Kazuo Sato as a macroeconomist: A quiet man who could see into the future

Celebration of Kazuo Sato’s Life

Kazuo Sato as a macroeconomist: A quiet man who

could see into the future

Koichi Hamada *

Yale University, Department of Economics, New Haven, CT 06520-8269, USA

Abstract

Kazuo Sato (1927–2004) contributed a great deal to index number theory, theory of production structure

and the contemporary state of the Japanese economy. He discovered an ideal formula for a log change index

number, based on his deep understanding in the production structure. He anticipated many contemporary

issues in Japan’s macroeconomy: the Paasche bias in the GDP deflator, index number problems when

industrial structures are under drastic changes, the potential output level or the output gap, and the role of

culture on saving behavior. Moreover, in his quiet manner, he devoted himself to serve the academic

community by editing the Japanese Economic Studies (now the Japanese Economy) by introducing and

translating many important articles that had been published in English – a deed of thankless effort.

# 2005 Elsevier Inc. All rights reserved.

Keywords: GDP deflator; Ideal index; Chain index; Output gap; Japan’s saving behavior

Kazuo Sato (1927–2004) left us a treasure of wisdom and enlightened us about economics.

Among his many valuable contributions to the academic community, the following three aspects

of his services stand out.

First, he carefully studied classic works in economic literature both from modern perspectives

and modern methodologies. Because of his thorough understanding of the achievements by old

masters, he could successfully foresee the future beyond the immediate. Second, while his

theoretical capacity excelled, he always managed to relate theory to actual empirical and

practical policy issues in the macroeconomy, in particular, with regard to Japan. The major

national accounting decisions on the GDP and its deflator in contemporary Japan are closely

connected to the index number problems that Kazuo Sato pioneered 30 years ago. Third, he was

willing to share his research time with important public services in academia. He not only

taught young minds to be excellent students, but also guided his friends as well as colleagues.

Journal of Asian Economics 16 (2005) 780–788

* Tel. +1 203 432 3610; fax: +1 203 432 3898.

E-mail address: [email protected].

1049-0078/$ – see front matter # 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.asieco.2005.08.011

In particular, he translated many books from Japanese to English and chose important articles

from Japanese journals and translated and edited these works into the volumes of The Japanese

Economic Studies (later The Japanese Economy). In short, he dared to serve the academic

community and international understanding through his often thankless labors.

1. Academic life of Kazuo Sato

Kazuo Sato was born on the January 5, 1927 in the ‘‘Elm City’’ of Japan, Sapporo in

Hokkaido. He graduated from the Economics Department at Hokkaido University and then

obtained a Ph.D. from Yale University in 1960. His dissertation was on price–cost structure and

the behavior of profit margins of U.S. manufacturing. It focused on the price–cost behavior that

was, and still is, the central issue in interpreting macroeconomic fluctuations. After teaching at

Osaka, he went to the United Nations Center for Development Planning, Projections and Policies

in New York as the Economic Affairs Officer. Later, he taught at the State University of New

York, Buffalo and at Rutgers University.

Kazuo has been on the list of Who’s Who in Economics: A bibliographical dictionary of major

economists since the first edition. He is also listed in Marquis Who’s Who.1 His achievements are

voluminous and his curriculum vitae is like a small book. Kazuo’s valuable contributions include

2 books, 4 edited books, 4 books in Japanese, and more than 70 academic journal articles, many

of which are in leading journals.

His interests in economics began with study of the Japanese economy and an econometric

model developed by Ichimura, Klein, Koizumi and Shinkai. Thus, his interest was nested in the

actual performance of the Japanese economy even before he turned to theoretical issues. His first

series of theoretical publications was on economic growth. Also, he generalized the neoclassical

theorem that Joan Robinson named ‘‘the golden rule’’ of Edmund Phelps.

Next he turned his attention to quantitative economics and to capital theory. Economists in

Cambridge, England, and economists in Cambridge, Massachusetts were engaged in a heated

controversy. Joan Robinson of Cambridge, England, led an attack on the aggregate production

function used by MIT, represented by Paul Samuelson and Robert Solow. At times the dispute

seemed like a religious war. As soon as a student wrote ‘‘K’’ for an aggregate capital, Joan

Robinson allegedly terminated the seminar with the result that, unbeknownst to her, young

people like Joseph Stiglitz, Jim Mirrlees and Tony Atkinson held the seminar in secret. On the

other hand, economists in Cambridge, Massachusetts often overstated the validity of using an

aggregate production function and the concept of aggregate capital.

