Vintage Models Research Paper

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Capital goods that are constructed at different moments in time embody the state of technology at the moment of their construction, thus giving rise to the notion of individual vintages of capital goods. These vintages differ in intrinsic “productive quality” because of ongoing technological progress, just like different vintages of wine can differ in quality. The basic idea underlying a vintage model is that the potential of technical change as an idea can only be realized in practice by first incorporating that idea in a piece of machinery and subsequently using that machinery to produce output. Because technical change is therefore embodied in individual pieces of machinery and equipment, vintage models emphasize the fact that complementary investment has to take place in order to realize the productivity promises of new ideas. There is also technical change not linked to investment that comes in the form of new ideas about the organization of production; this is called disembodied technical change in a vintage context. By contrast, an aggregate production function, which is still the most popular way of representing technology in large-scale macroeconomic models, assumes that capital is homogeneous and that the process of technical change can be represented as a continuous shift of the per capita production function that is independent of the rate of investment. Hence, all technical change is thought of as disembodied, and technology-induced reductions in unit production costs are therefore assumed to be independent of the actual level of investment.

The main focus of a vintage model is on the diffusion of technical change as opposed to endogenous growth theory that focuses on the source of technical change. The embodiment of technical change results in a capital stock that is heterogeneous in terms of the factor-productivity (hence the unit operating cost) associated with individual vintages. Depending on the type of vintage model on hand, the arrival of new superior technologies may render the old ones obsolete, leading to the economic scrapping of inferior equipment. It is through investment and disinvestment at both ends of the vintage spectrum that the average productivity characteristics of the capital stock can be made to change, though only relatively gradually.

Since the arrival of vintage models in the late 1950s and 1960s (see, for example, Johansen 1959; Salter 1960; Solow 1960; Phelps 1962, 1963; Jorgenson 1966; Solow et al. 1966), they have been used by economists interested in the connection between technical change and economic growth, because they highlight a number of important insights regarding the complementarity between productivity growth and investment. Firstly, productivity growth is positively influenced by gross investment. In the aggregate production function approach, labor productivity growth is as much the result of the growth in capital per capita (and is therefore linked to net investment per capita rather than gross investment) as it is the result of (labor-saving) technical change itself. Secondly, vintage models stress the idea that technical change has to be bought and paid for, rather than falling freely like “manna from heaven.” Consequently, anything that reduces incentives to invest in new machinery—for example, increasing uncertainty or a higher user cost of capital-—will reduce the speed of diffusion of technical change. Thirdly, under the embodiment assumption, the average productivity characteristics of the total capital stock will change only gradually as new capital goods fill the gaps left by the technical decay and economic scrapping of old capital goods. Hence, if one wanted to change the average characteristics of capital stock in a noticeable way, one would either have to engage in nonmarginal replacement investment, or start promoting investment in new technologies sooner rather than later.

There are different types of vintage models, ranging from putty-putty (Solow 1960; Phelps 1962), to putty-clay (Johansen 1959; Salter 1960; Phelps 1963), to clay-clay models (Kaldor and Mirrlees 1962; Solow et al. 1966). Even putty-semi-putty models exist (Fuss 1978). The somewhat far-fetched names come from the world of pottery (Phelps 1963). The term putty refers to clay that is still soft enough to change shape, whereas clay refers to the hard-baked state of that shape that cannot be changed anymore without breaking it. When applied to a technology, putty-ness describes a state in which there are many different techniques associated with a specific technology that one could choose to implement, whereas clay-ness implies that there is just one implementation of a technology available, and that it is impossible to change it without “breaking” it (and, thus, effectively discarding it). The first word (putty or clay) in the name of a vintage model refers to the size of the set of potentially available techniques before the moment that the actual hardware embodying the technique is installed (i.e., ex ante), and the second word (putty or clay) refers to the set of techniques still left after installation (i.e., ex post). A putty-clay model, therefore, covers a situation with (infinitely) many choices ex ante, and just one ex post (i.e., the one technique that has actually been implemented after making a choice from many techniques ex ante). Putty-putty models have infinitely many choices ex ante and ex post. A clay-clay model has just one technique to choose from, both ex ante and ex post. The putty-clay model is generally considered to be the most realistic vintage model because it recognizes that one generally has several production techniques to choose from, but also that once the machinery has been built and installed the choice for that technique can not be undone. Ex post “clay-ness” therefore represents the impossibility of reversing decisions made ex ante.

