the bivariate probit model maximum likelihood estimation pseudo true parameters and partial identification abstract this paper examines the notion of identification by functional form for two equation triangular systems for binary endogenous variables by providing a bridge between the literature on the recursive bivariate probit model and that on partial identification we evaluate the impact of functional form on the performance of quasi maximum likelihood estimators and investigate the practical importance of available instruments in both cases of correct and incorrect distributional specification finally we calculate average treatment effect bounds and demonstrate how properties of the estimators are explicable via a link between the notion of pseudo true parameters and the concepts of partial identification

semiparametric estimation of censored selection models with a nonparametric selection mechanism abstract in this paper estimation of the coefficients in a single index selectivity bias model is considered under the assumption that the selection correction function depends on the conditional mean of some observable selection variable the estimation method follows a familiar two step strategy the first step uses a nonparametric regression estimator for the selection variable while the second step uses a weighted instrumental variables estimator for the coefficients in the equation of interest the paper gives conditions under which the proposed estimator is root n consistent and asymptotically normal the proposed method is applied to data on labor supply

sharp bounds on treatment effects in a binary triangular system this paper considers the evaluation of the average treatment effect ate in a triangular system with binary dependent variables i impose a threshold crossing model on both the endogenous regressor and the outcome the bounds proposed by shaikh and vytlacil 2011 sv on the ate are sharp only under a restrictive condition on the support of the covariates and the instruments which rules out a wide range of models and many relevant applications in this setting i provide a methodology that allows the construction of sharp bounds on the ate by efficiently using the variation of covariates without imposing support restrictions

doubly robust estimation of the local average treatment effect curve we consider estimation of the causal effect of a binary treatment on an outcome conditionally on covariates from observational studies or natural experiments in which there is a binary instrument for treatment we describe a doubly robust locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates v when randomization of the instrument is only true conditionally on a high dimensional vector of covariates x possibly bigger than v we discuss the surprising result that inference is identical to inference for the parameters of a model for an additive treatment effect on the treated conditionally on v that assumes no treatment instrument interaction we illustrate our methods with the estimation of the local average effect of participating in 401 k retirement programs on savings by using data from the us census bureau s 1991 survey of income and program participation

estimation of heterogeneous individual treatment effects with endogenous treatments this article estimates individual treatment effects ite and its probability distribution in a triangular model with binary valued endogenous treatments our estimation procedure takes two steps

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

minimax regret treatment choice with covariates or with limited validity of experiments abstract this paper continues the investigation of minimax regret treatment choice initiated by manski 2004 consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a sample a certain scoring rule is known to achieve minimax regret in simple versions of this decision problem i investigate its sensitivity to perturbations of the decision environment in realistic directions they are as follows i treatment outcomes may be influenced by a covariate whose effect on outcome distributions is bounded in one of numerous probability metrics this is interesting because introduction of a covariate with unrestricted effects leads to a pathological result ii the experiment may have limited validity because of selective noncompliance or because the sampling universe is a potentially selective subset of the treatment population thus even large samples may generate misleading signals these problems are formalized via a bounds approach that turns the problem into one of partial identification in both scenarios small but positive perturbations leave the minimax regret decision rule unchanged thus minimax regret analysis is not knife edge dependent on ignoring certain aspects of realistic decision problems indeed it recommends to entirely disregard covariates whose effect is believed to be positive but small as well as small enough amounts of missing data or selective attrition all findings are finite sample results derived by game theoretic analysis

semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables this paper provides estimators of discrete choice models including binary ordered and multinomial response choice models the estimators closely resemble ordinary and two stage least squares the distribution of the model s latent variable error is unknown and may be related to the regressors e g the model could have errors that are heteroscedastic or correlated with regressors the estimator does not require numerical searches even for multinomial choice for ordered and binary choice models the estimator is root n consistent and asymptotically normal a consistent estimator of the conditional error distribution is also provided

identification and wavelet estimation of weighted ate under discontinuous and kink incentive assignment mechanisms abstract this paper studies identification estimation and inference of a weighted average treatment effect w ate parameter in a class of switching regime models where the agent s selection of treatment is affected by either a discontinuous or kink incentive assignment mechanism and some unobservable characteristic for each assignment mechanism we i establish identification and propose a local wavelet estimator of the w ate ii establish asymptotic properties of the local wavelet estimator including optimal convergence rate and asymptotic normality and iii investigate the finite sample performance of the local wavelet estimators and compare them with local polynomial estimators via an extensive simulation study we also propose an identification robust wavelet estimator of the w ate