Kazuo Sato did not himself engage in these philosophical or ideological debates. Instead, he

treated the aggregation problem as a purely theoretical, analytical, and empirical problem. He

found that the aggregation possibility depends on the nature of production of each firm, elasticity

of substitution, and the distribution of firm sizes. His book Production Function and Aggregation

is an important contribution to this highly politicized debate. This series of works was stimulated

during his stay at MIT in 1969–1970 where he was a visiting professor, invited by Solow.

Numerous articles appeared in leading economic journals, such as Review of Economic Studies,

Econometrica, Journal of Political Economy, and Quarterly Journal of Economics, to name a

few. Then he turned intensively to his original topics, the Japanese economy and

macroeconomics of developing countries.

K. Hamada / Journal of Asian Economics 16 (2005) 780–788 781

1 From this I learned that there are many kinds of Marquis Who’s Who.

His philosophy is well expressed in his book in Japanese, called Macroeconomic Theory

(Senka), literally translated ‘‘macroeconomics specialized.’’ The Japanese title sounds a little

archaic today, because ‘senka’ sounded like a course—sort of ‘‘second to the general course.’’

According to this book, macroeconomic theory is developed mostly in the United States and is

taught in Europe and Japan. In Japan, the U.S. macroeconomic text is the only standard way of

learning macroeconomics. Even though the nature of economic behavior is universal,

macroeconomic phenomenon can take different forms because there are different institutional

constraints in different countries. Studying macroeconomics with an American text is like

learning how to drive in bed with a manual! In order to have meaningful insight and useful

understanding of policy issues, you have to drive the car on the road.

2. Studies in index numbers

Richard Ruggles was Sato’s principal advisor at Yale, and Sato started his career by

considering the microeconomic foundation of the production structure and the aggregation

problem associated with index numbers. One of the areas where Sato contributed to the literature

is the field of the index number theory, and as we will see, his theoretical and statistical

achievements in this area now appear as the crucial questions concerning the Japanese economy.

The consumer price index, for example, is the aggregate price changes of many commodities

compressed into a single index by choosing weights to each price changes. There are several tests

proposed by Irving Fisher to ascertain the consistency of index numbers that aggregate the

changes of many items into a single entity.

(1) The Proportionality Test: A proportional change of all the components to keep the index

number constant;

(2) The Circular Test: The change of the index number from s to v is the product of the change of

index number from s to t and that of the index number from t to v when t is between s and v.

(3) The Determinateness Test: the index number remains finite or non-zero when a particular

component approaches zero.

(4) The Commensurability Test: A change in the unit of measurement of quantities or prices

keeps the index number constant.

(5) The Factor Reversal Test: The product of a quantity index (aggregate quantity change) and

the accompanying price index (aggregate price change) should be equal to the change in the

total product. The rate of increase in the nominal value of GDP should equal the rate of

increase in the price index and the rate of quantity index. In particular, the last test is a

meaningful and clear-cut criterion, and the well-known Fisher’s ideal index satisfies this test.

But it is hard, in general, to find a pair of the indexes that satisfy this criterion.2

Theil (1973) and Sato (1974) explored the ideal log-change index. The log change index is

sought because it satisfies the circular test and accordingly it is a chain index.

A chain index is an index that satisfies the circular test, that is, for h satisfying s < h < t,

Iðs; hÞIðh; tÞ ¼ Iðs; tÞ;

where I(s, t) is an index from s to t.

