Measuring the Time-Varying Market Efficiencyin the Prewar Japanese Stock Market

Akihiko Nodaa,b∗a Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan

b Keio Economic Observatory, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan

This Version: July 8, 2020

Abstract: This study explores the time-varying structure of market efficiency of the pre-war Japanese stock market based on Lo’s (2004) adaptive market hypothesis (AMH). Inparticular, we measure the time-varying degree of market efficiency using new datasets ofthe stock price index estimated by Hirayama (2017a,b, 2018, 2019a, 2020). The empiricalresults show that (1) the degree of market efficiency in the prewar Japanese stock marketvaried with time and that its variations corresponded with major historical events, (2)Lo’s (2004) the AMH is supported in the prewar Japanese stock market, (3) the differ-ences in market efficiency between the old and new shares of the Tokyo Stock Exchange(TSE) and the equity performance index (EQPI) depends on the manner in which theprice index is constructed, and (4) the price control policy beginning in the early 1930ssuppressed price volatility and improved market efficiency.

Keywords: Efficient Market Hypothesis; Adaptive Market Hypothesis; GLS-Based Time-Varying Model Approach; Degree of Market Efficiency; Equity Performance Index.

JEL Classification Numbers: C22; G12; G14; N20.

∗Corresponding Author. E-mail: noda@sanken.keio.ac.jp, Tel. +81-75-705-1510, Fax. +81-75-705-3227.

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1 IntroductionEconomists have been interested in whether Fama’s (1970) efficient market hypothesis(EMH) is supported in stock markets. However, controversy exists over the present stockmarket efficiency. Lo (2004) proposes an alternative—the adaptive market hypothesis(AMH)—to the EMH. The AMH asserts that markets evolve due to several reasons suchas behavioral biases and structural changes. He argues that it is not realistic to arguewhether the market is completely efficient as per the EMH. Lim and Brooks (2011)provide a survey of recent literature on the AMH as well. In the context of empiricalstudies of the AMH, various methodologies have been employed to explore the possibilitythat the stock market evolves and market efficiency changes over time. In particular,many studies examine whether the present stock market efficiency varies with time; thesestudies include Ito and Sugiyama (2009), Ito et al. (2014, 2016b), Kim et al. (2011), Limet al. (2013), and Noda (2016). They show that market efficiency varies with time incurrent stock markets with changes in market conditions. Meanwhile, few studies focuson stock market efficiency from a historical perspective because of the low availability ofprewar stock market data, except for the U.S. and Japan.

For the prewar U.S. stock market, two major long-run datasets exist, namely, theDow Jones Industrial Average index and the S&P 500 composite index. Choudhry (2010)investigates endogenous structural breaks in the U.S. stock market using the daily DowJones Industrial Average index during the World War II (WWII) period using Perron’s(1997) a structural shift-oriented test. He concludes that the breakpoints in the marketare consistent with major historical events during the war. Kim et al. (2011) apply thedaily Dow Jones Industrial Average index from 1900 to 2009 to examine time-varying re-turn predictability using automatic variance ratio-based test statistics.1 They find strongevidence indicating that return predictability changes over time, and it is associated withstock market volatility and economic fundamentals. Furthermore, they show that returnpredictability is time-varying due to changing market conditions, which is consistent withthe implications of the AMH. Ito et al. (2016b) employs the monthly S&P composite indexfrom 1871 to 2012 when applying a generalized least square (GLS)-based time-varyingautoregressive (AR) model to investigate whether the U.S. stock market evolves overtime. They conclude that market efficiency has changed through time, the U.S. stockmarket has evolved over time, and the AMH is supported in the U.S. stock market.

Unlike the prewar U.S. stock market, there is no composite stock market index for theprewar Japanese stock market. Therefore, earlier studies examine the EMH using variousstock market indices. Kataoka et al. (2004) employ the daily stock prices in 1903 aloneto examine whether the prewar Japanese stock market was efficient. They accordinglycalculate the autocorrelation coefficients to find that the market was almost efficient in theweak sense of Fama (1970). Suzuki (2012) assumes the same breakpoints that are detectedin Choudhry (2010) to investigate the relationship between breakpoints (major historicalevents) during the Pacific War and the variation of stock prices using daily stock marketdata.2 He concludes that market efficiency declined after the start of the Pacific Warand that the breakpoints are consistent with the variation of stock prices. Bassino and

1Some test statistics are as follows: Choi’s (1999) automatic variance ratio test, Escanciano andVelasco’s (2006) generalized spectral test, and Escanciano and Lobato’s (2009) automatic portmanteautest.

