At the origins of the life cycle hypothesis of Franco Modigliani and Richard Brumberg: an attempt at analysis

Abstract

This paper re-examines the origins of the Life-Cycle Hypothesis (LCH) originally formulated by Modigliani and Brumberg seventy years ago, using a combination of historical and archival analysis. The study compares Modigliani’s own account of the LCH with a range of other sources, including papers presented at the Conference on Savings in 1952, contemporary literature, and PhD dissertations of Hamburger and Brumberg. The analysis reveals that the idea of the LCH was somehow “in the air” in the early 1950s, although Modigliani-Brumberg’s formulation represents an ingenious theoretically-founded and empirically-testable formalisation of such a framework.

Keywords:

• Saving theory
• consumption theory
• Life-Cycle Hypothesis
• history of economic thought

JEL Codes:

• B21
• B22
• D15
• E21

1. Introduction

This article aims to provide new insights into the origins of Franco Modigliani’s and Richard’s Brumberg’s Life Cycle Hypothesis (LCH) through an historiographical and archival analysis, seventy years after its pioneering elaboration. In his autobiographical book published in 2001, Adventures of an Economist, Modigliani describes how in 1952 he had not written on saving since his contribution on the relative income hypothesis (Modigliani 1949), as he was engaged in a large-scale project on the subject of firms’ behaviour planning under uncertainty at the University of Illinois. However, in that year, Kenneth Kurihara asked him to contribute to a collective volume on post-Keynesian economics, and Modigliani, who had not yet clear what to write,¹ participated in a congress on savings in Minneapolis, together with his young graduate student Richard Brumberg. The Italo-American economist describes how the conference ‘annihilated them to death’ and led them to discuss where their colleagues were wrong in repeating that saving increased with income and that this held not only for individuals but also for the society (Modigliani 2001, 58). During that now legendary conversation with Brumberg, which took place in the return journey by car from Minneapolis to Urbana, Modigliani explains that they “were rewarded with a ray of light” and came to discover the fundamental intuition at the basis of the LCH, namely, that saving is meant to accumulate resources to pursue a stable average consumption over the life span (59), especially in the face of retirement. This intuition gave origin to two manuscripts by Modigliani and Brumberg (M-B): the first work, which dealt with the microeconomic implications of the LCH, was completed in 1952 and published in 1954 in the book edited by Kenneth Kurihara. The second paper, which contained the macroeconomic implications of the LCH, was completed in mid-1953 but was only published in 1980 in Modigliani’s Collected Papers due to various reasons.² Nonetheless, the manuscript was widely known within academia since the early 1950s (e.g., see Farrell 1959; M.R. Fisher 1987). Modigliani returned to work on the aggregate consumption function in later years, with his PhD student Albert Ando at the Carnegie Institute of Technology, and the resulting model came to be known as the Modigliani-Brumberg-Ando framework (M-B-A).³

Although it is impossible to reconstruct the exact process that led M-B to their fundamental intuition on the LCH, it is possible to try to identify the sources of inspiration that contributed to their discovery.⁴ In addition to Modigliani’s autobiographical book, the reference lists contained in M-B (1954, 1980) provide a valuable insight into the debate of the 1940s and early 1950s on consumption and saving behaviour, as well as the intellectual background that inspired the elaboration of the LCH. However, it has been argued that some relevant references in Modigliani’s early (and sometimes) later writings are missing. For example, Attanasio (2015) highlights the pioneering insight of Frank Ramsey’s (1928) work on an Overlapping Generation economy with Life-Cycle saving, never cited by Modigliani and his co-authors. Similarly, Martini and Spataro (2022) point out Carlo Casarosa’s 2002 work as the first to provide a detailed assessment of Roy Harrod’s Lecture Two in his book Towards a Dynamic Economics (1948) and James Duesenberry’s Section 9 of Chapter 3 in his book Income, Saving and the Theory of Consumer Behavior (1949) as pioneering contributions to the LCH. Modigliani acknowledged Harrod’s forerunning contribution to the LCH only in 1970 (Modigliani 1970), and he never cited Duesenberry’s insight on the LCH, despite both authors being credited by other scholars since the 1950s.⁵ Moreover, while M-B gave credit to the contributions of Dorothy Brady, Rose Friedman, and Margaret Reid as sources of both inspiration and empirical validation for their LCH, Modigliani referred to Irving Fisher’s intertemporal choice model only in 1975 (Modigliani 1975, 2).

The evolution of Modigliani’s approach to the theory of saving is impressive, given that in his 1947 article on the organisation of a socialist economy, he had argued that the primary reason individuals save is the desire to increase their wealth (Modigliani 1947b, 486). Moreover, in his 1949 work on the aggregate saving ratio, he had resorted the empirical work of Brady and R. Friedman (1947) to support his relative-income assumption. Hence, this work allowed also to re-discover the evolution of Modigliani’s thought on saving behaviour occurred between 1947 and 1952.

While previous work by Martini and Spataro (2022) focused on the analysis of Casarosa’s insights into the forerunners of the LCH (i.e. Harrod and Duesenberry), this work aims to provide a deeper insight into the origins of the LCH through a broader analysis of both historiographical and archival sources. To accomplish this task, we will examine the content of the volume that collected the papers presented at the conference on Savings held at the University of Minnesota in May 1952. In fact, while Modigliani described the symposium as leaving him and Brumberg less than enthusiastic, it (at least) provided them with the now legendary “light of ray” on the way home. Additionally, the symposium offered three references for M-B’s works, including the preliminary results of Reid’s unpublished work, and possibly, inspirational insights from other participants, which we will analyse in detail.

Next, we will scrutinise the list of references that M-B provided in their pioneering works. We aim to identify the most relevant works, both empirical and theoretical, which the authors considered as relevant for the genesis of the LCH. In particular, we will focus on some contributions that, although mentioned by M-B, have been overlooked by existing literature thus far. These include Umberto Ricci’s (1926, 1927) works on intertemporal choices, Janet A. Fisher’s (1952) life cycle hypothesis and cross-sectional statistical evidence, and Brady and Friedman (1947) work on budget data. While the lack of recognition of Ricci’s contribution to the LCH can be somewhat explained by the fact that his papers on saving theory were written in Italian, it is less justifiable when referring to the above-mentioned female economists. Hence, in this paper, we endeavour to fill this gap⁶.

Concerning the macroeconomic background and implications of the LCH, we will review Gustav Cassel (1932) and Hans Neisser (1944) works, as pioneering analyses of the relation between saving and demographic structure in a steadily growing economy, as later developed and refined, among others, by Harrod (1939) and M-B (1980). In addition to unveiling that Modigliani was aware of the debate on secular stagnation put forward by Alvin Hansen (1939, 1941) at least since 1946, we will also comment on the insights into the effects of declining population that John Maynard Keynes sketched in his barely mentioned 1937 article on The Eugenics Review, one year after the publication of The General Theory.

Finally, our archival research led us to examine the references contained in William Hamburger’s (1951) and Brumberg’s (1953a) PhD dissertations. As known, both students were involved in the issue of the consumption function under the supervision of Modigliani.⁷ However, it is less known that Brumberg was also involved with Milton Friedman. In particular, we aim to clarify whether Modigliani, in his supervising activities, had come to know about Harrod’s (1948) and Duesenberry’s (1949) pioneering insights into the LCH. Our findings are somewhat surprising. The analysis of Brumberg’s PhD dissertation and academic life, besides enriching the picture of the “common intellectual environment” mentioned by M. Friedman (Friedman 1957, 6, 12n), will also allow us to further clarify the role of Richard Stone and the Department of Applied Economics (DAE) in Cambridge (UK), in fuelling scientific research on the LCH in the early years.

This paper will proceed as follows. The next section will review the most significant papers presented at the 1952 conference on savings in Minneapolis, with a particular focus on George Garvy’s and Reid’s works. In section 3, the microeconomic background of the LCH model will be investigated, with a focus on the contributions of Ricci on the theory of intertemporal choices. Section 4 will analyse the microeconomic empirical background of the LCH, with an emphasis on the works of Brady, R. Friedman and J. Fisher. Section 5 will address the macroeconomic background and implications of the LCH, discussing the contributions of Cassel, Neisser, Hansen and Keynes. Section 6 will scrutinise the references in the PhD dissertations of Hamburger and Brumberg, with a sketch, in Section 7, of the role of Stone and DAE in early LCH studies. Conclusions will be presented in Section 8.

2. The conference on saving at Minneapolis in May 1952

Modigliani’s autobiography does not mention the title of the conference, but it is most likely to be the “Saving, Inflation and Economic Progress” conference held in Minneapolis from May 15-17, 1952. The conference was organised by the University of Minnesota and numerous financial organisations and the proceedings were published in a book in 1953, edited by Heller, Boddy, and Nelson. The fact that Modigliani, although invited, was not among the speakers, seems to confirm that he had abandoned the subject momentarily after his 1949 article. In Modigliani’s reference list, only three papers from the conference were included: Klein’s paper on data and concepts related to savings (Heller et al., 104 ff.), Goldsmith’s paper on empirical evidence of long-run trends and structural changes in savings (133 ff.) and Margaret Reid’s paper on savings in family units (218 ff.).⁸ Modigliani’s overall impression of the conference was not enthusiastic, but the event turned out to be critical for the beginning of the LCH and therefore a deeper insight into the volume is warranted.

2.1. The content of the book of the conference proceedings

The book is structured into four parts. Part I examines the “Savings Problem and Outlook in Broad Perspective”, while Part II contains technical papers on “Savings Concepts, Data, and Behavior”. Part III deals with the “Savings Problem in Underdeveloped Countries,” and Part IV consists of a single paper by George Garvy on “Savings and the Problem of Inflation in the United States,” which was not presented at the Conference, although it had been provided to the participants. Due to the mixed background of the “four hundred registrants” (Heller, Boddy, and Nelson 1953, viii), the planning committee opted for a more comprehensive approach that allowed representatives from political and financial institutions to actively participate in the conference sessions. Hence, the book reflects the rather nontechnical nature of the contributions.

The first section includes papers by various experts on savings and economic policy, including Canadian Minister of Finance Douglas Abbott, former British Chancellor of the Exchequer Hugh Gaitskell, and economists Hansen and Slichter. This section mainly deals with the issue of oversaving and public policies aimed to contrast its effects.⁹ The contributions of the second part, with a closer connection with issues concerned with LCH, were written, among others, by Irwin Friend, Lawrence Klein, R.W. Goldsmith, George Katona, James Deusenberry, Dorothy Brady, Margaret Reid, and James Morgan.