K. Hamada / Journal of Asian Economics 16 (2005) 780–788782

2 For a concise exposition of these tests, see, for example, Minotani (1880).

Accordingly, the chain I(0, 1), I(1, 2), . . ., I(t�1, 1) will satisfy the relationship

Ið0; tÞ ¼ Ið0; 1Þ; Ið1; 2Þ; . . . ; Iðt � 1; 1Þ:Theil and Sato found a few index formulae that satisfy approximately, but not exactly, the factor

reversal test. Finally, Sato (1976) found the index that endures the factor reversal test and fulfill

other economically meaningful requirements like the property of a chain index. He wrote about

the excitement,

‘‘. . . I report the discovery. Our (Theil’s and his) pessimism has proved premature. Indeed,

the formula was self-evident from the very beginning . . . we simply failed to see it.’’ (Sato,

1976, p. 223)3

Expressed his discovery, in his words and his notations as follows,

‘‘Consider the log-change price and quantum indexes between time 0 and 1

lnP ¼Xn

i¼1

fi lnpi1pi0

; lnQ ¼Xn

i¼1

fi lnqi1qi0

where ( pit, qit) are the price and quantity of the ith good at time t and fi is the weight for the ith

good such thatPn

i¼1 fi ¼ 1. . . .In full, the weight fi is

fi ¼Dwi=DwiPn

i¼1ðDwi=DwiÞwhere Dwi is the arithmetic change ðwi1 � wi0Þ and Dwi is the log-change ðlnwi1 � lnwi0Þ of the

ith expenditure share.’’

In the modern world where many new products are born in the market and many old products

disappear from the market, the question arises as to how to evaluate the standard of living when

the composition of products changes over time. Feenstra (1994) found that Sato’s formula, which

is also discovered by Vartia (1976), addressed this industrial situation where the components of

national product keep changing. This is one of the instances that clearly indicate that Sato’s

intuition carries across decades and horizons.

As is typical in his research, Sato based his index number study on a deep understanding of

classic economic literature by Fisher, Frisch, and Divisia. This motivated him to find appropriate

weights as in his log index to evaluate the situation. Here is another typical example where Sato’s

intuition is projected through history to contemporary policy situations. Currently, the Japanese

economy is experiencing rapid technological and compositional changes in commodities so that

the Laspeyres price index and the Paasche index of implicit GDP deflator show a substantial bias,

an upward bias in the former case and a downward bias in the latter. When the industrial structure

remains more or less stable, those biases are rather minor, but, when the structure is changing,

they diverge much from one another. For example, around 2003, the Laspeyres consumer price

index was close to zero while the Paasche GDP deflator was around �2 or �3%. People

wondered which indexes should be relied upon to assess the severity of deflation. Even when

computer-related prices are rapidly declining, the Paasche bias of the GDP deflator, which was

based on the weight of 5 years before, was large, and accordingly, real GDP tends to be

overestimated.


3 Sato (1976, p. 223).

For Japan, this is the right moment to consider the adoption of the time consistent chain index.

Under Sato (1976), there was the understanding that one has to rely on the Divisia index. By

choosing the duration (or unit) of time period short enough, the bias from the Laspeyres or the

Paasche index that fixes the reference period would be minimized. In fact, in December 2004, the

Economic and Social Research Institute (ESRI) of Japan’s Cabinet Office started to adopt the

chain index. Though the base year for the weight is a year before and not a quarter before, this

change seems to have served the purpose of reducing the bias. It is pity that Sato’s wisdom is now

difficult to communicate across the policy debates of index numbers in the current deflationary

economy in Japan (Dierwert, 2005).

All of these achievements of Sato on index numbers are related to his deep insight into the

production function. He conceived of the production function in two tiers, that is, composing

from an aggregation of production factors into semi-aggregated input factors and then from these

factors into the output. Contributions to the analysis of the field, in particular, his proposal to

build the two-tiered CES function, will be referred to by Saxonhouse (in the same issue).

3. Problems in the Japanese economy

Among his numerous articles on the state of the Japanese economy, I will refer to a few

important topics from so many which his analytical mind has dealt with.

3.1. Target wealth hypothesis

Sato maintained that the standard Friedman–Modigliani hypothesis could not fully explain the

Japanese high saving rate during the high growth period. Sato himself proposed the target wealth

hypothesis that Japanese households attempt to attain a certain level of wealth and comfort in

terms of stock like land and housing. This explains, according to him, the discrepancy of Japan’s

saving rate from the standard behavior.

3.2. Japan’s economic planning as an indicative planning

In Japan, ‘‘planning’’ was a popular word. The Economic Planning Agency (EPA), now the

Economic and Social Research Institute (ESRI) in the Cabinet Office, has important ‘‘plans.’’ Yet

Japan is, or has been, not a planned economy. Government may be able to suggest and guide the

flow of goods, but it cannot directly designate them. Sato’s piece convincingly shows that

planning in Japan is not genuine planning and nothing but an indicative planning, a concept often

used to describe the planning of the French economy. This type of planning worked because

private sectors would listen to the government and because the government possessed qualitative

instruments such as administrative guidance. The planning was effective in the areas that were

targeted by the government and had the support of the majority of private economic agents.