bounds on treatment effects from studies with imperfect compliance abstract this article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect the bounds provided are the tightest possible given the distribution of assignments treatments and responses the formulas show that even with high rates of noncompliance experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population

a structural analysis of the correlated random coefficient wage regression model abstract we estimate a dynamic programming model of schooling decisions in which the log wage regression function is set within a correlated random coefficient model we show that estimates of the dynamic programming model can be used to obtain a number of treatment effects including the local average treatment effect late however unlike late parameters obtained in a standard iv framework our late estimates are obtained without imposing separability between individual specific heterogeneity and schooling choices and are therefore not subject to a monotonicity restriction we find that returns to schooling are characterized by a high degree of dispersion across individuals

treatment effect bounds an application to swan ganz catheterization abstract we reanalyze data from the observational study by connors et al 1996 on the impact of swan ganz catheterization on mortality outcomes the study by connors et al 1996 assumes that there are no unobserved differences between patients who are catheterized and patients who are not catheterized and finds that catheterization increases patient mortality we instead allow for such differences between patients by implementing both the instrumental variable bounds of manski 1990 which only exploits an instrumental variable and the bounds of shaikh and vytlacil 2011 which exploit mild nonparametric structural assumptions in addition to an instrumental variable we propose and justify the use of indicators of weekday admission as an instrument for catheterization in this context we find that in our application the manski 1990 bounds do not indicate whether catheterization increases or decreases mortality where as the shaikh and vytlacil 2011 bounds reveal that at least for some diagnoses swan ganz catheterization reduces mortality at 7 days after catheterization we show that the bounds of shaikh and vytlacil 2011 remain valid under even weaker assumptions than those described in shaikh and vytlacil 2011 we also extend the analysis to exploit a further nonparametric structural assumption that doctors catheterize individuals with systematically worse latent health and find that this assumption further narrows these bounds and strengthens our conclusions in our analysis we construct confidence regions using the methodology developed in romano and shaikh 2008 we show in particular that the confidence regions are uniformly consistent in level over a large class of possible distributions for the observed data that include distributions where the instrument is arbitrarily weak

nonparametric and distribution free estimation of the binary threshold crossing and the binary choice models in this paper it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term this identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term the estimator is shown to be strongly consistent and a two step procedure for its calculation is developed the paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results

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

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

limited information estimators and exogeneity tests for simultaneous probit models a two step maximum likelihood procedure is proposed for estimating simultaneous probit models and is compared to alternative limited information estimators conditions under which each estimator attains the cramer rao lower bound are obtained simple tests for exogeneity based on the new two step estimator are proposed and are shown to be asymptotically equivalent to one another and to have the same local asymptotic power as classical tests based on the limited information maximum likelihood estimator finite sample comparisons between the new and alternative estimators are presented based on some monte carlo evidence the performance of the proposed tests for exogeneity is also assessed

endogenous selection or treatment model estimation in a sample selection or treatment effects model common unobservables may affect both the outcome and the probability of selection in unknown ways this paper shows that the distribution function of potential outcomes conditional on covariates can be identified given an observed variable v that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes selection model estimators based on this identification are provided which take the form of simple weighted averages gmm or two stage least squares these estimators permit endogenous and mismeasured regressors empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model

inference on causal effects in a generalized regression kink design we consider nonparametric identification and estimation in a nonseparable model where a continuous regressor of interest is a known deterministic but kinked function of an observed assignment variable we characterize a broad class of models in which a sharp regression kink design rkd or rk design identifies a readily interpretable treatment on the treated parameter florens heckman meghir and vytlacil 2008 we also introduce a fuzzy regression kink design generalization that allows for omitted variables in the assignment rule noncompliance and certain types of measurement errors in the observed values of the assignment variable and the policy variable our identifying assumptions give rise to testable restrictions on the distributions of the assignment variable and predetermined covariates around the kink point similar to the restrictions delivered by lee 2008 for the regression discontinuity design using a kink in the unemployment benefit formula we apply a fuzzy rkd to empirically estimate the effect of benefit rates on unemployment durations in austria

spectral measures and the bade reflexivity theorem let b be a strongly equicontinuous boolean algebra of projections on the quasi complete locally convex space x and assume that the space l x of continuous linear operators on x is sequentially complete for the strong operator topology methods of integration with respect to spectral measures are used to show that the closed algebra generated by b in l x consists precisely of those continuous linear operators on x which leave invariant each closed b invariant subspace of x