Irwin Friend, from the Department of Commerce, discussed the definition of saving adopted by the Department of Commerce in collecting data on national income and product accounts (85–87, 93). He argued that higher (lower) saving propensities tend to have deflationary (inflationary) consequences, with an impact on both the price level and real income. While a significant body of data appeared to support one or more hypotheses of stable saving-income relationships, he concluded that more empirical investigation is required to confirm the existence of such a relationship and its most satisfactory formulation (91). Interestingly, he argued that data on saving and income do not indicate that the rise in individual saving registered in 1950 and 1951 was confined to special groups in the population (102). We notice that this argument is in line with Brady’s studies and with Modigliani’s rejection of the argument that saving is a luxury good.

Future Nobel Laureate Klein disagreed about the view that saving is a mere deflationary force, in that it depends on the form of investment it finances (107–108): while residential housing is likely to be inflationary, being in competition with government purchases, government securities would be less inflationary. After distinguishing between different types of (inflationary or deflationary) saving, Klein concluded that, in order to fully understand how policy can influence savings in the desired directions, a theory of the determinants of saving is needed, mentioning age, racial, geographical and other demographic characteristics among possible relevant elements. As a consequence, according to Klein, an exhaustive analysis on savings needs much more data, classified by class of saver, form (i.e., contractual or voluntary, automatically offset – that is, implying real investment directly made by the saver- or not) and possible determinants of saving (such as age and family size). As an avenue for future research, Klein pointed out that the analysis of “saving during the family-life cycle” (116) presents interesting analytical problems, in that “panels of identical households traced through several years are needed, and such data are not available” (116). Finally, he concluded with a question “What is the formal relation between savings equations estimated directly from microeconomic survey data and from macroeconomic time series? Only tentative answers of limited usefulness can be given to these questions at present” (116). Hence, in his paper Klein pointed to the need of an encompassing model able to match both micro and macro empirical evidence on saving. Moreover, besides stressing the importance of analysing life-cycle saving, he anticipated the need for panel analysis carried out in modern micro-econometric studies.

Goldsmith’s paper on trends and structural changes in savings during the twentieth century is particularly noteworthy as it presented some of the key findings from his monumental work on personal and national savings in the U.S. from 1897 to 1949, which at the time was still unpublished. Goldsmith demonstrated that the distribution of national savings among saver groups had changed little over the last fifty years, excluding war periods, and provided that government pension and retirement funds were treated as personal savings. He also provided evidence of short-term procyclical fluctuations of the saving ratio, while the long-term rate of growth of saving had been quite close to that of national income, resulting in the well-known stylised fact that “national saving has averaged about one seventh of net national product, and personal saving about one eighth of personal disposable income” (139). Goldsmith emphasised the importance of both cross-sectional and longitudinal aggregate studies for a full comprehension of saving behaviour, although the former could only be carried out for the years 1935-36, 1941, and 1946-1951 at the time. Finally, Goldsmith documented a significant and continuous shift to the right in the saving function and an increase of the marginal propensity to save (i.e., the slope of the saving function) after the thirties (144–145). In terms of the forms of saving, he documented an increase of consumers’ durables and saving in the form of government and private pension reserves. Hence, in his contribution Goldsmith laid down the preliminary results of the most comprehensive empirical research on saving data of the 1950s, which would be at the basis of both M-B and other authors writings on the issue.

Katona commented on Galbraith’s analysis of war and post-war savings in the U.S. by emphasising consumers’ expectations. Based on the 1951-1952 Surveys of Consumer Finances, Katona showed how people’s optimism regarding the business cycle had been responsible for high expenditures in the post-war period and how, conversely, pessimism stimulated higher savings in the 1951-1952 years, thus stressing the role of expectations, which M-B took into account in their papers.

James Duesenberry, in his contribution on “Savings Behavior of Individuals”, emphasised the relevance of the level, composition, and distribution of wealth in savings behaviour and stressed the role of retirement savings, which, according to him, together with an increase in housing equity, amounted to about 70% of household savings both in pre- and post-Second World War periods. He also mentioned a recent paper by Kuznets (1952), who argued that saving consists of two parts: saving for retirement and saving by the rich. Rather surprisingly, while stressing the relevance of retirement saving, Duesenberry did not make any relevant reference to the micro and macroeconomic implications of the LCH that he had envisaged in his 1949 book.

A group of experts, including Brady, Reid, and Morgan, were asked to provide brief comments on Duesenberry’s work. Brady emphasised the importance of studying budget data to fully understand the determinants of saving, which she felt was often overlooked. She cited results from the Bureau of Labor Statistics to demonstrate the role of community in shaping households’ saving behaviour. Reid presented her preliminary findings on the relationship between saving and permanent income, which we will discuss in more detail in the next subsection. Finally, Morgan, from Michigan University, highlighted the need for a microfoundation of saving behaviour, by stating: “We have a rich field of research, for analyzing decisions in a search for the motives which prompted them. It may be a little while before we can derive generalizations simple enough for aggregative models […] but it seems clear that it is an analysis of consumer decisions, not of a single concept of saving, which is in order” (217).

The third part of the book focused on the savings problem in underdeveloped countries. The contributors generally agreed that poorer countries had a low rate of saving, and that their growth would remain slow unless they could access the savings of richer nations.

Overall, after analysing the book, we concluded that the three papers that M-B cited in their seminal works were in fact the most significant for the LCH, although some others emphasised the role of retirement savings and the need for a comprehensive theoretical model on saving behaviour. However, before discussing Reid’s contribution, which M-B considered crucial to the development of the LCH, we found Garvy’s chapter on “Savings and the problem of inflation in the United States” to be worth noting. As already mentioned, although this paper was not presented at the conference, it was circulated among participants beforehand (ix). Garvy, a Latvian economist naturalised American in 1940 and at that time employed at the Federal Reserve Bank of New York, presented post-war data on saving behaviour from the Survey of Consumer Finances conducted by the Survey Research Center in cooperation with the Board of Governors of the Federal Reserve System. He documented that from 1946-1950, the proportion of dissavers in the population ranged from 27-34%, with the same proportions present in each income group (except for the higher income bracket, where the proportion of dissavers was much lower- 11.15%. See Table 7, 347). On the basis of these data, the author commented that “the relatively large number of nouveaux pauvres and of retired persons who normally dissave goes a long way towards explaining the large proportion of dissavers in the lower income groups and the relatively large average amounts dissaved. We can thus consider the population as divided at any given time into two groups, savers and dissavers”.¹⁰ We do not know whether M-B read the draft of Garvy’s paper; in fact, M-B do not cite it, although M-B were aware that the “most elaborate of the studies [on cross-sectional data, A/N] have been those of the Survey Research Centre of the University of Michigan” (M-B 1954, 389).¹¹ In any case, in that occasion Garvy produced an important empirical analysis that clearly envisaged a LCH society, in which a significant proportion of dissavers is represented by retired people.

2.2. The contribution of Reid to the LCH

As known, Reid, like Brady, had been a colleague of Modigliani at University of Illinois from 1948 to 1950, when she joined University of Chicago after the “Bowen War”.¹² Although there is no evidence of correspondence between Modigliani and Reid in their respective papers at Duke University and the University of Chicago, we can gather information from their published writings.¹³ At the conference in Minneapolis, Reid presented the preliminary results of her (unpublished) paper, entitled: “The Relation of the Within-Group Permanent Component of Income to the Income Elasticity of Expenditures”.¹⁴ This work hinged on her previous 1952 contribution “Effect of Income Concept upon Expenditure Curves of Farm Families” based on the empirical insights provided by Friedman and Kuznets (1945) on the effect of changes in relative income status among independent professionals in the U.S. In that paper, Reid had claimed about the need of a measure of the “permanent component of income” in order to correctly “measure the effect of income on differences in expenditures among families at a given time or their response to income change when it does occur” (Reid 1952, 147–148).¹⁵ More precisely, Reid argued that annual fluctuations in personal income measurement, i.e., the transitory income component, due to chance events such as illness, temporary unemployment, and windfalls, twist the consumption curve towards the average and reduce the correlation between income and expenditures. However, unlike Brady and R. Friedman, who interpreted their empirical findings as validating the assumption that household consumption is a function of relative income, Reid pointed to a quite different explanation, which will be at the basis of both LCH and PIT, in that permanent income “is the type of income that families probably have in mind when planning their spending, i.e., the income to which their spending is either adjusted or in the process of being adjusted” (169), so that “expenditures tend to be directly correlated with the permanent component of income” (174). As a testable implication, Reid concluded by prefiguring an inverse relationship between income elasticity and the transitory component of income, a concept that will be further developed in her subsequent works and that will capture M-B’s attention. According to Reid, “It seems highly probable that the greater the importance of the transitory component of income the flatter will be the expenditure curve and hence the lower its coefficient of income elasticity” (164).

At the conference in Minneapolis, hinging on her previous insights, Reid provided empirical evidence that for groups of individuals with low correlation between current and previous income, the elasticity of consumption with respect of current income was relatively low (close to zero), while for households with high income correlation, the elasticity of consumption with respect of current income was higher (close to unity). Hence, she concluded that:

The relation of the coefficients of correlation of the incomes of consecutive years to the coefficients of income elasticity of expenditures for the separate years was such that there seemed very good reason to believe the percentage of income saved to be independent of the economic level of the separate families within the groups […] In other words, the analysis suggested that if we could measure and classify families by the permanent component of their income we would find the same percentage of their income saved at all economic levels. If this relationship existed in earlier years, it would contribute to a constancy of the saving ratio on a long time basis because with a rise in the permanent component of income, families would, as it were, move up in line with the pattern of the higher incomes within their group where the percentage of income spent and saved is the same as at the lower level. (Reid 1953, 219)

Although at the conference Reid presented only preliminary results of her still unpublished paper, M-B had the possibility to consult a preliminary draft and could benefit from extensive discussion and consultations with Reid. In fact they were so impressed by “Reid’s highly ingenious techniques and the meaning of her results” (M-B 1954, section II.4) that they explicitly mentioned the concept of permanent income (404) and used Reid’s findings¹⁶ as an empirical support of the cross-sectional implications of their theoretical model, in that “the correlation between current and previous income can be taken as an indirect, approximate measure of the degree to which the current income of each household is close to the level to which the household is adjusted [i.e. the permanent component of income]” (420). In fact, according to Reid’s assumptions, the elasticity of consumption to income depends on the relative variation in permanent and transitory incomes, such that the larger the fraction of the variation in measured income that is attributable to the variation in permanent income, the closer the elasticity is to unity. It is worth mentioning that M. Friedman also used this implication to explain why estimates of elasticity differ across household groups. In particular, in Chapter VII of his 1957 book on the Permanent Income Theory (PIT), devoted to the empirical test proposed by Reid, he found that the consumption elasticity to income for farmers is significantly lower than for nonfarmers, interpreting this result as validation of the permanent income hypothesis, as farmers experience more income variation due to transitory factors.

