# Cowles Foundation for Research in Economics, Yale University

# Cowles Foundation Discussion Papers

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### 1989

**900 Liquidity and Bankruptcy with Incomplete Markets: Pure Exchange***by*John Geanakoplos & Pradeep Dubey**CFP 899 Testing for a Unit Root by Generalized Least Squares Methods in the Time and Frequency Domains***by*Peter C.B. Phillips & In Choi**898R The Durbin-Watson Ratio Under Infinite Variance Errors***by*Peter C.B. Phillips & Mico Loretan**897R Time Series Regression with a Unit Root and Infinite Variance Errors***by*Peter C.B. Phillips**896 The Production Smoothing Model Is Alive and Well***by*Ray C. Fair**895 Repeated Trade and the Velocity of Money***by*Martin Shubik & Pradeep Dubey & Siddhartha Sahi**887 A New Proof of Knight's Theorem on the Cauchy Distribution***by*Peter C.B. Phillips**886 A Little Magic with the Cauchy Distribution***by*Peter C.B. Phillips

### 1988

**894 Nonparametric Tests of Maximizing Behavior Subject to Nonlinear Sets***by*Rosa L. Matzkin**893 Reflections on Econometric Methodology***by*Peter C.B. Phillips**892 The Interaction of Implicit and Explicit Contracts in Repeated Agency***by*David G. Pearce & Ennio Stacchetti**891 The Interaction of Implicit and Explicit Contracts in Repeated Agency***by*Martin Shubik**890 The Behavior of Home Buyers in Boom and Post-Boom Markets***by*Robert J. Shiller & Karl E. Case**889 Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models***by*Rosa L. Matzkin**888 The Macroeconomics of Government Finance***by*James Tobin & Michael Haliassos**885 The Power of Commitment***by*John Geanakoplos & Chien-fu Chou**884R Correlated Equilibrium with Generalized Information Structures***by*Geanakoplos & Adam Brandenburger & Eddie Dekel**883 The Shapes of Polyhedra***by*Herbert E. Scarf & R. Kannan & Laszlo Lovasz**882R Error Correction and Long Run Equilibrium in Continuous Time***by*Peter C.B. Phillips**881 Estimation and Inference in Models of Cointegration: A Simulation Study***by*Peter C.B. Phillips & Bruce E. Hansen**880 Testing for a Unit Root in the Presence of a Maintained Trend***by*Peter C.B. Phillips & Sam Ouliaris & Joon Y. Park**879R Default and Efficiency in a General Equilibrium Model with Incomplete Markets***by*Pradeep Dubey & John Geanakoplos & Martin Shubik**878 Capital Structure and dividend Irrelevance with Asymmetric Information***by*Philip H. Dybvig & Jaime F. Zender**877R Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation***by*Donald W.K. Andrews**876 The Stabilization of the U.S. Economy: Evidence from the Stock Market***by*Matthew D. Shapiro**875 Information and Timing in Repeated Partnerships***by*David G. Pearce & Dilip Abreu & Paul R. Milgrom**874R Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models***by*Donald W.K. Andrews**873 Spanning, Valuation and Options***by*Donald J. Brown & Stephen A. Ross**872 Spectral Regression for Cointegrated Time Series***by*Peter C.B. Phillips**871 Gold, Liquidity and Secured Loans in a Multistage Economy. Part I: Gold as Money***by*Martin Shubik & Shuntian Yao**870 Sources of Business Cycle Fluctuations***by*Matthew D. Shapiro & Mark W. Watson**869R Statistical Inference in Instrumental Variables***by*Peter C.B. Phillips & Bruce E. Hansen**868 Knightian Decision Theory and Econometric Inference***by*Truman F. Bewley**867 Warranties as Signals Under Consumer Moral Hazard***by*Nancy A. Lutz**866R Optimal Inference in Cointegrated Systems***by*Peter C.B. Phillips**865 The Characteristic Function of the Dirichlet and Multivariate F Distributions***by*Peter C.B. Phillips**864 Common Knowledge of Summary Statistics***by*Adam Brandenburger & John Geanakoplos**863 Generic Inefficiency of Stock Market Equilibrium When Markets Are Incomplete***by*John Geanakoplos & Michael Magill & Martine Quinzii & J. Dreze**862 Appropriating the Returns from Industrial R&D***by*Richard C. Levin & Alvin K. Klevorick & Richard R. Nelson & Sidney G. Winter**861 A Centered Projective Algorithm for Linear Programming***by*Michael J. Todd & Yinyu Ye**860 Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans***by*Philip H. Dybvig & Chi-fu Huang**859 Increases in Risk Aversion and Portfolio Choice in a Complete Market***by*Philip H. Dybvig**858 Stock Prices, Earnings and Expected Dividends***by*John Y. Campbell & Robert J. Shiller**857 The Informational Content of Ex Ante Forecasts***by*Ray C. Fair & Robert J. Shiller**775R A Theory of Hierarchies Based on Limited Managerial Attention***by*John Geanakoplos & Paul R. Milgrom

