nonparametric instrumental variables estimation for efficiency frontier the paper investigates endogeneity issues in nonparametric frontier models it considers a nonseparable model for a cost function c y u where c and y are the cost and the output u is uniform in 0 1 and is increasing with respect to u the cost frontier corresponds to u 0 and u can be interpreted as a normalized level of inefficiency the endogeneity issue arises when y is dependent of u for identification and estimation we use a nonparametric instrumental variables estimator of the model for fixed value u and obtain an estimate of the quantile cost frontier y this involves the solution of a non linear integral equation if the true frontier y 0 is wanted it is then estimated by estimating the bias correction y 0 y under additional regularity conditions the procedure is illustrated through a simulated sample and with an empirical application to the efficiency of post offices

instrumental variable quantile regression a robust inference approach abstract in this paper we develop robust inference procedures for an instrumental variables model defined by y d u where d u is strictly increasing in u and u is a uniform variable that may depend on d but is independent of a set of instrumental variables z the proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely the use of the proposed procedures is illustrated through two empirical examples

estimation of nonparametric models with simultaneity we introduce methods for estimating nonparametric nonadditive models with simultaneity the methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables such as ratios of derivatives or averages of products of derivatives of this density the estimators are therefore easily computed functionals of a nonparametric estimator of the density of the observable variables we consider in detail a model where to each structural equation there corresponds an exclusive regressor and a model with one equation of interest and one instrument that is included in a second equation for both models we provide new characterizations of observational equivalence on a set in terms of the density of the observable variables and derivatives of the structural functions based on those characterizations we develop two estimation methods in the first method the estimators of the structural derivatives are calculated by a simple matrix inversion and matrix multiplication analogous to a standard least squares estimator but with the elements of the matrices being averages of products of derivatives of nonparametric density estimators in the second method the estimators of the structural derivatives are calculated in two steps in a first step values of the instrument are found at which the density of the observable variables satisfies some properties in the second step the estimators are calculated directly from the values of derivatives of the density of the observable variables evaluated at the found values of the instrument we show that both pointwise estimators are consistent and asymptotically normal

smoothed gmm for quantile models abstract we consider estimation of finite dimensional parameters identified by general conditional quantile restrictions including instrumental variables quantile regression within a generalized method of moments framework moment functions are smoothed to aid both computation and precision consistency and asymptotic normality are established under weaker assumptions than previously seen in the literature allowing dependent data and nonlinear structural models simulations illustrate the finite sample properties an in depth empirical application estimates the consumption euler equation derived from quantile utility maximization advantages of quantile euler equations include robustness to fat tails decoupling risk attitude from the elasticity of intertemporal substitution and error free log linearization

uniformly semiparametric efficient estimation of treatment effects with a continuous treatment this article studies identification estimation and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption we show identification of the parameters of interest the dose response functions under the assumption that selection to treatment is based on observables we propose a semiparametric two step estimator and consider estimation of the dose response functions through moment restriction models with generalized residual functions that are possibly nonsmooth this general formulation includes average and quantile treatment effects as special cases the asymptotic properties of the estimator are derived namely uniform consistency weak convergence and semiparametric efficiency we also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice monte carlo simulations show that the proposed methods have good finite sample properties finally we apply the proposed

quantile regression for duration models with time varying regressors abstract since the seminal work of koenker and bassett 1978 quantile regression has become a widely used tool in duration analysis the existing literature however has focused on time invariant regressors even though time varying regressors are common in practice in this paper we introduce a quantile regression framework with time varying regressors and develop quantile regression estimators our estimators are motivated by manski s 1975 1985 maximum score estimator and chen s 2010 integrated maximum score estimator our estimators are consistent and asymptotically normal under some regularity conditions and perform well in finite samples our method is illustrated with an unemployment duration data set

identification and estimation of triangular simultaneous equations models without additivity this paper uses control variables to identify and estimate models with nonseparable multidimensional disturbances triangular simultaneous equations models are considered with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable also for any control variable identification results are given for quantile average and policy effects bounds are given when a common support assumption is not satisfied estimators of identified objects and bounds are provided and a demand analysis empirical example is given

testing a parametric quantile regression model with an endogenous explanatory variable against a nonparametric alternative abstract this paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables the paper presents a test of the hypothesis that g belongs to a finite dimensional parametric family against a nonparametric alternative the test is not subject to the ill posed inverse problem of nonparametric instrumental variable estimation under mild conditions the test is consistent against any alternative model in large samples its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is proportional to n 1 2 where n is the sample size monte carlo simulations illustrate the finite sample performance of the test

instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings this paper reports estimates of the effects of jtpa training programs on the distribution of earnings the estimation uses a new instrumental variable iv method that measures program impacts on quantiles the quantile treatment effects qte estimator reduces to quantile regression when selection for treatment is exogenously determined qte can be computed as the solution to a convex linear programming problem although this requires first step estimation of a nuisance function we develop distribution theory for the case where the first step is estimated nonparametrically for women the empirical results show that the jtpa program had the largest proportional impact at low quantiles perhaps surprisingly however jtpa training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution

instrumental variable estimators for binary outcomes instrumental variables ivs can be used to construct estimators of exposure effects on the outcomes of studies affected by nonignorable selection of the exposure estimators that fail to adjust for the effects of nonignorable selection will be biased and inconsistent such situations commonly arise in observational studies but are also a problem for randomized experiments affected by nonignorable noncompliance in this article we review iv estimators for studies in which the outcome is binary and consider the links between different approaches developed in the statistics and econometrics literatures the implicit assumptions made by each method are highlighted and compared within our framework we illustrate our findings through the reanalysis of a randomized placebo controlled trial and highlight important directions for future work in this area

on the testability of identification in some nonparametric models with endogeneity this paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity the first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions these conditions are typically referred to as completeness conditions the second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions for each of these hypothesis testing problems we provide conditions under which any test will have power no greater than size against any alternative in this sense we conclude that no nontrivial tests for these hypothesis testing problems exist publication abstract

existence and geometric properties of solutions of a free boundary problem in potential theory let 0 g h l rn n 2 be two given density functions at least one of them bounded away from zero outside a compact set and g holder continuous we prove that for any compactly supported positive measure which is sufficiently concentrated e g has sufficiently high n 1 dimensional density there exists a bounded open set rn such that the newtonian potential of the measure hln ghn 1 agrees with that of outside some regularity of is obtained as well as several results on the geometry of example if h and g are constant then for any x the inward normal ray of at x if it exists intersects the closed convex hull of typeset by ams tex 1 2 bjorn gustafsson and henrik shahgholian

a smoothed maximum score estimator for the binary response model this paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form the estimator is obtained by maximizing a smoothed version of the objective function of c manski s maximum score estimator the smoothing procedure is similar to that used in kernel nonparametric density estimation the resulting estimator s rate of convergence in probability is the fastest possible under the assumptions that are made the centered normalized estimator is asymptotically normally distributed methods are given for consistently estimating the parameters of the limiting distribution and for selecting the bandwidth required by the smoothing procedure copyright 1992 by the econometric society

weak identification robust tests in an instrumental quantile model abstract we develop a testing procedure that is robust to identification quality in an instrumental quantile model in order to reduce the computational burden a multi step approach is taken and a two step anderson rubin ar statistic is considered we then propose an orthogonal decomposition of the ar statistic where the null distribution of each component does not depend on the assumption of a full rank of the jacobian power experiments are conducted and inferences on returns to schooling using the angrist and krueger data are considered as an empirical example

finite sample inference for quantile regression models abstract under minimal assumptions finite sample confidence bands for quantile regression models can be constructed these confidence bands are based on the conditional pivotal property of estimating equations that quantile regression methods solve and provide valid finite sample inference for linear and nonlinear quantile models with endogenous or exogenous covariates the confidence regions can be computed using markov chain monte carlo mcmc methods we illustrate the finite sample procedure through two empirical examples estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling we find pronounced differences between asymptotic and finite sample confidence regions in cases where the usual asymptotics are suspect

identifying the average treatment effect in ordered treatment models without unconfoundedness we show identification of the average treatment effect ate when treatment is specified by ordered choice in cross section or panel models treatment is determined by location of a latent variable containing a continuous instrument relative to two or more thresholds we place no functional form restrictions on latent errors and potential outcomes unconfoundedness of treatment does not hold and identification at infinity for the treated is not possible yet we still show nonparametric point identification and estimation of the ate we apply our model to reinvestigate the inverted u relationship between competition and innovation and find no inverted u in us data

on the nonparametric identification of nonlinear simultaneous equations models comment on brown 1983 and roehrig 1988 this note revisits the identification theorems of brown 1983 and roehrig 1988 we describe an error in the proofs of the main identification theorems in these papers and provide an important counterexample to the theorems on the identification of the reduced form specifically the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions of these papers we provide conditions under which the reduced form is identified and is recoverable using the distribution of the endogenous variables conditional on the exogenous variables however these conditions place substantial limitations on the structural model we conclude the note with a conjecture that it may be possible to use classical exclusion restrictions to recover some of the key implications of the theorems in more general settings

local instrumental variables and latent variable models for identifying and bounding treatment effects this paper examines the relationship between various treatment parameters within a latent variable model when the effects of treatment depend on the recipient s observed and unobserved characteristics we show how this relationship can be used to identify the treatment parameters when they are identified and to bound the parameters when they are not identified

