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Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 RENNIE, Henry George, 1940- AGGREGATION THEORY, INVESTMENT BEHAVIOR AND RATIONAL LAG FUNCTIONS. The Ohio State University, Ph.D., 1973 Economics, theory ti University Microfilms,A XEROX Company, Ann Arbor, Michigan © Copyright by Henry George Rennie 1973 THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. AGGREGATION THEORY, INVESTMENT BEHAVIOR AND RATIONAL LAG FUNCTIONS DISSERTATION Presented in Partial Fulfillm ent of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Henry George Rennie, B.Sc., M.A. The Ohio State University 1973 Approved by ACKNOWLEDGMENTS I t ts my pleasure to acknowledge the assistance of various persons who contributed to this study. Special thanks are due my advisers, Professors E. Bal tens per ger, W. L. L'Esperance, and P. M attila, who gave me continual feedback throughout this study. I should, in particular, lik e to thank Professor L'Esperance for his encouragement from the inception to the completion of this study. An essential part of a study of this type is computer programming and I would lik e to thank my very competent assistants, Molly Garrett, Paul Hart, Andrew Hochstein, and John Irmen. To my typists, Mary Jane Donaldson, Mari Kanavel, and Carol Kaufman, thank you. The sacrifice involved in reaching the final product was borne by my family. To Heather, who went from speaking no English a t a l l , to saying, "daddy is making book," to, "is your dissertation finished, father?" and to Matthew who was apparently oblivious to it a l l , T.K.& H. And to my w ife, Phoebe, for her encouragement, thank you. 11 VITA 8 October 1940 Born - Greenock, Scotland, Gt. Britain 1963 ............... B.Sc., The Ohio State University, Columbus, Ohio 1964 ............... Research Assistant, Bureau of Business Research, The Ohio State University, Columbus, Ohio 1965 .............. M.A., The Ohio State University, Columbus, Ohio 1965-1969 . Teaching Associate, Department of Economics, The Ohio State University, Columbus, Ohio 1969-Present. Assistant Professor, Department of Economics, The University of Toledo, Toledo, Ohio PUBLICATIONS "Bayesian probability and the General pascal Distribution," American Statistical Association, Proceedings of the Business and Economic Statistics Section, 1972, 431-434. FIELDS OF STUDY Monetary Theory and Policy Econometrics International Trade and Development 11 f TABLE OF CONTENTS Page ACKNOWLEDGMENTS .............................................................................................. i i VITA ........................... , ....................................................................................1ii LIST OF TABLES.................................................................................................... vi LIST OF ILLUSTRATIONS.........................................................................................1x INTRODUCTION ................................................................................................... 1 Chapter I . AGGREGATION BIAS IN RATIONAL LAG FUNCTIONS .............................. 7 1. Aggregation and the aggregation problem 2. The meaning of "consistent aggregation" 3. Necessary and sufficient conditions for consistent aggregation 4. Approaches to the aggregation problem 5. The analogy approach to aggregation 6 . The relations between micro and macro parameters 7. A measure of the aggregation bias in macro-parameters 8 . The concept of a distributed lag 9. The rational lag function 10. The general Pascal distributed lag function 11. Parameter bias in rational lag forms 12. The relation between the estimated and the implied macro-parameters in rational lag functions 13. The effect of aggregation on the lag.structure and moments of a general Pascal lag function 14. Aggregation, minimum residual variance and model choice II. INVESTMENT.............................................................................................. 48 1. Introduction 2. Generalized accelerator mechanism 3. Theories of capital demand 4. Replacement investment 5. Models of Investment behavior 1 v Chapter Page I I I . ESTIMATION OF A RATIONAL LAG FUNCTION................................. 6 8 IV. EMPIRICAL: INVESTMENT THEORY PERFORMANCE........................... 75 1. Introduction 2. The sample 3. Measurement 4. Micro performance 5. Macro performance V. EMPIRICAL: AGGREGATION BIAS................................................. 103 1. Bias is the unconstrained macro coefficients 2. Bias in the lag structure and average lag 3. Bias in the aggregate residual variance 4. Bias and theory selection 5. The empirical literature: A comparison of findings VI. SUMMARY AND CONCLUSIONS...................................................... 169 1. Summary 2. Conclusions APPENDIX A. 177 B............................................................................................................. 211 C............................................................................................................. 224 D.....................................................................................................................231 E............................................................................................................. 238 F............................................................................................................. 261 G............................................................................................................. 265 H............................................................................................................. 277 1............................................................................................................. 284 J............................................................................................................. 288 BIBLIOGRAPHY........................................................................... 295 V LIST OF TABLES Table Page 1. Components of bias in the estimated aggregate parameters of a rational distributed lag function ............................. 37 2. Sample firms, their ranking by sales, assets, and net income, and th eir OBE-SEC industry group ....................... 77 3. Size distribution of firms within groups by average investment and capital stock ............................................... 78 4. Calculated replacement coefficients for twenty-seven firms and six industry groups ......... 82 5. Goodness of f it statistics-firms ...................................................... 90 6 . Number of times, out of twenty-seven, a theory had a lower standard error than competing theories .... 96 7. Number of desired capital stock coefficients and number at least twice th eir standard errors for twenty-seven companies .......................................................... 98 8 . Goodness of f it statistics-aggregates .................................... 100 9. Number of times, out of six, a theory had a lower standard error than competing theories ............................. 101 10. Number of desired capital stock coefficients and number at least twice th eir standard errors for six aggregates................................................................................ 1 0 2 11. Test results of parameter vector homogeneity by theory and group............................................................................................ 108 12. Average size of |(E-T)/E| over six industries by theory and coefficient ...............................................................114 13. Analysis of variance