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Full-Text Articles in Economics
Policy With Stochastic Hysteresis, Job Boerma, Georgii Riabov, Aleh Tsyvinski
Policy With Stochastic Hysteresis, Job Boerma, Georgii Riabov, Aleh Tsyvinski
Cowles Foundation Discussion Papers
This paper studies stochastic hysteresis − general dependence on the path of past decisions and shocks. We develop a new methodology for deriving the explicit dynamics of optimal policy with path-dependence and show that stochastic hysteresis changes optimal policy both qualitatively and quantitatively. We showcase our methodology by deriving new results for optimal policy with stochastic habits, tipping points, robustness concerns, limited commitment, and dynamic private information.
Belief Convergence Under Misspecified Learning: A Martingale Approach, Mira Frick, Ryota Iijima, Yuhta Ishii
Belief Convergence Under Misspecified Learning: A Martingale Approach, Mira Frick, Ryota Iijima, Yuhta Ishii
Cowles Foundation Discussion Papers
We present an approach to analyze learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel “prediction accuracy” order over subjective models, and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some long-run belief either locally or globally (i.e., from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously …
Robust Inference With Stochastic Local Unit Root Regressors In Predictive Regressions, Yanbo Liu, Peter C. B. Phillips
Robust Inference With Stochastic Local Unit Root Regressors In Predictive Regressions, Yanbo Liu, Peter C. B. Phillips
Cowles Foundation Discussion Papers
This paper explores predictive regression models with stochastic unit root (STUR) components and robust inference procedures that encompass a wide class of persistent and time-varying stochastically nonstationary regressors. The paper extends the mechanism of endogenously generated instrumentation known as IVX, showing that these methods remain valid for short and long-horizon predictive regressions in which the predictors have STUR and local STUR (LSTUR) generating mechanisms. Both mean regression and quantile regression methods are considered. The asymptotic distributions of the IVX estimators are new and require some new methods in their derivation. The distributions are compared to previous results and, as in …
Stability And Robustness In Misspecified Learning Models, Mira Frick, Ryota Iijima, Yuhta Ishii
Stability And Robustness In Misspecified Learning Models, Mira Frick, Ryota Iijima, Yuhta Ishii
Cowles Foundation Discussion Papers
We present an approach to analyze learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. Our main results provide general criteria to determine—without the need to explicitly analyze learning dynamics—when beliefs in a given environment converge to some long-run belief either locally or globally (i.e., from some or all initial beliefs). The key ingredient underlying these criteria is a novel “prediction accuracy” ordering over subjective models that refines existing comparisons based on Kullback-Leibler divergence. We show that these criteria can be applied, first, to unify and generalize various convergence results in previously studied settings. …
Belief Convergence Under Misspecified Learning: A Martingale Approach, Mira Frick, Ryota Iijima, Yuhta Ishii
Belief Convergence Under Misspecified Learning: A Martingale Approach, Mira Frick, Ryota Iijima, Yuhta Ishii
Cowles Foundation Discussion Papers
We present an approach to analyze learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel “prediction accuracy” order over subjective models, and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some long-run belief either locally or globally (i.e., from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously …
Belief Convergence Under Misspecified Learning: A Martingale Approach, Mira Frick, Ryota Iijima, Yuhta Ishii
Belief Convergence Under Misspecified Learning: A Martingale Approach, Mira Frick, Ryota Iijima, Yuhta Ishii
Cowles Foundation Discussion Papers
We present an approach to analyze learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel “prediction accuracy” order over subjective models, and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some long-run belief either locally or globally (i.e., from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously …
Informationally Robust Optimal Auction Design, Dirk Bergemann, Benjamin Brooks, Stephen Morris
Informationally Robust Optimal Auction Design, Dirk Bergemann, Benjamin Brooks, Stephen Morris
Cowles Foundation Discussion Papers
A single unit of a good is to be sold by auction to one of two buyers. The good has either a high value or a low value, with known prior probabilities. The designer of the auction knows the prior over values but is uncertain about the correct model of the buyers’ beliefs. The designer evaluates a given auction design by the lowest expected revenue that would be generated across all models of buyers’ information that are consistent with the common prior and across all Bayesian equilibria. An optimal auction for such a seller is constructed, as is a worst-case …
The Strategic Impact Of Higher-Order Beliefs, Yi-Chun Chen, Alfredo Di Tillio, Eduardo Faingold, Siyang Xiong
The Strategic Impact Of Higher-Order Beliefs, Yi-Chun Chen, Alfredo Di Tillio, Eduardo Faingold, Siyang Xiong
Cowles Foundation Discussion Papers
Previous research has established that the predictions made by game theory about strategic behavior in incomplete information games are quite sensitive to the assumptions made about the players’ infinite hierarchies of beliefs. We evaluate the severity of this robustness problem by characterizing conditions on the primitives of the model — the players’ hierarchies of beliefs — for the strategic behavior of a given Harsanyi type to be approximated by the strategic behavior of (a sequence of) perturbed types. This amounts to providing characterizations of the strategic topologies of Dekel, Fudenberg, and Morris (2006) in terms of beliefs. We apply our …
Robust Implementation In General Mechanisms, Dirk Bergemann, Stephen Morris
Robust Implementation In General Mechanisms, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.
