Global COE Hi-Stat Discussion Paper Series 254

Research Unit for Statisticaland Empirical Analysis in Social Sciences (Hi-Stat)

Rationality, Market and Rural Credit:
Case of Fude Association

Hi-Stat Discussion Paper

Kaixiang Peng

November 2012

Hi-Stat
Institute of Economic Research
Hitotsubashi University
2-1 Naka, Kunitatchi Tokyo, 186-8601 Japan
http://gcoe.ier.hit-u.ac.jp

Rationality, Market and Rural Credit: Case of Fude Association 1
Kaixiang Peng 2
Abstract: Researches about traditional rural credit always claimed it was composed byreciprocal credit between villagers and usury from outside societies. Contrarily, the credit
operation of Fude Association in a village of Taiwan shows that there is no clear classification
between reciprocal credit and usury, and the divergence in interest rates and loan sizes can be
explained by selections in an optimizing model. Meanwhile, this paper finds some special
deviations from rational decision, mainly according to the calculation cost. However, suchdeviations decreased when marketization developed and the benefit of rational calculation
increased, which illustrates the internal consistency between market economy and rationality.
JEL: D01, G23, N25
I. Introduction
In literatures about traditional rural credit, there also exist different traditions of study. In fact,
as rural credit has history much older than the development of modern market economy, kinds of
documents different from market records are left and illustrate the complex character of it. Thus,
it’s not surprising that, in the mainstream view, rural credit is guided by customs or non-economic
relationships at least before modernization. In a classic research about south-east Asian ruralsociety, Scott (1976, p.13-29) argues that surviving is the fundamental subject of traditionalpresents, which leads to the rural reciprocal relationship, while usury is left to despairing credit
just at lean years. Furthermore, while surviving desire is not in accordance with profit
maximization, marketization or capitalization will destroy traditional reciprocal relationship andresult in the more miserable situation of peasants.
For researches about rural credit in traditional Chinese society which this paper will focus on,
echoes of Scott (1976) are obvious. For example, Huang Zhongzhi (1992, p.111) classifies rural
credit into two types: one is reciprocal interest free credit between villagers without weighing
gains and losses, 3 and the other is loans from outside societies, always coming to be usuries to themiserable peasants. However, there are some subtle differences too. Although Scott (1976, p.58-90)
regards commercialization or marketization as a destruction factor together with colonialism,
Huang Zhongzhi (1992, p.305-310) tries to explain it by involution within family, which
contributes to the small peasant production persistent in the long history of China. Kishimoto Mio(2010, p.61-81) holds some similar viewpoint with Huang Zhongzhi (1992) as she pays attention
to the instability of traditional China caused more by market fluctuations than by natural disasters,
though she was obviously affected by Tawney’s describing of Chinese peasants’ struggle forsurviving cited in Scott (1976, p. 13-29). However, if market institution is active in the economic
relationship between families, there shouldn’t be natural division between reciprocal credit andusury, and, on the contrary, both of them should be the results of economic conditions. In fact,1

Thanks for the financial support from HKIHSS of Hong Kong University and National Natural Science
Foundation of China (No. 70928002). In addition, Yuru Lin provided generous help when I collect material in theInstitute of Taiwan History, Academia Sinica. It is especially appreciated by the author.
2
School of Economics, Henan University, Kaifeng, Henan Province, China. Email: kaixiangp@qq.com.
3
Obviously, we need other conditions, including extremely low marginal return of capital and symmetry of credit
demand, to reach the point that surviving economics means interest free. However, such economic reasoning is
scarce in Scott (1976) and Huang (1992).