Finally, M-B also used Reid’s argument to present another cross-sectional implication of the LCH, which suggests that the elasticity of consumption with respect to income should decrease with age, “the reason being that an increase of expected income, which accompanies the change in current income, produces a relatively larger increase in the anticipated total resources of a younger than of an older household, […] because of the greater number of years over which the higher level of income will be received (424).

3. The microeconomic foundations of the LCH in M-B’s writings: Ricci’s theory of saving

We now turn to analyse the literature that M-B cited as relevant for the theoretical foundation of the LCH. M-B documented how several scholars, starting from the late 1940s, had begun estimating consumption and saving functions that included explanatory variables beyond aggregate disposable income, such as “population, price level, past income, or the catch-all variable time”.¹⁷ However, M-B noted that the existing attempts until the early 1950s were unsatisfactory due to their mainly empirical approach, which called for “a conceptual framework to give coherence to past findings and guidance for the collection of more ‘facts” (M-B 1980, 129). Therefore, their aim was to provide a “general analytical framework which will […] provide a satisfactory bridge between cross-sectional findings and the findings of aggregative time series analysis” (M-B 1954, 389).

M-B (1954, 1980) recall that attempts to envisage a life-cycle framework for individuals, although in a non-formal way, had been already pursued by Cassel in his pioneering book A Theory of Social Economy (1932, 232–246) and, more recently, by Kuznets (1952). However, as noted by Blinder, “Franco Modigliani […] revived and gave empirical substance to I. Fisher’s theory of lifetime planning” (Blinder 1976, 87). Modigliani himself in 1975 explained that:

the challenge that Brumberg and I faced as we began our collaboration around 1950 was that of building, from the received theory of consumer choice over time à la Fisher, and a minimum set of plausible postulates, a unified model of consumption and saving behaviour, capable of accounting for, and integrating, all the macro and micro evidence […] and which could, in turn, lead to new, testable implications. (Modigliani 1975, 5)

It is important to note that M. Friedman dedicated the entire second chapter of his 1957 book A Theory of Consumption Function to derive his PIT on I. Fisher’s famous two-period model (also using the well-known two-period graph).¹⁸ I. Fisher’s theory, developed in his 1907 and 1930 works, had been widely known for more than 25 years by the mid-1950s, although it had been overshadowed by the Keynesian revolution.¹⁹ Thus, M. Friedman and M-B share the credit for reviving the somewhat out-of-fashion approach (for that time) of I. Fisher, thus setting the basis of modern micro-founded macroeconomic models of economic growth and business cycle.

However, Modigliani cited I. Fisher’s works only twenty years after his first contributions on the LCH (Modigliani 1975, 2). Interestingly enough, M-B explained that in applying the marginalist principle to their theory, they resorted to the framework of intertemporal choices elaborated in the “valuable contributions of Umberto Ricci” (1926, 1927),²⁰ an Italian economist at the University of Rome and, like Modigliani, exiled during the fascist regime. Indeed, I. Fisher laid down his theory on intertemporal choices in 1907, prior to Ricci’s works. Ricci, on his side, had contributed to popularising I. Fisher’s framework in Italy through his reviews in the Giornale degli Economisti in the early 1900s, albeit he did not always agree with the American economist. While it is possible that Modigliani had come to know about I. Fisher’s theory through the reading of Ricci’s writings in Italian, it is worth noting that Ricci, in his contributions of the 1920s, developed a theory of his own on saving, drawing on I. Fisher’s approach of intertemporal utility maximisation and extending it to a general equilibrium approach à la Walras.²¹

In the absence of any direct evidence of Modigliani’s previous studies on Ricci’s theory of savings,²² one could suppose that M-B’s citations of the Italian economist’s approach was most likely due to the “spiritual” closeness between Modigliani and Ricci, who in fact shared the fate of being Italian outcasts.²³ More fundamentally, we believe that Modigliani’s preference for the Italian economist’s works relies on the clarity of Ricci’s line of exposition of his saving theory, whose core, unlike I. Fisher’s, is condensed in half a page. It is thus instructive to follow Ricci’s own words on the theory of saving:

The simplest case that is humanly imaginable is the following: a man needs, in the present, only one economic good, […], and predicts that the need will return in the future with the same degrees of utility. […] If the amount of the present good […] exceeds the amount of the future good […], it is in the individual’s interest to transform a part of the present good into future good. […] Until when will it be in the individual’s interest to swap present wealth with future wealth? Or in other words, when will the individual have reached balance between present consumption and future consumption? When the final utility of the present good and that of the future good will be equal. […] If Primus has a certain amount of good in the present, and is sure to possess, when the future need will reappear, an equal amount of good as the present, he is already in equilibrium with respect to the distribution of his goods over time. In fact, the final utility of the present good and the final utility of the future good coincide. […] Finally, we will make a third assumption, that is, that the individual knows that he will be able to dispose of a greater amount in the future than he can enjoy at present. In this case, it would be in his interest to perform the operation that we have called the inverse of saving, that is, to anticipate the consumption of a part of the future good, […] if he lives in society, he can borrow a part of someone else’s savings, committing himself to return it later. […] In the example exposed is the core of the theory of saving. I will only have to gradually complicate and enrich it with subordinate hypotheses, to arrive at a satisfying theory. (Ricci 1926, 79–80, our translation from Italian)

Hence, Ricci presents his theory of saving choices starting from the two-period case in absence of intertemporal discounting and zero interest rate. Only later, having clarified that the nature of saving is to ensure the smoothing of consumption between the two periods of life in the face of variable lifetime resources, will he introduce intertemporal discounting and then a non-zero interest rate. In fact, M-B adopted the same effective line of exposition in their manuscripts.²⁴

It is worth adding that Ricci played a significant role in the less than enthusiastic early reception of Keynes’s General Theory in Italy. In a 1939 article, he criticised the functional relationship between saving and current income that Keynes had established, by arguing that saving decisions of rational agents are also influenced by expected future income:

for saving to grow, a comparative increase in present income with respect to future income is required (needs being equal). If, for example, present income grows but future income is expected to grow, this does not create a push towards new savings. (Ricci 1939, 201, our translation from Italian)

Once again, Ricci’s analysis shows that variations in “transitional income” in relation to “permanent income” are the real factors that influence saving decisions. This anticipation of M. Friedman and Modigliani’s intuitions by a few years is evident.²⁵

To conclude, in addition to the clarity of Ricci’s explanation of saving behaviour, another possible reason for M-B’s preference for Ricci’s works is that they wanted to distance themselves somewhat from M. Friedman’s work on PIT which, as already mentioned, was explicitly based on I. Fisher’s theory. Although the theoretical draft of the PIT had not yet been published while M-B were engaged in the writing of the LCH, M. Friedman had laid out its foundations in 1951²⁶ and it is possible that M-B had come to know it. The “influence of a common intellectual environment” in the elaboration of both LCH and PIT would be explicitly recalled by M. Friedman in his 1957 book.²⁷ While we will document this common environment in the sections that follow (and especially in Section 6), it is worth noting that Modigliani cited Ricci’s works in his 1985 Nobel Prize address, along with the then more popular contributions of I. Fisher.

4. The cross-sectional background of the LCH in the writings of Modigliani and Brumberg

After building on the marginal utility theory and presenting their results, M-B (1954) argued that the work of Brady and Friedman (1947) is supportive of the cross-sectional implications of their theory, as Modigliani already did in his 1949 article. Moreover, they pointed out that the impact of age on saving, which is a major novelty of the LCH, is supported by the empirical findings of Janet Fisher (1952). This section will review the works of these female economists, in that they turned out to be pivotal in the evolution of Modigliani’s approach to saving behaviour.

4.1. The contribution of Brady and Friedman (1947) and the LCH in the work of J. Fisher (1952)

In his 1949 paper “Fluctuations in the saving-income ratio: a problem in economic forecasting”, Modigliani had attempted to estimate the saving equation on longitudinal data by modifying the traditional Keynesian function through a cyclical component dependent on the difference between current aggregate income and previous peak income. Duesenberry had independently undertaken the same approach in 1949. Modigliani referred to the contribution of Brady and Friedman (1947) as a possible theoretical explanation for his approach, in that their analysis of cross-sectional data showed that the proportion of income saved by households appeared to be a function of the household’s community and relative income rather than absolute income, and the shift in consumption functions over time disappeared if income was measured relative to average household income.²⁸ Based on this finding, Modigliani in his 1949 contribution could then reconcile the positive dependence of the saving ratio on income within each period with the stability of the aggregate saving rate through time. Moreover, he could also provide an economically grounded explanation for the otherwise unjustifiable negative intercept of the aggregate saving equation, by arguing that it is generated by the inclusion among the poor of those “transiently poor who had managed to save in the past and/or would save in the future” (Modigliani 1975, 3).

M-B could not conduct any empirical tests for either the short-run or long-run implications of their model in their seminal writings on the LCH due to the lack of data on private net wealth, except for some indirect estimates provided by Hamburger (1951) and some preliminary figures by Goldsmith for a few selected years. Therefore, they relied on indirect estimates of the parameters of the LCH and existing empirical results provided by other authors. In this regard, M-B cited again Brady and R. Friedman’s contribution as supportive of the cross-sectional implications of their model, on the grounds that “households whose income is above the level to which they are ‘adjusted’ save an abnormally large proportion, and those whose income is below this level save an abnormally low proportion or even dissave” (M-B 1954, 418).²⁹

It is worth noting that although Modigliani had placed Brady and R. Friedman’s work at the core of his 1949 study, similarities between the latter work and the LCH cannot be stretched too far. In fact, unlike his previous work, Modigliani provided an explicit analytical foundation for the LCH. Moreover, although M-B claimed that the Modigliani-Duesenberry saving function is compatible with that stemming from the LCH, to the extent that the highest previous income is a good proxy for net worth,³⁰ the aggregate saving ratio equation estimated by Modigliani in 1949 with a positive intercept is, in fact, incompatible with the long-run implications of the LCH model. In the latter, on the contrary, the aggregate saving ratio turns out to be zero in the absence of economic growth.³¹ To sum up, M-B argued that the independence of the saving-income ratio from the level of income, a major proposition of the LCH, is supported by the empirical findings of Brady and R. Friedman, although they pointed to a different theoretical explanation, more in line, as we have seen, with Reid’s insights on permanent income.

Turning to J. Fisher’s contribution to the LCH, the American economist analysed the life-cycle behaviour of economic variables such as income, consumption, saving, and wealth for a sample of American households in a work published in 1952, developing on her PhD dissertation completed in 1950.