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

identification and estimation in a correlated random coefficients binary response model we study a linear index binary response model with random coefficients bb allowed to be correlated with regressors x we identify the mean of the distribution of b and show how the mean can be interpreted as a vector of expected relative effects we use instruments and a control vector v to make x independent of b given v this leads to a localize then average approach to both identification and estimation we develop a n consistent and asymptotically normal estimator of a trimmed mean of the distribution of bb explore its small sample performance through simulations and present an application

heterogeneous treatment effects instrumental variables without monotonicity imbens and angrist 1994 were the first to exploit a monotonicity condition in order to identify a local average treatment effect parameter using instrumental variables more recently heckman and vytlacil 1999 suggested the estimation of a variety of treatment effect parameters using a local version of their approach we investigate the sensitivity of the respective estimates to random departures from monotonicity approximations to the respective bias terms are derived in an empirical application the bias is calculated and bias corrected estimates are obtained the accuracy of the approximation is investigated in a monte carlo study

instrumental variables and the sign of the average treatment effect abstract this paper considers identification and inference about the sign of the average effect of a binary endogenous regressor or treatment on a binary outcome of interest when a binary instrument is available in this setting the average effect of the endogenous regressor on the outcome is sometimes referred to as the average treatment effect ate we consider four different sets of assumptions instrument exogeneity instrument exogeneity and monotonicity on the outcome equation instrument exogeneity and monotonicity on the equation for the endogenous regressor or instrument exogeneity and monotonicity on both the outcome equation and the equation for the endogenous regressor for each of these sets of conditions we characterize when i the distribution of the observed data is inconsistent with the assumptions and ii the distribution of the observed data is consistent with the assumptions and the sign of ate is identified a distinguishing feature of our results is that they are stated in terms of a reduced form parameter from the population regression of the outcome on the instrument in particular we find that the reduced form parameter being far enough but not too far from zero implies that the distribution of the observed data is consistent with our assumptions and the sign of ate is identified while the reduced form parameter being too far from zero implies that the distribution of the observed data is inconsistent with our assumptions for each set of restrictions we also develop methods for simultaneous inference about the consistency of the distribution of the observed data with our restrictions and the sign of the ate when the distribution of the observed data is consistent with our restrictions we show that our inference procedures are valid uniformly over a large class of possible distributions for the observed data that include distributions where the instrument is arbitrarily weak a novel feature of the methodology is that the null hypotheses involve unions of moment inequalities

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

identification of binary response models abstract this article studies identification of the threshold crossing model of binary response most research on binary response has considered specific estimators and tests the study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods it also clarifies the connections between reduced form and structural analyses of binary response data assume that the binary outcome z is determined by an observable random vector x and by an unobservable scalar u through a model z 1 x u 0 also assume that fu x the probability distribution of u conditional on x is continuous and strictly increasing given these maintained assumptions we investigate the identifiability of given the following restrictions on the distributions fu x x x mean independence quantile independence index sufficiency statistical independence and statistical independence with the distribution known we find that mean independence has n

regression and weighting methods for causal inference using instrumental variables please see the supplementary material for a correction and a new result recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables ivs for causal inference a basic idea is that ivs serve as an experimental handle the turning of which may change each individual s treatment status and through and only through this effect also change observed outcome the average difference in observed outcome relative to that in treatment status gives the average treatment effect for those whose treatment status is changed in this hypothetical experiment we build on the modern iv framework and develop two estimation methods in parallel to regression adjustment and propensity score weighting in the case of treatment selection based on covariates the iv assumptions are made explicitly conditional on covariates to allow for the fact that instruments can be related to these background variables the regression method focuses on the relationship between respo

