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

revealed preference tests for weak separability an integer programming approach we present the revealed preference conditions that characterize the data sets that are consistent with the maximization of a weakly separable utility function we show that verifying these revealed preference conditions is np hard we also present an integer programming approach which is particularly attractive in view of empirical analysis we demonstrate the versatility of this integer programming approach by showing that it allows for testing homothetic separability and weak separability of the indirect utility function we illustrate the practical usefulness of the approach by an empirical application to spanish household consumption data

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

hz algebra spectra are differential graded algebras we show that the homotopy theory of differential graded algebras coincides with the homotopy theory of h algebra spectra namely we construct quillen equivalences between the quillen model categories of unbounded differential graded algebras and h algebra spectra we also construct quillen equivalences between the differential graded modules and module spectra over these algebras we use these equivalences in turn to produce algebraic models for rational stable model categories we show that basically any rational stable model category is quillen equivalent to modules over a differential graded algebra with many objects

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

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 models for discrete outcomes single equation instrumental variable models for discrete outcomes are shown to be set identifying not point identifying for the structural functions that deliver the values of the discrete outcome bounds on identified sets are derived for a general nonparametric model and sharp set identification is demonstrated in the binary outcome case point identification is typically not achieved by imposing parametric restrictions the extent of an identified set varies with the strength and support of instruments and typically shrinks as the support of a discrete outcome grows the paper extends the analysis of structural quantile functions with endogenous arguments to cases in which there are discrete outcomes

identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables abstract we develop a novel identification method for a partially linear model with multiple endogenous variables of interest but a single instrumental variable which could even be binary we present an easy to implement consistent estimator for the parametric part this estimator retains n convergence rate and asymptotic normality even though we have a generated regressor in our setup the nonparametric part of the model is also identified we also outline how our identification strategy can be extended to a fully non parametric model finally we use our methods to assess the impact of smoking during pregnancy on birth weight

the identification problem in systems nonlinear in the variables this paper examines the identifiability of the coefficients of a single equation in a simultaneous equation model which is nonlinear only in the variables the concept of identifiability in this model is motivated and developed using the closely related concept of observational equivalence this framework is then utilized to develop necessary and sufficient conditions for identifiability when the disturbances are required to be independent of the exogenous variables the approach recommended by fisher is shown to yield sufficient but not necessary conditions for identifiability for several relatively common special cases the necessary and sufficient conditions are found to simplify to the familiar rank condition for identifiability in the linear model the simultaneous equation model that is nonlinear only in the variables has enjoyed widespread application in economics such models are linear in the parameters and typically seem to be linear in the variables as well when viewing a single equation in many models the nonlinearity in the variables arises due to endogenous variables entering in different forms in different equations logged and unlogged form for example in macroeconometric models nonlinearity in the variables arises when the model includes endogenous real nominal and price variables which are nonlinearly related 2 whatever the reason for the nonlinearity in the variables it is important to determine the conditions under which the equations of such models can be identified

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

identification of nonseparable triangular models with discrete instruments identification of nonseparable triangular models we study the identification through instruments of a nonseparable function that relates a continuous outcome to a continuous endogenous variable using group and dynamical systems theories we show that full identification can be achieved under strong exogeneity of the instrument and a dual monotonicity condition even if the instrument is discrete when identified the model is also testable our results therefore highlight the identifying power of strong exogeneity when combined with monotonicity restrictions

a closed form estimator for quantile treatment effects with endogeneity abstract this paper studies the estimation of quantile treatment effects based on the instrumental variable quantile regression ivqr model chernozhukov and hansen 2005 i develop a class of flexible plug in estimators based on closed form solutions derived from the ivqr moment conditions the proposed estimators remain tractable and root n consistent while allowing for rich patterns of effect heterogeneity functional central limit theorems and bootstrap validity results for the estimators of the quantile treatment effects and other functionals are provided monte carlo simulations demonstrate favorable finite sample properties of the proposed approach i apply my method to reanalyze the causal effect of 401 k plans

code construction for the t user noiseless adder channel a general method for constructing codes for the t user noiseless adder channel is proposed which achieves the largest sum rate known the authors consider a multiple access communication system in this system t statistically independent sources which use binary block codes c sub 1 c sub t of equal length n simultaneously transmit information via one common channel maintaining synchronization with respect to words and bits the output of the adder channel is the t l ary vector which is the component wise arithmetic sum of the transmitted binary vectors the task of the decoder is to uniquely determine the messages of all users