When M-B were writing, cross-sectional surveys on household expenditures, many of which were carried out in the 1930s, had already established a tradition in economic and sociological literature,³² although the data were affected by various problems, including the lack of agreement on the definitions of the variables under study.³³ Moreover, while data on households’ liquid assets were available, evidence on net worth was only indirect, at least until Goldsmith’s (1955) work. Studies mentioning “life cycle” had started to be published in the early 1950s, mainly by sociologists concerned with rural families. However, Woytinsky’s (1943) analysis of empirical data on the age distribution of incomes in US cross-sections appears, to the best of our knowledge, to be one of the first works written by an economist on the subject,³⁴ although not mentioned by J. Fisher nor by M-B. In her 1952 statistical work cited by M-B, Fisher explicitly introduces a “life cycle hypothesis” on the lifetime path of a household’s consumption, income, saving, and wealth. She presents the empirical evidence emerging from the 1947 Survey of Consumer Finances and writes that:

The study of consumers who are in different stages of the family life cycle should increase our knowledge of consumer behavior as a whole. The central question of this study is whether changes in the age composition of the population influence the national income and the proportion saved. We can approach the question by analyzing the financial position and economic behavior of consumer units in different age groups. More specifically, for different age groups, we shall examine the distribution of income and accumulated savings, and the patterns of current expenditure and saving out of income. From this approach, by use of cross-section data […]. (J. Fisher 1952, 77–78)

After defining the household’s life cycle as “the period from marriage through the death of both husband and wife”, she describes the expected lifetime path of a household’s income, consumption, and savings. As for the latter, she specifies:

The patterns described above suggest low saving or dissaving with marriage and the birth of children. If, then, income increases more rapidly than expenditures, a period of relatively high saving will accompany middle age, and if income falls more rapidly than expenditures, low saving or dissaving will characterize old age. However, if income falls less rapidly than expenditures or if it continues to rise, high saving will characterize old age. Probably both situations occur, but which, if either, predominates is the crucial question. (80)

In these lines, J. Fisher clearly outlines the life cycle of an individual’s saving that M-B later formalised through an analytical framework. Furthermore, while commenting on the results of the survey, J. Fisher explores how the reported data could be connected to her hypotheses (101). Regarding saving, she observes that dissaving does not mainly occur among consumers in the oldest age group, as these individuals seem to save an average percentage of their income similar to consumers in middle age groups and a higher percentage than consumers in the youngest age group. Additionally, the proportion of dissaving among consumer units in the oldest group tends to be relatively small compared to younger age groups. However, the author also argues that these findings do not necessarily disprove the hypothesis about dissaving among old people since different definitions of savings could lead to different conclusions.³⁵ Finally, J. Fisher found that data on average liquid asset holdings suggest a clearer overall life cycle pattern: an increase in holdings from the time of marriage through middle age and a slight decline in holdings with old age.

Overall, we can say that J. Fisher’s empirical findings, albeit not entirely univocal, and her LCH, represented a significant reference point for the development of M-B’s analytical model.

5. Macroeconomic implications and background of the LCH

Regarding the macroeconomic implications of the LCH, particularly the relationship between the aggregate saving ratio and economic growth, M-B (1980) cite Neisser’s work (1944) which dealt, although without an explicit micro-foundation, with link between aggregate saving and demographic structure in the context of the “secular stagnation” debate triggered by Hansen (1939, 1941).³⁶ Surprisingly enough, M-B only cite Cassel’s (1932) insights on individual life-cycle saving behaviour (M-B 1980, 191, 27n) and not his contributions to macroeconomic features of a growing economy. For this reason, we will briefly discuss Cassel’s work on this point. In his book A Theory of Social Economy, Cassel discussed the relationship between saving, demographic structure, and population growth in the context of a “uniformly progressive” (i.e., steadily growing) economy. He argued that

in a uniformly progressive economy there must be a constant accumulation of capital [positive saving, A/N]. The community may not consume the whole of its income, but must use part of this to increase its real capital […] A society with a growing population has, for this very reason, a greater need of capital disposal than a similar society whose population is stationary. (Cassel 1932, 221)

Cassel’s approach, later developed by Harrod (1939, 1948) – although in either work the Oxford economist did not acknowledge the pioneering work of the former –, contrasted with the classical view that the attainment of long-run stationary equilibrium would be driven by the Malthusian population adjustment mechanism and decreasing returns from land. Cassel concluded that in a growing society, other things being equal, the interest rate must be higher than in a stationary economy (221), indicating that prices will adjust to ensure the stability of the long-run growth process. This is the result of the “closed” general equilibrium model achieved by Ando and Modigliani (1959) and Tobin (1967) some years later.³⁷ Turning back to Cassel’s insight into the amount of saving in a growing economy, he is even more explicit when he writes:

It is therefore of the greatest importance to discover the real nature of saving and to recognise its function in a progressive economic system. Saving […] is not only possible, but is, in fact, an indispensable condition of uniform progress in any economic system. Only through such saving is the steady formation of new real capital at the same rate as the general economic progress made possible, and, with it, the uniform increase of the total available real capital and the proportionate expansion of production and the satisfaction of wants. (Cassel 1932, 40)

Hence, both quotations from Cassel point to the presence of saving as a necessary condition for a steadily growing equilibrium, which will be guaranteed by the price adjustment mechanism of competitive markets.

Regarding the direction and sign of the causal relationship between saving and growth, M-B (1980, 140–143) concluded, in contrast with the stagnationist view, that the saving ratio will remain constant and independent of the income level while being an increasing function of the rate of economic growth. At the time of M-B’s writing, the debate on the idea of “secular stagnation” put forth by Alvin Hansen and other scholars – such as Alan Sweezy, Benjamin Higgins, and Hansen’s students at Harvard like Everett Hagen, Paul Samuelson and Evsey Domar³⁸ – still had some influence, though less so. The discussion on secular stagnation began after the severe and prolonged depression of the 1930s, which did not fully recover until 1937. Some economists speculated that this may indicate a reversal in the secular trend of positive economic growth. Hansen (1939, 1941) proposed an explanation for this by identifying five major developments in the United States during the 1930s that contributed to the depression and incomplete recovery. These factors included a decrease in population growth rate, the end of the frontier, a lack of new industries, a shift from capital-using to capital-saving innovations, and an increase in corporate enterprise’s internal financing. These factors collectively reduced investment opportunities, while public savings remained high, leading to an intrinsic inability to achieve full employment without the implementation of public policies such as deficit spending and income redistribution.

Backhouse and Boianovsky (2016) note that, on one hand, Hansen’s concept of secular stagnation has nothing to do with the Keynesian argument that “rich people save proportionally more”, such that the average propensity to save increases as income grows (952). On the other hand, they claim that Hansen appears to have been influenced by Keynes’s article on population growth in the Eugenics Review (951). In this rarely cited paper, Keynes linked the demand for capital to the level of population, capital technique, and standard of living and analysed how changes in these factors could affect capital investment. He stated that an increase in population would proportionately increase the demand for capital and explored additional factors that could impact the aggregate average propensity to save and consume, such as changes in the size distribution of income and the age structure of the population. On this respect, he claimed that a more equal distribution of income would result in decreased savings (and increased consumption) given the level of income (Keynes 1937, 17) and that a decrease in family size (which initially leads to an increase in the age structure of the population) would increase “the proportion of national income which tends to be saved in conditions of full employment” (15). In other words, in this article Keynes indicates that saving, in a dynamic framework, is not only a function of income, as it was stated in The General Theory, but also of the distribution of income and of the age structure of the population.

Turning to analyse the British growth in income between 1860-1913, Keynes argued that it was mainly driven by increases in investment demand, which in turn were influenced by population growth and technological advancements allowing capital substitution for labour. However, Keynes did not cite any possible effect of the age structure on the average propensity to save. On the other hand, when discussing the effects of decreasing population since World War I, Keynes argued that while the major impact on the level of income will be exercised through a decline in investment demand, the decreasing population will also tend to increase the age structure of the population and thus the average propensity to save. He concluded that, in a stationary economy, the full employment level of savings could not be completely absorbed by the investment demand, so that either the interest rate must be reduced to stimulate investment, or wealth distribution must be altered in such a way to reduce aggregate savings and increase aggregate consumption (or both). In fact, in his 1937 article, Keynes took the Malthusian view of the long-term positive effects of decreasing population on per capita consumption, but also warned about the possible recessive effects of excess savings (i.e., higher unemployment). Keynes’s view on economic dynamics, being sketched in few pages, was somehow incomplete, especially because he did not fully discuss the implications of the age structure on aggregate saving nor the Malthusian argument in a growing economy. However, although his 1937 article was overshadowed by the revolutionary implications of The General Theory, it has been argued that in this contribution, Keynes anticipated both Harrod (1939) and the debate on secular stagnation.³⁹ Although the relation between Hansen and Keynes has been a rather controversial issue in history of economic thought,⁴⁰ Hansen shared with Keynes the idea of the need for public policies to achieve full employment also in the long-run, albeit he preferred fiscal rather than monetary policies⁴¹. In this respect, Hansen turned out to be more in line with the author of The General Theory, which doubted the effectiveness of monetary policies, than with the one of the 1937 article.

In the 1940s Hansen’s “stagnationist view” had been criticised by several authors under different respects. Some questioned the argument that population growth, discoveries of new resources, and technological progress are the main long-run causes of net investment (and thus, of aggregate demand). Another line of attack against Hansen’s argument, which is particularly relevant for the LCH, was put forward by Neisser (1944) and Terborgh (1945, 1946). These authors argued that Hansen had disregarded the fact that a declining rate of population growth means an ageing population, and, given that the aged are net dissavers, this in turn would imply lower aggregate saving, thus downsizing the problem of overaccumulation. It is interesting to quote directly Neisser’s words:

That at present private positive saving nevertheless exceeds private dissaving is attributable primarily to the fact that in a growing population the number of people who save is necessarily larger than the number of people who dissave. In other words, in a stationary population the investment activities of insurance companies, social security funds and savings banks would be considerably reduced, because their outgo would come very close to their intake. (Neisser 1944, 483)

Note, however, that Neisser came to a quite different conclusion with respect to M-B:

And I am quite far from saying that in a stationary population the net savings of individuals would in the aggregate equal zero; […] I only insist that in a society whose social, cultural and natural conditions remain the same, a stationary population will save less than a growing one. (Neisser 1944, 483–484)

Hence, although Neisser clearly identified the relationship between saving and demographic growth, he did not develop a micro-founded macro model to formalise his reasoning. As a result, he failed to reach the correct conclusion that aggregate saving will be zero at the stationary state, which had been demonstrated by Cassel in 1932 (97) and later by M-B (1980). Terborgh, on the same lines, writes:

I have no disagreement in principle with Dr. Hansen as to the impact of reduced population growth on investment opportunity. My point is simply that he has ignored its impact on saving, and that when the latter is taken into account there remains no presumption of an unfavorable shift in the relation of saving to investment. (Terborgh 1946, 170)

In his dispute with Terborgh, Hansen argued that the increase in dissaving among the retired population due to lower population growth would be counterbalanced by increased saving by productive age groups, as they have fewer children per worker or household (Hansen 1946, 16).