Scott (1976, p. 13-25) has tried to provide an economic explanation for surviving economics, but,at the same time, it always tends to be neglected and there seems to have an independent moral
principle when he argues about the functions of surviving economics. It goes further in Huang
Zhongzhi (1992, p.309), where small peasant rationality is stressed to be in contradiction to
optimizing principle, and hence, marketization is thought to occur without market rationality in
traditional China.
However, Peng, Chen and Yuan (2008) try to explain China’s rural credit by optimizing
activities in a competitive market. They show that credit, either usury or reciprocal low interest
rate loans, can be analyzed in a united model where usury is just a result of the higher average costof micro loans. They also find that there is no significant interest rate difference between loans
from villagers and other sources including professional moneylenders, if other conditions
controlled. This is quite in accordance with surveys of 555 MFIs (Microfinance Institutions) in2006 held by CGAP, which confirmed the inverse relationship between loan’s individual size andoperating expenses while scale benefits had been mostly captured by MFIs (Rosenberg et al.,2009). In addition, Peng, Chen and Yuan (2008) classified interest rate as implied and noted in
credit contracts. For the latter type which looks quite regulated, customs or some similar rules
rather than economic force might have stronger effect, although economic force could still workby other ways except interest rates, including loan screening, payment method and so on.
Although such regulation of noted interest rate leads to some deviation from normal market
mechanism, it is quite different to the description of Huang Zhongzhi (1992). If we turn to themicrofinance case introduced in this paper, more interesting deviations will be found. Then, why
they happened? How did they interact with market institution if it still played the main role?
For biases from idealized rationality or market equilibrium, researches about bounded
rationality or behavioral economics provide another angle. A famous example of Kahneman (1984)
is loss aversion, which can explain the conservative attitude to a bet even if it is fair. This is quite
similar with the conservative impression about traditional peasant. It may also play a role in thegenerally depreciating attitude toward usury even when it satisfies economic rationality or whatcalled “small peasant rationality”. Meanwhile, behavioral economists regard the pattern ofdecision making as psychological, which has little relation with social background. For example,
M. Keith Chen, et al. (2006) suggests that that loss aversion even extends beyond humans andmay be innate rather than acquired by learning. However, all above cited literatures about
traditional credit care about the social background deeply, which implies that the importance ofbiases from economic rationality should not be same under different situations and it should bebetter to be estimated empirically. Another related point is the bounded rationality. Restriction of
information and calculation ability could affect credit decision greatly in traditional rural society
as there were no statistic publications and modern mathematical or financial theory was notavailable. Since there are so many possible explanations about bounded rationality, it’s clear thatonce we want to testify the real importance of some specific bound, the problem also becomes
empirical as Rubinstein (1998, p.16) noted.
Therefore, the purpose of this paper is not to discuss the rationality behind rural credit bydefinitions or theories but to study it through an historical case. We will research the credit
relationship of the Fude Zhengshen Association (FDA) in Rinan Village, belonged to Tachia
Township, Taizhong County of Taiwan, mainly through its account books from 1915 to 1943,
which is kept in the Institute of Taiwan History, Academia Sinica. The FDA was set up to sacrificethe fortunate (Fu) and moral (De) god (Zhengshen) whose formal identity was the village god withthousands years tradition in China. In its operation, a fund was gathered and lent to its members
who were also the villagers. By this way, villagers got a source of credit and the interest provided
funds for FDA’s running expenses at the same time. Though it’s a too inconspicuous example toreach a general conclusion about traditional rural credit, there are reasons to select it as a research
object. First, we can get the nearly complete record of FDA’s credit operation from the accountbooks which show FDA’s interest rate rules and the reaction of its members. Second, theborrowers’ names were recorded in the books and they always borrowed repeatedly which makeus could control their personal characters. Combined with the detailed chorogophic materials, we
can get even more important personal information. The last and most important reason is there haschanges in the credit operation of the FDA which happened in the background of Taiwan’s
modernization. This provides us a chance to test different hypothesis about relationships between
rationality, traditional economy and market.
In the next section, the material and its background will be described in more details. Then,we will explore the interest rate of FDA, including its different forms and rules. In the fourth
section, the rationality behind the interest rate rules of FDA and the reactions of its members is
discussed and different hypothesis are tested. The last is a conclusion.
II. Material and Background
The account books of FDA have two volumes, containing eighties loan records from 1915 to1943. For every year, the records were updated at the night of Chinese calendar’s Jan. 15. As thebirthday of the village god is Feb.2 in Chinese calendar and Jan. 15 is an important festival justbefore it, villagers would gather at the night of Jan. 15 for celebration and take this opportunity toarrange the forthcoming sacrifice. Because the head of FDA, called censer head (Luzhu), isrotational, new head will be decided at this night too. Then the last head settled accounts of lastyear and turned the fund and account books to the new head. In order to settle accounts, every
lending, including its borrower’s name and its interest rate, would be recorded. During this annual
gathering, interest rate rule claimed by the FDA would be discussed too, and there was once thatthe members agreed to change the interest rate quotation by consensus at 1923.
Most of the loans were recorded in the money unit, Yuan. It’s the legal money in Taiwan after
the monetary reform carried out by Japanese colonial government at 1910s. Before 1930s the legalmoney was on the gold standard, but it turned to fiat money step by step after then. (Su Zhen,
1954, pp.9) The value of one Yuan during 1920s and 1930s was about 0.7 silver tael of Shanghai
and could buy about 10 kg. rice in Taizhong 4. (Statistics Department of Taiwan Chief Executive
Office, 1946, Tab. 320, Tab. 402) As Taiwan had finished monetary reform before mainland China,
money unit in FDA’s account books is much simpler. But there still has exceptions. Fractional
money in silver appeared several times and some of them were recorded in their unit inheritedfrom currencies before monetary reform without converting to Yuan. Their conversion would bevery complex according to the monetary institution before monetary reform, 5 but, fortunately,
there were cases in the account books to show that the conversion between fractional money and
Yuan for our sample had simplified to decimalism directly. We apply this principle to do
conversion when needed.
4

We change the unit from Dou to kilogram using the ratio 1: 7.8, which is documented in Chuan Hansheng, et al.
(1975).
5
Refer to Su (1954, pp.4).

