Estimating Life—Cycle Parameters from Consumption Behavior at Retirement”

Using pseudo-panel data, we estimate the structural parameters of a life—cycle consumption model with discrete labor supply choice. A focus of our analysis is the abrupt drop in consumption upon retirement for a typical household. The literature sometimes refers to the drop, which in the U.S. Consumer Expenditure Survey we estimate to be approximately 16%, as the “retirement—consumption puzzle.” Although a downward step in consumption at retirement contradicts predictions from life—cycle models with additively separable consumption and leisure, or with continuous work-hour options, a consumption jump is consistent with a setup having nonseparable preferences over consumption and leisure and requiring discrete work choices. This paper specifies a life—cycle model with these latter two elements, and it uses the empirical magnitude of the drop in consumption at retirement to provide an advantageous method of identifying structural parameters–most importantly, the intertemporal elasticity of substitution.

Repeated Choice: A Theory of Stochastic Intertemporal Preferences

We provide a repeated-choice foundation for stochastic choice. We obtain necessary and sufficient conditions under which an agent's observed stochastic choice can be represented as a limit frequency of optimal choices over time. In our model, the agent repeatedly chooses today's consumption and tomorrow's continuation menu, aware that future preferences will evolve according to a subjective ergodic utility process. Using our model, we demonstrate how not taking into account the intertemporal structure of the problem may lead an analyst to biased estimates of risk preferences. Estimation of preferences can be performed by the analyst without explicitly modeling continuation problems (i.e. stochastic choice is independent of continuation menus) if and only ifthe utility process takes on the standard additive and separable form. Applications include dynamic discrete choice models when agents have non-trivial intertemporal preferences, such as Epstein-Zin preferences. We provide a numerical example which shows the significance of biases caused by ignoring the agent's Epstein-Zin preferences

Preference symmetries, partial differential equations, and functional forms for utility

A discrete symmetry of a preference relation is a mapping from the domain of choice to itself under which preference comparisons are invariant; a continuous symmetry is a one-parameter family of such transformations that includes the identity; and a symmetry field is a vector field whose trajectories generate a continuous symmetry. Any continuous symmetry of a preference relation implies that its representations satisfy a system of PDEs. Conversely the system implies the continuous symmetry if the latter is generated by a field. Moreover, solving the PDEs yields the functional form for utility equivalent to the symmetry. This framework is shown to encompass a variety of representation theorems related to univariate separability, multivariate separability, and homogeneity, including the cases of Cobb–Douglas and CES utilityr. The work reported here was supported by a research fellowship from Nuffield College, Oxfor

Evaluating Asset-Pricing Models Using The Hansen-Jagannathan Bound: A Monte Carlo Investigation

We conduct Monte Carlo experiments to examine whether the bound proposed by Hansen and Jagannathan (1991) is a useful device for evaluating asset pricing models. Specifically, we use recently developed statistical tests, which are based on a 'distance' between the model and the Hansen-Jagannathan bound, to compute the rejection rates of true models. We provide finite-sample critical values for asset pricing models with time separable preferences, and show how they depend upon nuisance parameters—risk aversion and the rate of time preference. Further, we show that the finite-sample distribution of the test statistic associated with the risk-neutral case is extreme, in the sense that critical values based on this distribution will deliver type I errors no larger than intended—regardless of risk aversion or the rate of time preference. Extending the analysis to accommodate other preferences, we show that in the state non-separable case, the small-sample distributions of the test statistics are influenced significantly by the degree of intertemporal substitution, but not by attitudes toward risk. For habit formation preferences, the small-sample distributions are strongly influenced by the habit parameter. However, the maximal-size critical values for time-separable preferences are appropriate for habit formation as well as state non-separable preferences. We conclude that with these critical values the HJ bound is indeed a useful evaluation device. We then use the critical values to evaluate three asset pricing models using U.S. data. We find evidence against the time-separable model and mixed evidence on the remaining two models.

Labor supply models: unobserved heterogeneity, nonparticipation and dynamics

This chapter is concerned with the identification and estimation of models of labor supply. The focus is on the key issues that arise from unobserved heterogeneity, nonparticipation and dynamics. We examine the simple ‘static’ labor supply model with proportional taxes and highlight the problems surrounding nonparticipation and missing wages. The difference in differences approach to estimation and identification is developed within the context of the labour supply model. We also consider the impact of incorporating nonlinear taxation and welfare programme participation. Family labor supply is looked at from botht e unitary and collective persepctives. Finally we consider intertemporal models focusing on the difficulties that arise with participation and heterogeneity

Quantifying Inefficiency in Incomplete Asset Markets

It is known that the incompleteness of asset markets causes inefficiency in almost every equilibrium. Yet unexplored is the "size" of this inefficiency. The size of a Pareto improvement is the total willingness to pay for it, out of current consumption. Inefficiency is the maximum size of any Pareto improving reallocation. Inefficiency of US consumption in middle age is computed to be 10-11% of total consumption in youth, for CRRA parameters 1.5-3.25, in calibrated economy. The inefficiency of a general economy is approximated. A natural approximation, based on marginal rates of substitution (MRS), is preposterously crude in the calibrated economy, owing to a law of diminishing willingness to pay. Alternative approximations end up being functions of a classical notion, weighted social welfare maximized subject to resource constraints. They are simple, sharper in general and accurate in the calibrated economy.

Social welfare and profit maximization from revealed preferences

Consider the seller's problem of finding optimal prices for her $n$ (divisible) goods when faced with a set of $m$ consumers, given that she can only observe their purchased bundles at posted prices, i.e., revealed preferences. We study both social welfare and profit maximization with revealed preferences. Although social welfare maximization is a seemingly non-convex optimization problem in prices, we show that (i) it can be reduced to a dual convex optimization problem in prices, and (ii) the revealed preferences can be interpreted as supergradients of the concave conjugate of valuation, with which subgradients of the dual function can be computed. We thereby obtain a simple subgradient-based algorithm for strongly concave valuations and convex cost, with query complexity $O(m^2/\epsilon^2)$, where $\epsilon$ is the additive difference between the social welfare induced by our algorithm and the optimum social welfare. We also study social welfare maximization under the online setting, specifically the random permutation model, where consumers arrive one-by-one in a random order. For the case where consumer valuations can be arbitrary continuous functions, we propose a price posting mechanism that achieves an expected social welfare up to an additive factor of $O(\sqrt{mn})$ from the maximum social welfare. Finally, for profit maximization (which may be non-convex in simple cases), we give nearly matching upper and lower bounds on the query complexity for separable valuations and cost (i.e., each good can be treated independently)