Abstract
The Italian economist Carlo Casarosa published a study in 2002 claiming that there existed two contributions—one by Roy Harrod (1948, Lecture Two) and one by James Duesenberry (1949, Chapter III, Sect. 9)—that could be considered forerunners of Modigliani and Brumberg’s pioneering works about the Life Cycle Hypothesis (LCH). Those contributions, according to the Italian scholar, had been, until that moment, scarcely known by the scientific community. Particularly, he pointed out that, while Modigliani in 1970 eventually recognized Harrod’s contribution to the LCH, he never mentioned Duesenberry’s work. After presenting and commenting on the content of Casarosa’s investigation, in this paper we present the results of an extended historiographical analysis that we have carried out on the early literature about the LCH. Rather interestingly, our analysis shows that several economists, especially from Cambridge (UK), had acknowledged the role of Harrod (together with the one of Frank Ramsey) since early 1950s, while Duesenberry’s contribution to the LCH was completely ignored.
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Notes
A list, though not exhaustive, of relevant references is Modigliani (1966), (1970), (1975), (1986) and (1988), Modigliani and Ando (1957), Ando and Modigliani (1959), (1960) and (1963), Drèze and Modigliani (1975), Modigliani and Tarantelli (1975), Modigliani and Sterling (1983). On some occasion Modigliani referred to the LCH as to M-B-A model (see for example, Ando and Modigliani 1960, p. 78), to acknowledge Ando’s contribution.
“In Chapter 2 of Towards a Dynamic Economics, Sir Roy Harrod made a pioneering contribution to the study of aggregate saving by analysing the implications of the basic assumption that current saving decisions of households reflect an endeavour to achieve the preferred allocation of lifetime resources to consumption (and bequests) over the life cycle. Since that time, this approach has been pursued by a number of authors, both at the theoretical level and for the analysis of empirical data” (Modigliani 1970, p. 197).
In fact, Mayer (1972) includes Harrod’s theory within the “wealth theories”, while Duesenberry’s contribution on “relative income” within the “measured income theories”. The latter set includes both the models of “absolute income” (Keynes and others) and that of “relative income” itself (Mayer 1972, p. 16).
As for the Cambridge economist, Attanasio (2015) has recently argued that, in the light of his pioneering insight onto an Overlapping Generation Model provided in his famous 1928 article (see Ramsey 1928, pp. 557–8), Ramsey can (and must) to all extent be included within the restricted circle of authoritative forerunners of the LCH. We do agree with this argument, although Ramsey provided a very brief sketch of an OLG model. In any case, in this work we will deal with Ramsey’s insight only indirectly, given that our main focus is on Carlo Casarosa’s work, who did not discuss the contribution of the Cambridge economist.
See Casarosa (2002), p. 66.
The present and all other translations of the Italian text of Casarosa are made by the authors.
It is worth recalling Modigliani’s own words: “our purpose was to show that all the well-established empirical regularities could be accounted for in terms of rational, utility-maximizing, consumers allocating optimally their resources to consumption over their life, in the spirit of Irving Fisher (1930)” (Modigliani, 1986, p. 299). Moreover, commenting on the list of motives for saving that Keynes presented in Chapter 9 of his General Theory (Keynes 1936), some years later, Modigliani argued that “five of these, which include “to increase one's future income” or “to insure one's independence and power”, implied that all, or nearly all, the accumulation would finally wind up as bequeathed wealth. This, in turn, meant that most private wealth originated through bequests – that is, it either had been received through bequests or was destined to be bequeathed. And, indeed, how else could society accumulate wealth?” (Modigliani, 1988, p. 15). Modigliani clearly aimed at stressing that “one of the most significant early results of the Life Cycle Hypothesis was to establish that, even in the absence of bequests, the mere fact that income dries up with retirement could generate, for the entire economy, an amount of (hump) wealth quite large relative to income” (ibidem, p. 16).
