Knowledge that Transforms

USING EXPECTED-UTILITY THEORY, economists model risk aversion as arising solely because the utility function over wealth is concave.This diminishing-marginal-utility-ofwealth theory of risk aversion is psychologically intuitive, and surely helps explain some of our aversion to large-scale risk: We dislike vast uncertainty in lifetime wealth because a dollar that helps us avoid poverty is more valuable than a dollar that helps us become very rich.Yet this theory also implies that people are approximately risk neutral when stakes are small.Arrow (1971, p. 100) shows that an expected-utility maximizer with a differentiable utility function will always want to take a sufficiently small stake in any positiveexpected-value bet.That is, expected-utility maximizers are (almost everywhere) arbitrarily close to risk neutral when stakes are arbitrarily small.While most economists understand this formal limit result, fewer appreciate that the approximate risk-neutrality prediction holds not just for negligible stakes, but for quite sizable and economically important stakes.Economists often invoke expected-utility theory to explain substantial (observed or posited) risk aversion over stakes where the theory actually predicts virtual risk neutrality.While not broadly appreciated, the inability of expected-utility theory to provide a plausible account of risk aversion over modest stakes has become oral tradition among some subsets of researchers, and has been illustrated in writing in a variety of different contexts using standard utility functions.2In this paper, I reinforce this previous research by presenting a theorem that calibrates a relationship between risk attitudes over small and large stakes.The theorem shows that, within the expected-utility model, anything but virtual risk neutrality over modest stakes implies manifestly unrealistic risk aversion over 1 Many people, including

This paper develops a new concept of separability with overlapping groups—latent separability. This is shown to provide a useful empirical and theoretical framework for investigating the grouping of goods and prices. It is a generalization of weak separability in which goods are allowed to enter more than one group and where the composition of groups is identified by the choice of group specific exclusive goods. Latent separability is shown to be equivalent to weak separability in latent rather than purchased goods and provides a relationship between separability and household production theory. For the popular class of linear, almost ideal and translog demand models and their generalizations, we provide a method for choosing the number of homothetic separable groups. A detailed method for exploring the composition of the separable groups is also presented. These methods are applied to a long time series of British individual household data on the consumption of twenty two nondurable and service goods.

Blume and Easley (1992) show that if agents' have the same savings rule, those who maximize the expected logarithm of next period's outcomes will eventually hold all wealth (i.e. are ‘most prosperous’). However, if no agent adopts this rule then the most prosperous are not necessarily those who make the most accurate predictions. Thus, agents who make inaccurate predictions need not be driven out of the market. In this paper, it is shown that, among agents who have the same intertemporal discount factor (and who choose savings endogenously), the most prosperous are those who make accurate predictions. Hence, convergence to rational expectations obtains because agents who make inaccurate predictions are driven out of the market.

This paper surveys research on the welfare cost of inflation. New estimates are provided, based on U.S. time series for 1900–94, interpreted in a variety of ways. It is estimated that the gain from reducing the annual inflation rate from 10 percent to zero is equivalent to an increase in real income of slightly less than one percent. Using aggregate evidence only, it may not be possible to estimate reliably the gains from reducing inflation further, to a rate consistent with zero nominal interest.

In the setting of ‘affine’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

Data snooping occurs when a given set of data is used more than once for purposes of inference or model selection. When such data reuse occurs, there is always the possibility that any satisfactory results obtained may simply be due to chance rather than to any merit inherent in the method yielding the results. This problem is practically unavoidable in the analysis of time-series data, as typically only a single history measuring a given phenomenon of interest is available for analysis. It is widely acknowledged by empirical researchers that data snooping is a dangerous practice to be avoided, but in fact it is endemic. The main problem has been a lack of sufficiently simple practical methods capable of assessing the potential dangers of data snooping in a given situation. Our purpose here is to provide such methods by specifying a straightforward procedure for testing the null hypothesis that the best model encountered in a specification search has no predictive superiority over a given benchmark model. This permits data snooping to be undertaken with some degree of confidence that one will not mistake results that could have been generated by chance for genuinely good results.

We give a characterization of the set of group-strategyproof, Pareto-optimal, and reallocation-proof allocation rules for the assignment problem, where individuals are assigned at most one indivisible object, without any medium of exchange. Although there are no property rights in the model, the rules satisfying the above criteria imitate a trading procedure with individual endowments, in which individuals exchange objects from their hierarchically determined endowment sets in an iterative manner. In particular, these assignment rules generalize Gale's top trading cycle procedure, the classical rule for the model in which each individual owns an indivisible good.

In this paper, we consider identification and estimation in panel data discrete choice models when the explanatory variable set includes strictly exogenous variables, lags of the endogenous dependent variable as well as unobservable individual-specific effects. For the binary logit model with the dependent variable lagged only once, Chamberlain (1993) gave conditions under which the model is not identified. We present a stronger set of conditions under which the parameters of the model are identified. The identification result suggests estimators of the model, and we show that these are consistent and asymptotically normal, although their rate of convergence is slower than the inverse of the square root of the sample size. We also consider identification in the semiparametric case where the logit assumption is relaxed. We propose an estimator in the spirit of the conditional maximum score estimator (Manski (1987)) and we show that it is consistent. In addition, we discuss an extension of the identification result to multinomial discrete choice models, and to the case where the dependent variable is lagged twice. Finally, we present some Monte Carlo evidence on the small sample performance of the proposed estimators for the binary response model.