### 1987

**856R VAR Models as Structural Approximations***by*Ray C. Fair**855 Renegotiation-Proof Equilibria: Collective Rationality and Intertemporal Cooperation***by*David G. Pearce**854 A Note on an Optimal Garnishing Rule***by*Martin Shubik & Pradeep Dubey**853 Investor Behavior in the 1987-10 Stock Market Crash: Survey Evidence***by*Robert J. Shiller**852 Multiple Regression with Integrated Time Series***by*Peter C.B. Phillips**851 Prices of Single Family Homes Since 1970: New Indexes for Four Cities***by*Karl E. Case & Robert J. Shiller**850R The Noncooperative Equilibria of a Trading Economy with Complete Markets and Consistent Prices***by*Siddhartha Sahi & Shuntian Yao**849 Inventories, Investment, Inflation and Taxes***by*James Tobin**848 An Aggregative Disequilibrium Model of the U.S. Labour Market***by*Vassilis A. Hajivassiliou**847R Asymptotic Properties of Residual Based Tests for Cointegration***by*Peter C.B. Phillips & Sam Ouliaris**846 Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations***by*Peter C.B. Phillips**845R Partially Identified Econometric Models***by*Peter C.B. Phillips**844 Testing Strictly Concave Rationality***by*Rosa L. Matzkin & Marcel K. Richter**843 The Term Structure of Interest Rates. U.S. Government Term Structure Data***by*Robert J. Shiller & J. Huston McCulloch**842 Bimodal t-Ratios***by*Peter C.B. Phillips & Vassilis A. Hajivassiliou**841 Silver and Gold and Liquidity***by*Martin Shubik**840 Joint Distribution Theory for Some Statistics Based on LIML and TSLS***by*Grant H. Hillier**839 Effects of the Changing U.S. Age Distribution on Macroeconomic Equations***by*Ray C. Fair & Kathryn M. Dominguez**838 Valuation and Optimality in Exchange Economies with a Countable Number of Agents***by*Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw**837 Implementational Issues and Computational Performance Solving Applied General Equilibrium Models with SLCP***by*Thomas Rutherford**836 A Modeling System for Applied General Equilibrium Analysis***by*Thomas Rutherford**835 Knightian Decision Theory, Part II. Intertemporal Problems***by*Truman F. Bewley**834R Equilibria in Exchange Economies with a Countable Number of Agents***by*Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw**833R Econometric Modeling as Information Aggregation***by*Ray C. Fair & Robert J. Shiller**832 Inference in Econometric Models with Structural Change***by*Donald W.K. Andrews & Ray C. Fair**831 The Effect of Economic Events on Votes for President: 1984 Update***by*Ray C. Fair**830 Semiparametric Estimation of Monotonic and Concave Utility Functions: The Discrete Choice Case***by*Rosa L. Matzkin**829 Game Theory. Models of Strategic Behavior and Nuclear Deterrence***by*Martin Shubik**828 Measuring Market Power in U.S. Industry***by*Matthew D. Shapiro**827R Distributional Analysis of Portfolio Choice***by*Philip H. Dybvig**826R Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market***by*Philip H. Dybvig**825 Sequential Games of Resource Extraction: Existence of Nash Equilibria***by*Rabah Amir**824R Conditional and Unconditional Statistical Independence***by*Peter C.B. Phillips**823 Spherical Matrix Distributions and Cauchy Quotients***by*Peter C.B. Phillips**822 Are Cyclical Fluctuations in Productivity Due More to Supply Shocks or Demand Shocks?***by*Matthew D. Shapiro**821 Supply Shocks in Macroeconomics***by*Matthew D. Shapiro**820 The Future of Social Security: One Economist's Assessment***by*James Tobin**818 Optimal Choice of Monetary Policy Instruments in a Macroeconometric Model***by*Ray C. Fair**817 Financial Intermediaries***by*James Tobin**816 Ultimate Sources of Aggregate Variability***by*Robert J. Shiller**815 Sources of Output and Price Variability in a Macroeconometric Model***by*Ray C. Fair

