Bayesian inference in a sample selection model

This paper develops methods of Bayesian inference in a sample selection model. The main feature of this model is that the outcome variable is only partially observed. We first present a Gibbs sampling algorithm for a model in which the selection and outcome errors are normally distributed. The algorithm is then extended to analyze models that are characterized by nonnormality. Specifically, we use a Dirichlet process prior and model the distribution of the unobservables as a mixture of normal distributions with a random number of components. The posterior distribution in this model can simultaneously detect the presence of selection effects and departures from normality. Our methods are illustrated using some simulated data and an abstract from the RAND health insurance experiment.     

Regression density estimation using smooth adaptive Gaussian mixtures

We model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the components changing smoothly as a function of the covariates. The model extends the existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when the number of covariates is large. Furthermore, we typically need fewer components, which makes it easier to interpret the model and speeds up the computation. The second main extension is to introduce a novel variable selection prior into all the components of the model. The variable selection prior acts as a self-adjusting mechanism that prevents overfitting and makes it feasible to fit flexible high-dimensional surfaces. We use Bayesian inference and Markov Chain Monte Carlo methods to estimate the model. Simulated and real examples are used to show that the full generality of our model is required to fit a large class of densities, but also that special cases of the general model are interesting models for economic data.     

Estimating willingness to pay for medicare using a dynamic life-cycle model of demand for health insurance

Medicare is the largest health insurance program in the US. This paper uses a dynamic random utility model of demand for health insurance in a life-cycle human capital framework with endogenous production of health to calculate the individual willingness to pay (WTP) for Medicare. The model accounts for the feature that the demand for health insurance is derived through the demand for health, which is jointly determined with the production of health over the life-cycle. The WTP measure incorporates the effects of Medicare insurance on aggregate consumption through effects on medical expenditures and mortality, and consumption utility of health. The model is estimated using panel data from the Health and Retirement Study. The average WTP or change in lifetime expected utility resulting from delaying the age of eligibility to 67 is found to be $ 24,947 in 1991 dollars ($ 39,435 in 2008 dollars). However, there is considerable variation in the WTP, e.g., in 1991 dollars the WTP of individuals who have less than a high school education and are white is $ 28,347 ($ 44,810 in 2008 dollars), while the WTP of those with at least a college degree and who are neither white nor black is $ 15,584 ($ 24,635 in 2008 dollars). More generally, the less educated have a higher WTP to avoid a policy change that delays availability of Medicare benefits. Additional model simulations imply that the primary benefits of Medicare are insurance against medical expenditures with relatively smaller benefits in terms of improved health status and longevity. Medicare also leads to large increases in medical utilization due to deferring of medical care prior to eligibility.     

Doubly robust uniform confidence band for the conditional average treatment effect function

In this paper, we propose a doubly robust method to estimate the heterogeneity of the average treatment effect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment effect but the covariates of interest for analyzing heterogeneity are of much lower dimension. Our proposed estimator is doubly robust and avoids the curse of dimensionality. We propose a uniform confidence band that is easy to compute, and we illustrate its usefulness via Monte Carlo experiments and an application to the effects of smoking on birth weights.     

A flexible parametric approach for estimating switching regime models and treatment effect parameters

In this paper, we propose a flexible, parametric class of switching regime models allowing for both skewed and fat-tailed outcome and selection errors. Specifically, we model the joint distribution of each outcome error and the selection error via a newly constructed class of multivariate distributions which we call generalized normal mean–variance mixture distributions. We extend Heckman’s two-step estimation procedure for the Gaussian switching regime model to the new class of models. When the distributions of the outcome errors are asymmetric, we show that an additional correction term accounting for skewness in the outcome error distribution (besides the analogue of the well known inverse mill’s ratio) needs to be included in the second step regression. We use the two-step estimators of parameters in the model to construct simple estimators of average treatment effects and establish their asymptotic properties. Simulation results confirm the importance of accounting for skewness in the outcome errors in estimating both model parameters and the average treatment effect and the treatment effect for the treated.     

A structural analysis of the correlated random coefficient wage regression model

We estimate a dynamic programming model of schooling decisions in which the log wage regression function is set within a correlated random coefficient model. We show that estimates of the dynamic programming model can be used to obtain a number of treatment effects, including the local average treatment effect (LATE). However, unlike LATE parameters obtained in a standard IV framework, our LATE estimates are obtained without imposing separability between individual specific heterogeneity and schooling choices and are therefore not subject to a “monotonicity” restriction. We find that returns to schooling are characterized by a high degree of dispersion across individuals.     

