nonparametric estimation of distributional policy effects this paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest in contrast to other methods we do not restrict attention to the effect on the mean in particular our method can be used to conduct inference on the change of the distribution function as a whole its moments and quantiles inequality measures such as the lorenz curve or gini coefficient and to test for stochastic dominance the practical applicability of our procedure is illustrated via a simulation study and an empirical example

regression discontinuity design with many thresholds abstract numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments a common practice is to normalize all the cutoffs to zero and estimate one effect this procedure identifies the average treatment effect ate on the observed distribution of individuals local to existing cutoffs however researchers often want to make inferences on more meaningful ates computed over general counterfactual distributions of individuals rather than simply the observed distribution of individuals local to existing cutoffs this paper proposes a consistent and asymptotically normal estimator for such ates when heterogeneity follows a non parametric function of cutoff characteristics in the sharp case the proposed estimator converges at the minimax optimal rate of root n for a specific choice of tuning parameters identification in the fuzzy case with multiple cutoffs is impossible unless heterogeneity follows a finite dimensional function of cutoff characteristics under parametric heterogeneity this paper proposes an ate estimator for the fuzzy case that optimally combines observations to maximize its precision

nonparametric policy analysis abstract this article considers the problem of predicting the mean effect of a change in the distribution of certain policy related variables on a dependent variable y this is conventionally done using a parametric model if however the conditional expectation of y given policy and nonpolicy variables x is unaltered by the policy intervention and if the support of x after the policy intervention lies within the support of x before the intervention then this analysis can be performed nonparametrically the proposed nonparametric estimator is developed for the model yj g xj a dj uj where g is a continuous unknown function of the continuous variables x dj is an m vector of dummy variables a is an m vector of unknown parameters representing fixed cell specific effects and uj is an error term with e uj xj dj 0 the estimand is b eg xj eg xj where x and x respectively denote the values of x before and after the policy intervention a nonparametric estimator bn is propo

nonparametric identification under discrete variation this paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates the function delivers values of a discrete or continuous outcome and instruments may be discrete valued application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions the results are used to investigate the nonparametric identifying power of the quarter of birth instruments used in angrist and krueger s 1991 study of the returns to schooling

tighter bounds in triangular systems abstract we study a nonparametric triangular system with potentially discrete endogenous regressors and nonseparable errors like in other work in this area the parameter of interest is the structural function evaluated at particular values we impose a global exclusion and exogeneity condition in contrast to chesher 2005 but develop a rank condition which is weaker than chesher s the alternative rank condition can be satisfied for binary endogenous regressors and it often leads to an identified interval tighter than chesher 2005 s minimum length interval we illustrate the potential of the new rank condition using the angrist and krueger 1991 data

efficient semiparametric estimation of quantile treatment effects this paper develops estimators for quantile treatment effects under the identifying restriction that selection to treatment is based on observable characteristics identification is achieved without requiring computation of the conditional quantiles of the potential outcomes instead the identification results for the marginal quantiles lead to an estimation procedure for the quantile treatment effect parameters that has two steps nonparametric estimation of the propensity score and computation of the difference between the solutions of two separate minimization problems root n consistency asymptotic normality and achievement of the semiparametric efficiency bound are shown for that estimator a consistent estimation procedure for the variance is also presented finally the method developed here is applied to evaluation of a job training program and to a monte carlo exercise results from the empirical application indicate that the method works relatively well even for a data set with limited overlap between treated and controls in the support of covariates the monte carlo study shows that for a relatively small sample size the method produces estimates with good precision and low bias especially for middle quantiles

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

the conditional distribution of excess returns an empirical analysis abstract in this article we describe the cumulative distribution function of excess returns conditional on a broad set of predictors that summarize the state of the economy we do so by estimating a sequence of conditional logit models over a grid of values of the response variable our method uncovers higher order multidimensional structure that cannot be found by modeling only the first two moments of the distribution we compare two approaches to modeling one based on a conventional linear logit model and the other based on an additive logit the second approach avoids the curse of dimensionality problem of fully nonparametric methods while retaining both interpretability and the ability to let the data determine the shape of the relationship between the response variable and the predictors we find that the additive logit fits better and reveals aspects of the data that remain undetected by the linear logit the additive model retains its superiority even in out of sample prediction and portfolio s

more on confidence intervals for partially identified parameters this paper extends imbens and manski s 2004 analysis of confidence intervals for interval identified parameters the extension is motivated by the discovery that for their final result imbens and manski implicitly assumed locally superefficient estimation of a nuisance parameter i reanalyze the problem both with assumptions that merely weaken this superefficiency condition and with assumptions that remove it altogether imbens and manski s confidence region is valid under weaker assumptions than theirs yet superefficiency is required i also provide a confidence interval that is valid under superefficiency but can be adapted to the general case a methodological contribution is to observe that the difficulty of inference comes from a preestimation problem regarding a nuisance parameter clarifying the connection to other work on partial identification

superconvergence of a collocation type method for simple turning points of hammerstein equations approximation d un point de retournement simple de l equation d hammerstein dependant d un parametre

