Diplomacy and International Relationship of Song Dynasty
— A Quantitative Analysis
Introduction:
Song dynasty, due to its continuous defeats against the nomads, is usually viewed as a weak
dynasty. However, the population of north Song Dynasty is about double the figure of Tang Dynasty
and Song Dynasty also witnessed great progress in market system and technology1. The highest
total annual governmental income in the Tang Dynasty was more than 52.3 million, while the total
annual governmental income during the Tianxi period of the Northern Song Dynasty increased to
more than 150 million, about three times that of the Tang Dynasty2. The strong economic power of
Song and the weak military power of Song Dynasty seems to have challenged the conventional
wisdom that a strong state is a state which is capable of allocate resources. In this article, I will try
to explain why the prosperity of Song dynasty is key to its military weakness and its appeasement
foreign policy. Then I will try to modefllise the case. The model will be used to explain why some
countries tend to be more military while others put peace as their primary concern. The independent
variables used will be the relative wealthiness(rW) of the countries concerned, the ratio of
casualties(Ca), the relative cost of wars(rC) which will also take into account the chance cost of the
human resources. The dependent variable will be the overall surplus to resolve dispute by war.
QI, Xia. History of Economics of Song Dynasty. Shanghai People's Publishing House, 1987. 漆
侠. 宋代经济史. 上海⼈⺠出版社, 1987.
1
QUAN, Hansheng. The Relationship between Government Revenue in Tang and Song Dynasties
and Currency Economy, 1948. 全汉升. 唐宋政府岁⼊与货币经济的关系. 1948.
2
Outline:
I.
Facts of economy and political system of Song Dynasty and its diplomatic strategy
A. Strong economy and stable politics however…
B. …confusingly weak military capacity,…
II. Simplified model to account for the paradox between strong and stable political and economical
system and military weakness
A. … to be accounted in a simplified model,…
B. … which can have a broader use.
I.
Facts of economy and political system of Song Dynasty and its diplomatic strategy
In order to formulate a systematic explanation about the correlation between economic
prosperity and military weakness, this part will make a short summary about the history of
economy(A) and its international relationship characterised by weak military power and
appeasement policy(B).
A. Strong economy and stable politics however…
To provide the overall economic situation of Song Dynasty, this part will cover three major
components: the estimated Gross Domestic Production, the annual governmental income and the
development of commodity economy.
Firstly, the GDP and GDP per capita will be discussed. According to Augus Maddison, the
GDP of China in 11th century was about 23% or world GDP3, comparable to US’s economic
position in 2018: 23.91% of world GDP. However, this comparison is a bit misleading because
world economy was not established yet at that time. Thus, to understand Song’s economic power
properly, a vertical comparison among China’s dynasties is necessary. Considering the fact that the
territory controlled by Song Dynasty is considerably smaller than that of other dynasties, it would
be safer to compare GDP per capita of Song. Maddison estimated that GDP per capita in China was
about 600 USD by the USD value of 1990, this figure was only overtaken by contemporary China
in 1950s4. Quantitive history specialist of Hong Kong University of Science and Technology,
Guanglin Liu, the development of average income of Chinese citizen followed a U-shape, with the
peak at the end of North Song Dynasty and Qian Long era in Qing Dynasty. The average income in
Song was estimated to be about 7.4 Liang silver per year5. Liang in Song meant 31.25g, thus the
overall income is about 231.25g silver per year. This estimation is close to what Maddison
estimated. However, Madison’s estimation that China’s GDP per capita remained at about 600USD
from 1000s to 1800s has been contested by several Chinese scholars. Di Liu believed that among
Ming Dynasty, China’s GDP per capita was lower than 390USD, at some points even lower than
Angus, Maddison. Études du Centre de développement L'économie mondiale statistiques
historiques: statistiques historiques. OECD publishing, 2003.
3
4
Ibid
LIU, Guanglin. “The estimation of long-term development of income of citizens among Song and
Ming dynasty”, Journal of Tsinghua University (Philosophy and Social Sciences), 2009, No. 3. 刘光
临:《宋明间国⺠收⼊⻓期变动之蠡测》,《清华⼤学学报》(哲学社会科学版)2009年第3期.
5
320USD6. Guanglin’s estimation saying there is another peak at Qing Qianlong was also contested7.
However, Song Dynasty as a period when China’s economy was strong and stable is rarely
contested in terms of GDP.
Then, when it comes to the annual income of Song, the figure became surprisingly high.
Here, the annual income of Tang is compared with Song (see Table 1).
