Solow's Harrod: Transforming macroeconomic dynamics into a model of long-run growth

Abstract

Modern growth theory derives mostly from Solow's “A Contribution to the Theory of Economic Growth” (1956). Solow's own interpretation locates its origins in his view that Harrod's growth model implied a tendency toward progressive collapse of the economy. He formulates his view in terms of Harrod's invoking a fixed-coefficients production function. We challenge Solow's reading of Harrod's “Essay in Dynamic Theory,” arguing that Harrod's object in providing a “dynamic” theory had little to do with the problem of long-run growth as Solow understood it, but instead addressed medium-run fluctuations, the “inherent instability” of economies. Solow's interpretation of Harrod was grounded in a particular culture of understanding embedded in the practice of formal modelling that emerged in economics in the post-Second World War period. Solow's interpretation, which ultimately dominated the profession's view of Harrod, is a case study in the difficulties in communicating across distinct interpretive communities and of the potential for losing content and insights in the process. Harrod's objects – particularly, of trying to account for a tendency of the economy toward chronic recessions – were lost to the mainstream literature.

Keywords:

• Economic growth
• Roy Harrod
• Robert Solow
• dynamics
• dynamic instability
• knife-edge
• warranted rate of growth
• natural rate of growth

JEL Codes:

• B22
• O4
• E12
• E13
• N1
• B31

Acknowledgements

We thank Robert Solow for providing us with his unpublished manuscript (Solow 2009). The paper originates from each author's independent paper, both presented at the 10th annual Summer Institute for the Preservation of the History of Economics, University of Richmond, 19–22 June 2009. Verena Halsmayer is indebted to the participants of the workshop “History of ‘Economics as Culture’” 2012 (University of Cergy-Pontoise), the Spring School “Geschichte und Soziologie der Sozial- und Kulturwissenschaften” 2011 (University of Graz) and the HISRECO 2012 (University of Porto), where she presented a related paper. Kevin Hoover thanks the many people who commented on various versions of his precursor paper (“Was Harrod Right?”) at numerous conferences and departmental seminars, and particularly to Pedro Garcia Duarte, who was the discussant at the Second International Symposium on the History of Economic Thought, 5–6 August 2013 at the University of São Paulo. We would also like to thank the referees of this journal for their many helpful and thorough comments.

Notes

¹ Another recent interpretation is to be found in La Grandville (2007): “[I]n the first part of the twentieth century, a fixed relationship was posited between factor inputs and output … In one form or another this led … Harrod (1948), and Domar (1946) to dire predictions about the future of the economy: it was bound either to a waste of resources or to ever-increasing unemployment, unless the growth rate of labour happened to be exactly equal to the savings rate divided by the fixed capital–output ratio” (La Grandville 2007, p. 16).

² See Besomi (1998), Besomi (1999) and especially Besomi (2001). Other authors who have pointed to misrepresentations of Harrod's work are Kregel (1980) and Asimakopulos (1985).

³ It is worth noting from the outset that our concern is with Harrod and not with Evsey Domar. The bracketing of Harrod's analysis with Domar's growth model is actually part of the culture of misunderstanding that we are addressing.

⁴ When no confusion arises, references to Solow (1956) and Harrod (1939) are by page number only, omitting author and publication date.

⁵ The term “capital deepening” is not mentioned in Solow's “Contribution,” but he mentions it in a letter to Eisner the same year: "From a different point of view, if we imagine a society committed to maintain full employment at every moment of time, there will still be a multiplicity of ways this can be accomplished, some with much investment and some with little. Now Harrod is a subtle enough man to see this. He does make a few remarks to that effect in his book, as your quotes show. (By the way, the word ‘deepening’ goes well beyond this literature to Hawtrey and perhaps earlier.)” (Solow to Eisner, 14 June 1956, Solow Papers, Box 54, File E: 2 of 2). Domar, in the context of his work on economic growth and employment, also speaks of “deepening of capital” (Domar 1946, p. 142).

⁶ Wan (1971, Figure 2.5, p. 41) presents a similar figure.

⁷ Harrod (p. 16) himself does not use the term capital–output ratio, but refers to “the value of the capital goods required for the production of a unit increment of output.” His use of the plural “goods” and the qualification “value,” already indicates that he does not have a single-good, physical production function in mind. Where it causes no confusion, we will continue to refer to Harrod's C as the “capital–output ratio.”

⁸ Disinvestment is only relative to the size of the labour force because capital is permanent and there is no depreciation in the model.

⁹ The “Inada conditions” later provided a set of sufficient regularity conditions to guarantee the existence, uniqueness, and stability of a well-behaved steady-state equilibrium in which no knife-edge phenomena can occur (Inada 1963).

