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Fazer uma tese de doutorado é uma tarefa das mais ingratas. Digo “fazer” por que escrevê-la é apenas a parte mais dolorosa do processo. Você batalha por anos a fio, tenta fechar um tema que dá uma contribuição mínima a um canto de um sub-campo de uma área de estudos dentro de uma vasta rede de acadêmicos gabaritados que parecem já ter pensado em tudo o que você se desdobra para conceber… e fizeram melhor do que você seria capaz de fazer.

Alguns aspiram a encarnar a grandiosidade e tornar-se celebridades. Outros se satisfazem em estar em contato com estas. Eu sou deste último tipo. Não à toa, eu estudo história das ideias; uma área marginal e pouco glamourosa da ciência econômica.

Pois bem, minha pesquisa tentava compreender a evolução conceitual da inércia inflacionária aqui no pensamento brasileiro (acesso à tese por aqui). Acabei tropeçando numa conexão inusitada entre duas áreas aparentemente desconectadas entre si.

Serendipity

Notei uma similaridade visual entre o principal modelo que organizou as discussões sobre indexação no Brasil e alguns desenvolvimentos da economia neoclássica no momento histórico em que os economistas se debruçavam sobre um tópico “nada” econômico: gestão de estoques (artigo sobre o tema aqui).

A figura abaixo retrata um modelo publicado em um artigo de 1950 de Kenneth Arrow e dois importantes co-autores, em que abordavam as condições para uma política ótima de estoques.

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Figura 1 – Non-optimal and Optimal inventory policy. Source: Arrow, Harris & Marshack (1950, p. 253)

Poucos anos depois, Nicholas Kaldor apresentaria em palestra na FGV no Rio de Janeiro um modelo de aceleração inflacionária (figura abaixo) no contexto de reajustes periódicos de rendas nominais, depois conhecido por indexação.

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Figura 2 -Kaldor´s Real Wage ” Zig-Zag ” diagram. Source: Kaldor (1957c, p. 68).

Mais tarde, esta representação gráfica se tornaria o “cavalo de batalha” das reflexões sobre inflação persistente, com as contribuições de Simonsen (1964) em A Experiência Inflacionária no Brasil (abaixo) e de Felipe Pazos (1972).

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Indo à fonte

Minha preocupação era se, porventura, Kaldor e Arrow haviam trabalhado juntos em algum projeto no final dos anos 1940 e início dos anos 1950, antes de Kaldor vir para o Brasil em 1957.

Como não conseguia encontrar base documental para esta conexão (ainda hoje as evidências são fracas), optei por escrever para vários acadêmicos especialistas em áreas que tangenciavam meu tópico. Após receber as atenciosas respostas destes pesquisadores, percebi que ninguém sabia exatamente do que eu estava falando.

Foi então que senti o peso e a solidão de ser um “especialista” em “algo interessante” – como todos alegavam – mas completamente irrelevante – pois ninguém havia-se interessado pelo problema.

Dei-me conta de que o primeiro autor do artigo de 1950, o nobelista Kenneth Arrow estava vivo e muito ativo, com seus mais de 90 anos de idade.

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Kenneth Arrow – Nobel em Economia em 1972 por suas contribuições no campo dos modelos de equilíbrio geral

Com a maior despretensão, escrevi para ele num sábado à noite, em mais uma maratona de pesquisa e redação, com a certeza de que meu e-mail cairia em uma caixa de mensagens indesejadas.

A Surpresa

Ao acordar no domingo pela manhã, abri minha caixa de e-mails e lá estavam as DUAS mensagens. Não satisfeito em me responder da primeira vez, Arrow se debruça rapidamente sobre a minha hipótese e, após algum tempo de pesquisa, atenciosa e graciosamente me escreve nova mensagem, sugerindo outras vias de análise e de implicações das teorias que estava buscando compreender.

Com o intuito de registrar o material, reproduzo a seguir a “gloriosa” – para mim pelo menos – troca de mensagens com o grande Kenneth Arrow com o intuito de incentivar os jovens pesquisadores brasileiros a não temer o desprezo dos grandes pensadores ainda vivos. Como já aprendemos desde cedo em nossas conquistas amorosas: o “não” nós já temos.

A Missiva

(No arquivo você pode ter acesso à troca impressa diretamente de minha conta de e-mail).
A primeira mensagem que enviei faz uma rápida apresentação da tese e do problema da conexão Arrow-Kaldor.

On Dec 13, 2014, at 4:11 AM, Andre R Carvalho wrote:

Dear Prof. Arrow,

I am a PhD candidate at the University of São Paulo, Brazil, and I am doing some research on the forerunners of the inertial inflation theory that informed the stabilization attempts throughout the eighties and nineties in Latin America. I write to you in search of some clues regarding the connection between Nicholas Kaldor, Baumol’s 1952 inventory-theoretic approach to money demand and his connections to the inventory theory carried out at the Cowles Commission.

Let me provide you with a brief outline of what I am looking for.

