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Full-Text Articles in Social and Behavioral Sciences
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS’s) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS’s. We provide methods of constructing QLR tests …
Bayes Correlated Equilibrium And The Comparison Of Information Structures, Dirk Bergemann, Stephen Morris
Bayes Correlated Equilibrium And The Comparison Of Information Structures, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call Bayes correlated equilibrium. We describe a partial order on many player information structures — which we call individual sufficiency — under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative definitions of correlated equilibrium in incomplete information games and of …
Optimism And Pessimism With Expected Utility, David Dillenberger, Andrew Postlewaite, Kareen Rozen
Optimism And Pessimism With Expected Utility, David Dillenberger, Andrew Postlewaite, Kareen Rozen
Cowles Foundation Discussion Papers
Savage (1954) provided a set of axioms on preferences over acts that were equivalent to the existence of an expected utility representation. We show that in addition to this representation, there is a continuum of other “expected utility” representations in which for any act, the probability distribution over states depends on the corresponding outcomes. We suggest that optimism and pessimism can be captured by the stake-dependent probabilities in these alternative representations; e.g., for a pessimist, the probability of every outcome except the worst is distorted down from the Savage probability. Extending the DM’s preferences to be defined on both subjective …
Optimally Empty Promises And Endogenous Supervision, David A. Miller, Kareen Rozen
Optimally Empty Promises And Endogenous Supervision, David A. Miller, Kareen Rozen
Cowles Foundation Discussion Papers
We study optimal contracting in team settings, featuring stylized aspects of production environments with complex tasks. Agents have many opportunities to shirk, task-level monitoring is needed to provide useful incentives, and because it is difficult to write individual performance into formal contracts, incentives are provided informally, using wasteful sanctions like guilt and shame, or slowed promotion. These features give rise to optimal contracts with “empty promises” and endogenous supervision structures. Agents optimally make more promises than they intend to keep, leading to the concentration of supervisory responsibility in the hands of one or two agents.
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CS’s) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CS’s are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t; and quasi-likelihood ratio tests and CS’s whose critical values are designed to yield robustness to …
Public Goods Through Taxation In A General Equilibrium Economy: Experimental Evidence, Juergen Huber, Martin Shubik, Shyam Sunder
Public Goods Through Taxation In A General Equilibrium Economy: Experimental Evidence, Juergen Huber, Martin Shubik, Shyam Sunder
Cowles Foundation Discussion Papers
We use a laboratory experiment to compare general equilibrium economies in which agents individually allocate their private goods among consumption, investment in production and maintenance of a depreciating public facility. The public facility is financed either by voluntary anonymous contributions (VAC) or taxes. We find that rates of taxation chosen by majority vote remain at an intermediate level, converging neither to zero nor to 100%, and the experimental economies sustain public goods at levels between the finite- and infinite-horizon optima. This contrasts with a rapid decline of public goods under voluntary anonymous contributions (VAC). Both the payoff efficiency and production …
Correlated Equilibrium In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Correlated Equilibrium In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We define a notion of correlated equilibrium for games with incomplete information in a general setting with finite players, finite actions, and finite states, which we call Bayes correlated equilibrium. The set of Bayes correlated equilibria of a fixed incomplete information game equals the set of probability distributions over actions, states and types that might arise in any Bayes Nash equilibrium where players observed additional information. We show that more information always shrinks the set of Bayes correlated equilibria.
