Who Benefits from Marriage?*

The phenomenon that married men earn higher average wages than unmarried men – the marriage premium – is well known. However, the robustness of the premium across the wage distribution and the underlying causes of the marriage premium are unclear. Focusing on the entire wage distribution and employing recently developed semi‐non‐parametric tests for quantile treatment effects, our findings cast doubt on the robustness of the premium. We find that the premium is explained by selection above the median, whereas a positive premium is obtained only at very low wages. The causal effect at low wages may be attributable to employer discrimination.     

On Bayesian analysis and computation for functions with monotonicity and curvature restrictions

Our goal is inference for shape-restricted functions. Our functional form consists of finite linear combinations of basis functions. Prior elicitation is difficult due to the irregular shape of the parameter space. We show how to elicit priors that are flexible, theoretically consistent, and proper. We demonstrate that uniform priors over coefficients imply priors over economically relevant quantities that are quite informative and give an example of a non-uniform prior that addresses this issue. We introduce simulation methods that meet challenges posed by the shape of the parameter space. We analyze data from a consumer demand experiment.     

Exogeneity in structural equation models

The practical relevance of several concepts of exogeneity of treatments for the estimation of causal parameters based on observational data are discussed. We show that the traditional concepts, such as strong ignorability and weak and super-exogeneity, are too restrictive if interest lies in average effects (i.e. not on distributional effects of the treatment). We suggest a new definition of exogeneity, KL-exogeneity. It does not rely on distributional assumptions and is not based on counterfactual random variables. As a consequence it can be empirically tested using a proposed test that is simple to implement and is distribution-free.     

Edgeworth expansions and normalizing transforms for inequality measures

Finite sample distributions of studentized inequality measures differ substantially from their asymptotic normal distribution in terms of location and skewness. We study these aspects formally by deriving the second-order expansion of the first and third cumulant of the studentized inequality measure. We state distribution-free expressions for the bias and skewness coefficients. In the second part we improve over first-order theory by deriving Edgeworth expansions and normalizing transforms. These normalizing transforms are designed to eliminate the second-order term in the distributional expansion of the studentized transform and converge to the Gaussian limit at rate O(n⁻¹)$O\left(n^{-1}\right)$. This leads to improved confidence intervals and applying a subsequent bootstrap leads to a further improvement to order O(n^−3/2)$O\left(n^{-3/2}\right)$. We illustrate our procedure with an application to regional inequality measurement in Côte d’Ivoire.     

Estimation of collective household models with Engel curves

The structural consumer demand methods used to estimate the parameters of collective household models are typically either very restrictive and easy to implement or very general and difficult to estimate. In this paper, we provide a middle ground. We adapt the very general framework of [Browning, M., Chiappori, P.A., Lewbel, A., 2004. Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power, Boston College Working Papers in Economics 588] by adding a simple restriction that recasts the empirical model from a highly nonlinear demand system with price variation to a slightly nonlinear Engel curve system. Our restriction has an interpretation in terms of the behaviour of household scale economies and is testable. Our method identifies the levels of (not just changes in) household resource shares, and a variant of equivalence scales called indifference scales. We apply our methodology to Canadian expenditure data.     

Testing and imposing Slutsky symmetry in nonparametric demand systems

Maximization of utility implies that consumer demand systems have a Slutsky matrix which is everywhere symmetric. However, previous non- and semi-parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition, nor do they offer powerful tests of this restriction. We use nonparametric modeling to test and impose Slutsky symmetry in a system of expenditure share equations over prices and expenditure. In this context, Slutsky symmetry is a set of nonlinear cross-equation restrictions on levels and derivatives of consumer demand equations. The key insight is that due to the differing convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives, both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were (locally) linear. We establish large and finite sample properties of our methods, and show that our test has advantages over the only other comparable test. All methods we propose are implemented with Canadian micro-data. We find that our nonparametric analysis yields statistically significantly and qualitatively different results from traditional parametric estimators and tests.     

EL inference for partially identified models: Large deviations optimality and bootstrap validity

This paper addresses the issue of optimal inference for parameters that are partially identified in models with moment inequalities. There currently exists a variety of inferential methods for use in this setting. However, the question of choosing optimally among contending procedures is unresolved. In this paper, I first consider a canonical large deviations criterion for optimality and show that inference based on the empirical likelihood ratio statistic is optimal. Second, I introduce a new empirical likelihood bootstrap that provides a valid resampling method for moment inequality models and overcomes the implementation challenges that arise as a result of non-pivotal limit distributions. Lastly, I analyze the finite sample properties of the proposed framework using Monte Carlo simulations. The simulation results are encouraging.     

Extending the regression-discontinuity approach to multiple assignment variables

The recent scholarly attention to the regression-discontinuity design has focused exclusively on the application of a single assignment variable. In many settings, however, exogenously imposed cutoffs on several assignment variables define a set of different treatments. In this paper, we show how to generalize the standard regression-discontinuity approach to include multiple assignment variables simultaneously. We demonstrate that fitting this general, flexible regression-discontinuity model enables us to estimate several treatment effects of interest.     

Reliable inference for the Gini index

Although attention has been given to obtaining reliable standard errors for the plug-in estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference based on the approximation is checked in a number of simulation experiments, and is found to be very good unless the tail of the underlying distribution is heavy. Bootstrap methods are presented which alleviate this problem except in cases in which the variance is very large or fails to exist. Similar methods can be used to find reliable standard errors of other indices which are not simply linear functionals of the distribution function, such as Sen’s poverty index and its modification known as the Sen–Shorrocks–Thon index.     

The impact of the National School Lunch Program on child health: A nonparametric bounds analysis

Children in households reporting the receipt of free or reduced-price school meals through the National School Lunch Program (NSLP) are more likely to have negative health outcomes than observationally similar nonparticipants. Assessing causal effects of the program is made difficult, however, by missing counterfactuals and systematic underreporting of program participation. Combining survey data with auxiliary administrative information on the size of the NSLP caseload, we extend nonparametric partial identification methods that account for endogenous selection and nonrandom classification error in a single framework. Similar to a regression discontinuity design, we introduce a new way to conceptualize the monotone instrumental variable (MIV) assumption using eligibility criteria as monotone instruments. Under relatively weak assumptions, we find evidence that the receipt of free and reduced-price lunches improves the health outcomes of children.     

Wages and Ageing: Is There Evidence for the ‘Inverse‐U’ Profile?*

How individual wages change with time is one of the crucial determinants of labour market decisions including the timing of retirement. The focus of this paper is the relationship between age and wages with special attention given to individuals nearing retirement. The analysis is presented in a comparative context for Britain and Germany looking at two longitudinal data sets (BHPS and SOEP, respectively) for the years 1995–2004. We show the importance of cohort effects and selection out of employment which determine the downward‐sloping part of the ‘inverse‐U’ profile observed in cross‐sections. There is little evidence that wages fall with age.