# Cowles Foundation for Research in Economics, Yale University

# Cowles Foundation Discussion Papers

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### 1993

**1053 Nonlinear Econometric Models with Deterministically Trending Variables***by*Donald W.K. Andrews & C. John McDermott**1052 On the Sources and Significance of Interindustry Differences in Technological Opportunities***by*Alvin K. Klevorick & Richard C. Levin & Richard R. Nelson & Sidney G. Winter**1051 Classical Estimation Methods for LDV Models Using Simulation***by*Vassilis A. Hajivassiliou & Paul A. Ruud**1050 The Money Rate of Interest and the Influence of Assets in a Multistage Economy with Gold or Paper Money: Part II***by*Martin Shubik & Shuntian Yao**1049 Simulating Normal Rectangle Probabilities and Their Derivatives: The Effects of Vectorization***by*Vassilis A. Hajivassiliou**1048 Aggregate Income Risks and Hedging Mechanisms***by*Robert J. Shiller**1047 Fully Modified Least Squares and Vector Autoregression***by*Peter C.B. Phillips**1046 The Money Rate of Interest and the Influence of Assets in a Multistage Economy with Gold or Paper Money: Part I***by*Martin Shubik & Shuntian Yao**1045 Measuring the Impact of Global Warming in Agriculture***by*Robert Mendelsohn & William D. Nordhaus & Daigee Shaw**1044 Behavioral Heterogeneity and Cournot Oligopoly Equilibrium***by*Jean-Michel Grandmont**1043 A Strategic Market Game with Seigniorage Costs of Fiat Money***by*Martin Shubik & D.P. Tsomocos**1042 An Old Keynesian Counterattacks***by*James Tobin**1030R Poverty in Relation to Macroeconomic Trends, Cycles, and Policies***by*James Tobin

### 1992

**1041 An Alternative Theory of Firm and Industry Dynamics***by*Richard Ericson & Ariel Pakes**1040 Hyper-Consistent Estimation of a Unit Root in Time Series Regression***by*Peter C.B. Phillips**1039 Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models***by*Peter C.B. Phillips**1038 Time Series Modeling with a Bayesian Frame of Reference: Concepts, Illustrations and Asymptotics***by*Peter C.B. Phillips & Werner Ploberger**1037 Some Dynamics of a Strategic Market Game with a Large Number of Agents***by*John H. Miller & Martin Shubik**1036 Measuring Asset Values for Cash Settlement in Derivative Markets: Hedonic Repeated Measures Indices and Perpetual Futures***by*Robert J. Shiller**1035 The Large Sample Correspondence Between Classical Hypothesis Tests and Bayesian Posterior Odds Tests***by*Donald W.K. Andrews**1034 A Nine Variable Probabilistic Macroeconomic Forecasting Model***by*Christopher A. Sims**1033 Construction of Stationary Markov Equilibria in a Strategic Market Game***by*Ioannis Karatzas & Martin Shubik & William D. Sudderth**1032 The Complex of Maximal Lattice Free Simplices***by*Imre Barany & Roger Howe & Herbert E. Scarf**1029 Tjalling Charles Koopmans (August 28, 1910-February 26, 1985)***by*Herbert E. Scarf**1028 On the Periodic Structure of the Business Cycle***by*Eric Ghysels**1027 Christmas, Spring and the Dawning of Economic Recovery***by*Eric Ghysels**1026 Approximately Median-Unbiased Estimation of Autoregressive Models with Applications to U.S. Macroeconomic and Financial Time Series***by*Donald W.K. Andrews & Hong-Yuan Chen**1025 Bayes Methods for Trending Multiple Time Series with an Empirical Application to the US Economy***by*Peter C.B. Phillips**1024 Bayes Models and Forecasts of Australian Macroeconomic Time Series***by*Peter C.B. Phillips**1023 Bayesian Model Selection and Prediction with Empirical Applications***by*Peter C.B. Phillips**1022 Expectations Driven Nonlinear Business Cycles***by*Jean-Michel Grandmont**1020 An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables***by*Donald W.K. Andrews**1019 Rolling the 'Dice': An Optimal Transition Path for Controlling Greenhouse Gases***by*William D. Nordhaus**1018 A Note on the Dual Approach to the Existence and Characterization of Optimal Consumption Decisions Under Uncertainty and Liquidity Constraints***by*Vassilis A. Hajivassiliou & Yannis M. Ioannides**1017 Posterior Odds Testing for a Unit Root with Data-Based Model Selection***by*Peter C.B. Phillips & Werner Ploberger**1016 Optimal Changepoint Tests for Normal Linear Regression***by*Donald W.K. Andrews & Inpyo Lee & Werner Ploberger**1015 Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative***by*Donald W.K. Andrews & Werner Ploberger**1014 Transactions Loans, Intertemporal Loans, Variable Velocity, the Rates of Interest and Commodity Money: Part 1. Transactions Loans***by*Martin Shubik & Shuntian Yao**1013 Money (for New Palgrave Money and Finance)***by*James Tobin**1012 Expanding the Scope of Expectations Data Collection: The U.S. and Japanese Stock Markets***by*Robert J. Shiller & Fumiko Kon-Ya & Yoshiro Tsutsui**1011 Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy***by*Christopher A. Sims**1010 The Impact of Climate on Agriculture: A Ricardian Approach***by*Robert Mendelsohn & William D. Nordhaus & Shaw, Daigee**1009 The 'DICE' Model: Background and Structure of a Dynamic Integrated Climate-Economy Model of the Economics of Global Warming***by*William D. Nordhaus**1008 Empirical Implications of Arbitrage-Free Asset Markets***by*S. Maheswaran & Christopher A. Sims**1005 Estimates of the Bias of Lagged Dependent Variable Coefficient Estimates in Macroeconomic Equations***by*Ray C. Fair**1004 The Cowles Commission Approach, Real Business Cycle Theories, and New Keynesian Economics***by*Ray C. Fair

