Charles F. Manski

Identification of Endogenous Social Effects: The Reflection Problem

This paper examines the reflection problem that arises when a researcher observing the distribution of behaviour in a population tries to infer whether the average behaviour in some group influences the behaviour of the individuals that comprise the group. It is found that inference is not possible unless the researcher has prior information specifying the compisition of reference groups. If this information is available, the prospects for inference depend critically on the population relationship between the variables defining reference groups and those directly affecting outcomes. Inference is difficult to implossible if these variables are functionally dependent or are statistically independent. The prospects are better if the variables defining reference groups and those directly affecting outcomes are moderately related in the population.

The structure of random utility models

I am grateful to Joseph B. Kadane for numerous constructive suggestions offered during discussions of this research. The financial sponsorship of the U.S. Department of Transportation through grant DOT-OS-4006 is also acknowledged. The opinions and conclusions expressed herein are solely those of the author.

The Estimation of Choice Probabilities from Choice Based Samples

Ti-H CONCERN of this paper is the estimation of the parameters of a probabilistic choice model when choices rather than decision makers are sampled. Existing estimation methods presuppose an exogeneous sampling process, that is one in which a sequence of decision makers are drawn and their choice behaviors observed. In contrast, in choice based sampling processes, a sequence of chosen alternatives are drawn and the characteristics of the decision makers selecting those alternatives are observed. The problem of estimating a choice model from a choice based sample has suibstantive interest because data collection costs for such processes are often considerably smaller than for exogeneous sampling. Particular instances of this differential occur in the analysis of transportation behavior. For example, in studying choice of mode for work trips, it is often less expensive to survey transit users at the station and auto users at the parking lot than to interview commuters at their homes. Similarly, in examining choice of destination for shopping trips, surveys conducted at various shopping centers offer significant cost savings relative to home interviews.2 While interest in transportation applications provided the original motivation for our work, it has become apparent that choice based sampling processes can be cost effective in the analysis of numerous decision problems. In particular, wherever decision makers are physically clustered according to the alternatives they select, choice based sampling processes can achieve economies of scale not available with exogeneous sampling. Some non-transportation decision problems in which decision makers do cluster as described include the schooling decisions of students, the job decisions of workers, the medical care decisions of patients and the residential location decisions of households. Realization of the sampling cost benefits of choice based samples presupposes of course that the parameters of the underlying choice model can logically be inferred from such samples and that a tractable estimator with desirable statistical properties can be found. We shall, in this paper, confirm the logical supposition, develop a suitable estimator, and characterize the behavior of existing, exogeneous sampling, estimators in the context of choice based samples. An outline of the presentation and summary of major results follows.

College Choice in America

The most crucial choice a high school graduate makes is whether to attend college or to go to work. Here is the most sophisticated study of the complexities behind that decision. Based on a unique data set of nearly 23,000 seniors from more than 1,300 high schools who were tracked over several years, the book treats the following questions in detail: Who goes to college? Does low family income prevent some young people from enrolling, or does scholarship aid offset financial need? How important are scholastic aptitude scores, high school class rank, race, and socioeconomic background in determining college applications and admissions? Do test scores predict success in higher education? Using the data from the National Longitudinal Study of the Class of 1972, the authors present a set of interrelated analyses of student and institutional behavior, each focused on a particular aspect of the process of choosing and being chosen by a college. Among their interesting findings: most high school graduates would be admitted to some four-year college of average quality, were they to apply; applicants do not necessarily prefer the highest-quality school; high school class rank and SAT scores are equally important in college admissions; federal scholarship aid has had only a small effect on enrollments at four-year colleges but a much stronger effect on attendance at two-year colleges; the attention paid to SAT scores in admissions is commensurate with the power of the scores in predicting persistence to a degree. This clearly written book is an important source of information on a perpetually interesting topic.

MAXIMUM SCORE ESTIMATION OF THE STOCHASTIC UTILITY MODEL OF CHOICE

This paper introduces a class of robust estimators of the parameters of a stochastic utility function. Existing maximum likelihood and regression estimation methods require the assumption of a particular distributional family for the random component of utility. In contrast, estimators of the ‘maximum score’ class require only weak distributional assumptions for consistency. Following presentation and proof of the basic consistency theorem, additional results are given. An algorithm for achieving maximum score estimates and some small sample Monte Carlo tests are also described.

Semiparametric analysis of discrete response. Asymptotic properties of the maximum score estimator

Abstract This paper is concerned with the estimation of the model MED(y|x) = xβ from a random sample of observations on (sgn y, x). Manski (1975) introduced the maximum score estimator of the normalized parameter vector β ∗ = β/∦β∦ . In the present paper, strong consistency is proved. It is also proved that the maximum score estimate lies outside any fixed neighborhood of β∗ with probability that goes to zero at exponential rate.

Anatomy of the Selection Problem

This article considers anew the problem of estimating a regression E(y|x) when realizations of (y, x) are sampled randomly but y is observed selectively. The central issue is the failure of the sampling process to identify E(y|x). The problem faced by the researcher is to find correct prior restrictions which, when combined with the data, identify the regression. Two kinds of restrictions are examined here. One, which has not been studied before, is a bound on the support of y. Such a bound implies a simple, useful bound on E(y|x). The other, which has received much attention, is a separability restriction derived from a latent variable model.

Nonparametric Analysis of Randomized Experiments with Missing Covariate and Outcome Data

Abstract Analysis of randomized experiments with missing covariate and outcome data is problematic, because the population parameters of interest are not identified unless one makes untestable assumptions about the distribution of the missing data. This article shows how population parameters can be bounded without making untestable distributional assumptions. Bounds are also derived under the assumption that covariate data are missing completely at random. In each case the bounds are sharp; they exhaust all of the information available given the data and the maintained assumptions. The bounds are illustrated with applications to data obtained from a clinical trial and data relating family structure to the probability that a youth graduates from high school.

Monotone Treatment Response

This paper investigates what may be learned about treatment response when it is assumed that response functions are monotone, semimonotone, or concave-monotone. Nothing is assumed about the process of treatment selection and cross-individual restrictions on response are not imposed. The idea is to determine, for every member of the population, the response functions that pass through the realized (treatment, outcome) pair and that are consistent with the assumption imposed. These findings are then aggregated to determine what can be learned about the population distribution of response. The analysis is applied to the econometrics of demand and production.

The Use of Intentions Data to Predict Behavior: A Best-Case Analysis

Abstract In surveys individuals are routinely asked to predict their future behavior, that is, to state their intentions. This article studies the relationship between stated intentions and subsequent behavior under the “best-case” hypothesis that individuals have rational expectations and that their responses to intentions questions are best predictions of their future behavior. The objective is to place an upper bound on the behavioral information contained in intentions data and to determine whether prevailing approaches to the analysis of intentions data respect the bound. The analysis focuses on the simplest form of intentions questions, those that call for yes/no predictions of binary outcomes. The article also discusses “forced-choice” questions, which are distinct from, but are sometimes confused with, intentions questions. A primary lesson is that not too much should be expected of intentions data. It is shown that intentions data bound but do not identify the probability that a person will behav...