a simulation based estimator for hidden markov random fields an estimator for estimating the parameters of a markov random field x from inaccurate observations is introduced the author considers first a markov gibbs random field x x sub i j on a lattice l i j i 1 2 n j 1 2 m the marginal distributions of x sub i j x sub i u j v u v 1 0 1 are first estimated from an image then random fields x are simulated with the probability of x sub i u j v b nearly equal to the estimate of p x sub i j x sub i u b a simulation method similar to the gibbs sampler is used the parameters of the markov random field model are estimated from the x s with the pseudolikelihood method

criteria for closedness of spectral measures and completeness of boolean algebras of projections abstract the intimate connection between spectral measures and complete boolean algebras of projections in banach spaces was intensively investigated by w bade in the 1950s linear operators iii spectral operators wiley interscience new york 1971 chap xvii it is well known that the most satisfactory situation occurs when the boolean algebra is actually complete rather than just complete this makes it desirable to have available criteria not just in banach spaces but also in the nonnormable setting which can be used to determine the completeness of boolean algebras of projections such criteria which should be effective and applicable in practice as general as possible and apply to extensive classes of spaces are presented in this article a series of examples shows that these criteria are close to optimal

semiparametric bounds on treatment effects we present a variety of semiparametric models that produce bounds on the average causal effect of a binary treatment on a binary outcome the semiparametric assumptions exploit variation in observable covariates to narrow the bounds in our main model the outcome is determined by a generalized linear model but the treatment may be arbitrarily endogenous our bounding strategy does not require the existence of an instrument but incorporating an instrument narrows the bounds the bounds are further improved by combining the semiparametric model with the joint threshold crossing assumption of shaikh and vytlacil 2005

dynamic treatment effects this paper develops robust models for estimating and interpreting treatment effects arising from both ordered and unordered multi stage decision problems identification is secured through instrumental variables and or conditional independence matching assumptions we decompose treatment effects into direct effects and continuation values associated with moving to the next stage of a decision problem using our framework we decompose the iv estimator showing that iv generally does not estimate economically interpretable or policy relevant parameters in prototypical dynamic discrete choice models unless policy variables are instruments continuation values are an empirically important component of estimated total treatment effects of education we use our analysis to estimate the components of what late estimates in a dynamic discrete choice model

analysis of the bias of matching and difference in difference under alternative earnings and selection processes matching and difference in difference did are two widespread methods that use pre treatment outcomes to correct for selection bias i detail the sources of bias of both estimators in a model of earnings dynamics and entry into a job training program jtp and i assess their performances using monte carlo simulations of the model calibrated with realistic parameter values i find that matching generally underestimates the average causal effect of the program and gets closer to the true effect when conditioning on an increasing number of pre treatment outcomes when selection bias is symmetric around the treatment date did is consistent when implemented symmetrically i e comparing outcomes observed the same number of periods before and after the treatment date when selection bias is not symmetric monte carlo simulations show that symmetric did still performs better than matching especially in the middle of the life cycle these results are consistent with estimates of the bias of matching and did from randomly assigned jtps some of the virtues of symmetric did extend to programs other than jtps allocated according to a cutoff eligibility rule

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

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

confidence intervals for the quantile of treatment effects in randomized experiments abstract in this paper we explore partial identification and inference for the quantile of treatment effects for randomized experiments first we propose nonparametric estimators of sharp bounds on the quantile of treatment effects and establish their asymptotic properties under general conditions second we construct confidence intervals for the bounds and the true quantile by using the approach in chernozhukov et al 2009 third under additional conditions we develop a new approach to construct confidence intervals for the bounds and the true quantile and refer to it as the order statistic approach a simulation study is conducted to investigate the finite sample performance of both approaches

estimation of marginal effects in semiparametric selection models with binary outcomes this paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting we focus on developing an estimator for the marginal effects this marginal effect estimator uses only observations where the selection probability is above a certain threshold a key innovation is that this high probability set is adaptive to the data we establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends monte carlo studies show that these estimators perform well in finite samples

semiparametric estimation of monotone and concace utility functions for polychotomous choice models this paper introduces a semiparametric estimation method for polychotomous choice models the method does not require a parametric structure for the systematic subutility of observable exogenous variables the distribution of the random terms is assumed to be known up to a finite dimensional parameter vector in contrast previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified the systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory the estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent a computational technique to calculate the estimators is developed copyright 1991 by the econometric society