Table 1. The comparison of annual governmental income of Tang of Song. (Remade after Quan, 1948)
The table above compared the annual governmental income of Tang and North Song with
several typical period chosen, the data is taken from the research of Quan8. The units account for
three different kinds of governmental income: coins (Guan), and equivalent price of corn (Dan) and
cloth (Pi). Generally speaking, Tang’s governmental income is about one third to half of Song’s.
The huge diverse in 780-781 compared with 1021-1022 is because of the civil war was just
appeased in Tang during that time. Some scholars argued the hyper inflation of Song Dynasty and
LIU, Di. The economic study on the GDP of China in 1600-1840: a review on Angus Maddison’s
estimation of the GDP of Ming and Qing. PP. 26-29, 31. 刘逖 :《1600~1840前近代中国总量经济研
究———兼论安格斯 · ⻨迪森对明清GDP的估算》，第 26~29、31⻚。
6
LI, Daokui. JIN, Xingye. GUAN, Hanhui. “The GDP of China in history and its international
comparison: a review on bibliography”. China Journal of economics，Vol. 4, No.2: 14-36 June 2017. 李
稻葵，⾦星晔，管汉晖. 《中国历史 ＧＤＰ核算及国际⽐较：⽂献综述》China Journal of
economics，Vol. 4, No.2: 14-36 June 2017.。
7
QUAN, Hansheng. The Relationship between Government Revenue in Tang and Song Dynasties
and Currency Economy, 1948. 全汉升. 唐宋政府岁⼊与货币经济的关系. 1948.
8
believed that Song’s actual governmental income was lower than that of Tang9. However, Bao
answered that his understanding of Song’s hyper inflation is exaggerated10. Another critical point to
be put here is that Guan in Song is 770 coins, while in Tang is 1000 coins, which was neglected in
Quan’s research. These factors put into consideration, it is still safe to say, Tang’s governmental
income was only half to two thirds of Song’s.
Finally, the establishment of commodity economy will be discussed. According to Qixia’s
History of Economics of Song Dynasty, during Chunxi and Shaoxi, the non-agricultural tax income
account for about 80% of state income11, which is unprecedented and much higher than that of
Ming12 and Qing dynasty. Some argued that this is because in Song, there are tax collecting stations,
Qia, all among the main roads. The number of Qia in Song peaked at 2200 while in Ming, there
were only 11. However, this saying neglects an important economic principle, that is, if the
commercial tax is too high, there won’t even be trades in significant amount, neither will it be such
a huge amount of non-agricultural tax income, as predicted by Laffer Curve. Thus, it is fair to say
that the commodity economy was well established and the purchasing power of civilians were
strong.
B. …confusingly weak military capacity,…
LIU, Guanglin. “Market, war and fiscal state: a revisit on the fiscal policy of Song”. Journal of
history of Taiwan National University. Issue No. 42. 12.2008. pp. 221-285. 刘光临，《市场，战争
和财政国家——对南宋税赋问题的再思考》台⼤历史学报第42期，2008年12⽉，221-285⻚。
9
BAO, Weimin. “Another revisit on the fiscal policy of Song: answer to Mr, Liu Guanglin”. Journal
of history of Taiwan National University. Issue No. 46. 12. 2010. pp. 177-229.包伟⺠《再论南宋国
家财政的⼏个问题——答刘光临君》 台⼤历史学报第46期，2010年12⽉，177-229⻚。
10
QI, Xia. History of Economics of Song Dynasty. Shanghai People's Publishing House, 1987. 漆
侠. 宋代经济史. 上海⼈⺠出版社, 1987.
11
HUANG, Ray. Taxation and Governmental Finance in Sixteenth-Century Ming China, Cambridge
Studies in Chinese History, Literature and Institutions,1974.
12
In this subpart, a brief introduction will be made to give an overall view of Song’s military
weakness and its appeasement diplomatic strategy.
Song Dynasty which is historically divided into North and South marked by the loss of
former capital Kaifeng, Henan and the reestablishment of the state in Hangzhou, Zhejiang covered
319 years, thus also experienced changes in the diplomatic strategies. However, there were only
three major periods, early North Song Dynasty, revival of South Song Dynasty and the early
resistance against Mongols, of active pursuit of resistance or reconquest of the lost land. The rest of
Song diplomatic strategy is dominated by four major characteristics: 1. “Guarding the centre while
weakening the outside," the characteristic of only guarding several strongholds and key cities while
letting the majority of the state unattended. 2. Actively seeking peace. 3. Emphasising the
importance of moral influence. 4. Compromising and surrendering in front of a strong enemy13.