This irreversibility of investment ex post implies that one would have to try to forecast changes in factor prices ex ante, and incorporate these forecasts into the factor proportions that are to be embodied in the new vintage under consideration. For example, a rise in wages not properly foreseen would result in a labor intensity of production ex ante that is too high (with hindsight), and that would lead to an economic lifetime that is consequently too short (the economic lifetime of a vintage is equal to the duration of the period over which it would be most profitable to operate that vintage; see Malcomson 1975). In putty-putty models, such lifetime effects of forecasting errors do not exist, as one can continuously and costlessly adjust factor proportions (i.e., production techniques) to the current factor price situation on every vintage installed, from the newest to those installed in the distant past. Obviously, the latter situation is less relevant in practice, even though elegant in theory.

From a policy point of view, the irreversibility of investment is important, as it implies that humanity’s trust in technical change to solve some of its problems—for example, global warming—may involve high investment costs. The latter are routinely ignored in an aggregate production function setting, as technical change is assumed to take place regardless of the level of investment. Consequently, an aggregate production function approach would tend to underestimate the real cost of technical change while neglecting the positive link between the effective pace of technical change (insofar as the latter is embodied in machinery and equipment), and the rate of investment. In a putty-clay setting, on the other hand, a large volume of replacement investment would be required to change the energy consumption characteristics of the aggregate capital stock in a nonmarginal way. Thus, either one would be forced to bear very large (just-in-time) adjustment costs, or, from a risk-diversification point of view, one would have to promote investment in new energy-saving technologies sooner rather than later. Interestingly, Schumpeterian endogenous growth theory (see, for example, Aghion and Howitt 1998) points out that the expectation of new technological breakthroughs that might or might not arrive just in time may actually have the opposite effect—namely, the postponement of investment. In any case, the embodiment of technical change in combination with the irreversibility of investment underlines the potential role of policymakers in reducing adjustment costs and smoothing transition shocks that are largely ignored in aggregate production function settings.


  1. Aghion, Philippe, and Peter Howitt. 1998. Endogenous Growth Theory. Cambridge, MA: MIT Press.
  2. Fuss, Melvyn A. 1978. Factor Substitution in Electricity Generation: A Test of the Putty-Clay Hypothesis. In Production Economics: A Dual Approach to Theory and Applications, eds. Melvyn A. Fuss and Daniel McFadden, 187–213. Amsterdam: North-Holland.
  3. Johansen, Leif. 1959. Substitution versus Fixed Production Coefficients in the Theory of Economic Growth: A Synthesis. Econometrica 27 (2): 157–176.
  4. Kaldor, Nicholas, and James A. Mirrlees. 1962. A New Model of Economic Growth. Review of Economic Studies 29 (3): 174–192.
  5. Malcomson, James M. 1975. Replacement and the Rental Value of Capital Equipment Subject to Obsolescence. Journal of Economic Theory 10 (1): 24–41.
  6. Phelps, Edmund S. 1962. The New View of Investment: A Neoclassical Analysis. Quarterly Journal of Economics 76 (4): 548–567.
  7. Phelps, Edmund S. 1963. Substitution, Fixed Proportions, Growth, and Distribution. International Economic Review 4 (3): 265–288.
  8. Salter, W. E. G. 1960. Productivity and Technical Change. Cambridge, U.K.: Cambridge University Press.
  9. Solow, Robert M. 1960. Investment and Technical Progress. In Mathematical Methods in the Social Sciences, 1959; Proceedings, eds. Kenneth J. Arrow, Samuel Karlin, and Patrick Suppes, 89–104. Stanford, CA: Stanford University Press.
  10. Solow, Robert M., James Tobin, Carl Christian von Weizsacker, and Menahem Yaari. 1966. Neoclassical Growth with Fixed Factor Proportions. Review of Economic Studies 33 (2): 79–115.

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