be characterized as benevolent
dictators rather than as stationary bandits who set tax rates optimally to maximize
extraction of revenue (Olson, 2000)2.
The remainder of this paper is organized as follows. Section 2 introduces a simple
2
It is interesting to note that Olson (2000) has the Chinese warlords in the 1920s as his lead
example for the notion of “stationary bandits”.
4 game-theoretic model where the levels of state spending for coercion and taxation are
jointly determined in a sub-game perfect equilibrium.
Section 3 describes the data from 261 prefectures in late imperial China circa
1820, and focuses on the determinants of per capita land tax in each prefecture. We
observe a lot of variations in per capita land taxes across prefectures3. Among
explanatory variables, we include army size and postal distance to Beijing as proxies
for state coercion and agency costs respectively, various measures of allegiance,
cropland per capita, population density, agricultural suitability, as well as a rich set of
geographic and climate controls. In fact, the choice of historical China as an
interesting case study is largely driven by this unusual data availability.
Section 4 presents empirical results, which are consistent with the theory of
relative state power. The empirical strategy exploits exogenous variations in army
sizes due to the need for national defense and natural geographical conditions, and
uses optimal GMM estimation under over-identification. We also conduct a variety of
robustness checks with similar results. Section 5 concludes the paper.
2. The Model and Hypotheses
2.1. Players and Technology
The taxation game is played between two types of players: the ruler and the
3
In particular, the standard deviation of land tax per capita was almost as large as the mean,
implying a much larger variance than the mean (see Table 3).
5 worker class. All players are selfish and risk-neutral income maximizers with moves
and payoffs as follows.
The ruler has incomes from two sources: direct benefit from power (benefit) and
taxation of workers’ wages.4 Direct benefit f is determined outside of the model so
that the ruler concentrates on maximizing tax revenue.
The ruler is not liquidity constrained. She spends e  0 to build state capacity in
violence (state coercive power), which would inflict cost c(e) to a rebelling worker.5
The technology c(e) turns the ruler's spending e into effective coercive power, which is
increasing at an ever lower rate, i.e. c()  0 and c()  0 . Moreover, we assume
c(0)  0 . Relying on c(e) , the ruler taxes the workers on their wages at rate r   0,1 .
There are two types of workers, worker A and worker B, and each has mass one.
Let w  0 be the wage for a worker, where w is exogenously given and reflects the
level of development or labor productivity. The cost of rebellion is  c(e)  z  for
worker A, and  c(e)  z  for worker B, where c(e) is the systematic cost from state
violence, while z  0 and z  0 are the idiosyncratic costs specific to each type of
worker. It is assumed that z is prohibitively high such that worker B, a loyalist, never
rebels. On the other hand, z is low enough that worker A, an opportunist, may decide
4
The phrase “direct benefit from power” is from Maskin and Tirole (2004). Examples of it are
incomes from corruption, natural resource rent and foreign aid (as in Besley and Persson, 2011a, b)
and large gaps between illicit rent and tax revenue (as in Acemoglu, 2005, and Sng, 2014). It also
includes psychological satisfaction derived from being in power, such as national and historical
legacy (Olson, 2000, p.13f)
5
Although referred to as technology, c(e) is a mix of technology and factors such as will power
and social norms, e.g., c(e) is smaller if killing is not as easy because of social norms. Note that
the ruler may also spend tax revenue on public goods that help increase his tax base (Olson, 2000,
p.9f). For better focus, this is omitted from our simple model.
6 to work (W) or to rebel (R), i.e. his action a  W , R . If both workers work, the total
tax revenue would be 2rw and net revenue g  (2rw  e) . If worker A rebels, the total
tax revenue would be rw and net revenue g  (rw  e  h) , where h  0 is loss caused by
the rebels.
Assumption: For simplicity, assume h is prohibitively high such that the ruler
never would want worker A to rebel in equilibrium6.
If worker A rebels, he has probability    0, 1 to usurp power from the ruler,
where  is exogenously given7. If his rebellion is successful, once in power he can tax
worker B for revenue rw and receive f, just as his predecessor would do. His income
would then be ( rw  f ) . Weighting it by  and subtracting from it  c(e)  z  , his
expected rebelling income is  (rw  f )  c(e)  z  . On the other hand, if worker A
works, his after-tax income is (1  r ) w .
The payoffs for the ruler and worker A are summarized in Table 1 (worker B is
silent and ignored).