The first characteristic was determined by the highly centralised military system of Song
Dynasty, whose influence will be discussed in the following part, which is called “the division of
three powers”. The most trained and experienced army, and usually also the longest in number, was
settled at the capital under the administration of Shu’mi Yuan, however they only determine the
distribution of the military power, the department that really direct the military activities was San Ya
(“three bureaus”). While the regional and local army was put under Bing Bu (“the bureau of
army”)14. This military system efficiently prevented any local unrest and military rebellion to be
really challenging.
However, when it comes to the external wars, this system is extremely unstable and
inefficient. It took too long for the army to appear at the battlefield, especially compared to the
ZHANG, Yunzheng. The study on the diplomatic ideologies of Song. University of Henan, 2010.
張云箏. 宋代外交思想研究.河南⼤學,2010.
13
GONG, Yanming. “The study on the military structure of Song”. Journal of Tsinghua University
(Philosophy and Social Sciences), 2017, 2017,32(04):66-78+192. 龔延明.宋代軍權三分制研究[J].清
華⼤學學報(哲學社會科學版),2017,32(04):66-78+192.
14
nomads “on the horse back”. Thus, Song’s external wars were generally characterised by failures
(see table 2).
Table 2. Summary of the outcomes of major external
wars of Song (Yang, 2020)
Then the appeasement policy, which is characterised by Song’s giving silver and cloth to
other states in exchange for peace, of Song will be illustrated. This policy is mainly used towards
Liao, Xia and Jin (see Table 3).
Table 3. Total silver and cloth given to three major military threats of Song (Yang, 2020)
The table is made after the treaties signed by Song, the historical documentaries made by the
chancellor of Yuan, Toqto’a, of both Liao1516 and Jin17, together with some articles on this topic18.
Liang, under Song’s standard, was the same value as Guan, though certain fluctuations in practise
existed. The same with Pi. Thus we can add them up in order to compare that amount with the
annual governmental income of Song (see Table. 4).
Toqto’a, “The fifth part of th history of Shengzong”, Liao Shi, Zhonghua Publishing House,
1974. Page 153-166. 脱脱，圣宗本纪五，辽史，中华书局，1974。153-166⻚。
15
Toqto’a, “The second part of the history of Xingzong”, Liao Shi, Zhonghua Publishing House,
1974. Page 225-236. 脱脱，世宗本纪，辽史，中华书局，1974。225-236⻚。
16
Toqto'a, “history of Xizong”, Jin Shi, Zhonghua Publishing House, 1975. Page 69-90. 脱脱，熙
宗本纪，⾦史，中华书局，1974。69-90⻚。
17
ZHU, Ruixi. “The annual payment for peace during Song Dynasty”, The study on Yue Fei, No. 3
(1992) 朱瑞熙：《宋朝的岁币》,《岳⻜研究》第3辑（1992）
18
Table 4. The amount of silver and cloth given to other states compared to the governmental income
throughout Song (Yang, 2020)
* Some of the years the amount was not paid due to the outbreak of war
** This percentage is calculated with a certain degree of simplification: the annual governmental income of
North Song used that of 1048-1049, that of South Song used the figure of 1180s.
*** Theoretically, Liang and Pi were of same value, thus in this table, they were not separated, however,
the price of them fluctuated throughout history.
**** The figure here didn’t sum up the figure in Table 3 because Table 3 included several one-time
payments
***** Xia’s payment also included certain amount of tea, but according to the price of Tea in Song, that
amount is negligible.
The price of silver, cloth and tea are mentioned in the book of Wencheng Wang1920.
Although a lot of simplification and assumptions were made when making Table 4, it is still clear
that Suibi (“annual payment by Song to maintain peace”) was not a huge amount compared to that
of Song governmental income, contrary to conventional wisdom saying that Suibi exerted a huge
burden on Song and led to hyper inflation of Jiaozi (“the paper currency used in Song”). If we
WANG, Wencheng. The study on the monetisation of silver in Song. Press of University of
Yunnan, 2001. Page 174. 王⽂成，《宋代⽩银货币化研究》，云南⼤学出版社2001年版，第174
⻚。
19
The appendix of the fluctuation of the price of silver in North Song. Ibid. Page 171-178. 《北宋
银价变动简表》。同上，第175-178⻚。
20
compare Suibi with the military expenditure of Song to maintain army (see Table 5), it is clearly
favourable for Song to use appeasement policy than turn to real wars.
