STATISTICAL INFERENCE
IN DYNAMIC ECONOMIC MODELS

by
COWLES COMMISSION RESEARCH STAFF MEMBERS
AND GUESTS
Edited by
TJALLING C. KOOPMANS
With Introduction by
JACOB MARSCHAK
John Wiley & Sons, Inc., New York
Chapman & Hall, Limited, London
1950
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TABLE OF CONTENTS

Chapter  Page 
Preliminary Pages
Principles of Notation xiii 

INTRODUCTION

I.  Statistical Inference in Economics: An Introduction, by J. Marschak

PART ONE: SIMULTANEOUS EQUATION SYSTEMS

II.  Measuring the Equation Systems of Dynamic Economics, by T.C. Koopmans, H. Rubin, and R.B. Leipnik 53 

Problems of Identification

III.  Note on the Identification of Economic Relations, by A. Wald 238 
IV.  Generalization of the Concept of Identification, by L. Hurwicz 245 
V.  Remarks on Frisch's Confluence Analysis and Its Use in Econometrics, by T. Haavelmo 258 

Problems of Structural and Predictive Estimation

VI.  Prediction and Least Squares, by L. Hurwicz 266 
VII.  The Equivalence of Maximum-Likelihood and Least-Squares Estimates of Regression Coefficients, by T.C. Koopmans 301 
VIII.  Remarks on the Estimation of Unknown Parameters in Incomplete Systems of Equations, by A. Wald 305 
IX.  Estimation of the Parameters of a Single Equation by the Limited-Information Maximum-Likelihood Method, by T.W. Anderson, Jr. 311 

Problems of Computation

X.  Some Computational Devices, by H. Hotelling 323 

PART TWO: PROBLEMS SPECIFIC TO TIME SERIES

Trend and Seasonality

XI.  Variable Parameters in Stochastic Processes: Trend and Seasonality, by L. Hurwicz 329 
XII.  Nonparametric Tests against Trend, by H.B. Mann 345 
XIII.  Tests of Significance in Time-Series Analysis, by R.L. Anderson 352 

Estimation Problems

XIV.  Consistency of Maximum-Likelihood Estimates in the Explosive Case, by H. Rubin 356 
XV.  Least-Squares Bias in Time Series, by L. Hurwicz 365 

Continuous Stochastic Processes

XVI.  Models Involving a Continuous Time Variable, by T.C. Koopmans 384 

PART THREE: SPECIFICATION OF HYPOTHESES

XVII.  When Is an Equation System Complete for Statistical Purposes?, by T.C. Koopmans 393 
XVIII.  Systems with Nonadditive Disturbances, by L. Hurwicz 410 
XIX.  Note on Random Coefficients, by H. Rubin 419 
References 423 
Index 429 
Corrections to Volume