Yukitoshi Matsushita

Empirical likelihood for regression discontinuity design

This paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs. We consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric. The proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes, unlike the conventional Wald-type method. These features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils’ scholastic achievements. Furthermore, for the sharp regression discontinuity design, we show that the empirical likelihood statistic admits a higher-order refinement, so-called the Bartlett correction. Bandwidth selection methods are also discussed.

Estimation and Inference of Discontinuity in Density

Continuity or discontinuity of probability density functions of data often plays a fundamental role in empirical economic analysis. For example, for identification and inference of causal effects in regression discontinuity designs it is typically assumed that the density function of a conditioning variable is continuous at a cutoff point that determines assignment of a treatment. Also, discontinuity in density functions can be a parameter of economic interest, such as in analysis of bunching behaviors of taxpayers. To facilitate researchers to conduct valid inference for these problems, this article extends the binning and local likelihood approaches to estimate discontinuity of density functions and proposes empirical likelihood-based tests and confidence sets for the discontinuity. In contrast to the conventional Wald-type test and confidence set using the binning estimator, our empirical likelihood-based methods (i) circumvent asymptotic variance estimation to construct the test statistics and confidence sets; (ii) are invariant to nonlinear transformations of the parameters of interest; (iii) offer confidence sets whose shapes are automatically determined by data; and (iv) admit higher-order refinements, so-called Bartlett corrections. First- and second-order asymptotic theories are developed. Simulations demonstrate the superior finite sample behaviors of the proposed methods. In an empirical application, we assess the identifying assumption of no manipulation of class sizes in the regression discontinuity design studied by Angrist and Lavy (1999).

Second-Order Refinement of Empirical Likelihood for Testing Overidentifying Restrictions

This paper studies second-order properties of the empirical likelihood overidentifying restriction test to check the validity of moment condition models. We show that the empirical likelihood test is Bartlett correctable and suggest second-order refinement methods for the test based on the empirical Bartlett correction and adjusted empirical likelihood. Our second-order analysis supplements the one in Chen and Cui (2007) who considered parameter hypothesis testing for overidentified models. In simulation studies we find that the empirical Bartlett correction and adjusted empirical likelihood assisted by bootstrapping provide reasonable improvements for the properties of the null rejection probabilities.

Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect

In the past few decades, much progress has been made in semiparametric modeling and estimation methods for econometric analysis. This paper is concerned with inference (i.e., confidence intervals and hypothesis testing) in semiparametric models. In contrast to the conventional approach based on t-ratios, we advocate likelihood-based inference. In particular, we study two widely applied semiparametric problems, weighted average derivatives and treatment effects, and propose semiparametric empirical likelihood and jackknife empirical likelihood methods. We derive the limiting behavior of these empirical likelihood statistics and investigate their finite sample performance via Monte Carlo simulation. Furthermore, we extend the (delete-1) jackknife empirical likelihood toward the delete-d version with growing d and establish general asymptotic theory. This extension is crucial to deal with non-smooth objects, such as quantiles and quantile average derivatives or treatment effects, due to the well-known inconsistency phenomena of the jackknife under non-smoothness.

Public health and multiple-phase mortality decline: Evidence from industrializing Japan

&NA; A growing body of literature shows the mitigating effects of water‐supply systems on the mortality rates in large cities, yet the heterogeneities in the effects have been understudied. This study fills in the gap in existing knowledge by providing evidence for non‐linearity in the effects of clean water using semiparametric fixed effects approach with city‐level nationwide longitudinal dataset between 1922 and 1940, which covers 91% of total city population. According to our baseline estimate, the clean water accounts for approximately 27% of the decrease in the crude death rate in this period. Our results also indicate the heterogeneities in the improving effects of clean water with respect to the coverage of tap water among citizens. We found evidence that the installation of the water‐supply system itself decreased waterborne infections and infant mortality but did not substantially improve the overall mortality rate in the initial phase. However, the subsequent expansion of tap water could result in a continuous decline in the overall risk of deaths in the second phase. HighlightsWe estimate the heterogeneous treatment effects of safe water on the mortality rates.Semiparametric fixed effects approach is implemented to identify the non‐linearity.A long‐run city‐level panel data covering more than 90% of city population is used.Multiple‐phase decline of mortality rates as for water accessibility is observed.

Moment Estimation of the Probit Model with an Endogenous Continuous Regressor

We propose an efficient moment estimator for the probit model with a continuous endogenous regressor. The estimation can be readily implemented using a standard statistical package that can estimate a non-linear system two-stage least squares (instrumental variable) estimator.