Table 5. The expenditure on army during North Song Dynasty (Yang, 2020)
* Total number of army is calculated by the number given by documents, certain amounts of exaggeration
is very likely. An estimation of vacancy rate is about 30-40%.
** The expenditure is calculated by the statement of Cai Xiang, a stateman of Song, in 1065, that central
army cost 50 Guan a year and local army 30 Guan a year. Here the weighted average is used.
This table is made with the data of the amount of army provided by Zhimiao Zhang21, the
expenditure on army provided by Cai Xiang22, the governmental expenditure used the data of the
most close year.
II. Simplified model to account for the paradox between strong and stable political and economical
system and military weakness
The economic and diplomatic situation of Song was introduced in general in previous part,
some explanations about why Song would prefer to use appeasement policy were mentioned, in this
ZHANG, Zhimiao. A brief study on “San Rong” of North Song and its harm. Journal of Xinyu
School. 2014,19(02):120-122. 張⾄邈.淺析北宋“三冗”現象及其危害.新余學院学報,
2014,19(02):120-122.
21
CAI, Xiang. “Guo Lun Yao Mu”. Si Ku Quan Shu. Chapiter No. 22. Zhonghua Pressing House.
Aug. 2003. 蔡襄。《国论要⽬》。 《四库全书》，卷22 中华书局 2003年⼋⽉。
22
part they will be simplified into several key aspects (A). Then the flaws and limitation about the
model will be discussed, some of the cases that can also be explained by this model will be
mentioned briefly (B).
A. … to be accounted in a simplified model,…
In this part, I will only try to establish a correlation formula. A causal model is impossible
for now because the only case studied here is Song China. Even if the model is based on the whole
history of human kind, it is still impossible to make it causal from empirical study. Some of the
reasons will be provided here or in the next subpart.
First to be discussed is the relative wealthiness of the countries concerned (rW). Here rW
will be accounted for using the relative GDP per capita. This figure is important because it is an
important index of the opportunity cost of sending a man to frontier and also illustrates what it
really means economically to lose a man in the battle. Because of the lack of data about GDP per
capita about Liao, Jin and Xia, this figure will be estimated by the estimation of the GDP per capita
of immigrants countries in Europe given by Maddison23, which is approximately 400USD, adjusted
as USD in 1990, per year while that of Song is around 450USD when established and soon reached
600USD. The difference isn’t that huge in absolute amount but we need to take into account the
existence of subsistence level, which is the minimum income to make one alive. Only GDP per
capita minus that amount can be considered the real surplus of a man, that is to say the “economic
value” of him. The subsistence level is estimated to be around 200 euro to 300 euro in 201624, take
Angus, Maddison. Table 3-1b. PIB par habitant et écart entre les régions, 1000-1998. Études du
Centre de développement L'économie mondiale statistiques historiques: statistiques historiques.
OECD publishing, 2003. Page 134.
23
Subsistence level - on the way to better support for deprived people, Center for Policy Studies,
EU, 2018 Elatusmiinimum – teel parema toeni puudustkannatavatele inimestele, Center for Policy
Studies, EU, 2018
24
into account the inflation and exchange rate, that would be around 129.35 USD to 194,02 USD in
1990. Here the middle value is taken to be 161.68 USD. So the surplus would be 238,32 USD
against 438,32 USD. That means the opportunity cost of sending one man to battle is 1.84 times
higher than that of Liao, Jin and Xia (rW of Song is 1.84, of Jin is 1). rW is also important to
calculate the potential economic benefit one country may get. Casualty ratio (rCa) is also an
important factor if we want to figure out the benefit and cost of war. Here, in order to simplify the
case, casualty ratio will be set at 5:1, this is estimated from several major campaigns among Jin and
Song (rCa of Song is 5, of Jin is 1). The relative cost of war, Song’s military expenditure has been
discussed before, here Jin’s structure of military expenditure will be used to mimic Jin, Liao and
Xia because Jin is the only country with sufficient data. The annual income of military official,
Qianhu, (“the officer of one thousand”) was 50 Liang, barely more than the soldier of Song’s central
army. That of high rank soldier is 10 Guan, low rank soldiers only have 4 Guan25. This is
considerably lower than that of Song. The supply of the army, for nomads, is usually only the feed
of horses and men because they are typically not armoured and if they attack China, usually they
can get supplied directly from robbing villages so the cost of transportation of supply is neglected.