We notice that, formally, the problem of the individual at the beginning of his/her adult life can be posed as follows: \(Max~U = \sum\nolimits_{i = 1}^L {{\beta ^{i - 1}}v\left( {{c_i}} \right),}\) s.t. \(\sum\nolimits_{i = 1}^L {\frac{{{c_i}}}{{{{\left( {1 + r} \right)}^{i - 1}}}} \le {W_1}}\) and \(w_{L} \ge 0,\) where \(v\left( {c_{i} } \right)\) is the intertemporal utility defined over individual consumption, \(c_{i} > 0\), \(v^{\prime} > 0\), \(v^{\prime\prime} < 0;\) \(\beta \equiv \frac{1}{1 + \delta }\) is the individual discount factor and \(\delta > 0\) is the individual discount rate, \({W_1} = \sum\nolimits_{i = 1}^N {\frac{{{y_i}}}{{{{\left( {1 + r} \right)}^{i - 1}}}} + {a_1}}\) is lifetime wealth in present value, \(y_{i}\) is the labor income in period i in real terms, \(a_{1}\) is the starting level of wealth in real terms, potentially different from zero, r is the real interest rate, supposed constant. First order conditions for an interior solution yield: \(MRS_{t,t + 1} \equiv \frac{{v^{\prime}\left( {c_{t} } \right)}}{{v^{\prime}\left( {c_{t + 1} } \right)}} = \frac{1 + r}{{1 + \delta }}\), which is the well-known Euler equation stating that the marginal rate of substitution of consumption between two periods must equate the interest factor.
Casarosa (2002, p. 77) points out that the hypothesis of static expectations is too restrictive, although it was rather the rule at the time Modigliani and Brumberg wrote their articles, and, thus, represents a limiting feature of the M-B LCH (on this respect, see also Farrell 1970). In fact, he will explore the implications of taking account of rational expectations (and family composition) in a paper published in 2010 (see Casarosa and Spataro 2010). Indeed, we note that Modigliani was familiar with the issue of how to model economic agents’ expectations, albeit, as discussed in Hands (1990), being a forerunner of the “rational expectation” hypothesis (Grunberg and Modigliani, 1954), he simply disregarded it in his publications on the grounds of either pragmatism or simply because he found it not fully convincing in describing the actual behavior of individuals. In any case Modigliani discussed the role of expectations in the LCH on several occasions (e.g., Modigliani 1966). For a deeper and interesting insight, see Hartley (2004).
It is worth noting that neither Harrod cites Duesenberry nor the latter cites the former in their books. Casarosa argues that the American economist completes his own monograph [Duesenberry (1949)] before the publication of Harrod's work and, therefore, probably without knowing the results contained in the latter book and that “it is much more likely that Modigliani and Brumberg glimpsed Duesenberry's ideas than Harrod's” (Casarosa 2002, p. 63). The first fact is probably true, given that in the preface of his volume, Duesenberry writes that “under the title “The Consumption Function” the original version of this book was submitted as a doctoral dissertation at the University of Michigan in February 1948”. The second guess by Casarosa can be agreed with too, although it is worth recalling that, as Harrod writes in the first page of the foreword of his book, “these lectures were composed during the autumn of 1946 and delivered in the University of London in February 1947”.
We note that Cassel (1932) used the same assumptions when introducing the case of a Uniformly Progressing State (par. 6, pp. 32 ff.). According to Kurz and Salvadori (2003), the model of exogenous growth provided by Cassel can be considered the “proximate starting point of the development of neoclassical growth theory” (Kurz and Salvadori 2003, p. 18).
For a deeper insight see Comim (2000).