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

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

rank estimators for monotonic index models we present a new class of rank estimators of scaled coefficients in semiparametric monotonic linear index models the estimators require no subjective bandwidth choices and have attractive computational properties we establish n consistency and asymptotic normality and provide the general form and consistent estimators of the asymptotic covariance matrix we also provide a generalization covering single equation multiple indices models satisfying certain monotonicity constraints an analogue of consistency when all explanatory variables are categorical is established and an application is presented

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

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

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

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

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

rank estimation of a generalized fixed effects regression model abstract this paper considers estimation of a fixed effects version of the generalized regression model of han 1987 journal of econometrics 35 303 316 the model allows for censoring places no parametric assumptions on the error disturbances and allows the fixed effects to be correlated with the covariates we introduce a class of rank estimators that consistently estimate the coefficients in the generalized fixed effects regression model the maximum score estimator for the binary choice fixed effects model is part of this class like the maximum score estimator the class of rank estimators converge at less than the n rate smoothed versions of these estimators however converge at rates approaching the n rate in a version of the model that allows for truncated data a sufficient condition for consistency of the estimators is that the error disturbances have an increasing hazard function

minimum distance from independence estimation of nonseparable instrumental variables models abstract i develop a semiparametric minimum distance from independence estimator for a nonseparable instrumental variables model an independence condition identifies the model for many types of discrete and continuous instruments the estimator is taken as the parameter value that most closely satisfies this independence condition implementing the estimator requires a quantile regression of the endogenous variables on the instrument so the procedure is two step with a finite or infinite dimensional nuisance parameter in the first step i prove consistency and establish asymptotic normality for a parametric but flexibly nonlinear outcome equation the consistency of the nonparametric bootstrap is also shown i illustrate the use of the estimator by estimating the returns to schooling using data from the 1979 national longitudinal survey

testing for monotonicity in unobservables under unconfoundedness monotonicity in a scalar unobservable is a common assumption when modeling heterogeneity in structural models among other things it allows one to recover the underlying structural function from certain conditional quantiles of observables nevertheless monotonicity is a strong assumption and in some economic applications unlikely to hold e g random coefficient models its failure can have substantive adverse consequences in particular inconsistency of any estimator that is based on it having a test for this hypothesis is hence desirable this paper provides such a test for cross section data we show how to exploit an exclusion restriction together with a conditional independence assumption which in the binary treatment literature is commonly called unconfoundedness to construct a test our statistic is asymptotically normal under local alternatives and consistent against global alternatives monte carlo experiments show that a suitable bootstrap procedure yields tests with reasonable level behavior and useful power we apply our test to study the role of unobserved ability in determining black white wage differences and to study whether engel curves are monotonically driven by a scalar unobservable

local indirect least squares and average marginal effects in nonseparable structural systems we study the scope of local indirect least squares lils methods for nonparametrically estimating average marginal effects of an endogenous cause x on a response y in triangular structural systems that need not exhibit linearity separability or monotonicity in scalar unobservables one main finding is negative in the fully nonseparable case lils methods cannot recover the average marginal effect lils methods can nevertheless test the hypothesis of no effect in the general nonseparable case we provide new nonparametric asymptotic theory treating both the traditional case of observed exogenous instruments z and the case where one observes only error laden proxies for z

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

nonparametric estimation of homothetic and homothetically separable functions for vectors x and w let r x w be a function that can be nonparametrically estimated consistently and asymptotically normally we provide consistent asymptotically normal estimators for the functions g and h where r x w h g x w g is linearly homogeneous and h is monotonic in g this framework encompasses homothetic and homothetically separable functions such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications extensions to related functional forms include a generalized partly linear model with unknown link function we provide simulation evidence on the small sample performance of our estimator and we apply our method to a chinese production dataset

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

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

a family of good uniquely decodable code pairs for the two access binary adder channel an explicit construction is presented of uniquely decodable code pairs for the two access binary erasure channel through a computer search we found many code pairs coming from this construction with a rate pair above the nonconstructive lower bound known in the literature also presented is a simple uniquely decodable code pair with a high rate pair found by a different method

