東京大学社会科学研究所
ディスカッションペーパーシリーズ
F-141

Informational Efficiency under the Shogunate Governance:
Concentration and Integration of the Rice Market in Tokugawa Japan
Graduate School of Economics, Tokyo University,
Yasuo Takatsuki
Institute of Social Science, The University of Tokyo
Discussion Paper Series
F-141
September, 2008

Informational Efficiency under the Shogunate Governance:
Concentration and Integration of the Rice Market in Tokugawa Japan *ISS Discussion Paper Series
F-141
November 2008
Yasuo Takatsuki†

Graduate School of Economics
The University of Tokyo

Abstract
In the Tokugawa period, the market transaction explosively grew, and the local markets of all
Japan were effectively integrated as a national market. This is the common view shared among
the historians. Then, an important question is how these markets performed. To evaluate theperformance, this paper focusses on the co-movement of rice prices between Osaka and Otsu.
Applying the Granger causality test, it is shown that the Otsu market had reflected the rice prices
in Osaka within two days in the early 19th century, and within a day in the mid-19th century.
This change had stemmed from the development of the communication technology. The ricemerchants' appetite for the information had made the co-movement of the rice prices so fast that
the Otsu market did not need even one trading day to reflect the rice prices in Osaka.
Key words: Tokugawa period, the Dojima rice market, market integration
JEL: G20, N25, N75* The author is deeply thankful to Masaki Nakabayashi, Matao Miyamoto, Kosuke Oya, Yuzo
Honda, Katsuya Takii, Shingo Ishiguro, Junichiro Ishida, Takashi Shimizu, Ryo Horii, Toshihiro
Matsumura, Dan Sasaki, Tetsuji Okazaki, Naofumi Nakamura, Masayuki Tanimoto, Ryuzo Miyao,
Masato Shizume, Kazuyuki Inagaki and other participants of seminars at University of Osaka,
University of Tokyo, University of Kobe, the Bank of Japan. This research has been supported by
Grant-in-Aid for JSPS Fellows(20-10163), JSPS Grant-in-Aid (18203024)and Research Grant ofJapanese Bankers Association.
† Corresponding address: Graduate School of Economics, University of Tokyo, Hongo 7-3-1,
Bunkyo-ku, Tokyo 113-0033, Japan. Phone: +81-3-3812-2111. E-mail address: tktk_y@ybb.ne.jp.

I. Introduction
Under the governance mechanism established by the Tokugawa Shogunate in Edo,1 theShogunate and the feudal lords collected the rice in tax,2 and shipped to the market for
financing their budget. This system of taxation originally emerged based on the developmentof local markets, then lead to a sophisticated rice transaction mechanism in Osaka. The rice
market in Osaka was called the Dojima rice market, and it was chartered by the Tokugawa
Shogunate in 1730. The trades at the Osaka market was made through not the rice in kind,but the rice bills (“Kome kitte”),3 and the claim over rice in kind represented by the rice bill
was protected by the Shogunate. 4 The distribution network and the judicial system which
provided by the Shogunate had made Osaka the center of the market with sophisticatedtrading mechanism.
The local markets, in turn, followed this trading system. One typical example of such a
local market was the Otsu market. Otsu is located near Osaka, and it had second largest
rice market after the Osaka market. The rice market in Otsu — “goyo komekaisyo (Therice market authorized by the Shogunate, henceforth referred to as the Otsu market)”, waschartered by the Shogunate in 1735. Both Otsu and Osaka were belonged to the Shogunate
domain. While the Shogunate gave feudal lords the authority to rule their domains, it had
its own domains (“Ten-ryo”) in various regions in Japan, which covered most important anddeveloped city such as Osaka and Otsu. The trades in the Shogunate domain were under
the jurisdiction of the Shogunate local court. In fact, as mentioned later, the Otsu market
had basically similar trading system with the Osaka market, including judicial system.
These institutions made the market transaction in Tokugawa period explosively grew,
and the local markets of all Japan were effectively integrated as a national market. Then,
an important and exciting question is how these institutions performed.
According to the neoclassical economics, sufficient development of market transaction
1

Edo was the Shogunate capital, lately renamed as Tokyo in 1868.
Tax here mentions the total amount of tax and rent, accrued to the Shogunate and the feudal lords.
3
A rice bill was issued by the feudal lord’s warehouse, and it represented certain amount of rice. It was2

introduced as a means to reduce the transaction costs of trading large volume of rice.
4
See Takatsuki (2008).