Table 1. Payoffs
Ruler
2rw  e  f
Ir  
 rw  e  h
Worker A
W
if a  
R
 (1  r ) w
W
IA  
if a  
 (rw  f )  c(e)  z
R
r   0,1 ; e, z  0 ;  , w, f , h  0 ; c(0)  0 , c  0 , c  0
6
This assumption does not mean that popular uprisings would never occur. Instead, it means that
the ruler is not a roving bandit, and he never expects to have rebellions ex ante.
7
Wang (2012) discusses how to endogenize the probability of successful rebellion. However, the
central messages from the theory remain the same. Thus, this assumption is made for brevity. 7 Information and the moves: Information is complete and perfect. The ruler moves
first to decide on spending e and tax rate r. These decisions are truthfully announced
and irreversible. After that, worker B sets to work, while worker A chooses to work or
rebel, with respective consequences as specified above.
2.2. Subgame Perfect Equilibrium
By backward induction, we know that the condition to ensure worker A’s choice of
work, a  W is
(1  r ) w   (rw  f )  c(e)  z .
(1)
Define
r0 
1
c ( e)  z   f

1 
w(1   )
(2)
as the highest tax rate which worker A will accept. In other words, the ruler can tax
maximally up to r  r 0 without causing a rebellion. Clearly, r 0 is increasing in the
spending e for state coercion. Given e (hence also c(e) ) and all the other parameters,
there is an r 0 such that worker A’s preference is to work if r  [0, r 0 ] , but to rebel
if r  (r 0 ,1] .
To maximize tax revenue, the ruler always sets tax rate at r 0 . Inserting (2) into the
ruler’s objective function, the optimization problem is
max 2r 0 (e) w  e  f .
e
The first-order condition for optimization is
8 (3)
c(e* ) 
1 
.
2
(4)
The second-order condition is satisfied iff c  0 as we assumed. From (4), it is easy
to see that
e*
1

 0 . What this means is that, intuitively, when the odds of
 2c(e* )
successful rebellion  become higher, spending e is less effective at deterring worker
A from rebelling. This leads to a lower optimal level of e. Lemma The pair (r * , e* )   r 0 (e* ), e*  that results from (2) and (4) constitutes a
Subgame Perfect Equilibrium (SPE) of the game.
2.3. Comparative Statics and Hypotheses
The above model generates a number of interesting testable hypotheses.
Hypothesis 1. The equilibrium tax rate r * increases with the equilibrium spending
on coercion e* .
This is evident from equation (2). In fact, a central message of our theory is that a
state with greater coercive power can tax more. So if there is an exogenous shock to
c’(e) resulting in a higher equilibrium spending e* , the shock also leads to a higher
equilibrium tax rate r * .
Additional hypotheses can be easily derived through comparative statics. Note
that the SPE (r * , e* ) is a function of the structural parameters  , w, f , z . Applying the
total differentiation method to (2) and (4), which is a special variation of the Implicit
Function Theorem, yields the following comparative statics results straightforwardly
9 (see Table 2)8.
Table 2. Comparative Statics
r *
1

0
z w(1   )
 c(e* )
r *
1
*

  *  f  wr   0
 w(1   )  2c (e )

r *


0
f
w(1   )

r * 1  1
1
 
 r *   0 if r * 
w w  (1   )
1 

From Table 2, we establish the following additional hypotheses.
Hypothesis 2. The equilibrium tax rate r * increases with z , the idiosyncratic cost
of rebellion to the rebels.
The intuition is simple. The state can tax a citizen more heavily if he is loathe to
engage in popular uprisings. An implication of Hypothesis 2 is that the tax rate should
be set lower for a region dominated by minority groups with little allegiance to the
central government, hence lower z (e.g. lower moral cost of rebellion).
Moreover, the equilibrium tax rate r * decreases with  , the probability of
successful rebellion. The reason is that better odds of successful rebellion provide a
stronger motivation for people to rebel. A lower tax rate is needed to offset the
stronger motivation and appease them.
8
For illustration, from equation (2) we get (1   ) wr  w  c(e)  z   f . Apply total
differentiation with respect to  , we then get (1   )wdr  wrd  cde  f d , i.e.,
dr
de
(1   ) w
 wr  c
 f . The rest follows in the same manner.
d
d
10 Hypothesis 3. When the coercion technology becomes more efficient, the
equilibrium coercion level and the equilibrium tax rate r * both rise.
Without loss of generality, assume for example that the coercion technology has
the special form of kc(e) . It is straightforward to obtain that
 e*
c

 0 and
k
kc
r *
c2

 0 . In other words, if the state can hit the rebel more effectively at
k
w(1   )c
any given level of e, then it is worthwhile for the ruler to increase the spending for
coercion and tax more.