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Maximum Likelihood Estimation And Uniform Inference With Sporadic Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS’s) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS’s. We provide methods of constructing QLR tests …
Estimates Of The Social Cost Of Carbon: Background And Results From The Rice-2011 Model, William D. Nordhaus
Estimates Of The Social Cost Of Carbon: Background And Results From The Rice-2011 Model, William D. Nordhaus
Cowles Foundation Discussion Papers
A new and important concept in global warming economics and policy is the social cost of carbon or SCC. This concept represents the economic cost caused by an additional ton of carbon-dioxide emissions or its equivalent. The present study describes the development of the concept as well as its analytical background. We estimate the SCC using an updated version of the RICE-2011 model. Additional concerns are uncertainty about different aspects of global warming as well as the treatment of different countries or generations. The most important results are: First, the estimated social cost of carbon for the current time (2015) …
On Bartlett Correctability Of Empirical Likelihood In Generalized Power Divergence Family, Lorenzo Camponovo, Taisuke Otsu
On Bartlett Correctability Of Empirical Likelihood In Generalized Power Divergence Family, Lorenzo Camponovo, Taisuke Otsu
Cowles Foundation Discussion Papers
Baggerly (1998) showed that empirical likelihood is the only member in the Cressie-Read power divergence family to be Bartlett correctable. This paper strengthens Baggerly’s result by showing that in a generalized class of the power divergence family, which includes the Cressie-Read family and other nonparametric likelihood such as Schennach’s (2005, 2007) exponentially tilted empirical likelihood, empirical likelihood is still the only member to be Bartlett correctable.
A Theory Of Asset Prices Based On Heterogeneous Information, Elias Albagli, Christian Hellwig, Aleh Tsyvinski
A Theory Of Asset Prices Based On Heterogeneous Information, Elias Albagli, Christian Hellwig, Aleh Tsyvinski
Cowles Foundation Discussion Papers
We propose a theory of asset prices that emphasizes heterogeneous information as the main element determining prices of different securities. Our main analytical innovation is in formulating a model of noisy information aggregation through asset prices, which is parsimonious and tractable, yet flexible in the specification of cash flow risks. We show that the noisy aggregation of heterogeneous investor beliefs drives a systematic wedge between the impact of fundamentals on an asset price, and the corresponding impact on cash flow expectations. The key intuition behind the wedge is that the identity of the marginal trader has to shift for different …
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure, Donald W.K. Andrews, Xu Cheng
Cowles Foundation Discussion Papers
This paper determines the properties of standard generalized method of moments (GMM) estimators, tests, and confidence sets (CS’s) in moment condition models in which some parameters are unidentified or weakly identified in part of the parameter space. The asymptotic distributions of GMM estimators are established under a full range of drifting sequences of true parameters and distributions. The asymptotic sizes (in a uniform sense) of standard GMM tests and CS’s are established. The paper also establishes the correct asymptotic sizes of “robust” GMM-based Wald, t , and quasi-likelihood ratio tests and CS’s whose critical values are designed to yield robustness …
Financing Of Public Goods Through Taxation In A General Equilibrium Economy: Theory And Experimental Evidence, Juergen Huber, Martin Shubik, Shyam Sunder
Financing Of Public Goods Through Taxation In A General Equilibrium Economy: Theory And Experimental Evidence, Juergen Huber, Martin Shubik, Shyam Sunder
Cowles Foundation Discussion Papers
We compare general equilibrium economies in which building and maintenance of a depreciating public facility is financed either by anonymous voluntary contributions or by taxing agents on their income from private production. Agents start with an endowment of private goods and money, while the government starts with an endowment of public good and money. All private goods produced are tendered for sale in exchange for money in a sell-all market mechanism. Agents’ proceeds from sale are taxed, and they individually allocate their private goods between current consumption and investment in production for the following period. The optimal levels of supply …
Career Concerns With Coarse Information, Alessandro Bonatti, Johannes Hörner
Career Concerns With Coarse Information, Alessandro Bonatti, Johannes Hörner
Cowles Foundation Discussion Papers
This paper develops a model of career concerns. The worker’s skill is revealed through output, wage is based on expected output, and so on assessed ability. Specifically, effort increases the probability that a skilled worker achieves a one-time breakthrough. Effort levels at different times are strategic substitutes. Equilibrium effort (and, if marginal cost is convex, wage) is single-peaked with seniority. The agent works too little, too late. Both delay and underprovision of effort worsen if effort is observable. If the firm commits to wages but faces competition, the optimal contract features piecewise constant wages as well as severance pay.