### 1991

**999 The Tail Behavior of Maximum Likelihood Estimates of Cointegrating Coefficients in Error Correction Models***by*Peter C.B. Phillips**998 Unit Roots***by*Peter C.B. Phillips**997 A Reexamination of the Consumption Function Using Frequency Domain Regressors***by*Dean Corbea & Sam Ouliaris & Peter C.B. Phillips**996 Classification of Two-Person Ordinal Bimatrix Games***by*Imre Barany & J. Lee & Martin Shubik**995 Preface to Eduard Marz, Schumpeter, English Translation, Yale University Press***by*James Tobin**994R Price Flexibility and Output Stability: An Old Keynesian View***by*James Tobin**993 International Currency Regimes, Capital Mobility, and Macroeconomic Policy***by*James Tobin**992 Commentary on Irving Fisher, The Nature of Capital and Income (1906)***by*James Tobin**991 On the Internationalization of Portfolios***by*William C. Brainard & James Tobin**990 An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming***by*William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross**989 How Fast Do Old Men Slow Down?***by*Ray C. Fair**988 The Ecology of Markets***by*William D. Nordhaus**987 Transformations of the Commodity Space, Behavioral Heterogeneity and the Aggregation Problem***by*Jean-Michel Grandmont**986 Bayesian Routes and Unit Roots: de rebus prioribus semper est disputandum***by*Peter C.B. Phillips**985 Comment on 'To Criticize the Critics,' by Peter C. B. Phillips***by*Christopher A. Sims**984 Dynamic Structural Models: Problems and Prospects. Mixed Continuous Discrete Controls and Market Interactions***by*Ariel Pakes**983 Repeated Games: Cooperation and Rationality***by*David G. Pearce**982 Stabilizing the Soviet Economy***by*William D. Nordhaus**981 A Bound of the Proportion of Pure Strategy Equilibria in Generic Games***by*Faruk Gul & David G. Pearce & Ennio Stacchetti**980 Time Series Modelling with a Bayesian Frame of Reference: 1. Concepts and Illustrations***by*Peter C.B. Phillips & Werner Ploberger**979 Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?***by*Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt**978 The Spurious Effect of Unit Roots on Exogeneity Tests in Vector Autoregressions: An Analytical Study***by*Hiro Y. Toda & Peter C.B. Phillips**977 Vector Autoregression and Causality***by*Hiro Y. Toda & Peter C.B. Phillips**976 An 'Average' Lyapunov Convexity Theorem and Some Core Equivalence Results***by*Lin Zhou**975 Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models***by*Donald W.K. Andrews**974 A Refined Bargaining Set of an n-Person Game and Endogenous Coalition Formation***by*Lin Zhou**973 Dual Distribution in Franchising***by*Nancy T. Gallini & Nancy A. Lutz**972 Strictly Fair Allocations in Large Exchange Economies***by*Lin Zhou**971 Arithmetic Repeat Sales Price Estimators***by*Robert J. Shiller**970 Actual and Warranted Relations Between Asset Prices***by*Andrea E. Beltratti & Robert J. Shiller**969 Economic Equilibrium and Soviet Economic Reform***by*Herbert E. Scarf**968 Tests of Specification for Parametric and Semiparametric Models***by*Yoon-Jae Whang & Donald W.K. Andrews**966 The Invisible Hand in Modern Macroeconomics***by*James Tobin**965 Shortest Integer Vectors***by*Herbert E. Scarf & Shallcross, David F.**1007 Simulation Estimation Methods for Limited Dependent Variable Models***by*Vassilis A. Hajivassiliou**1006 Index-Based Futures and Options Markets in Real Estate***by*Karl E. Case & Robert J. Shiller & Allan N. Weiss**1003 Unidentified Components in Reduced Rank Regression Estimation of ECM's***by*Peter C.B. Phillips**1002 A Bayesian Analysis of Trend Determination in Economic Time Series***by*Eric Zivot & Peter C.B. Phillips**1001 Vector Autoregression and Causality: A Theoretical Overview and Simulation Study***by*Hiro Y. Toda & Peter C.B. Phillips**1000 The Long-Run Australian Consumption Function Reexamined: An Empirical Exercise in Bayesian Influence***by*Peter C.B. Phillips

