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on Utility Models and Prospect Theories |
| By: | Lu, Jingfeng; Perrigne, Isabelle |
| Abstract: | Estimating bidders’ risk aversion in auctions is a challeging problem because of identification issues. This paper takes advantage of bidding data from two auction designs to identify nonparametrically the bidders’ utility function within a private value framework. In particular, ascending auction data allow us to recover the latent distribution of private values, while first-price sealed-bid auction data allow us to recover the bidders’ utility function. This leads to a nonparametric estimator. An application to the US Forest Service timber auctions is proposed. Estimated utility functions display concavity, which can be partly captured by constant relative risk aversion. |
| Keywords: | Risk Aversion; Nonparametric Identi.cation; Nonparametric and Semipara-metric Estimation; Timber Auctions. |
| JEL: | D44 C14 |
| Date: | 2006–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:948&r=upt |
| By: | Kowal, Paweł |
| Abstract: | We consider nested utility function with nonhomothetic subutility functions. We express demand functions for aggregate goods in terms of marshalian and hicksian demands associated with the standard consumer problem of maximization of aggregate utility function. We also presents a simple method of calibrating such a demand system. |
| Keywords: | demand systems; nonhomothetic preferences |
| JEL: | D11 |
| Date: | 2006–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:931&r=upt |
| By: | Kurz, Mordecai; Motolese, Maurizio |
| Abstract: | We present a theoretical and empirical evaluation of the role of market belief in the structure of risk premia. To that end we employ a familiar asset pricing model for which we develop in detail the belief structure. The novelty in this development is the treatment of individual and market beliefs as Markov state variables. Moreover, the market belief is observable and the paper explains how we extract it from the data. The advantage of our formulation is that it permits a closed form solution of equilibrium prices hence we can trace the exact effect of market belief on the time variability of equilibrium risk premia. We present a model of asset pricing with diverse beliefs. We then explore the conditions under which diverse beliefs arise. We then derive the equilibrium asset pricing and the risk premium which the model implies. Since asset prices are affected by the dynamics of market belief, the component of market risk which is determined by the belief of agents is thus termed “Endogenous Uncertainty.” The theoretical conclusions are tested empirically for investments in the futures markets, the bond markets. Our main theoretical and empirical result is that fluctuations in the market belief about state variables are a dominant factor determining the time variability of risk premia. More specifically, we show that when the market holds abnormally favorable belief about future payoffs of an asset the market views the long position as less risky and hence the risk premium on that asset declines. This means that fluctuations in risk premia are inversely related to the degree of market optimism about future prospects of asset payoffs. This effect is very strong and empirically very dominant. The strong effect of market belief on market risk premia offers two additional perspectives. First, it offers an additional way of showing (for those who have any doubt) that fundamental factors affect market dynamics but perceptions have equally important effect on volatility. Second, that market belief is actually an observable data which can be used for a deeper understanding of the basic causes of stochastic volatility and time variability of risk premia. |
| Keywords: | Risk premium; heterogenous beliefs; market state of belief; asset pricing; Bayesian learning; updating beliefs; Rational Beliefs. |
| JEL: | D8 G12 D84 |
| Date: | 2006–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:247&r=upt |
| By: | Kurz, Mordecai |
| Abstract: | Abstract: The paper contrasts theories that explain diverse belief by asymmetric private information (in short PI) with theories which postulate agents use subjective heterogenous beliefs (in short HB). We focus on problems where agents forecast aggregates such as profit rate of the S&P500 and our model is similar to the one used in the literature on asset pricing (e.g. Brown and Jennings (1989), Grundy and McNichols (1989), Allen, Morris and Shin (2003)). We first argue there is no a-priori conceptual basis to assuming PI about economic aggregates. Since PI is not observed, models with PI offer no testable hypotheses, making it possible to prove anything with PI. In contrast, agents with HB reveal their forecasts hence data on market belief is used to test hypotheses of HB. We show the common knowledge assumptions of the PI theory are implausible. The theories differ on four main analytical issues. (1) The