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Full-Text Articles in Economics
The Generalized War Of Attrition, Jeremy I. Bulow, Paul D. Klemperer
The Generalized War Of Attrition, Jeremy I. Bulow, Paul D. Klemperer
Cowles Foundation Discussion Papers
We generalize the War of Attrition model to allow for N + K firms competing for N prizes. Two special cases are of particular interest. First, if firms continue to pay their full costs after dropping out (as in a standard-setting context), each firm’s exit time is independent both of K and of the actions of other players. Second, in the limit in which firms pay no costs after dropping out (as in a natural-oligopoly problem), the field is immediately reduced to N + 1 firms. Furthermore, we have perfect sorting, so it is always the K -1 lowest-value players …
Promises Promises, John Geanakoplos
Promises Promises, John Geanakoplos
Cowles Foundation Discussion Papers
In the classical general equilibrium model, agents keep all their promises, every good is traded, and competition prevents any agent from earning superior returns on investments in financial markets. In this paper I introduce the age-old problem of broken promises into the general equilibrium model, and I find that a new market dynamic emerges. Given the legal system and institutions, market forces of supply and demand will establish the collateral levels which are required to secure promises. Since physical collateral will typically be scarce, these collateral levels will be set so low that there is bound to be some default. …
Hyperfinite Asset Pricing Theory, M. Ali Khan, Yeneng Sun
Hyperfinite Asset Pricing Theory, M. Ali Khan, Yeneng Sun
Cowles Foundation Discussion Papers
We present a model of a financial market which unifies the capital-asset-pricing model (CAPM) of Sharpe-Lintner, and the arbitrage pricing theory (APT) of Ross. The model is based on a recent theory of hyperfinite processes, and it uncovers asset pricing phenomena which cannot be treated by classical methods, and whose asymptotic counterparts are not already, or even readily, apparent in the setting of a large but finite number of assets. In the model, an asset’s unexpected return can be decomposed into a systematic and an unsystematic part, as in the APT, and the systematic part further decomposed leads to a …
On The Number Of Bootstrap Repetitions For Bootstrap Standard Errors, Confidence Internals, And Tests, Donald W.K. Andrews, Moshe Buchinsky
On The Number Of Bootstrap Repetitions For Bootstrap Standard Errors, Confidence Internals, And Tests, Donald W.K. Andrews, Moshe Buchinsky
Cowles Foundation Discussion Papers
This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, and tests. For each of these problems, the paper provides a three-step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval endpoint(s), test’s critical value, or test’s p -value based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B = ∞. Monte Carlo simulations show that the proposed methods work quite well. The results apply quite generally to parametric, semiparametric, …
Prices, Asset Markets And Indeterminacy, Heracles M. Polemarchakis, P. Siconolfi
Prices, Asset Markets And Indeterminacy, Heracles M. Polemarchakis, P. Siconolfi
Cowles Foundation Discussion Papers
Competitive equilibrium allocations are indeterminate when the net trades in commodities are constrained, while the asset market is incomplete
Bayesian Posterior Distributions In Limited Information Analysis Of The Simultaneous Equations Model Using The Jeffreys’ Prior, John C. Chao, Peter C.B. Phillips
Bayesian Posterior Distributions In Limited Information Analysis Of The Simultaneous Equations Model Using The Jeffreys’ Prior, John C. Chao, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the use of the Jeffreys’ prior in Bayesian analysis of the simultaneous equations model (SEM). Exact representations are obtained for the posterior density of the structural coefficient beta in canonical SEM’s with two endogenous variables. For the general case with m endogenous variables and an unknown covariance matrix, the Laplace approximation is used to derive an analytic formula for the same posterior density. Both the exact and the approximate formulas we derive are found to exhibit Cauchy-like tails analogous to comparable results in the classical literature on LIML estimation. Moreover, in the special case of a two-equation, …
Market Diffusion With Two-Sided Learning, Dirk Bergemann, Juuso Välimäki
Market Diffusion With Two-Sided Learning, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
The diffusion of a new product of uncertain value is analyzed in a duopolistic market in continuous time. The two sides of the market, buyers and sellers, learn the true value of the new product over time as a result of experimentation. Buyers have heterogeneous preferences over the products and sellers compete in prices. The pricing policies and market shares of the sellers in the unique Markov perfect equilibrium are obtained explicitly. The dynamics of the equilibrium market shares display excessive sales of the new product relative to the social optimum in early stages and too low sales later on. …
Conditional Independence Restrictions: Testing And Estimation, Oliver B. Linton, Pedro Gozalo
Conditional Independence Restrictions: Testing And Estimation, Oliver B. Linton, Pedro Gozalo
