Regression discontinuity design with covariates

In this paper, the regression discontinuity design (RDD) is generalized to account for differences in observed covariates X in a fully nonparametric way. It is shown that the treatment effect can be estimated at the rate for one-dimensional nonparametric regression irrespective of the dimension of X. It thus extends the analysis of Hahn, Todd and van der Klaauw (2001) and Porter (2003), who examined identification and estimation without covariates, requiring assumptions that may often be too strong in applications. In many applications, individuals to the left and right of the threshold differ in observed characteristics. Houses may be Cconstructed in different ways across school attendance district boundaries. Firms may differ around a threshold that implies certain legal changes, etc. Accounting for these differences in covariates is important to reduce bias. In addition, accounting for covariates may also reduces variance. Finally, estimation of quantile treatment effects (QTE) is also considered.

A Note on Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables

This note argues that nonparametric regression not only relaxes functional form assumptions vis-a-vis parametric regression, but that it also permits endogenous control variables. To control for selection bias or to make an exclusion restriction in instrumental variables regression valid, additional control variables are often added to a regression. If any of these control variables is endogenous, OLS or 2SLS would be inconsistent and would require further instrumental variables. Nonparametric approaches are still consistent, though. A few examples are examined and it is found that the asymptotic bias of OLS can indeed be very large.Endogeneity, nonparametric regression, instrumental variables

Regression discontinuity design with covariates

In this paper, the regression discontinuity design (RDD) is generalized to account for differences in observed covariates X in a fully nonparametric way. It is shown that the treatment effect can be estimated at the rate for one-dimensional nonparametric regression irrespective of the dimension of X. It thus extends the analysis of Hahn, Todd and van der Klaauw (2001) and Porter (2003), who examined identification and estimation without covariates, requiring assumptions that may often be too strong in applications. In many applications, individuals to the left and right of the threshold differ in observed characteristics. Houses may be constructed in different ways across school attendance district boundaries. Firms may differ around a threshold that implies certain legal changes, etc. Accounting for these differences in covariates is important to reduce bias. In addition, accounting for covariates may also reduces variance. Finally, estimation of quantile treatment effects (QTE) is also considered.Treatment effect, causal effect, complier, LATE, nonparametric regression, endogeneity

Quantile Treatment Effects in the Regression Discontinuity Design: Process Results and Gini Coefficient

This paper shows nonparametric identification of quantile treatment effects (QTE) in the regression discontinuity design. The distributional impacts of social programs such as welfare, education, training programs and unemployment insurance are of large interest to economists. QTE are an intuitive tool to characterize the effects of these interventions on the outcome distribution. We propose uniformly consistent estimators for both potential outcome distributions (treated and non-treated) for the population of interest as well as other function-valued effects of the policy including in particular the QTE process. The estimators are straightforward to implement and attain the optimal rate of convergence for one-dimensional nonparametric regression. We apply the proposed estimators to estimate the effects of summer school on the distribution of school grades, complementing the results of Jacob and Lefgren (2004).quantile treatment effect, causal effect, endogeneity, regression discontinuity

Quantile Treatment Effects in the Regression Discontinuity Design

This paper shows nonparametric identification of quantile treatment effects (QTE) in the regression discontinuity design (RDD) and proposes simple estimators. Quantile treatment effects are a very helpful tool to characterize the effects of certain interventions on the outcome distribution. The distributional impacts of social programs such as welfare, education, training programs and unemployment insurance are of large interest to economists.quantile treatment effect, causal effect, endogeneity, regression discontinuity

Exploiting regional treatment intensity for the evaluation of labour market policies

We estimate the effects of active labour market policies (ALMP) on subsequent employment by nonparametric instrumental variables and matching estimators. Very informative administrative Swiss data with detailed regional information are combined with exogenous regional variation in programme participation probabilities, which generate an instrument within well-defined local labour markets. This allows pursuing instrumental variable as well as matching estimation strategies. A specific combination of those methods identifies a new type of effect heterogeneity. We find that ALMP increases individual employment probabilities by about 15% in the short term for unemployed that may be called 'marginal' participants. The effects seem to be considerably smaller for those unemployed not marginal to the participation decision.Local average treatment effect, conditional local IV, active labour market policy, state borders, geographic variation, Switzerland, Fuller estimator