semiparametric estimation of a simultaneous game with incomplete information abstract this paper studies the problem of estimating the normal form payoff parameters of a simultaneous discrete game where the realization of such payoffs is not common knowledge the paper contributes to the existing literature in two ways first by making a comparison with the complete information case it formally describes a set of conditions under which allowing for private information in payoffs facilitates the identification of various features of the game second focusing on the incomplete information case it presents an estimation procedure based on the equilibrium properties of the game that relies on weak semiparametric assumptions and relatively flexible information structures which allow players to condition their beliefs on signals whose exact distribution function is unknown to the researcher the proposed estimators recover unobserved beliefs by solving a semiparametric sample analog of the population bayesian nash equilibrium conditions the asymptotic features of such estimators are studied for the case in which the distribution of unobserved shocks is known and the case in which it is unknown in both instances equilibrium uniqueness is assumed to hold only in a neighborhood of the true parameter value and for a subset z of realizations of the signals multiple equilibria are allowed elsewhere in the parameter space and no equilibrium selection theory is involved extensions to games where beliefs are conditioned on unobservables as well as general games with many players and actions are also discussed an empirical application of a simple capital investment game is included

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

testing for causal effects in a generalized regression model with endogenous regressors a unifying framework to test for causal effects in nonlinear models is proposed we consider a generalized linear index regression model with endogenous regressors and no parametric assumptions on the error disturbances to test the significance of the effect of an endogenous regressor we propose a statistic that is a kernel weighted version of the rank correlation statistic tau of kendall 1938 the semiparametric model encompasses previous cases considered in the literature continuous endogenous regressors blundell and powell 2003 and a single binary endogenous regressor vytlacil and yildiz 2007 but the testing approach is the first to allow for i multiple discrete endogenous regressors ii endogenous regressors that are neither discrete nor continuous e g a censored variable and iii an arbitrary mix of endogenous regressors e g one binary regressor and one continuous regressor

intersection bounds estimation and inference we develop a practical and novel method for inference on intersection bounds namely bounds defined by either the infimum or supremum of a parametric or nonparametric function or equivalently the value of a linear programming problem with a potentially infinite constraint set we show that many bounds characterizations in econometrics for instance bounds on parameters under conditional moment inequalities can be formulated as intersection bounds our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters and also applies to models with inequalities that are nonseparable in parameters since analog estimators for intersection bounds can be severely biased in finite samples routinely underestimating the size of the identified set we also offer a median bias corrected estimator of such bounds as a by product of our inferential procedures we develop theory for large sample inference based on the strong approximation of a sequence of series or kernel based empirical processes by a sequence of penultimate gaussian processes these penultimate processes are generally not weakly convergent and thus are non donsker our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes our construction also provides new adaptive inequality moment selection methods we provide conditions for the use of nonparametric kernel and series estimators including a novel result that establishes strong approximation for any general series estimator admitting linearization which may be of independent interest

identification in nonparametric simultaneous equations models this paper provides conditions for identification of functionals in nonparametric simultaneous equations models with nonadditive unobservable random terms the conditions are derived from a characterization of observational equivalence between models we show that in the models considered observational equivalence can be characterized by a restriction on the rank of a matrix the use of the new results is exemplified by deriving previously known results about identification in parametric and nonparametric models as well as new results a stylized method for analyzing identification which is useful in some situations is also presented

identifying effects of multivalued treatments multivalued treatment models have typically been studied under restrictive assumptions ordered choice and more recently unordered monotonicity we show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity our results rely on two main assumptions treatment assignment must be a measurable function of threshold crossing rules and enough continuous instruments must be available we illustrate our approach for several classes of models

robust causal inference with continuous instruments using the local instrumental variable curve instrumental variables are commonly used to estimate effects of a treatment afflicted by unmeasured confounding and in practice instruments are often continuous e g measures of distance or treatment preference however available methods for continuous instruments have important limitations they either require restrictive parametric assumptions for identification or else rely on modelling both the outcome and the treatment process well and require modelling effect modification by all adjustment covariates in this work we develop the first semiparametric doubly robust estimators of the local instrumental variable effect curve i e the effect among those who would take treatment for instrument values above some threshold and not below in addition to being robust to misspecification of either the instrument or treatment or outcome processes our approach also incorporates information about the instrument mechanism and allows for flexible data adaptive estimation of effect modification we discuss asymptotic properties under weak conditions and use the methods to study infant mortality effects of neonatal intensive care units with high versus low technical capacity using travel time as an instrument

