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Full-Text Articles in Social and Behavioral Sciences

Uniqueness And Stability Of Equilibrium In Economies With Two Goods, John Geanakoplos, Kieran James Walsh Aug 2016

Uniqueness And Stability Of Equilibrium In Economies With Two Goods, John Geanakoplos, Kieran James Walsh

Cowles Foundation Discussion Papers

We offer new sufficient conditions ensuring demand is downward sloping local to equilibrium. It follows that equilibrium is unique and stable in the sense that rising supply implies falling prices. In our setting, there are two goods, which we interpret as consumption in different time periods, and many impatience types. Agents have the same Bernoulli utility function, but the types differ arbitrarily in time preference. Our main result is that if endowments are identical and utility displays nonincreasing absolute risk aversion, then market demand is strictly downward sloping local to equilibrium. We discuss implications for the Diamond-Dybvig literature.


Contracting With Word-Of-Mouth Management, Yuichiro Kamada, Aniko Öry (Oery) Jul 2016

Contracting With Word-Of-Mouth Management, Yuichiro Kamada, Aniko Öry (Oery)

Cowles Foundation Discussion Papers

We incorporate word of mouth (WoM) in a classic Maskin-Riley contracting problem, allowing for referral rewards to senders of WoM. Current customers’ incentives to engage in WoM can affect the contracting problem of a firm in the presence of positive externalities of users. We fully characterize the optimal contract scheme and provide other comparative statics. In particular, we show that offering a free contract is optimal only if the fraction of premium users in the population is small. The reason is that by offering a free product, the firm can incentivize senders to talk by increasing expected externalities that they …


The Design And Price Of Information, Dirk Bergemann, Alessandro Bonatti, Alex Smolin Jul 2016

The Design And Price Of Information, Dirk Bergemann, Alessandro Bonatti, Alex Smolin

Cowles Foundation Discussion Papers

This paper analyzes the trade of information between a data buyer and a data seller. The data buyer faces a decision problem under uncertainty and seeks to augment his initial private information with supplemental data. The data seller is uncertain about the willingness-to-pay of the data buyer due to this private information. The data seller optimally offers a menu of (Blackwell) experiments as statistical tests to the data buyer. The seller exploits differences in the beliefs of the buyer’s types to reduce information rents while limiting the surplus that must be sacrificed to provide incentives.


The Design And Price Of Information, Dirk Bergemann, Alessandro Bonatti, Alex Smolin Jul 2016

The Design And Price Of Information, Dirk Bergemann, Alessandro Bonatti, Alex Smolin

Cowles Foundation Discussion Papers

A data buyer faces a decision problem under uncertainty. He can augment his initial private information with supplemental data from a data seller. His willingness to pay for supplemental data is determined by the quality of his initial private information. The data seller optimally offers a menu of statistical experiments. We establish the properties that any revenue-maximizing menu of experiments must satisfy. Every experiment is a non-dispersed stochastic matrix, and every menu contains a fully informative experiment. In the cases of binary states and actions, or binary types, we provide an explicit construction of the optimal menu of experiments.


Common Ownership, Competition, And Top Management Incentives, Miguel Antón, Florian Ederer, Mireia Giné, Martin Schmalz Jul 2016

Common Ownership, Competition, And Top Management Incentives, Miguel Antón, Florian Ederer, Mireia Giné, Martin Schmalz

Cowles Foundation Discussion Papers

Standard corporate finance theories assume the absence of strategic product market interactions or that shareholders don’t diversify across industry rivals; the optimal incentive contract features pay-for-performance relative to industry peers. Empirical evidence, by contrast, indicates managers are rewarded for rivals’ performance as well as for their own. We propose common ownership of natural competitors by the same investors as an explanation. We show theoretically and empirically that executives are paid less for own performance and more for rivals’ performance when the industry is more commonly owned. The growth of common ownership also helps explain the increase in CEO pay over …


Consumers On A Leash: Advertised Sales And Intertemporal Price Discrimination, Aniko Öry Jul 2016

Consumers On A Leash: Advertised Sales And Intertemporal Price Discrimination, Aniko Öry

Cowles Foundation Discussion Papers

The Internet allows sellers to track “window shoppers,” consumers who look but do not buy, and to lure them back later by targeting them with an advertised sale. This new technology thus facilitates intertemporal price discrimination, but simultaneously makes it too easy for a seller to undercut her regular price. Because buyers know they could be lured back, the seller is forced to set a lower regular price. Advertising costs can, therefore, serve as a form of commitment: a seller can actually benefit from higher costs of advertising. Based on this framework, the impact of commitment on prices, profits, and …


Contracting With Word-Of-Mouth Management, Yuichiro Kamada, Aniko Öry (Oery) Jul 2016