Thus, we get 83 loan records according to 37 borrowers for research in this paper. Most of
the borrowers were personal, but a few of them may be families which were entitled by house (Wu)or clan. Despite the fact that Rinan was a normal village with about only one thousand people,
from the local chronicles, we can find relatively numerous biographies referring to kinds of local
elite who had affected the local society. For the 37 borrowers in our sample, two were recorded in
the chronicles. One was surnamed Guo and had the family seniority as Mu, which means it
belonged to the richest family of Rinan village and even Tachia Township during the early 20th
century. They leased land in the township and established a rice factory near the rail station when
it was constructed in 1922. Guo Murong, the representative of his family, was active in Taizhong’s
industrial society and became one of the managers of local cooperatives promoted by Japanesecolonial government. Another was Ye Qingjiang who was a landlord of Rinan village and famousfor his activity in charity. (Liao Ruiming et al., 2007, p.1520, p.1562) In the borrowers, ten
surnames were found, but 80% of the 83 loans were lent to the four main surnames including
Chen, Guo, Lin and Ye. This is in accordance with the surname distribution of residents (LiaoRuiming et al., 2007, p.1438).
Apparently, the credit of FDA was restricted to villagers and should be classified toreciprocal relationship if we accept definition of Huang Zhongzhi (1992, p.111) in his description
about mainland China. Of cause, there were many similarities in the popular organizations andpractices of mainland China and the Chinese immigrant society of Taiwan. In fact, except forresidents surnamed Guo who might source from the aboriginal, all other main surnames cited
above immigrated from Fujiang and Guangdong of mainland China. (Liao Ruiming et al., 2007,
p.1430) Hence, it’s not surprising that the FDA kept typical Chinese tradition in its religion andoperation. However, the traditional form itself does not provide support for reciprocality, as it’s
obvious that the primary function of FDA’s loan is to fund its operation. Although the FDA could
act as an institution for local charity if it could be sustained, market method may be more efficient
before this situation reached. Especially, when the development process of Taiwan is considered,
we would be more conscious about reciprocality. It’s known that immigrants of Taiwan’s west
coast, where Rinan located, were composed of croppers and merchants from southeast China, whowere not only for surviving but also for profit. That would destroy the symmetry of credit demand
between residents while it is crucial for the reciprocal relationship to last. Another related point isthat more definite institutions, including land ownership registration, are believed to be founded
when the exploitation of Taiwan started in Qing Dynasty (David Faure, 2010, p.14), which would
not only promote kinds of immigrants but also make market institution play a more important rolein the immigrant society.
Meanwhile, as the discussion about account money has shown, the colonial government by
Japanese shouldn’t be neglected. In the view of Scott (1976, p.58-90), colonial government tended
to destroy the traditional surviving economics by normalized institutions, such as stiff taxation andmodern legal systems. As to Taiwan’s situation, some similarities can be found, including
requisition of common land and clarifying land ownership. At the same time, colonial government
seems to be more success in Taiwan which is supported by the evidences of per capita income andwelfare status (Wu and Lu, 2008). Modernization started in this period with the improvement oftransportation, water conservancy, financial institutions and so on. (Zhang Hanyu, 1955, p.74-79)
One most important change to Rinan village during our researched period was that the coast
railway went into operation and a station was set at Rinan in 1922. The convenience caused bythis traffic improvement would provide more economic opportunities as proved by the increase of
population (Zhang Qingzhong, et al., 2004, p.195-198). 6 Although traditional handicraft industry
and seaport economy faced more competing after the railway operated (Chen Yanzheng, et al.,
1989, p.213), these side effects seemed much weaker for Tachia Township. Except for the
improvement of traffic condition, cooperative was set up at Tachia in 1915 and Guo Murong from
Rinan was entitled as a director (Liao Ruiming et al., 2007, p.1562). However, there is no material
to show its effects on local society, and we will discuss it in next section. As a whole, economic
status was more likely to be improved during this period and threaten to survive should be
weakened, which was on the contrary to Scott (1976, p.58-90). Although the FDA kept its
traditional appearance, its substance would have been changing in the modernization process.
On the other hand, as the FDA was a traditional Chinese organization, conflicts between its
practice and the colonial legal system happened inescapably. For example, law of 1923 claimed
that the property of god association was not owned by the association but by its members, whichchallenged the traditional operation (Lin and Huang, 2001, p.268). Further, the “Japaneselizing”(皇民化) movement began in 1941 gave the heaviest beat to the god associations, and Chinese
belief and culture was restrained greatly in this movement (Lin and Huang, 2001, p.268). From theaccount book of FDA, we can see that the cash credit disappeared after 1941. It seems thatmovement had much greater effect than law to local society, as the relationships in local society
were reshaped more dramatically by forces in the movement. Since what we will research is therelationships besides politics, the period from 1915 to 1938 is suitable for there was no great
movement happened.
III. Exploring interest rates of the FDA
In the FDA’s interest rate rules, the key point is that two stages were divided by the size ofloans. For loans less than one Yuan, annual rate was 100%, while, for loans above one Yuan, it
was just 50% before 1923, then adjusted to 30% and further dropped to 20% after 1933. These
were the claimed interest rate, but exceptions existed in practice. For example, for loans exceeding
10 Yuan or with long-term, interest rate would be discussed specially and always reach a favorable
level below 15%, considering such loans could save transaction costs compared to tiny andtemporary lending. Measured by the interest rate level, especially for the micro loans, thereciprocality suggested by Huang Zhongzhi (1992) can’t hold. Moreover, even compared withother god associations whose interest rate was always 20% or even lower7, the FDA’s credit seems
not only close to usury but also illegal. However, we should notice that normal god associations
loan their fund to the head in lump sum, and then, their interest rate should be correspond to themost favorite type of FDA. Therefore, the FDA didn’t require higher interest rate in fact. On thecontrary, it was more flexible to the members as the association met micro demand directly andprovided more selections for related borrowers. Since the difference of interest rate cannot be
attributed to social relationships, the classification between usury and reciprocal credit argued by
Scott (1976) or Huang Zhongzhi (1992) also can’t be valid, while size affect shown by Peng, Chen
and Yuan (2008) would work. An additional question is that why the FDA made interest rate rules
6

See also Wu and Lu (2008).
A collection of Taiwan’s materials can refer to Lin Zhen (1961, p.260-302). As the tradition of god association
could be formed before the exploitation of Taiwan, situation of Fujian is comparable too. From Yang Guozhen, etal. (1990), we can even find loans from associations whose sacred god was the same as FDA. Their interest rates
were about 10% to 20% which was much lower than FDA, while their loan sizes were large compared to loans ofFDA.