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

sensitivity of spin glass order to temperature changes by a loop expansion around parisi s mean field theory for an ising spin glass it is shown that the overlap of the magnetization patterns belonging to two different temperatures t and t vanishes to any order si t si t 0 while the correlation overlap sisj t sisj t calculated to first loop order and for technical reasons for dimensions d 8 only is found to decay exponentially with a characteristic length approximately t t 1

nonparametric instrumental variables estimation of a quantile regression model we consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression error conditional on an instrumental variable to be zero the resulting estimating equation is a nonlinear integral equation of the first kind which generates an ill posed inverse problem the integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically we show that the estimator is mean square consistent derive its rate of convergence in probability and give conditions under which this rate is optimal in a minimax sense the results of monte carlo experiments show that the estimator behaves well in finite samples

topology of quadrature domains we address the problem of topology of quadrature domains namely we give upper bounds on the connectivity of the domain in terms of the number of nodes and their multiplicities in the quadrature identity

local identification of nonparametric and semiparametric models in parametric nonlinear structural models a classical sufficient condition for local identification like fisher 1966 and rothenberg 1971 is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix we derive an analogous result for the nonparametric nonlinear structural models establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification importantly we show that additional conditions are often needed in nonlinear nonparametric models to avoid nonlinearities overwhelming linear effects we give restrictions on a neighborhood of the true value that are sufficient for local identification we apply these results to obtain new primitive identification conditions in several important models including nonseparable quantile instrumental variable iv models and semiparametric consumption based asset pricing models

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

conditions for identification in nonparametric and parametric models on presente une definition formelle de l identification dans un contexte non parametrique sur la base des travaux de koopmans et reiersol 1950

some properties of two phase quadrature domains abstract in this paper we investigate general properties of the two phase quadrature domain which was recently introduced by emamizadeh prajapat and shahgholian the concept which is a generalization of the well known one phase domain introduces substantial difficulties with interesting features even richer than those of the one phase counterpart for given positive constants and two bounded and compactly supported measures we investigate the uniqueness of the solution of the following free boundary problem 1 u in r n n 2 u 0 in r n where it is further required that the supports of should be inside this in general may fail and give rise to non existence of solutions along the paths to various properties that we state and prove here we also present several conjectures and open problems that we believe should be true

iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression this paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression we propose a regularized newton type iteration and establish convergence and convergence rate results a particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption we demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model this is illustrated in computed examples with simulated data

nonparametric iv estimation of local average treatment effects with covariates in this paper nonparametric instrumental variable estimation of local average treatment effects late is extended to incorporate covariates estimation of late is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models including covariates in the estimation of late is necessary when the instrumental variable itself is confounded such that the iv assumptions are valid only conditional on covariates previous approaches to handle covariates in the estimation of late relied on parametric or semiparametric methods in this paper a nonparametric estimator for the estimation of late with covariates is suggested that is root n asymptotically normal and efficient

estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals this paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables this is a nonparametric nonlinear instrumental variables iv problem we propose a class of penalized sieve minimum distance psmd estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space some of the psmd procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty others use large dimensional sieves with lower semicompact and or convex penalties we establish their consistency and the convergence rates in banach space norms such as a sup norm or a root mean squared norm allowing for possibly noncompact infinite dimensional parameter spaces for both mildly and severely ill posed nonlinear inverse problems our convergence rates in hilbert space norms such as a root mean squared norm achieve the known minimax optimal rate for the nonparametric mean iv regression we illustrate the theory with a nonparametric additive quantile iv regression we present a simulation study and an empirical application of estimating nonparametric quantile iv engel curves

