Extended Models for Quantal Response Data

There is much current interest in trying to improve the fit of the classical logit and probit models for quantal response data. This is done through transforming the dose scale and/or embedding a classical model in a richer parametric family. This paper provides an historical review of the development of this work, and attempts to make practical recommendations. Much of the work extends directly to the case of logistic regression.     

Sentencing Illicit Drug Traffickers: How do the Courts Handle Random Sampling Issues?

While many European justice systems distinguish between possession of and trafficking in illicit drugs, sentencing in drug cases in those countries tends not to depend (at least formally) upon the quantity of drugs seized from a defendant, but rather on the circumstances in which the defendant was found with drugs. Courts in the United States, on the other hand, penalize those convicted of drug crimes through an elaborate system of sentencing rules and guidelines. These sentences depend only upon the amount of drugs (possibly adjusted for circumstances) and the defendant's criminal history. Because of the enormous amount of work needed to determine drug type and quantity in each case, sampling the evidence and estimates of drug quantity have been accepted in most courts in the United States. During the last two years, several major developments in U.S. federal sentencing have taken place. It all started in June 2000 with the Supreme Court case Apprendi v. New Jersey , in which Justice O'Connor, in dissent, termed a "watershed in constitutional law". Prior to Apprendi , a judge would sentence a convicted drug trafficker to imprisonment using the preponderance standard of proof on the quantities of drugs seized. The affect of Apprendi is to make more juries decide the quantity of drugs by the reasonable doubt standard. Although Apprendi had nothing to do with illicit drugs, the implication now is that all federal sentencing protocols are under revision. Since Apprendi was decided, huge numbers of cases involving convicted drug traffickers have relied upon its reasoning on appeal, with the result that a ruling from the Supreme Court on further clarification of this issue is expected. This article discusses the impact so far of Apprendi on statistical issues involved in estimating total drug quantity and considers possible future directions under the changing protocols.     

The demand for food and beverages in Norway

The demand for food and beverages is estimated within a three-stage demand model. The separability structure of the model is checked by nonparametric tests. Some generalized axiom of revealed preference (GARP) violations are detected in one of the subsystems. However, they are removed by small adjustments in the quantities of fish, and the violations are interpreted as results of measurement errors. The almost ideal demand system is used in the static and a dynamic version. The results of various specification and misspccification tests suggest that the static version performs poorly as compared with the dynamic version. Norwegian demand elasticities for disaggregate food commodities have rarely been estimated within a system framework, so the results are of intrinsic interest. The elasticities estimated by using the dynamic model are of the expected signs and reasonable magnitudes. The values are stable over time for most commodities. Elasticities estimated within a subsystem are conditional on the goods included in that system, and they may differ from the more policy relevant unconditional elasticities estimated within a system including all goods. Adjustment formulas are used to approximate the unconditional elasticities from the estimated conditional elasticities. There are considerable differences between the numerical values of the conditional and unconditional elasticities for several of the foods. The unconditional own-price elasticities are in the interval-0.20 to-0.89. The own-price elasticities for hot drinks and for milk are most inelastic. The unconditional expenditure elasticities for food-away-from-home, fish, soft drinks, and alcoholic beverages are above one, while the expenditure elasticity for hot drinks is about zero.     

A multistage stochastic programming model for the New Zealand dairy industry

This paper presents an application of multistage stochastic programming to a production planning problem for Fonterra, a leading company in the New Zealand dairy industry, taking into account uncertain milk supply, price–demand curves and contracting. We describe a model for Fonterra's supply chain, and a model for uncertain milk supply. We then present a multistage stochastic quadratic programming model and a decomposition algorithm to compute an optimal sales policy, which is tested in simulation against a deterministic policy.     

Closed-loop equilibrium in a multi-stage innovation race

Summary. We examine a multistage model of an R&D race where players have multiple projects. We also develop perturbation methods for general dynamic games that can be expressed as analytic operators in a Banach space. We apply these perturbation methods to solve races with a small prize. We compute second-order asymptotically valid solutions for equilibrium and socially optimal decisions to determine qualitative properties of equilibrium. We find that innovators invest relatively too much on risky projects. Strategic reactions are ambiguous in general; in particular, a player may increase expenditures as his opponent moves ahead of him. Received: January 3, 2002; revised version: June 14, 2002 RID="*" ID="*" This is the final version of Judd (1985). The author gratefully acknowledges the comments of anonymous referees, Paul Milgrom, seminar participants at Northwestern University, the University of Chicago, the 1984 Summer Meetings of the Econometric Society, University of California at Berkeley, Stanford University, and Yale University, and the financial support of the National Science Foundation (SES-8409786, SES-8606581)     

A multistage model to evaluate the efficiency the bar industry

This research examines the efficiency of Spanish bar firms using a panel data of 1071 firms during the period 2005–2014. The analysis begins with the estimation of a dynamic multistage Data Envelopment Analysis (DEA) model to evaluate firm efficiency. Second, the study analyzes regional efficiency across regions and provinces. Third, the study sheds light on the link between efficiency scores, and location, economic conditions, labour skills and training, health, pollution problems and other environmental variables and information and communication technologies. The results offer novel insights into socioeconomic and environmental factors and regional efficiency by focusing on an industry that has yet to be explored.     

Optimal contest design under reverse-lottery technology

In this paper, we study effort-maximizing contest design under the “reverse” nested lottery contest model of Fu et al. (2014) — which is the “mirror image” of the conventional nested lottery contest of Clark and Riis (1996). We show that under the reverse-lottery technology, a single-stage winner-take-all grand contest dominates all other feasible designs when the contest is sufficiently noisy. This result is in dramatic contrast to the conventional wisdom on the optimality of multistage elimination contests that is grounded under the conventional nested lottery contest technology in the literature. In the framework of a noisy-performance ranking model, the conventional and reverse models differ only in the noise on players’ performance. Our study therefore reveals the important role that the noise term plays in modeling imperfectly discriminatory contests.