distortions of asymptotic confidence size in locally misspecified moment inequality models this paper studies the behavior under local misspecification of several confidence sets css commonly used in the literature on inference in moment in equality models we propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods this criterion is then applied to compare across test statistics and critical values employed in the construction of css we find two important results under weak assumptions first we show that css based on subsampling and generalized moment selection andrews and soares 2010 suffer from the same degree of asymptotic confidence size distortion despite the fact that asymptotically the latter can lead to css with strictly smaller expected volume under correct model specification second we show that the asymptotic confidence size of css based on the quasi likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of css based on the modified method of moments test statistic

inference for the correlation coefficient between potential outcomes in the gaussian switching regime model abstract we propose estimators of sharp bounds on the correlation coefficient between potential outcomes in the gaussian switching regime model and develop an asymptotically uniformly valid and non conservative confidence set for the true correlation coefficient a boundary interior category selection procedure is proposed to deal with discontinuity of the pointwise asymptotic distribution of estimators of the sharp bounds our confidence set is easy to implement it takes the form of a closed interval and its critical values have closed form expressions simulation study reveals the better finite sample performance of our confidence set than the naive confidence set ignoring the discontinuity issue

estimating dynamic models of imperfect competition we describe a two step algorithm for estimating dynamic games under the assumption that behavior is consistent with markov perfect equilibrium in the first step the policy functions and the law of motion for the state variables are estimated in the second step the remaining structural parameters are estimated using the optimality conditions for equilibrium the second step estimator is a simple simulated minimum distance estimator the algorithm applies to a broad class of models including industry competition models with both discrete and continuous controls such as the ericson and pakes 1995 model we test the algorithm on a class of dynamic discrete choice models with normally distributed errors and a class of dynamic oligopoly models similar to that of pakes and mcguire 1994

a two stage procedure for partially identified models abstract this paper studies a two stage procedure for estimating partially identified models based on chernozhukov hong and tamer s 2007 theory of set estimation and inference we consider the case where a sub vector of parameters or their identified set can be estimated separately from the rest possibly subject to a priori restrictions our procedure constructs the second stage set estimator and confidence set by taking appropriate level sets of a criterion function using a first stage estimator to impose restrictions on the parameter of interest we give conditions under which the two stage set estimator is a set valued random element that is measurable in an appropriate sense we also establish the consistency of the two stage set estimator

instrumental variables regression with weak instruments this paper develops asymptotic distribution theory for instrumental variable regression when the partial correlation between the instruments and a single included endogenous variable is weak here modeled as local to zero asymptotic representations are provided for various instrumental variable statistics including the two stage least squares tsls and limited information maximum likelihood liml estimators and their t statistics the asymptotic distributions are found to provide good approximations to sampling distributions with just 20 observations per instrument even in large samples tsls can be badly biased but liml is in many cases approximately median unbiased the theory suggests concrete quantitative guidelines for applied work these guidelines help to interpret angrist and krueger s 1991 estimates of the returns to education whereas tsls estimates with many instruments approach the ols estimate of 6 the more reliable liml and tsls estimates with fewer instruments fall between 8 and 10 with a typical confidence interval of 6 14

informational content of special regressors in heteroskedastic binary response models we quantify the informational content of special regressors in heteroskedastic binary response models with median independent or conditionally symmetric errors based on lewbel 1998 a special regressor is additively separable in the latent payoff and conditionally independent from the error term we find that with median independent errors a special regressor does not increase the identifying power by a criterion in manski 1988 or lead to positive fisher information for the coefficients even though it does help recover the average structural function with conditionally symmetric errors a special regressor improves the identifying power and the information for coefficients is positive under mild conditions we propose two estimators for binary response models with conditionally symmetric errors and special regressors

testing the order of a model using locally conic parametrization population mixtures and stationary arma processes in this paper we address the problem of testing hypotheses using the likelihood ratio test statistic in nonidentifiable models with application to model selection in situations where the parametrization for the larger model leads to nonidentifiability in the smaller model we give two major applications the case where the number of populations has to be tested in a mixture and the case of stationary arma p q processes where the order p q has to be tested we give the asymptotic distribution for the likelihood ratio test statistic when testing the order of the model in the case of order selection for armas the asymptotic distribution is invariant with respect to the parameters generating the process a locally conic parametrization is a key tool in deriving the limiting distributions it allows one to discover the deep similarity between the two problems