### 1990

**967 The Method of Simulated Scores for the Estimation of LDV Models with an Application to External Debt Crisis***by*Vassilis A. Hajivassiliou & Daniel McFadden**964 A Strategic Market Game with a Mutual Bank with Fractional Reserves and Redemption in Gold (A Continuum of Traders)***by*Martin Shubik & D.P. Tsomocos**963 Default and Bankruptcy in a Multistage Exchange Economy***by*Martin Shubik**962 On the Convex Hull of the Integer Points***by*Antal Balog & Imre Barany**961 A Strategic Market Game of a Finite Economy with a Mutual Bank***by*Martin Shubik & Jingang Zhao**960 Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models***by*Vassilis A. Hajivassiliou & Axel Borsch-Supan**959 The Price for the Widow's Cruse: Or the Value of an Infinitely Productive Asset***by*Martin Shubik**958 Least Concavity and the Distribution-Free Estimation of Non-Parametric Concave Functions***by*Rosa L. Matzkin**957 Estimation of Multinomial Models Using Weak Monotonicity Assumptions***by*Rosa L. Matzkin**956 The Hybrid Solutions of an n-Person Game***by*Jingang Zhao**955 International Diversification of Social and Private Risk: The US and Japan***by*Stephen S. Golub**954 Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies***by*Lin Zhou**953 Stock Prices and Bond Yields: Can Their Co-Movements Be Explained in Terms of Present Value Models?***by*Robert J. Shiller & Andrea E. Beltratti**952 Popular Attitudes Towards Free Markets: The Soviet Union and the United States Compared***by*Robert J. Shiller & Maxim Boycko & Vladimir Korobov**951 A Functional Central Limit Theorem for Strong Mixing Stochastic Processes***by*Donald W.K. Andrews & David Pollard**950 To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends***by*Peter C.B. Phillips**949 A Shortcut to LAD Estimator Asymptotics***by*Peter C.B. Phillips**948 Operational Algebra and Regression t-Tests***by*Peter C.B. Phillips**947 Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns***by*Peter C.B. Phillips & Mico Loretan**946 The Generalized Basis Reduction Algorithm***by*Herbert E. Scarf & Laszlo Lovasz**945 The Frobenius Problem and Maximal Lattice Free Bodies***by*Herbert E. Scarf & Shallcross, David F.**944 Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis***by*Eric Zivot & Donald W.K. Andrews**943 Tests for Parameter Instability and Structural Change with Unknown Change Point***by*Donald W.K. Andrews**942 An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator***by*Donald W.K. Andrews & Christopher J. Monahan**941 Voting by Committees***by*Salvador Barbera & Hugo Sonnenschein & Lin Zhou**940 Generic Uniform Convergence***by*Donald W.K. Andrews**939 Financial Integration, Liquidity and Exchange Rates***by*Vittorio Grilli & Nouriel Roubini**938 Aggregation and Social Choice: A Mean Voter Theorem***by*Andrew Caplin & Barry Nalebuff**937 Aggregation and Imperfect Competition: On the Existence of Equilibrium***by*Andrew Caplin & Barry Nalebuff**936 A Colored Version of Tverberg's Theorem***by*Imre Barany & D.G. Larman**935 Testing Game Theoretic Models of Price-Fixing Behaviour***by*Vassilis A. Hajivassiliou**934 Growth and Distribution: A Neoclassical Kaldor-Robinson Exercise***by*James Tobin