### 1986

**819R Statistical Inference in Regressions with Integrated Processes: Part 2***by*Peter C.B. Phillips & Joon Y. Park**814R A Strategic Market Game with Complete Markets***by*Rabah Amir & Siddhartha Sahi & Martin Shubik**813 International Evidence on the Demand for Money***by*Ray C. Fair**812 The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors***by*Robert J. Shiller & John Y. Campbell**811R Statistical Inference in Regressions with Integrated Processes: Part 1***by*Peter C.B. Phillips & Joon Y. Park**810 Interest Rate and Exchange Rate Determination***by*Ray C. Fair**809R Testing for Cointegration Using Principal Component Measures***by*Peter C.B. Phillips & Sam Ouliaris**808 Forecasting the Depression: Harvard Versus Yale***by*Ray C. Fair & Matthew D. Shapiro & Kathryn M. Dominguez**807 Knightian Decision Theory: Part 1***by*Truman F. Bewley**806 The Unique Minimal Cash Flow Competitive Equilibrium***by*Martin Shubik**805 A Game Theoretic Approach to the Theory of Money and Financial Institutions***by*Martin Shubik**804 Enough Commodity Money and the Selection of a Unique Competitive Equilibrium***by*Martin Shubik**803 Temporal Dependence in Limited Dependent Variable Models: Theoretical and Monte-Carlo Results***by*Vassilis A. Hajivassiliou**802 Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors***by*Peter C.B. Phillips & Joon Y. Park**801 On the Formulation of Wald Tests of Nonlinear Restrictions***by*Peter C.B. Phillips & Joon Y. Park**800 Power in Econometric Applications***by*Donald W.K. Andrews**799 Limiting Distributions of the Number of Pure Strategy Nash Equilibria in n-Person Games***by*Imelda Yeung Powers**798 On the Performance of Least Squares in Linear Regression with Undefined Error Means***by*Donald W.K. Andrews**797 Quasirents, Influence and Organization Form***by*Paul R. Milgrom**796 Weak Convergence to the Matrix Stochastic Integral BdB***by*Peter C.B. Phillips**795R Testing for a Unit Root in Time Series Regression***by*Peter C.B. Phillips & Pierre Perron**794 Survey Evidence on Diffusion of Interest Among Institutional Investors***by*Robert J. Shiller & John Pound**793 Resources, Technology, and Development: Will the Table Be Bare When Poor Countries Get There?***by*William D. Nordhaus**792 Two Misspecification Tests for the Simple Switching Regressions Disequilibrium Model***by*Vassilis A. Hajivassiliou**791 Toward a Theory of Discounted Repeated Games with Imperfect Monitoring***by*Dilip Abreu & David G. Pearce & Ennio Stacchetti**790 Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers***by*Donald W.K. Andrews**789 Defense Economics and Economic Warfare Revisited***by*J. Hoult Verkerke & Martin Shubik**788 Trends Versus Random Walks in Time Series Analysis***by*Steven N. Durlauf & Peter C.B. Phillips**787 Issues Arising in Management and Control of Naval Forces***by*P. Bracken & Martin Shubik**786 Best Median Unbiased Estimation in Linear Regression with Bounded Asymmetric Loss Functions***by*Donald W.K. Andrews & Peter C.B. Phillips**785 Cointegration and Tests of Present Value Models***by*John Y. Campbell & Robert J. Shiller**784 Edgeworth Equilibria in Production Economies***by*Charalambos Aliprantis & Donald J. Brown & Owen Burkinshaw**783 The Share Economy: A Symposium***by*John Andrew & William D. Nordhaus**782R Towards a Unified Asymptotic Theory for Autoregression***by*Peter C.B. Phillips**781R Regression Theory for Near-Integrated Time Series***by*Peter C.B. Phillips**780 The Monetary-Fiscal Mix: Long-Run Implications***by*James Tobin**695 The Behavior of U.S. Short-Term Interest Rates Since 1979-10***by*Richard H. Clarida & Benjamin M. Friedman