2Suzuki (2012) focuses on major historical events during WWII as follows: (1) Attack on PearlHarbor on December 7, 1941; (2) the Japanese conquest of Burma from January to May 1942; and (3)the Battle of Midway in June 1942.

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Lagoarde-Segot (2015) use the daily stock prices from 1931 through 1940 when applyingEngle et al.’s (1987) the generalized AR conditional heteroskedasticity (GARCH)-in-meanmodel to investigate information efficiency in the prewar Japanese stock market. Theyfind that the 1930s-era Japanese stock market deviated from weak-form efficiency. Notethat earlier studies employ stock prices per industry, or a pseudo-volume-weighted priceindex, as their datasets and apply somewhat unsophisticated empirical methodologies.3Moreover, the sample period of most studies is too short to examine whether the modernstock market evolves and market efficiency changes over time in the sense of the AMH.

We have two approaches, namely, conventional statistical tests and time-series mod-els, to examine the AMH. The first approach constitutes the GLS-based time-varyingparameter models developed by Ito et al.’s (2014; 2016b; 2017). They aim to estimatethe degree of market efficiency together with its statistical inference on stock markets. Forinstance, Noda (2016) employs a GLS-based time-varying parameter model to investigatewhether the AMH is supported in the present Japanese stock market; the study concludesthat it is supported.4 Another approach is Kim et al.’s (2011) the automatic varianceratio test using moving-window samples. This approach is a conventional statistical testused to examine the AMH. However, it is widely known that the moving-window methodposes a problem of determining the optimal window width for the test statistic becausethe optimal window width changes from sample to sample. In contrast, GLS-based time-varying parameter models do not depend on sample size. Thus, this study employs prewarJapanese stock market data as an example in the modern period to examine Lo’s (2004)AMH as applied to the modern stock market. In particular, we measure the degree ofmarket efficiency with statistical inferences using a GLS-based time-varying parametermodel. Furthermore, we investigate the relationships between major historical events andvariations in market efficiency.

The remaining paper is organized as follows: Section 2 presents our empirical methodfor estimating the degree of market efficiency based on Ito et al.’s (2014; 2016b; 2017)the GLS-based time-varying parameter model. Section 3 introduces new datasets ofthe price index for the prewar Japanese stock market estimated by Hirayama (2017a,b,2018, 2019a, 2020) and presents the results of selected statistical tests. Section 4 showsour empirical results using GLS-based time-varying parameter models and discusses therelationships between major historical events and time-varying market efficiency in theprewar Japanese stock market. Section 5 concludes the paper.

2 The ModelThis section provides a brief review of Ito et al.’s (2014; 2016b; 2017) GLS-based time-varying parameter model. In this study, we employ an AR model as a special case oftheir model to obtain the degree of market efficiency in the prewar Japanese stock marketat each period using its univariate data. We then study the time-varying nature of themarket’s function.

Suppose that pt is a stock price at t period. Our main focus is reduced to the following3It is notable that those price indices cannot accurately reflect the value of capital in the whole stock

market.4In the recent study, Noda (2020) also employs a GLS-based time-varying parameter model to investi-

gates the AMH in the cryptocurrency markets. He finds that the AMH is supported in the cryptocurrencymarkets.

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condition, which is defined by Fama (1970):

E [xt | It−1] = 0, (1)

where xt = ln pt−ln pt−1. In other words, the time-t expected return given the informationset available at t− 1 is zero.

When xt is stationary, the Wold decomposition allows us to regard the time-seriesprocess of xt as

xt = φ0 + φ1ut + φ2ut−1 + · · · ,

where {ut} follows an independent and identically distributed (i.i.d.) process with a zeromean, and a variance of σ2,

∑∞i=0 φ

2i < ∞ with φ0 = 1. We can see that the EMH

holds if and only if φ (L) = 1. This suggests that the way the market deviates from anefficient market reflects the impulse response, which is a series of {ut}s. Let us constructan index based on the impulse response to investigate whether the EMH holds for theprewar Japanese stock market.