In Harrod’s words: “there remains the saving required to provide for the saver’s needs during his own life-time, saving destinated to be subsequently dissipated in dis-saving. I shall call this hump-saving” (Harrod 1948, p. 49). Later, he adds that “the hump of savings at any times embodies the savings of people of all ages; it is a cross-section” (ibidem). In fact, Modigliani can be rightly agreed with when arguing that this terminology is somehow confusing, given that the hump-wealth would have been more appropriate (Modigliani 1986, p. 300). In an interesting review of Harrod’s book, Joan Robinson, rather surprisingly, writes that “unfortunately his exposition is so idiosyncratic, and the matter is so closely packed in the small compass of five lectures, that his book is extremely hard to follow (the original audience of the lectures must have had a strenuous time of it)” (Robinson 1949, p. 69).
Please note that Harrod cites Cassel, who had reached the same conclusions, when discussing about “saving for posterity” (Harrod 1948, p. 49), although he does not mention Cassel’s contribution on the link between saving and population growth. Moreover, Harrod does not cite the work of Neisser (1944).
Joan Robinson defines Harrod’s line of reasoning in this respect, as “an argument of some subtlety” (Robinson 1949, p. 74).
We can summarise Harrod’s line of reasoning as follows: 1) there seems no general presumption that the rate of saving will be precisely what is required to sustain a steady advance of production with the rate of interest constant (Harrod 1948, p. 54); 2) we may have to contemplate a continuously rising or falling rate of interest (more likely a falling interest rate in presence of positive per capita growth and stationary population) (ibidem); 3) in general, financial markets are not prepared to manage the systematic fall in the interest rate required to absorb the over-saving of a growing economy (ibidem, p. 62); 4) a public intervention is needed to restore the harmony between “thriftiness” and capital requirements, through monetary policies aimed at controlling (reducing) the interest rate; 5) however, according to Harrod, the latter will not suffice given that is far from clear how aggregate saving will react to changes in the interest rate, so that he also suggests that the latter should be accompanied by accommodating fiscal policies.
As already quoted above, in the preface of the book Duesenberry refers to his 1948 doctoral dissertation, giving evidence that his ideas were elaborated well before 1949. On the other hand, Harrod delivered his lectures at the University of London in February 1947.
Current economic literature refers to this phenomenon as the “ratchet effect”. That was also discussed by Modigliani in his 1949 article.
Tobin (1967, p. 143) refers to this situation as the “golden age”.
Casarosa does not discuss the second part of Duesenberry’s conclusion, according to which “if on the other hand the retired population buys annuities or fixed interest securities they will not share in the capital gains associated with the increase in income. The rate of saving will then be dependent on the rate of increase of income” (Duesenberry 1949, p. 43). Casarosa is right in considering, Dusenberry’s argument as flawed. In fact, the American economist seems to envisage two distinct cases: one in which wealth of each cohort does not grow, and the other one in which wealth (stocks) for individuals of each cohort increases at the economy’s rate of growth due to some externality or, say, capital gains. However, the latter case is not possible, given that, if this were the case, aggregate wealth would grow both because of new flows of savings (that each year increase at the per-capita income pace) and because of Duesenberry’s envisaged “capital gains”. However, this rate of growth of wealth would be higher than the one ensuring the steady state.
Duesenberry (1949, p. 45) also adds that the propensity to save of an individual is a raising function of his/her percentile position in the income distribution.
Modigliani cited Harrod’s book in Ando and Modigliani (1959), although with regard to the issue of stability and growth (p. 501), not on “hump saving”. The citation contains anyway a mistake in the year of publication of the book: 1952 instead of 1948.
In our opinion this is merely a typo, because Harrod refers correctly, when proposing a way of measuring the parameter e, to the elasticity of marginal utility of income (Harrod 1948, p. 44).
Once again, it is worth recalling that Harrod, in any case. does not discuss the role of wealth in affecting saving behavior, apart from the very narrow channel of its effect on the individuals’ time preference, T).
