Semiparametric Bayesian inference in smooth coefficient models

We describe procedures for Bayesian estimation and testing in both cross sectional and longitudinal data smooth coefficient models (with and without endogeneity problems). The smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate. In the approach we describe, points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves. The algorithms we describe are quite simple to implement - estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model, and estimation in the hierarchical models only involves simulation from standard distributions. We apply our methods by fitting several hierarchical models using data from the National Longitudinal Survey of Youth (NLSY). We explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability. In a generalization of this model, we also permit endogeneity of schooling and describe simulation-based methods for inference in the presence of the endogeneity problem. We find returns to schooling are approximately constant throughout the ability support and that simpler (and often used) parametric specifications provide an adequate description of these relationships.

Schools, School Quality and Academic Achievement: Evidence from the Philippines

A broad literature seeks to assess the importance of schools, proxies for school quality, and family background on children's achievement growth using the education production function. Using rich data from the Philippines, we introduce and estimate a model that imposes little structure on the relationship between intake achievement and follow-up achievement and evaluate school performance based on this estimated relationship. Our methods nest typical value added specifications that use test score gains as the outcome variable and models assuming linearity in the relationship between intake and follow-up scores. We find evidence against the use of value-added models for our data and show that such models give very different assessments of school performance in the Philippines. Using a variety of tests we find that schools matter in the production of student achievement, though variation in performance across schools only explain about 6 percent of the total (conditional) variation in follow-up achievement. Schools providing basic facilities - in particular schools providing electricity - are found to perform much better in the production of achievement growth.

Bayesian Modeling of School Effects Using Hierarchical Models with Smoothing Priors

We describe a new and flexible framework for modeling school effects. Like previous work in this area, we introduce an empirical model that evaluates school performance on the basis of student level test-score gains. Unlike previous work, however, we introduce a flexible model that relates follow-up student test scores to baseline student test scores and explore for possible nonlinearities in these relationships. Using data from High School and Beyond (HSB) and adapting the methodology described in Koop and Poirier (2004a), we test and reject the use of specifications that have been frequently used in research and as a basis for policy. We find that nonlinearities are important in the relationship between intake and follow-up achievement, that rankings of schools are sensitive to the model employed, and importantly, that commonly used specifications can give different and potentially misleading assessments of school performance. When estimating our preferred semiparametric specification, we find small but ``significant'' impacts of some school quality proxies (such as district-level expenditure per pupil) in the production of student achievement.

Bayesian Analysis of Structural Effects in an Ordered Equation System

We describe a new simulation-based algorithm for Bayesian estimation of structural effects in models where the outcome of interest and an endogenous treatment variable are ordered. Our algorithm makes use of a reparameterization, suggested by Nandram and Chen (1996) in the context of a single equation ordered-probit model, which significantly improves the mixing of the standard Gibbs sampler. We illustrate the improvements afforded by this new algorithm in a generated data experiment and also make use of our methods in an empirical application. Specifically, we take data from the National Longitudinal Survey of Youth (NLSY) and investigate the impact of maternal alcohol consumption on early infant health. Our results show clear evidence that the health outcomes of infants whose mothers drink while pregnant are worse than the outcomes of infants whose mothers never consumed alcohol while pregnant. In addition, the estimated parameters clearly suggest the need to control for the endogeneity of maternal alcohol consumption.

Semiparametric Bayesian inference in multiple equation models

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We develop an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent normal-Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two-equation structural model drawn from the labour and returns to schooling literatures

Bayesian Semiparametric Inference in Multiple Equation Models

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We derive an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent Normal-Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two-equation structural model drawn from the labor and returns to schooling literatures.nonparametric regression; nonparametric instrumental variables; SUR model; endogeneity; nonlinear simultaneous equations

Controlling for Observed and Unobserved Site Characteristics in Rum Models of Recreation Demand

�Random Utility Maximization (RUM) models of recreation demand are typically plagued by limited information on environmental and other attributes characterizing the available sites in the choice set. To the extent that these unobserved site attributes are correlated with the observed characteristics and/or the key travel cost variable, the resulting parameter estimates and subsequent welfare calculations are likely to be biased. In this paper we develop a Bayesian approach to estimating a RUM model that incorporates a full set of alternative specific constants, insulating the key travel cost parameter from the influence of the unobserved site attributes. In contrast to estimation procedures recently outlined in Murdock (2006), the posterior simulator we propose (combining data augmentation and Gibbs sampling techniques) can be used in the more general mixed logit framework in which some parameters of the conditional utility function are random. Following a series of generated data experiments to illustrate the performance of the simulator, we apply the estimation procedures to data from the Iowa Lakes Project. In contrast to an earlier study using the same data (Egan \textit{et al.} \cite{eganetal}), we find that, with the addition of a full set of alternative specific constants, water quality attributes no longer appear to influence the choice of where to recreate.nonmarket valuation; water quality; discrete choice

What Are the Consequences of Consequentiality?

We offer an empirical test of a theoretical result in the contingent valuation literature. Specifically, it has been argued from a theoretical point of view that survey participants who perceive a survey to be ``consequential'' will respond to questions truthfully regardless of the degree of perceived consequentiality. Using survey data from the Iowa Lakes Project, we test this supposition. Specifically, we employ a Bayesian treatment effect model in which the degree of perceived consequentiality, measured as an ordinal response, is permitted to have a structural impact on willingness to pay (WTP) for a hypothetical environmental improvement. We test the theory by determining if the WTP distributions are the same for each value of the ordinal response. In our survey data, a subsample of individuals were randomly assigned supporting information suggesting that their responses to the questionnaires were important and will have an impact on policy decisions. In conjunction with a Bayesian posterior simulator, we use this source of exogenous variation to identify the structural impacts of consequentiality perceptions on willingness to pay, while controlling for the potential of confounding on unobservables. We find evidence consistent with the ``knife-edge'' theoretical results, namely that the willingness to pay distributions are equal among those believing the survey to be at least minimally consequential, and different for those believing that the survey is irrelevant for policy purposes.nonmarket valuation

Experimental demonstration of direct path state characterization by strongly measuring weak values in a matter-wave interferometer

A novel method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently Vallone and Dequal showed theoretically that weak measurements are not a necessary condition to determine the weak value [Phys. Rev. Lett. 116, 040502 (2016)]. Here we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system's quantum state was characterized via direct measurements using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones. Our results are not limited to neutron interferometry, but can be used in a wide range of quantum systems.Comment: 5 pages, 3 figure