The modern theory of consumption rests on the idea that individuals maximize lifetime utility subject to an intertemporal budget constraint. The idea is based on the Life
Cycle – Permanent Income Hypothesis, as extended by Hall (1978) with the introduction of the rational expectations assumption. Hall derived clear theoretical and empirical implications from the optimality condition of the maximisation problem faced by the consumer—the Euler equation. Starting with Hall, the literature focused on testing the model of intertemporal utility maximization relying on the Euler equation but found several results at odds with theoretical predictions. The two subsequent decades were therefore dedicated to progressively modifying and enriching the original version of the model so as to render it able to explain the data. It is now possible to construct rich versions of the intertemporal utility maximization model able to replicate most observed facts.

This paper is devoted to reconstructing the evolution of the theoretical view on consumer behaviour stemming from the Euler equation approach to consumption, investigating how the need to account for the puzzling empirical evidence through more sophisticated versions of the model has implied relevant theoretical changes with respect to the original formulation. In particular, the question addressed is whether the necessary introduction of highly specific assumptions both on preferences and on the budget constraint affects the generality of the theoretical conclusions of the model. In fact, each of the extensions of the model that the literature has proposed ends up being crucial for the ability of the Euler equation framework to replicate the specific empirical evidence taken into consideration. Rather than representing refinements of the basic model that may contribute to form a more general view of consumption behaviour, each of these extensions thus ends up constituting a model in itself. For that matter, the intertemporal utility maximization framework, in its most general formulation, is not endowed with specific theoretical content but is rather a basic methodological tool of reasoning, which can give indications on consumption behaviour only through the specification of hypotheses on preferences and on the stochastic environment faced by the consumer. Despite their crucial role in defining the implications of the model, no consensus has emerged on which extensions should be adopted in defining the general approach to consumption. Finally, the paper argues that the variability of the theoretical implications of the model of intertemporal maximization affects the possibility of using it for policy purposes.