Raising a horse for riding in China is about 5000RMB now for a year, adjusted to USD in 1990
would be 407,4 USD, approximately 948g silver, that is to say 28.73 Liang. That is to say, overall,
the average cost of maintaining a soldier in Song and Jin had a ratio of 1.5:1 (rAM of Song is 1.5,
of Jin is 1). A note is to be added here, the cost of army in Song didn’t take into account the cost of
horses and supply. Although the number of horses in Song may not be large, the cost of supply is
not negligible. Thus the real ratio might be higher than 2. Two time factors will be added time
engaged in war (tW) and time of peace (tP). The relative size of army will be used as (rSA),
however to simplify, we assume the soldiers involved were the same in ratio with that of the army
WANG, Mingqian. A brief study on the fiscal system of Liao and Jin. Journal of Changchun
Higher School of Finance, 2012(02):1-7. 王明前.遼⾦⼆朝財政體系初探.⻑春⾦融⾼等專科學校學
報,2012(02):1-7.
25
in reserve. (0.8 for Song, 1 for Jin) The average life span at that time was about 40. Thus, we
assume the people robbed have about 20 years of wealth accumulation and the people killed can
continue to produce 15 years of wealth.
Now, a formula considering solely economic factors can be formulated. The ‘ is used to say
the figure should use that of the other part.
Surplus of war = wealth can be gathered by robbing - opportunity cost - the cost of
life - the cost of maintaining an army
=20*a’*rW’*rCa'-b*rW*tW/(tW+tP)*rSA-a*15*rW*rCa-rAM*rSA*(tW+tP)/tW
For Jin:
=20*a’*1.84*5 - b*1*tW/(tW+tP)*1 - a*15*1*1-1*1*(tW+tP)/tW
=180a’ - b*tW/(tW+tP) - 15a - (tW+tP)/tW
For Song:
=20a’*1*1 - b*1.84*tW/(tW+tP)*0.8 - a*15*1.84*5-1.5*0.8*(tW+tP)/tW
=20a’ -1.472*b*tW/(tW+tP) - 138a - 1.2*(tW+tP)/tW
(a here is a parameter to account for the loss of life, b here is the number of soldier involved,
altogether as parameter for the scale of war)
Consider two situations, it is clear that Song would prefer to have fewer wars where fewer
people are involved. However, for Jin (or Liao and Xia), their surplus of war is largely positive.
That accounted for the reason why Song as a state don’t want to enter into wars. Other
reasons such as the lower status of military officials compared to Jin, the centralisation of army of
Song which erased the possibility of internal turmoil thus in the long run lowering the battle
capacity of soldiers may also be taken into account.
What can be concluded in the formula is that approximately the country with higher rW*rCa
will be reluctant to turn to war. In our case, compare the military expenditure of Song and the
possible loss of GDP due to war to the amount of Suibi. Appeasement is the most rational choice.
The overall Suibi paid was barely two years’ military cost.
B. … which can have a broader use.
The situation where there is an imbalance between military and economic power happened
frequently in human history. The imbalance is characterised by a stagnation of individual combat
power compared to economic growth. Thus, even if individual combat power is really higher than
competitors, if the economic gap is larger, the state will not turn to war either. We would use that as
a reason to explain why Tang didn’t put Huns and Xiyu in direct control as constant war was
rationally avoided by Tang. However, in that case, the cost for supply would have significant
influence and should be taken into the model.
This kind of situation can also be witnessed in Europe when Byzantine and Rome
continuously paid certain amount of money to nomads to maintain peace on the border.
More contemporarily this can be witnessed in US’s invasion into Afghanistan.
This model can be made more flexible and powerful if we compare the surplus of war and
surplus of cooperation. Further more, if we broaden the concept of war to competition, we can
compare the surplus of competition to the surplus of cooperation. However, the second broadening
will require the model to include far more things than it is now.
Some limitations on this model:
First and more obviously, in this model, states are economically rational. That is to say, they
only consider economic benefits of the state and they are completely precise in the calculation. This
is completely impossible, in real world, we have ideology, patriotism and cultural differences in
play. Thus, the mental benefit might be different with the economic one. For example, taking
Jerusalem is much more beneficial than the city itself. The leaders of states are not at all rational.
Secondly, this simplification made state a unit. However, in real world, there are
sophisticated internal structures of states. For example, a state may be not benefitted as a whole
when it comes to war but if the dominant group of people are benefitted, they may force the state
into war regardless of the loss of the people.
Thirdly, the model’s data is sometimes very difficult to collect and is a backward induction.
That is too say, I am trying to account for why an event is happening from its outcome. However, in
real world, the outcome can not be predicted.
Even with the flaws mentioned, the model is still useful to account for certain historical
events and predict which states are more likely to turn to war and conflicts as a solution.