The relation between the equilibrium tax rate r * and the exogenously given wage
rate w is more complicated. Theoretically, it can go either way. As wage increases, the
rebel has more to gain once he is in power, hence he is more motivated to rise up
against taxation (known as the "greed" motive), and a lower tax rate is needed to
appease the potential rebel. On the other hand, at higher wages the opportunity cost of
soldiering is also higher (known as the "grievance" motive), implying that rich people
are less willing to take to arms. When this latter motive dominates, higher taxes can
be levied on those earning higher wages. Thus in general the net effect of wages on
taxation is ambiguous depending on the relative strength of these two motivations.
However, in our model, equilibrium tax rate r * increases in wage
whenever r * 
1
1
holds. If   0.05 , this requires that r * 
 0.95 , which is
1 
1  0.05
a condition quite easy to satisfy in practice. Even in the extreme case
where   1 (successful uprising guaranteed), this inequality requires only r *  0.5 ,
11 which is still reasonable. These numerical examples suggest the following hypothesis.
Hypothesis 4. With parameter values in reasonable ranges, the equilibrium tax
rate r * increases with w.
Below we will test the above hypotheses, all of which turn out to be consistent
with empirical evidence.
3. Data
In this section we take the theory of relative state power to a unique data set from
261 prefectures in late imperial China circa 1820, and focus on the determinants of
per capita land tax across prefectures. The definitions of variables and data sources are
described below.
3.1. Cropland, Population, and Tax
The empirical counterpart of the theoretical tax rate is land tax per capita in late
imperial China, where land tax was the primary source of revenue in an agricultural
society. The data for total land tax in 1820 (tax) for each prefecture in China is
derived from Liang (1980), which compiles information about cropland and land tax
in the Qing dynasty from the Grand Gazetteer of the Qing during the Reign of Jiaqing
(Jiaqing Chongxiu Yitong Zhi). The payment of land tax could take three forms, i.e.
land tax payable in taels of silver, grain, or cereal. We use Grain Price Database in
the Qing Dynasty (Wang, 2009)9 to retrieve the prices of grain and cereal for each
9
This data set is available at http://140.109.152.38/DBIntro.asp. Since 1736, provincial
governments were required to report grain prices in each prefecture within their province. Thanks
12 prefecture in 1820, and convert all land tax into taels of silver.
The population of each prefecture in 1820 in thousands (pop) is derived from Cao
(2001), which is widely considered the most authoritative study on historical Chinese
demography. The dependent variable of this study, land tax per capita (taxpc), is
simply defined as total land tax in 1820 (tax) divided by population in 1820 (pop).
Since land tax in late imperial China only changed slowly over time (Wang, 1974; Liu
and Fei, 1977), we define an alternative measure of land tax per capita taxpc1776 as
total land tax in 1820 (tax) divided by population in 1776 (pop1776) as a robustness
check.
The data for cropland in mu (land) are also taken from Liang (1980). Dividing
land by pop yields cropland per capita (landpc), which may be used as a proxy for
wage, since income per capita depends heavily on land per capita in an agricultural
society. The data for the area of each prefecture in km2 (area) are from Cao (2001).
Dividing pop by area yields population density (pdensity), which is another proxy for
wage, or level of development in general (Acemoglu et al., 2002). Alternatively, we
define pdensity1776 as the ratio of pop1776 to area. These two proxies of wage are
used to test Hypothesis 4 that the equilibrium tax rate increases with the wage.
All croplands were not quite the same, since some were fertile and blessed with
an auspicious climate, while others were not. Following ecologists' approach, we
to decades of work by Yeh-chien Wang, data from the archives became a complete database,
which has been used by Shiue and Keller (2007) to examine market integration in 18th-century
China. 13 measure the agricultural suitability as the product of climate suitability and soil
suitability. The original data are drawn from Ramankutty et al. (2002), which provides
agricultural suitability data at the 0.5-degree grid level10. We define the agricultural
suitability (agrisuit) of each prefecture as the average value of grid cells within its
boundary.
3.2. Army
A key explanatory variable is the state's spending on coercive power proxied by
the size of army, which is used to test Hypothesis 1 that the equilibrium tax rate rises
with equilibrium spending on coercion. Since the data for army size are not available
at the prefectural level, we use the size of the provincial army (army) instead11, which
is available from An Investigation of the Royal Military System (Wen, 1861). As an
alternative measure, we also consider the direct distance from each prefecture to the
nearest military center where the (Manchu) Eight Banners Army was stationed. The
locations of these military centers are also available from Wen (1861), while the direct
distance is computed with Chinese Historical GIS (CHGIS, Harvard Yenching
Institute, version 5). However, this alternative measure performs rather poorly, and for
a good reason, i.e. a military center typically did not have jurisdiction over prefectures
in neighboring provinces. Therefore, we focus on the size of provincial army (army)
as a proxy for state coercive power.