pricing theory under PI implies prices have infinite memory and at each t depend upon unobservable variables. In contrast, under HB prices have finite memory and depend only upon observable variables. (2) The “Beauty Contest” implications of the two are different. Under PI today’s price depends upon today’s market belief about tomorrow’s mean belief about “fundamental” variables. Under HB it depends upon today’s market belief about tomorrow’s market beliefs. Tomorrow’s beliefs are, in part, beliefs about future beliefs and are often mistaken. Market forecast mistakes are key to Beauty Contests, and are a central cause of market uncertainty called “endogenous uncertainty.” (3) Contrary to PI, theories with HB have wide empirical implications which are testable with available data. (4) PI theories assume unobserved data and hence do not restrict behavior, while rationality conditions impose restrictions on any HB theory. We explain the tight restrictions on the model’s parameters imposed by the theory of Rational Beliefs. |
| Keywords: | private information; Bayesian learning; updating beliefs; heterogenous beliefs; asset pricing; Rational Beliefs. |
| JEL: | G12 D82 D84 |
| Date: | 2006–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:233&r=upt |
| By: | Woźny, Łukasz; Garbicz, Marek |
| Abstract: | In this paper we identify how changes in the income tax rate affect the labour supply under interdependent utility functions. To reach that aim we create a model of the economy in which households choosing their optimal labour supply take into account not only their income, tax rate and individual consumption but also so called relative consumption level (Garbicz 1997). Taking into account the last issue we significantly modify the well known Becker model (1965). We conduct a comparative statics exercise using na lattice and supermodular game theory. Thanks to which we show sufficient and necessary conditions for a labour supply to be monotonic function of the income tax rate. We analyze the economic behaviour under static and dynamic setup. Under quite general assumptions concerning the household utility function we show that the higher the tax rate the lower the macroeconomic labour supply. Additionally we show the possibility of multiple equilibria in the economy that offers the explanation of differences in the working time between e.g. European countries and the US as well as discrepancies between micro and macroeconomic elasticity of labour supply (see Alesina, Glaeser, and Sacerdote 2005). |
| Keywords: | supermodularity; lattice programming; multiplicity; interdependent preferences; labour supply; |
| JEL: | D11 J22 |
| Date: | 2005–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:462&r=upt |
| By: | Antonella Campana (Department SEGeS, University of Molise); Paola Ferretti (Department of Applied Mathematics, University of Venice) |
| Abstract: | In this paper we consider the problem of studying the gap between bounds of risk measures for sums of non-independent random variables. Owing to the choice of the context where to set the problem, namely that of distortion risk measures, we first deduce an explicit formula for the risk measure of a discrete risk by referring to its writing as sum of layers. Then, we examine the case of sums of discrete risks with identical distribution. Upper and lower bounds for risk measures of sums of risks are presented in the case of concave distortion functions. Finally, the attention is devoted to the analysis of the gap between risk measures of upper and lower bounds, with the aim of optimizing it. |
| Keywords: | Distortion risk measures, discrete risks, concave risk measure, upper and lower bounds, gap between bounds |
| JEL: | D81 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:vnm:wpaper:146&r=upt |
| By: | Murphy, Roy E |
| Abstract: | It is assumed that human knowledge-building depends on a discrete sequential decision-making process subjected to a stochastic information transmitting environment. This environment randomly transmits Shannon type information-packets to the decision-maker, who examines each of them for relevancy and then determines his optimal choices. Using this set of relevant information-packets, the decision-maker adapts, over time, to the stochastic nature of his environment, and optimizes the subjective expected rate-of-growth of knowledge. The decision-maker’s optimal actions, lead to a decision function that involves his view of the subjective entropy of the environmental process and other important parameters at each stage of the process. Using this model of human behavior, one could create psychometric experiments using computer simulation and real decision-makers, to play programmed games to measure the resulting human performance. |
| Keywords: | decision-making; dynamic programming; entropy; epistemology; information theory; knowledge; sequential processes; subjective probability |
| JEL: | C61 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:16&r=upt |