Knowledge that Transforms

By using nonparametric kernel estimation method and a central limit theorem for degenerate U-statistics of order higher than two, the authors develop several consistent model specification tests in the context of a nonparametric regression model. These include tests for omitted variables, tests for a partially linear model, and tests for a semiparametric single index model. The asymptotic normality of the test statistics are established under the respective null hypotheses and consistent estimators of the asymptotic variances are provided. Copyright 1996 by The Econometric Society.

This paper constructs a space of states of the world representing the exhaustive uncertainty facing each player in a strategic situation. The innovation is that preferences are restricted primarily by 'regularity' conditions and need not conform with subjective expected utility theory. The construction employs a hierarchy of preferences, rather than of beliefs as in the standard Bayesian model. Applications include the provision of foundations for a Harsanyi-style game of incomplete information and a rich framework for the axiomatization of solution concepts for complete information normal form games. Copyright 1996 by The Econometric Society.

We present and analyze a model of noncooperative bargaining among n participants, applied to situations describable as games in coalitional form. This leads to a unified solution theory for such games that has as special cases the Shapley value in the transferable utility (TU) case, the Nash bargaining solution in the pure bargaining case, and the recently introduced Maschler-Owen consistent value in the general nontransferable utility (NTU) case. Moreover, we show that any variation (in a certain class) of our bargaining procedure which generates the Shapley value in the TU setup must yield the consistent value in the general NTU setup.

[We propose a nonparametric estimation procedure for continuous-time stochastic models. Because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process, we leave the volatility function unrestricted and estimate it nonparametrically. Only discrete data are used but the estimation procedure still does not rely on replacing the continuous-time model by some discrete approximation. Instead the drift and volatility functions are forced to match the densities of the process. We estimate the stochastic differential equation followed by the short-term interest rate and compute nonparametric prices for bonds and bond options.]

This paper examines how, in the presence of individual risk, economic efficiency can be achieved without an unrealistically large number of contingent claims. Market uncertainty is specified in such a way that general types of individual risk and collective risk are properly accounted for and so that, specifically, market clearing is always satisfied ex post as well as ex ante. We show that consistency of beliefs and optimality of allocation can be guaranteed with an appropriate array of pure Arrow securities to spread collective risk and mutual insurance policies to pool individual risk. When there is individual risk common to like groups of individuals, pooling risk by means of mutual insurance permits substantial economizing on market transactions, as compared to those required if dealing instead with the full complement of pure Arrow securities. We show that if there are N households (consisting of H types), each facing the possibility of being in S individual states together with T collective states, then ensuring Pareto optimality requires only H(S-1)T independent mutual insurance policies plus T pure Arrow securities. Our results also help to clarify the question of which missing markets may affect allocational efficiency.

Egalement paru dans : INRA-ESR Toulouse Série D ; 92-04D et 94-04D

A random price adjustment model is developed for an exchange economy which is decentralized in that the trades permitted to an agent and the resulting price changes depend only on the commodity vector currently held by that agent, and not on the whole economy. We obtain asymptotic results as the number of agents goes to infinity, subject to stability assumptions on the price paths. With probability arbitrarily close to one the price path in our model will approximate the price path of the corresponding tatonnement process on a rapid time scale, and will then remain close to a limit price. Moreover, the economy will approach a competitive equilibrium, and the process will be feasible in the sense that the market maker's inventory is approximately constant over time. Copyright 1996 by The Econometric Society.

This paper develops an asymptotic theory of Bayesian inference for time series. A limiting representation of the Bayesian data density is obtained and shown to be of the same general exponential form for a wide class of likelihoods and prior distributions. Continuous time and discrete time cases are studied. In discrete time, an embedding theorem is given which shows how to embed the exponential density in a continuous time process. From the embedding we obtain a large sample approximation to the model of the data that corresponds to the exponential density. This has the form of discrete observations drawn from a nonlinear stochastic differential equation driven by Brownian motion. No assumptions concerning stationarity or rates of convergence are required in the asymptotics. Some implications for statistical testing are explored and we suggest tests that are based on likelihood ratios (or Bayes factors) of the exponential densities for discriminating between models.

It is widely known that conditional covariances of asset returns change over time. Researchers adopt many strategies to accommodate conditional heteroskedasticity. Among the most popular: (a) chopping the data into short blacks of time and assuming homoskedasticity within the blocks, (b) performing one-sided rolling regressions, in which only data from, say, the preceding five year period is used to estimate the conditional covariance of returns at a given date, and (c) two-sided rolling regressions which use, say, five years of leads and five years of lags. GARCH amounts to a one-sided rolling regression with exponentially declining weights. We derive asymptotically optimal window lengths for standard rolling regressions and optimal weights for weighted rolling regressions. An empirical model of the S&P 500 stock index provides and example.

We examine in this paper a new natural restriction on utility functions, namely that adding an unfair background risk to wealth makes risk-averse individuals behave in a more risk-averse way with respect to any other independent risk. This concept is called risk vulnerability. It is equivalent to the condition that an undesirable risk can never be made desirable by the presence of an independent, unfair risk. Moreover, under risk vulnerability, adding an unfair background risk reduces the demand for risky assets. Risk vulnerability generalizes the concept of properness (individually undesirable, independent risks are always jointly undesirable) introduced by Pratt and Zeckhauser (1987). It implies that the two first derivatives of the utility function are concave transformations of the original utility function. Under decreasing absolute risk aversion, a sufficient condition for risk vulnerability is local properness, i.e. r'' ≥ r'r, where r is the Arrow-Pratt coefficient of absolute risk aversion.