conditional empirical likelihood estimation and inference for quantile regression models abstract this paper considers two empirical likelihood based estimation inference and specification testing methods for quantile regression models first we apply the method of conditional empirical likelihood cel by kitamura et al 2004 empirical likelihood based inference in conditional moment restriction models econometrica 72 1667 1714 and zhang and gijbels 2003 sieve empirical likelihood and extensions of the generalized least squares scandinavian journal of statistics 30 1 24 to quantile regression models second to avoid practical problems of the cel method induced by the discontinuity in parameters of cel we propose a smoothed counterpart of cel called smoothed conditional empirical likelihood scel we derive asymptotic properties of the cel and scel estimators parameter hypothesis tests and model specification tests important features are i the cel and scel estimators are asymptotically efficient and do not require preliminary weight estimation ii by inverting the cel and scel ratio parameter hypothesis tests asymptotically valid confidence intervals can be obtained without estimating the asymptotic variances of the estimators and iii in contrast to cel the scel method can be implemented by some standard newton type optimization simulation results demonstrate that the scel method in particular compares favorably with existing alternatives

identification in a generalization of bivariate probit models with dummy endogenous regressors abstract this paper provides identification results for a class of models specified by a triangular system of two equations with binary endogenous variables the joint distribution of the latent error terms is specified through a parametric copula structure that satisfies a particular dependence ordering while the marginal distributions are allowed to be arbitrary but known this class of models is broad and includes bivariate probit models as a special case the paper demonstrates that having an exclusion restriction is necessary and sufficient for global identification in a model without common exogenous covariates where the excluded variable is allowed to be binary having an exclusion restriction is sufficient in models with common exogenous covariates that are present in both equations the paper then extends the identification analyses to a model where the marginal distributions of the error terms are unknown

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

specification analysis of linear quantile models this paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels these tests may be applied to assess the validity of post estimation inferences regarding the effect of conditioning variables on the distribution of outcomes we show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure monte carlo evidence and an application to the empirical analysis of age earnings curves are included

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

quantile regression methods for recursive structural equation models abstract two classes of quantile regression estimation methods for the recursive structural equation models of chesher 2003 identification in nonseparable models econometrica 71 1405 1441 are investigated a class of weighted average derivative estimators based directly on the identification strategy of chesher is contrasted with a new control variate estimation method the latter imposes stronger restrictions achieving an asymptotic efficiency bound with respect to the former class an application of the methods to the study of the effect of class size on the performance of dutch primary school students shows that i reductions in class size are beneficial for good students in language and for weaker students in mathematics ii larger classes appear beneficial for weaker language students and iii the impact of class size on both mean and median performance is negligible

some incomplete but boundedly complete location families a general result concerning noncompleteness of location families of probability measures on euclidean space is pointed out examples include boundedly complete families such as those generated by certain scale mixtures of the standard gaussian distribution these examples illuminate completeness criteria for location families and compare favourably in simplicity with previously known examples of incomplete boundedly complete nonlocation families

regularity of a free boundary with application to the pompeiu problem in the unit ball b 0 1 let u and a domain in n solve the following overdetermined problem u in b 0 1 02 u jruj 0 inb 0 1 n where denotes the characteristic function and the equation is satisfled in the sense of distributions if the complement of does not develop cusp singularities at the origin then we prove is analytic in some small neighborhood of the origin the result can be modifled to yield for more general divergence form operators as an application of this then we obtain the regularity of the boundary of a domain without the pompeiu property provided its complement has no cusp singularities

global solutions to bubble growth in porous media abstract we study a moving boundary problem modeling an injected fluid into another viscous fluid the viscous fluid is withdrawn at infinity and governed by darcy s law we present solutions to the free boundary problem in terms of time derivative of a generalized newtonian potentials of the characteristic function of the bubble this enables us to show that the bubble occupies the entire space as the time tends to infinity if and only if the internal generalized newtonian potential of the initial bubble is a quadratic polynomial howison 1985 7 and dibenedetto and friedman 1986 2 studied such behavior but for bounded bubbles we extend their results to unbounded bubbles

inference in censored models with endogenous regressors this paper analyzes the linear regression model y x with a conditional median assumption med e z 0 where z is a vector of exogenous instrument random variables we study inference on the parameter when y is censored and x is endogenous we treat the censored model as a model with interval observation on an outcome thus obtaining an incomplete model with inequality restrictions on conditional median regressions we analyze the identified features of the model and provide sufficient conditions for point identification of the parameter we use a minimum distance estimator to consistently estimate the identified features of the model we show that under point identification conditions and additional regularity conditions the estimator based on inequality restrictions is n normal and we derive its asymptotic variance one can use our setup to treat the identification and estimation of endogenous linear median regression models with no censoring a monte carlo analysis illustrates our estimator in the censored and the uncensored case