We can easily obtain the impulse response by using an AR model and algebraicallycomputing its estimates. We find that the process of the return of stock price x isinvertible under some conditions. We estimate the following time-varying AR(q) model:

xt = α0 + α1xt−1 + α2xt−2 + · · ·+ αqxt−q + εt, (2)

where εt is an error term with E [εt] = 0, E [ε2t ] = σ2, and E [εtεt−m] = 0 for all m 6= 0.We can regard any AR(q) model as VAR(1) for a certain q-vector in accordance withLütkepohl (2005, p.15). Thus, we can employ Ito et al.’s (2014; 2016b; 2017) approachwhen we define a degree of market efficiency. In the case of a univariate model, we obtainthe degree computed through the AR estimated coefficients, α̂1, · · · , α̂q, as follows:

ζ =

∣∣∣∣∣∑q

j=1 α̂j

1−∑q

j=1 α̂j

∣∣∣∣∣ . (3)

It measures the deviation from an efficient market. Note that in the case of an efficientmarket where α1 = α2 = · · · = αq = 0, the degree ζ becomes zero; otherwise, ζ deviatesfrom zero. Hence, we call ζ the degree of market efficiency. When we find a large deviationof ζ from 0 (both positive and negative), we consider it evidence of market inefficiency.Moreover, we can construct the degree that would change with time when we obtaintime-varying estimates of the coefficients in Equation (2).

Adopting a method developed by Ito et al. (2014, 2016b, 2017), we estimate ARcoefficients at each period in order to obtain the degree defined in Equation (3) at eachperiod. In practice, following their idea, we use a model in which all the AR coefficients,except for the one that corresponds to the intercept term, α0, follow independent randomwalk processes. That is, we suppose

αl,t = αl,t−1 + vl,t, (l = 1, 2, · · · , q), (4)

where {vl,t} satisfies E [vl,t] = 0, E[v2l,t]

= σ2 and E [vl,tvl,t−m] = 0 for all l and m 6= 0.The method of Ito et al. (2014, 2016b, 2017) allows us to estimate the GLS-based time-varying AR (TV-AR) model:

xt = α0 + α1,txt−1 + α2,txt−2 + · · ·+ αq,txt−q + εt, (5)

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together with Equation (4).To conduct a statistical inference on our time-varying degree of market efficiency,

we apply a residual bootstrap technique to the TV-AR model above. We build a setof bootstrap samples of the TV-AR estimates under the hypothesis that all the TV-AR coefficients are zero. This procedure provides us with a (simulated) distribution ofthe estimated TV-AR coefficients, assuming the stock return processes are generatedunder the efficient market hypothesis. Then, we compute the corresponding distributionsof the impulse response and degree of market efficiency. Finally, by using confidencebands derived from such simulated distributions, we conduct a statistical inference onour estimates and detect periods when the prewar Japanese stock market experiencedmarket inefficiency.

3 DataWe use three different datasets of the prewar Japanese stock markets calculated by Hi-rayama (2017a,b, 2018, 2019a, 2020): the old shares of the Tokyo Stock Exchange (TSE),the new shares of the TSE, and the equity performance index (EQPI).5 In the prewarJapanese stock market, Noda (1980) describes the “Installment Payment System.” Asmentioned in Hamao et al. (2009), large companies could issue more than one class ofshares with different proportions of paid-in shares under this system. Therefore, the dif-ference between the two types of TSE shares is simply whether fully paid-in shares wereoffered or not. The old and new shares were based on the stock price of the TSE andboth were volume-weighted indices.6 Table 1 demonstrates the differences between thewell-known stock price indices and the EQPI in prewar Japan.

(Table 1 around here)

As mentioned in Hirayama (2017a,b, 2018, 2019a, 2020), the EQPI was the first capitalization-weighted index in the prewar Japanese stock market. We can understand the value ofcapital in the stock market by using the capitalization-weighted index. Hirayama pro-vides three types of monthly average price indices for each dataset: the price index (PI),the adjusted price index (API), and the total return index (TRI). The sample periods ofdatasets are quite different: from September 1878 to April 1943 for the old shares, fromJune 1924 to April 1943 for the new shares, and from June 1924 to August 1945 for theEQPI. We take the log first differences of the time series of prices to obtain the returnsof the indices. Figures 1, 2, and 3 present time series plots of the returns for each priceindex.

