Endogeneity in quantile regression models: a control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature and on possible extensions and limitations of the estimation approach. Finally, the numerical performance and usefulness of the estimator are illustrated by the results of Monte Carlo experiments and two empirical examples, demand for fish and returns to schooling.

Estimating panel data duration models with censored data

This paper presents a method for estimating a class of panel data duration models, under which an unknown transformation of the duration variable is linearly related to the observed explanatory variables and the unobserved heterogeneity (or frailty) with completely known error distributions. This class of duration models includes a panel data proportional hazards model with fixed effects. The proposed estimator is shown to be n1/2-consistent and asymptotically normal with dependent right censoring. The paper provides some discussions on extending the estimator to the cases of longer panels, multiple states, and endogenous explanatory variables. Some Monte Carlo studies are carried out to illustrate the finite-sample performance of the new estimator.

Nonparametric Tests of Conditional Treatment Effects

We develop a general class of nonparametric tests for treatment effects conditional on covariates. We consider a wide spectrum of null and alternative hypotheses regarding conditional treatment effects, including (i) the null hypothesis of the conditional stochastic dominance between treatment and control groups; (ii) the null hypothesis that the conditional average treatment effect is positive for each value of covariates; and (iii) the null hypothesis of no distributional (or average) treatment effect conditional on covariates against a one-sided (or two-sided) alternative hypothesis. The test statistics are based on L_{1}-type functionals of uniformly consistent nonparametric kernel estimators of conditional expectations that characterize the null hypotheses. Using the Poissionization technique of Gine et al. (2003), we show that suitably studentized versions of our test statistics are asymptotically standard normal under the null hypotheses and also show that the proposed nonparametric tests are consistent against general fixed alternatives. Furthermore, it turns out that our tests have non-negligible powers against some local alternatives that are n^{-1/2} different from the null hypotheses, where n is the sample size. We provide a more powerful test for the case when the null hypothesis may be binding only on a strict subset of the support and also consider an extension to testing for quantile treatment effects. We illustrate the usefulness of our tests by applying them to data from a randomized, job training program (LaLonde (1986)) and by carrying out Monte Carlo experiments based on this dataset.Average treatment effect, Conditional stochastic dominance, Poissionization, Programme evaluation

Uniform confidence bands for functions estimated nonparametrically with instrumental variables

This paper is concerned with developing uniform confidence bands for functions estimated nonparametrically with instrumental variables. We show that a sieve nonparametric instrumental variables estimator is pointwise asymptotically normally distributed. The asymptotic normality result holds in both mildly and severely ill-posed cases. We present an interpolation method to obtain a uniform confidence band and show that the bootstrap can be used to obtain the required critical values. Monte Carlo experiments illustrate the finite-sample performance of the uniform confidence band.

SEMIPARAMETRIC ESTIMATION OF A BINARYRESPONSE MODEL WITH A CHANGE-POINTDUE TO A COVARIATE THRESHOLD

This paper is concerned with semiparametric estimation of a threshold binaryresponse model. The estimation method considered in the paper is semiparametricsince the parameters for a regression function are finite-dimensional, whileallowing for heteroskedasticity of unknown form. In particular, the paper considersManski (1975, 1985)'s maximum score estimator. The model in this paper isirregular because of a change-point due to an unknown threshold in a covariate.This irregularity coupled with the discontinuity of the objective function of themaximum score estimator complicates the analysis of the asymptotic behavior ofthe estimator. Sufficient conditions for the identification of parameters are givenand the consistency of the estimator is obtained. It is shown that the estimator ofthe threshold parameter is n-consistent and the estimator of the remainingregression parameters is cube root n-consistent. Furthermore, we obtain theasymptotic distribution of the estimators. It turns out that a suitably normalizedestimator of the regression parameters converges weakly to the distribution towhich it would converge weakly if the true threshold value were known andlikewise for the threshold estimator.Binary response model, maximum score estimation, semiparametricestimation, threshold regression, nonlinear random utility models.

"Characterization of the Asymptotic Distribution of Semiparametric M-Estimators"

This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspecification. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The first-stage nonparametric estimation may depend on finite dimensional parameters. We characterize: (1) conditions under which the first-stage estimation of nonparametric components do not affect the asymptotic distribution, (2) conditions under which the asymptotic distribution is affected by the derivatives of the first-stage nonparametric estimator with respect to the finite-dimensional parameters, and (3) conditions under which one can allow non-smooth objective functions. Our framework is illustrated by applying it to three examples: (1) profiled estimation of a single index quantile regression model, (2) semiparametric least squares estimation under model misspecification, and (3) a smoothed matching estimator.

Reform of Unemployment Compensation in Germany: A Nonparametric Bounds Analysis Using Register Data

Economic theory suggests that an extension of the maximum length of entitlement for unemployment benefits increases the duration of unemployment. Empirical results for the reform of the unemployment compensation system in Germany during the 1980s are less clear. The analysis in this paper is motivated by the controversial empirical findings and by recent developments in econometrics for partial identification. We use extensive administrative data with the drawback that registered unemployment is not directly observed. For this reason we bound the reform effect on unemployment duration over different definitions of unemployment. By exploiting the richness of the data we use a nonparametric approach without imposing critical parametric model assumptions. We identify a systematic increase in unemployment duration in response to the reform in samples that amount to less than 15% of the unemployment spells for the treatment group. --unemployment duration,definition of unemployment,nonparametric bounds analysis,(quantile-) treatment effect

Ability, sorting and wage inequality

In this paper we examine the importance of heterogeneity and self-selection into schooling for the study of inequality. Changes in inequality over time are a combination of price changes, selection bias and composition effects. To distinguish them, we estimate a semiparametric selection model for a sample of white males surveyed (during the 1990s) by the National Longitudinal Survey of Youth, but our results are applicable to broader analyses of inequality. In our data, as college enrollment increases in the economy, average college wages decrease and average high school wages increase, and therefore inequality between college and high school groups decreases. Moreover, selection bias causes us to understate the growth of different measures of the average return to schooling in our sample. It also leads us to understate the increase in wage dispersion at the top of the college wage distribution, and to overstate it at the bottom of the college wage distribution.Comparative advantage, composition effects, local instrumental variables, selection bias, semiparametric estimation, wage distribution.