Knowledge that Transforms

Econometric analyses of treatment response commonly use instrumental variable (IV) assumptions to identify treatment effects. Yet the credibility of IV assumptions is often a matter of considerable disagreement. There is therefore good reason to consider weaker but more credible assumptions. To this end, we introduce monotone instrumental variable (MIV) assumptions and the important special case of monotone treatment selection (MTS). We study the identifying power of MIV assumptions alone and combined with the assumption of monotone treatment response (MTR). We present an empirical application using the MTS and MTR assumptions to place upper bounds on the returns to schooling

This paper explores how Bayes-rational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may type-specific ‘herds’ eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history offers no decisive lessons for anyone, and each type's actions forever nontrivially split between two actions. To verify that our identified limit outcomes do arise, we exploit the Markov-martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.

A valid Edgeworth expansion is established for the limit distribution of density-weighted semiparametric averaged derivative estimates of single index models. The leading term that corrects the normal limit varies in magnitude, depending on the choice of bandwidth and kernel order. In general this term has order larger than the n−1/2 that prevails in standard parametric problems, but we find circumstances in which it is O(n−1/2), thereby extending the achievement of an n−1/2 Berry-Esseen bound in Robinson (1995a). A valid empirical Edgeworth expansion is also established. We also provide theoretical and empirical Edgeworth expansions for a studentized statistic, where some correction terms are different from those for the unstudentized case. We report a Monte Carlo study of finite sample performance.

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality, or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines. We also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another. The sampling distribution of convenient dual estimators for the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study data bases.

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.

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 propose a simple adaptive procedure for playing a game. In this procedure, players depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies (these measures are updated every period). It is shown that our adaptive procedure guaranties that with probability one, the sample distributions of play converge to the set of correlated equilibria of the game. To compute these regret measures, a player needs to know his payoff function and the history of play. We also offer a variation where every player knows only his own realized payoff history (but not his payoff function).

This paper studies the monotonicity of individual and market demand with the aid of the indirect utility function. We identify sufficient (and in a sense, necessary) conditions on an agent's indirect utility which will guarantee that he has a monotonic demand function. Our conditions also point to a natural way of extending the result of Hildenbrand (1983). Hildenbrand showed that market demand is monontonic if the income distribution has a downward sloping density, even though individual agents' demand function might violate monotonicity. Using the indirect utility function, we introduce a measure of violations of individual monotonicity that allows us to identify a larger class of density functions that will generate a monotonic market demand.