This article surveys the development of nonparametric models and methods for estimation of choice models with nonlinear budget sets.The discussion focuses on the budget set regression, that is, the conditional expectation of a choice variable given the budget set.Utility maximization in a nonparametric model with general heterogeneity reduces the curse of dimensionality in this regression.Empirical results using this regression are different from maximum likelihood and give informative inference.The article also considers the information provided by kink probabilities for nonparametric utility with general heterogeneity.Instrumental variable estimation and the evidence it provides of heterogeneity in preferences are also discussed.
On caracterise les axiomes faible et fort de preference revelee en termes de m-rationalite. Cette caracterisation eclaire le lien fondamental avec les axiomes de comportement de Richter pour la g-rationalite. L'approche presentee ici, est motivee par un operateur de complementarite, defini sur des preferences, qui montre le rapport logique entre ces deux concepts de choix rationnel
[The existence of equilibrium and Pareto optimal allocations in economies with an infinite number of commodities is studied. It is shown that any topology stronger than the Mackey topology might lead to the nonexistence of nontrivial Pareto optimal allocations. I.e., there exists a well behaved economy with preferences that are continuous in this topology and without individually rational Pareto optimal allocations. A converse of this theorem, a slight modification of Bewley's [2] existence of equilibrium theorem, is also proved. Using a characterization of the Mackey topology in terms of impatience of consumers, due to Brown and Lewis [3], an interpretation of the theorem above is given: a topology is such that continuity with respect to it implies existence of nontrivial Pareto optimal allocations if and only if it also implies impatience on the part of the consumers.]
On decrit une representation tabulaire simplifiee qui fait ressortir une hypothese structurale implicite importante dans des modeles de selection bases sur la censure
[Caves and Christensen [16] have provided a procedure for displaying the regular regions of a flexible functional form in the 2-good homothetic and nonhomothetic cases and in the 3-good homothetic case. We extend the procedure to the nonhomothetic 3-good case, and we apply the extended procedure to the translog, generalized Leontief, and minflex Laurent flexible functional form. In addition, we acquire the regular regions for the minflex Laurent model in the 2-good nonhomothetic case and superimpose the resulting regions on those already found by Caves and Christensen for the translog and generalized Leontief models. We find that the new minflex Laurent model generally has the largest regular regions of the three flexible functional forms. In addition, the regular region of the minflex Laurent model is found to expand as real income increases. As a result, that model is particularly well suited for use with time series data, which typically is characterized by positive long term growth trends in real income. In such applications, all recent data and future forecasts can be expected to lie within the regular region of the minflex Laurent model. Although it is possible for some of the earliest data to fall outside that regular region, the model's regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets. The regular region of each of three models moves when the model's parameters are changed. With the generalized Leontief or translog model, the regular region's shape, location, and size are unpredictable without prior knowledge of the model's parameters. With either of those two models, the intersection of the model's regular regions, as the parameters are changed, is contained within a very small neighborhood of the one point at which we require the model to be regular. With the minflex Laurent model, the primary properties of the regular regions are invariant to the values of the parameters, and the intersection of the displayed regular regions is a very large unbounded set. The width of that intersection increases without limit as real income increases.]
This paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices. In this model, asset prices and their stochastic properties are determined endogenously. One principal result is a partial differential equation which asset prices must satisfy. The solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy. IN THIS PAPER, we develop a general equilibrium asset pricing model for use in applied research. An important feature of the model is its integration of real and financial markets. Among other things, the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables. The model is fully consistent with rational expectations and maximizing behavior on the part of all agents. Our framework is general enough to include many of the fundamental forces affecting asset markets, yet it is tractable enough to be specialized easily to produce specific testable results. Furthermore, the model can be extended in a number of straightforward ways. Consequently, it is well suited to a wide variety of applications. For example, in a companion paper, Cox, Ingersoll, and Ross [7], we use the model to develop a theory of the term structure of interest rates. Many studies have been concerned with various aspects of asset pricing under uncertainty. The most relevant to our work are the important papers on intertemporal asset pricing by Merton [19] and Lucas [16]. Working in a continuous time framework, Merton derives a relationship among the equilibrium expected rates of return on assets. He shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model. Lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes. The random output of these processes is exogenously determined and perishable. Assets are defined as claims to all or a part of the output of a process, and the equilibrium determines the asset prices. Our theory draws on some elements of both of these papers. Like Merton, we formulate our model in continuous time and make full use of the analytical tractability that this affords. The economic structure of our model is somewhat similar to that of Lucas. However, we include both endogenous production and
This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis. These place predominant emphasis on the expected values of future spot rates or holdingperiod returns. In its simplest form, the expectations hypothesis postulates that bonds are priced so that the implied forward rates are equal to the expected spot rates. Generally, this approach is characterized by the following propositions: (a) the return on holding a long-term bond to maturity is equal to the expected return on repeated investment in a series of the short-term bonds, or (b) the expected rate of return over the next holding period is the same for bonds of all maturities. The liquidity preference hypothesis, advanced by Hicks [16], concurs with the importance of expected future spot rates, but places more weight on the effects of the risk preferences of market participants. It asserts that risk aversion will cause forward rates to be systematically greater than expected spot rates, usually