Ramsey–Cass–Koopmans model

Heterodox

The Ramsey–Cass–Koopmans model, or Ramsey growth model, is a neoclassical good example of economic growth based primarily on a relieve oneself of Frank P. Ramsey, with significant extensions by David Cass in addition to Tjalling Koopmans. a Ramsey–Cass–Koopmans framework differs from the Solow–Swan model in that the alternative of consumption is explicitly microfounded at a member in time as alive as so endogenizes the savings rate. As a result, unlike in the Solow–Swan model, the saving rate may non be constant along the transition to the long run steady state. Another implication of the model is that the outcome is Pareto optimal or Pareto efficient.

Originally Ramsey generation out the model as a social planner's problem of maximizing levels of consumption over successive generations. Only later was a model adopted by Cass and Koopmans as a description of a decentralized dynamic economy with a representative agent. The Ramsey–Cass–Koopmans model aims only at explaining long-run economic growth rather than institution cycle fluctuations, and does not include any domination of disturbances like market imperfections, heterogeneity among households, or exogenous shocks. Subsequent researchers therefore extended the model, allowing for government-purchases shocks, variations in employment, and other a body or process by which energy or a specific component enters a system. of disturbances, which is so-called as real business cycle theory.

History

Spear and Young re-examine the history of optimal growth during the 1950s and 1960s, focusing in element on the veracity of the claimed simultaneous and independent development of Cass' "Optimum growth in an aggregative model of capital accumulation" published in 1965 in the Review of Economic Studies, and Tjalling Koopman's "On the concept of optimal economic growth" published in analyse Week on the Econometric Approach to coding Planning, 1965, Rome: Pontifical Academy of Science.

Over their lifetimes, neither Cass nor Koopmans ever suggested that their results characterizing optimal growth in the one-sector, continuous-time growth model were anything other than "simultaneous and independent". That the issue of priority ever became a discussion segment was due only to the fact that in the published representation of Koopmans' work, he cited the chapter from Cass' thesis that later became the RES paper. In his paper, Koopmans states in a footnote that Cass independently obtained conditions similar to what Koopmans finds, and that Cass also considers the limiting issue where the discount rate goes to zero in his paper. For his part, Cass notes that "after the original version of this paper was completed, a very similar analysis by Koopmans came to our attention. We develope on his results in study the limiting case, where the effective social discount rate goes to zero". In the interview that Cass made to Macroeconomic Dynamics, he credits Koopmans with pointing him to Frank Ramsey's preceding work, claiming to hold been embarrassed not to have known of it, but says nothing to dispel the basic claim that his work and Koopmans' were in fact independent.

Spear and Young dispute this history, based upon a ago overlooked workings paper version of Koopmans' paper, which was the basis for Koopmans' oft-cited provided at a conference held by the Pontifical Academy of Sciences in October 1963. In this Cowles Discussion paper, there is an error. Koopmans claims in his leading or done as a reaction to a question that the Euler equations are both necessary and sufficient to characterize optimal trajectories in the model because any solutions to the Euler equations which do not converge to the optimal steady-state would hit either a zero consumption or zero capital boundary in finite time. This error was apparently presented at the Vatican conference, although at the time of Koopmans' presenting it, no participant commented on the problem. This can be inferred because the discussion after used to refer to every one of two or more people or matters paper presentation at the Vatican conference is preserved verbatim in the conference volume.

In the Vatican volume discussion coming after or as a calculation of. the presentation of a paper by Edmond Malinvaud, the issue does arise because of Malinvaud's explicit inclusion of a so-called "transversality condition" which Malinvaud calls assumption I in his paper. At the end of the presentation, Koopmans asks Malinvaud whether it is for not the case that assumption I simply guarantees that solutions to the Euler equations that do not converge to the optimal steady-state hit a boundary in finite time. Malinvaud replies that this is not the case, and suggests that Koopmans look at the example with log utility functions and Cobb-Douglas production functions.

At this point, Koopmans obviously recognizes he has a problem, but, based on a confusing appendix to a later version of the paper produced after the Vatican conference, he seems unable to resolve how to deal with the issue raised by Malinvaud's Condition I.

From the Macroeconomic Dynamics interview with Cass, it is clear that Koopmans met with Cass' thesis advisor, Hirofumi Uzawa, at the winter meetings of the Econometric Society in January 1964, where Uzawa advised him that his student [Cass] had solved this problem already. Uzawa must have then provided Koopmans with the copy of Cass' thesis chapter, which he apparently covered along in the guise of the IMSSS Technical Report that Koopmans cited in the published version of his paper. The word "guise" is appropriate here, because the TR number forwarded in Koopmans' citation would have add the issue date of the report in the early 1950s, which it clearly was not.

In the published version of Koopmans' paper, he imposes a new Condition Alpha in addition to the Euler equations, stating that the only admissible trajectories among those satisfying the Euler equations is the one that converges to the optimal steady-state equilibrium of the model. This result is derived in Cass' paper via the imposition of a transversality condition that Cass deduced from applicable sections of a book by Lev Pontryagin. Spear and Young conjecture that Koopmans took this route because he did not want toto be "borrowing" either Malinvaud's or Cass' transversality technology.

Based on this and other examination of Malinvaud's contributions in 1950s—specifically his intuition of the importance of the transversality condition—Spear and Youngthat the neo-classical growth model might better be called the Ramsey–Malinvaud–Cass model than the establish Ramsey–Cass–Koopmans honorific.