Returns to Private Education in Peru

The private provision of educational services has been representing an increasing fraction of the Peruvian schooling system, especially in recentdecades. While there have been many claims about the differences in quality between private and public schools, there is no complete assessment of the different impacts of these two type of providers on the labor markets. This paper attempts to provide such a comprehensive overview by exploring private-public differences in the individual returns to education in Urban Peru. Exploiting a rich pair of data sets (ENNIV 1997 and 2000) that include questions on type of education (public vs. private) for each educational level (primary, secondary, technical tertiary and university tertiary) to a representative sample of adults, this paper measures the differences in labor earnings for all possible educational trajectories. The results indicate higher returns to education for those who attended private schools than those who attended the public system. Nonetheless, these higher returns also show higher dispersion, reflecting wider quality heterogeneity within the private system. The private-public differences in returns are more pronounced at the secondary than at any other educational level. On the other hand, the private-public differences in returns from technical education are almost nonexistent. A cohort approach paired with a rolling-windows technique allows us to capture generational evolutions of the private-public differences. The results indicate that these differences have been increasing during the last two decades.

Optimal Bandwidth Choice for Robust Bias Corrected Inference in Regression Discontinuity Designs

Modern empirical work in Regression Discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show they yield suboptimal confidence intervals in terms of coverage error. We establish valid coverage error expansions for RBC confidence interval estimators and use these results to propose new inference-optimal bandwidth choices for forming these intervals. We find that the standard MSE-optimal bandwidth for the RD point estimator is too large when the goal is to construct RBC confidence intervals with the smallest coverage error. We further optimize the constant terms behind the coverage error to derive new optimal choices for the auxiliary bandwidth required for RBC inference. Our expansions also establish that RBC inference yields higher-order refinements (relative to traditional undersmoothing) in the context of RD designs. Our main results cover sharp and sharp kink RD designs under conditional heteroskedasticity, and we discuss extensions to fuzzy and other RD designs, clustered sampling, and pre-intervention covariates adjustments. The theoretical findings are illustrated with a Monte Carlo experiment and an empirical application, and the main methodological results are available in \texttt{R} and \texttt{Stata} packages

On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference

Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias correction can be preferred to undersmoothing for minimizing coverage error and increasing robustness to tuning parameter choice. This is achieved using a novel, yet simple, Studentization, which leads to a new way of constructing kernel-based bias-corrected confidence intervals. In addition, for practical cases, we derive coverage error optimal bandwidths and discuss easy-to-implement bandwidth selectors. For interior points, we show that the MSE-optimal bandwidth for the original point estimator (before bias correction) delivers the fastest coverage error decay rate after bias correction when second-order (equivalent) kernels are employed, but is otherwise suboptimal because it is too "large". Finally, for odd-degree local polynomial regression, we show that, as with point estimation, coverage error adapts to boundary points automatically when appropriate Studentization is used; however, the MSE-optimal bandwidth for the original point estimator is suboptimal. All the results are established using valid Edgeworth expansions and illustrated with simulated data. Our findings have important consequences for empirical work as they indicate that bias-corrected confidence intervals, coupled with appropriate standard errors, have smaller coverage error and are less sensitive to tuning parameter choices in practically relevant cases where additional smoothness is available

Regression Discontinuity Designs Using Covariates

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions, and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. An empirical illustration and an extensive simulation study is presented. All methods are implemented in \texttt{R} and \texttt{Stata} software packages

Robust Methods for Program Evaluation.

My dissertation research focuses on different approaches to conduct robust estimation and inference in the context of program evaluation. In Chapter 1, I look at the effects of teacher and peer characteristics on student achievement in the STAR Project conducted in Tennessee in the late 1980s. It generalizes previous empirical research by allowing unobserved effects to enter the structural function nonseparably. No functional form assumptions are needed for identification. The empirical analysis looks at the effects of class size, teacher experience and gender composition of the classroom on test scores. Findings suggest that nonseparable heterogeneity is an important source of individual-level variation in academic performance. In Chapter 2, a joint work with Matias Cattaneo and Rocio Titiunik, we study robust inference in the context of regression discontinuity (RD) design. Local polynomial estimators are routinely employed to construct confidence intervals for treatment effects. The performance of these confidence intervals in applications, however, may be seriously hampered by their sensitivity to the specific bandwidth employed. Available bandwidth selectors typically yield a large bandwidth, leading to data-driven confidence intervals that may be severely biased. We propose new theory-based, more robust confidence interval estimators for average treatment effects at the cutoff in sharp RD, sharp kink RD, fuzzy RD and fuzzy kink RD designs, constructed using a bias-corrected RD estimator together with a novel standard error estimator. Finally, in Chapter 3, also written jointly with Matias Cattaneo and Rocio Titiunik, we present new results regarding RD plots, which are nowadays widely used in applications, despite its formal properties being unknown: these plots are typically presented employing ad hoc choices of tuning parameters. We formally study the most common RD plot based on an evenly-spaced binning of the data, and propose an optimal data-driven choice for the number of bins. In addition, we introduce an alternative RD plot based on quantile-spaced binning, study its formal properties, and propose the corresponding optimal data-driven choice for the number of bins. The main proposed data-driven selectors employ spacings-based estimators, which are simple and easy to implement in applications because they do not require additional choices of tuning parameters.PhDEconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108970/1/calonico_1.pd

nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference

Nonparametric kernel density and local polynomial regression estimators are very popular in statistics, economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as a preliminary ingredient entering some other estimation or inference procedure. This article describes the main methodological and numerical features of the software package nprobust, which offers an array of estimation and inference procedures for nonparametric kernel-based density and local polynomial regression methods, implemented in both the R and Stata statistical platforms. The package includes not only classical bandwidth selection, estimation, and inference methods (Wand and Jones 1995; Fan and Gijbels 1996), but also other recent developments in the statistics and econometrics literatures such as robust bias-corrected inference and coverage error optimal bandwidth selection (Calonico, Cattaneo, and Farrell 2018, 2019a). Furthermore, this article also proposes a simple way of estimating optimal bandwidths in practice that always delivers the optimal mean square error convergence rate regardless of the specific evaluation point, that is, no matter whether it is implemented at a boundary or interior point. Numerical performance is illustrated using an empirical application and simulated data, where a detailed numerical comparison with other R packages is given

nprobust: Nonparametric Kernel-Based Estimation and Robust Bias-Corrected Inference

Nonparametric kernel density and local polynomial regression estimators are very popular in Statistics, Economics, and many other disciplines. They are routinely employed in applied work, either as part of the main empirical analysis or as a preliminary ingredient entering some other estimation or inference procedure. This article describes the main methodological and numerical features of the software package nprobust, which offers an array of estimation and inference procedures for nonparametric kernel-based density and local polynomial regression methods, implemented in both the R and Stata statistical platforms. The package includes not only classical bandwidth selection, estimation, and inference methods (Wand and Jones, 1995; Fan and Gijbels, 1996), but also other recent developments in the statistics and econometrics literatures such as robust bias-corrected inference and coverage error optimal bandwidth selection (Calonico, Cattaneo and Farrell, 2018, 2019). Furthermore, this article also proposes a simple way of estimating optimal bandwidths in practice that always delivers the optimal mean square error convergence rate regardless of the specific evaluation point, that is, no matter whether it is implemented at a boundary or interior point. Numerical performance is illustrated using an empirical application and simulated data, where a detailed numerical comparison with other R packages is given

Racial discrimination in medical care settings and opioid pain reliever misuse in a U.S. cohort: 1992 to 2015

BACKGROUND: In the United States whites are more likely to misuse opioid pain relievers (OPRs) than blacks, and blacks are less likely to be prescribed OPRs than whites. Our objective is to determine whether racial discrimination in medical settings is protective for blacks against OPR misuse, thus mediating the black-white disparities in OPR misuse. METHODS: We used data from 3528 black and white adults in the Coronary Artery Risk Development in Young Adults (CARDIA) study, an ongoing multi-site cohort. We employ causal mediation methods, with race (black vs white) as the exposure, lifetime discrimination in medical settings prior to year 2000 as the mediator, and OPR misuse after 2000 as the outcome. RESULTS: We found black participants were more likely to report discrimination in a medical setting (20.3% vs 0.9%) and less likely to report OPR misuse (5.8% vs 8.0%, OR = 0.71, 95% CI = 0.55, 0.93, adjusted for covariates). Our mediation models suggest that when everyone is not discriminated against, the disparity is wider with black persons having even lower odds of reporting OPR misuse (OR = 0.63, 95% CI = 0.45, 0.89) compared to their white counterparts, suggesting racial discrimination in medical settings is a risk factor for OPR misuse rather than protective. CONCLUSIONS: These results suggest that racial discrimination in a medical setting is a risk factor for OPR misuse rather than being protective, and thus could not explain the seen black-white disparity in OPR misuse

Geodesy and metrology with a transportable optical clock

partially_open24openGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, DavideGrotti, Jacopo; Koller, Silvio; Vogt, Stefan; Häfner, Sebastian; Sterr, Uwe; Lisdat, Christian; Denker, Heiner; Voigt, Christian; Timmen, Ludger; Rolland, Antoine; Baynes, Fred N.; Margolis, Helen S.; Zampaolo, Michel; Thoumany, Pierre; Pizzocaro, Marco; Rauf, Benjamin; Bregolin, Filippo; Tampellini, Anna; Barbieri, Piero; Zucco, Massimo; Costanzo, Giovanni A.; Clivati, Cecilia; Levi, Filippo; Calonico, David