Career Concerns And Market Structure, Alessandro Bonatti, Johannes Hörner
Career Concerns And Market Structure, Alessandro Bonatti, Johannes Hörner
Cowles Foundation Discussion Papers
This paper analyzes the impact of market structure on career concerns. Effort increases the probability that a skilled agent achieves a one-time breakthrough. Wages are based on assessed ability and on expected output. For any wage, the agent works too little, too late. Under short-term contracts, effort and wages are single-peaked with seniority, due to the strategic substitutability of effort levels at different times. Both delay and underprovision of effort worsen if effort is observable. Commitment to wages by competing firms mitigates these inefficiencies. In that case, the optimal contract features piecewise constant wages and severance pay.
Testing For Common Trends In Semiparametric Panel Data Models With Fixed Effects, Yonghui Zhang, Liangjun Su, Peter C.B. Phillips
Testing For Common Trends In Semiparametric Panel Data Models With Fixed Effects, Yonghui Zhang, Liangjun Su, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper proposes a nonparametric test for common trends in semiparametric panel data models with fixed effects based on a measure of nonparametric goodness-of-fit (R²). We first estimate the model under the null hypothesis of common trends by the method of profile least squares, and obtain the augmented residual which consistently estimates the sum of the fixed effect and the disturbance under the null. Then we run a local linear regression of the augmented residuals on a time trend and calculate the nonparametric R² for each cross section unit. The proposed test statistic is obtained by averaging all cross sectional …
Meritocracy Voting: Measuring The Unmeasurable, Peter C.B. Phillips
Meritocracy Voting: Measuring The Unmeasurable, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Learned societies commonly carry out selection processes to add new fellows to an existing fellowship. Criteria vary across societies but are typically based on subjective judgments concerning the merit of individuals who are nominated for fellowships. These subjective assessments may be made by existing fellows as they vote in elections to determine the new fellows or they may be decided by a selection committee of fellows and officers of the society who determine merit after reviewing nominations and written assessments. Human judgment inevitably plays a central role in these determinations and, notwithstanding its limitations, is usually regarded as being a …
Financing Of Public Goods Through Taxation In A General Equilibrium Economy: Experimental Evidence, Juergen Huber, Martin Shubik, Shyam Sunder
Financing Of Public Goods Through Taxation In A General Equilibrium Economy: Experimental Evidence, Juergen Huber, Martin Shubik, Shyam Sunder
Cowles Foundation Discussion Papers
We use a laboratory experiment to compare general equilibrium economies in which agents individually allocate their private goods among consumption, investment in production, and replenishing/ refurbishing a depreciating public facility in a dynamic game with long-term investment opportunities. The public facility is financed either by voluntary anonymous contributions (VAC) or taxes. We find that rates of taxation chosen by majority vote remain at an intermediate level (far from zero or 100%), and the experimental economies sustain public goods at levels between the finite- and infinite-horizon optima. This contrasts with a rapid decline of public goods under VAC. Both the payoff …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for all possible private information structures that the agents may have. Our characterization of these robust predictions relies on an epistemic result which establishes a relationship between the set of Bayes Nash equilibria and the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior information of the analyst …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information refines the set of equilibrium predictions. We consider information sharing among firms under demand uncertainty and find newly optimal information policies via …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information refines the set of equilibrium predictions. We consider information sharing among firms under demand uncertainty and find newly optimal information policies via …
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Robust Predictions In Games With Incomplete Information, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
We analyze games of incomplete information and offer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. The set of outcomes that can arise in equilibrium for some information structure is equal to the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoffs and normally distributed uncertainty in terms of restrictions on the first and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior knowledge about the private information …
Generic Results For Establishing The Asymptotic Size Of Confidence Sets And Tests, Donald W.K. Andrews, Xu Cheng, Patrik Guggenberger
Generic Results For Establishing The Asymptotic Size Of Confidence Sets And Tests, Donald W.K. Andrews, Xu Cheng, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of confidence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic has a discontinuity in its limit distribution. The results are illustrated in three examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic …
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper shows that moment inequality tests that are asymptotically similar on the boundary of the null hypothesis exist, but have poor power. Hence, existing tests in the literature, which are asymptotically non-similar on the boundary, are not deficient. The results are obtained by first establishing results for the finite-sample multivariate normal one-sided testing problem. Then, these results are shown to have implications for more general moment inequality tests that are used in the literature on partial identification.
