# ABSTRACT OF PAPER

Title: The Euler equation approach and utility functions: a critical view

Author: *Pignalosa Daria*

The modern literature on consumption is based on the Life Cycle - Permanent Income Hypothesis developed by Modigliani and Brumberg (1954) and Friedman (1957). According to this model, consumers allocate resources over time in order to maximize lifetime utility subject to a budget constraint. Hall (1978) extended the model to the case of uncertainty with the introduction of the rational expectations assumption, and proposed to use the first order conditions of the intertemporal optimization problem faced by the consumer to derive a set of orthogonality conditions. This approach, known as the Euler equation approach, allows to both test the validity of the model and to estimate some of the structural parameters of the utility function. Although it has been challenged several times, the Euler equation approach has become the standard approach to consumer behavior. In its more general formulation, the standard framework encompasses many types of consumption behavior and has almost no testable implications. In order to take it to the data it is therefore necessary to construct a specific model which forces to make a number of modelling choices and to specify individual preferences. Hall adopted a quadratic utility function and found that consumption is a martingale, but his result is due to the linearity of marginal utility associated with quadratic preferences. Hallâ€™s contribution, highly influential on subsequent research, proves that the choice of the utility function is crucial for the implications of the model. The paper considers the most relevant parameters characterizing utility functions, i.e. the coefficients of relative and absolute risk aversion, the intertemporal elasticity of substitution, the coefficients of relative and absolute prudence. After discussing the meaning of each preference parameter, we highlight the relations between them. We thus show that, despite measuring different aspects of preferences, the main parameters have close mathematical relationships between each other, which impose strict constraints on preferences. We conclude with a survey of the most popular utility functions adopted in the literature on the consumption Euler equation, emphasizing the implications of their properties in terms of individual preferences, the features that make their use appealing, and the role they played in the theoretical and empirical research. The analysis suggests that the choice of a specific functional form is crucial for the implications of the model in terms of consumer behavior and is often made regardless of the features which make that function a plausible representation of individual preferences.

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