M. R. Fisher (1956) writes that “as an early state of the investigation, the writer benefitted from discussions with Professor Milton Friedman of Chicago and the late Dr. R. E. Brumberg of Cambridge and has been materially able to view an advance mimeographed copy of the former’s forthcoming publication on the Consumption Function” (pp. 262–263). On the Palgrave Dictionary Fisher specifies again that: “early attempts to establish such a linkage were made by Irving Fisher (1930) and again by Harrod (1948) with his notion of hump saving, but a sharply defined hypothesis which carried the argument forward both theoretically and empirically with its range of well-specified tests for cross-section and time series evidence was first advanced in 1954 by M-B. Both their papers and advance copies of the permanent income theory of Milton Friedman (1957) were circulating in 1953 and led to M. R. Fisher carrying out tests of the theories even preceding publication of Friedman’s work (1956)” (M. R. Fisher, 1987, p. 177).
Among other citations of Harrod’s contribution to the LCH, see Walker (1962, p. 1). Tobin (1967) simply states that the source of his graphs is “the life cycle theory proposed by Fisher and later by Modigliani and Brumberg” (p. 132). In turn, Buiter (2003) states that, thanks to his early contributions, “after Friedman (1957) and Modigliani (M-B, 1954; Ando and Modigliani, 1963), Tobin comes a close third as regards the significance of his contributions to the life- cycle/permanent income approach” (p. F590).
On the same lines, see Bread (2011, p. 140).
Modigilani and Brumberg give an account of the empirical results contained in Hamburger’s PhD dissertation by devoting to it Sect. 4.3, entitled The Hamburger Test, and introducing it as follows: “in a pioneering contribution, William Hamburger fitted a regression using estimates of consumption, income, and assets that are conceptually almost identical with our own, and produced (sometimes before the genesis of this paper) a consumption function that compares favourably with D-M [Duesenberry-Modigliani, N. o. A.] function for the period 1929–1950 over which it was tested” (M-B 1980, p. 178). Then they go on commenting on the limits of the methodology adopted by Hamburger, although concluding that “his empirical findings appear to agree remarkably well with our a priori estimates” (ibidem, p. 181).
The programme of the Conference, which took place on the 30th of December 1953 in New York, is available on line on the webpage of the American Economic Association: https://www.aeaweb.org/conference/1953. In the same session, chaired by Raymond Goldsmith, Modigliani presented the first paper written with Brumberg and later published in 1954, and Margaret Reid presented a paper entitled Random Variations in Income and Their Effect on Income Expenditure Curves. The discussant was Hendrik Samuel Houthakker from the Cowles Commission.
Although, as argued by Ando and Modigliani (1963), “if we interpret the highest previous peak income as that of a proxy for net worth, then the Duesenberry-Modigliani consumption function can be considered as providing a good empirical approximation to the consumption function discussed in this paper. […] At the same time the present model has the advantage that the hypotheses on which it rests are explicitly stated as specifications of the consumer’s utility function. It is also analytically more convenient as a building block in models of economic growth and fluctuations, as we have endeavored to demonstrate in various contributions” (p. 80).
Modigliani was asked by Robert Strotz, the managing editor of Econometrica, to which he had submitted the second manuscript written with Brumberg on the macroeconomic implications of the LCH, to mention the names of those who had already read his work and he provided the name of Duesenberry together with the ones of Christ, Klein and Brown.
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Acknowledgements
The authors are grateful to an anonymous referee for valuable suggestions and to the Editor for his kind support. The usual disclaimer applies. Although the conception and drafting of the text is the outcome of joint research, Sections 2, 3.1.2, 3.2.1 are attributable to Luca Spataro, and Sections 3.1.1, 3.2.2, 4 are attributable to Alice Martini, the remaining Sections have been coauthored.
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Martini, A., Spataro, L. The contribution of Carlo Casarosa on the forerunners of the life cycle hypothesis by Franco Modigliani and Richard Brumberg. Int Rev Econ 69, 71–101 (2022). https://doi.org/10.1007/s12232-021-00386-w
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DOI: https://doi.org/10.1007/s12232-021-00386-w