It is worth mentioning that Modigliani had been involved in the “stagnationist” controversy in mid-1940s, although only marginally. In 1944-1948, Modigliani worked closely with Neisser on a project at the Institute of World Affairs in New York, which led to the joint publication of National Incomes and International Trade in 1953. Modigliani also recalls that 1946 was the starting year of his work on saving (Modigliani 2001, sect. 15). In the same year,⁴² he wrote a review of Terborgh’s 1945 book “The Bogey of Economic Maturity” in Social Research. In that short paper, although arguing that the author tends to treat the opposing arguments as if they were propaganda, rather than engaging with them in a productive way, Modigliani basically agreed with Terborgh in criticising the idea that the economy has reached a “mature” state. However, the Italo-American economist also stressed the relevance of the role of public policy in maintaining full employment⁴³.

To conclude, Keynes (1937), Neisser (1944) and Hansen (1939, 1941) recognised the importance of the age distribution of the population in determining consumption and saving functions, and, although in a non-formalised way, anticipated the connection between aggregate saving and population growth many years before it became the subject of debate following the publication of the LCH. In particular, M-B followed Neisser’s argument in denying the stagnationist conclusion (M-B 1980, 193, 53n), without mentioning Keynes’s insights.

6. The precursors of the LCH in Hamburger (1951) and Brumberg (1953a) PhD dissertations

Martini and Spataro (2022) recently documented that several authors, particularly those associated with the Department of Applied Economics (DAE) at Cambridge (UK), began mentioning Harrod (and Ramsey) as forerunners of the LCH since the publication of M-B’s first paper in 1954. These authors include M. R. Fisher (1956), Farrell (1959), Brumberg (in a posthumous 1956 article edited by Christ and Stone) and, later, other authors such as Phelps (1968). Although Harrod’s contribution was widely recognised after Modigliani’s acknowledgement in 1970 (e.g., Mayer 1972), the only scholar, to the best of our knowledge, to have fully addressed Harrod’s contribution is Casarosa (2002), who also uncovered how Duesenberry’s insight on the LCH had been completely overlooked by later literature.

The works of Hamburger are particularly informative in this regard, for at least three reasons. First, M-B cited Hamburger’s unpublished PhD dissertation in both their articles, and in their second article they devoted a section to analysing the “Hamburger test” (M-B 1980, 178–181). Second, in his 1955 article published in Econometrica, Hamburger stated that “It is based on the statistical portion of my dissertation, ‘Consumption and Wealth,’ completed in 1951 at the University of Chicago, under the direction of Milton Friedman, O. H. Brownlee, and Franco Modigliani”.⁴⁴ Hence, Modigliani had been involved in supervising Hamburger’s dissertation. Third, Martini and Spataro (2022) document that in another article published in The Review of Economic Studies, Hamburger listed a series of references concerning contributions that “related consumption to the theory of choice” (Hamburger 1954, 23), including, among the theoretical works, Ramsey (1928), Duesenberry (1949, 6–46) and, as for empirical contributions, Brumberg (1953a) and M-B (1954, 1953, 1980, A/N). Moreover, they note that although the citation of Duesenberry includes the pages of Sect. 9 of Chapter III of his 1949 book, in the text of the article there is no reference to the LCH nor to its implications at the aggregate level. Finally, while citing Ramsey (1928), Hamburger does not cite Harrod (1948). Based on this information, Martini and Spataro (2022) could not draw any conclusion on whether Hamburger (and indirectly, Modigliani, as a supervisor) had read Harrod’s 1948 book while completing his PhD dissertation.

As for Brumberg’s works, Martini and Spataro (2022) recall that part of his PhD thesis had been published posthumously in 1956 in The Economic Journal, thanks to the editorial work of Stone and Christ, who saw it as a “reasonable approximation to consumption levels during the war years [and] left [it] in draft form due to the premature death of Richard Brumberg in August 1954” (Brumberg 1956, 66, 1n) limiting their intervention to minor editorial changes. Martini and Spataro find that the contributions cited in this paper, besides M-B (1954), are Ramsey (1928), Harrod’s (1948) Lecture Two, Graaff (1950), Tobin (1947), Hamburger (1951) and M. Friedman’s book on PIT “to be published”. Finally, citation of Duesenberry (1949) is only concerned with the “relative income” hypothesis, not with Duesenberry’s insights into the LCH. Martini and Spataro admit that they could not verify whether these references were due to the “minor editorial changes” operated by Stone and Christ to Brumberg’s draft nor whether they were already present in Brumberg’s unpublished dissertation of 1953, arguing, however, that Brumberg could have come to know about Harrod’s and Ramsey’s contributions while being in Cambridge, where, besides Stone, also economists such as Graaff, M. R. Fisher, and Farrell worked.

Trying to answer these open questions, we had consulted both Hamburger’s and Brumberg’s dissertations, held at the Libraries of University of Chicago and Johns Hopkins University, respectively, whose analysis will be reported in the subsections that follow.

6.1. The list of references in William Hamburger’s PhD dissertation

Hamburger submitted his thesis to the Department of Economics at the University of Chicago in December 1951. By comparing it with the article in Econometrica, it emerges that the latter is an extension of Chapters I-III of Hamburger’s PhD thesis, with the inclusion of more recent data. In particular, in Chapter I of the thesis, Footnote 2 contains a list of references that is very similar to the one presented in Hamburger’s 1954 article (including citation of Ramsey’s 1928 article), with two main differences. First, the PhD dissertation only cites 3 pages of Duesenberry’s book (34–35), which focus on the microeconomic foundations of the model, whereas the article cites pages 6–46, which also include the macroeconomic implications that are quite similar – although not always correct – to those stemming from M-B’s LCH. Second, the list of references in the PhD dissertation includes Harrod (1948), which, however, was omitted in the 1954 article. In particular, the pages in question (35–62) are those concerned with Harrod’s Lecture Two, which, as known, contains the macroeconomic implications of Harrod’s theory that anticipated the LCH. While it is unclear why Hamburger did not cite Harrod’s book in his articles, it is now evident that he mentioned Harrod’s Lecture Two in his PhD dissertation, as well as Duesenberry’s 1949 book, under the supervision of Friedman and Modigliani. Interestingly, in his 1951 work Hamburger did not mention Irving Fisher, despite his model seems to naturally descent from I. Fisher’s intertemporal choice approach, in the spirit of M. Friedman’s PIT. Instead, in presenting the microeconomic foundations of his framework, he made reference again to page 42 of Harrod’s 1948 book and to pages 227-236 of Hicks’s 1946 Value and Capital, while pointing to Ramsey’s formulation in case the individual “plans to leave an estate” (Hamburger 1951, 3).

It is worth noting that in the same year in which Hamburger completed his PhD dissertation, M. Friedman had sketched “The earliest written version of the [PIT] hypothesis […] in a four-page typescript dated June 8, 1951” (Friedman 1957, ix, 1n), following several discussions on the new theory with his wife, Brady and Reid. After reading Hamburger’s thesis, it is clear that it was built upon the theoretical framework that represented “the joint product of the group” (ix, 1n), which had been working on the permanent income hypothesis for some time, although Hamburger’s presentation of his theoretical model is just sketched in an informal way.

As neither Modigliani’s nor Reid’s papers contain any correspondence between the two former colleagues at the University of Illinois, we can only infer that Modigliani’s shift from the relative income to permanent income and then LCH as the main determinants of household consumption and saving must have occurred, in a direct way, through the conference in Minnesota and, in broader sense, through the “common intellectual environment” from which M. Friedman benefitted as well.

6.2. The list of references in Bumberg’s PhD dissertation and other insights

Brumberg’s PhD dissertation was submitted to the Faculty of Philosophy of The Johns Hopkins University in 1953. Although the date is missing, it is presumed to have been by the end of the summer of the same year. In fact, the very sparse information available from existing studies tell us that Brumberg completed his PhD thesis at Johns Hopkins University under the supervision of Christ by mid-1953, after both he and Modigliani had left the University of Illinois, and after the second paper on the LCH had been completed.⁴⁵ From the lists of “Doctoral dissertations in political economy in progress in American universities and colleges” as of the 15^th of June – i.e., the end of academic years- published in the September issue the American Economic Review yearly, it emerges that: 1) until 15^th of June 1952, Brumberg did not undertake his PhD studies; 2) until June 1953, his thesis was “in preparation” with “probable year of dissertation” 1954; 3) in June 1954, Brumberg had earned his PhD.⁴⁶ Moreover, we know that after completing his PhD thesis, in 1953, Brumberg joined the DAE at Cambridge University in the UK to study the life cycle model together with Stone and Farrell⁴⁷ and that he passed away in August 1954 while at Cambridge. Hence, in the light of all these facts, the end of the summer is the most likely date of completion of Brumberg’s PhD dissertation. Moreover, given that M. Friedman completed the first draft of his book by the summer of 1953⁴⁸ and that he wrote that “Richard Brumberg read an early version of the manuscript in its entirety and made numerous valuable suggestions for its improvement and expansion” (Friedman 1957, x), the dates provided in the above mentioned documents made it possible to suppose that Brumberg read M. Friedman’s manuscript after completing his PhD dissertation and before leaving for Cambridge (i.e. between September and October 1953). To better understand the connection between M. Friedman and Brumberg, it is worth reporting the brief resume of Brumberg’s academic life contained on the last page of Brumberg’s PhD dissertation.

Richard E. Brumberg was born in Chicago, Illinois, on the 22nd of November, 1928. He entered the College of the University of Chicago in 1946 and, after graduating from the College in 1948, he spent the next two years as a graduate student in the Department of Economics of that university. In 1950, entered the University of Illinois on a research assistantship in Economics. He received his Master of Arts degree in 1951. During the following year, he held a teaching assistantship and continued his studies at Illinois. In 1952, he was admitted to the Johns Hopkins University, where he has been a student and junior instructor (Brumberg 1953a, 85).