10
The agricultural suitability data can be downloaded from
http://www.sage.wisc.edu/atlas/maps.php?datasetid=19&includerelatedlinks=1&dataset=19.
11
A provincial army included the (Manchu) Eight Banners Army and the (Han) Green Standard
Army. From an administrative perspective, the maintenance of local stability was mostly the duty
of the provincial government, led by the provincial governor. Therefore, for our purpose the size
of the provincial army mattered more than the size of the army stationed in each prefecture.
14 An obvious challenge in estimating the effect of army size on tax rate is its
potential endogeneity. As clear from the model in Section 2, the size of the army as a
proxy for coercive spending and the tax rate are jointly determined, so the causality
can go both ways. We use two instrumental variables to overcome the endogeneity of
army. First, we exploit the exogenous variation of army size due to the need for
national defense, and use a dummy representing whether a prefecture is located in a
province on the frontier with a foreign country, or a potentially rebellious autonomous
region (frontier) as an IV for army. Specifically, frontier takes on the value of one for
any prefecture in Zhili, Shanxi, Shaanxi, Gansu, Guangxi and Yunan provinces, and
zero otherwise. Obviously, frontier is correlated with army, since a frontier province
typically had a larger army for national defense. The correlation coefficient is 0.352 in
the sample, which is significant at the 1% level. On the other hand, the variation in
army size due to the need for foreign defense arguably had nothing to do with
domestic tax issues.
The second IV for army is the ruggedness of the terrain. We used visual
inspection in Google Earth to determine whether the dominant terrain of a prefecture
is rugged (rugged). The size of the army is correlated with rugged, because a rugged
terrain typically discourages the deployment of an army. The correlation coefficient is
-0.182 in the sample, and significant at the 1% level. On the other hand, rugged
appears to be exogenous, since we have already controlled for cropland per capita,
agricultural suitability, and population density as alternative channels for rugged to
affect the tax rate.
15 In addition, we follow Nunn and Puga (2011) to define an alternative measure of
terrain ruggedness12, rugged2, which first computes a terrain ruggedness index for
each 30-by-30 arc-second cell as the square root of the sum squared differences in
elevation in eight directions, then averages this index over the entire portion of the
prefecture not covered by water. However, rugged2 only measures small-scale terrain
irregularities, and the correlation coefficient between rugged2 and army is just -0.105
and only significant at the 10% level. Therefore, rugged2 appears to be a weaker IV
than rugged, and the former is only used as a robustness check. The correlation
coefficient between these two measures of terrain ruggedness is 0.584.
3.3. Agency Cost
Following Sng (2014), we use the postal distance from the provincial capital to
Beijing (pdprov), and the direct distance from the prefectural seat to the provincial
capital (dpref), as two proxies for agency costs13. The data for pdprov are derived
from Collected Statutes of the Qing Dynasty by Imperial Order (QDZH, 1985, v. 121),
which describes royal postal routes from Beijing to each provincial capital, and the
corresponding postal distance in 'li' units, which is converted into kilometers14. The
data for dpref are computed in CHGIS. We also define a dummy capturing whether
the prefectural seat housed the provincial capital (prov_capital) according to China
12
We thank Ting Chen and Chicheng Ma for sharing the data, which are computed with SGS
Digital Elevation Model (DEM) at 90 square-meter-cell grid resolution, matched with CHGIS,
Version 4, 2007.
13
Sng (2014) uses the sum of dprov and dpref as an explanatory variable. However, more
information may be gained if dprov and dpref are included as two separate regressors. Moreover,
the nature of postal distance and directional distance are not quite the same.
14
The formula for conversion is 1 li = 0.576 km according to Yang et al. (2008), p.2248. 16 Historical Atlas (Tan,1982). Obviously, for prefectures with prov_capital = 1, we
have dpref = 0.
While the direct distance is merely a geographic feature, the postal distance was
not. The imperial postal routes might be designed to pass through regions of higher
population density and greater tax potential. To deal with the potential problem of
endogeneity, we follow Sng (2014) and use the direct distance from the provincial
capital to Beijing (dprov) as an IV for the postal distance from the provincial capital to
Beijing (pdprov). These two measures of distance are highly correlated, with a
correlation coefficient of 0.98. On the other hand, there is no obvious reason for the
direct distance to affect tax per capita other than through the postal distance, thus
dprov appears to be exogenous.