Cowles Foundation Discussion Papers
We propose a nonparametric empirical distribution function based test of an hypothesis of conditional independence between variables of interest. This hypothesis is of interest both for model specification purposes, parametric and semiparametric, and for non-model based testing of economic hypotheses. We allow for both discrete variables and estimated parameters. The asymptotic null distribution of the test statistic is a functional of a Gaussian process. A bootstrap procedure is proposed for calculating the critical values. Our test has power against alternatives at distance n -1/2 from the null; this result holding independently of dimension. Monte Carlo simulations provide evidence on size …
Spurious Regression Unmasked, Peter C.B. Phillips
Spurious Regression Unmasked, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper argues that trending time series can admit valid regression representations even when the dependent variable and the regressors are statistically independent, i.e., in situations that are presently characterized in the literature as “spurious regressions.” Our theory is directed mainly at the two classic examples of regressions of stochastic trends on time polynomials and regressions among independent random walks. But it has more general applicability and, we think, wider implications. Contrary to established wisdom, our theory justifies regressions of this type as valid models for the data. The radical conclusion that emerges from this study is that there are …
Price Variations In A Stock Market With Many Agents, Per Bak, Maya Paczuski, Martin Shubik
Price Variations In A Stock Market With Many Agents, Per Bak, Maya Paczuski, Martin Shubik
Cowles Foundation Discussion Papers
Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large variations may be due to a crowd effect, where agents imitate each other’s behavior. The variations over different time scales can be related to each other in a systematic way, similar to the Lévy stable distribution proposed by Mandelbrot to describe real market indices. In the simplest, least realistic case, exact results for the statistics of the variations are derived by mapping onto a …
Exchange And Optimality, S. Ghosal, Heracles M. Polemarchakis
Exchange And Optimality, S. Ghosal, Heracles M. Polemarchakis
Cowles Foundation Discussion Papers
A feasible social state is irreducible if and only if, for any non-trivial partition of individuals with two groups, there exists another feasible social state at which every individual in the first group is equally well-off and someone strictly better-off. Competitive equilibria decentralize irreducible Pareto optimal social states
Efficiency Gains From Quasi-Differencing Under Nonstationarity, Peter C.B. Phillips, Chin Chin Lee
Efficiency Gains From Quasi-Differencing Under Nonstationarity, Peter C.B. Phillips, Chin Chin Lee
Cowles Foundation Discussion Papers
A famous theorem on trend removal by OLS regression (usually attributed to Grenander and Rosenblatt, 1957) gave conditions for the asymptotic equivalence of GLS and OLS in deterministic trend extraction. When a time series has trend components that are stochastically nonstationary, this asymptotic equivalence no longer holds. We consider models with integrated and near-integrated error processes where this asymptotic equivalence breaks down. In such models, the advantages of GLS can be achieved through quasi-differencing and we give an asymptotic theory of the relative gains that occur in deterministic trend extraction in such cases. Some differences between models with and without …
The Limiting Behavior Of Kernel Estimates Of The Lyapunov Exponent For Stochastic Time Series, Yoon-Jae Whang, Oliver B. Linton
The Limiting Behavior Of Kernel Estimates Of The Lyapunov Exponent For Stochastic Time Series, Yoon-Jae Whang, Oliver B. Linton
Cowles Foundation Discussion Papers
This paper derives the asymptotic distribution of a smoothing-based estimator of the Lyapunov exponent for a stochastic time series under two general scenarios. In the first case, we are able to establish root-T consistency and asymptotic normality, while in the second case, which is more relevant for chaotic processes, we are only able to establish asymptotic normality at a slower rate of convergence. We provide consistent confidence intervals for both cases. We apply our procedures to simulated data.
Estimated Inflation Costs Had European Unemployment Been Reduced In The 1980s By Macro Prices, Ray C. Fair
Estimated Inflation Costs Had European Unemployment Been Reduced In The 1980s By Macro Prices, Ray C. Fair
Cowles Foundation Discussion Papers
This paper uses a multicountry econometric model to estimate what the inflation costs would have been if macropolicies had reduced European unemployment in the 1982:1-1990:4 period. A “non-NAIRU” framework is proposed for thinking about these costs.
Nash And Walras Equilibrium Via Brouwer, John Geanakoplos
Nash And Walras Equilibrium Via Brouwer, John Geanakoplos
Cowles Foundation Discussion Papers
The existence of Nash and Walras equilibrium is proved via Brouwer’s Fixed Point Theorem, without recourse to Kakutani’s Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-concave preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.”