7different to other similar associations. It’s perhaps that the interest rate regulation was weaker inthis obscure village, or, there were fewer villagers who involved in great business and could
absorb a large sum at one time. Any way, it’s fortunate for our research because the seemingly
trivial status of Rinan village made interest rate more flexible, which means more could be
discovered in the interest rate.
Besides cash loans, there were special loans of sacrifices, such as orange and dishes, whose
annual interest rate was 100% in kind and this rate was kept until 1943 when the account bookended. 8 Such loan in kind was always as tiny as one or two oranges, one bowl of dishes, and soon. Its interest rate was the same as small cash loans too. Meanwhile, there may be special
meanings in the sacrifice loans or we have to suggest that demand about such ordinary food is asurgent as cash. Actually, similar customs could be found extensively in the Qing Dynasty. For
example, in Beijing, people borrowed the paper ingot which was a special sacrifice to the god of
wealth, and paid back doubled to win the god’s blessing (Li Hongruo, 1886, pp.3; Chong Yi, 1982,p.87). Same practice in Shanghai was recorded, but it was under the name of a god governing theunderworld (Gu Bingquan, 2001, p.33). It’s more exaggerated in Guangzhou, where peopleborrowed several wen from the Kwan-yin Bodhisattva and paid back tens and hundreds times in
the next year (Chen Kun, 1996, p.2801). These ritualized activities could be ascribed to Frazer’s“Homoeopathic Magic” (Frazer, 1922, p.12) perfectly. As orange and dish were homophonic withpropitiousness and treasure separately in Chinese, borrowers paid back double symbolizing their
propitiousness and treasure would be doubled too. In this operation, the 100% or higher interest
rate is more like a special bribe to the god than usury under the name of god. Of cause, theincentive behind related activities also exposed that exorbitant repayment, including interest rate
as high as 100%, could be accepted by the popular moral, which is contradictory to the critiques ofusury since Aristotle in the Western history.
The interest rate of sacrifice loans kept constant according to the mental or religious
implication in such ritual operations. As a custom, it is important and interesting for a traditionalsociety, but the sacrifice loans are very tiny in amount and their economic meaning is limited
actually. More importantly, the benefit of these loans lies in the “Homoeopathic Magic”, which isquite different to normal credit we care about in this paper. For these reasons, we will turn to cash
loans below. From fig.1, where the interest rates of settled transactions are plot point by point, it’s
clear that they drop significantly. As described above, the quoted interest rate for loans exceeding
1 Yuan decreased step by step, but, the more important reason is that there were much fewer microloans after 1923. This expanding of loan size will be discussed in next section, because it may betactical reaction to the adjustment of interest rate rules, which need special analysis. Now, let’slook at other exogenous factors which might work directly to the decrease of interest ratequotations for loans above 1 Yuan.
From fig.1, the interest rates of banks, including the Taiwan, Zhanghua, Japan and Shanghai
series, dropped during 1920s too, but their time point was not in coherence with the FDA, as
far-east finance market was still in crisis and bank interest rate kept high when the FDA cut down
its interest rate in 1923. In fact, far-east industry and financial market flourished during the FirstWorld War which foreshadowed depression after the war. (Chen, 1953, p.146) Meanwhile, themarket turbulence of world around didn’t affect FDA, and, even the interest rate of Zhanghua
Bank, a modern financial institution relatively near to Rinan, kept a remarkable gap with market
8

There was only one exception in 1938 where meat pie was borrowed with 50% interest rate.

centers at Taipei, Tokyo or Shanghai. If we confess the financial integration between Rinan andthe institutional financial market was still very weak, had it improved during 1920s? It’s true tosome extent as the interest rate gap between the FDA and banks decreased, and some similarity intheir trends after 1920s, which will be tested further, appeared. However, judged from their changeorder, this is mainly the result of FDA’s interest rate cut, and there was also little direct evidence
that institutional finance contributed to it. A difficulty in estimating the role of institutional financeis that Tachia cooperative, the first modern financial institute near Rinan, was set up in 1915,
while we have no material about the interest rate of FDA before then to discuss the function of thiscooperative directly. However, comparing to the normal situation of Taiwan and Fujian since Qing
Dynasty 9, the interest rate of FDA before 1923 was still quite high, closely to the upper limit of
popular private interest rate. It’s nearly impossible that the interest rate of FDA would be higher
before 1915 and decrease after the cooperative founded.
If we turn away from development of institutional finance, the most coincident events are thecompleteness of lengthwise railway and the foundation of Rinan Station at 1922. As we havediscussed, traffic improvement provided more opportunity which would increase credit demandand decrease transaction cost. When villagers could get loans at lower price by other ways and had
more demand for loans exceeding one Yuan, they would have incentive to cut down the interest
rate for larger loans and related suggestions would also have more opportunities to reach aconsensus in the meetings of FDA.
Fig. 1 Trend of Interest Rate: Taiwan and around100

Taiwan.Bank
Zhanghua.BankJapan
Shanghai
FDA

Interest Rate (annual, %)

50
30
20
15

10

0
1910

1920

1930

1940

Year

Source: Taiwan and Zhanghua Bank, Chen Rongfu (1953); Japan, Homer and Sylla (1996); Shanghai,
Shanghai Branch of PBC (1960).

In order to explore the interest rate of FDA formally, we next regress interest rate against
related factors to discriminate their effects. Our basic regression function is specified as below:
3

rate = β 0 + ∑ β1i Di + β 2 log( prin) + β3term + β 4bankr + β5train + θ ⋅ debtor + µ (*)
i =19Related discussion can be found in Wang Siqing (1994) and Peng, Chen and Yuan (2008).