### 1989

**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**933 Testing for a Unit Root in the Presence of Deterministic Trends***by*Peter C.B. Phillips & Peter Schmidt**932 Asymptotics for Linear Processes***by*Peter C.B. Phillips & Victor Solo**931 On the Theory of Macroeconomic Policy***by*James Tobin**930 Mathematical Programming and Economic Theory***by*Herbert E. Scarf**929 Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations***by*In Choi & Peter C.B. Phillips**928 Estimating Long Run Economic Equilibria***by*Peter C.B. Phillips & Mico Loretan**927 Alternative Approaches to the Political Business Cycle***by*William D. Nordhaus**925 Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality***by*Donald W.K. Andrews & Yoon-Jae Whang**924 Risk Analysis in Economics: An Application to University Finances***by*William D. Nordhaus**923 Inflationary Expectations and Price Setting Behavior***by*Ray C. Fair**922 Warranties, Durability, and Maintenance: Two Sided Moral Hazard in a Continuous-Time Model***by*Nancy A. Lutz & Philip H. Dybvig**921 Full Information Estimation and Stochastic Simulation of Models with Rational Expectations***by*Ray C. Fair & John B. Taylor**920 Renegotiation and Symmetry in Repeated Games***by*David G. Pearce & Dilip Abreu & Ennio Stacchetti**919 An Introduction to General Equilibrium with Incomplete Asset Markets***by*John Geanakoplos**918 A Nonparametric Maximum Rank Correlation Estimator***by*Rosa L. Matzkin**917 On Integer Points in Polyhedra: A Lower Bound***by*Imre Barany & Roger Howe & Laszlo Lovasz**916 Neighbors of the Origin for Four by Three Matrices***by*David F. Shallcross**915 The Reconciliation of Micro and Macro Economics***by*Martin Shubik**914 Game Theory Without Partitions, and Applications to Speculation and Consensus***by*John Geanakoplos**913 The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets***by*John Geanakoplos & Martin Shubik**912 Existence of Walras Equilibrium Without a Price Player of Generalized Game***by*John Geanakoplos & Pradeep Dubey**911 Do the Secondary Markets Believe in Life After Debt?***by*Vassilis A. Hajivassiliou**910 Asymptotics for Semiparametric Econometric Models: III. Testing and Examples***by*Donald W.K. Andrews**909R Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation***by*Donald W.K. Andrews**908R Asymptotics for Semiparametric Econometric Models: I. Estimation***by*Donald W.K. Andrews**907 An Empirical Process Central Limit Theorem for Dependent Non-Identically Distributed Random Variables***by*Donald W.K. Andrews**906 Asymptotic Optimality of Generalized C_{L}, Cross-Validation, and Generalized Cross-Validation in Regression with Heteroskedastic Errors***by*Donald W.K. Andrews**905 Market Innovation and Entrepreneurship: A Knightian View***by*Truman F. Bewley**904 Gold, Liquidity and Secured Loans in a Multi-Stage Economy. Part II. Many Durables, Land and Gold***by*Martin Shubik & Shuntian Yao**903 The Transactions Cost of Money (A Strategic Game Analysis)***by*Martin Shubik & Shuntian Yao**902 Solving Systems of Simultaneous Equations in Economics***by*John Geanakoplos & Shafer, Wayne**901 Observability and Optimality***by*John Geanakoplos & Heracles M. Polemarchakis**900 Liquidity and Bankruptcy with Incomplete Markets: Pure Exchange***by*John Geanakoplos & Pradeep Dubey**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

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