Knowledge that Transforms

This paper uses revealed preference inequalities to provide the tightest possible (best) nonparametric bounds on predicted consumer responses to price changes using consumer-level data over a finite set of relative price changes. These responses are allowed to vary nonparametrically across the income distribution. This is achieved by combining the theory of revealed preference with the semiparametric estimation of consumer expansion paths (Engel curves). We label these expansion path based bounds on demand responses as E-bounds. Deviations from revealed preference restrictions are measured by preference perturbations which are shown to usefully characterize taste change and to provide a stochastic environment within which violations of revealed preference inequalities can be assessed.

We combine choice data in the ultimatum game with the expectations of proposers elicited by subjective probability questions to estimate a structural model of decision making under uncertainty. The model, estimated using a large representative sample of subjects from the Dutch population, allows both nonlinear preferences for equity and expectations to vary across socioeconomic groups. Our results indicate that inequity aversion to one's own disadvantage is an increasing and concave function of the payoff difference. We also find considerable heterogeneity in the population. Young and highly educated subjects have lower aversion for inequity than other groups. Moreover, the model that uses subjective data on expectations generates much better in- and out-of-sample predictions than a model which assumes that players have rational expectations.

We consider a cross-calibration test of predictions by multiple potential experts in a stochastic environment. This test checks whether each expert is calibrated conditional on the predictions made by other experts. We show that this test is good in the sense that a true expert—one informed of the true distribution of the process—is guaranteed to pass the test no matter what the other potential experts do, and false experts will fail the test on all but a small (category I) set of true distributions. Furthermore, even when there is no true expert present, a test similar to cross-calibration cannot be simultaneously manipulated by multiple false experts, but at the cost of failing some true experts.

We study a model of lumpy investment wherein establishments face persistent shocks to common and plant-specific productivity, and nonconvex adjustment costs lead them to pursue generalized (S, s) investment rules. We allow persistent heterogeneity in both capital and total factor productivity alongside low-level investments exempt from adjustment costs to develop the first model consistent with the cross-sectional distribution of establishment investment rates. Examining the implications of lumpy investment for aggregate dynamics in this setting, we find that they remain substantial when factor supply considerations are ignored, but are quantitatively irrelevant in general equilibrium. The substantial implications of general equilibrium extend beyond the dynamics of aggregate series. While the presence of idiosyncratic shocks makes the time-averaged distribution of plant-level investment rates largely invariant to market-clearing movements in real wages and interest rates, we show that the dynamics of plants' investments differ sharply in their presence. Thus, model-based estimations of capital adjustment costs involving panel data may be quite sensitive to the assumption about equilibrium. Our analysis also offers new insights about how nonconvex adjustment costs influence investment at the plant. When establishments face idiosyncratic productivity shocks consistent with existing estimates, we find that nonconvex costs do not cause lumpy investments, but act to eliminate them.

A general equilibrium search model makes layoff costs affect the aggregate unemployment rate in ways that depend on equilibrium proportions of frictional and structural unemployment that in turn depend on the generosity of government unemployment benefits and skill losses among newly displaced workers. The model explains how, before the 1970s, lower flows into unemployment gave Europe lower unemployment rates than the United States and also how, after 1980, higher durations have kept unemployment rates in Europe persistently higher than in the United States. These outcomes arise from the way Europe's higher firing costs and more generous unemployment compensation make its unemployment rate respond to bigger skill losses among newly displaced workers. Those bigger skill losses also explain why U.S. workers have experienced more earnings volatility since 1980 and why, especially among older workers, hazard rates of gaining employment in Europe now fall sharply with increases in the duration of unemployment.

We propose inference procedures for partially identified population features for which the population identification region can be written as a transformation of the Aumann expectation of a properly defined set valued random variable (SVRV). An SVRV is a mapping that associates a set (rather than a real number) with each element of the sample space. Examples of population features in this class include interval-identified scalar parameters, best linear predictors with interval outcome data, and parameters of semiparametric binary models with interval regressor data. We extend the analogy principle to SVRVs and show that the sample analog estimator of the population identification region is given by a transformation of a Minkowski average of SVRVs. Using the results of the mathematics literature on SVRVs, we show that this estimator converges in probability to the population identification region with respect to the Hausdorff distance. We then show that the Hausdorff distance and the directed Hausdorff distance between the population identification region and the estimator, when properly normalized by , converge in distribution to functions of a Gaussian process whose covariance kernel depends on parameters of the population identification region. We provide consistent bootstrap procedures to approximate these limiting distributions. Using similar arguments as those applied for vector valued random variables, we develop a methodology to test assumptions about the true identification region and its subsets. We show that these results can be used to construct a confidence collection and a directed confidence collection. Those are (respectively) collection of sets that, when specified as a null hypothesis for the true value (a subset of values) of the population identification region, cannot be rejected by our tests.

We show that a simple "reputation-style" test can always identify which of two experts is informed about the true distribution. The test presumes no prior knowledge of the true distribution, achieves any desired degree of precision in some fixed finite time, and does not use "counterfactual" predictions. Our analysis capitalizes on a result of Fudenberg and Levine (1992) on the rate of convergence of supermartingales. Copyright

The copyright to this Article is held by the Econometric Society. It may be downloaded, printed and reproduced only for educational or research purposes, including use in course packs. No downloading or copying may be done for any commercial purpose without the explicit permission of the Econometric Society. For such commercial purposes contact the Office of the Econometric Society (contact information may be found at the website

While the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations, we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors-in-variables models with continuously distributed variables. Our main identifying assumption is that, conditional on the value of the true regressors, some “measure of location” of the distribution of the measurement error (e.g., its mean, mode, or median) is equal to zero. The proposed approach relies on the eigenvalue–eigenfunction decomposition of an integral operator associated with specific joint probability densities. The main identifying assumption is used to “index” the eigenfunctions so that the decomposition is unique. We propose a convenient sieve-based estimator, derive its asymptotic properties, and investigate its finite-sample behavior through Monte Carlo simulations.