In (*), Di is a dummy variable, valued one if principle exceeds one Yuan in period i, used tocontrol the quotations of three periods: 1915-1922; 1923-1933; 1934-1938. Though scaleeconomy is embedded clearly in the quotation of FDA, it’s not captured completely as thequotation was still too regulated and there were cases that the interest rate was decided specially.
We add the logarithm of principal, log(prin), to represent this further effect. A related item is term,
for the effect of longer term is similar to larger scale. Bank interest rate and the foundation of
Rinan station are included by bankr and train. For bankr, we use the lending rate of Taiwan Bank
lagged one year, 10 and train is a dummy variable valued one after 1922. In order to control
personal characters whose importance in personal credit is often claimed, dummies represent
different debtors are included in (*) by the dummy vector named debtor.
Table 1 reports the main regression results. In result (1) and (2), we control personal
character by 35 debtor dummies, and only scale economy represented by the quotation rule andprinciple is significant steadily. Since debtor dummies are too many compared to the number ofobservations, which makes their coefficients bewildering and stochastic even if some of them aresignificant, we drop the dummies except those according to Guo and Ye whose personal characterare outstanding as introduced above. Then, we get the result (3). It’s strange that Guo’s coefficient
is significantly negative while that of Ye is very insignificant, though they should both have good
credit. Check of the data shows that this is due to an outlier where Guo borrowed 50.59 Yuan at
the minimum rate of 10%. If this observation is omitted, result (4) shows that both Guo and Ye
become very insignificant, while bank rate and train are significant when Guo and Ye are droppedin (5). It’s not surprising to find that personal character has no significant effect on interest rate,considering games of the FDA members were repeated, their information was nearly transparent
and they have the same belief of Fude God. Meanwhile, it should be noted that bankr could only
explain a small part of the change of FDA’s interest rate as the coefficient of period is in muchgreater scale. On the contrary, the importance of train is more than it appeared since not only its
main effect has captured by period dummies, but also integration between interest rate of bank and
FDA after mid 1920s should be attributed to it as discussed.
A possible problem for the regression is the endogeneity of principle. As we will discuss later,
if the quotation is known ex ante and there is breakpoint at one Yuan, chance for arbitrage willappear, which makes loan size endogenous. This means the scale effect represented by principal orloan size in (*) may be endogenous, but this is quite weakened when interest rate rule, which is themain source of endogeneity, is included in regression. Meanwhile, for loans whose interest rate
deviate from quotation and decided by consensus specially, principal is decided firstly, and interest
rate, which becomes ex post now, is very difficult to expect by information out of (*). In either
situation, the endogenous problem is nearly excluded in fact. However, in order to weaken theendogeneity further and understand the scale effect better, in specification (6), the effect ofprinciple for loans below 1 Yuan and exceeding 1 Yuan is discriminated. The result shows that thenegative relationship just comes from loans exceeding 1 Yuan. Actually, if the scale economy lies
in some fixed cost as Peng, Chen and Yuan (2008) suggested, it is easy to understand that evendouble interest of micro loans can’t pay the cost and the 100% interest rate of FDA is still
restrained, which explains why the scale economy doesn’t work below one Yuan. We will touchupon the interest rate limit problem again in discussion about the decision of FDA.
10
In fact, we have tried the contemporary interest rate of Taiwan Bank and Zhanghua Bank, but they are not assignificant as lagged interest rate. Hence, we drop them for collinearity through a stepwise procedure.

Table 1
Variable(1)(2)

117.53

C

***

(3)

100.11***(15.87)(7.98)-52.39-60.80(4)

87.06(7.22)

(5)

83.95

***

(6.27)

***

(6)

83.95
(7.17)***

85.56(8.20)***I(prin≥1)
Period1
Period2
Period3log(prin)

***

***

(10.04)(6.17)-70.46-75.90***(12.17)-72.84***(6.57)***-76.68***(11.13)(6.08)

-4.73

-2.49

(2.01)**(1.02)-49.10(4.55)***-64.09(4.86)***-66.47(4.54)

***

-2.69

**

(0.77)-46.17(3.98)***-64.80(4.20)***-66.83(3.92)

***

-2.24

***

(0.67)***-44.60(3.99)***-58.27(4.02)***-61.13(3.76)***(0.65)

train

R

2

(6.89)***-63.43(6.74)***(3.22)-3.58(0.66)
-6.28

-5.69

-5.51

-6.03

*

(3.31)

-0.65

0.20

0.57

(0.61)(0.31)(0.30)

-3.98

-2.01

-5.76

(6.56)(7.65)(3.26)(5.42)

**

2.16

0.93

0.98

2.03

(2.86)

-3.86

-3.79

(3.26)(3.28)**(0.30)

0.64*(0.26)

0.61-4.33(3.28)

-6.87

-1.83

**

***

**

(3.79)(3.40)

yeq

debtor-60.57

-2.24

guom

F stat. of

***

***

prin≥1bankr(6.60)-3.54

prin<1term-46.76

0.61
**

-8.27
(3.35)**(0.30)**-7.64(3.70)**(3.11)

2.68

-0.26

(6.89)(5.98)

0.95

0.96

**

0.94

0.94

Note: standard errors are provided in “( )”; superscript ***, ** and * mean significant at 1%, 5% and 10%
separately.

IV. Arbitrage about the interest rate quotation
As shown by the regression analysis of equation (*), the interest rate arrangement of FDA ismainly impersonal and members could decide their credit amount according to it. This forms atypical game in economic terms. Then, will the association and its member act in a rational way as
the optimizing theory expects? Or, if there was deviation from the theory in some situations, did itchange with the modernization progress? Answers about these questions will be helpful forunderstanding the marketization and the essence of economic rationality.
It’s useful to look at the distribution of loan size at first. From fig.2, we can find that principal
concentrates at one Yuan (e0) with a sharp left drop, which is different from normal micro credit
distribution with its peak close to zero. An apparent explanation is to avoid exchange cost by
loaning integer amount, but this can’t explain why the proportion of small change loans decreased

greatly and concentrating at one Yuan strengthened after 1923, when the interest rate for loans
exceeding one Yuan was lowered. On the contrary, the endogeneity of credit size to the interest
rate gap illustrates that we should pay more attention to the arbitrage about one Yuan loans, as
larger gap means more room for arbitrage. However, when members acted in this way, it may be
not optimal for FDA to leave a so great gap in the interest rate quotation. Then, how should weunderstand the reaction between FDA and its members?
Fig.2 Histogram of loan sizes
1915-1922
20
15
10