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

accounting for the black white wealth gap a nonparametric approach many applications involve a decomposition of the mean intergroup difference in a given variable into the portion attributable to differences in the distribution of one or more explanatory variables and that due to differences in the conditional expectation function this article notes two interrelated reasons why the blinder oaxaca b o method the approach most commonly used in the literature may yield misleading results we suggest a natural solution that both provides a more reliable answer to the original problem and affords a richer examination of the sources of intergroup differences in the variable of interest the conventional application of the b o method requires a parametric assumption about the form of the conditional expectation function furthermore it often uses estimates based on that functional form to extrapolate outside the range of the observed explanatory variables we show that misspecification of the conditional expectation function is likely to result in nontrivial errors in infer

robust stability of continuous time difference systems in this paper some special results about the robust stability of a linear continuoustime difference system are given these results may be treated as a natural generalization of the well known results on the schur stability of polynomial families defined by convex polytopes in the coefficient space

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

nonparametric estimation of nonadditive random functions we present estimators for nonparametric functions that are nonadditive in unobservable random terms the distributions of the unobservable random terms are assumed to be unknown we show that when a nonadditive nonparametric function is strictly monotone in an unobservable random term and it satisfies some other properties that may be implied by economic theory such as homogeneity of degree one or separability the function and the distribution of the unobservable random term are identified we also present convenient normalizations to use when the properties of the function other than strict monotonicity in the unobservable random term are unknown the estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal we extend the results to functions that depend on a multivariate random term the results of a limited simulation study are presented

on the role of the propensity score in efficient semiparametric estimation of average treatment effects in this paper the role of the propensity score in the efficient estimation of average treatment effects is examined under the assumption that the treatment is ignorable given some observed characteristics it is shown that the propensity score is ancillary for estimation of the average treatment effects the propensity score is not ancillary for estimation of average treatment effects on the treated it is suggested that the marginal value of the propensity score lies entirely in the dimension reduction efficient semiparametric estimators of average treatment effects and average treatment effects on the treated are shown to take the form of relevant sample averages of the data completed by the nonparametric imputation method it is shown that the projection on the propensity score is not necessary for efficient semiparametric estimation of average treatment effects on the treated even if the propensity score is known an application to the experimental data reveals that conditioning on the propensity score may even result in a loss of efficiency

inference on regressions with interval data on a regressor or outcome this paper examines inference on regressions when interval data are available on one variable the other variables being measured precisely let a population be characterized by a distribution p y x v v 0 v 1 where y r 1 x r k and the real variables v v 0 v 1 satisfy v 0 v v 1 let a random sample be drawn from p and the realizations of y x v 0 v 1 be observed but not those of v the problem of interest may be to infer e y x v or e v x this analysis maintains interval i monotonicity m and mean independence mi assumptions i p v 0 v v 1 1 m e y x v is monotone in v mi e y x v v 0 v 1 e y x v no restrictions are imposed on the distribution of the unobserved values of v within the observed intervals v 0 v 1 it is found that the immi assumptions alone imply simple nonparametric bounds on e y x v and e v x these assumptions invoked when y is binary and combined with a semiparametric binary regression model yield an identification region for the parameters that may be estimated consistently by a modified maximum score mms method the immi assumptions combined with a parametric model for e y x v or e v x yield an identification region that may be estimated consistently by a modified minimum distance mmd method monte carlo methods are used to characterize the finite sample performance of these estimators empirical case studies are performed using interval wealth data in the health and retirement study and interval income data in the current population survey

identification of marginal effects in nonseparable models without monotonicity nonseparable models do not impose any type of additivity between the unobserved part and the observable regressors and are therefore ideal for many economic applications to identify these models using the entire joint distribution of the data as summarized in regression quantiles monotonicity in unobservables has frequently been assumed this paper establishes that in the absence of monotonicity the quantiles identify local average structural derivatives of nonseparable models

partial distributional policy effects in this paper we propose a method to evaluate the effect of a counterfactual change in the unconditional distribution of a single covariate on the unconditional distribution of an outcome variable of interest both fixed and infinitesimal changes are considered we show that such effects are point identified under general conditions if the covariate affected by the counterfactual change is continuously distributed but are typically only partially identified if its distribution is discrete for the latter case we derive informa tive bounds making use of the available information we also discuss estimation and inference

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

confidence intervals for partially identified parameters recently a growing body of research has studied inference in settings where parameters of interest are partially identified in many cases the parameter is real valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data for this case confidence intervals cis have been proposed that cover the entire identification region with fixed probability here we introduce a conceptually different type of confidence interval rather than cover the entire identification region with fixed probability we propose cis that asymptotically cover the true value of the parameter with this probability however the exact coverage probabilities of the simplest version of our new cis do not converge to their nominal values uniformly across different values for the width of the identification region to avoid the problems associated with this we modify the proposed ci to ensure that its exact coverage probabilities do converge uniformly to their nominal values we motivate this modified ci through exact results for the gaussian case