¹⁰ See, for instance, Hahn and Matthews (1964), Wan (1971), Hacche (1979), Pugno (1998), the contributions in Rampa et al. (1998) as well as the already mentioned Kregel (1980), Asimakopulos (1985), Besomi (1999) and Besomi (2001).

¹¹ There was some ambiguity with regard to Harrod's definition of dynamics: At another place in the “Essay,” Harrod defines dynamic theory as dealing with situations in which “certain forces are operating steadily to increase or decrease certain magnitudes in the system” (Harrod 1939, p. 14).

¹² The survey of Hahn and Matthews (1964, pp. 804–805) already drew a distinction between instability in the sense of a failure of equilibrium convergence to the steady-state path (“equilibrium dynamics’) and instability in the sense of nonconvergence from a nonequilibrium point to an equilibrium, but not necessarily steady-state, path (“disequilibrium dynamics”). Hahn and Matthews (p. 810) see Harrod as noting both kinds of instability, but they reserve the term knife-edge for the second kind of instability. This is puzzling since “knife-edge” is Solow's coinage and, as they note, he is concerned only with the first kind of instability.

¹³ Besomi mentions Yeager's (1954) “nervous tightrope walker” as the forerunner of Solow's knife-edge (Yeager 1954, p. 59, cited after Besomi 1999, p. 204).

¹⁴ In a related unpublished paper, Hoover (2008) provides a preliminary test that favours Harrod conjecture for US data.

¹⁵ The proper warranted rate has, as far as we can tell, been mentioned only twice in the journal literature by Wright (1949, p. 326) and by Yeager (1954, p. 62, fn. 17). Neither appears to grasp its analytical importance and each treats it as a reflection of Harrod's confusion and a lack of clarity. Kregel (1980) and Besomi (2001) do discuss Harrod's related view that the warranted rate can be dragged up or down by extended divergence from the actual rate, but not the asymmetry that Harrod highlights as the constitutional weakness in the economy. Besomi (1999, p. 137) briefly mentions the proper warranted rate – but, again, only in the context of adjustment of the warranted rate.

¹⁶ The notion of cultures of understanding bears a family resemblance to Fleck's (1935) concept of thought collectives, Kuhn's (1962) paradigms, and Lakatos's (1978) methodological research programmes. While we accept the genuine resemblance of these ideas to our own use of a “culture of understanding,” we reject any extreme reading of them that suggests insuperable incommensurability – rather than intrinsic difficulty in communication – across communities. “Misreadings” and “misunderstandings” as described above are an intrinsic and prevalent feature of science as a cultural and social enterprise. Depending on the closeness and overlapping of communities and their practices difficulties in communication might be overcome more easily or pose serious difficulties of grasping the meaning of products of a different community. See Fish (1980) for the notion of interpretive communities and Hoover (1991, 1994) for arguments against insuperable incommensurability.

¹⁷ For a treatment of the Harrod–Keynes correspondence, see Kregel (1980) and especially Besomi (1995); on Harrod's 1938 draft of the “Essay,” see Besomi (1996); and on the changes he added reacting to Keynes’ and Marschak's criticism, see Sember (2010). Young (1989) provides a detailed account of Harrod's work on the trade cycle leading up to the “Essay” (see pp. 48–50 on the importance of Keynes's Treatise).

¹⁸ Data are drawn from searches on JSTOR archive, executed on 25 November 2012, for the use of “model” or “models” for 173 economics journals and 29 general science journals, counting the number of articles using one of the search terms as a percentage of all articles. For economics journals: 1930–1939 = 14%; 1946–1955 = 42%. For general science journals: 1930–1939 = 14%; 1946–1955 = 23%.

¹⁹ Frisch (1933), Tinbergen (1939) and Samuelson (1939); also see discussions in Louçã (2007), Boumans (2005) and Morgan (2012, ch. 6).

²⁰ Harrod himself pointed to the difference between his capital coefficient and Domar's σ a few years later: “[H]e [Domar] designates the potential increase of output per unit of new investment by the symbol σ. I, on the other hand, make no explicit reference to this increased productivity, but … considered how many units of new investment are required, on the assumption that the new investment is properly utilised, to produce an extra unit of output; this I designated C_r” (Harrod 1959, p. 452; cf. Hagemann 2009, p. 70).