Counts50

1923-1938
20
15
10
5
0

e-2

e-1

e0

e1

e2

e3

e4

Principal

In order to detect what questioned above, we’d better start from a standard optimizing
problem of the FDA and its members. At first, the FDA decides its interest rate quotation by
maximizing its object, e.g., profit. Suppose the quotation is required to take a two stage form tosave menu cost and negotiating cost. 11 Then, the profit maximization could be defined as below.
q*

ω

∞

0

q

ω

(1) max=
Π r a ∫ qdF (q ) + r bω ∫ * qdF (q ) + r b ∫ qdF (q ) − E (C (q ))a br , r ,ωIn (1), the two stage quotation is defined as ra for principle lower than ω, and rb elsewhere.
Borrowing reserve price function as q is known to the FDA, and the status of members is
supposed to be stochastic whose distribution is defined as F(q). However, according to thequotation rule, the reserve price function will not equal to the real demand function, because
borrowers, whose demand is lower than ω but exceed some level, e.g., q*, would borrow ω toarbitrage as will be discussed below. The minus item in (1) is the expected cost which may depend
not only on the total loan scale but also on the distribution of every loan size. For the main
problem of FDA is scarce of demand as discussed in section III, we don’t add credit amountconstraint to the solution of (1).
In addition, we suppose the reserve price function of borrowers has a quasi log-linear form
for convenience, which is defined in (2).
(2) ln q =β 0 + β1r + ε

11Actually, the FDA’s quotation was not complete since members would discuss interest rate for extra large orlong term loans specifically as we pointed out in section III. This also illustrates that the simple form of quotationis selected mainly to save menu cost and negotiating cost. If such costs are great enough and there is no
substitution between extra large loans and one Yuan loans, we can suppose the quotation form is given forconvenience.

Of cause, profit should not be the exact object of FDA, but it’s a useful start point and wewill discuss how it might be deviated through empirical analysis. An actual obstacle for the FDA’s
optimization is the strategy of members, which will make the problem difficult to solve since thequotation will affect the lend size in the pattern shown in fig.2. Under the rationality assumption,
the FDA should take the reaction of members into consideration and get first derivative conditionas (3.1)~(3.3). Meanwhile, if its rationality is bounded for constraint of calculation ability, terms
mixed with reaction of members in (3.1)~(3.3) might be omitted.
∆a
qa*
∂Π
β 0 + β1r a +ε
a
a *
b
(3.1)
=(1 + r β1 ) ∫ edF (ε ) + (r q − r ω f (∆ a ))( * − β1 ) − ECa
−∞
∂r a
q
∞
b
∂Π
b
=
+
(1
)
r
e β0 + β1r +ε dF (ε ) + (1 − f (∆ b )) β1r bω + ω ( F (∆ b ) − F (∆ a ))
β
1
b
∫
∆
b
∂r
(3.2)
q*
+ ( r a q* − r bω f (∆ a ) ) b* − ECb
q

qω*
∂Π
b
a *
b
b
(3.3) = r ( F ( ∆ a ) − F (∆ b )) + ( r q − r ω f (∆ a ) ) * + ( f (∆ b ) − 1)r − ECω∂ωqIn (3), ∆ a = ln q* − β 0 − β1r a , ∆ b = ln ω − β 0 − β1r b . F(•) and f(•) represent distribution
and density function of ε separately. EC and q* with lower subscript means related partial
derivatives, through which the strategy of members are taken into FDA’s consideration.
As making exchange is relatively expensive for micro loans, it seems quite reasonable to set
ω at one Yuan and (3.3) has little need to refer in fact. In addition, since the fund of FDA didn’t
come from outside credit but gathered through contribution, its cost, EC, mainly consisted of the
management cost and exchange cost, and only the latter would relate to the controlled variables.
Moreover, because the need of exchange is decided by the proportion of micro loans below one
Yuan, the marginal cost of interest rate adjustment will mainly come from its affect on the loan
size distribution.
Once the interest rate quotation is decided, members will decide their amounts to borrow. For
arbitrage, they will tend to borrow one Yuan even if the needed amount is smaller than it. Thus,
the breakpoint in the interest rate quotation causes nonlinearity in the borrower’s strategy. Given
the marginal utility or reserve price function of borrower, tradeoff between the decrease of reserve
price and interest rate when borrowing more decides the one Yuan arbitrage as shown by fig.3 orequation (4). From fig.3, it is easy to see that if shadowed area A is greater than B, members
would borrow ω though the reserve price curve intersects supply curve at q*. This arbitrage gives
Fig.3
(4).
r

 β 0 + β1r a + ε , q ≤ q*(4) ln q  ω ,=q* < q ≤ ω β + β rb + ε , q ≥ ω
1
 0

D
ra

A
S

rb

B

In theory, q* should be derived from SA= SB, whereq*ωprincipal

=
SA

ra

ln q − β1 ( r − r )dr , S B∫ b e=
*

a

r

∫

rb

(ω − eln q − β1 ( r − r ) )dr*(ln q − ln ω + β1r ) β1*aaThe equation, SA= SB, can be simplified into (5), which shows the equilibrium relationshipbetween interest rate quotation and q*.
(5) 1 + ln(q* ω ) − β1 (r a − r b ) − q* ω =0Obviously, q* tends to increase if the gap between ra and rb shortened. Since increase of q* or
the threshold for arbitrage means some loans will retreat from ω to q*, exchange cost will increase
accordingly. Then, for the items in (3), there areqa* ≤ 0, qb* ≥ 0, ECa ∝ f (∆ a ) ⋅ qa* ≤ 0, ECb ∝ f (∆ a ) ⋅ qb* ≥ 0 .
(4) also provides conditions for empirical analysis through the data introduced in section II,
where ra, rb and q are known. As (4) is highly nonlinear, we will use methods of moment toestimate the reserve price function and the threshold q*. The moment conditions can be derived
from (4), which are listed below.
ln q − β 0 − β1r
 E (ε | q ≤ q* ) =ε dF (ε )
∫