From Brumberg’s short biography, we got the impression that Brumberg may have met M. Friedman before meeting Modigliani, while he was studying at the University of Chicago between 1946 and 1950 and, thus, could have interacted with M. Friedman. This intuition found confirmation in the article that Brumberg published in 1953 in The Economic Journal, titled “Ceteris Paribus for Supply Curves”. In this article Brumberg, after acknowledging M. Friedman for his “criticisms and valuable suggestions” (Brumberg 1953b, 462, 1n) writes that “To the author’s knowledge, the most complete discussion available of the ceteris paribus for supply curves is in an unpublished paper by Milton Friedman” (463) and in a footnote of the same page he specifies that this material is “The Relationship Between Supply Curves and Cost Curves” (notes used in advanced-price theory course, The University of Chicago, 1950), pp. 2 f. (Hectographed)” (463, 2n).

Hence, we can conclude that Brumberg had been cooperating with both Modigliani and M. Friedman in the early 1950s.

Before turning to the list of references of Brumberg’s thesis, it is worth spending some words on other parts of such work, which will help retrieve useful information on the origins of the LCH, as well as some traits of the author, given that very little is known about Brumberg’s academic and personal life. In the preface of his dissertation, Brumberg expresses his gratitude towards Machlup and Christ of the Johns Hopkins University for their guidance and assistance in the preparation of his study.⁴⁹ He specifically acknowledges Christ’s patience and encouragement during the statistical tests conducted in the summer (presumably the summer of 1953), and, rather interestingly, Machlup for suggesting the research topic (iv). After expressing his gratitude towards Modigliani for the opportunity to partake in the research and praising him for his intellectual tolerance and willingness to help others learn, Brumberg confirms Modigliani’s version of their joint discovery of the LCH, writing that:

My concern with the problems that are the substance behind this study goes back to an argument with Professor Franco Modigliani, of Carnegie Institute of Technology. Our argument eventually grew into two papers, in which we presented theoretical foundations for the analysis of individual and aggregate behavior with respect to saving.⁵⁰ (iv)

Turning to the content of the dissertation, the work is composed of two parts: the first part presents “a resume of research conducted with Professor Franco Modigliani on the theory of consumers’ behaviour with respect to saving” (abstract without page). Following the line of exposition of M-B’s papers, Brumberg constructs an individual saving function based on “accepted economic theory” and some additional assumptions. By summing up these individual functions, Brumberg provides an aggregate saving function that depends on current income, average expected income, current holdings of assets, and the age distribution of the population. The second part of the dissertation is devoted to empirical estimations of such a function. The derived function is tested through statistical regressions on time series data (making use of two still unpublished works by Goldsmith and Lain and Klein),⁵¹ whose results, in more synthetic form, would be contained in Brumberg’s posthumous 1956 paper.

Regarding the list of references contained in Brumberg’s PhD dissertation, we discovered that the works by Ramsey (1928), Harrod (1948), and Graaff (1950) were not cited, nor was the (still unpublished) book of M. Friedman. Hence, it can be concluded that Brumberg most likely became fully aware of the existence and content of such works after his stay in Cambridge, although he and Modigliani cited Hamburger’s PhD dissertation, containing the reference to Harrod’s Lecture Two and Ramsey’s (1928) work.

7. The role of Richard Stone and DAE (Cambridge) in the early studies of the LCH⁵²

Following in Brumberg’s footsteps after his doctoral dissertation, we came across the Third Report on the activities of the Department of Applied Economics (DAE henceforth) at Cambridge University for the years 1951-1953, published in February 1954 (DAE. 1954), under the direction of Stone. Under the heading “International Survey of the Consumption Function,” the report confirms the presence of Brumberg in Autumn 1953 at DAE. Moreover, we learned that at Cambridge, Brumberg, where he had gone to continue his studies on the LCH together with Stone and Farrell at the DAE, had started to carry out tests on the consumption function on international data:

Mr R.E. Brumberg was appointed in October 1953 to work on a study to investigate the form and stability of the consumption function in a number of different countries. Various behaviour patterns that have been observed to hold in the United States are being tested for other countries with the aid of time series and cross-section data. (DAE. 1954, 13)

Interestingly, Brumberg’s thesis revealed that the young economist had already had the opportunity to interact with Stone in year 1953. At page 25, Brumberg reports that:

I am indebted to classroom discussions of Mr. Richard Stone for this explanation of the usefulness of first differences in time series regressions. For their weakness in forecasting, see Richard Stone and S. J. Prais, “‘Forecasting from Econometric Equations: A Further Note on Derationing,” Economic Journal, Vol. LXII (March, 1953), pp. 191-193. (Brumberg 1953a, 25, 2n)

We found confirmation of the presence of the would be 1984 Nobel Prize Laureate at the Johns Hopkins University in the above mentioned DAE report, where it is stated that Stone

spent the period January to June 1953 on sabbatical leave in the United States where he had accepted an appointment as Visiting Professor of Political Economy at the Johns Hopkins University, Baltimore, during the second semester of the academic year. (DAE. 1954, 16)

Under Stone’s leadership, DAE was highly influential in shaping the direction of econometric research, somehow comparable to the Cowles Commission in the U.S.⁵³ Although Stone received his Nobel Prize for his contribution to national accounting in 1984, perhaps his greatest work lies in his analysis of consumer demand and his major contributions in econometrics, including in Keynesian macro-econometric modeling.⁵⁴ Stone’s association with Keynes began when he attended Keynes’s lectures as a student, and during World War II, he served as Keynes’s assistant.⁵⁵ In 1945, Keynes recommended Stone as the first Director of the Cambridge DAE, despite his initial criticism of econometrics in his 1939 review of Tinbergen. Keynes seems to have changed his opinion on econometrics by the time of the White Paper on Employment Policy in 1944, where he acknowledged that theoretical economics was now mature enough to be applied practically and predicted a new era of statistical prosperity.

As shown by the four reports that the DAE produced under Stone’s direction, many notable economists and econometricians gained valuable experience at the DAE, which had access to advanced computing technologies, including the legendary Electronic Delay Storage Automatic Calculator (EDSAC) developed at the Cambridge Mathematical Laboratory. According to Durbin (who elaborated the famous Durbin-Watson test at DAE⁵⁶), this computing facility was indeed one of the assets of the DAE, with a room with “perhaps eight or ten young ladies operating desk calculators, supervised by an older lady of forbidding demeanour. They did the computing”.⁵⁷

From the Third Report of DAE it also emerged that Farrell, most influential in scrutinising and popularising the LCH since the early stages, in 1953 had returned to DAE after spending some years in the U.S.⁵⁸:

Michael Farrell, who left the Department in September 1951 to take up a Commonwealth Fund Fellowship, has continued some of the work which he began in the Department. He has now returned to Cambridge as a University Assistant Lecturer, and has prepared two papers, ‘Demand for Motor Cars in the United States’ which was read to the Royal Statistical Society in February 1954 and is to be published in the Society’s Journal, and ‘Some Aggregation Problems in Demand Analysis’ which is to appear in the Review of Economic Studies [1953]. (DAE. 1954, 16)

M.R. Fisher recalls that Farrell had spent two years with the Cowles Commission for Research in Economics, in which he had the opportunity to interact with Modigliani, Brumberg and M. Friedman.⁵⁹

Finally, the DAE Report shows that M.R. Fisher, as well particularly influential in the early development of the LCH and PIT, “had been associated with the Department’s work” (16).

The evidence collected so far, together with the fact that Modigliani worked within the Keynesian framework concerning the shape and the stability of the consumption function, well clarifies the reason why the DAE, explicitly established by Keynes, had become so active in the analysis of the implications of the LCH and had been an ideal work for Brumberg to further develop his studies.

8. Conclusions

This paper provides new insights into the origins of the pioneering work of Modigliani and Brumberg (M-B) on the life cycle hypothesis (LCH). Based on an examination of various historiographical and archival materials, it turned out that the sources of inspiration for the elaboration of the LCH were multiple. As for the theoretical framework, besides the insights stemming from Modigliani’s studies on the project ‘Expectations and Business Fluctuations’ that he had been carrying out when still at University of Illinois, Ricci’s marginalist theory on saving decisions, now almost neglected, provided a surprisingly clear conceptual framework and an analytical microeconomic basis for the LCH. However, we argue that the “common intellectual environment” recalled by M. Friedman (Friedman 1957, 6, 12n) from which both Modigliani and M. Friedman benefitted, played a crucial role too in originating the analytical formulation and the emergence of the micro and macroeconomic implications of the LCH. This fertile common framework was represented, in a broader sense, by the vivid debate on the Keynesian consumption function erupted since the publication of The General Theory, which had already produced both theoretical models and empirical estimates. In narrower sense, such a “common intellectual environment” was represented by the contributions of, and in some case direct collaboration with, three female economists – Brady, R. Friedman and Reid – and two PhD students such as Brumberg and Hamburger.

Despite Modigliani’s emphasis on the now proverbial and still mysterious “ray of light”, M-B participation in the 1952 Minneapolis Savings conference was particularly significant for the formulation of the LCH. At that conference, in fact, M-B could receive inspirational insights from the preliminary results of Goldsmith, from Klein’s authoritative arguments and Garvy’s cross-sectional evidence pointing to LCH behaviour of American households. Most importantly, M-B were able to discover Reid’s still unpublished paper exploring the relationship between within-group permanent income components and expenditure elasticity, which would be one of the main cross-sectional empirical implications of LCH.

As far as other cross-section implications of the LCH are concerned, particularly significant were Cassel’s early insights and the somehow overlooked empirical work on budget data of Janet Fisher. In particular, in her statistical analysis on consumption and saving, J. Fisher was explicitly guided by a “life-cycle hypothesis”, which represented an innovative and rigorous conceptual framework, drawing from the tradition of sociologist literature on poverty and on the pioneering insights of Woytinsky’s (1943) work on the cross-sectional age distribution of income.

As for the macroeconomic implications of LCH, the insights of Cassel onto a “progressive economy”, and Neisser’s contribution on the debate on secular stagnation initiated by Hansen represented important points of reference.

Looking for “missing quotations” in Modigliani’s early writings in the LCH, we highlighted Keynes’s (1937) lecture on the consequences of population decline on economic development and on the possible role of age distribution in affecting aggregate saving and economic development. However, many of Keynes’s conclusions presented in that paper turned out to be in line with those put forward by Hansen through his concept of secular stagnation, which we showed that Modigliani had been familiar with at least since 1946. Other relevant missing quotations emerging from our study are the cross-sectional evidence provided by Garvy at the conference in Minneapolis, which clearly pointed to an LCH-shape of saving in the U.S., and the already mentioned Woytinsky (1943) insights into the LCH of income. However, the most glaring and puzzling missing citations remain Harrod’s (1948) Lecture Two and, perhaps to a lesser extent, Section 9 of Chapter 3 of Duesenberry’s (1949) book and Ramsey’s (1928) article. In the present paper we hope to have added another piece to the mosaic of this well-known but still unfinished story by revealing that Modigliani, involved in the supervision of Hamburger’s doctoral dissertation, had most likely become aware of both Harrod’s and Ramsey’s pioneering contributions on LCH and OLG economies, respectively, since both works were cited by the doctoral student of the University of Chicago. We also discovered that Brumberg had already collaborated with M. Friedman and also with Stone, although only through “classroom discussion”, before joining the Department of Applied Economics at Cambridge.

