Knowledge that Transforms

The paper is a discussion of the interpretation of game theory. The first half of the paper deals with the notion of "strategy". The paper endorses the view that equilibrium strategy describes a player's plan of action, as well as those considerations which support the optimality of his plan rather than being merely described as a "plan of action". In the second half of the paper it is argued that a good model in game theory has to be realistic in the sense that it provides a model for the perception of real life social phenomena. It should incorporate a description of the relevant factors involved, as perceived by the decision makers. Copyright 1991 by The Econometric Society.

The theory applying to dynamic programming has furnished a useful set of techniques for the analysis of many types of sequential models. This theory, however, has not yielded heretofore much information about the differentiability properties of optimal solutions. This aspect is of particular interest as regards the qualitative analysis of optimal paths, where differentiable methods are often called into play. This paper shows roughly that if the objective is twice continuously differentiable and strongly concave, then any interior optimal path is continuously differentiable with respect to the initial state. Copyright 1991 by The Econometric Society.

A method is presented for estimating nonlinear simultaneous equations and transformation models in the presence of disturbance distribution of unknown form. It asymptotically achieves the lower variance bound for instrumental variables estimates. The author avoids smoothed nonparametric estimation, his instruments averaging over the unsmoothed empirical distribution of preliminary residuals. He allows for stationary serial dependence. In various settings, estimates are proposed and large-sample inference rules justified, these being unaffected if the optimal instruments use only an arbitrarily small vanishing fraction of the residuals. The author investigates theoretically the effect of such computational savings on the goodness of the normal approximation. Copyright 1991 by The Econometric Society.

The author considers frequency domain time series analysis, where smoothing in nonparametric spectrum estimation is data-dependent. Uniform convergence of spectrum estimates is established and applied to a semiparametric model, parameterized over possibly only a subset of the frequencies, in which disturbances have nonparametric autocorrelation. Optimal instruments depend on the disturbance spectrum and frequency response function, which is nonparametric in incomplete systems. The author justifies feasible, optimal parameter estimates. The degree of smoothing is allowed to depend on the data in a general way. The author proves consistency of a cross-validation method of automatic smoothing and applies it to a semiparametric model. Copyright 1991 by The Econometric Society.

This paper introduces a semiparametric estimation method for Polychotomous Choice models. The method does not require a parametric structure for the systematic subutility of observable exogenous variables. The distribution of the random terms is assumed to be known up to a finite-dimensional parameter vector. In contrast, previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified. The systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory. The estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent. A computational technique to calculate the estimators is developed. Copyright 1991 by The Econometric Society.

This paper establishes the asymptotic normality of series estimators for nonparametric regression models. Gallant's Fourier flexible form estimators, trigonometric series estimators, and polynomial series estimators are prime examples of the estimators covered by the results. The results apply to a wide variety of estimates in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic or heteroskedastic. The paper also considers series estimators for additive interactive regression, semiparametric regression, and semiparametric index regression models, and shows them to be consistent and asymptotically normal. Copyright 1991 by The Econometric Society.

The authors describe a model of general equilibrium with incomplete markets in which firms can innovate by issuing arbitrary, costly securities. When short sales are prohibited, firms behave competitively and equilibrium is efficient. When short sales are allowed, these classical properties may fail. If unlimited short sales are allowed, imperfect competition may persist even when the number of potential innovators is large. If limited short sales are allowed, perfect competition may obtain in the limit, but equilibrium can be inefficient because of the presence of an externality: the private benefits of innovation for firms differ from the social benefits. Copyright 1991 by The Econometric Society.

ABSTRACT A positive slope of the yield curve is associated with a future increase in real economic activity: consumption (nondurables plus services), consumer durables, and investment. It has extra predictive power over the index of leading indicators, real short‐term interest rates, lagged growth in economic activity, and lagged rates of inflation. It outperforms survey forecasts, both in‐sample and out‐of‐sample. Historically, the information in the slope reflected, inter alia , factors that were independent of monetary policy, and thus the slope could have provided useful information both to private investors and to policy makers.

Section I: Introductin to Finance and the Mathematics of Continuous-Time Models 1 Modern Finance 2 Introduction to Portfolio Selection and Capital Market Theory: Static Analysis 3 On the Mathematics and Economic Assumptions of Continuous-Time Financial Models Section II: Optimum Consumption and Portfolio Selection in Continuous-Time Models 4. Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case 5. Optimum Consumption and Portfolio Rules in a Continuous-Time Model 6. Further Developments in theory of Optimal Consumption and Portfolio Selection Section III: Warrant and Option Pricing Theory 7. A Complete Model of Warrant Pricing the Maximizes Utility 8. Theory of Rational Option Pricing 9. Option Pricing when Underlying Stock Returns are Discontinuous 10. Further Developments in Option Pricing Theory Section IV: Contingent-Claims Analysis in the Theory of Corporate Finance and Financial Intermediation 11. A Dynamic General Equilibrium Model of the Asset Market and its Application to the Pricing of the Capital Structure of the Firm 12. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates 13. On the Pricing of Contingent Claims and the Modigliani-Miller Theorem 14. Contingent Claims Analysis in the Theory of Corporate Finance and Financial Intermediation Section V: An Intertemporal-Equilibrium Theory of Finance 15. An Intertemporal Capital Asset Pricing Model 16. A General Equilibrium Theory of Finance in Continuous-Time Section VI: Applications of the Continuous-Time Model to Selected Issues in Public Finance 17. An Asymptotic Theory of Growth Under Uncertainty 18. On Consumption-Indexed Public Pension Plans 19. An Analytic Derivation of the Cost of Loan Guarantees and Deposit Insurance 20. On the Cost of Deposit Insurance when there are Surveillance Costs

ABSTRACT This paper suggests that the interactions of security trades and quote revisions be modeled as a vector autoregressive system. Within this framework, a trade's information effect may be meaningfully measured as the ultimate price impact of the trade innovation. Estimates for a sample of NYSE issues suggest: a trade's full price impact arrives only with a protracted lag; the impact is a positive and concave function of the trade size; large trades cause the spread to widen; trades occurring in the face of wide spreads have larger price impacts; and, information asymmetries are more significant for smaller firms.