Contracting With Word-Of-Mouth Management, Yuichiro Kamada, Aniko Öry (Oery)

Cowles Foundation Discussion Papers

We propose a model for word of mouth (WoM) management where a firm has two tools at hand: referral rewards and offering a free contract. Current customers’ incentives to engage in WoM can affect the contracting problem of a rm in the presence of positive externalities of users. Formally, we consider a classic Maskin-Riley contracting problem for the receiver of WoM where the firm can pay the sender’s referral rewards and a sender experiences positive externalities if the receiver adopts. A free contract can incentivize WoM because the higher adoption probability increases the expected externalities that the sender receives. We …


Contracting With Word-Of-Mouth Management, Yuichiro Kamada, Aniko Öry (Oery) Jul 2016

Contracting With Word-Of-Mouth Management, Yuichiro Kamada, Aniko Öry (Oery)

Cowles Foundation Discussion Papers

We incorporate word of mouth (WoM) in a classic Maskin-Riley contracting problem, allowing for referral rewards to senders of WoM. Current customers’ incentives to engage in WoM can affect the contracting problem of a firm in the presence of positive externalities of users. We fully characterize the optimal contract scheme and provide comparative statics. In particular, we show that offering a free contract is optimal only if the fraction of premium users in the population is small. The reason is that by offering a free product, the firm can incentivize senders to talk by increasing expected externalities that they receive …


Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár Jun 2016

Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár

Cowles Foundation Discussion Papers

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum mean-squared error results in CIs that are nearly efficient and …


Doing More When You're Running Late: Applying Marginal Treatment Effect Methods To Examine Treatment Effect Heterogeneity In Experiments, Amanda E. Kowalski Jun 2016

Doing More When You're Running Late: Applying Marginal Treatment Effect Methods To Examine Treatment Effect Heterogeneity In Experiments, Amanda E. Kowalski

Cowles Foundation Discussion Papers

I examine treatment effect heterogeneity within an experiment to inform external validity. The local average treatment effect (LATE) gives an average treatment effect for compliers. I bound and estimate average treatment effects for always takers and never takers by extending marginal treatment effect methods. I use these methods to separate selection from treatment effect heterogeneity, generalizing the comparison of OLS to LATE. Applying these methods to the Oregon Health Insurance Experiment, I find that the treatment effect of insurance on emergency room utilization decreases from always takers to compliers to never takers. Previous utilization explains a large share of the …


Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár Jun 2016

Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár

Cowles Foundation Discussion Papers

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We give sharp efficiency bounds of using different kernels, and derive the optimal bandwidth for constructing honest CIs. We show that using the bandwidth that minimizes the maximum meansquared error results in CIs that are nearly efficient and …


Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár Jun 2016

Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár

Cowles Foundation Discussion Papers

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive and tabulate novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive …


Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár Jun 2016

Simple And Honest Confidence Intervals In Nonparametric Regression, Timothy B. Armstrong, Michal Kolesár

Cowles Foundation Discussion Papers

We consider the problem of constructing honest confidence intervals (CIs) for a scalar parameter of interest, such as the regression discontinuity parameter, in nonparametric regression based on kernel or local polynomial estimators. To ensure that our CIs are honest, we derive novel critical values that take into account the possible bias of the estimator upon which the CIs are based. We show that this approach leads to CIs that are more efficient than conventional CIs that achieve coverage by undersmoothing or subtracting an estimate of the bias. We give sharp efficiency bounds of using different kernels, and derive the optimal …


Mcmc Confidence Sets For Identified Sets, Xiaohong Chen, Timothy M. Christensen, Elie Tamer May 2016

Mcmc Confidence Sets For Identified Sets, Xiaohong Chen, Timothy M. Christensen, Elie Tamer

Cowles Foundation Discussion Papers

In complicated/nonlinear parametric models, it is generally hard to determine whether the model parameters are (globally) point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of parameters in econometric models defined through a likelihood or a vector of moments. The CSs for the identified set or for a function of the identified set (such as a subvector) are based on inverting an optimal sample criterion (such as likelihood or continuously updated GMM), where the cutoff values are computed via Monte Carlo simulations directly from a quasi posterior distribution of the criterion. We establish new …


Energy Prices, Pass-Through, And Incidence In U.S. Manufacturing, Sharat Ganapati, Joseph S. Shapiro, Reed Walker May 2016

Energy Prices, Pass-Through, And Incidence In U.S. Manufacturing, Sharat Ganapati, Joseph S. Shapiro, Reed Walker