a practical two step method for testing moment inequalities this paper considers the problem of testing a finite number of moment inequalities we propose a two step approach in the first step a confidence region for the moments is constructed in the second step this set is used to provide information about which moments are negative a bonferonni type correction is used to account for the fact that with some probability the moments may not lie in the confidence region it is shown that the test controls size uniformly over a large class of distributions for the observed data an important feature of the proposal is that it remains computationally feasible even when the number of moments is large the finite sample properties of the procedure are examined via a simulation study which demonstrates among other things that the proposal remains competitive with existing procedures while being computationally more attractive

sharp identification regions in models with convex moment predictions we provide a tractable characterization of the sharp identi cation region of the parameters in a broad class of incomplete econometric models models in this class have set valued predictions that yield a convex set of conditional or unconditional moments for the observable model variables in short we call these models with convex moment predictions examples include static simultaneous move nite games of complete and incomplete information in the presence of multiple equilibria best linear predictors with interval outcome and covariate data and random utility models of multinomial choice in the presence of interval regressors data given a candidate value for we establish that the convex set of moments yielded by the model predictions can be represented as the aumann expectation of a properly de ned random set

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

non parametric tests of returns to scale this paper discusses various statistics for testing hypotheses regarding returns to scale in the context of non parametric models of technical efficiency in addition the paper presents bootstrap estimation procedures which yield appropriate critical values for the test statistics evidence on the true sizes and power of the various proposed tests is obtained from monte carlo experiments this paper is an extension of earlier work in manage sci 44 1998 49 j appl statist 27 2000b 779 c 2002 elsevier science b v all rights reserved

a test of non identifying restrictions and confidence regions for partially identified parameters abstract we propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables which do not necessarily identify the data generating process the restrictions can be derived from any model of interactions allowing censoring and multiple equilibria when the restrictions are parameterized the test can be inverted to yield confidence regions for partially identified parameters thereby complementing other proposals primarily chernozhukov et al chernozhukov v hong h tamer e 2007 estimation and confidence regions for parameter sets in econometric models econometrica 75 1243 1285

measures of the sensitivity of regression estimates to the choice of estimator abstract let y 1 y n denote independent real valued observations each of the form y j x j e j where x j is a fixed covariate vector and are unknown parameters e1 e n are identically distributed according to a symmetric density p this article considers the sensitivity of point estimates of to the choice of estimator from classes of estimators based on the l estimators of kroenker and portnoy specific measures of sensitivity are proposed these measures are applied to several datasets

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

weighted ks statistics for inference on conditional moment inequalities abstract this paper proposes set estimators and conservative confidence regions for the identified set in conditional moment inequality models using kolmogorov smirnov statistics with a truncated inverse variance weighting with increasing truncation points the new weighting differs from those proposed in the literature in two important ways first this paper shows that estimators based on ks statistics with the proposed weighting function converge to the identified set at a faster rate than existing procedures based on bounded weight functions in a broad class of models this provides a theoretical justification for inverse variance weighting in this context and contrasts with analogous results for conditional moment equalities in which optimal weighting only affects the asymptotic variance the results on rates of convergence of set estimators are the first such results even for the existing procedures and involve developing the first general framework for determining consistency and rates of convergence for set estimators and confidence regions in this context second the new weighting changes the asymptotic behavior including the rate of convergence of the ks statistic itself requiring a new asymptotic theory in choosing the critical value a series of examples illustrate the broad applicability of the results

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

testing for central dominance method and application central dominance cd introduced in gollier 1995 journal of economic theory is a risk concept that differs from stochastic dominance sd in an important way in particular cd implies a deterministic comparative static of a change in decision when risk changes but sd does not have such an implication in this paper we propose the first test of central dominance which amounts to checking a functional inequality we derive the asymptotic distribution of a lower bound of the proposed test and suggest a bootstrap procedure to compute the critical values we also conduct simulations to evaluate the performance of this test our empirical study finds clear evidence of cd relations between the s p 500 index return distributions during 2001 2013 and results in unambiguous implications for investment decisions

selective convexity in dea models in this paper we introduce a concept of selective convexity into the models of data envelopment analysis dea in this development each input and output can be judged individually with respect to its compliance with the convexity assumption the decision making units can be used to form convex combinations provided they are different only on the inputs and outputs for which the convexity assumption is accepted the free disposal hull standard variable returns to scale and quasi concave dea models are all special cases in the range of models obtained in this paper operationally the new models are solved as mixed integer linear programs both in the input and output oriented scenarios