(Figures 1, 2, and 3 around here)

Table 2 shows the descriptive statistics for the returns. We confirm that the mean ofreturns on the total return index is higher than those of the price index and the adjustedprice index. That is, the income gain is higher than the capital gain in the prewarJapanese stock market; therefore, we must take the dividend into account.

(Table 2 around here)5Hereafter, we call the old (new) shares of the TSE as “old (new) shares.”6Note that the TSE was a limited liability company and published its own securities in prewar Japan.

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Table 2 also shows the results of the unit root test with descriptive statistics for the data.For estimations, all variables that appear in the moment conditions should be stationary.We apply the Elliott et al.’s (1996) augmented Dickey–Fuller GLS (ADF-GLS) test toconfirm whether the variables satisfy the stationarity condition. We employ the modi-fied Bayesian information criterion (MBIC) instead of the modified Akaike informationcriterion (MAIC) to select the optimal lag length. This is because, from the estimatedcoefficient of the detrended series, ψ̂, we do not find the possibility of size-distortions(see Elliott et al. (1996); Ng and Perron (2001)). The ADF-GLS test rejects the nullhypothesis that the variables (all returns) contain a unit root at the 1% significancelevel.

4 Empirical Results4.1 Preliminary Estimations

We first assume a time-invariant AR(q) model with a constant and employ Schwarz’s(1978) Bayesian information criteria (SBIC) to select the optimal lag order in our pre-liminary estimations. Table 3 summarizes our preliminary results for a time-invariantAR(q) model. In the estimations, we choose a fourth-order autoregressive (AR(4)) modelfor the old shares, a first-order autoregressive (AR(1)) model for the new shares, and asecond-order autoregressive (AR(2)) model for the EQPI.

(Table 3 around here)

Table 3 also shows that the cumulative sum of the AR estimates for the case of the oldshares is the smallest, followed by the EQPI and the new shares, in that order.7 As canbe seen, the old TSE shares are the most efficient. Considering this result as well as thelimited explanatory power of time-invariant AR models, we should pay more attentionto the time-varying nature of the market efficiency of the prewar Japanese stock market.

Next, we investigate whether the parameters are constant in the above AR(q) modelsusing Hansen’s (1992) parameter constancy test under the random parameters hypothesis.Table 4 also presents the test statistics; we reject the null of constant parameters againstthe parameter variation as a random walk at the 1% significance level. Therefore, weestimate the time-varying parameters of the above AR models to investigate whethergradual changes occurred in the prewar Japanese stock market. These results suggestthat the time-invariant AR(q) model does not apply to our data and that the TV-AR(q)model is a better fit.

From a historical viewpoint, the prewar Japanese stock market experienced variousexogenous shocks such as bubbles, economic or political crises, natural disasters, policychanges, and wars. Table 4 summarizes the major historical events during the period ofthe prewar Japanese stock market.

(Table 4 around here)

We consider that these events affected the stock price formation. We estimate the degreeof time-varying market efficiency using a GLS-based TV-AR model in the next subsection.

7The averages of the cumulative sum of the AR estimates are 0.0588 (old shares), 0.2735 (new shares),and 0.1624 (EQPI).

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4.2 Time-Varying Degree of Market Efficiency and its Interpretations

(Figures 4, 5, and 6 around here)

Figures 4, 5, and 6 show that the degree of market efficiency in the prewar Japanesestock market fluctuated over time. We find that the prewar Japanese market was almostefficient, but the efficiency was quite volatile throughout the sample period. We nextinterpret the degree variations in light of the major historical events as shown in Table 4.Note that the interpretation of market efficiency until the 1923 Great Kanto Earthquakeis restricted to the old shares because the datasets for the new shares and EQPI are notavailable prior to June 1924.

We first discuss how the establishment of the Exchange Law in October 1893 affectedstock market efficiency. Figure 4 shows the time-varying market efficiency. We can seethat the market efficiency of the API and the TRI improved, whereas the PI’s was barelyaffected. As described by Kataoka (1987), most of the investors in the Meiji era aimed atfunding limited liability companies, and not portfolio selection. This is why the law hada negligible impact on the market efficiency of the PI. Therefore, the establishment of thelaw improved only the market efficiency of the API and the TRI through the relaxing ofthe time-inconsistency problem. We next confirm how the two wars, namely, the Sino-Japanese War (1894–1895) and the Russo-Japanese War (1904–1905), influenced marketefficiency. We find that market efficiency remained almost flat during the two wars andrapidly worsened after the wars as shown in Figure 4. It is widely known that after thosetwo wars, the prewar Japanese stock market experienced a bubble economy. In otherwords, speculated investment might have caused the high volatility of the stock pricesand worsened market efficiency. We also find that the TRI of market efficiency was mostaffected by the two wars.