Kaldor spent some months in Latin America in 1956, where he lectured in CEPAL (Chile) and in Brazil. Before coming to Chile, that same year, he spent a few weeks with Prof. Scitovsky at Stanford, where you were also at the time. (But, by then, I believe you were no longer working on these inventory policy models). At this time, Kaldor developed a sawtooth shaped illustration of real wages under chronically inflationary conditions, which is likely to have informed both of the later developments of such a theory in Latin American quarters. However, simply stating that he is a forerunner of such a modeling representation seems to miss the more relevant question of how he came about this diagrammatic representation.

By looking into this rather unexpected connection, I came across some common ground between some of Nicholas Kaldor´s contributions to the inflation theories in developing countries and current developments in inventory theory. Your 1950 paper, alongside Harris and Marschak, has shown rather crucial at this specific juncture. In fact, the first model of inventory dynamics under certainty is the very representation that was later to be celebrated in Latin America as a close depiction of real wages under chronic inflation.

However, I have not been able to adequately substantiate this connection due to lack of references on the importance of inventory theory to developments in economics as well as to other disciplines.  Two lines of investigation were raised as a consequence of this findings, namely:

1) Kaldor’s Academic networks: I have learned about Kaldor´s participation in the US and UK bombing surveys in the immediate post-war period and, also, of his personal relationships with von Neumann and Tibor Scitovsky. It was suggested to me by one of his biographers that Kaldor was closely connected to Marschak and maybe this is a likely link between these two threads of theory based on the same diagrammatic representation. Do you have any recollections of Kaldor participating in any meetings or seminars, or of him being in touch with members of the Commission or of having exchanged ideas on these matters with anyone working on those models?

2) Inventory-theoretic approaches: Your paper – Arrow, Harris and Marschak (1950 – Optimal Inventory Policy) – anticipates, via inventory theory, the very representation Kaldor sets forth six years later in 1956. More than that, Baumol’s 1952 paper also makes use of such sawtooth-shaped representation (which was direclty inspired by a paper published by Whitin, in 1952, also on inventory models). That made me wonder if there was something to be hoped, at the time, by adopting this inventory-inspired type of modeling, an avenue of theoretical development that was later abandoned.   but I was wondering if there is anything more substantial in terms of knowledge sharing and cross-fertilization between these research quarters.

That being said,  I was hoping you could give me some guidance based on your recollections of those times, maybe sources and papers I could look this up in. Also, any information you may have that is not published but maybe useful in this search would be greatly appreciated, especially in what concerns the influence of this inventory-theoretic approach within the intellectual environment of the early 1950s.

I thank you in advance for your attention, apologize for demanding so much of your memory and hope this message finds you in good health.

Best regards,

André Roncaglia de Carvalho

University of São Paulo

Graduate Program in Development Economics


A resposta do Prof. Arrow veio cerca de 13 horas depois.


On Dec 13, 2014, at 6:22 PM, Arrow Kenneth J. wrote:

Dear Mr Roncaglia de Carvalho:

You are raising a very good historical question.  I have only a shallow knowledge of these events.

As you note, Harris, Marschak, and I developed the theory of optimal inventory replacement in the deterministic case before going on to the case of uncertain demands.  Under conditions of economies of scale in ordering, one gets a periodic order policy, which gives rise to a “saw-tooth” behavior of inventories.  (As we noted, similar results had earlier been found by R. H. Wilson.)

I do not know who first had the idea of reinterpreting the model to cover changing prices in the face of inflation  There are several names that come to mindL:  Andrew Caplan (at Columbia University), Yoram Weiss (Tel Aviv University), and Eytan Sheshinski (Hebrew University).

I had not connected Nicholas Kaldor with this literature, but that just shows my ignorance.  

With regard to the inventory-theoretic models of demand for money, I remember finding some papers from the 1930s by Edward Shaw and by Moses Abramovitz.  A related, much earlier paper, is one by Francis Edgeworth (probabily in the 1880s), about the reserves which a bank should hold if its depositors have random times for withdrawal; he derived a square-root model. Tobin developed a model similar to Baumol’s, though independently.  Both acknowledged that they had been anticipated by Maurice Allais. But all this literature seems different from the menu-cost theory of price adjustment.

If you wish, I will make more of an effort to put flesh on these observations.

Yours,

Kenneth J. Arrow


Não satisfeito com sua primeira resposta, o Prof. Arrow responde espontaneamente poucas horas depois:


Em 14/12/2014, à(s) 05:26, Arrow Kenneth J. <arrow@stanford.edu> escreveu:
Dear Mr. Roncaglia de Carvalho:
The Wikepedia article on, “Menu Cost Economics,” gives credit to Sheshinski and Weiss for introducing the hypothesis of fixed costs to changing prices (1977).  I have no idea how Kaldor picked it up.
Sincerely yours,
Kenneth J. Arrow

Lisonjeado pela inesperada atenção, finalizo nossa comunicação agradecendo ao professor:


Dear Prof. Arrow,

You are too kind and thoughtful!

Thank you for your attention on this matter. You’ve been extremely helpful and gave me important hints of where to look for other references, which I have already found to be crucial to my argument.

I wish you merry holidays and a great year in 2015.

Best wishes,

André


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