Robust Implementation In General Mechanisms, Dirk Bergemann, Stephen Morris
Robust Implementation In General Mechanisms, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces.
Robust Implementation: The Case Of Direct Mechanisms, Dirk Bergemann, Stephen Morris
Robust Implementation: The Case Of Direct Mechanisms, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice at every type profile. In an interdependent value environment with single crossing preferences, we identify a strict contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict EPIC and the contraction property are also necessary for robust implementation in any mechanism. The contraction property essentially requires that the interdependence is not too large. In a …
Robust Implementation In Direct Mechanisms, Dirk Bergemann, Stephen Morris
Robust Implementation In Direct Mechanisms, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent value environment with single crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones. The contraction property requires that …
Robust Implementation: The Case Of Direct Mechanisms, Dirk Bergemann, Stephen Morris
Robust Implementation: The Case Of Direct Mechanisms, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice at every type profile. In an interdependent value environment, we identify a strict contraction property on the preferences which together with strict ex post incentive compatibility and the strict single crossing property is sufficient to guarantee robust implementation in the direct mechanism. The contraction property essentially requires that the interdependence is not too large. In a linear signal model, the contraction property is equivalent to an interdependence matrix having …
Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag
Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag
Cowles Foundation Discussion Papers
We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. The resulting optimal pricing policy under either criterion yields a robust policy to the model uncertainty. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always …
Robust Monopoly Pricing: The Case Of Regret, Dirk Bergemann, Karl Schlag
Robust Monopoly Pricing: The Case Of Regret, Dirk Bergemann, Karl Schlag
Cowles Foundation Discussion Papers
We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. The robust version of the problem is distinct in two aspects: (i) the seller minimizes regret rather than maximizes revenue, and (ii) the seller only knows that the true distribution of the valuations is in a neighborhood of a given model distribution. We characterize the robust pricing policy as the solution to a minimax problem for small and large neighborhoods. In contrast to the classic monopoly policy, which is a single deterministic price, the robust policy is always a random pricing policy, or equivalently, …
Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag
Robust Monopoly Pricing, Dirk Bergemann, Karl Schlag
Cowles Foundation Discussion Papers
We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version of the problem the seller only knows that demand will be in a neighborhood of a given model distribution. We characterize the optimal pricing policy under two distinct, but related, decision criteria with multiple priors: (i) maximin expected utility and (ii) minimax expected regret. While the classic monopoly policy and the maximin criterion yield a single deterministic price, minimax regret always prescribes a random pricing policy, or equivalently, a multi-item menu policy. The resulting optimal pricing policy under either criterion …
Robust Implementation: The Role Of Large Type Spaces, Dirk Bergemann, Stephen Morris
Robust Implementation: The Role Of Large Type Spaces, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with a social choice function. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces. It requires that there not be too much interdependence of types. We characterize robust monotonicity for some interesting economic environments. We …
Generalized Potentials And Robust Sets Of Equilibria, Stephen Morris, Takashi Ui
Generalized Potentials And Robust Sets Of Equilibria, Stephen Morris, Takashi Ui
Cowles Foundation Discussion Papers
This paper introduces generalized potential functions of complete information games and studies the robustness of sets of equilibria to incomplete information. A set of equilibria of a complete information game is robust if every incomplete information game where payoffs are almost always given by the complete information game has an equilibrium which generates behavior close to some equilibrium in the set. This paper provides sufficient conditions for the robustness of sets of equilibria in terms of argmax sets of generalized potential functions and shows that the sufficient conditions generalize the existing sufficient conditions for the robustness of equilibria.
On The Performance Of Least Squares In Linear Regression With Undefined Error Means, Donald W.K. Andrews
On The Performance Of Least Squares In Linear Regression With Undefined Error Means, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers the linear regression model with multiple stochastic regressors, intercept, and errors that have undefined means. This model is of interest from a robustness perspective as a polar case. Generally, least squares estimators are inconsistent in this context. It is shown, however, that this inconsistency is restricted to the estimation of the intercept, if the regressors are highly variable. Rates of convergence of the least squares slope estimators are determined, and are shown to exceed the standard rate, n -1/2 , in certain contexts. The results place no restrictions on the temporal dependence of the errors, and require …