He also points out that the indicative planning could work on foreign economic agents as a

trade barrier. When the indicative planning was effective, underlying economic relations tended

to be long term and informality or non-transparency prevailed.

‘‘To foreigners, . . . Japanese markets are not open because they cannot break into Japanese

markets in which long-term economic relationships have already been firmly established.

Counted this way, one may say that indicative planning has been effective in Japan because

Japanese markets are closed.’’


This paper is so clearly written along with Komiya (1975) that it can be recommended, as a

most suitable assignment on this subject for a class in Japanese economy.

3.3. Cross-country differences in preferences on saving behavior and the role of culture

It is only recently that mainstream economists started seriously considering the role of

differences in taste and differences in culture as well as the endogenous process of the formation

of taste, with respect to economic behavior. As a preliminary study, Leff and Sato (1975)

estimated a uniform saving function in several countries using the appropriate econometric

method available at that time and found the possibility that homogeneous saving functions might

apply to Brazil, Costa Rica, Israel, the Philippines, and Taiwan. They detected, at the same time,

the positive influence of a higher growth rate on saving. They asserted that in developing

countries, ratchet effects and dynamic adjustment took place in response to changes in income.

This work is related to the explanation of high saving rates in Japan as well as to the target wealth

hypothesis mentioned above.

Is it important to notice the differences in preferences and the importance of culture and

institutions? To answer the question, Leff and Sato (1993) estimated saving and investment

functions with time series data for a set of 82 countries in the world. This can be regarded as one

of the pioneering papers in this direction. They took sociology and psychology seriously and did

not bend to the criticism (attributed to Robert Solow) that sociological considerations tend to

‘‘end in a blaze of amateur sociology.’’ After all, Leff and Sato were rather modest, ‘‘(I)n

analyzing international saving and investment behavior, it is necessary to ‘psychologize’

(interpret the psyches of) relevant economic agents. . . . [But] our results provide empirical

support for the person-in-the street’s perception that sociocultural conditions matter for

international differences in economic performance to make their cases in full.’’

4. Japan’s potential output and the GDP gap

One of the heated macroeconomic debates in the ‘‘lost decade’’ after 1990 in Japan is whether

the Japanese economy has been operating near the full employment level or at a level much

below it. The Economic Planning Agency (EPA) (2000) and the Bank of Japan, for example,

gave ‘‘optimistic estimates’’ . . . ‘‘optimistic’’ for the policy maker but ‘‘pessimistic’’ on the

potential growth path. According to EPA (2000), the GDP gap, measured by the percentage

discrepancy of the actual GDP from the potential GDP, was just �4.8% in December 2000. In

1996, it had even turned into a positive figure of +3%. On the other hand, Niwa (2000) and

Shishido (2000) take the pessimistic view. For example, Shishido claims that the GDP gap was

as large as �35% in 1998. Sato pays attention to the co-linearity between capital and capacity

growth and concludes that the Japanese economy was operating with the output gap of 9% rather

than the official figure of 4%.

Aside from the technical use of the CES functions in Sato’s estimates rather than the Cobb–

Douglas production functions, Sato characterizes the difference of approaches in the following

manner. ‘‘The optimistic estimate is based on the assumption that the technology input is adjusted

to keep the actual GDP path. . . . By contrast, the pessimistic estimate assumes that the

technology input . . . remained invariant through the period . . .. Obviously, as time went on, the

potential growth path deviated upward further and further from the actual growth path. In other

words, both of the groups obtained what they wanted from their respective assumptions’’ Sato

(2001).


Considering the rapidly aging population and declining working hour, I have a certain

reservation concerning Sato’s estimate because the co-linearity he mentioned about the high

growth period might have changed in the late 1990s, when industrial structures were rapidly

changing. I do not necessarily follow the approach by Fumio Hayashi and Ed Prescott (2002) in

which potential GDP is almost equated to the actual output. Still, more microeconomic

considerations seem to be necessary than Sato took. I regret that I have not discussed the matter

with Kazuo in more detail.