3.4. Allegiance
To test Hypothesis 2 that tax rate rises with the cost of rebelling, we exploit the
fact that a prefecture dominated by minority groups usually showed little allegiance to
the central government, and had few scruples in contemplating a rebellion. To capture
this effect, we define minority1 as an indicator of the presence of minority groups in a
prefecture during 1661-1820 according to Atlas for Chinese History (Guo, 1996, v.2,
p.103-106). However, the definition of minority1 may be too loose, since the
presence of minority groups in a prefecture need not imply their dominance. As an
alternative measure, we define minority2 as whether there was any autonomous
county, autonomous zhou (city), or autonomous region (province) after 1949
17 according to China Historical Atlas (Tan,1982) and Atlas of China (Dizhi Press
Editorial Office, 2011). The advantage of minority2 is that it does indicate the
presence of dominant minority groups, while its disadvantage lies in the time
mismatch, since the distribution of minority groups could have changed due to
migration during 1820-1949. Nevertheless, since minority1 outperforms minority2,
and these two measures are highly correlated, with a correlation coefficient of 0.65,
we only use minority1 in the regressions.
In the Qing dynasty, municipalities under direct control of the provincial
government, known as "zhili ting", were often set up in regions dominated by
minorities. Hence, we define another proxy for minority groups, ting, to indicate
whether the prefectural unit was a zhili ting.
Moreover, we look at the frequency of past uprisings as an ad hoc measure of a
prefecture's readiness to take to arms, or absence of allegiance. For this purpose, we
define riot1 as the number of peasant uprisings in a prefecture since the beginning of
the Qing (Manchu) dynasty's rule in mainland China in 1644 until 1820. However, the
invasion of the Manchu army was met with sustained resistance by the Han majority,
which did not die down until the suppression of the Revolt of the Three Feudatories in
1682. Thus, many peasant uprisings before 1682 were actually part of the
anti-Manchu resistance movement. Hence, we define an alternative measure riot2 as
the number of peasant uprisings in a prefecture during 1682-1820. Both riot1 and
riot2 are derived from A Chronology of Warfare in Dynastic China (China’s Military
18 History Editorial Committee, 2003), which has been used by Chen (2014) and Jia
(2014) to study peasant uprisings in historical China. Since riot2 outperforms riot1,
and these two measures are highly correlated with a correlation coefficient of 0.71, we
only use riot2 in the regressions.
3.5. Geography
As geographic controls, we define latitude, longitude, and elevation as the
latitude, longitude and elevation of the prefectural seat respectively. Both latitude and
longitude are directly available from CHGIS. With the latitude and longitude of the
prefectural seat at hand, we use Google Earth to determine its elevation from the sea
level. Moreover, we define a dummy capturing whether a prefecture had a coastline
(coast), and a dummy for whether a prefecture was passed through by the Yangtze
River or the Grand Canal (river). The data for both coast and river are derived from
China Historical Atlas (Tan,1982). The variable coast is used as a proxy for less
efficient coercion technology, since rebels in a coastal prefecture had the option of
taking to the sea to avoid punishment. An additional geographic control is the size of
prefecture, measured by its area (area) as noted before.
3.6. Climate
As climate controls, we derive historical weather data from Collected Maps of
Droughts and Floods in China in the Past Five Hundred Years (State Meteorological
Society, 1981), which provides annual information on the weather for locations
19 throughout China dating back to 147015, and which has been used by Shiue and Keller
(2007) and Jia (2014). This data set contains a variable dryness, a discrete indicator of
the degree of aridity, which is coded in the following way:
1
2

dryness  3
4

 5
if exceptional flood
if limited flood
if normal weather
if limited drought
if exceptional drought
(5)
We compute the average dryness during 1644-1820 for each prefecture, and still
denote it as dryness. Since climate volatility may also matter, we compute the
standard deviation of dryness, and denote it as dry_std.
Summary statistics for the above variables are presented in Table 3.
Table 3. Summary Statistics
Variable
taxpc
army
frontier
rugged
rugged2
pdprov
dprov
dpref
prov_capital
minority1
ting
riot2
coast
landpc
pdensity
Observation
261
261
261
261
261
261
261
261
261
261
261
261
261
261
261
Mean
110.49
46.57
0.36
0.59
2.30
1970.63
1193.33
198.58
0.07
0.49
0.06
0.18
0.14
1911.88
134.11
Std. Dev.
