This paper discusses the discounted utility (DU) model: its historical development, underlying assumptions, and "anomalies" - the empirical regularities that are inconsistent with its theoretical predictions. We then summarize the alternate theoretical formulations that have been advanced to address these anomalies. We also review three decades of empirical research on intertemporal choice, and discuss reasons for the spectacular variation in implicit discount rates across studies. Throughout the paper, we stress the importance of distinguishing time preference, per se, from many other considerations that also influence intertemporal choices.

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Time Discounting and Time Preference: A Critical Review

the total number of papers may exceed 10,000. Nevertheless, cost consideration forced us to consider mostly published papers and technical reports in English. 4 Formula 4 in Seifert (1991) is in error—a multiplier of n, of cell size, is missing in the numerator. 5 Unfortunately, the technique of meta-analysis cannot be applied, at present time, to such effects because the distribution of dis based on a sampling of people, whereas the statistics of techniques such as ARIMA are based on the distribution of a sampling of observations in the time domain regardless of the size of the people sample involved (i.e., there is no way to compare a sample of 100 points in time with a sample of 100 people). That is, a sample of 100 points in time has the same degrees of freedom if it were based on an observation of 1 person or of 1,000 people. 258 KLUGER AND DENISI From the papers we reviewed, only 131 (5%) met the criteria for inclusion. We were concerned that, given the small percentage of usable papers, our conclusions might not fairly represent the larger body of relevant literature. Therefore, we analyzed all the major reasons to reject a paper from the meta-analysis, even though the decision to exclude a paper came at the first identification of a missing inclusion criterion. This analysis showed the presence of review articles, interventions of natural feedback removal, and papers that merely discuss feedback, which in turn suggests that the included studies represent 1015% of the empirical FI literature. However, this analysis also showed that approximately 37% of the papers we considered manipulated feedback without a control group and that 16% reported confounded treatments, that is, roughly two thirds of the empirical FI literature cannot shed light on the question of FI effects on performance—a fact that requires attention from future FI researchers. Of the usable 131 papers (see references with asterisks), 607 effect sizes were extracted. These effects were based on 12,652 participants and 23,663 observations (reflecting multiple observations per participant). The average sample size per effect was 39 participants. The distribution of the effect sizes is presented in Figure 1. The weighted mean (weighted by sample size) of this distribution is 0.41, suggesting that, on average, FI has a moderate positive effect on performance. However, over 38% of the effects were negative (see Figure 1). The weighted variance of this distribution is 0.97, whereas the estimate of the sampling error variance is only 0.09. A potential problem in meta-analyses is a violation of the assumption of independence. Such a violation occurs either when multiple observations are taken from the same study (Rosenthal, 1984) or when several papers are authored by the same person (Wolf, 1986). In the present investigation, there were 91 effects derived from the laboratory experiments reported by Mikulincer (e.g., 1988a, 1988b). This raises the possibility that the average effect size is biased, because his studies manipulated extreme negative FIs and used similar tasks. In fact, the weighted average d in Mikulincer's studies was —0.39; whereas in the remainder of the

The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory.

We review 74 experiments with no, low, or high performance-based financial incentives. The modal result has no effect on mean performance (though variance is usually reduced by higher payment). Higher incentive does improve performance often, typically judgment tasks that are responsive to better effort. Incentives also reduce “presentation” effects (e.g., generosity and risk-seeking). Incentive effects are comparable to effects of other variables, particularly “cognitive capital” and task “production” demands, and interact with those variables, so a narrow-minded focus on incentives alone is misguided. We also note that no replicated study has made rationality violations disappear purely by raising incentives.

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The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework

Based on courses developed by the author over several years, this book provides access to a broad area of research that is not available in separate articles or books of readings. Topics covered include the meaning and measurement of risk, general single-period portfolio problems, mean-variance analysis and the Capital Asset Pricing Model, the Arbitrage Pricing Theory, complete markets, multiperiod portfolio problems and the Intertemporal Capital Asset Pricing Model, the Black-Scholes option pricing model and contingent claims analysis, 'risk-neutral' pricing with Martingales, Modigliani-Miller and the capital structure of the firm, interest rates and the term structure, and others.

Theory of Financial Decision Making

The basic paradigm of asset pricing is in vibrant f lux. The purely rational approach is being subsumed by a broader approach based upon the psychology of investors. In this approach, security expected returns are determined by both risk and misvaluation. This survey sketches a framework for understanding decision biases, evaluates the a priori arguments and the capital market evidence bearing on the importance of investor psychology for security prices, and reviews recent models.