on the optimization of fuzzy decision trees the induction of fuzzy decision trees is an important way of acquiring imprecise knowledge automatically fuzzy id3 and its variants are popular and efficient methods of making fuzzy decision trees from a group of training examples this paper points out the inherent defect of the likes of fuzzy id3 presents two optimization principles of fuzzy decision trees proves that the algorithm complexity of constructing a kind of minimum fuzzy decision tree is np hard and gives a new algorithm which is applied to three practical problems the experimental results show that with regard to the size of trees and the classification accuracy for unknown cases the new algorithm is superior to the likes of fuzzy id3

on the asymptotics of constrained m estimation limit theorems for an m estimate constrained to lie in a closed subset of r d are given under two different sets of regularity conditions a consistent sequence of global optimizers converges under chernoff regularity of the parameter set a n consistent sequence of local optimizers converges under clarke regularity of the parameter set in either case the asymptotic distribution is a projection of a normal random vector on the tangent cone of the parameter set at the true parameter value limit theorems for the optimal value are also obtained agreeing with chernoff s result in the case of maximum likelihood with global optimizers

the set of weighted regression estimates abstract we present in this article several results that characterize the set of all weighted regressions the set of weighted regression estimates is the set of all generalized least squares estimates for covariance matrices that have positive weights on the diagonal and have zeroes elsewhere the study of sets of estimates is a method for dealing with distributional uncertainty which does not require the strong assumption of a particular distribution we show that the set of weighted regressions is the union of the bounded convex polytopes formed by the hyperplanes on which residuals are zero for the two dimensional case we provide a simple method for outlining the set and give an efficient method for selecting the weighted regressions that determine the convex hull of the set finally we discuss two examples that illustrate the use of these results

likelihood ratio of unidentifiable models and multilayer neural networks this paper discusses the behavior of the maximum likelihood estimator mle in the case that the true parameter cannot be identified uniquely among many statistical models with unidentifiability neural network models are the main concern of this paper it is known in some models with unidentifiability that the asymptotics of the likelihood ratio of the mle has an unusually larger order using the framework of locally conic models put forth by dacunha castelle and gassiat as a generalization of hartigan s idea a useful sufficient condition of such larger orders is derived this result is applied to neural network models and a larger order is proved if the true function is given by a smaller model also under the condition that the model has at least two redundant hidden units a log n lower bound for the likelihood ratio is derived

asymptotics for likelihood ratio tests under loss of identifiability this paper describes the large sample properties of the likelihood ratio test statistic lrts when the parameters characterizing the true null distribution are not unique it is well known that the classical asymptotic theory for the likelihood ratio test does not apply to such problems and the lrts may not have the typical chi squared type limiting distribution this paper establishes a general quadratic approximation of the log likelihood ratio function in a hellinger neighborhood of the true density which is valid with or without loss of identifiability of the true distribution under suitable conditions the asymptotic null distribution of the lrts under loss of identifiability can be obtained by maximizing the quadratic form these results extend the work of chernoff and le cam in particular applications to testing the number of mixture components in finite mixture models are discussed

efficient estimation of monotone boundaries let g 0 1 0 1 be a monotone nondecreasing function and let g be the closure of the set x y is an element of 0 1 x 0 1 0 less than or equal to y less than or equal to g x we consider the problem of estimating the set g from a sample of i i d observations uniformly distributed in g the estimation error is measured in the hausdorff metric we propose the estimator which is asymptotically efficient in the minimax sense

globally optimal fuzzy decision trees for classification and regression a fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure this extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods while remaining easily interpretable fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a cart decision tree a training rule for fuzzy trees similar to backpropagation in neural networks is designed this rule corresponds to a global optimization algorithm that fixes the parameters of the fuzzy splits the method developed for the automatic generation of fuzzy decision trees is applied to both classification and regression problems in regression problems it is seen that the continuity constraint imposed by the function representation of the fuzzy tree leads to substantial improvements in the quality of the regression and limits the tendency to overfitting in classification fuzzification provides a means of uncovering the structure of the probability distribution for the classification errors in attribute space this allows the identification of regions for which the error rate of the tree is significantly lower than the average error rate sometimes even below the bayes misclassification rate