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

posterior consistency of nonparametric conditional moment restricted models this paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite dimensional parameter g0 we estimate it in a quasi bayesian way based on the limited information likelihood and investigate the impact of three types of priors on the posterior consistency i truncated prior priors supported on a bounded set ii thin tail prior a prior that has very thin tail outside a growing bounded set and iii normal prior with nonshrinking variance in addition g0 is allowed to be only partially identified in the frequentist sense and the parameter space does not need to be compact the posterior is regularized using a slowly growing sieve dimension and it is shown that the posterior converges to any small neighborhood of the identified region we then apply our results to the nonparametric instrumental regression model finally the posterior consistency using a random sieve dimension parameter is studied

testing for separability in structural equations abstract separability is an important feature of structural equations as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation this paper provides a nonparametric test for separability in structural equations the test is based on a conditional independence test recently developed by huang et al 2013 building on consistent procedures of bierens 1982 1990 and stinchcombe and white 1998 the test is easy to implement and achieves n local power we apply our test to study interest rate elasticities of loan demand in microfinance and the impact of education on wages

censored regression quantiles with endogenous regressors this paper develops a semiparametric method for estimation of the censored regression model when some of the regressors are endogenous and continuously distributed and instrumental variables are available for them a distributional exclusion restriction is imposed on the unobservable errors whose conditional distribution is assumed to depend on the regressors and instruments only through a lower dimensional control variable here assumed to be the difference between the endogenous regressors and their conditional expectations given the instruments this assumption which implies a similar exclusion restriction for the conditional quantiles of the censored dependent variable is used to motivate a two stage estimator of the censored regression coefficients in the first stage the conditional quantile of the dependent variable given the instruments and the regressors is nonparametrically estimated as are the first stage reduced form residuals to be used as control variables the second stage estimator is a weighted least squares regression of pairwise differences in the estimated quantiles on the corresponding differences in regressors using only pairs of observations for which both estimated quantiles are positive i e in the uncensored region and the corresponding difference in estimated control variables is small the paper gives the form of the asymptotic distribution for the proposed estimator and discusses how it compares to similar estimators for alternative models

measurement errors in quantile regression models abstract this paper develops estimation and inference for quantile regression models with measurement errors we propose an easily implementable semiparametric two step estimator when repeated measures for the covariates are available building on recent theory on z estimation with infinite dimensional parameters consistency and asymptotic normality of the proposed estimator are established we also develop statistical inference procedures and show the validity of a bootstrap approach to implement the methods in practice monte carlo simulations assess the finite sample performance of the proposed methods we apply the methods to the investment equation model using a firm level data with repeated measures of investment demand tobin s q we document strong heterogeneity in the sensitivity of investment to tobin s q and cash flow across the conditional distribution of investment the cash flow sensitivity is relatively larger at the lower part of the distribution providing evidence that these firms are more exposed to and dependent on fluctuations in internal finance

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

testing conditional independence via rosenblatt transforms this paper proposes new tests of conditional independence of two random variables given a single index involving an unknown finite dimensional parameter the tests employ rosenblatt transforms and are shown to be distribution free while retaining computational convenience some results from monte carlo simulations are presented and discussed

identification and estimation of time varying nonseparable panel data models without stayers abstract this paper explores the identification and estimation of nonseparable panel data models we show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable the conditional distributions of unobservable variables do not change over time and the joint support of explanatory variables satisfies some weak assumptions to identify the target parameters existing studies assume that the structural function does not change over time and that there are stayers namely individuals with the same regressor values in two time periods our approach by contrast allows the structural function to depend on the time period in an arbitrary manner and does not require the existence of stayers in estimation part of the paper we propose parametric and nonparametric estimators that implement our identification results monte carlo studies indicate that our parametric estimator performs well in finite samples finally we extend our identification results to models with discrete outcomes and show that the structural function is partially identified

dummy endogenous variables in weakly separable models in this paper we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term the model is not required to be strictly increasing in the error term and the class of models considered includes limited dependent variable models such as discrete choice models conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions

efficient instrumental variables estimation of nonlinear models this paper considers asymptotically efficient instrumental variables estimation of nonlinear models in an i i d environment the class of models includes nonlinear simultaneous equations models and other models of interest a problem in constructing efficient instrumental variables estimators for such models is that the optimal instruments involve a conditional expectation calculation of which can require functional form assumptions for the conditional distribution of endogenous variables as well as integration nonparametric methods provide a way of avoiding this difficulty here it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators also ways of choosing the nonparametric estimate in applications are discussed two types of nonparametric estimates of the optimal instruments are considered each involves nonparametric regression one by nearest neighbor and the other by series approximation the finite sample properties of the estimators are considered in a small sampling experiment involving an endogenous dummy variable model