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Investor Psychology and Asset Pricing

Levy and Markowitz showed, for various utility functions and empirical returns distributions, that the expected utility maximizer could typically do very well if he acted knowing only the mean and variance of each distribution. Levy and Markowitz considered only situations in which the expected utility maximizer chose among a finite number of alternate probability distributions. The present paper examines the same questions for a case with an infinite number of alternate distributions, namely those available from the standard portfolio constraint set. IT IS FREQUENTLY ASSERTED that mean-variance analysis applies exactly only when distributions are normal or utility functions quadratic, suggesting that it gives almost optimum results only when distributions are approximately normal or utility functions look almost like a parabola. On the other hand, in a recent paper Levy and Markowitz [6] showed empirically that the ordering of portfolios by the mean-variance rule was almost identical to the order obtained by using expected utility for various utility functions and historical distributions of returns. For example, the authors calculated an "exact" expected utility (of, say, a logarithmic utility function) for each of 149 mutual funds by attributing an equal probability for each year in the sample. Using the same data, the expected utility was approximated by a function of mean and variance U = f(E, V), where E represents the mean and V represents the variance. The exact expected utility and the approximation based only on E and V were found to be highly correlated. The analysis was repeated for various sets of data and various utility functions, and the same results were obtained in almost every case. Good results were obtained, then, when EU and f(E, V) were compared for a finite number of portfolios, e.g., 149 mutual funds. However, it may be that f(E, V) would do less well when asked to find the best portfolio among the infinite number of possible mixtures of a finite number of securities. In this case, the exact maximizing of expected utility might lead to quite different results than those obtained by using the mean-variance approximation. The aim of the present paper is to compare the expected utility of the optimum portfolio for given utility functions with the expected utility of well-selected portfolios from the mean

Mean-Variance Versus Direct Utility Maximization

A computer-controlled multistage portfolio selection task was devised to test experimentally basic assumptions underlying the separation theorem and the capital asset pricing modeL Although most of the subjects diversified among the three risky assets, the introduction of a riskless asset did not have the effect predicted by the separation theorem, nor were the subjects affected by systematic changes in the variance-covariance matrix of the risky returns. However, performance improved as the reward was increased tenfold. The capital asset pricing model (CAPM), proposed by William Sharpe, 1964; John Lintner, 1965; and Jan Mossin, 1966, has been the predominant normative as well as positive theory for determining assets' returns and prices in financial markets. The CAPM has a wide range of implications for various financial issues including the allocation of risky assets, price predictions, performance indices, and market efficiency tests, as well as tools for corporate finance decisions such as capital structure, costs of financial sources, and prices of new issues. During the last decade numerous theoretical studies have examined and extended the CAPM. A most recent development is the

Experimental Tests of the Separation Theorem and the Capital Asset Pricing Model

STOCHASTIC DOMINANCE CRITERIA for decision making under uncertainty have been developed and discussed by Quirk and Saposnik [29], Fishburn [4], [5], Levy [16], [18], [19], [20], Hadar and Russell [6], [7], [8], Hanoch and Levy [10], Rothschild and Stiglitz [30], [31], Levy and Paroush [21], Levy and Sarnat [22], Levhari, Paroush and Peleg [13], Whitmore [36] and others. Recently, Markowitz [27] has developed an algorithm for Second Degree Stochastic Dominance. In spite of the tremendous volume of work which has been published recently on stochastic dominance rules, this framework is still lagged behind the mean-variance rule with respect to the induced results. The two stumbling blocks in the development and application of stochastic dominance rules are: (a) in general, one does not know the statistical distribution of a mix of random variables, (b) unlike the meanvariance model, the inclusion of a riskless asset in the portfolio does not yield the equilibrium results derived by Sharpe [32], [33], Lintner [23], [24], and Mossin [28]. The ability to borrow and lend money at a riskless interest rate reduces the mean-variance efficient set of risky assets to only one unlevered portfolio. Each investor diversifies between this optimal unlevered portfolio and riskless bonds (or borrowing) in accordance with his preferences. The above property (which is known as the Separation Theorem) makes it possible to reach many important conclusions with respect to the investor's behavior and to determine the equilibrium prices of risky assets. However, these conclusions are obtained at the cost of making assumptions; we assume either risk aversion and normal distributions of return or that the investor's preference can be described by a quadratic utility function. The deficiencies of the quadratic utility function are well-known. Should there be no reason to believe that returns are normally distributed, one cannot apply the mean-variance rule. Thus, when one has no information on the distribution of returns or is not willing to make any assumption on the distribution of returns, stochastic dominance rules must be employed. Stochastic dominance rules require no information on the distributions and very little information on the investor's preferences. Thus, it is natural that the restrictions imposed by these rules may be so strong that the induced efficient set of investment portfolios will be relatively large and sometimes almost of the same size as the feasible set. The concern of this paper is to develop stochastic dominance rules which do not require more assumptions on the distributions of returns and also provide an

Yoram Kroll

Papers

Mean-Variance Versus Direct Utility Maximization

Experimental Tests of the Separation Theorem and the Capital Asset Pricing Model

Ordering uncertain options with borrowing and lending

Experimental tests of the mean-variance model for portfolio selection

Further Tests of the Separation Theorem and the Capital Asset Pricing Model