Two puzzles regarding the replacement ratio in the context of renewal theory

Abstract

The models Feldstein and Rothschild, on the hand, and Jorgenson on the other adopted in 1974 to highlight the replacement ratio are identical. Yet, the authors reached opposite conclusions and the latter's view prevailed, which is weaker in terms of theoretical and empirical foundations. This paper argues that both puzzles may be resolved by reference to the differences in the methodological preconceptions of the authors involved, the operational advantages of the theorem of proportionality, the accumulated data that facilitate research, the inertia of the status quo, the lack of a model leading to a more useful theorem, the lack of communication among economists and their aversion toward complex solutions and policy prescriptions. In this light it is concluded that the time has come for research efforts to be directed towards constructing and testing models in which the useful life of capital is determined endogenously in the presence of embodied technological change.

Keywords:

• proportionality hypothesis
• useful life
• renewal theory
• durability aggregation
• replacement
• instrumentalism
• formalism

JEL Codes::

• B21
• B41
• E22

Acknowledgements

This paper proved quite lucky. First, because it was read by unknown referee(s) who devoted more than their fair share of time and effort in finding even minute blemishes and pointing them out to me; and, secondly, because they went out of their way to suggest ideas as to how I could deal with issues of major concern. Consequently, I am grateful to the editor for his encouragement and patience and to the referee(s) for their generous help. Finally, I wish to extend my appreciation to my friend and colleague A.D. Karayiannis, who read various versions of the paper and helped me improve it significantly.

Notes

 1. So indifferent was Haavelmo regarding the usefulness of received replacement theory that he did not make even a single reference to the contributions by these writers.

 2. For the sake of historical accuracy it should be noted that at about the same period other leading contributors to the neoclassical theory of capital adopted various ad hoc approaches to modeling depreciation. For example, Solow (1956) ignored depreciation altogether, whereas Samuelson (1962) introduced proportionality on the grounds that:

‘To keep the alpha good homogeneous independently of age, one has to assume a force of mortality independent of age (or an exponential life table). This means that physical depreciation is always directly proportional to the physical stock of alpha, K _a : Depreciation equals δ _a times K _a where the average length of life of alpha is the reciprocal of the δ _a factor’ (p. 197).

 3. At that time prevalent among economists was the view that the only way to beat a theory is by another theory, not by ‘data’ alone. An exposition of the foundations of this view is found in Hirschman (1970, pp. 67–68). However, in the following decades mainstream economists shifted to the view, which is consistent with Friedman's (1953) famous methodology essay, that theories stand or fall on the basis of their ability to predict what the data reveal.

 4. Moreover, it may be of some interest to mention that Jorgenson (1974) ignored also the sharp criticisms of his arguments by Feldstein (1972/1974).

 5. Actually Jorgenson used the geometric distribution. He did so on the grounds that he employed discrete analysis. Had he applied continuous analysis, he would have assumed that the decline in the relative efficiency of capital followed the exponential distribution. But the results would have been just the same.

 6. A single investment is defined as one completed all at once. In contrast, multiple investments are an investment completed piecemeal over a certain period.

 7. Friedman (1953) introduced this approach into economics following the epistemologist Duhem (1908), who recommended using theories as instruments and without concern if they are true or if their assumptions are realistic. According to the latter, what is important is whether the predictions derived from theories match appearances (phenomena), thus implying that models are useful not as causal explanations, but ‘as if’ ways of highlighting what appears before us.

 8. Drawing on the debate that took place in the American Economic Review in the 1960s and the subsequent appraisal by Caldwell (1982), one would be justified in concluding that leading authorities in the group of realists were Machlup (1955, 1964) and Samuelson (1963, 1965).

 9. For a brief but more detailed account of the principles that guide contemporary research in the empirical sciences, see Appendix B.

10. To be sure, both parties in the debate employed mathematical techniques that were admirably advanced at the time. But in no way can they be categorized as formalists, because their emphasis was not on the techniques of the analysis but on the premises and the structure and the results of their models.

11. Note that this is exactly the problem that Koopmans (1979, pp. 11–12) and Goldfarb (1997) have discussed and to which I will return shortly below.

12. In particular, the probability distribution function that underlies the reliability and hazard functions in this case is Weibull with shape and scale parameters equal to 2 and 1, respectively.

13. As defined by Lipsey in the above reference, an anomaly arises when conflicts exist within a subject. Consequently, the controversy surrounding the applicability of the theorem of proportionality constitutes a genuine anomaly in economics.