Knowledge that Transforms

We study a definition of subjective beliefs applicable to preferences that allow for the perception of ambiguity, and provide a characterization of such beliefs in terms of market behavior. Using this definition, we derive necessary and sufficient conditions for the efficiency of ex ante trade and show that these conditions follow from the fundamental welfare theorems. When aggregate uncertainty is absent, our results show that full insurance is efficient if and only if agents share some common subjective beliefs. Our results hold for a general class of convex preferences, which contains many functional forms used in applications involving ambiguity and ambiguity aversion. We show how our results can be articulated in the language of these functional forms, confirming results existing in the literature, generating new results, and providing a useful tool for applications. Copyright 2008 The Econometric Society.

Traditional discrete-choice models assume buyers are aware of all products for sale. In markets where products change rapidly, the full information assumption is untenable. I present a discrete-choice model of limited consumer information, where advertising influences the set of products from which consumers choose to purchase. I apply the model to the U.S. personal computer market where top firms spend over $2 billion annually on advertising. I find estimated markups of 19% over production costs, where top firms advertise more than average and earn higher than average markups. High markups are explained to a large extent by informational asymmetries across consumers, where full information models predict markups of one-fourth the magnitude. I find that estimated product demand curves are biased toward being too elastic under traditional models. I show how to use data on media exposure to improve estimated price elasticities in the absence of micro ad data. Copyright 2008 The Econometric Society.

In the past few decades multistore retailers, especially those with 100 or more stores, have experienced substantial growth. At the same time, there is widely reported public outcry over the impact of these chain stores on other retailers and local communities. This paper develops an empirical model to assess the impact of chain stores on other discount retailers and to quantify the size of the scale economies within a chain. The model has two key features. First, it allows for flexible competition patterns among all players. Second, for chains, it incorporates the scale economies that arise from operating multiple stores in nearby regions. In doing so, the model relaxes the commonly used assumption that entry in different markets is independent. The lattice theory is exploited to solve this complicated entry game among chains and other discount retailers in a large number of markets. It is found that the negative impact of Kmart's presence on Wal-Mart's profit was much stronger in 1988 than in 1997, while the opposite is true for the effect of Wal-Mart's presence on Kmart's profit. Having a chain store in a market makes roughly 50% of the discount stores unprofitable. Wal-Mart's expansion from the late 1980s to the late 1990s explains about 40–50% of the net change in the number of small discount stores and 30–40% for all other discount stores. Scale economies were important for Wal-Mart, but less so for Kmart, and the magnitude did not grow proportionately with the chains' sizes.

We design experiments to jointly elicit risk and time preferences for the adult Danish population. Since subjects are generally risk averse, we find that joint elicitation provides estimates of discount rates that are significantly lower than those found in previous studies and more in line with what would be considered as a priori reasonable rates. The statistical specification relies on a theoretical framework that involves a latent trade-off between long-run optimization and short-run temptation. Estimation of this specification is undertaken using structural, maximum likelihood methods. Our main results based on exponential discounting are robust to alternative specifications such as hyperbolic discounting. These results have direct implications for attempts to elicit time preferences, as well as debates over the appropriate domain of the utility function when characterizing risk aversion and time consistency.

We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent sources of uncertainty. We prove that dynamic completeness of the candidate equilibrium price process follows from mild exogenous assumptions on the economic primitives of the model. Our result is universal, rather than generic: dynamic completeness of the candidate equilibrium price process and existence of equilibrium follow from the way information is revealed in a Brownian filtration, and from a mild exogenous nondegeneracy condition on the terminal security dividends. The nondegeneracy condition, which requires that finding one point at which a determinant of a Jacobian matrix of dividends is nonzero, is very easy to check. We find that the equilibrium prices, consumptions, and trading strategies are well-behaved functions of the stochastic process describing the evolution of information. We prove that equilibria of discrete approximations converge to equilibria of the continuous-time economy.

This paper derives asymptotic power envelopes for tests of the unit root hypothesis in a zero-mean AR(1) model. The power envelopes are derived using the limits of experiments approach and are semiparametric in the sense that the underlying error distribution is treated as an unknown infinite-dimensional nuisance parameter. Adaptation is shown to be possible when the error distribution is known to be symmetric and to be impossible when the error distribution is unrestricted. In the latter case, two conceptually distinct approaches to nuisance parameter elimination are employed in the derivation of the semiparametric power bounds. One of these bounds, derived under an invariance restriction, is shown by example to be sharp, while the other, derived under a similarity restriction, is conjectured not to be globally attainable.

We develop a framework to assess how successfully standard time series models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric series. The properties of these weighted averages are then compared to the asymptotic implications of a number of common time series models. We apply the framework to twenty U.S. macroeconomic and financial time series using frequencies lower than the business cycle. Copyright 2008 The Econometric Society.

We consider a dynamic Bertrand game in which prices are publicly observed and each firm receives a privately observed cost shock in each period. Although cost shocks are independent across firms, within a firm costs follow a first-order Markov process. We analyze the set of collusive equilibria available to firms, emphasizing the best collusive scheme for the firms at the start of the game. In general, there is a trade-off between productive efficiency, whereby the low-cost firm serves the market in a given period, and high prices. We show that when costs are perfectly correlated over time within a firm, if the distribution of costs is log-concave and firms are sufficiently patient, then the optimal collusive scheme entails price rigidity: firms set the same price and share the market equally, regardless of their respective costs. When serial correlation of costs is imperfect, partial productive efficiency is optimal. For the case of two cost types, first-best collusion is possible if the firms are patient relative to the persistence of cost shocks, but not otherwise. We present numerical examples of first-best collusive schemes.

We study how professional players and college students play zero-sum two-person strategic games in a laboratory setting. We first ask professionals to play a 2 × 2 game that is formally identical to a strategic interaction situation that they face in their natural environment. Consistent with their behavior in the field, they play very close to the equilibrium of the game. In particular, (i) they equate their strategies' payoffs to the equilibrium ones and (ii) they generate sequences of choices that are serially independent. In sharp contrast, however, we find that college students play the game far from the equilibrium predictions. We then study the behavior of professional players and college students in the classic O'Neill 4 × 4 zero-sum game, a game that none of the subjects has encountered previously, and find the same differences in the behavior of these two pools of subjects. The transfer of skills and experience from the familiar field to the unfamiliar laboratory observed for professional players is relevant to evaluate the circumstances under which behavior in a laboratory setting may be a reliable indicator of behavior in a naturally occurring setting. From a cognitive perspective, it is useful for research on recognition processes, intuition, and similarity as a basis for inductive reasoning.

We use the control function approach to identify the average treatment effect and the effect of treatment on the treated in models with a continuous endogenous regressor whose impact is heterogeneous. We assume a stochastic polynomial restriction on the form of the heterogeneity, but unlike alternative nonparametric control function approaches, our approach does not require large support assumptions.