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new confidence interval (CI) for the autoregressive parameter (AR) in an AR(1) model that allows for conditional heteroskedasticity of general form and AR parameters that are less than or equal to unity. The CI is a modification of Mikusheva’s (2007a) modification of Stock’s (1991) CI that employs the least squares estimator and a heteroskedasticity-robust variance estimator. The CI is shown to have correct asymptotic size and to be asymptotically similar (in a uniform sense). It does not require any tuning parameters. No existing procedures have these properties. Monte Carlo simulations show that the CI performs well …
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
A Conditional-Heteroskedasticity-Robust Confidence Interval For The Autoregressive Parameter, Donald W.K. Andrews, Patrik Guggenberger
Cowles Foundation Discussion Papers
This paper introduces a new confidence interval (CI) for the autoregressive parameter (AR) in an AR(1) model that allows for conditional heteroskedasticity of general form and AR parameters that are less than or equal to unity. The CI is a modification of Mikusheva’s (2007a) modification of Stock’s (1991) CI that employs the least squares estimator and a heteroskedasticity-robust variance estimator. The CI is shown to have correct asymptotic size and to be asymptotically similar (in a uniform sense). It does not require any tuning parameters. No existing procedures have these properties. Monte Carlo simulations show that the CI performs well …
The Demonetization Of Gold: Transactions And The Change In Control, Thomas Quint, Martin Shubik
The Demonetization Of Gold: Transactions And The Change In Control, Thomas Quint, Martin Shubik
Cowles Foundation Discussion Papers
Three models of a monetary economy are considered, in order to show the effects of a gold demonetization: the first with a gold money, the second with demonetized gold but no central bank, and the third with demonetized gold, but with a central bank. The distinctions between ownership and control are discussed.
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Similar-On-The-Boundary Tests For Moment Inequalities Exist, But Have Poor Power, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper shows that moment inequality tests that are asymptotically similar on the boundary of the null hypothesis exist, but have very poor power. Hence, existing tests in the literature, which are asymptotically non-similar on the boundary, are not deficient. The results are obtained by first establishing results for the finite-sample multivariate normal one-sided testing problem. Then, these results are shown to have implications for more general moment inequality tests that are used in the literature on partial identification.
Information Aggregation, Investment, And Managerial Incentives, Elias Albagli, Christian Hellwig, Aleh Tsyvinski
Information Aggregation, Investment, And Managerial Incentives, Elias Albagli, Christian Hellwig, Aleh Tsyvinski
Cowles Foundation Discussion Papers
We study the interplay of share prices and firm decisions when share prices aggregate and convey noisy information about fundamentals to investors and managers. First, we show that the informational feedback between the firm’s share price and its investment decisions leads to a systematic premium in the firm’s share price relative to expected dividends. Noisy information aggregation leads to excess price volatility, over-valuation of shares in response to good news, and undervaluation in response to bad news. By optimally increasing its exposure to fundamental risks when the market price conveys good news, the firm shifts its dividend risk to the …
Irving Fisher, Debt Deflation And Crises, Robert J. Shiller
Irving Fisher, Debt Deflation And Crises, Robert J. Shiller
Cowles Foundation Discussion Papers
It is the 100th anniversary of Irving Fisher’s 1911 book The Purchasing Power of Money . But, more important than that, it is a good time, during the current financial turmoil, to reconsider some of his theories again, in light of current events. And I think that some of his theories about variations in the purchasing power of money are very important today, have been underappreciated, and are worthy of considering anew.