95.35
45.05
0.48
0.49
1.82
985.43
563.07
123.44
0.25
0.50
0.23
0.52
0.35
1444.97
144.34
Min
1.15
9.442
0
0
0.04
190.08
141.12
0
0
0
0
0
0
17.41
0.45
Max
611.22
208.61
1
1
9.72
3415.68
2090.19
872.90
1
1
1
4
1
6974.89
874.1
15
The sources of State Meteorological Society (1981) include rainfall records from weather
stations, official documents of the Ming and Qing dynasties (the Veritable Records of the Ming
and Qing Dynasties, the History of the Ming Dynasty and the Qing Dynasty), as well as more than
2200 local gazetteers. 20 agrisuit
area
latitude
longitude
elevation
river
dryness
dry_std
261
261
261
261
261
261
261
261
0.68
16029.46
30.67
111.64
470.79
0.17
2.94
0.86
0.58
19404.51
4.99
5.81
606.75
0.38
0.10
0.25
0.003
1270
20.01
95.79
6
0
2.71
0.25
9.34
192200
40.97
121.54
2966
1
3.18
1.29
4. Empirical Results
Based on the above discussions, we specify the benchmark equation for the
determination of land tax per capita in prefecture i as follows,
taxpci   0  1armyi  β2di  β3 w i  β4 z i  β5 xi   i ,
(6)
where taxpc is land tax per capita, army is the size of the provincial army as a proxy
for the state's coercive spending, di = (pdprov, dpref, prov_capital) is a vector of
proxies for agency costs measuring the distance from a prefecture to political
centers, wi = (landpc, pdensity, agrisuit) is a vector of proxies for wage measuring
cropland per capita, population density, and agricultural suitability respectively, z i =
(minority1, ting, riot2) is a vector of proxies for allegiance measuring the presence of
minority groups and the frequency of past riots respectively16, and xi = (area, latitude,
longitude, elevation, river, coast, dryness, dry_std) is a vector of geographic and
climate controls.
To tackle the endogeneity of army and pdprov (the postal distance from provincial
16
Since minority1 and minority2 are highly correlated, and the former outperforms the latter, we
only keep minority1 in the regression. Similarly, we keep riot2 in the equation, but drop riot1.
21 capital to Beijing), we use three IVs as discussed in Section 3, i.e. frontier (dummy
for frontier province), rugged (dummy for rugged terrain), and dprov (direct
distance from the provincial capital to Beijing). With three valid IVs at hand for two
endogenous variables, we conduct efficient GMM estimation under overidentification.
The results are presented in column (1) of Table 4.
First and foremost, the coefficient of army is positively significant at the 1% level,
which supports the central message of Hypothesis 1, i.e. a state with more coercive
power can set a higher tax rate. On the other hand, the coefficients of the three
distance measures (pdprov, dpref, prov_capital) as proxies for agency cost are all
insignificant, which casts doubt on the role of agency costs emphasized by Sng (2014).
Intuitively, the importance of state coercion over agency costs may be due to the fact
that it was much more costly to move an entire army around than simply sending a
couple special envoys to audit local officials.
Among proxies for lack of allegiance, the coefficients of minority1 and ting are
both negatively significant at the 5% level, which lends support to Hypothesis 2, i.e.
the tax rate was set lower for regions dominated by minority groups with little
allegiance. However, the coefficient of the number of prior peasant uprisings (riot2) is
not significant.
The coefficient of coast is negatively significant at the 1% level. One explanation
is to recognize that rebels in a coastal prefecture had the option of taking to the sea as
22 pirates17, making it more difficult to defeat them completely. Thus, it is more difficult
for the state to punish rebels in a coastal prefecture, which means that the coercive
technology c(e) is less efficient for a coastal prefecture. Therefore, the negative effect
of coast is consistent with Hypothesis 3, which posits that the equilibrium tax rate
rises with the efficiency of coercion technology.
Among proxies for wage, the coefficients of cropland per capita (landpc) and
population density (pdensity) are both positively significant at the 1% level, which is
consistent with Hypothesis 4, i.e. the tax rate was set progressively higher for richer
regions, where the opportunity cost of rebellion was higher since there was more to
lose from a failed rebellion. However, while the coefficient of agricultural suitability
(agrisuit) is positive, it is not significant. Perhaps the effect of agrisuit has already
been represented through cropland per capita and population density.