5. Kazuo Sato as a provider of intellectual public good

He served also the public good in the economic profession by translating so many articles and

monographs from Japanese into English. Many books in Japan have been translated from foreign

languages into English, French, and German. Japanese readers can know what the main currents

in economics in the world are.4 The reverse translation of similar books into Japanese is much

more sparse. Often achievements of Japanese authors have not been recognized because it has

been written in Japanese. In this sense, there is an asymmetric gap of information flow because of

the language difference. The Japanese Economic Studies started by Sato filled the gap. (Sato

wanted to let non-Japanese speaking audiences know the existence of valuable work in Japanese.)

The work of translation is time consuming, sometimes even boring, and brings only a very

limited academic credit to a translator. (It was a great source of encouragement for Japanese

economists. At the same time, of course, he stimulated, with his translations and discussions, the

young generation in the United States who studied the Japanese economy seriously.)

To repeat, the translation and editing of the Japanese Economic Studies was a formidable task.

First of all, choosing meaningful articles is not so easy (I helped him once or twice and realized

the difficulty). Even after choices have been made, translating required discipline. His work was

‘‘en no shita no chikara mochi (like Atlas who supports the sky),’’ that is, he volunteered to do

thankless work.

In his interview with Yasuo Hoshino in the Journal of Administrative Science in his last year

(Hoshino, 2004), Kazuo Sato remarks on the difficulty of editing The Japanese Economy because

of the difference of economists’ culture between the United States and Japan. In the United

States, according to Sato, scholars are well respected. In contrast, in Japan economists in

journalism and academic economists are not clearly identified, and the former seems to dominate

the latter. On the other hand, in Japan, serious academic articles do not necessarily focus on the

up-to-date policy issues. Therefore, translation of merely academic articles in Japan to English

cannot attract sufficient readers. Incidentally, without denying its importance, Sato points out the

limitation of journals from Japan under the government support, like Japan Echo where

unsolicited (submitted) articles are not included and because, by the author’s interpretation, the

opinions on it may be regarded to echo the position of the government. Among other things, Sato

emphasized the success of the current journal, Journal of Asian Economics, because of its

expanding demand for knowledge in Asian nations and expanding supply of output by younger

economists.

Along with this style of devotion to the professional circle, another important contribution

of Kazuo was his help and guidance to the students of economics and the Japanese economy.


4 A drawback from this is the fact that in Japan interpreting foreign economic doctrines is counted as academic

achievements and that independent thinking has often been discouraged.

The milieu was the Japanese Economic Seminar, which has been an extremely successful long-

lasting seminar series inaugurated and organized by Hugh Patrick since nearly half a century ago

and held at Columbia and in Washington. Jim Nakamura, who was one of Kazuo’s most

sympathetic friends, showed me a voluminous record of how many times Kazuo Sato attended

this seminar, presented many papers and gave substantive comments to all the papers, regardless

of whether or not he was a discussant or paper presenter himself.

6. Personal recollections

I would like to finish this memorandum with my personal reflection. The following is a part of

the note which was prepared for his informal 70th birthday occasion at the Japan Economic

Seminar at Columbia University.

In 1962, I went up to Sato’s office in the United Nations that beautifully overlooked the East

River, without a written but oral recommendation from my teacher at the University of Tokyo,

Ryuichiro Tachi. I was a graduate student who had just arrived in New York on my way to Yale

for graduate studies. He kindly welcomed my visit and gave me many pieces of valuable advice.

He even took me to a dinner, a smorgasbord that looked like a feast to a young student. Then

throughout my graduate student days, and throughout my life, he guided me as a mentor. Also,

whenever it became late he took me to his home and Mrs. Sato, Midori, extended her warm

hospitality. That reminded me of the family atmosphere I had left in Japan.

During these days, I asked silly questions. For example, how can I get good grades? He would

just smile. I did not know at that time that the career objective of an economist is neither to collect

honors nor necessarily to increase the number of publications. What matters is the intensity of

substance of our economic messages and the content in the way we interact with our students and

colleagues. We see how Kazuo showed this to us by the way he worked and lived.

As a visiting professor at MIT, Sato took Katsuhito Iwai and Takenori Inoki for discussions at

the top of the Sloan building that overlooked the Charles. Hiaroyuki Chuma was his student at

SUNY.