Cowles Foundation Discussion Papers

This paper studies how increases in energy input costs for production are split between consumers and producers via changes in product prices (i.e., pass-through). We show that in markets characterized by imperfect competition, marginal cost pass-through, a demand elasticity, and a price-cost markup are sucient to characterize the relative change in welfare between producers and consumers due to a change in input costs. We find that increases in energy prices lead to higher plant-level marginal costs and output prices but lower markups. This suggests that marginal cost pass-through is incomplete, with estimates centered around 0.7. Our confidence intervals reject both …


The Incidence Of Carbon Taxes In U.S. Manufacturing: Lessons From Energy Cost Pass-Through, Sharat Ganapati, Joseph S. Shapiro, Reed Walker May 2016

The Incidence Of Carbon Taxes In U.S. Manufacturing: Lessons From Energy Cost Pass-Through, Sharat Ganapati, Joseph S. Shapiro, Reed Walker

Cowles Foundation Discussion Papers

This paper estimates how increases in production costs due to energy inputs affect consumer versus producer surplus (i.e., incidence). In doing so, we develop a general methodology to measure the incidence of changes in input costs that can account for three first-order issues: factor substitution amongst inputs used for production, incomplete pass-through of input costs, and industry competitiveness. We apply this methodology to a set of U.S. manufacturing industries for which we observe plant-level output prices and input costs. We find that about 70 percent of energy price-driven changes in input costs are passed through to consumers. This implies that …


Expected Worth For 2 × 2 Matrix Games With Variable Grid Sizes, Michael R. Powers, Martin Shubik, Wen Wang May 2016

Expected Worth For 2 × 2 Matrix Games With Variable Grid Sizes, Michael R. Powers, Martin Shubik, Wen Wang

Cowles Foundation Discussion Papers

We offer a detailed examination of a broad class of 2 x 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.


Mechanism Design With Partially Verifiable Information, Roland Strausz May 2016

Mechanism Design With Partially Verifiable Information, Roland Strausz

Cowles Foundation Discussion Papers

In mechanism design with (partially) verifiable information, the revelation principle obtains in full generality if allocations are modelled as the product set of outcomes and verifiable information. Incentive constraints fully characterize the implementable set of these product-allocations. The revelation principle does not generally hold when an allocation is modelled as only an outcome. However, any outcome of an implementable product-allocation is also implementable under this restricted modelling, provided that the mechanism designer can expand communication by adding unverifiable messages and restrict communication by limiting the use of messages. A canonical representation of such mechanisms is presented, implying that an inalienable …


Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár May 2016

Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár

Cowles Foundation Discussion Papers

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is …


Reputation Building Under Uncertain Monitoring, Joyee Deb, Yuhta Ishii May 2016

Reputation Building Under Uncertain Monitoring, Joyee Deb, Yuhta Ishii

Cowles Foundation Discussion Papers

We study a canonical model of reputation between a long-run player and a sequence of short-run opponents, in which the long-run player is privately informed about an uncertain state that determines the monitoring structure in the reputation game. The long-run player plays a stage-game repeatedly against a sequence of short-run opponents. We present necessary and sufficient conditions (on the monitoring structure and the type space) to obtain reputation building in this setting. Specifically, in contrast to the previous literature, with only stationary commitment types, reputation building is generally not possible and highly sensitive to the inclusion of other commitment types. …


Monte Carlo Confidence Sets For Identified Sets, Xiaohong Chen, Timothy M. Christensen, Elie Tamer May 2016

Monte Carlo Confidence Sets For Identified Sets, Xiaohong Chen, Timothy M. Christensen, Elie Tamer

Cowles Foundation Discussion Papers

In complicated/nonlinear parametric models, it is generally hard to know whether the model parameters are point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of full parameters and of subvectors in models defined through a likelihood or a vector of moment equalities or inequalities. These CSs are based on level sets of optimal sample criterion functions (such as likelihood or optimally-weighted or continuously-updated GMM criterions). The level sets are constructed using cutoffs that are computed via Monte Carlo (MC) simulations directly from the quasi-posterior distributions of the criterions. We establish new Bernstein-von Mises (or …


The Incidence Of Carbon Taxes In U.S. Manufacturing: Lessons From Energy Cost Pass-Through, Sharat Ganapati, Joseph S. Shapiro, Reed Walker May 2016

The Incidence Of Carbon Taxes In U.S. Manufacturing: Lessons From Energy Cost Pass-Through, Sharat Ganapati, Joseph S. Shapiro, Reed Walker

Cowles Foundation Discussion Papers

This paper studies how changes in energy input costs for U.S. manufacturers affect the relative welfare of manufacturing producers and consumers (i.e., incidence). In doing so, we develop a novel partial equilibrium methodology designed to estimate the incidence of input taxes. This method simultaneously accounts for three determinants of incidence that are typically studied in isolation: incomplete pass-through of input costs, differences in industry competitiveness, and substitution amongst inputs used for production. We apply this methodology to a set of U.S. manufacturing industries for which we observe plant-level unit prices and input choices. We find that about 70 percent of …


Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár May 2016

Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár

Cowles Foundation Discussion Papers

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is …


Expected Worth For 2 × 2 Matrix Games With Variable Grid Sizes, Michael R. Powers, Martin Shubik, Wen Wang May 2016

Expected Worth For 2 × 2 Matrix Games With Variable Grid Sizes, Michael R. Powers, Martin Shubik, Wen Wang

Cowles Foundation Discussion Papers

We offer a detailed examination of a broad class of 2 × 2 matrix games as a first step toward considering measures of resource distribution and efficiency of outcomes. In the present essay, only noncooperative equilibria and entropic outcomes are considered, and a crude measure of efficiency employed. Other solution concepts and the formal construction of an efficiency index will be addressed in a companion paper.


Reputation With Opportunities For Coasting, Heski Bar-Isaac, Joyee Deb May 2016

Reputation With Opportunities For Coasting, Heski Bar-Isaac, Joyee Deb

Cowles Foundation Discussion Papers

Reputation concerns can discipline agents to take costly effort and generate good outcomes. But what if outcomes are not always observed? We consider a model of reputation with shifting observability, and ask how this affects agents’ incentives. We identify a novel and intuitive mechanism by which infrequent observation or inattention can actually strengthen reputation incentives and encourage effort. If an agent anticipates that outcomes may not be observed in the future, the benefits from effort today are enhanced due to a “coasting” effect. By investing effort when outcomes are more likely observed, the agent can improve her reputation, and when …


Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár May 2016

Optimal Inference In A Class Of Regression Models, Timothy B. Armstrong, Michal Kolesár

Cowles Foundation Discussion Papers

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression. Our main assumption is that the regression function is known to lie in a convex function class, which covers most smoothness and/or shape assumptions used in econometrics. We derive finite-sample optimal CIs and sharp efficiency bounds under normal errors with known variance. We show that these results translate to uniform (over the function class) asymptotic results when the error distribution is …


Money And Status: How Best To Incentivize Work, Pradeep Dubey, John Geanakoplos May 2016

Money And Status: How Best To Incentivize Work, Pradeep Dubey, John Geanakoplos

Cowles Foundation Discussion Papers

Status is greatly valued in the real world, yet it has not received much attention from economic theorists. We examine how the owner of a firm can best combine money and status to get her employees to work hard for the least total cost. We find that she should motivate workers of low skill mostly by status and high skill mostly by money. Moreover, she should do so by using a small number of titles and wage levels. This often results in star wages to the elite performers. By analogy, the governance of a society should pay special attention to …


The Incidence Of Carbon Taxes In U.S. Manufacturing: Lessons From Energy Cost Pass-Through, Sharat Ganapati, Joseph S. Shapiro, Reed Walker May 2016

The Incidence Of Carbon Taxes In U.S. Manufacturing: Lessons From Energy Cost Pass-Through, Sharat Ganapati, Joseph S. Shapiro, Reed Walker

Cowles Foundation Discussion Papers

This paper studies how changes in energy input costs for U.S. manufacturers affect the relative welfare of manufacturing producers and consumers (i.e. incidence). In doing so, we develop a partial equilibrium methodology to estimate the incidence of input taxes that can simultaneously account for three determinants of incidence that are typically studied in isolation: incomplete pass-through of input costs, differences in industry competitiveness, and factor substitution amongst inputs used for production. We apply this methodology to a set of U.S. manufacturing industries for which we observe plant-level unit prices and input choices. We find that about 70 percent of energy …


Three Lectures On The Theory Of Money And Financial Institutions: Lecture 1: A Nontechnical Overview, Martin Shubik Apr 2016

Three Lectures On The Theory Of Money And Financial Institutions: Lecture 1: A Nontechnical Overview, Martin Shubik

Cowles Foundation Discussion Papers

This is a nontechnical retrospective paper on a game theoretic approach to the theory of money and financial institutions. The stress is on process models and the reconciliation of general equilibrium with Keynes and Schumpeter’s approaches to non-equilibrium dynamics.


Motivational Ratings, Johannes Hörner, Nicolas Lambert Apr 2016

Motivational Ratings, Johannes Hörner, Nicolas Lambert

Cowles Foundation Discussion Papers

Rating systems not only provide information to users but also motivate the rated agent. This paper solves for the optimal (effort-maximizing) rating system within the standard career concerns framework. It is a mixture two-state rating system. That is, it is the sum of two Markov processes, with one that re-effects the belief of the rater and the other the preferences of the rated agent. The rating, however, is not a Markov process. Our analysis shows how the rating combines information of different types and vintages. In particular, an increase in effort may affect some (but not all) future ratings adversely.