### 1985

**779 Auction Theory***by*Paul R. Milgrom**778 Walrasian Indeterminacy and Keynesian Macroeconomics***by*John Geanakoplos & Polemarchakis, Heracles M.**777 On Finitely Repeated Games and Pseudo-Nash Equilibria***by*Chien fu Chou & John Geanakoplos**776 Neoclassical Theory in America: J.B. Clark and Fisher***by*James Tobin**774 Forecasting Efficiency: Concepts and Applications***by*William D. Nordhaus**773 Comparative Statics and Local Indeterminacy in OLG Economies: An Application of the Multiplicative Ergodic Theorem***by*John Geanakoplos & Donald J. Brown**772R The Term Structure of Euromarket Interest Rates: An Empirical Investigation***by*John Y. Campbell & Richard H. Clarida**771 International Lending and Borrowing in a Stochastic Sequence Equilibrium***by*Richard H. Clarida**770R Real Indeterminacy with Financial Assets***by*John Geanakoplos & Andreu Mas-Colell**769 The Balance of Payments Adjustment Mechanism in a Rational Expectations Equilibrium***by*Richard H. Clarida**768 Multiple Time Series Regression with Integrated Processes***by*Peter C.B. Phillips & Steven N. Durlauf**767 Fractional Matrix Calculus and the Distribution of Multivariate Tests***by*Peter C.B. Phillips**766 The Uses, Value and Limitation of Game Theoretic Methods in Defense Analysis***by*Martin Shubik**765 Asymptotic Expansions in Nonstationary Vector Autoregressions***by*Peter C.B. Phillips**764 Existence, Regularity, and Constrained Suboptimality of Competitive Allocations When the Asset Market Is Incomplete***by*John Geanakoplos & Heracles M. Polemarchakis**763R Random Cell Chi-Square Diagnostic Tests for Econometric Models: II. Theory***by*Donald W.K. Andrews**762 Random Cell Chi-Square Diagnostic Tests for Econometric Models: I. Introduction and Applications***by*Donald W.K. Andrews**761R Asymptotic Results for Generalized Wald Tests***by*Donald W.K. Andrews**760 Sections and Extensions of Concave Functions***by*Roger Howe**759 The Many Properties of Money: A Strategic Market Game Analysis***by*Martin Shubik**758 An Unbiased Reexamination of Stock Market Volatility***by*N. Gregory Mankiw & David Romer & Matthew D. Shapiro**757 Understanding Spurious Regressions in Econometrics***by*Peter C.B. Phillips**756R Edgeworth Equilibria***by*Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw**754 A Characterization of Globally Optimal Paths in the Non-Classical Growth Model***by*Rabah Amir**753 Enough Gold in a Society Without and With Money-Lenders***by*Martin Shubik**752 Mass-Economies with Vital Small Coalitions; the F-Core Approach***by*Peter J. Hammond & P. Kane & Myrna Holtz Wooders**751 A Model of a Sudden-Death Field-Goal Football Game as a Sequential Duel***by*Siddhartha Sahi & Martin Shubik**750 The Numeraire, Money and the Missing Degree of Freedom***by*Martin Shubik**749 Relying on the Information of Interested Parties***by*Paul R. Milgrom & John Roberts**747 Some Three Person Games in Coalitional Form for Teaching and Experimentation***by*Martin Shubik**746 An Axiomatization of Utility and Subjective Probability Based on Objective Probability***by*Mamoru Kaneko**745R Coordinating Coordination Failures in Keynesian Models***by*Russell Cooper & John Andrew**744 The Use of Simple Games to Illustrate Concepts and to Provide Experimental Evidence***by*Martin Shubik**743 Do We Reject Too Often? Small Sample Bias in Tests of Rational Expectations***by*N. Gregory Mankiw & Matthew D. Shapiro**742 Aggregation and Linearity in the Provision of Intertemporal Incentives***by*Bengt Holmstrom & Paul R. Milgrom**741 Two Stage and Related Estimators and Their Applications***by*Adrian Pagan**740R Time Series Regression with a Unit Root***by*Peter C.B. Phillips**739 The Distribution of FIML in the Leading Case***by*Peter C.B. Phillips**738 Risk and Return: Consumption Beta Versus Market Beta***by*Matthew D. Shapiro & N. Gregory Mankiw**736 Capital Utilization and Capital Accumulation: Theory and Evidence***by*Matthew D. Shapiro