−∞

∞
ε dF (ε ) E (ε | q ≥ ω ) =∫ln ω − β 0 − β1r b

(6) 
N
E ( a=) F (∆ a )

N


N
E ( ω ) = F (∆ b ) − F (∆ a )

N

*

a

It should be noted that we don’t use SA= SB or (5) to get (6), because the equilibrium
condition under perfect rationality might not hold empirically. Then, q* will not be derived from (5)directly, but be estimated from (6) together with β0 and β1, which means we could test thetheoretical relation (5) by the estimated results. Since it’s difficult to get analytic solution from themoment condition (6) and the sample is small, we apply bootstrap method to get distributions of
the estimations, while ε is supposed to be normally distributed. Fig.4 plots the bootstrap
distribution of β1’s MM estimation. As fig.2 have shown that the debt sum concentrates on one to
two Yuan heavily, it’s not surprising that the credit demand is quite inelastic and the empirical
distributions of different periods all peak near zero. However, the more important point is theextension of left tail or the increase of elasticity after 1922. Compared with fig.2, this is inaccordance with increase of larger sum loans and more arbitrage on one Yuan. The later pointneeds more explanation. As shown in fig.3, more elasticity means increase of SA’s area relative to
SB, which will lead to the decrease of threshold q* and more loans of one Yuan.
Especially, the largest lend below one Yuan is 0.75 before 1923 and this is also the MM
estimation of q* for the first period. It happens to be an exactly “right” calculation for a verticalreserve price curve, as loan of 0.75 Yuan with 100% interest rate will pay the same as loan of 1
Yuan with 50% interest rate. However, it’s quite impossible for the elasticity to be zero exactly or
for the surplus 0.25 Yuan to be in vain absolutely. Another more reasonable explanation is that
calculation with a zero elasticity hypothesis is much simpler. Thus, elasticity or preference might
not change in fact, but the opportunity cost of a simplified calculation was increased when the
Rinan station was founded and more market opportunity appeared. Of course, elasticity may alsochange in other ways not related to preference. For example, when market opportunity is scarce,
most debt may be caused by emergent, inelastic and scattered need. In both cases, market
development provides more reasonable explanations for the increase of elasticity and proportionof larger loans.
Fig.4 Histogram of β1’s MM estimation by bootstrap
1923-1933

1915-1922
600

500

1934-1938

700

800

600

700

600
500
400
500
400
300

400
300
300

200
200
200
100

0
-0.02

100

-0.015-0.01-0.005

0

0
-0.03

100

-0.02

-0.01

0

0
-0.03

-0.02

-0.01

0

Note: The histogram composed by 1000 times bootstrap resampling, where the singular samples are dropped.

Above explanation means optimization isn’t realized perfectly. In fact, fig.2 has led us to
doubt whether it was too progressive after 1922 while it might be too conservative before then.
This can be solved by testing the rationality of FDA’s members represented by the optimizing
condition SA=SB or (5). Fig. 5 plots the bootstrap histograms of SA-SB in different periods.
Similarly to the zero peak of β1’s histogram, there is left peak for SA-SB. Meanwhile, fig.5 showsthat the optimizing condition can be rejected just for the first period, which means people became
more “rational” from being too “conservative” as credit had been more elastic after 1922.
However, it may be not exact to say the change of rationality. As our discussion about fig.4 has
shown, SA=SB will hold for the first period, if the elasticity was set zero or if the calculation costand market status are considered. Fig.5 supports our argument further, because the optimizing
condition became acceptable after 1922, when market condition was improved and calculation
cost became insignificant compared with related benefit. So, it’s fairer to suggest bounded
rationality than some natural pattern different from rationality as behavioral economists would
argue. Furthermore, the bound of rationality is not fixed, and marketlization tends to relax it,
which means market economy and economic rationality could enforce each other and construct aninternal consistent hypothesis. It’s a positive support for analysis market economy with rationality
assumption.

Fig.5 Histogram of SA-SB
1923-1933

1915-1922600

1934-1938

800

900

700

800

500
700

600
400

600
500
500
400

300

400
300
200

300
200

200

100
100

0
20

30

40

50

0
-30

100

-20

-10

0

10

20

0
-20

0

20

40

60

80

Note: The histogram composed by 1000 times bootstrap resampling, where the singular samples are dropped.

