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

Quantile regression with varying coefficients

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines. The proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm. The proposed Rao-score-type test that assesses the model against a linear model is also easy to implement. We provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic. Empirical results are also provided, including an application of the methodology to forced expiratory volume (FEV) data.Comment: Published at http://dx.doi.org/10.1214/009053606000000966 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator

Identifying Asset Poverty Thresholds New methods with an application to Pakistan and Ethiopia

Understanding how households escape poverty depends on understanding how they accumulate assets over time. Therefore, identifying the degree of linearity in household asset dynamics, and specifically any potential asset poverty thresholds, is of fundamental interest to the design of poverty reduction policies. If household asset holdings converged unconditionally to a single long run equilibrium, then all poor could be expected to escape poverty over time. In contrast, if there are critical asset thresholds that trap households below the poverty line, then households would need specific assistance to escape poverty. Similarly, the presence of asset poverty thresholds would mean that short term asset shocks could lead to long term destitution, thus highlighting the need for social safety nets. In addition to the direct policy relevance, identifying household asset dynamics and potential asset thresholds presents an interesting methodological challenge to researchers. Potential asset poverty thresholds can only be identified in a framework that allows multiple dynamic equilibria. Any unstable equilibrium points would indicate a potential poverty threshold, above which households are expected to accumulate further and below which households are on a trajectory that makes them poorer over time. The key empirical issue addressed in the paper is whether such threshold points exist in Pakistan and Ethiopia and, if so, where they are located. Methodologically, the paper explores what econometric technique is best suited for this type of analysis. The paper contributes to the small current literature on modeling nonlinear household welfare dynamics in three ways. First, it compares previously used techniques for identifying asset poverty traps by applying them to the same dataset, and examines whether, and how, the choice of estimation technique affects the result. Second, it explores whether other estimation techniques may be more suitable to locate poverty thresholds. Third, it adds the first study for a South Asian country and makes a comparison with Ethiopia. Household assets are combined into a single asset index using two techniques: factor analysis and regression. These indices are used to estimate asset dynamics and locate dynamic asset equilibria, first by nonparametric methods including LOWESS, kernel weighted local regression and spline smoothers, and then by global polynomial parametric techniques. To combine the advantages of nonparametric and parametric techniques - a flexible functional form and the ability to control for covariates, respectively - the paper adapts a mixed model representation of a penalized spline to estimate asset dynamics through a semiparametric partially linear model. This paper identifies a single dynamic asset equilibrium with a slightly concave dynamic asset accumulation path in each country. There is no evidence for multiple dynamic equilibria. This result is robust across econometric methods and across different ways of constructing the asset index. The concave accumulation path means that poorer households recover more slowly from asset shocks. Concavity also implies that greater initial equality of assets would lead to higher growth. Moreover, the dynamic asset equilibria are very low. In Pakistan it is below the average asset holdings of the poor households in the sample. In Ethiopia, the equilibrium is barely above the very low mean. This, together with the slow speed of asset accumulation for the poorest households, suggests that convergence towards the long run equilibrium may be slow and insufficient for rural households in Pakistan and Ethiopia to escape poverty.Poverty dynamics, Semiparametric Estimation, Penalized Splines, Pakistan, Ethiopia, Consumer/Household Economics, I32, C14, O12,

Nonparametric Option Pricing under Shape Restrictions

Frequently, economic theory places shape restrictions on functional relationships between economic variables. This paper develops a method to constrain the values of the first and second derivatives of nonparametric locally polynomial estimators. We apply this technique to estimate the state price density (SPD), or risk-neutral density, implicit in the market prices of options. The option pricing function must be monotonic and convex. Simulations demonstrate that nonparametric estimates can be quite feasible in the small samples relevant for day-to-day option pricing, once appropriate theory-motivated shape restrictions are imposed. Using S&P500 option prices, we show that unconstrained nonparametric estimators violate the constraints during more than half the trading days in 1999, unlike the constrained estimator we propose.

Employee Heterogeneity and Within-Firm Experience-Earnings Profiles: A Nonparametric Analysis

Abstract Motivated by a priori uncertainty with respect to the parametric specification of the earnings function, I model the earnings function as semiparametric partially linear model and follow the estimation approach described in Robinson (1988). Using data from the personnel records of a large major UK based financial sector employer, I let years of within-firm and pre-firm experience form the nonparametrically modelled component of the earnings function. It is shown that the estimated within-firm experience earnings profiles, which are conditional upon a given number years of pre-firm experience accumulated before entry, converge and even overtake as years of pre-firm experience increases. This result can be explained with the recognition of unobservable explanatory variables, such as the match and individual quality of the employees, both of which are a function of years of within- and pre-firm experience and wages