1

could lead to a Pareto-efficient allocation of resource. Unfortunately, it is not easy to directly
evaluate the Pareto-efficiency of the real economy. But, market transaction, that could
deriver efficient resource allocation, needs an important condition — informational efficiency.
Using this basic but important idea, Fama (1970) establish the useful and practical measure
to evaluate markets.
The informational efficiency is a proxy to measure how much, how fast, and how accurately available information is incorporated into the prices. Fama (1970) has classified thisinformational efficiency into three categories based on what is meant as “available information”; Namely, the weak, semistrong, and strong forms.
Among these criteria, the weak form efficiency is the most basic but important criterion,
because if it does not hold, then neither the semi-strong form nor the strong form efficiency
will be satisfied. The weak-form efficiency exists if the prices fully reflect all the information
contained in the history of past prices and returns. In such a situation, the traders can notearn excess profits from using only the information of past prices and returns.
The author has already documented that the weak form efficiency was achieved at the
Osaka market. 5 What we need to do as the next step is to inquire the co-movement ofprices between Osaka and the local market. As in the case of trading system, it is quite
natural to think that the prices in Osaka were also referred by the local market.
The literature have already inquired the Osaka market and the local markets co-moved,
focussing on the price correlation. They found a high correlation among them, and thoughtthat coefficient of correlation showed that Osaka worked as a center market. However, thecoefficient of correlation, on which the literature relied, can tell us only the results of theco-movement among the valuables. To argue that Osaka was the center market, we need toobserve not the results but the process of the transmission of the prices. As mentioned later,
this paper relies on the bivariate Granger causality test.
Moreover, the price indices they used were not frequent at all — monthly or yearly. In
the Tokugawa period, the letters from Edo to Osaka, distance between which was about 500
kilometers, were delivered within about 6 days, and the letters from Osaka to Otsu, distance5

See Takatsuki (2007).

2was about 50 kilometers, were delivered within a day. This implies that the prices at Osaka
could be transmitted to very distant markets within a week, or to neighboring markets withina day. Under such a dense communication, the monthly or yearly price indices could mean
nothing about the informational efficiency.
Therefore, we need to construct more reliable and highly frequent price index from an
original historical document. Our new source is “Yorozu souba nikki (Daily memorandum ofcommodity price indices)”. From this memorandum, we can construct the daily price index
both in Osaka and Otsu during the period from 1798 to 1856. Relying on this new index,
this paper will evaluate the co-movement of prices between Osaka and Otsu.
The structure of this paper is as follows. Section II introduces the institutional aspectsof the Dojima market and the Otsu market, and reviews the daily price index which was
newly constructed. This section serves as background for subsequent discussions. Section
III lays out the model for capturing the co-movement of prices, and presents results followedby the concluding remarks.

II. Institutions and the price index
Trades in the Osaka market
First, the trade activities in Osaka will be introduced.6 The rices, collected and shippedby the feudal lords, were stored in the warehouses, and sold at the auction where officiallychartered rice brokers bid. Rice brokers who made a successful bid received the rice bills
which, per unit, was worth 1500kg real rice stored in the warehouses.7 The rice brokers
in principle could have submitted their rice bills to the warehouse and received real rice inexchange. However, in reality they mainly sold the bills in the secondary market; the Dojima
rice market. Thus, the spot market in Osaka should be regarded as the exchange market ofrice bills, not the rice in kind.
6
7

See Miyamoto (1988) and Schaede (1989) for further institutional descriptions of the Dojima rice market.
In the late 17th century, each rice bill corresponded to a particular set of rice that the broker won at theauction. In late times, this correspondence gradually collapsed and rice bills came to take on the characterof securities. See, Shimamoto (1960).