Generalized smooth finite mixtures

We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates through a link function. Our MCMC methodology allows for Bayesian variable selection among the covariates in the mixture components and in the mixing weights. The model’s parameterization and variable selection prior are chosen to prevent overfitting. We use simulated and real data sets to illustrate the methodology.     

Time and causality: A Monte Carlo assessment of the timing-of-events approach

We present new Monte Carlo evidence regarding the feasibility of separating causality from selection within non-experimental duration data, by means of the non-parametric maximum likelihood estimator (NPMLE). Key findings are: (i) the NPMLE is extremely reliable, and it accurately separates the causal effects of treatment and duration dependence from sorting effects, almost regardless of the true unobserved heterogeneity distribution; (ii) the NPMLE is normally distributed, and standard errors can be computed directly from the optimally selected model; and (iii) unjustified restrictions on the heterogeneity distribution, e.g., in terms of a pre-specified number of support points, may cause substantial bias.     

股权激励如何驱动企业研发支出？——基于股权激励异质性的视角

股权激励被视为解决研发支出中代理冲突的重要工具,但现有经验证据并不稳定甚至相互矛盾。基于股权激励异质性的视角,本文引入新的股权激励特征——股权激励价值的股价及股价波动率敏感性,考察股权激励对企业研发支出的驱动机制,并利用2006-2012年我国实施股权激励的上市公司作为样本进行检验。研究发现:股权激励对企业研发支出的驱动机制包含风险规避效应与激励效应两个相反维度,最终驱动方向与强度取决于两类效应的博弈;限制性股票的风险规避效应显著强于股票期权;股票期权的激励效应显著强于限制性股票;市场竞争程度、企业产权性质与授予动机对限制性股票与股票期权的两类效应产生调节作用。     

A semi-parametric Bayesian approach to the instrumental variable problem

We develop a Bayesian semi-parametric approach to the instrumental variable problem. We assume linear structural and reduced form equations, but model the error distributions non-parametrically. A Dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors. Our implementation of the Dirichlet process prior uses a normal distribution as a base model. It can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components. We demonstrate that this procedure is both feasible and sensible using actual and simulated data. Sampling experiments compare inferences from the non-parametric Bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics. When errors are non-normal, our procedure is more efficient than standard Bayesian or classical methods.     

Learning and the value of information: Evidence from health plan report cards

This paper develops a framework to analyze the value of information in the context of health plan choice. We use a Bayesian learning model to estimate the impact and value of information using data from a large employer, which started distributing health plan ratings to its employees in 1997. We estimate the parameters of the model with simulated maximum likelihood, and use the estimates to quantify the value of the report card information. We model both continuous specifications with Gaussian priors and signals, and discrete specifications with Beta priors and Binomial signals. We find that the release of information had a statistically significant effect on health plan choices. Consumers were willing to pay about $330 per year per below expected performance rating avoided, and the average value of the report card per employee was about $20 per year. We find large variation in valuations across different performance domains, but no significant evidence of heterogeneity based on observable employee characteristics or unobservable dimensions.     

Enticing the Stork: Can we Evaluate Pro‐Natal Policies Before Having Children?

Aside from immigration, the only meaningful demographic lever available to policymakers attempting to moderate the rate of ageing is the birth rate. This article departs from previous analyses of pro‐natal policies by studying determinants of pro‐natal options ex ante, which represents an advantage for policymakers looking to craft policies with prior knowledge of whether or not a demographic policy will have a significant effect. Our multinomial regression model for a US sample involving college students shows that the preferred choice of pro‐natal incentive is dependent on gender, economic class, number of planned children and migrant status. We find that females are more likely than males to choose any pro‐natal incentive over no incentive. The highest odds for increasing planned number of children are for maternity leave and parental leave options. Respondents associating themselves with the poorest economic class are more likely to choose daycare or government grant as pro‐natal options.     

