Snapshot samples

We consider a coverage model where an initial event that occurs at some point in time triggers an activity of random duration that leads to some subsequent event. A snapshot sample is constructed at a fixed point in chronological time either by sampling only subjects where the initial event has occurred but the subsequent event has yet to occur (active subjects), or by sampling only subjects where both the initial and subsequent events have occurred (inactive subjects). The biases inherent in snapshot sampling can be neatly characterized by the properties of two random variables: the history (defined as the time the initial event occurs as measured into the past from the chronological point of sampling), and the active time (defined as the length of time between the initial and subsequent events). Though snapshot samples are biased, recognizing the biases enables correct inferences to be drawn from snapshot-sampled data. Considering only the case where and are independent random variables, this paper presents the probability models associated with snapshot sampling, demonstrates the problems that can occur, offers procedures for overcoming these problems, and applies the methods to interesting data sets.     

School Choice and the Distributional Effects of Ability Tracking: Does Separation Increase Inequality?

Tracking programs have been criticized on the grounds that they harm disadvantaged children. The bulk of empirical research supports this view, but existing studies compare outcomes across students placed in different tracks. Track placement is likely to be endogenous with respect to student outcomes. We use a new strategy for overcoming the endogeneity of track placement and find no evidence that tracking hurts low-ability children. Previous studies have also been based on the assumption that students' enrollment decisions are unrelated to whether or not the school tracks. When we account for the possibility that tracking programs affect school choice, we find evidence that they may help low-ability children.     

Elicitation using multiple price list formats

We examine the properties of a popular method for eliciting choices and values from experimental subjects, the multiple price list format. The main advantage of this format is that it is relatively transparent to subjects and provides simple incentives for truthful revelation. The main disadvantages are that it only elicits interval responses, and could be susceptible to framing effects. We consider extensions to address and evaluate these concerns. We conclude that although there are framing effects, they can be controlled for with a design that allows for them. We also find that the elicitation of risk attitudes is sensitive to procedures, subject pools, and the format of the multiple price list table, but that the qualitative findings that participants are generally risk averse is robust. The elicitation of discount rates appear less sensitive to details of the experimental design. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C9, D81, D91 An erratum to this article is available at .     

From edgeworth to fisher to vickrey: A comment on Michael J. Boskin's Vickrey lecture

Irving Fisher has been overlooked as an influence on William Vickrey's work on taxation and as a link between Edgeworth and Vickrey. Vickrey was Fisher's last and greatest student.     

Symmetry and order in the portfolio allocation problem

Summary. This research studies the role of multivariate distribution structures on random asset returns in determining the optimal allocation vector for an expected utility maximizer. All our conclusions pertain for the set of risk averters. By carefully disturbing symmetry in the distribution of the, possibly covarying, returns, we ascertain the ordinal structure of the optimized allocation vector. Rank order of allocations is also established when a permutation symmetric random vector is mapped into the returns vector through location and scale shifts. It is shown that increased dispersion in the vectors of location and scale parameters benefit, ex-ante, investors as does a decrease in the rank correlation coefficient between the location and scale parameter vectors. Revealed preference comparative static results are identified for the location and scale vectors of asset returns. For most issues addressed, we arrive at much stronger inferences when a safe asset is available. Received: August 8, 2000; revised version: January 8, 2001     

A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELS

This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity.     

Analysis of Beef Producers' Risk Management Perceptions and Desire for Further Risk Management Education

Beef cattle producers were surveyed in Texas and Nebraska to investigate perceptions of sources of risk, the effectiveness of risk management strategies, and interest in further risk management education, particularly production risk, using probit analysis. Important decision variables identified are age, prior use of risk management tools, previous attendances of risk management education, and risk aversion. Severe drought and cattle price variability are identified as primary risk factors with potential to affect farm income. Extremely cold weather and disease are of less importance. Understocking pasture and storing hay are perceived most effective as risk management options.