From July 1914 to November 1918, World War I was experienced across the globe.The Japanese economy rose through increasing exports because the main battlefieldsof the war were in Europe. This is well known as the inter-WWI bubble economy inJapan. Figure 4 indicates that market efficiency rapidly worsened until March 1920,when the post-war depression began. Now we find that the most inefficient market wasthe PI, followed in order by API and TRI. After the collapse of the bubble economy inMarch 1920, Japan went through a serious depression. Consequently, market efficiencyimproved because speculative investment was suppressed. In September 1923, the GreatKanto Earthquake occurred. The earthquake was the impetus for ending market efficiencyimprovements that resulted in the market’s relative worsening. However, the market ranefficiently in terms of the absolute level. This result is consistent with Suzuki and Yuki(2019). They apply the daily stock prices during the 100 days before and after the GreatKanto Earthquake and employ Perron’s (1989) unit root test with a known breakpointto examine whether stock prices formed efficiently after the earthquake. They concludethat stock prices reflected various data correctly even after the earthquake occurred. Themarket efficiency itself declined relatively because the extensive monetary easing policyadopted by the Bank of Japan to support earthquake recovery led to high and volatilestock prices. In terms of market efficiency, we can see that the variation of PI, API, andTRI are almost indifferent after the Great Kanto Earthquake. Hirayama (2017b) statesthat the Tokyo Stock Exchange had not revised the stock prices after ex-rights since theseventh capital increase in September 1920. This caused a serious downward bias of thereturns on the API and TRI. Consequently, the market efficiency of each return came tohave a similar tendency.

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The Japanese government established the amended Bank Law to reorganize and mergethe banking sector in March 1927. Figures 4, 5, and 6 show that the market efficiencyof the old and new shares declined from 1928 to 1929 through the establishment of thelaw. This is because the old and new shares are volume-weighted indices and stronglyaffected by the bank sector.8 On the other hand, the policy effect on the EQPI waslimited because the EQPI is a capitalization-weighted index. This result is consistentwith the conclusion of Teranishi (2004), who argues that the policy effect of this law wasprominent in 1928 and 1929. The Great Depression of 1929 severely affected the globaleconomy. Since the Depression, each government has restricted foreign trade to protectdomestic industries. Figures 4, 5, and 6 demonstrate that market efficiency improvedduring the Depression through the suppression of speculative investment. The Japanesegovernment abandoned the gold standard and adopted the managed currency system inDecember 1931 to recover the economy. Market efficiency rapidly improved after thepolicy change.

After the Great Depression, Japan moved into a period of war. In February 1936,a group of young officers of the Imperial Japanese Army attempted a military coupcommonly called “The February 26 Incident.” They killed Korekiyo Takahashi (Japan’sfinance minister) who was a famous economic policymaker in prewar Japan. As a result,the military began to seize the initiative for policymaking on behalf of the government.However, the incident had little effect on market efficiency as shown in Figures 4, 5, and6. This is because Prime Minister Giichi Tanaka’s cabinet had already approved “TheOutline of the General Mobilization Affairs Plan” in June 1929 to control prices. As aresult, the incident did not affect a fluctuation of stock prices. Then, Prime MinisterFumimaro Konoe’s cabinet established the “National Mobilization Law” in April 1938to severely suppress price volatility in various markets. This study finds that the 1930sJapanese stock market was almost efficient, but it contradicts the findings of Bassinoand Lagoarde-Segot (2015). This difference can be attributed to the dataset and theempirical method used in Bassino and Lagoarde-Segot (2015). Their dataset containsperiods of high-level price volatility, such as the Great Depression and WWII. In fact,the volatility of the stock return was too intensive, as shown in Figure 1 of Bassino andLagoarde-Segot (2015). They also estimate a time-invariant GARCH-in-mean model toinvestigate information efficiency using the aforementioned periods’ dataset; it is obviousthat market efficiency tends to be inefficient when a high-level price volatility dataset isused.9