Table 4. Determinants of Land Tax Per Capita
Dependent Variable: taxpc
(1) GMM
***
army
pdprov
dpref
prov_capital
minority1
ting
riot2
0.973
(0.300)
0.00513
(0.0150)
0.0561
(0.0495)
19.04
(24.72)
-28.74**
(13.40)
-43.16**
(18.57)
0.0901
(2) GMM
***
0.974
(0.299)
0.00806
(0.0152)
0.0409
(0.0493)
16.33
(24.50)
-27.67**
(13.21)
-41.37**
(17.46)
-1.446
(2) IGMM
***
0.973
(0.300)
0.00512
(0.0150)
0.0564
(0.0494)
19.21
(24.71)
-28.71**
(13.40)
-43.12**
(18.54)
0.0472
17
Piracy was a serious problem during the Ming Dynasty (1368-1644), the immediate
predecessor of the Qing dynasty. See, for example, Kung and Ma (2014).
23 (3) LIML
0.980***
(0.303)
0.00551
(0.0151)
0.0487
(0.0508)
18.67
(24.72)
-29.54**
(13.46)
-42.60**
(18.28)
0.0876
coast
landpc
pdensity
agrisuit
area
latitude
longitude
elevation
river
dryness
dry_std
_cons
N
R2
p-value for Hansen J
p-value for GMM C
F-Stat for army
F-Stat for pdprov
(8.495)
-76.14***
(22.64)
0.0249***
(0.00440)
0.332***
(0.0994)
4.331
(3.765)
-0.000127
(0.000317)
-6.108**
(2.464)
2.790
(2.292)
0.0466***
(0.0116)
9.686
(18.48)
63.14
(45.19)
118.5***
(32.57)
-458.1
(305.3)
(8.529)
-82.71***
(22.62)
0.0242***
(0.00434)
0.289***
(0.0939)
4.021
(3.739)
-0.0000472
(0.000326)
-5.309**
(2.402)
3.377
(2.180)
0.0413***
(0.0117)
7.520
(18.16)
44.13
(44.84)
111.3***
(32.21)
-480.5
(293.4)
(8.497)
-76.26***
(22.64)
0.0249***
(0.00440)
0.331***
(0.0994)
4.337
(3.764)
-0.000125
(0.000317)
-6.102**
(2.463)
2.788
(2.291)
0.0465***
(0.0116)
9.636
(18.47)
63.01
(45.17)
118.5***
(32.57)
-457.6
(305.1)
(8.567)
-78.62***
(22.81)
0.0248***
(0.00442)
0.322***
(0.0998)
4.359
(3.753)
-0.000133
(0.000322)
-6.025**
(2.475)
2.805
(2.268)
0.0446***
(0.0120)
7.593
(18.55)
56.73
(45.78)
117.4***
(32.55)
-438.7
(302.8)
261
0.327
0.409
0.000
10.695
418.436
261
0.324
0.236
0.000
10.707
435.658
261
0.327
0.410
0.000
10.695
418.436
261
0.325
10.695
418.436
Note: Robust standard errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.
Among geographic controls, the coefficients of area, longitude and river are all
insignificant. The coefficient of latitude is negatively significant at the 5% level,
implying that south China, with its lower latitude, paid more tax than north China. It
is widely recognized that south China had higher agricultural productivity than north
24 China in pre-modern times18. Therefore, lower latitude could proxy for higher
productivity or labor wages, which were associated with a higher tax rate according to
Hypothesis 4.
The coefficient of elevation is positively significant at the1% level, implying that
a prefecture with a higher altitude paid more tax. A possible explanation is that a
high-elevation prefecture was typically located in a frontier province with a larger
provincial army, and hence paid more tax. In fact, elevation and frontier are positively
correlated, with a correlation coefficient of 0.49 in the sample.
Among climate controls, the coefficient of dryness is insignificant, while the
coefficient of dry_st , a measure of rainfall volatility, is positively significant at the
1% level, which appears to be counterintuitive at first sight. A possible reconciliation
has to do with China's climate and geography. While the eastern part of China is
generally more fertile and productive, it is also more heavily influenced by the fickle
monsoon, with larger climate volatility. In fact, dry_st and longitude are highly
correlated in the sample, with a correlation coefficient of 0.64. Therefore, climate
volatility (dry_std ) may proxy for higher agricultural productivity, which had a
positive effect on the tax rate.
A number of test statistics are reported at the bottom of Table 4. For the baseline
specification in column (1), the p-value for the Hansen J statistic for overidentification
18
Since south China is typically more mountainous than north China, it makes more sense to
define an alternative measure of population density, pdensity1, as the ratio of population to
cropland as a proxy for productivity and economic development. By this measure, latitude and
pdensity1 are positively correlated with a correlation coefficient of 0.155 significant at 5%
(p-value 0.0121).