3Issuing a rice bill without inventory was officially prohibited by the Shogunate in 1761.
However, it did not mean that this restriction was literally complied by the warehouses, andit was known to the governor in Osaka.8 That is, while the governor implicitly permitted
issuing a rice bill without inventory, he did not allow the warehouses to dishonor a rice bill.
This meant that claim over rice in kind represented by the rice bill was protected by the
local court in Osaka. 9
In the spot market, the rice bills were required to be delivered in exchange for cash withinfour days after the transaction. While the traders who could join in the market were limited
to officially chartered rice brokers, anybody who paid some amount of fee to the charteredtraders could join in the market.
There were about 30 kinds of rice bills issued by feudal lords’ warehouses, and the traders’association choose one rice bill among those 30 rice bills as the standard rice. This standard
rice was exactly the underlying asset for futures trade. Like the spot market, the tradersin this market were formally limited to officially authorized members. However, any traders
could actually join the market by paying a little amount of fee to the authorized traders.
The fee associated with the futures trades was less than that of the spot trades. In addition, amount of cash needed in the futures market was relatively smaller than that in the
spot market. These features of the futures market had attracted many traders, especially
speculators.
In principle, the futures market traders had to close their positions by buying back or
selling back before the maturity date; That is, “roll over” across the trading periods wasstrictly prohibited. For example, a trader who made a long position during the trading period
must close his position until the maturity date by selling same amount of the contract. The
settlement by delivery was permitted in the maturity date, while a constraint designated by
Tokugawa Shogunate was imposed. That is, in the Osaka market, the allowed amount of
the settlement by delivery was strictly limited to the fixed level; 1000 rice bills for the wholemarket. Under this constraint, the futures market participants the rice bills thorough the
8

The governor here, “Osaka-Machi-Bugyo”, was in charge of judiciary, police, and other administrative

services.
9
For farther description, see Takatsuki (2008).

4

futures market. Usually, net settlements were the dominant method of the settlement.
Both the spot and the futures market have three separate trading seasons: January 4–
April 27(28), May 7–October 8 (9), and October 17–December 23 (24)10 . These seasons werecalled spring market, summer market, and winter market, respectively. The markets wereclosed for about 10 days between any of the two trading season. Every time the trading
season started, futures market committee were supposed to re-select the standard rice, it
was usually the case that the standard rice was selected from Big five lords’ warehouses11 .
Trading began at about 8 a.m. in the futures market, followed by the spot trading whichbegan at about 10 a.m. Both trading began with opening price presented by the board
members of the Dojima market. In the futures market, the opening price was determinedby the closing price of the previous day. On the other hand, the opening price in the spot
market was determined by two factors; the closing price in the previous day and the pricemovements of futures preceding the spot market.
In both markets, the price was fixed by an open-out-cry system. Traders in the circuit
shout the price with gestures which stand for either “ask” or “bid”. The price was fixed
only when the ask price and the bid price matched with each other. Every time a trading
deal was established, the clerk beat out the wood stick and shouted the price. In the future
market, the trading records were not written down until the completion of the trade in aday. After the trade was closed, the traders submitted the record to the clearing house. The
clearing house checked each traders’ transaction and canceled out his buying and selling.
Finally, each traders’ remaining position was kept in the record.
The spot market closed around the noon. On the other hand, the futures trade had a
one-hour recess at noon and continued the trading until around 2 p.m. The closing price ofthe futures market was fixed by a special method. First, the clerk put fire on the fuse cord.
The traders were allowed to trade until the fire extinguished. The closing price of the day
was determined by the price at the moment the fire went out.
These features, introduced above, indicate that the trades at the Osaka market was
1011

The dates in parentheses are those for spot market.
That is, Kaga, Chikuzen, Chugoku, Higo, Hiroshima. Each was regarded as satisfying the condition,

namely credibility and liquidity.

5designed not only for the real demand, but also for the speculation. In other words, it
was designed for accumulating traders’ information. The concentration of rice and theinformation has made Osaka the center of the market at that time.

Trades in the Otsu market
Some feudal lords, whose domain allocated along the coast of the Japan Sea, tended to ship
their rices to Otsu. As in Osaka, the rices were stored in the warehouses, and sold at theauction. Then, the rice bills were issued and traded at the Otsu markets. The rice bills
here were also, per unit, worth 1500kg rice in kind stored in the warehouses, 12 and claim
over rice in kind represented by the rice bill was protected by the governor in Otsu.13 Given
that both markets were located in the Shogunate domain, it was rather natural that both
systems were similar.
The rice bills traded at the spot market in Otsu were mainly issued by Wakasa warehouse, and Hikone warehouse. The former was called “Kumagawa-mai (The rice cropped in
Kumagawa district, henceforth referred to as the Kumagawa rice)”, and the latter was called“Sawa-mai (The rice cropped in Sawayama district, henceforth referred to as the Sawa rice)”.
Although a standard rice was not officially chosen, the Kumagawa rice was recognized as akind of standard rice in Otsu.14 Both Kumagawa rice and Sawa rice were designated as theunderlying assets for the futures trades; That is, there existed mainly two futures markets— the Kumagawa futures market, and the Sawa futures market. While the “Yorozu souba
nikki (Daily memorandum of commodity price indices)”, our new source for constructing adaily price index, recorded the prices of both markets, only the Kumagawa futures prices
can be tracked continuously. We focus on the Kumagawa market.
While the trading activities in Otsu have not been clearly described, especially comparedto Osaka, we can draw outlines.
Trading began at about 10 a.m. in the spot market and the kumagawa futures market.
Both trading began with the opening price presented by the board members of the market.
12