In Figures 4, 5, and 6, the old and the new shares indicate that market efficiencymaintained a high level until the Pacific War and rapidly declined during the war. Thisresult is consistent with Suzuki (2012), who investigates the market efficiency during thePacific War using the new TSE-based volume-weighted index. In contrast, the marketefficiency of the EQPI had been improving. The differences between the types of indicesaffected the differences in the variations of market efficiency. As mentioned above, this

8Investors often used the system of stock collateral lending to pay supplementary installments asshown in Shimura (1965) and Noda (1980). The TSE experienced nine capital increases in total; thetrading volumes of its shares accounted for much of the total trading volume in the prewar Japanesestock market (see Hirayama (2019b) for details). Therefore, we can consider that an amendment of theBank Law heavily influenced the prices of the TSE shares through the restructuring of the bank sector.

9In practice, we estimate the time-varying degree of market efficiency using the 1930s Japanese stockmarket monthly data similar to Bassino and Lagoarde-Segot (2015) and find that, during most of the1930s, the Japanese stock market was statistically inefficient. See the online appendix for more details,available at https://at-noda.com/appendix/prewar_stock_appendix.pdf

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is because the old and new shares heavily related to the bank sector, but the EQPIdid not. In particular, Fujino and Teranishi (2000) and Utsunomiya (2011) reveal thatthe government bonds to total financial assets ratio rapidly increased starting in 1941when the Pacific War occurred. The market efficiency of the EQPI continued improvingbecause (1) the EQPI is simply a capitalization-weighted index, and (2) price volatilityhad been prevented by the price control policy. Although Hirayama (2020) describes thata price formation function in the wartime Japanese stock market had worked partiallyeven under the price control policy, we find that the price control policy suppressed pricevolatility and improved market efficiency on the whole, as did Ito et al. (2016a, 2018).

5 Concluding RemarksIn this study, we apply Lo’s (2004) AMH to investigate whether the market efficiencyof the prewar Japanese stock market changed over time. In practice, we estimate thedegree of market efficiency based on Ito et al.’s (2014; 2016b; 2017) GLS-based time-varying parameter model. We summarize the results as follows. First, the degree ofmarket efficiency in the prewar Japanese stock market varied with time and its variationcorresponded with major historical events. Second, the results support Lo’s (2004) AMHon the prewar Japanese stock market, as well as Noda (2016). Third, the variation ofmarket efficiency of each return became almost equivalent after the rapid capital increasesin the early 1920s. Fourth, the variation of market efficiencies is quite different betweenthe old/new shares of the TSE and the EQPI. We find that this difference dependson whether the price index is volume-weighted or capitalization-weighted. Lastly, pricecontrol policy starting in the early 1930s suppressed price volatility. As a result, theprewar Japanese stock market operated more efficiently even during WWII.

AcknowledgmentsThe author would like to thank Kenichi Hirayama, Mikio Ito, Shinya Kajitani, YumikoMiwa, Masato Shizume, Shiba Suzuki, Tatsuma Wada, Takenobu Yuki, and the seminarparticipants at Keio University and Meiji University for their helpful comments andsuggestions. The author is also grateful for the financial assistance provided by theMurata Science Foundation and the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research, under grant numbers 17K03809, 17K03863, 18K01734, and19K13747. All data and programs used are available upon request.

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Noda, M. (1980), The History of the Emergence of Japanese Capital Markets (inJapanese), Yuhikaku.

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Schwarz, G. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6,461–464.

Shimura, K. (1965), An Analysis of Japanese Capital Markets (in Japanese), Universityof Tokyo Press.

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11

Table1:

Cha

racteristics

ofPrice

Indicesin

thePrewar

Japa

nese

StockMarket

Datab

ase

Typ

esof

Averag

eIndex

SamplePeriods

AdjustedIndex

TotalInd

exTo

yoKeizaiS

himpo

SimplePrice

Averag

e1916

/01-44

/05

No

No

Ban

kof

Japa

nSimplePrice

Averag

e19

24/0

1-42

/06

No

No

Toky

oStockExcha

nge

Volum

e-weigh

ted

1921

/01-45

/08

No

No

Nippo

nKan

gyoBan

kSimplePrice

Averag

e1910

/12-45

/01

No

No

EQPI(H

irayam

a(201

7a,2

020))

Cap

italization-weigh

ted

1924

/06-45

/08

Yes

Yes

Notes:

(1)Thistablereliesheavily

onHirayam

a(2017a).