25 test is 0.281, which accepts the null hypothesis that all instrumental variables are
exogenous. On the other hand, the p-value for the GMM C statistic testing for the
endogeneity is 0.006, which strongly rejects the null hypothesis that both army and
pdprov are exogenous. The F statistic for the first-stage regression with army as the
dependent variable is 10.649, while the F statistic for the first-stage regression with
pdprov as the dependent variable reaches as high as 414.657. Since both F statistics
exceed the rule-of-thumb critical value of 10, we conclude that these instruments are
not weak.
Column (2) of Table 4 uses rugged2 instead of rugged as an IV for army size, and
the results are very similar. Column (3) uses iterative GMM instead of two-step GMM,
and the results still barely change. Since the F statistic for the first-stage regression
with army as the dependent variable is only slighter larger than 10, column (4) reports
estimation by Limited Information Maximum Likelihood (LIML), which is known to
have better finite sample properties with weak instruments. The results are again quite
similar.
Table 5 conducts additional robustness checks. Since the tax quota only changed
slowly over time (Wang, 1974; Liu and Fei, 1977), in column (1) of Table 5 we
change the dependent variable to taxpc1776, which is computed as the ratio of land
tax in 1820 to population in 1776; similarly, we use pdensity1776 (population in 1776
divided by area) instead of pdensity as a regressor. The results remain similar to those
in Table 4.
26 Historically, land tax quota may have been set in consideration of cropland as
well as population (Wang, 1974). In column (2) of Table 5, we change the dependent
variable to land tax per mu of cropland (taxpl). The results are again qualitatively
similar to Table 4, with the exception that minority1, ting, and dry_std are no longer
significant.
27 Table 5. Robustness Checks
(1) taxpc1776
army
pdprov
dpref
prov_capital
minority1
ting
riot2
coast
landpc
***
1.378
(0.460)
0.000391
(0.0181)
0.0775
(0.0586)
19.92
(31.51)
-46.36***
(17.33)
-55.71**
(22.77)
10.36
(16.24)
-89.05***
(30.82)
0.0253***
(0.00669)
pdensity
pdensity1776
agrisuit
area
longitude
latitude
elevation
river
dryness
dry_std
_cons
0.605***
(0.133)
5.355
(4.683)
-0.000144
(0.000334)
0.183
(2.362)
-9.181***
(3.141)
0.0485***
(0.0156)
5.769
(19.76)
39.63
(87.44)
150.7***
(39.43)
-34.83
(371.5)
28 (2) taxpl
0.000629**
(0.000302)
-0.00000468
(0.0000129)
0.0000572
(0.0000447)
0.00687
(0.0160)
-0.0151
(0.0104)
-0.0252
(0.0227)
0.0182
(0.0168)
-0.0495***
(0.0189)
-0.0000190***
(0.00000312)
0.000163**
(0.0000733)
0.00248
(0.00307)
-0.000000211
(0.000000245)
0.00306*
(0.00175)
-0.00532**
(0.00211)
0.0000426***
(0.0000125)
0.00861
(0.0125)
0.00636
(0.0338)
0.0300
(0.0278)
-0.169
(0.247)
N
R2
p-value for Hansen J
p-value for GMM C
F-Stat for army
F-Stat for pdprov
261
0.0839
0.281
0.006
10.649
414.657
261
0.177
0.679
0.0197
10.695
418.436
Note: Robust standard errors in parentheses. * p < 0.1, ** p < 0.05, *** p < 0.01.
5. Conclusion
We have introduced a theory of relative state power to explain taxation levels under
autocracy. The model used to advance the theory sheds light on a most important issue
in the political economics of development, i.e., taxation under autocracy. We have also
empirically tested the hypotheses derived from the model. The findings are entirely
consistent with the predictions of the theory.
The findings of this study have important policy implications. One of them is that,
to avoid political violence, a revenue-maximizing ruler should adopt different policies
on taxation across regions, imposing differentiated tax rates across regions according
to local conditions of incomes, effectiveness of state coercion and attitudes towards
violence. Tax rates should also be adjusted in response to changes in these conditions,
e.g., an adversarial income shock resulting from a natural disaster. It is also politically
beneficial to adopt lower taxes in earlier stages of development.
As fruitful as it is, this work is only a first step towards understanding the
critically important issue of taxation in autocracies in light of the theory of relative
state power. Some of the assumptions made in the model can also be relaxed to allow
richer results. For example, we can relax the assumption that the ruler never wants a
29 rebellion, to study when she might tax people like a roving bandit. The model can also
be extended in different directions for additional insights, e.g., asymmetric
information on worker types, endogenous odds of successful rebellion, the role of
public goods and that of technology (productivity). On the empirical side, it would be
most important and interesting to use cross-country data to test the predictions of the
theory in an international setting.
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32

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