²¹ A similar argument was made by Hamberg (1952, p. 446, fn. 2) who investigated the consequences of the full employment growth rate exceeding the rate of growth required for the full utilisation of capital. He reproached Harrod for discussing only “the Keynesian case” – i.e., for not considering the full implications of the situation in which “the full employment growth rate exceed the full capacity one …” and thinking only about the inflationary aspects of this situation.” Hamberg, as Solow later, recognised only the possible divergence between the warranted and natural rates, thus ignoring Harrod's instability principle.

²² See Kregel (1980) for an earlier treatment of the differences between Harrod's work and the “Harrod–Domar” model.

²³ This point is also made by Asimakopulos (1985): “For Harrod's purposes, this moving equilibrium should have the characteristics of a trendline – it should be one that the economy would follow in the absence of disturbances. The development of the model within a Keynesian framework where uncertainty over future conditions prevailed made it difficult to explain why the entrepreneurs’ investment decisions would lead the economy along such a path. Harrod, when challenged by Alexander, saw the need for an explanation, but his resort to a ‘representative entrepreneur’ [in Harrod (1951)] was an evasion of a real problem for his theory, not a solution” (Asimakopulos 1985, p. 633).

²⁴ Solow thanked John Chipman for a remark on Harrod's answer to Pilvin's article (Solow 1956, p. 83).

²⁵ In his answer to Pilvin's article, Harrod criticised the use of a production function and especially the accompanying assumption that the rate of interest “will move in such a way as to change the productive process employed, causing it to move in an appropriate fashion along the curve of the production function” . Harrod brings forward several arguments that, although the rate of interest “plays some part” in changing the capital–labour ratio, it is not as important as Pilvin thinks (Hagemann 2009, p. 83 and Besomi 1999, p. 204).

²⁶ For the contexts and practices Solow's (1956) model emerged from, see Halsmayer (2014) and Backhouse (2012).

²⁷ Harrod (1973, ch. 3) shows Harrod's battle against the interpretation of his instability as a “knife-edge” problem.

²⁸ For example, Solow's misplaced emphasis on the nature of the production function has not escaped notice. As already observed (see fn. 12 above), Hahn and Matthews (1964) point to different notions of instability. Similarly, Burmeister and Dobell (1970, p. 41) are unusual among textbook authors in noting the issue : “studying the Harrod position as if it were based essentially on a technological hypothesis about the production function, namely that it shows fixed proportions, misses the essential feature of Harrod's analysis.

²⁹ The authors are thankful to Roger E. Backhouse who brought this letter to their attention.

³⁰ Years later, Solow recognised that Harrod had in mind two kinds of instability, but stuck to the notion that Harrod's work implied a constant capital coefficient: “One can mean two different things by the phrase ‘Harrod's knife-edge.’ One is the effective-demand instability argument that you elucidate. The other is an existence question: the idea, also to be found sometimes in Harrod, that equilibrium growth need not be possible if n, S, and the capital–output ratio are independently given constants. In 1956, I was mainly discussing this second meaning” (Solow to Nikaido, 29 March 1976; cf. Boianovsky and Hoover 2009, pp. 7–8).

³¹ Data are the number of articles in economics journals in the JSTOR archive in which (“Harrod” and “growth”) or (“Solow” and “growth”), scaled by the total number of articles and indexed so that the maximum value (177 for Solow in 1970) = 100. Harrod data run 1939–2005; Solow data, 1952–2005. Data were collected from 79 journals in JSTOR on 8 May 2008.

³² As Solow mentions a few years before the publication of his “Contribution”: “[S]uppose that people are endowed with perfect foresight as to the future of prices, output, and interest rate. This is always a hard assumption to swallow, and it turns up often in economics. In the present context, it is perhaps not so bad. For one thing, we are not interested in deducing the implications of any particular method of forming expectations about the future; we might just as well assume the future to be known. Second, we are concerned with a long-run equilibrium situation, which is hardly compatible with consistently false expectations” (Solow 1953–1954, p. 76).

³³ Geertz (1973) defines culture as a “historically transmitted pattern of meanings embodied in symbols, a system of inherited conceptions expressed in symbolic form” (p. 89). Geertz develops the concept of “thick description” as his method of doing ethnography. With regard to scientific cultures, the basic idea is to make scientific practices plausible in a manner that would allow outsiders to get a grip of the meaning of the participants’ procedures and problems.

³⁴ “I may not have been as clear then as I am now about the distinction between the two notions of instability” (Solow 1988, p. 310). The authors thank one of the referees for pointing them to that statement.

³⁵ Assous (2013) documents Solow's efforts after 1956 to integrate Keynesian short-run and neoclassical long-run factors into a “medium-run macroeconomics.”

Additional information

Funding

Verena Halsmayer's work was supported by the Austrian Science Fund [grant number W 1228-G13].