top down induction of fuzzy pattern trees fuzzy pattern tree induction was recently introduced as a novel machine learning method for classification roughly speaking a pattern tree is a hierarchical tree like structure whose inner nodes are marked with generalized fuzzy logical operators and whose leaf nodes are associated with fuzzy predicates on input attributes a pattern tree classifier is composed of an ensemble of such pattern trees one for each class label this type of classifier is interesting for several reasons for example since a single pattern tree can be considered as a kind of logical description of a class it is quite appealing from an interpretation point of view moreover in terms of classification accuracy the method has shown promising performance in first experimental studies yet as will be argued in this paper the algorithm that has originally been proposed for learning fuzzy pattern trees from data offers scope for improvement here we propose a new method that modifies the original proposal in several ways notably our learning algorithm reverses the direction of pattern tree construction from bottom up to top down additionally a different termination criterion is proposed that is more adapted to the learning problem at hand experimentally it will be shown that our approach is indeed able to outperform the original learning method in terms of predictive accuracy

semiparametric identification of binary decision games of incomplete information with correlated private signals abstract this paper studies the identification and estimation of a static binary decision game of incomplete information we make no parametric assumptions on the joint distribution of private signals and allow them to be correlated we show that the parameters of interest can be point identified subject to a scale normalization under mild support requirements for the regressors publicly observed state variables and errors private signals following manski and tamer 2002 we propose a maximum score type estimator for the structural parameters and establish the asymptotic properties of the estimator

efficiency analysis with ratio measures abstract in applications of data envelopment analysis dea data about some inputs and outputs is often available only in the form of ratios such as averages and percentages in this paper we provide a positive answer to the long standing debate as to whether such data could be used in dea the problem arises from the fact that ratio measures generally do not satisfy the standard production assumptions e g that the technology is a convex set our approach is based on the formulation of new production assumptions that explicitly account for ratio measures this leads to the estimation of production technologies under variable and constant returns to scale assumptions in which both volume and ratio measures are native types of data the resulting dea models allow the use of ratio measures as is without any transformation or use of the underlying volume measures this provides theoretical foundations for the use of dea in applications where important data are reported in the form of ratios

inference for parameters defined by moment inequalities using generalized moment selection the topic of this paper is inference in models in which parameters are defined by moment inequalities and or equalities the parameters may or may not be identified this paper introduces a new class of confidence sets and tests based on generalized moment selection gms gms procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative the power of gms tests is compared to that of subsampling m out of n bootstrap and plug in asymptotic pa tests the latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size in a uniform sense for the moment inequality equality model gms tests are shown to have asymptotic power that dominates that of subsampling m out of n bootstrap and pa tests subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of pa tests

a plug in approach to support estimation we suggest a new approach based on the use of density estimators for the problem of estimating the compact support of a multivariate density this subject motivated in terms of pattern analysis by grenander has interesting connections with detection and clustering a natural class of density based estimators is defined universal consistency results and convergence rates are established for these estimators with respect to the usual measure based metric d between sets further convergence rates with respect to both d and the hausdorff metric d h are also obtained under some fairly intuitive shape restrictions

asymptotically exact inference in conditional moment inequality models this paper derives the rate of convergence and asymptotic distribution for a class of kolmogorov smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions using these results i propose tests that are more powerful than existing approaches for choosing critical values for this test statistic i quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches a monte carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples in an application to a regression of prescription drug expenditures on income with interval data from the health and retirement study confidence regions based on the new tests are substantially tighter than those based on existing methods

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

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

structural estimation of pairwise stable networks with nonnegative externality abstract this paper develops a framework to structurally estimate pairwise stable networks with nonnegative externality we characterize pairwise stable equilibria as a fixed point of a certain mapping and show that the set of pairwise stable equilibria with nonnegative externality is a complete lattice we extend the characterization to an econometric framework for structural estimation based on the moment inequality model we apply our methodology to friendship networks of students in the united states using data from add health we find that the preference toward racial homophily is overestimated if we do not control for the preference toward clustering

induction of fuzzy decision trees abstract most decision tree induction methods used for extracting knowledge in classification problems do not deal with cognitive uncertainties such as vagueness and ambiguity associated with human thinking and perception in this paper cognitive uncertainties involved in classification problems are explicitly represented measured and incorporated into the knowledge induction process a fuzzy decision tree induction method which is based on the reduction of classification ambiguity with fuzzy evidence is developed fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise conflict and missing information

specification tests for partially identified models defined by moment inequalities this paper studies the problem of specification testing in partially identified models defined by moment in equalities this problem has not been directly addressed in the literature although several papers have suggested a test based on checking whether confidence sets for the parameters of interest are empty or not referred to as test bp we propose two new specification tests denoted test rs and test rc that achieve uniform asymptotic size control and dominate test bp in terms of power in any finite sample and in the asymptotic limit