As a concluding comment, we must admit that questions as to why Modigliani waited until 1970 before citing Harrod’s Lecture Two, and never cited Ramsey’s article, still remain unanswered. This is all the more true in light of the fact that, as we have shown, since the early years following the publication of his article with Brumberg, several Cambridge economists, and even Hamburger in earlier years, had clearly suggested the anticipatory role that the two English economists, both grown up under John Maynard Keynes, had played in providing a theory of saving that was strongly connected with that derived from the LCH.⁶⁰ Needless to say, the above unresolved issues, while representing an interesting intellectual challenge from the perspective of the history of economic thought and, therefore, worthy of further study, do not diminish the value of the originality of M-B’s contribution, whose model remains to this day one of the most fascinating and long-lasting examples of rigorous theoretical and empirical analysis in the history of economics. In fact, although M-B were not the first to recognise the importance of the life cycle of individuals and the connections between the aggregate propensity to save and the growth rate of the economy, they firmly established the LCH within the marginalist framework of intertemporal choices, introduced a formalised overlapping generations model into economic theory, and derived the determinants of the aggregate saving rate in a rigorous manner, thus correcting the intuitively-based propositions formulated by their predecessors. Moreover, differently from their predecessors, Modigliani and his co-authors drew full policy implications from their model and provided several rigorous empirical tests on it.

Acknowledgements

The authors would like to thank the Editor, two anonymous Referees and Carlo Casarosa for their helpful comments on a previous version of the manuscript. The usual disclaimer applies. Although the conception and drafting of the text is the outcome of joint research, Sections 2.1, 3, 5, 6.1 are attributable to Alice Martini, Sections 2.2, 4, 6.2, 7 are attributable to Luca Spataro and the remaining Sections 1 and 8 have been co-authored.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 However, in the introductory footnotes of both articles with Brumberg, Modigliani specified that “my contribution to this paper is a direct outgrowth of the research carried out as director of the project ‘Expectations and Business Fluctuations’”, thus emphasizing the similarity of the relation between “consumption, assets, income expectations, and the life cycle of income as developed in this paper and the relation between production, inventories, sales expectations, and the seasonal cycle of sales” as developed in his studies with Sauerlender, later published in 1955 (see M-B 1954, 388, 2n).

2 See Modigliani (2001, 68). One reason was the early death of Richard Brumberg in 1954, which caused Modigliani to lose interest in revising the manuscript for eventual publication. Additionally, Modigliani feared that the manuscript was too long. The paper was 99 pages long and, although submitted to Econometrica in 1953 (see, Franco Modigliani Papers, Box C03, correspondence of Modigliani with Strotz, Co-editor of the journal), was only published in Vol. II of Modigliani’s Collected Papers, in its original formulation. For a deeper reconstruction on the fate of second paper, see Rancan 2020, 125 ff).

3 See, in particular, Modigliani and Ando (1957) and Ando and Modigliani (1959, 1960, 1963).

4 Several authors have provided valuable reconstructions of the Italo-American’s intellectual production on the LCH. See, for example, Kouri (1986), Casarosa (2002), Deaton (2005), Szenberg and Ramrattan (2008), Puttaswamaiah (2009), Read (2011), and Rancan (2020). Moreover, the Modigliani Papers kept at the David Rubenstein Rare Book and Manuscript Library of Duke University, represent a precious direct source of information. However, folders on the LCH start from 1953, that is, mainly after the writing of the two papers by M-B. The content of these documents has been already deeply analyzed by Rancan in several works, especially in Rancan (2020), to whom we point the interested reader.

5 Earlier assessments of Lecture Two of Harrod’s book had been provided by Higgins (1948), Robinson (1949) and Graaff (1950), in fact before the publication of M-B (1954). As for Duesenberry’s insights into the LCH, Martini and Spataro (2022) could find only a citation in Hamburger (1955). In fact, Mayer (1972), while including Harrod’s theory within the “wealth theories”, considers Duesenberry’s work on “relative income” as part of the “measured income theories”. On the same lines, see Branson (1979, ch. 10), although the latter does not cite Harrod’s nor Duesenberry’s insights into LCH.

6 For example, the works by Brady and R. Friedman and by Reid are discussed by Rancan (2020) but not mentioned by Szenberg and Ramrattan (2008). Kouri (1986) mentions only the former, while none of them mentions J. Fisher’s work.

7 See Martini and Spataro (2022, 94).

8 We could reconstruct M-B’s participation at such conference on the basis that in their first paper (published in 1954 but terminated in 1952), M-B cite the three papers presented at the conference without making reference to the book containing the proceedings. In fact, the book was published in 1953. On the other hand, the book is explicitly mentioned in M-B (1980), completed in mid 1953, in which Goldsmith’s chapter (although without reference to the pages), is mentioned. See M-B (1980, 192, 44n).

9 Specifically, Hansen argued that the high public expenditure for defense had been the primary reason for the increase of investment and consumption expenditures that occurred in the U.S. in the postwar period. He also attributed the fact that this happened at almost full employment without inflationary pressure to two elements: the ability to expand production and high savings. On the other hand, Goldenweiser, while defining government saving as “absurd”, replied that the argument that there are not enough outlets for investment, so that government spending in excess of revenue would be necessary, demonstrates “how little imagination humans really have,” given that it has been demonstrated that “outlets are innumerable” (Heller, Boddy, and Nelson 1953, 58).

10 See Garvy (1953, 348). Similar insights are contained in Garvy (1948) and Katona 1949b), who used the same source of data, for different years. Only the latter work, documenting a systematic portion of dissavers among income groups for the years 1946 and 1947 in the US, is cited in M-B (1954, 407, 33n). Interestingly, in the latter work Katona showed evidence that “the largest proportion of dissavers is found (in both years) among those with a past income decrease and an expected income increase. In other words, an income decline that is believed to be temporary was frequently associated with spending more than one’s income”, while “the smallest number of dissavers is found (in both years) among those whose income did not change and was not expected to change. Income stability was not associated frequently with spending more than one’s income” (Katona 1949b, 100). This empirical evidence, although not pointing directly to the LCH, was however clearly in line with its underlining idea of saving as “temporary income”.

11 See also M-B (1954, 398, 18n, 414, 49n), where they cite Katona’s 1951 analysis on the same data.

12 It is useful to recall that Modigliani accepted a job offer at University of Illinois in November 1948, being asked to act as a supervisor of large-scale research project (Expectations and Business Fluctuations). Reid and Brady were also working at the University of Illinois in the same period, the former being involved in the analysis of household production and consumption, the latter being involved in researching on personal income distribution and savings, on the basis of family budget data. Due to the “Bowen war” (see Rancan 2020, chap. 4; Solberg and Tomilson 1997), Reid resigned in 1950 and joined University of Chicago. After resigning from the University of Illinois in 1951, Brady rejoined the Bureau of Labor Statistics and in 1958 became a Professor of Economics at the Wharton School at the University of Pennsylvania. As for Modigliani, the extremely difficult circumstances of the Department convinced him to move to the Carnegie Institute of Technology in September 1952, where he remained until 1960; then, after a period at Northwestern University (1960-1962), he joined MIT, where he spent the rest of his academic life (see Modigliani 2001, Section 20).

13 Besides M-B acknowledgements in their 1954 contribution, we could find only indirect evidence of interaction between Modigliani and Reid, in that the latter, in a letter to M. Friedman, shared with him her talks with Modigliani, who had been with her in the same section at the AEA meeting held in December 1953. In that occasion Modigliani presented the first paper on cross sectional implications of the LCH with Brumberg (see Letter of M. Reid to M. Friedman, February 7, 1954, Milton Friedman papers, Box 232, Folder 13, Hoover Institution Library & Archives, quoted also in Burns 2022).

14 Results were published, modified and expanded, in two papers with Dunsing in 1956 and 1958. See Forget (2022).

15 M-B, following Reid (1952), also mention the contribution by Vickrey (1947), who argued that consumption is more reliable than current income as a measure of the permanent component of income and that the size composition of the household influenced saving behavior (M-B 1954, 422, 44n).

16 As M-B pose it: “These results were first reported in a brief communication presented at the Conference on Saving, Inflation and Economic Progress, University of Minnesota, in May, 1952. The authors have also had the opportunity to consult a preliminary draft on “The Relation of the Within-Group Permanent Component of Income to the Income Elasticity of Expenditures,” and have had the benefit of extensive discussion and consultations with Miss Reid. The hypothesis tested in the above-mentioned paper had already been partly anticipated in Reid’s earlier contribution, “Effect of Income Concept upon Expenditure Curves of Farm Families,” Studies in Income and Wealth, Vol. XV, especially pp. 133–139” (M-B. 1954, 422, 45n).

17 Garvy (1948, 416). M-B argue that “probably the opening gun in this campaign was the paper by W. S. Woytinsky [1946, A/N]” (M-B 1980, 190, 8n). In particular, they cited Tobin (1947), Klein (1951), and Hamburger (1951) as early attempts to add (some measure of) wealth within the set of explanatory variables of aggregate consumption. For an analysis of Tobin’s contribution, see Buiter (2003, F590–F595) and Dimand (2011, 170–171). For a survey of early empirical estimations of the consumption function, see Ferber (1953).

18 M. Friedman (1957, 6), claimed that the Fisherian approach to individual consumption behavior is the “pure theory of consumer behavior” and that it makes the wealth approach a sounder account than Keynes’s” (Chao 2003, 84). M. Friedman, like Schumpeter and Tobin, referred to I. Fisher as to “the greatest economist the United States has ever produced” (Friedman 1994, 37).

19 Dimand and Geanakoplos point out that “in the money and fluctuations literature, I. Fisher was the most-cited economist in the 1920s (with Mitchell second, and the young Keynes tenth). By the 1940s, I. Fisher vanished completely from citation lists as John Maynard Keynes captured the profession’s attention” (Dimand and Geanakoplos 2005, 4).

20 M-B (1954, 390, 7n; 1980, 191, 29n, 32n). We thank an anonymous referee for suggesting that we scrutinize Ricci’s works in deeper detail.

21 For a deeper insight on Ricci’s thought, also in relation to I. Fisher, see Pavanelli (2006) and the references contained therein. See also Bini and Fusco (2004) for a wider presentation of Ricci’s life.