semiparametric instrumental variable estimation of treatment response models this article introduces a new class of instrumental variable iv estimators for linear and nonlinear treatment response models with covariates the rationale for focusing on nonlinear models is that if the dependent variable is binary or limited or if the effect of the treatment varies with covariates a nonlinear model is appropriate in the spirit of roehrig econometrica 56 1988 433 identification is attained nonparametrically and does not depend on the choice of the parametric specification for the response function of interest one virtue of this approach is that it allows the researcher to construct estimators that can be interpreted as the parameters of a well defined approximation to a treatment response function under functional form misspecification in contrast to some usual iv models heterogeneity of treatment effects is not restricted by the identification conditions the ideas and estimators in this article are illustrated using iv to estimate the effects of 401 k retirement programs on savings

conditional mean estimation via jump diffusion processes in multiple target tracking recognition a new algorithm is presented for generating the conditional mean estimates of functions of target positions orientations and type in recognition and tracking of an unknown number of targets and target types taking a bayesian approach a posterior measure is defined on the tracking target parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model and a prior based on airplane dynamics the newtonian force equations governing rigid body dynamics are utilized to form the prior density on airplane motion the conditional mean estimates are generated using a random sampling algorithm based on jump diffusion processes for empirically generating mmse estimates of functions of these random target positions orientations and type under the posterior measure results are presented on target tracking and identification from an implementation of the algorithm on a networked silicon graphics workstation and decmpp maspar parallel machine

linear instrumental variable estimation of limited dependent variable models with endogenous explanatory variables abstract the purpose of this paper is to present and analyze an instrumental variables estimator for limited dependent variable models that does not require functional form assumptions for the distribution of disturbances this estimator is a weighted instrumental variables estimator where the weight is the ratio of a multivariate normal density to the actual density of the instrumental variables a semi non parametric estimator of the weights is presented and some conjectures concerning the asymptotic distribution of the estimator are discussed

partial identification in triangular systems of equations with binary dependent variables this paper studies the special case of the triangular system of equations in vytlacil and yildiz 2007 where both dependent variables are binary but without imposing the restrictive support condition required by vytlacil and yildiz 2007 for identification of the average structural function asf and the average treatment effect ate under weak regularity conditions we derive upper and lower bounds on the asf and the ate we show further that the bounds on the asf and ate are sharp under some further regularity conditions and an additional restriction on the support of the covariates and the instrument

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

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

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

inference in nonparametric instrumental variables with partial identification this paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework we construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction the same test statistic can be employed under identification in which case the hypothesis is whether the true model satisfies the posited property an almost sure consistent bootstrap procedure is provided for obtaining critical values possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set as an illustration we obtain confidence intervals for the level and slope of brazilian fuel engel curves a monte carlo study examines finite sample performance

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

testing the correlated random coefficient model the recent literature on instrumental variables iv features models in which agents sort into treatment status on the basis of gains from treatment as well as on baseline pretreatment levels components of the gains known to the agents and acted on by them may not be known by the observing economist such models are called correlated random coefficient models sorting on unobserved components of gains complicates the interpretation of what iv estimates this paper examines testable implications of the hypothesis that agents do not sort into treatment based on gains in it we develop new tests to gauge the empirical relevance of the correlated random coefficient model to examine whether the additional complications associated with it are required we examine the power of the proposed tests we derive a new representation of the variance of the instrumental variable estimator for the correlated random coefficient model we apply the methods in this paper to the prototypical empirical problem of estimating the return to schooling and find evidence of sorting into schooling based on unobserved components of gains

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

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

counting rotten apples student achievement and score manipulation in italian elementary schools abstract we derive bounds on the distribution of math and language scores of elementary school students in italy correcting for pervasive manipulation a natural experiment that randomly assigns external monitors to schools is used to deal with endogeneity of manipulation as well as its mismeasurement in the data bounds are obtained from properties of the statistical model used to detect classes with manipulated scores and from restrictions on the relationship between manipulation and true scores our results show that regional rankings by academic performance are reversed once manipulation is taken into account

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