I heard an unconfirmed anecdote from Katsuhito Iwai. When Kazuo was a graduate student,

Robert Summers and Kazuo Sato used to ride from New Haven to Cambridge to use the, at that

time, the most advanced computer facilities at MIT. Robert Summers was amazed at the fact that

Kazuo Sato hardly uttered any words during the ride.5 In any case, he was a ‘‘quiet man.’’

Exceptionally, he brightened up when he talked about professional accomplishments of his wife

and as well as his children. And, when he had one or two glasses of beer with company and city

lights twinkled in the streets in Manhattan, his conversations gained momentum. Occasionally,

then came some critical remarks about profession from his lips. ‘‘Young referees hardly know

traditional literature.’’ ‘‘I discovered such surprising observations on the data of Japan’s

macroeconomy. Young scholars in Japan should be more interested in what their own economy in

Japan tells them than in what foreign economists wrote than.’’

Kazuo Sato always kept working, kept publishing important articles until later years, even

though he had some serious health problems. His wife told me that he once started thinking of his

research and left a concert his wife enticed him to join. When he was healthy, he liked to visit


5 Kazuo might have kept silence, though, according to the Japanese traditional etiquette to avoid disturbing the

respected and honored person.

informal restaurants and to travel. He collected Asian art pieces like Buddhist statues. His real

hobby, however, was essentially economics. He assisted Jan Dutta in the publication of the

Journal of Asian Economics and kept enlightening many participants of the Japan Economic

Seminar, including Tetsuji Yamada of Rutgers and Junji Narita of Aoyama Gakunin University.

His wife, Midori as well as Tetsuji heard to him tell that he kept discovering new facts and new

theories almost every day. It is a pity that he could not publish all of his ideas, but he must have

been one of the blessed scholars who could end their lives feeling that their researches were

blossoming.

References

By Kazuo Sato

Leff, N. H., & Sato, K. (1975). A simultaneous-equations model of savings in developing countries. Journal of Political

Economy, 83, 1217–1228.

Leff, N. H., & Sato, K. (1993). Homogenous preferences and heterogeneous growth performance: International

differences in saving and investment behavior. Kyklos, 46, 203–223.

Sato, K. (1974). Ideal index numbers that almost satisfy the factor reversal text. The Review of Economics and Statistics,

56(4), 549–552.

Sato, K. (1976, May). The ideal log-change index number. The Review of Economics and Statistics, 58(2), 223–228.

Sato, K. (2001, Spring). Japan’s GDP estimates: A critical review. Journal of Asian Economics, 12(1), 21–36.

General

Dierwert, E. (2005). Some issues concerning index number theory. Paper presented in the Seminar on the Next Step for

Japanese SNA, April 2005 at the Economic and Social Research Institute (ISRI), Cabinet Office of Japanese

Government.

Feenstra, R. C. (1994). New product varieties and the measurement of international prices. American Economic Review,

84, 157–177.

Hayashi, F., & Prescott, E. C. (2002). The 1990s in Japan: A lost decade. Review of Economic Dynamics, 5, 206–235.

Hoshino, Y. (2004). Interview with Professor Kazuo Sato. Japanese Journal of Administrative Science, 17(3), 197–199.

Komiya, R. (1975). Economic planning in Japan. Challenge, 18(May–June), 9–20.

Minotani, C. (1880). Keizai Shisu (Economic index numbers). In Keizaigaku Daijiten (Large dictionary of economics).

Tokyo: Toyokeizai Shinposha.

Theil, H. (1973). A new Index Number Formula. Review of Economics and Statistics, 55, 498–502.

Vartia, Y. O. (1976). Ideal log-change index numbers. Scandinavian Journal of Statistics, 3, 121–126.

www. conference on the next step for Japanese SNA

Economic Planning Agency (Japan). (2000). Keizai Hakusho (annual paper on the Japanese Economy). Tokyo

Government Printing Office.

Niwa, H. (2000). The recent deflationary gap in Japan: A quantitative measurement. Journal of Asian Economies, 11(2),

245–258.

Shishido, S. (2000, August). Japan’s economic growh and policy making in the context of Leontief’s contributions. Paper

presented to the 13th International Conference on Input–Output Techniques.


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Kazuo Sato as a macroeconomist: A quiet man who could see into the future