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

identification in nonseparable models weak nonparametric restrictions are developed sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable these derivatives can exhibit stochastic variation in a microeconometric context this allows the impact of a policy intervention as measured by the value of a structural derivative to vary across people who are identical as measured by covariates when the restrictions are satisfied quantiles of the distribution of a policy impact across people can be identified the identification restrictions are local in the sense that they are specific to the values of the covariates and the specific quantiles of latent variables at which identification is sought the conditions do not include the commonly required independence of latent variables and covariates they include local versions of the classical rank and order conditions and local quantile insensitivity conditions values of structural derivatives are identified by functionals of quantile regression functions and can be estimated using the same functionals applied to estimated quantile regression functions

on quadrature domains and the schwarz potential abstract let t be a distribution in r n whose support is compact a domain in r n is said to be a quadrature domain with respect to t if supp t and h h t for all functions h which are harmonic and integrable over we denote this by q t hl 1 this is equivalent to saying that there is a solution u called the modified schwarz potential to the following overdetermined cauchy problem u 1 t in and u u 0 on in this paper we investigate different properties of quadrature domains we show that if t is a fixed distribution then bounded domains in q t hl1 are uniformly bounded later we prove that if the modified schwarz potential of a domain is a polynomial then is a half space we also study the uniqueness problem namely we show that if d and are in q t hl1 v and u are the msps of d and respectively and sup d u 0 then meets x v x consequently if v 0 then d 0

a discontinuity test for identification in triangular nonseparable models this paper presents a test for the validity of control variable approaches to identification in triangular nonseparable models assumptions commonly imposed to justify such methods include full independence of instruments and disturbances and existence of a reduced form that is strictly monotonic in a scalar disturbance we show that if the data has a particular structure namely that the distribution of the endogenous variable has a mass point at the lower or upper boundary of its support validity of the control variable approach implies a continuity condition on an identified function which can be tested empirically

iv models of ordered choice this paper studies single equation instrumental variable models of ordered choice in which explanatory variables may be endogenous the models are weakly restrictive leaving unspecied the mechanism that generates endogenous variables these incomplete models are set not point identifying for parametrically e g ordered probit or nonparametrically specied structural functions the paper gives results on the properties of the identied set for the case in which potentially endogenous explanatory variables are discrete the results are used as the basis for calculations showing the rate of shrinkage of identied sets

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

instrumental variables estimators of nonparametric models with discrete endogenous regressors this paper discusses estimation of nonparametric models whose regressor vectors consist of a vector of exogenous variables and a univariate discrete endogenous regressor with finite support both identification and estimators are derived from a transform of the model that evaluates the nonparametric structural function via indicator functions in the support of the discrete regressor a two step estimator is proposed where the first step constitutes nonparametric estimation of the instrument and the second step is a nonparametric version of two stage least squares linear functionals of the model are shown to be asymptotically normal and a consistent estimator of the asymptotic covariance matrix is described for the binary endogenous regressor case it is shown that one functional of the model is a conditional on covariates local average treatment effect that permits both unobservable and observable heterogeneity in treatments finite sample properties of the estimators from a monte carlo simulation study illustrate the practicability of the proposed estimators

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

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

cross section and panel data estimators for nonseparable models with endogenous regressors we propose two new methods for estimating models with nonseparable errors and endogenous regressors the first method estimates a local average response one estimates the response of the conditional mean of the dependent variable to a change in the explanatory variable while conditioning on an external variable and then undoes the conditioning the second method estimates the nonseparable function and the joint distribution of the observable and unobservable explanatory variables an external variable is used to impose an equality restriction at two points of support on the conditional distribution of the unobservable random term given the regressor and the external variable our methods apply to cross sections but our lead examples involve panel data cases in which the choice of the external variable is guided by the assumption that the distribution of the unobservable variables is exchangeable in the values of the endogenous variable for members of a group

identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity we extend the identification results for nonparametric simultaneous equations models in matzkin 2008 to situations where the observations on the vector of dependent variables might be limited and where the number of exogenous unobservable variables is larger than the number of dependent variables