Knowledge that Transforms

[The matrix weighted average (H = V extasciicircum-1) extasciicircum-1Hb, where H and V are symmetric positive definite matrices and b is a vector, is shown to lie in one ellipsoid if V is bounded from below, V "* @ extless V, another ellipsoid if V is bounded from above, V @ extless V*, and another ellipsoid if V is bounded from above and below, V "*@ extless V @ extless V*. These results are applied to bound the posterior mean vector of the normal linear regression model.]

One of the most fundamental market mechanisms is the clearing house, where orders are accumulated over time and the market is cleared periodically. The issue addressed in this study is the statistical behavior of the market under this neutral mechanism in the framework of a tractable stochastic model which captures the underlying uncertainties and indivisibilities in the demand and supply schedules. Applying renewal theory, we derive closed-form results for the behavior of prices and quantities, and pursue the implications of the possibility of no-trade and the multiplicity of market-clearing prices.

THIS PAPER IS yet another in a rapidly growing series (e.g. [2]-[11]) on strategic approaches to economic equilibrium. Our aim here is to make precise the remark implicitly due to Bertrand [1 or 10, Ch. 4, 5] that if the agents in an economy use price-setting strategies then the strategic Nash equilibria will, in fact, be Walrasian; and this without any assumption of a large number of small However, in our models, not only prices but also quantities are set by the agents. Thus it might actually be more appropriate to call them Bertrand-Cournot types of models. We begin with a standard Walras exchange economy with a finite number of traders and commodities. This is recast as a game in strategic form in essentially two different ways. There is a trading-post for each commodity to which traders send contingent statements about how much they wish to buy and sell, and at what prices. In Model 1, the trading point is determined by the intersection of the aggregate supply and demand curves. In Model 2, trade takes place so as to meet as many contingent statements as possible. Each buyer whose orders are filled pays the price he quoted, using a fiat money which can be borrowed costlessly and limitlessly. But after trade is over there is a settlement of accounts and a penalty is levied on those who are bankrupt. No attempt is made to model the penalty in any detail. It is simply described in the form of a disutility. But this in turn may be imagined to stem from confiscation of assets (see Remark 5) or the necessity of procuring highly-priced loans, etc. Call a noncooperative equilibrium if it turns out that no trader is isolated, i.e., trapped as the sole buyer or seller at some trading-post. Then our results may be described as follows. In Model 1, the active2 N.E. of the game coincide with the C.E. of the market; furthermore there is a subset of tight, active N.E. which also coincide with the C.E., and each N.E. in this subset is strong

The time path of asset prices is studied within a stationary experimental environment. After several replications prices converge to a perfect foresight equilibrium. A sequential market having an "informational trap" and a futures market are also studied.

Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.

[It is increasingly recognized that Tobin's conjecture that investment is a function of marginal q is equivalent to the firm's optimal capital accumulation problem with adjustment costs. This paper formalizes this idea in a very general fashion and derives the optimal rate of investment as a function of marginal q adjusted for tax parameters. An exact relationship between marginal q and average q is also derived. Marginal q adjusted for tax parameters is then calculated from data on average q assuming the actual U.S. tax system concerning corporate tax rate and depreciation allowances.]

Kemp and Long demonstrated that it may be preferable to exploit high and low cost resource deposits simultaneously and not in sequence as is typically assumed in the resources literature. They show that it is desirable to delay extraction from low cost pools in order to smooth consumption over time, if the resource in the ground is society's only store of wealth. This paper considers a model in which extracted resources can be converted into capital which may either be consumed or stored to provide for consumption later on. We find that a sufficient condition for the strict sequencing of extraction to be optimal is that stored capital be productive so that it can be used to produce additional capital.