Otsu-Shi-Shi gekan (The history of Otsu city — volume.3), pp.94-95.
Otsu-Shi-Shi gekan (The history of Otsu city — volume.3), pp.80-81.
14
Otsu-Shi-Shi gekan (The history of Otsu city — volume.3), pp.94-95.
13

6

As mentioned in the section III, the opening price here was determined refereing the prices
in Osaka on the previous day. The kumagawa futures market closed at about 2 p.m. as a
general rule.
While traders both in the spot market and the futures market were formally limited to
officially chartered members, they joined the market by a small transaction fee.15 In the
Kumagawa futures market, the traders closed their positions by buying back or selling backin principal. These procedures of the futures market were similar to those in Osaka.
On the other hand, there existed some differences. The settlement by delivery waspermitted in the maturity date without any constraints, and the traders in Otsu could “rollover” the trades across the trading periods. While the Osaka markets was closed between
each trading periods, the Otsu market had been open throughout the year.

The new price index
As mentioned above, since non-frequent price indices can mean nothing about the informational efficiency, we need to construct highly frequent price index from an original historical
document. Our new source, “Yorozu souba nikki (Daily memorandum of commodity priceindices)”, is the memorandum described by the contemporary rice merchant who traded riceand fertilizer. Although he traded mainly in the Otsu market, he regularly recorded bothprices in Osaka and Otsu. It mentions that his trades in Otsu were closely linked with theprices in Osaka.
From this memorandum, we can construct daily price index both in Osaka and Otsu,
which covers the period from 1798 to 1856.16 Among the prices, we will focus on i) the futures
price in Osaka, and ii) the futures price of Kumagawa rice in Otsu. In Osaka, as mentioned
above, the opening price in the spot market was determined by the price movements offutures market, and the spot market was closed about 3 hours before the closing time of
the futures market. For this reason, all prices in Osaka can be seen as summarized in the
futures price. On the other hand, since the price indices of Sawa rice and the spot prices
15
16

Otsu-Shi-Shi gekan (The history of Otsu city — volume.3), p.85.
The prices in the period from 1819 to 1839 can not be observed because the documents’ state of preser-

vation is very poor.

7

of Kumagawa rice can not be tracked continuously, the futures prices of Kumagawa rice
are used as representative prices of the Otsu market. Using these two price indices, we willinquire the co-movement of prices between Osaka and Otsu.

III. The co-movement of rice prices between Osaka andOtsu
The communication between Osaka and Otsu
Following historical document was submitted by the rice merchants to the governor in Otsu.
It reports the trading systems and practices in Otsu, focussing on the relationship between
Osaka and Otsu.
Since the rice prices in Osaka are representative prices of all rice markets, any
trader in Otsu can not trade without the information about the rice prices in
Osaka. A market report from Osaka, which records the prices in the previous
day, arrives at the Otsu market in every morning. In addition, some traders
personally gather the information of the Osaka markets before the market reportarrives at Otsu, because they are eager to catch the information as soon as
possible. 17
There are at least two points to be noted. First, the traders in Otsu market referred theprices in Osaka as representative ones. This supports the results of Takatsuki (2007); theOsaka market had achieved the informational efficiency at least in terms of weak form. In
fact, a market report from Osaka can be found in many other markets. It is not only the
Otsu market, but also many other local markets that tried to know the prices in Osaka assoon as they could. The rice price indices in Osaka were indeed referred as the informative
prices by the local markets.
17“Ho-reki 11 nen ku-gatsu, bugyo-no otazune-ni kootauru ko-jo-syo (The report submitted to the governor

in September 1761)”, cited by Otsu-shi-shi — tyu-kan (The history and culture of Otsu city — volume.2),
pp.856-859.