### 1984

**735 The Dynamic Demand for Capital and Labor***by*Matthew D. Shapiro**734R A Note on the Unbiasedness of Feasible GLS, Quasi-Maximum Likelihood, Robust Adaptive, and Spectral Estimators of the Linear Model***by*Donald W.K. Andrews**733 Games with Perceptive Commanders But Less Perceptive Subordinates***by*Martin Shubik**732 Testing the Random Walk Hypothesis: Power Versus Frequency of Observation***by*Pierre Perron & Robert J. Shiller**731 The Exact Distribution of the Wald Statistic: The Non-Central Case***by*Sam Ouliaris & Peter C.B. Phillips**730 A Note on Enough Money in a Strategic Market Game with Complete or Fewer Markets***by*Martin Shubik**729 Managerial Incentives and Capital Management***by*Bengt Holmstrom & I. Ricard & Joan Costa**728 Neighborhood Systems for Production Sets with Indivisibilities***by*Herbert E. Scarf**727 Expansionary Government Policy in an Economy with Commodity and Labor***by*Russell Cooper**726 Optimal Cartel Equilibria with Imperfect Monitoring***by*Dilip Abreu & David G. Pearce & Ennio Stacchetti**725 Trends, Random Walks, and Tests of the Permanent Income Hypothesis***by*Matthew D. Shapiro & N. Gregory Mankiw**724 On a General Existence Theorem for Marginal Cost Pricing Equilibria***by*Donald J. Brown & Geoffrey M. Heal & M. Ali Khan & Rajiv Vohra**722 The Exact Distribution of the Wald Statistic***by*Peter C.B. Phillips**721 Testing for Serial Correlation and Unit Roots Using a Computer Function Routine Bases on ERA's***by*Peter C.B. Phillips & R.C. Reiss**720 General Equilibrium with Wage Rigidities: An Application to Belgium***by*Victor Ginsburgh & Ludo Van der Heyden**719R Stock Prices and Social Dynamics***by*Robert J. Shiller**718 The Use of Expected Future Variables in Macroeconometric Models***by*Ray C. Fair**717R Empirical Tests of the Rationality of Economic Forecasters: A Fixed Horizons Approach***by*William D. Nordhaus & Steven N. Durlauf**716 Product Warranties and Double Moral Hazard***by*Russell Cooper & T.W. Ross**715 Strategic Market Games: A Dynamic Programming Application to Money, Banking and Insurance***by*Martin Shubik**714 Plausible Outcomes for Games in Strategic Form***by*Martin Shubik**713 The Many Approaches to the Study of Monopolistic Competition***by*Martin Shubik**712 Nuclear Warfare, C_{3}I and First and Second Scenarios (A Sensitivity Analysis)***by*Martin Shubik & Bracken, J. & Tulowitzki, Haviv**711R A Mean-Variance Approach to Fundamental Valuations***by*James Tobin**710R Stability Comparisons of Estimators (5/1985 and 11/1985)***by*Donald W.K. Andrews**709 Price and Advertising Signals of Product Quality***by*Paul R. Milgrom & John Roberts**708R Job Discrimination, Market Forces and the Invisibility Hypothesis***by*Paul R. Milgrom**707 Estimated Trade-Offs Between Unemployment and Inflation***by*Ray C. Fair**706 The Cooperative Form, the Value and the Allocation of Joint Costs and Benefits***by*Martin Shubik**705R Consumption, Liquidity Constraints and Asset Accumulation in the Presence of Random Income Fluctuations***by*Richard H. Clarida**704 A Comparison of the Michigan and Fair Models: Further Results***by*Ray C. Fair & Lewis Alexander**703 A Comparison of the Michigan and Fair Models***by*Ray C. Fair & Lewis Alexander**702 Conditional Projection by Means of Kalman Filtering***by*Richard H. Clarida & Diane Coyle**701 On the Stochastic Steady-State Behavior of Optimal Asset Accumulation in the Presence of Random Wage Fluctuations and Incomplete Markets***by*Richard H. Clarida**700 A General Equilibrium Expression of the Paradox of Thrift***by*Christophe Chamley**699 Optimal Taxation of Capital Income in Economies with Identical Private and Social Discount Rates***by*Christophe Chamley**698 A Zero-One Result for the Least Squares Estimator***by*Donald W.K. Andrews