Partial identification of willingness-to-pay using shape restrictions with an application to the value of a statistical life

Economists often analyze cross-sectional data to estimate the value people implicit place on attributes of goods using hedonic methods. Usually strong enough assumptions are made on the functional form of utility to point identify individuals' willingness-to-pay (WTP) for changes in attribute levels. Instead, this paper develops a new way to partially identify WTP under a weak set of conditions on the shape of individual indifference curves. In particular, indifference curves are assumed to be increasing and convex in an attribute-cost space that is finitely bounded above. These shape restrictions provide informative partial identification without relying on functional form restrictions for utility. Identification given general, potentially discrete, as well as smooth price functions is analyzed. To illustrate this method, we contribute to the literature on the value of a statistical life (VSL) by analyzing labor market data to study people's willingness to pay (WTP) for reductions in levels of fatal risk. The paper contrasts VSL estimates from conventional analysis with the bounds obtained under this new approach using a common data set. The data are shown to be consistent with a wide range of WTP values even given equilibrium and credible shape restrictions. This suggests that conventional estimates may be driven by functional form restrictions imposed on utility rather than by the data or properties of equilibrium.

Partial Identification of Willingness-to-Pay Using Shape Restrictions with an Application to the Value of a Statistical Life

Economists often analyze cross-sectional data to estimate the value people implicit place on attributes of goods using hedonic methods. Usually strong enough assumptions are made on the functional form of utility to point identify individuals' willingness-to-pay (WTP) for changes in attribute levels. Instead, this paper develops a new way to partially identify WTP under a weak set of conditions on the shape of individual indifference curves. In particular, indifference curves are assumed to be increasing and convex in an attribute-cost space that is finitely bounded above. These shape restrictions provide informative partial identification without relying on functional form restrictions for utility. Identification given general, potentially discrete, as well as smooth price functions is analyzed. To illustrate this method, we contribute to the literature on the value of a statistical life (VSL) by analyzing labor market data to study people's willingness to pay (WTP) for reductions in levels of fatal risk. The paper contrasts VSL estimates from conventional analysis with the bounds obtained under this new approach using a common data set. The data are shown to be consistent with a wide range of WTP values even given equilibrium and credible shape restrictions. This suggests that conventional estimates may be driven by functional form restrictions imposed on utility rather than by the data or properties of equilibrium.hedonic, partial identification, value of a statistical life, shape restrictions

Partial Identification of Willingness-to-Pay Using Shape Restrictions with an Application to the Value of a Statistical Life

Economists often analyze cross-sectional data to estimate the value people implicit place on attributes of goods using hedonic methods. Usually strong enough assumptions are made on the functional form of utility to point identify individuals' willingness-to-pay (WTP) for changes in attribute levels. Instead, this paper develops a new way to partially identify WTP under a weak set of conditions on the shape of individual indifference curves. In particular, indifference curves are assumed to be increasing and convex in an attribute-cost space that is finitely bounded above. These shape restrictions provide informative partial identification without relying on functional form restrictions for utility. Identification given general, potentially discrete, as well as smooth price functions is analyzed. To illustrate this method, we contribute to the literature on the value of a statistical life (VSL) by analyzing labor market data to study people's willingness to pay (WTP) for reductions in levels of fatal risk. The paper contrasts VSL estimates from conventional analysis with the bounds obtained under this new approach using a common data set. The data are shown to be consistent with a wide range of WTP values even given equilibrium and credible shape restrictions. This suggests that conventional estimates may be driven by functional form restrictions imposed on utility rather than by the data or properties of equilibrium

Inference on Peer Effects with Missing Peer Data: Evidence from Project STAR

This paper studies peer effects on student achievement among first graders randomly assigned to classrooms in Tennessee's Project STAR. The analysis uses previously unexploited pre-assignment achievement measures available for 60 percent of students. Data are not missing at random, making identification challenging. The paper develops new ways, given random assignment of individuals to classes, to identify peer effects without imposing other missing-data assumptions. Estimates suggest positive effects of mean peer lagged achievement on average. Allowing heterogeneous effects, evidence suggests lower-achieving students benefit more than higher-achieving students do from increases in peer mean. Further, the bias in a widely used, poorly understood peer-effects estimator is analyzed, implying that caution is warranted in interpreting many peer-effects estimates extant in the literature.

When Does Teacher Incentive Pay Raise Student Achievement? Evidence from Minnesota's Q-Comp Program

Since 2005, dozens of Minnesota school districts have implemented pay for performance (P4P) plans as part of the state's Quality Compensation (Q-Comp) program. This paper performs the first systematic study of Q-Comp's impact on student achievement, exploiting variation across districts in the timing of participation as well as in the design of districts' P4P plans to study effects on achievement for grades 3 through 8. Results show a consistent zero average effect of Q-Comp participation on both reading and math achievement. However, effects on reading achievement differ depending on the design of the P4P plan. Specifically, districts offering greater rewards for teacher-centered actions or outcomes evidently experienced large gains in reading (0.11 SD per $1,000 bonus) while those offering rewards based on school-wide goals or formal subjective evaluations did not. Gains from specific P4P design features were not consistently evident in math. We also study effects on other outcomes, such as teacher characteristics and parent demand.

Identification of Peer Effects with Missing Peer Data: Evidence from Project STAR

This paper studies peer effects on student achievement among first graders randomly assigned to classrooms in Tennessee’s Project STAR. The analysis uses previously unexploited pre-assignment achievement measures available for 60 percent of students. Data are not missing at random, making identification challenging. The paper develops new ways, given random assignment of individuals to classes, to identify peer effects without imposing other missing-data assumptions. Estimates suggest positive effects of mean peer lagged achievement on average. Allowing heterogeneous effects, evidence suggests lower-achieving students benefit more than higher-achieving students do from increases in peer mean. Further, the bias in a widely used, poorly understood peer-effects estimator is analyzed, implying that caution is warranted in interpreting many peer-effects estimates extant in the literature.peers, missing data, education

Same Program, Different Outcomes: Understanding Differential Effects from Access to Free, High-Quality Early Care

The Infant Health and Development Program (IHDP) was designed to promote the development of low-birth weight (up to 2,500 grams) and premature (up to 37 weeks gestational age) infants. There is evidence that the IHDP intervention, a randomly-assigned bundle of services including primarily free, high-quality child care from 12 to 36 months, boosted cognitive and behavioral outcomes by the time participants at the end of the intervention. The literature has established that the intervention was more effective among the subsample of heavier low birth weight (2,000-2,500 grams) than among those born lighter. Among the heavier group, it was more effective for children from lower-income families. Families who participated in the intervention were diverse in key observable characteristics like income, race or ethnicity. In addition, families reallocated their time in different ways when then had the opportunity to use the free services provided by the IHDP. The goal of this paper is to understand the economic decisions and constraints faced by households who gained access to the IHDP and explain their differential behavior. In order to do so, we propose an economic model, construct measures of theoretically-relevant drivers of postnatal investment decisions, and explore patterns of heterogeneity in parental response and child development along these dimensions

Effects of Unionization on Workplace-Safety Enforcement: Regression-Discontinuity Evidence

We study how union certification affects the enforcement of workplace-safety laws. To generate credible causal estimates, a regression discontinuity design compares outcomes in establishments where unions barely won representation elections to outcomes in establishments where union barely lost such elections. The study combines two main datasets: the census of National Labor Relations Board (NLRB) representation elections and the Occupational Safety and Health Administration's (OSHA) enforcement database since 1985. There is evidence of positive effects of union certification on establishment's rate of OSHA inspection, the share of inspections carried out in the presence of a labor representative, violations cited, and penalties assessed