8

Second, the traders in Otsu were eager to know the prices at the Osaka market as soon
as they could. This means that they could not earn the excess profits anymore, only fromthe market report arrived in the morning.
The rice merchants’ appetite for the excess profits have led to the development of communication technique. According to the “Yorozu souba nikki”, the prices in Osaka weretransmitted to Otsu within a day from 1840. By this stage, the communication methods
developed from the mailman to the flag signaling. In fact, while the “Yorozu souba nikki”
recorded the closing prices of the Osaka rice market before 1818, it came to record not only
the closing prices but also the intra-day prices after 1840. This clearly shows that dense
trades both in Osaka and Otsu required update of communication technique.
How did these developments influence the co-movement of prices between Osaka andOtsu? This is the question to be answered in the following section.

The test statistics
To inquire the points, this paper relies on the bivariate Granger causality test. Here weestimate the two-variable vector auto regressive (VAR) model to assess the co-movement ofprices between Osaka and Otsu. The model includes the futures prices in Osaka and thefutures prices of the Kumagawa rice in Otsu. The VAR model is given as follows;y t = ψ 1 y t−1 + ψ 2 y t−2 + · · · + ψ p y t−p + ut ,where y is the two-dimensional vector, consisted of the logarithmic returns of the futures
market both in Osaka and Otsu, u is the white noise vector, and t is timing.
Running the least square analysis, we can observe the cross-interaction between Osakaand Otsu. The optimal number of lags is determined by the S.B.I.C (Schwarz’s BaysianInformation Criterion).

The results
The results of the tests are shown in Table 1. In the period from 1798 to 1818, the futures
prices in Otsu obviously followed the prices in Osaka. In addition, according to the S.B.I.C,
9

the futures prices in Osaka tended to precede those in Otsu by one trading day. This result
implies that the Otsu market reflected the prices in Osaka within two days. Here we need toremember that, in this period, the information about the Osaka market was transmitted to
Otsu by mailman. Hence, the delay of one trading day does not necessarily mean that the
Otsu market took two trading days to reflect the prices in Osaka. Given the communication
technique on those days, the Otsu market had reacted to the Osaka market, right aftermarket participants received a market report.
On the other hand, in the period from 1840 to 1856, there did not exist clear lead-lag
relationship between the two. There are two possible ways to understand. First, both prices
moved independently. Second, both prices moved simultaneously. In both cases, the lead-lag
relationship can never be detected by the VAR model.
To inquire which case had happened, the coefficient of correlation was calculated. Table
2 shows that both prices are highly correlated with each other, and the coefficient in thelatter period is bigger than that in the earlier period. This implies that both prices moved
simultaneously; That is, the Otsu market reflected the prices in Osaka with in a day. It was
the development of the communication technique that brought about this result. After thisstage, the Otsu market did not need even one trading day to reflect the prices in Osaka.

Concluding Remarks
The co-movement of prices in Tokugawa period had reached a level not previously experienced. The Otsu market did not need even one trading day to reflect the prices in Osaka inthe early 19th century, and the traders at that time could not earn the excess profits without
the latest information about the Osaka market.
Osaka indeed worked as a center market, and neighboring markets followed Osaka sufficiently fast. Distribution network had led to a sophisticated trading system in Osaka, andintegration of the rice market had led to a dense communication network between the center
market and the local markets.

10References
Fama, E.F., “Efficient Capital Markets:A Review of Theory and Empirical Work,” The
Journal of Finance, 1970, 25 (2), 383–417.
Miyamoto, M., Kinsei Nihon no Shijo Keizai (The marketet Economy of Pre-Modern
Japan, Yuuhikaku, 1988.
Schaede, U., “Forwards and futures in Tokugawa-period Japan,” Journal of Banking and
Finance, 1989, 13, 487–513.
Shimamoto, T., Kuramai Kitte no Kisoteki Kenkyu (A Fundamental Study on the RiceBills), Sangyo-Keizaisha, 1960.
Takatsuki, Y., “The formation of the efficient market in Tokugawa Japan,” Discussion
Papers In Economics And Business Graduate School of Economics and Osaka Schoolof International Public Policy (OSIPP), Osaka University, 2007, 06-28 (Rev.2).
, “Komekitte Saikou (Reconsideration of the rice bills),” Institute of Social Science, The
University of Tokyo, Discussion Paper Series, 2008, J-169.

Historical document“Yorozu Souba Nikki (Daily memorandum of commodity price indices),” held by Kokubungaku Kenkyushiryokan Rekishishiryo Etsuranjimushitsu (Office of Archives Services in National Institute of Japanese Literature), Tokyo, Japan.