Nash And Walras Equilibrium Via Brouwer, John Geanakoplos
Nash And Walras Equilibrium Via Brouwer, John Geanakoplos
Cowles Foundation Discussion Papers
The existence of Nash and Walras equilibrium is proved via Brouwer’s Fixed Point Theorem, without recourse to Kakutani’s Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.”
Nash And Walras Equilibrium Via Brouwer, John Geanakoplos
Nash And Walras Equilibrium Via Brouwer, John Geanakoplos
Cowles Foundation Discussion Papers
The existence of Nash and Walras equilibrium is proved via Brouwer’s Fixed Point Theorem, without recourse to Kakutani’s Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.”
The Hangman's Paradox And Newcomb's Paradox As Psychological Games, John Geanakoplos
The Hangman's Paradox And Newcomb's Paradox As Psychological Games, John Geanakoplos
Cowles Foundation Discussion Papers
We present a (hopefully) fresh interpretation of the Hangman’s Paradox and Newcomb’s Paradox by casting the puzzles in the language of modern game theory, instead of in the realm of epistemology. Game theory moves the analysis away from the formal logic of the puzzles toward more practical problems, such as: On what day would the executioner hang the prisoner if he wanted to surprise him as much as possible? How should a surprise test be administered? We argue that both the Hangman’s Paradox and Newcomb’s Paradox are analogous to a well-known phenomenon in game theory, that giving a player an …
Tests Of Seasonal And Non-Seasonal Serial Correlation, Donald W.K. Andrews, Xuemei Liu, Werner Ploberger
Tests Of Seasonal And Non-Seasonal Serial Correlation, Donald W.K. Andrews, Xuemei Liu, Werner Ploberger
Cowles Foundation Discussion Papers
This paper considers tests for seasonal and non-seasonal serial correlation in time series and in the errors of regression models. The problem of testing for white noise against multiplicative seasonal ARMA(l,l)-ARMA(l,l) alternatives is investigated. This testing problem is non-standard due to nuisance parameters that appear under the alternative but not under the null hypothesis. The likelihood ratio (LR), sup Lagrange multiplier (LM), and exponential average LM and LR tests are considered and are shown to be asymptotically admissible for multiplicative seasonal ARMA(l,l)-ARMA(l,l) alternatives. In addition, they are shown to be consistent against all (weakly stationary strong mixing) non-white noise alternatives. …
A Scorecard For Indexed Government Debt, John Y. Campbell, Robert J. Shiller
A Scorecard For Indexed Government Debt, John Y. Campbell, Robert J. Shiller
Cowles Foundation Discussion Papers
Within the last five years, Canada, Sweden and New Zealand have joined the ranks of the United Kingdom and other countries in issuing government bonds that are indexed to inflation. Some observers of the experience in these countries have argued that the United States should follow suit. This paper provides an overview of the issues surrounding debt indexation, and it tries to answer three empirical questions about indexed debt. First, how different would the returns on indexed bonds be from the returns on existing US debt instruments? Second, how would indexed bonds affect the government’s average financing costs? Third, how …
Hedging With Derivatives In Incomplete Markets, Charalambos D. Aliprantis, Donald J. Brown, J. Werner
Hedging With Derivatives In Incomplete Markets, Charalambos D. Aliprantis, Donald J. Brown, J. Werner
Cowles Foundation Discussion Papers
We present necessary and sufficient conditions on the asset span of incomplete derivative markets for insuring marketed portfolios. If the asset span is finite dimensional there exists a polynomial-time algorithm for deciding if every marketed portfolio is insurable, moreover this algorithm computes the minimum cost insurance portfolio. In addition, we extend the Cox-Leland characterization of optimal portfolio insurance in complete derivative markets to asset spans of incomplete derivative markets where every marketed portfolio is insurable.
Matrices With Identical Sets Of Neighbors, Imre Bárány, Herbert E. Scarf
Matrices With Identical Sets Of Neighbors, Imre Bárány, Herbert E. Scarf
Cowles Foundation Discussion Papers
Given a generic m by n matrix A , a lattice point h in Z is a neighbor of the origin if the body { x : Ax < b }, with b i = max{0, a i h }, i = 1, …, m , contains no lattice point other than 0 and h . The set of neighbors, N ( A ), is finite and Asymmetric. We show that if A’ is another matrix of the same size with the property that sign a i h = sign a i ’ h for every i and every h in N ( A ), then A’ has precisely the same set of neighbors as A . The collection of such matrices is a polyhedral cone, described by a finite set of linear inequalities, each such inequality corresponding to a generator of one of the cones C i = pos( h in N ( A ): a i h < 0}. Computational experience shows that C i has “few” generators. We demonstrate this in the first nontrivial case n = 3, m = 4.