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

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

when are two commutative c algebras stably homotopy equivalent let x and y be finite connected cw complexes with base points and let k denote the c algebra of compact operators on a separable infinite dimensional complex hilbert space the purpose of this paper is to study the question of when c0 x k is homotopy equivalent to c0 y k here c0 x is as usual the c algebra of continuous complex valued functions which vanish at the base point recall that two c algebras a and b are said to be homotopy equivalent written a b if there are homomorphisms a b and b a for which and may be deformed by a path of endomorphisms to the identity maps ida a a and idb b b respectively two c algebras a and b are called stably homotopy equivalent if a k b k this should not be confused with the notion of stable homotopy of spaces used in topology so another way of stating the problem we consider is when are c0 x and c0 y stably homotopy equivalent to begin with we should remark that the analogous question for homotopy equivalence has a simple answer c0 x and c0 y are homotopy equivalent if and only if x and y are based homotopy equivalent the situation for stable homotopy equivalence is more complicated and is closely related to k theory for example if two c algebras are stably homotopy equivalent then they have the same k theoretic invariants the main purpose of this paper is to show that the converse is not true we give an example of two spaces x and y which cannot be distinguished by

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

graph theoretic approaches to the code construction for the two user multiple access binary adder channel we relate coding for the two user multiple access binary adder channel to a problem in graph theory known as the independent set problem graph theoretic approaches to coding for both synchronized and nonsynchronized two user adder channels are presented using the tu an theorem on the independence number of a simple graph we are able to improve the lower bounds on the achievable rates of uniquely and delta decodable codes for the synchronized adder channel derived by kasami and lin we are also able to derive lower bounds on the achievable rates of uniquely decodable codes for the nonsynchronized adder channel we show that the rates of deaett wolf codes for the nonsynchronized adder channel fall below the bounds synchronizing sequences for the nonsynchronized adder channel are constructed

testing multivariate economic restrictions using quantiles the example of slutsky negative semidefiniteness abstract this paper is concerned with testing a core economic restriction negative semidefiniteness of the slutsky matrix we consider a system of nonseparable structural equations with infinite dimensional unobservables and employ quantile regression methods because they allow us to utilize the entire distribution of the data difficulties arise because the restriction involves several equations while the quantile is a univariate concept we establish that we may use quantiles of linear combinations of the dependent variable develop a new empirical process based test that applies kernel quantile estimators and investigate its finite and large sample behavior finally we apply all concepts to canadian microdata

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

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

a note on the estimation of a distribution function and quantiles by a kernel method there has recently been extensive work on the estimation by kernel methods of probability densities and their derivatives for a review see wertz 1978 for estimating the cumulative distribution function the empirical distribution function f is in a sense already quite smooth although it is known that further smoothing can be an advantage the object of the present note is to report briefly an investigation of kernel estimation applied to distribution function and quantiles further details are available from the author for independent and identically distributed random variables x1 x the usual kernel estimator of the density f is

identification of nonseparable models using instruments with small support i consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables if both the outcome and first stage equations are strictly increasing in a scalar unobservable then many kinds of continuous discrete and even binary instruments can be used to point identify the levels of the outcome equation this contrasts sharply with related work by imbens and newey 2009 that requires continuous instruments with large support one implication is that assumptions about the dimension of heterogeneity can provide nonparametric point identification of the distribution of treatment response for a continuous treatment in a randomized controlled experiment with partial compliance

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

nonparametric errors in variables models with measurement errors on both sides of the equation abstract measurement errors are often correlated as in surveys where respondent s biases or tendencies to err affect multiple reported variables we extend schennach 2007 to identify moments of the conditional distribution of a true y given a true x when both are measured with error the measurement errors in y and x are correlated and the true unknown model of y given x has nonseparable model errors after showing nonparametric identification we provide a sieve generalized method of moments based estimator of the model and apply it to nonparametric engel curve estimation in our application measurement errors on the expenditures of a good y are by construction correlated with measurement errors in total expenditures x this problem which is present in many consumption data sets has been ignored in most demand applications we find that accounting for this problem casts doubt on hildenbrand s 1994 increasing dispersion assumption

on independence conditions in nonseparable models observable and unobservable instruments this paper develops identification results employing independence conditions among unobservable variables the independence conditions are used to derive first stage nonseparable reduced form functions once constructed these reduced form functions are employed to express the derivatives of nonseparable structural functions in terms of the derivatives of the reduced form functions for models with simultaneity we obtain the new results by combining the independence assumptions together with parametric specifications and exclusion restrictions for models with triangularity we allow all functions to be nonparametric and nonseparable in unobservable random terms for the latter we provide several equivalence results and discuss some of the trade offs between observable and unobservable instruments

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

new uniquely decodable codes for the t user binary adder channel with 3 le t le 5 new uniquely decodable ud codes for 3 4 and 5 user binary adder channels are obtained in a computer search these codes improve the highest known rate of ud codes for such channels to log2 600 6ap1 5381 1 75 and log2 192 4ap1 8962 respectively