Hospital competition under pay‐for‐performance: Quality,mortality, and readmissions

Health outcomes, such as mortality and readmission rates, are commonly used as indicators of hospital quality and as a basis to design pay‐for‐performance (P4P) incentive schemes. We propose a model of hospital behavior under P4P where patients differ in severity and can choose hospital based on quality. We assume that risk‐adjustment is not fully accounted for and that unobserved dimensions of severity remain. We show that the introduction of P4P which rewards lower mortality and/or readmission rates can weaken or strengthen hospitals' incentive to provide quality. Since patients with higher severity have a different probability of exercising patient choice when quality varies, this introduces a selection bias (patient composition effect) which in turn alters quality incentives. We also show that this composition effect increases with the degree of competition. Critically, readmission rates suffer from one additional source of selection bias through mortality rates since quality affects the distribution of survived patients. This implies that the scope for counterproductive effects of P4P is larger when financial rewards are linked to readmission rates rather than mortality rates.     

A latent class poisson regression model for heterogeneous count data

In this paper an approach is developed that accommodates heterogeneity in Poisson regression models for count data. The model developed assumes that heterogeneity arises from a distribution of both the intercept and the coefficients of the explanatory variables. We assume that the mixing distribution is discrete, resulting in a finite mixture model formulation. An EM algorithm for estimation is described, and the algorithm is applied to data on customer purchases of books offered through direct mail. Our model is compared empirically to a number of other approaches that deal with heterogeneity in Poisson regression models.     

Public university orientation for high-school students. A quasi-experimental assessment of the efficiency gains from nudging better career choices

We adopt a quasi-experimental approach to measure the causal effect, on first-year students in bachelor-level courses at the Department of Economics and Business Studies of the University of Genoa, Italy, of having been treated to a recently activated orientation program when they were high school seniors. Improvements are evaluated at the end of the first academic year in terms of grade point average (GPA), inactivity (failing to pass even a single exam) and number of successfully completed exams. Treatment effects on GPA are estimated both for the overall treatment group and for subsamples consisting of treated students with high and with low high school exit grades. After performing several sensitivity checks, a sizeable treatment effect is confirmed both in terms of inactivity and in terms of average GPA. No clear effect was found on the number of exams. Effects on GPA are considerably stronger on students with lower high school exit grades.     

Variable selection and functional form uncertainty in cross-country growth regressions

Regression analyses of cross-country economic growth data are complicated by two main forms of model uncertainty: the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function. Most discussions in the literature address these problems independently, yet a joint treatment is essential. We present a new framework that makes such a joint treatment possible, using flexible nonlinear models specified by Gaussian process priors and addressing the variable selection problem by means of Bayesian model averaging. Using this framework, we extend the linear model to allow for parameter heterogeneity of the type suggested by new growth theory, while taking into account the uncertainty in selecting explanatory variables. Controlling for variable selection uncertainty, we confirm the evidence in favor of parameter heterogeneity presented in several earlier studies. However, controlling for functional form uncertainty, we find that the effects of many of the explanatory variables identified in the literature are not robust across countries and variable selections.     

Evolution of forecast disagreement in a Bayesian learning model

We estimate a Bayesian learning model with heterogeneity aimed at explaining expert forecast disagreement and its evolution over horizons. Disagreement is postulated to have three components due to differences in: (i) the initial prior beliefs, (ii) the weights attached on priors, and (iii) interpreting public information. The fixed-target, multi-horizon, cross-country feature of the panel data allows us to estimate the relative importance of each component precisely. The first component explains nearly all to 30% of forecast disagreement as the horizon decreases from 24 months to 1 month. This finding firmly establishes the role of initial prior beliefs in generating expectation stickiness. We find the second component to have barely any effect on the evolution of forecast disagreement among experts. The importance of the third component increases from almost nothing to 70% as the horizon gets shorter via its interaction with the quality of the incoming news. We propose a new test of forecast efficiency in the context of Bayesian information processing and find significant heterogeneity in the nature of inefficiency across horizons and countries.     

The government wage bill and private activity

We estimate the macroeconomic effects of public wage expenditures in U.S. data by identifying shocks to public employment and public wages using sign restrictions. We find that public employment shocks are mildly expansionary at the federal level and strongly expansionary at the state and local level by crowding in private consumption and increasing labor force participation and private sector employment. Similarly, state and local government wage shocks lead to increases in consumption and output, while shocks to federal government wages induce significant contractionary effects. In a stylized DSGE model we show that the degree of complementarity between public and private goods in the consumption bundle is key for explaining the observed heterogeneity.