Unconditional Quantile Treatment Effects under Endogeneity

This paper develops IV estimators for unconditional quantile treatment effects (QTE) when the treatment selection is endogenous. In contrast to conditional QTE, i.e. the effects conditional on a large number of covariates X, the unconditional QTE summarize the effects of a treatment for the entire population. They are usually of most interest in policy evaluations because the results can easily be conveyed and summarized. Last but not least, unconditional QTE can be estimated at √n rate without any parametric assumption, which is obviously impossible for conditional QTE (unless all X are discrete). In this paper we extend the identification of unconditional QTE to endogenous treatments. Identification is based on a monotonicity assumption in the treatment choice equation and is achieved without any functional form restriction. Several types of estimators are proposed: regression, propensity score and weighting estimators. Root n consistency, asymptotic normality and attainment of the semiparametric efficiency bound are shown for our weighting estimator, which is extremely simple to implement. We also show that including covariates in the estimation is not only necessary for consistency when the instrumental variable is itself confounded but also for efficiency when the instrument is valid unconditionally. Monte Carlo simulations and two empirical applications illustrate the use of the proposed estimators.instrumental variables, quantile treatment effects, nonparametric regression

Regional treatment intensity as an instrument for the evaluation of labour market policies

The effects of active labour market policies (ALMP) on individual employment chances and earnings are evaluated by nonparametric instrumental variables based on Swiss administrative data with detailed re-gional information. Using an exogenous variation in the participation probabilities across fairly autonomous regional units (cantons) generated by the federal government, we identify the effects of ALMP by comparing individuals living in the same local labour market but in different cantons. Taking account of small sample problems occurring in IV estimation, our results suggest that ALMP increases individual employment probabilities by about 15% in the short term for a weighted subpopulation of compliers.Local average treatment effect, active labour market policy, state borders, geographic variation, weak instruments, small sample problems of IV, Switzerland, Fuller estimator

Unconditional quantile treatment effects under endogeneity

This paper develops IV estimators for unconditional quantile treatment effects (QTE) when the treatment selection is endogenous. In contrast to conditional QTE, i.e. the effects conditional on a large number of covariates X, the unconditional QTE summarize the effects of a treatment for the entire population. They are usually of most interest in policy evaluations because the results can easily be conveyed and summarized. Last but not least, unconditional QTE can be estimated at pn rate without any parametric assumption, which is obviously impossible for conditional QTE (unless all X are discrete). In this paper we extend the Identification of unconditional QTE to endogenous treatments. Identification is based on a monotonicity assumption in the treatment choice equation and is achieved without any functional form restriction. Several types of estimators are proposed: regression, propensity score and weighting estimators. Root n consistency, asymptotic normality and attainment of the semiparametric efficiency bound are shown for our weighting estimator, which is extremely simple to implement. We also show that including covariates in the estimation is not only necessary for consistency when the instrumental variable is itself confounded but also for efficiency when the instrument is valid unconditionally. Monte Carlo simulations and two empirical applications illustrate the use of the proposed estimators.

Immigration and Heterogeneous Labor in Western Germany: A Labor Market Classification Based on Nonparametric Estimation

This paper presents a methodology to identify net demand shocks as well as wage rigidities in heterogeneous labor markets on the basis of nonparametric regression. We show how this approach can be used to make suggestions for immigration policy in economies with labor market rigidities. In an application to western Germany it is demonstrated that nonparametric regression is feasible in higher dimensions with only a few thousand observations. In sum, labor markets able to absorb immigrants are characterized by above average age and by professional occupations. On the other hand, labor markets for young workers in service occupations are identified to exhibit rising unemployment due to wage rigidities and are therefore not recommended for immigration. --wage,unemployment,migration,rigidity,nonparametric regression