As members arbitraged with the interest rate quotation rather rational, how did the FDA react
to it? When we turn to the test of (3), things become quite different. Our method is similar to thetest of (5) and the bootstrap histogram of (3) is plotted in fig.6.12 However, the optimizing
condition that the first derivative equals to zero is rejected generally. The partial derivative isnegative to ra while it is positive to rb for all periods, which verifies the intuition that optimized
interest rate quotation shouldn’t have so dramatic shift from 100% to 50% or 30% at one Yuan. In
fact, deviation from (3.2) is not difficult to understand since there was competing private credit
market for larger loans and its popular interest rate was just about 20% to 30%. When the entrance
obstacle of credit market was weakened and borrowing elasticity increased after 1922, derivative
to rb also increased. Deviation from (3.2) thus reflects the competitive market pressure, which
isn’t included in our model explicitly, rather than rejects the optimization of FDA.
Meanwhile, the negative derivative to ra seems quite unreasonable, since decreasing ra from
100% would gain Pareto improvement even if the FDA looked for other subjects such as charity.
Exchange cost, omitted in fig.6, might provide some explanation, for exorbitant ra will push more
small change borrowers to borrow one Yuan. However, exchange cost can’t explain why deviationfrom (3.1) was weakened greatly after 1922, while ECa would increase with more elastic demand
curve 13. Therefore, exchange cost should not be the key point for the decision of ra, once monetaryreform had succeeded in uniting fractional money. Another possibility lies in calculation cost. As
we have noted, omitting the strategy of members could make the problem much simpler and savethe calculation cost greatly. This gives fig.7, where the items related to partial derivatives of q* in(3) are omitted. It’s clear that partial derivative of ra shifts to be positive for all periods, whichbecomes in accordance with interest rate regulation and easy to understand, considering 100%interest rate had long been regarded as the upper limit of tolerance in traditional literatures. Thus,
the departure from (3.1) should be explained by calculation cost, combining with a customaryinterest rate limit at 100%, which is also consistent with the ritualized interest rate in loan ofsacrifices. In contrast to the test of member’s rationality through fig.5, the calculation cost of FDA
worked for all periods, although the scale decreased after 1922. However, it’s not surprising if we
12

Because exchange cost is very difficult to be included explicitly in our model, it is omitted in computation,
which is acceptable as ECa and ECb are relative small in (3.1) and (3.2), according to our discussion about themonetary institution.
13
In our computation results, not only q*a for the latter periods increased, but also f(△a) increased slightly too.
Both of them tend to increase the effect of ra to exchange cost.

notice that the optimization problem of FDA is much more complex and it has to be solved bycollective decision. As introduced in section II, the decision process was some colligation of ideas
from members with different situations and subjects, and further, the more powerful members
would pay more attention to lower rb which had more correlation with their own interests. So, therejection of (3.1) means more likely to suggest the agent problem tangled with difficulties incalculation than reject personal rationality simply.
Fig.6 Histogram of (3)800

1915-1922

1923-1933

800

600

600

400

400

200

200

1000

1934-1938

800
600
400

0
-6

-4

-2

0

2

0
-0.03

200
-0.02

-0.01

0

0.01

0
-0.15

-0.1

-0.05

0

0.05

-2

0

2

4

Derivative to ra
400

600

600

300
400

400
200
200

200
100

0
1

2

3

4

5

0
-2

0

2

4

6

0
-4

b

Derivative to r

Note: The histogram composed by 1000 times bootstrap resampling, where the singular samples are dropped.

Fig.7 Histogram of (3): omitting the indirect effects
1915-1922

1923-1933

800

800

600

600

400

400

200

200

0
0

0
0

1934-1938
1000
800
600
400

0.5

1

1.5

200
0.05

0.1

0.15

0.2

0
0

0.5

1

1.5

a

Derivative to r
400

300

600

300
200

400
200

100

200
100

0
-1

0

1

2

3

0
-2

0

2

4

Derivative to rb

6

0
-4

-2

0

2

4

Note: The histogram composed by 1000 times bootstrap resampling, where the singular samples are dropped.

V. Conclusion
Traditional rural economy is often believed to have some special pattern, such as surviving
economy or small peasant economy, where rural credit is divided into reciprocal lending between
villagers and the usury from market. However, we find this can’t hold in the case of FDA. The
FDA provided credit for villagers, but its interest rate for micro loans was set to be as high asusury by consensus of its members, according to the scale diseconomy of those loans. At the sametime, though the FDA is a local religious institution, its interest rate is comparable to other privatecredit in fact and adapts to competing from credit market. Furthermore, marketization didn’t
aggravate usury as Scott (1976) argued. On the contrary, the interest rate was lowered and thereeven appeared integration between rural credit and institutional financial market when market
condition was improved by railway. It should also be noted that institutional factors, including theland ownership and modern cooperatives which were more often cited, could explain little about
the variation of interest rates.
Meanwhile, in the argument about small peasant economy before modernization, therationality of peasant was thought to be not according to calculation about benefits and costs. We
do find deviations from optimal solution given the FDA’s interest rate rule, but it just reflects thatthe calculation cost shouldn’t be neglected and the calculation process tends to be simplified forcost saving. In our findings, the calculation problem leads to some special calculation procedures
which could be attributed to bounded rationality or mental accounting, rather than the small
peasant rationality. More importantly, when more market opportunities appeared and the benefit ofcalculation increased, deviations from optimal equilibrium also decreased. This shows that theimportance of deviations from complete rationality is more depending on social institutions thanphysiological elements, which proves the internal consistent between market economy andeconomic rationality.
According to our findings, the arbitrage of FDA members was more extended in micro loans
after 1922, which could reflect the effects of marketization on the daily life at the micro level. It
seemingly supports the usual attack on marketization, but, when the cause is that the benefit ofcalculation increased, the meaning of daily rationalization becomes not so negative certainly. In
the FDA’s operation, something kept unchanged during the marketization is the ritual sacrificeloan. Ironically, ritualization actually restricts this kind of loan to a tiny scale, even if the FDA is areligious organization. In addition, in Rinan village where formal interest rate regulation was weak,the customary limit as high as 100% was really worked. However, it’s much higher than the legal
limit and only affects very little loans, e.g., those much less than one Yuan. Thus, religion or
custom also can’t constitute a significant rational pattern in the traditional economic life we
explored. Nevertheless, the aim of this paper isn’t to claim the universality of economic rationality,but, when we understand the deviation from rationality more clearly, we can use the theories basedon rationality hypothesis better even in analyzing the traditional economy.
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