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Precautionary Saving and Asset Pricing: Implications of Separating Time and Risk Preferences Charles Allen Nadeau Iowa State University

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Precautionary Saving and Asset Pricing: Implications of Separating Time and Risk Preferences Charles Allen Nadeau Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1996 Precautionary saving and asset pricing: implications of separating time and risk preferences Charles Allen Nadeau Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Economics Commons Recommended Citation Nadeau, Charles Allen, "Precautionary saving and asset pricing: implications of separating time and risk preferences " (1996). Retrospective Theses and Dissertations. 11329. https://lib.dr.iastate.edu/rtd/11329 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI fikns the text directly from the ori^al or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, wl^e others may be from any type of computer printer. The quality of this reproduction is depeodent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. 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UMI A Bell & Howell Information Company 300 North Ze^ Road, Ann Aiirar MI 48106-1346 USA 313/761-4700 800/521-0600 Precautionary saving and asset pricing: Implications of separating time and risk preferences by Charles Allen Nadeau A Dissertation Submitted to the Graduate Faculty in Partial Fulfilhnent of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department: Economics Major: Economics Approved; Signature was redacted for privacy. [n CM^epfM Work Signature was redacted for privacy. Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1996 UMI N\iinber: 9626058 UMI Microform 9626058 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 ii for my wife Elisabet iii TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1 CHAPTER 2: EU AND GEU PREFERENCES 9 Introduction 9 Two Period EU Preferences 12 Two Period GEU Preferences 23 Literature Review 30 Recursive GEU and Asset Pricing 40 CHAPTER 3: GEU AND PRECAUTIONARY SAVING 44 Basic Model Features 44 Individual Preferences and the Budget Constraint 46 Solution Methods 49 Certainty Case 51 Stochastic Endowment Income 53 Stochastic Capital Income 60 Stochastic Wage Income 66 Stochastic Endowment and Wage Income 70 Stochastic Wage and Capital Income 75 Stochastic Endowment and Capital Income 79 CHAPTER 4: EU AND PRECAUTIONARY SAVING 84 Introduction 84 Basic Model Features 85 Stochastic Endowment Income 86 Stochastic Capital Income 89 Stochastic Wage Income 92 Stochastic Endowment and Wage Income 93 Stochastic Wage and Capital Income 94 Stochastic Endowment and Capital Income 95 CHAPTER 5; GEU AND ASSET PRICING 97 Introduction 97 Euler Equations and Intertemporal Asset Pricing Models 97 Recursive Utility 100 Hansen-Jagaimathan (HJ) Volatility Bounds 104 Literature Review 108 Models 111 iv Model of Epstein and Zin (1991) 111 Model of Kandel and Stambaugh (1991) 114 Model of Kocherlakota (1995) 116 Data 117 Consumption Data 118 Treasury Bill Return Data 121 Market Return Data 124 Estimation and Results 124 Discussion and Conclusions 130 CHAPTER 6: CONCLUSIONS 135 REFERENCES 138 APPENDIX A: CHAPTER 3 DERIVATIONS 148 APPENDIX B: CHAPTER 4 DERIVATIONS 156 1 CHAPTER 1; INTRODUCTION It is a topic of active research in consumer and capital theory to determine how to characterize preferences about uncertainty and intertemporal choice. Stochastic choice problems in intertemporal environments have traditionally been approached by assuming that the decision-makers preferences can be represented by a state- and time-separable von Neumann-Morgenstem (VNM) utility function. This representation of preferences offers an elegant and powerful way to analyze temporal behavior under uncertainty. However, a number of researchers have recently begun to look outside of the expected utility framework to model a number of different intertemporal macroeconomic and microeconomic problems.^ These efforts have appeared largely in response to the growing body of laboratory evidence which casts doubt upon the descriptive validity of expected utility• • modeling in• general 2 as well as the theoretical and empirical problems encountered by using intertemporal extensions of it. These newer models have also been used in attempts to significantly improve the explanation of non-experimental evidence. It is well-known that the functional form of a cardinal VNM utility index is constrained in both static and intertemporal environments by several "axioms" which effectively limit the selection of preference representations available to the modeler. In particular, a VNM index is required by a "compound probabilities" axiom to be linear in ' For examples see Hall (1988), Epstein and Zin (1989,1991), Persson and Svensson (1989), Barsky (1989), Weil (1990i Fanner (1990), Kandel and Stambaugh (1991), Duffie and Epstein (1992^ Campbell (1993), and Obstfeld (1994a, 1994b). ^ For cites see Machina (1982), Duffie (1992), Quiggin (1993), and Harless and Camerer (1994). This laboratory evidence contrasts with a substantial amount of non-experimental evidence that conforms reasonably well with the expected utility hypothesis. 2 the probabilities in order to generate consistent choice behavior under risk? It is shown in chapter two that this restriction is quite limiting in an intertemporal setting in that the functional forms chosen to model risk attitude and intertemporal substitution cannot be made independently. An important consequence of this fimctional form inflexibility is that the coefficient of relative risk aversion and the elasticity of intertemporal substitution are artificially constrained to be reciprocals, and thus indistinguishable, in the standard isoelastic and time-additive case/ The issue addressed in this paper is fimdamentally a modeling one and involves a characterization of intertemporal preferences under uncertainty that produces consistent choice behavior for an individual, and which also relaxes the preference restrictions implicitly imposed by maintaining all of the axioms of the expected utility hypothesis.^ A "generalized" expected utility (GEU) model of individual preferences is used which relaxes the preference restrictions by a slight weakening of the expected utility axioms, and which generates choice behavior that generally is not replicated by using a single cardinal utility fimction over outcomes. This weakening of the axiomatic structure underlying expected utility modeling occurs by abandoning the axiom relating to the treatment of compoimd probabilities in a way first suggested by Selden (1978). The generalized model used here maintains all of the other axioms of expected utility and is used in an attempt to clearly understand the intertemporal factor allocations of individuals facing income risk. In addition, a recursive ' This linearity requirement refers to a model with a discrete number of possible states. In a model with an infinite number of states, it can be reinterpreted as linearity in the expectations operator. Thus, by discarding this axiom a modeler produces a utility index that is generally nonlinear in the probabilities or expectations operator. * The elasticity of intertemporal substitution is an important preference concept in economics; see Hall (1988) for discussion. It can be thought of as measuring the change in consumption growth precipitated by a change in the intertemporal price of consumption, where the price is usually taken to be the current real interest rate. The model used in chapter three demonstrates that when leisure as well as consimiption enters the utility fimction the intertemporal price of leisure (i.e. the intertemporal wage ratio) also affects the willingness to transfer resources across time periods. ' As Farmer (1990) points out in a multiperiod context, it is also difficult to derive closed-form solutions to stochastic intertemporal choice problems when all of the axioms are retained since such problems quickly become intractable. 3 infinite-horizon extension of the basic two period framework is evaluated for purposes of pricing assets. Two questions are explicitly addressed in the paper: (i) does independent
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