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

impossibility results for nondierentiable functionals we examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution this situation arises in a number of applications of bounds analysis and moment inequality models and in recent work on estimating optimal dynamic treatment regimes drawing on earlier work relating dierentiability to the existence of unbiased and regular estimators we show that if the target object is not continuously dierentiable in the parameters of the data distribution there exist no locally asymptotically unbiased estimators and no regular estimators this places strong limits on estimators bias correction methods and inference procedures

nonparametric inference for counterfactual means bias correction confidence sets and weak iv abstract this paper supplements manski 1990 and manski and pepper 2000 and contributes to the literature by introducing the concept of weak iv for the partially identified mean counterfactual outcomes when an instrumental variable iv or a monotone instrumental variable miv is available iv or miv assumption respectively developing asymptotically uniformly valid confidence sets for the counterfactual mean outcomes and average treatment effects under the assumptions correcting biases of estimates of bounds on the counterfactual mean outcomes under the assumptions we apply the confidence sets to further examining the effect of family intactness on a child s high school graduation originally studied in manski et al 1992

partial identification using random set theory abstract this paper illustrates how the use of random set theory can benefit partial identification analysis we revisit the origins of manski s work in partial identification e g manski 1989 manski 1990 focusing our discussion on identification of probability distributions and conditional expectations in the presence of selectively observed data statistical independence and mean independence assumptions and shape restrictions we show that the use of the choquet capacity functional and the aumann expectation of a properly defined random set can simplify and extend previous results in the literature we pay special attention to explaining how the relevant random set needs to be constructed depending on the econometric framework at hand we also discuss limitations in the applicability of specific tools of random set theory to partial identification analysis

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

pivotal statistics for testing structural parameters in instrumental variables regression we propose a novel statistic for testing the structural parameters in instrumental variables regression the statistic is straightforward to compute and has a limiting distribution that is pivotal with a degrees of freedom parameter that is equal to the number of tested parameters it therefore differs from the anderson rubin statistic whose limiting distribution is pivotal but has a degrees of freedom parameter that is equal to the number of instruments and the likelihood based wald likelihood ratio and lagrange multiplier statistics whose limiting distributions are not pivotal we analyze the relationship between the statistic and the concentrated likelihood of the structural parameters and show that its limiting distribution is not affected by weak instruments we discuss examples of the non standard shapes of the asymptotically pivotal confidence sets that can be constructed using the statistic and investigate its power properties to show its importance for practical purposes we apply the statistic to the angrist krueger 1991 data and find similar results as in staiger and stock 1997 this discussion paper has resulted in a publication in econometrica 2002 70 5 1781 1803

confidence sets for partially identified parameters that satisfy a finite number of moment inequalities this paper proposes a computationally simple way to construct confidence sets for a parameter of interest in models comprised of moment inequalities building on results from the literature on multivariate one sided tests i show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities the associated test statistic has an asymptotic chi bar square distribution and can be inverted to construct an asymptotic confidence set for the parameter of interest even if that parameter is only partially identified critical values for the test are easily computed and a monte carlo study demonstrates implementation and finite sample performance

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

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

bayesian moment based inference in a regression model with misclassification error we present a bayesian analysis of a regression model with a binary covariate that may have classification measurement error prior research demonstrates that the regression coefficient is only partially identified we take a bayesian approach which adds assumptions in the form of priors on the unknown misclassification probabilities the approach is intermediate between the frequentist bounds of previous literature and strong assumptions which achieve point identification and thus preferable in many settings we present two simple algorithms to sample from the posterior distribution when the likelihood function is not fully parametric but only satisfies a set of moment restrictions we focus on how varying amounts of information contained in a prior distribution on the misclassification probabilities change the posterior of the parameters of interest while the priors add information to the model they do not necessarily tighten the identified set however the information is sufficient to tighten bayesian inferences we also consider the case where the mismeasured binary regressor is endogenous we illustrate the use of our bayesian approach in a simulated data set and an empirical application investigating the association between narcotic pain reliever use and earnings

bounds on treatment effects on transitions abstract this paper considers the identification of treatment effects on conditional transition probabilities we show that even under random assignment only the instantaneous average treatment effect is point identified since treated and control units drop out at different rates randomization only ensures the comparability of treatment and controls at the time of randomization so that long run average treatment effects are not point identified instead we derive bounds on these average effects our bounds do not impose semi parametric restrictions for example proportional hazards we also explore assumptions such as monotone treatment response common shocks and positively correlated outcomes that tighten the bounds