Three Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Three Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Cowles Foundation Discussion Papers
Arrow’s original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but complicating the second step. I give three brief proofs, all of which turn on replacing the decisive/pivotal voter with an extremely pivotal voter (a voter who by unilaterally changing his vote can move some alternative from the bottom of the social ranking to the top), thereby simplifying both steps in Arrow’s proof. My …
Semiparametric Estimation Of A Sample Selection Model, Donald W.K. Andrews, Marcia A. Schafgans
Semiparametric Estimation Of A Sample Selection Model, Donald W.K. Andrews, Marcia A. Schafgans
Cowles Foundation Discussion Papers
This paper provides a consistent and asymptotically normal estimator for the intercept of a semiparametrically estimated sample selection model. The estimator uses a decreasingly small fraction of all observations as the sample size goes to infinity, as in Heckman (1990). In the semiparametrics literature, estimation of the intercept typically has been subsumed in the nonparametric sample selection bias correction term. The estimation of the intercept, however, is important from an economic perspective. For instance, it permits one to determine the “wage gap” between unionized and nonunionized workers, decompose the wage differential between different socioeconomic groups (e.g., male-female and black-white), and …
A Stopping Rule For The Computation Of Generalized Method Of Moments Estimators, Donald W.K. Andrews
A Stopping Rule For The Computation Of Generalized Method Of Moments Estimators, Donald W.K. Andrews
Cowles Foundation Discussion Papers
To obtain consistency and asymptotic normality, a generalized method of moments (GMM) estimator typically is defined to be an approximate global minimizer of a GMM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. In consequence, practitioners usually ignore the problem and take the GMM estimator to be the result of a local optimization algorithm. This yields an estimator that is not necessarily consistent and asymptotically normal. The use of a local optimization algorithm also can run into the problem of instability due to flats or ridges in the criterion function, …
Three Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Three Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Cowles Foundation Discussion Papers
Arrow’s original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but complicating the second step. I give three brief proofs, all of which turn on replacing the decisive/pivotal voter with an extremely pivotal voter (a voter who by unilaterally changing his vote can move some alternative from the bottom of the social ranking to the top), thereby simplifying both steps in Arrow’s proof. My …
Testing The Standard View Of The Long-Run Unemployment-Inflation Relationship, Ray C. Fair
Testing The Standard View Of The Long-Run Unemployment-Inflation Relationship, Ray C. Fair
Cowles Foundation Discussion Papers
The results in this paper, based on estimating and testing price equations for 30 countries, do not support the standard view of the long-run relationship between unemployment and inflation. They overwhelmingly reject the dynamics implied by the standard view. Wage equations are also estimated and tested. The paper also attempts to estimate the functional form of the relationship between measures of demand pressure and price and wage levels, but no strong conclusions emerge.
Market Experimentation And Pricing, Dirk Bergemann, Juuso Välimäki
Market Experimentation And Pricing, Dirk Bergemann, Juuso Välimäki
Cowles Foundation Discussion Papers
We present a continuous-time model of Bayesian learning in a duopolistic market. Initially the value of one product offered is unknown to the market. The market participants learn more about the true value of the product as experimentation occurs over time. Firms set prices to induce experimentation with their product. The aggregate outcomes are public information. As agents learn from the experiments of others, informational externalities arise. Surprisingly, the informational externality leads to too much learning. Buyers do not consider the impact of their experimentation on other buyers while the sellers internalize the gains from experiments conducted by the buyers. …
Two Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Two Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Cowles Foundation Discussion Papers
The first proof shows that Arrow’s axioms guarantee neutrality: every social choice must be made in exactly the same way, which quickly leads to dictatorship. The second proof clarifies the last step, and also confirms the intimate connection between Arrow’s Impossibility Theorem and the Condorcet triple. The second proof shows that a doubly pivotal agent must be a dictator; the Condorcet triple guarantees the existence of a doubly pivotal agent. Neutrality guarantees the existence of a (symmetrically) doubly pivotal agent.
Three Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Three Brief Proofs Of Arrow's Impossibility Theorem, John Geanakoplos
Cowles Foundation Discussion Papers
Arrow’s original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but complicating the second step. I give three brief proofs, all of which turn on replacing the decisive/pivotal voter with an extremely pivotal voter (a voter who by unilaterally changing his vote can move some alternative from the bottom of the social ranking to the top), thereby simplifying both steps in Arrow’s proof. My …