(2)“A

djustedIndex”

deno

testhemod

ified

priceindexin

thecase

ofex-rightsan

dad

dition

alpa

id-in

capital.

(3)“Total

Inde

x”deno

testhemod

ified

priceindex,

which

addition

ally

accoun

tsforthedividend

.

12

Figure 1: The Returns of the Old Shares (TSE)

−1.

00.

00.

51.

0

PI

Time

Ret

urns

1878.1 1891.03 1903.09 1916.03 1928.09 1941.03

−1.

00.

00.

51.

0

API

Time

Ret

urns

1878.1 1891.03 1903.09 1916.03 1928.09 1941.03

−1.

00.

00.

51.

0

TRI

Time

Ret

urns

1878.1 1891.03 1903.09 1916.03 1928.09 1941.03

Note: R version 4.0.2 was used to compute the statistics.

13

Figure 2: The Returns of the New Shares (TSE)

−1.

00.

00.

51.

0

PI

Time

Ret

urns

1924.07 1928.08 1932.1 1936.12 1941.02

−1.

00.

00.

51.

0

API

Time

Ret

urns

1924.07 1928.08 1932.1 1936.12 1941.02

−1.

00.

00.

51.

0

TRI

Time

Ret

urns

1924.07 1928.08 1932.1 1936.12 1941.02

Note: As for Figure 1.

14

Figure 3: The Returns of the Equity Performance Index

−1.

00.

00.

51.

0

PI

Time

Ret

urns

1924.07 1928.08 1932.1 1936.12 1941.02 1945.04

−1.

00.

00.

51.

0

API

Time

Ret

urns

1924.07 1928.08 1932.1 1936.12 1941.02 1945.04

−1.

00.

00.

51.

0

TRI

Time

Ret

urns

1924.07 1928.08 1932.1 1936.12 1941.02 1945.04

Note: As for Figure 1.

15

Table2:

Descriptive

Statistics

andUnitRoo

tTe

sts

Old

New

EQPI

RPI

RAPI

RTRI

RPI

RAPI

RTRI

RPI

RAPI

RTRI

Mean

-0.0005

0.00

560.01

11-0.000

3-0.000

90.00

06-0.000

20.00

060.00

52SD

0.11

050.09

570.09

700.0655

0.06

520.06

530.04

660.04

580.0462

Min

-1.007

7-0.4611

-0.444

3-0.207

3-0.207

3-0.207

3-0.163

3-0.163

3-0.158

0Max

0.46

180.4618

0.46

180.22

580.22

580.22

580.1991

0.19

910.19

91ADF-G

LS-24.28

06-23.03

88-23.41

92-11.1159

-10.85

71-10.90

09-10.83

14-10.80

81-11.2741

Lags

00

00

00

00

0φ̂

0.13

460.18

570.16

990.28

900.31

040.30

680.36

430.36

630.32

93N

775

226

254

Notes:

(1)“O

ld,”

“New

,”an

d“E

QPI”

deno

tetheold

shares

oftheTSE

,thenew

shares

oftheTSE

,an

dtheequity

performan

ceindex,

respectively.

(2)“R

PI,”“R

API,”an

d“R

TRI”deno

tethereturnson

thepriceindex,

thead

justed

priceindex,

andthetotalreturnindex,

respectively.

(3)“A

DF-G

LS”deno

testheADF-G

LStest

statistics,“La

gs”deno

testhelagorderselected

bytheMBIC

,and

“φ̂”deno

testhecoeffi

cients

vector

intheGLS

detrende

dseries

(see

Equ

ation(6)in

Ngan

dPerron(2001)).

(4)In

compu

ting

theADF-G

LStest,amod

elwithatimetrendan

daconstant

isassumed.The

critical

valueat

the1%

sign

ificanc

elevelfor

theADF-G

LStest

is“−

3.4

2.”

(5)“N

”deno

testhenu

mbe

rof

observations.

(6)R

version4.0.2was

used

tocompu

tethestatistics.

16

Table3:

Prelim

inaryEstim

ations

andParam

eter

Con

stan

cyTe

sts

Old

New

EQPI

PI

API

TRI

PI

API

TRI

PI

API

TRI

Constant

−0.

