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Matching with Complementary Contracts
Marzena Rostek, Nathan Yoder
In this paper, we show that stable outcomes exist in matching environments with complementarities, such as social media platforms or markets for patent licenses. Our results apply to both nontransferable and transferable utility settings, and allow for multilateral agreements and those with externalities. In particular, we show that stable outcomes in these settings are characterized by the largest fixed point of a monotone operator, and so can be found using an algorithm; in the nontransferable utility case, this is a one‐sided deferred acceptance algorithm, rather than a Gale–Shapley algorithm. We also give a monotone comparative statics result as well as a comparative static on the effect of bundling contracts together. These illustrate the impact of design decisions, such as increased privacy protections on social media, or the use of antitrust law to disallow patent pools, on stable outcomes.
The objective of this paper is to identify and estimate network formation models using observed data on network structure. We characterize network formation as a simultaneous‐move game, where the utility from forming a link depends on the structure of the network, thereby generating strategic interactions between links. With the prevalence of multiple equilibria, the parameters are not necessarily point identified. We leave the equilibrium selection unrestricted and propose a partial identification approach. We derive bounds on the probability of observing a subnetwork, where a subnetwork is the restriction of a network to a subset of the individuals. Unlike the standard bounds as in Ciliberto and Tamer (2009), these subnetwork bounds are computationally tractable in large networks provided we consider small subnetworks. We provide Monte Carlo evidence that bounds from small subnetworks are informative in large networks.
Leave-out estimation of variance components
Patrick Kline, Raffaele Saggio, Mikkel Sølvsten
We propose leave‐out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An approximation algorithm is provided that enables accurate computation of the estimator in very large data sets. We study the large sample properties of our estimator allowing the number of regressors to grow in proportion to the number of observations. Consistency is established in a variety of settings where plug‐in methods and estimators predicated on homoscedasticity exhibit first‐order biases. For quadratic forms of increasing rank, the limiting distribution can be represented by a linear combination of normal and non‐central χ2 random variables, with normality ensuing under strong identification. Standard error estimators are proposed that enable tests of linear restrictions and the construction of uniformly valid confidence intervals for quadratic forms of interest. We find in Italian social security records that leave‐out estimates of a variance decomposition in a two‐way fixed effects model of wage determination yield substantially different conclusions regarding the relative contribution of workers, firms, and worker‐firm sorting to wage inequality than conventional methods. Monte Carlo exercises corroborate the accuracy of our asymptotic approximations, with clear evidence of non‐normality emerging when worker mobility between blocks of firms is limited.
Paralyzed by Fear: Rigid and Discrete Pricing under Demand Uncertainty
Cosmin Ilut, Rosen Valchev, Nicolas Vincent
We propose a new theory of price rigidity based on firms' Knightian uncertainty about their competitive environment. This uncertainty has two key implications. First, firms learn about the shape of their demand function from past observations of quantities sold. This learning gives rise to kinks in the expected profit function at previously observed prices, making those prices both sticky and more likely to reoccur. Second, uncertainty about the relationship between aggregate and industry‐level inflation generates nominal rigidity. We prove the main insights analytically and quantify the effects of our mechanism. Our estimated quantitative model is consistent with a wide range of micro‐level pricing facts that are typically challenging to match jointly. It also implies significantly more persistent monetary non‐neutrality than in standard models, allowing it to generate large real effects from nominal shocks.
Non-Clairvoyant Dynamic Mechanism Design
Vahab Mirrokni, Renato Paes Leme, Pingzhong Tang, Song Zuo
We introduce a new family of dynamic mechanisms that restricts sellers from using future distributional knowledge. Since the allocation and pricing of each auction period do not depend on the type distributions of future periods, we call this family of dynamic mechanisms non‐clairvoyant.
Eliminating Uncertainty in Market Access: The Impact of New Bridges in Rural Nicaragua
Wyatt Brooks, Kevin Donovan
We measure the impact of increasing integration between rural villages and outside labor markets. Seasonal flash floods cause exogenous and unpredictable loss of market access. We study the impact of new bridges that eliminate this risk. Identification exploits variation in riverbank characteristics that preclude bridge construction in some villages, despite similar need. We collect detailed annual household surveys over three years, and weekly telephone followups to study contemporaneous effects of flooding. Floods decrease labor market income by 18 percent when no bridge is present. Bridges eliminate this effect. The indirect effects on labor market choice, farm investment, and savings are quantitatively important and consistent with the predictions of a general equilibrium model in which farm investment is risky, and households manage labor market risk and agricultural risk simultaneously. In the calibrated model, the increase in consumption‐equivalent welfare is substantially larger than the increase in income due to the ability to mitigate risk.
