Finance and General Equilibrium, Redux
Therefore, we can understand the work of Cox et al. (1981, 1985a, 1985b) as an attempt to connect the insights of no arbitrage back to economic “fundamentals”.
In work on contingent claims analysis, such as option pricing, it is common, and to a first approximation reasonable, to insist only on a partial equilibrium between the prices of the primary and derivative assets.
For something as fundamental as the rate of interest, however, a general equilibrium model is to be preferred. (Cox et al. 1981: 773)To do this, the authors built on Ross’s own arbitrage pricing theory (Ross 1976b) to produce a general equilibrium model driven by a k-dimensional vector of state variables. In the end they were forced to specialize the model considerably in order to achieve definite results for the dynamics of interest rates and the term structure, and as a consequence economics did not pick it up.
A more successful attempt to do essentially the same thing was the real business cycle literature which started from the other end, with its foundations in economics, and then imported no arbitrage under the disarming name of rational expectations. The connection to finance was made through the Euler equation of consumption that lies at the heart of both modern finance and modern macroeconomics. Economists like to write the equation like this:
In this equation Cit is the consumption of consumer i at time t, U is a function that translates consumption into utility terms, δ is the subjective discount rate, and Rjt 1 1 is the gross return on asset j in the period between t and t 1 1.
For finance, this equation is about how asset prices depend on time and risk preference, the equation is called the “consumption CAPM”, and the asset in question is typically equity or long term bonds (Breeden 1979).
But the same equation can be used to talk about the intertemporal fluctuation of income, and as such is at the core of both real business cycle theory (Kydland and Prescott 1982) and its new Keynesian variants (Woodford 2003) that see the economy through the lens of the so-called dynamic stochastic general equilibrium (DSGE) model. In this application, the asset is typically capital, or a rate of interest.The link to finance, and the foundational role of no arbitrage and the martingale, comes clear when we write the Euler equation instead as:
where M is a stochastic discount factor treated as a free variable that must fit the cross section pattern of asset returns R. (Note how the characteristic utility foundations of economics disappear in this finance formulation.) Under the martingale equivalent measure, this equation can equivalently be written as:
the latter formulation being exactly analogous to Samuelson (1965).
Thus it is that modern finance, having grown up outside of economics and independent from almost all of the intellectual inheritance of the field, re-entered economics and in doing so quite completely transformed it. The monetary Walrasianism of Tobin and Modigliani survives in elementary textbooks, and in policy discussion circles, but hardly a trace can be found in the advanced academic literature. Originally conceived as an account of how government can make use of imperfections in markets as leverage for moving the economy closer to the complete markets ideal, monetary Walrasianism has in the past 40 years had its institutional and intellectual foundations cut out from under it by a combination of financial innovation and deregulation, both domestically and internationally. The audacious finance project has come to pass; is economics irrelevant?