22 We also scrutinized four articles of the young Modigliani, dealing with price controls, prices and corporative prices, autarky and the international division of labour, have been published in their English translation in Rivista Internazionale di Scienze Sociali 113 (4), (2005): 559–591. In those articles there is no mention to Ricci’s works. For a deeper analysis of the early writings of Modigliani in Italy, see Michelini (2020).

23 We also recall that Jacob Marschak, Modigliani’s mentor at the New School of Social Sciences, the so-called University of Exiles, had translated Ricci’s paper on the classification of demand curves on the basis of the elasticity concept from Italian into German. See Ricci (1931). Hence, it is also possible that Modigliani had been introduced to Ricci’s works by Marschak.

24 See “Assumption III” in M-B (1954, 396 ff; 1980, 136 ff, 160 ff).

25 Some authors have argued that Modigliani’s adoption of a mathematical approach to saving, like other Keynesian economists in the U.S., represented a retreat from political issues and a safe harbor after the episodes of McCarthyist pressure that had befallen him at the University of Illinois. However, we note that the tension towards a neoclassical synthesis of the Keynesian doctrine, with an abundant use of mathematics, had guided Modigliani since his doctoral dissertation and was a characteristic trait of the New School in New York, started by Jacob Marschak, who had been Modigliani’s mentor. As recalled by Hagemann, “Still, we often think of the New School tendencies as unorthodox and politically on the left. And they generally were. But in this instance, Modigliani came under the influence of the New School refugee economist with the most impressive career in American economics [Marschak, A/N]. The result of this influence is a largely neoclassical synthesis of Keynes” (Hagemann 2017, 956). For a deeper insight into the dispute on the effects of McCarthyism on economics, see also Weintraub (2017) and Rancan (2020, ch.4).

26 See Friedman (1957, ix).

27 See Friedman (1957, 6, 12n). M. Friedman writes that it was Brady to urge him to write the book and that the latter was in fact the result of a joint work of a group that included Brady, Reid and R. Friedman (Friedman 1957, ix). Interestingly, M. Friedman writes that “a number of other friends have also read one or another version of the manuscript and have been generous with helpful comments. The late Richard Brumberg read an early version of the manuscript in its entirety and made numerous valuable suggestions for its improvement and expansion” (x). Moreover, Modigliani had got a six-month fellowship in Political economy at Chicago in Autumn 1948 and since that year until 1951 he had been research consultant for the Cowles Commission, whose seminars were regularly held at the University of Chicago (Rancan 2020, 84, 6n), although M. Friedman was rather in conflict with the scientific approach adopted at the Cowles Commission (Christ 1994, 35). Finally, in 1951 Modigliani acted as a member of the dissertation committee of Hamburger, at the University of Chicago, together with M. Friedman and O.H. Brownlee. See later on, Section 6.

28 See also Brady (1952).

29 In another occasion, Modigliani summarized his findings by stating that, similarly to the PIT, the LCH implies that “the high savers are not the rich, but the temporarily rich (i.e., rich relative to their own normal income)” (Barnett and Solow 2000, 239). As for the main differences between LCH and PIT see, for example, Branson (1979, ch. 10) and Kouri (1986).

30 See M-B. (1980, 177–178).

31 See also Ando and Modigliani (1963, 76–80).

32 For example, for the U.S., the Consumer Purchases Study, Spending and Saving in Wartime, records from the Farmers Home Administration, Surveys of Consumer Finances, the Liquid Assets Survey. See J. Fisher (1950, 1952), Brady in Heller, Boddy, and Nelson (1953, 204). Furthermore, according to J. Fisher, “Because of little interest in the age factor, information was not collected on the economic behavior of different age groups prior to 1930” (J. Fisher 1950, 8).

33 See Brady (1951) and Friend and Klein in Heller, Boddy, and Nelson (1953).

34 Glick (1989) dates back the origins of the “life-cycle of family” approach to the book of Sorokin, Zimmerman, and Galpin (1931), within the rural sociology literature. Later works are Glick (1947), Beegle and Loomis (1948), both including the term “Life cycle” within their titles. Finally, Woytinsky (1943) recalls as a notable previous work, the book by the English sociologist Seebohm Rowntree, who, in 1901 described the poverty risk by analyzing the data on poverty in the city of York for year 1899, showing that the poverty risk was strictly related to the life cycle of workers (see Rowntree 1901).

35 In particular, she argues that “if transfer payments were excluded from both income and saving, many more consumers in the oldest age group would probably be found to have dissaved. Moreover, if durable goods purchases were classified as savings instead of as expenditures, many more consumers in the younger age groups would probably be classified as savers instead of dissavers” (101). The same argument will be used by M-B in commenting J. Fisher’s empirical findings in their 1954 work.

36 Among other theoretical works M-B (1954, 1980) cite de Scitovszky, who posed the assumption that “the accumulation of wealth diminishes the desire to save” (de Scitovszky 1941, 72). However, he also writes that “population growth raises the marginal productivity of capital by diminishing its quantity relatively to that of labour; it diminishes the propensity to save by lowering real income per head (owing to the law of non-proportional returns)” (87), thus going in opposite direction with respect to M-B. As known, the subject was further developed by Pigou (1943), who argued, in contrast with Keynes, that deflation would have contributed to restore full employment, by increasing the purchasing power of those assets with value fixed in money terms and, thus, reducing savings at a level “no greater than could be absorbed in investment at the institutional minimum of the rate of interest” (M-B 1980, 151–152).

37 In this respect, it is worth briefly recalling the contribution of Jannie Graaff (1950), a South African economist who had been working at Cambridge University. In fact, it was Graaff who, commenting on Harrod’s results outlined in Lecture Two of his 1948 book Towards a Dynamic Economics, correctly anticipated the findings on the relation between interest rate, aggregate wealth and wealth-income ratio that Modigliani would have explained in his Nobel Lecture. On that occasion, Modigliani explained how the effect of the interest rate on wealth crucially depends on the relative strength of the substitution and income effect, governed by parameter e, the elasticity of intertemporal substitution, which Graaff had discovered in his 1950 pioneering contribution. See Modigliani (1986, 303–304).

38 See Martini and Spataro (2021).

39 See Thirlwall (1987, 20–21). In fact, in these lines Keynes seems to have in mind the exact equilibrium relation between the aggregate saving rate (s), the capital-income ratio (K/Y) and the economy’s rate of growth (g), which will be later formulated by Harrod (1939), that is s/g=(K/Y), when he writes that: “I think we can safely say […] that the proportion of the national income which would be saved today in conditions of full employment lies somewhere between 8 per cent and 15 per cent of the income of each year. What annual percentage increase in the stock of capital would this rate of saving involve? […] The existing national stock of capital is equal to about four times a year’s national income. […] It follows that new investment at a rate of somewhere between 8 per cent and 15 per cent of a year’s income means a cumulative increment in the stock of capital of some- where between 2 per cent and 4 per cent. per annum” (Keynes 1937, 16). The above relation will be used by M-B (1980, 143), although citing neither Keynes (1937) nor Harrod (1939).

40 For a deeper insight, see Mehrling (1997) and Backhouse and Boianovsky (2016). For a more complete analysis of Keynes’s writings on population, see Toye (1997).

41 See, for example, Hansen (1939, 10–12).

42 See Modigliani (1946). Rancan documents that in that year Modigliani started a collaboration with Neisser at the Institute of World Affairs on the subject, which in 1946 produced a publication in the U.S. Department of Commerce Bulletin entitled “Cyclical and Secular Factors in the Relationships between Income, Consumption and Savings” (see Rancan 2020, ch. 3). Moreover, at the end of 1946 Modigliani presented the first version of his 1949 paper at the AEA Conference, whose shorter version was published in Social Research the following year (see Modigliani 1947a). The collaboration between Modigliani and Neisser is also documented by Modigliani’s acknowledgements of Neisser’s support and advice contained in his 1947a and 1949 articles.

43 It Is worth recalling that in their second paper M-B dedicated a section to discuss the effectiveness of (monetary) policies aimed at restoring the equality between aggregate saving and investment and concluded by doubting the real effectiveness of such a policy (see M-B 1980, 151–158).

44 Hamburger (1955, 1, 1n).

45 Modigliani (2001, Sect. 19). He also recalls that at Johns Hopkins University worked such economists as Kuznets, Domar, Machlup.

46 See AER (1952-1954).

47 Rancan (2020, 119 ff). See also this section, further below.

48 Reid, Margaret G. Papers, Box 6, Folder 1, Hanna Holborn Gray Special Collections Research Center, University of Chicago Library, letter of Milton Friedman to Margaret Reid, August 17, 1953.

49 Fritz Machlup was a marginalist Austrian academician who concluded his thesis under the supervision of Mises and then found an occupation at the University of Buffalo in 1933. Being persecuted by the Nazis for his Jewish origins, he remained in the U.S. and became an American citizen in 1940. More detailed information on Machlup’s academic life is provided in Haberler (1983) and Klausinger (2014). Carl Christ was an econometrician who graduated at Chicago and had been a Research Associate at the Cowles Commission from 1949-1950, where he got contact with Modigliani. His collected papers on econometrics, history of econometrics and economic policy were published in 1996 (Christ 1996).

50 The author thanks also Professor G. Heberton Evans, Jr., Chairman of the Department of Political Economy at the Johns Hopkins University, for enabling him to visit Professor Modigliani in Pittsburgh (see also Modigliani 2001, Sect. 19), most likely, to terminate the second paper on the LCH.

51 References are, respectively, to the drafts of the works later published in Goldsmith (1955) and Frane and Klein (1955).

52 We thank an anonymous referee for pointing us to analyse the role of DAE in the early stages of the LCH.

53 See Epstein (1987, 142). For an analysis into the role of DAE to econometrics, see Smith (1998) and Thomas (2017).

54 Deaton argues that Stone’s greatest contributions were in his empirical analysis of consumer behavior and his contribution to econometric methodology (Deaton 1987, 510). Klein praised Stone’s exceptional skills in data collection, statistical manipulation, theoretical methods of statistics, and theoretical economics (Klein 1952, 104). For a deeper insight on Stone’s life, see Pesaran and Harcourt (2000), Smith (2019) and the bibliography contained therein.

55 See Pesaran and Harcourt (2000, 148 ff).

56 See DAE. (1954, 17).

57 Quoted in Smith (1998, 98).

58 Farrell was Joint Managing Editor of The Review of Economic Studies from 1965 to 1968 and a Fellow of the Econometric Society. For a deeper insight into Farrell’s academic life, see M. R. Fisher (1976) and Bliss (2008).

59 M. R. Fisher (1976), 371. See also Farrell (1959, 678, 1n).

60 As for the subject of the long oblivion of Ramsey’s contributions in the economic science, see Duarte (2009).