0012

0.00

450.00

99−

0.00

04−

0.00

090.00

02-0.000

40.00

030.0042

[0.0

037]

[0.0

033]

[0.0

034]

[0.0

042]

[0.0

041]

[0.0

042]

[0.0

030]

[0.0

029]

[0.0

030]

Rt−

10.15

150.20

610.1776

0.26

230.27

960.27

860.34

860.34

040.30

91[0.0

424]

[0.0

483]

[0.0

450]

[0.0

605]

[0.0

530]

[0.0

519]

[0.0

381]

[0.0

399]

[0.0

380]

Rt−

2−

0.05

17−

0.07

35−

0.06

83−

−−

−0.

1734−

0.17

80−

0.15

94[0.0

340]

[0.0

423]

[0.0

427]

−−

−[0.0

543]

[0.0

563]

[0.0

531]

Rt−

30.01

580.00

520.0165

−−

−−

−−

[0.0

402]

[0.0

424]

[0.0

392]

−−

−−

−−

Rt−

4−

0.04

80−

0.07

69−

0.07

80−

−−

−−

−[0.0

344]

[0.0

417]

[0.0

387]

−−

−−

−−

R̄2

0.01

960.04

370.0327

0.06

050.07

000.06

940.10

500.10

190.08

38LC

26.900

362

.883

466.756

418

.160

617

.462

617

.589

721

.421

721

.059

320

.558

6Notes:

(1)“R

t−p,”

“R̄2,”

and“L

C”deno

tetheAR(p)estimate,

thead

justed

R2,an

dtheHan

sen’s(1992)

jointL

statisticwithvarian

ce,

respectively.

(2)New

eyan

dWest’s(1987)

robu

ststan

dard

errors

arebe

tweenbrackets.

(3)R

version4.0.2was

used

tocompu

tetheestimates.

17

Table 4: Major Historical Events in Prewar Japan

Periods Major historical eventsMarch 1893 Exchange Law establishedJuly 1894 – April 1895 Sino-Japanese War occurredFebruary 1904 – September 1905 Russo-Japanese War occurredJuly 1914 – November 1918 World War I occurredSeptember 1923 Great Kanto Earthquake occurredMarch 1927 Amended Bank Law establishedOctober 1929 – March 1933 Great Depression occurredDecember 1931 Managed Currency System establishedFebruary 1936 February 26 Incident occurredSeptember 1939 – August 1945 World War II occurredDecember 1941 Pacific War occurred

Note: This table is constructed following Institute for Monetary and Economic Studies, Bank ofJapan (1993).

18

Figure 4: Time-Varying Degree of Market Efficiency (Old Shares)

0.0

0.5

1.0

1.5

2.0

PI

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1879.02 1891.07 1904.01 1916.07 1929.01 1941.07

0.0

0.5

1.0

1.5

2.0

API

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1879.02 1891.07 1904.01 1916.07 1929.01 1941.07

0.0

0.5

1.0

1.5

2.0

TRI

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1879.02 1891.07 1904.01 1916.07 1929.01 1941.07

Notes:

(1) The panels of the figure show the time-varying degree of market efficiency for the PI (first panel), API(second panel), and TRI (third panel).

(2) The dashed red lines represent the 99% confidence intervals of the efficient market degrees.

(3) We run the bootstrap sampling 10,000 times to calculate the confidence intervals.

(4) R version 4.0.2 was used to compute the estimates.

19

Figure 5: Time-Varying Degree of Market Efficiency (New Shares)

0.0

0.5

1.0

1.5

2.0

PI

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1924.08 1928.09 1932.11 1937.01 1941.03

0.0

0.5

1.0

1.5

2.0

API

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1924.08 1928.09 1932.11 1937.01 1941.03

0.0

0.5

1.0

1.5

2.0

TRI

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1924.08 1928.09 1932.11 1937.01 1941.03

Note: As for Figure 4.

20

Figure 6: Time-Varying Degree of Market Efficiency (EQPI)

0.0

0.5

1.0

1.5

2.0

PI

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1924.09 1928.1 1932.12 1937.02 1941.04

0.0

0.5

1.0

1.5

2.0

API

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1924.09 1928.1 1932.12 1937.02 1941.04

0.0

0.5

1.0

1.5

2.0

TRI

Time

Deg

ree

of M

arke

t Effi

cien

cy

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

1924.09 1928.1 1932.12 1937.02 1941.04

Note: As for Figure 4.

21