Documents published by the public offices
Otsu-shi-shi — ge-kan (The history of Otsu city — volume.3), published by the governmentof Otsu city in 1942.
Otsu-shi-shi — tyu-kan (The history and culture of Otsu city — volume.2), published by
Otsu education organization in 1911.
11

Table.1 The results of the Granger causality tests
Year

Direction

Optimal No.
of lags

Degree offreedomp-value at the
optimal lags

1798

Otsu→Osaka
Osaka→Otsu

1

117

0.663
0.000

Osaka →

Otsu

1799

Otsu→Osaka
Osaka→Otsu

1

132

0.130
0.000

Osaka →

Otsu

1800

Otsu→Osaka
Osaka→Otsu

1

144

0.239
0.000

Osaka →

Otsu

1801

Otsu→Osaka
Osaka→Otsu

1

174

0.740
0.000

Osaka →

Otsu

1802

Otsu→Osaka
Osaka→Otsu

1

169

0.863
0.000

Osaka →

Otsu

1803

Otsu→Osaka
Osaka→Otsu

1

167

0.822
0.000

Osaka →

Otsu

1804

Otsu→Osaka
Osaka→Otsu

1

161

0.279
0.000

Osaka →

Otsu

1805

Otsu→Osaka
Osaka→Otsu

1

184

0.945
0.129

None

1806

Otsu→Osaka
Osaka→Otsu

1

143

0.145
0.000

Osaka →

1807

Otsu→Osaka
Osaka→Otsu

1

189

0.048
0.752

None

1808

Otsu→Osaka
Osaka→Otsu

1

138

0.069
0.000

Osaka →

Otsu

1809

Otsu→Osaka
Osaka→Otsu

1

163

0.717
0.000

Osaka →

Otsu

1810

Otsu→Osaka
Osaka→Otsu

1

131

0.288
0.000

Osaka →

Otsu

1811

Otsu→Osaka
Osaka→Otsu

1

166

0.809
0.000

Osaka →

Otsu

1812

Otsu→Osaka
Osaka→Otsu

1

150

0.053
0.006

Osaka →

Otsu

1813

Otsu→Osaka
Osaka→Otsu

1

235

0.045
0.399

None

1814

Otsu→Osaka
Osaka→Otsu

1

201

0.415
0.032

None

1815

Otsu→Osaka
Osaka→Otsu

1

81

0.682
0.000

Osaka →

Causality

Otsu

Otsu

Table.1 continued
Year

Direction

Optimal No.
of lags

Degree offreedomp-value at the
optimal lags

1816

Otsu→Osaka
Osaka→Otsu

1

187

0.355
0.000

Osaka →

Otsu

1817

Otsu→Osaka
Osaka→Otsu

2

193

0.149
0.000

Osaka →

Otsu

1818

Otsu→Osaka
Osaka→Otsu

1

180

0.745
0.003

Osaka →

Otsu

1840

Otsu→Osaka
Osaka→Otsu

1

141

0.147
0.790

None

1841

Otsu→Osaka
Osaka→Otsu

1

202

0.813
0.141

None

1842

Otsu→Osaka
Osaka→Otsu

1

172

0.323
0.462

None

1843

Otsu→Osaka
Osaka→Otsu

1

233

0.041
0.483

None

1846

Otsu→Osaka
Osaka→Otsu

1

209

0.350
0.000

Osaka →

1851

Otsu→Osaka
Osaka→Otsu

1

203

0.351
0.594

None

1854

Otsu→Osaka
Osaka→Otsu

1

207

0.695
0.913

None

1855

Otsu→Osaka
Osaka→Otsu

1

207

0.067
0.156

None

1856

Otsu→Osaka
Osaka→Otsu

1

203

0.709
0.756

None

Note)
・The optimal number of lags is determined by the S.B.I.C.
・The significance level is 1%.

Causality

OtsuTable.2 Correlation between Osaka and Otsu
Year

The coefficientYear

The coefficient

PeriodAverage

1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812

0.401
0.574
0.793
0.635
0.453
0.559
0.878
-0.203
0.698
0.709
0.511
0.821
0.243
-0.250
0.414

1813
1814
1815
1816
1817
1818
1840
1841
1842
1843
1846
1851
1854
1855
1856

0.707
0.846
0.562
0.889
0.929
0.390
0.898
0.679
0.726
0.656
0.519
0.844
0.663
0.827
0.172

all
1798-1818
1834-1856

0.588
0.554
0.667