Segmentary Lineage Organization and Conflict in Sub-Saharan Africa
Jacob Moscona, Nathan Nunn, James A. Robinson
We test the longstanding hypothesis that ethnic groups organized around “segmentary lineages” are more prone to conflict. Ethnographic accounts suggest that in such societies, which are characterized by strong allegiances to distant relatives, individuals are obligated to come to the aid of fellow lineage members when they become involved in conflicts. As a consequence, small disagreements often escalate into larger‐scale conflicts involving many individuals. We test for a link between segmentary lineage organization and conflict across ethnic groups in sub‐Saharan Africa. Using a number of estimation strategies, including a regression discontinuity design at ethnic boundaries, we find that segmentary lineage societies experience more conflicts, and particularly ones that are retaliatory, long in duration, and large in scale.
Heterogeneous Markups, Growth, and Endogenous Misallocation
Markups vary systematically across firms and are a source of misallocation. This paper develops a tractable model of firm dynamics where firms' market power is endogenous and the distribution of markups emerges as an equilibrium outcome. Monopoly power is the result of a process of forward‐looking, risky accumulation: firms invest in productivity growth to increase markups in their existing products but are stochastically replaced by more efficient competitors. Creative destruction therefore has pro‐competitive effects because faster churn gives firms less time to accumulate market power. In an application to firm‐level data from Indonesia, the model predicts that, relative to the United States, misallocation is more severe and firms are substantially smaller. To explain these patterns, the model suggests an important role for frictions that prevent existing firms from entering new markets. Differences in entry costs for new firms are less important.
Optimal Monitoring Design
George Georgiadis, Balazs Szentes
This paper considers a Principal–Agent model with hidden action in which the Principal can monitor the Agent by acquiring independent signals conditional on effort at a constant marginal cost. The Principal aims to implement a target effort level at minimal cost. The main result of the paper is that the optimal information‐acquisition strategy is a two‐threshold policy and, consequently, the equilibrium contract specifies two possible wages for the Agent. This result provides a rationale for the frequently observed single‐bonus wage contracts.
Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity
Guido M. Kuersteiner, Ingmar R. Prucha
This paper considers a class of generalized methods of moments (GMM) estimators for general dynamic panel models, allowing for weakly exogenous covariates and cross‐sectional dependence due to spatial lags, unspecified common shocks, and time‐varying interactive effects. We significantly expand the scope of the existing literature by allowing for endogenous time‐varying spatial weight matrices without imposing explicit structural assumptions on how the weights are formed. An important area of application is in social interaction and network models where our specification can accommodate data dependent network formation. We consider an exemplary social interaction model and show how identification of the interaction parameters is achieved through a combination of linear and quadratic moment conditions. For the general setup we develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions. This is an important ingredient to a tractable asymptotic distribution of our estimators. In general, the asymptotic distribution of our estimators is found to be mixed normal due to random norming. However, the asymptotic distribution of our test statistics is still chi‐square.
Analysis of Testing-Based Forward Model Selection
This paper analyzes a procedure called Testing‐Based Forward Model Selection (TBFMS) in linear regression problems. This procedure inductively selects covariates that add predictive power into a working statistical model before estimating a final regression. The criterion for deciding which covariate to include next and when to stop including covariates is derived from a profile of traditional statistical hypothesis tests. This paper proves probabilistic bounds, which depend on the quality of the tests, for prediction error and the number of selected covariates. As an example, the bounds are then specialized to a case with heteroscedastic data, with tests constructed with the help of Huber–Eicker–White standard errors. Under the assumed regularity conditions, these tests lead to estimation convergence rates matching other common high‐dimensional estimators including Lasso.
A patient player privately observes a persistent state and interacts with an infinite sequence of myopic uninformed players. The patient player is either a strategic type who maximizes his payoff or one of several commitment types who mechanically play the same action in every period. I focus on situations in which the uninformed player's best reply to a commitment action depends on the state and where the total probability of commitment types is sufficiently small. I show that the patient player's equilibrium payoff is bounded below his commitment payoff in some equilibria under some of his payoff functions. This is because he faces a trade‐off between building his reputation for commitment and signaling favorable information about the state. When players' stage‐game payoff functions are monotone‐supermodular, the patient player receives high payoffs in all states and in all equilibria. Under an additional condition on the state distribution, my reputation model yields a unique prediction on the patient player's equilibrium payoff and on‐path behavior.
Bootstrap-Based Inference for Cube Root Asymptotics
Matias D. Cattaneo, Michael Jansson, Kenichi Nagasawa
This paper proposes a valid bootstrap‐based distributional approximation for M‐estimators exhibiting a Chernoff (1964)‐type limiting distribution. For estimators of this kind, the standard nonparametric bootstrap is inconsistent. The method proposed herein is based on the nonparametric bootstrap, but restores consistency by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate. This modification leads to a generic and easy‐to‐implement resampling method for inference that is conceptually distinct from other available distributional approximations. We illustrate the applicability of our results with four examples in econometrics and machine learning.
Corrigendum to “Trading and Information Diffusion in Over-the-Counter Markets”
Ana Babus, Péter Kondor, Yilin Wang