a complete fuzzy decision tree technique in this paper a new method of fuzzy decision trees called soft decision trees sdt is presented this method combines tree growing and pruning to determine the structure of the soft decision tree with refitting and backfitting to improve its generalization capabilities the method is explained and motivated and its behavior is first analyzed empirically on 3 large databases in terms of classification error rate model complexity and cpu time a comparative study on 11 standard uci repository databases then shows that the soft decision trees produced by this method are significantly more accurate than standard decision trees moreover a global model variance study shows a much lower variance for soft decision trees than for standard trees as a direct cause of the improved accuracy

is this the least squares estimate it is shown that the sum of squares can have several local minima with a positive probability for any intrinsically nonlinear regression with infinite tails therefore the availability of global criteria is crucial the concept of the local convexity level for the sum of squares in nonlinear regression models is introduced a general formula for this local convexity level is derived and it is shown that the local convexity level is equal to the minimum of the squared radius of the full curvature of the expectation surface of the nonlinear regression two general global criteria are formulated the ideas are illustrated by four types of nonlinear model namely polylinear power linear m regression and exponential regression models the suggested global criteria are shown to work well for real life data

pattern trees induction a new machine learning method fuzzy classification is one of the most important applications in fuzzy set and fuzzy logic related research its goal is to find a set of fuzzy rules that form a classification model most of the existing fuzzy rule induction methods e g the fuzzy decision trees fdts induction method focus on searching rules consisting of triangular norms t norms i e and only but not triangular conorms t conorms or explicitly this may lead to the omission of generating important rules that involve t conorms explicitly this paper proposes a type of tree termed pattern trees pts that makes use of different aggregations including both t norms and t conorms like decision trees pts are an effective tool for classification applications this paper discusses the difference between decision trees and pts and also shows that the subsethood based method sbm and the weighted subsethood based method wsbm are two specific cases of pt induction a novel pt induction method is proposed using similarity measure and fuzzy aggregations the comparison to other classification methods including sbm wsbm c4 5 nearest neighbor support vector machine and fdt induction shows that 1 pts can obtain high accuracy rates in classifications 2 pts are robust to overfltting and 3 pts especially simple pattern trees spts maintain compact tree structures

a dual approach to inference for partially identified econometric models abstract this paper considers inference for the set i of parameter values that minimize a criterion function chernozhukov et al 2007 cht develop a general theory of estimation and inference using the level set of a criterion function we establish a dual relationship between the level set estimator and its support function and show that the properly normalized support function provides alternative wald type inference methods these methods can be used to obtain confidence sets for i and points inside it for models with finitely many moment inequalities we show that our wald type statistic is asymptotically equivalent to cht s statistic under regularity conditions

global sensitivity results for generalized least squares estimates abstract the covariance matrix for the residuals of a regression process is written as the identity matrix plus a matrix v the matrix v is bounded from above and the corresponding set of generalized least squares estimates is identified the extreme estimates in this set are functions of the usual t statistics in particular the number t k 8 1 2 t measures the influence of reweighting extreme observations where t k gives the degrees of freedom t is the t statistic and the weights on observations are allowed to vary by a factor of at most 2

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

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

some impossibility theorems in econometrics with applications to structural and dynamic models general characterizations of valid confidence sets and tests in problems which involve locally almost unidentified lau parameters are provided and applied to several econo metric models two types of inference problems are studied i inference about parame ters which are not identifiable on certain subsets of the parameter space and ii inference about parameter transformations with discontinuities when a lau parameter or parametric function has an unbounded range it is shown under general regularity conditions that any valid confidence set with level 1 a for this parameter must be unbounded with probability close to 1 a in the neighborhood of nonidentification subsets and will have a nonzero probability of being unbounded under any distribution compatible with the model no valid confidence set which is almost surely bounded does exist these properties hold even if identifying restrictions are imposed similar results also obtain for parameters with bounded ranges consequently a confidence set which does not satisfy this characterization has zero coverage probability level this will be the case in particular for wald type confidence intervals based on asymptotic standard errors furthermore wald type statistics for testing given values of a lau parameter cannot be pivotal functions i e they have distributions which depend on unknown nuisance param eters and even cannot be usefully bounded over the space of the nuisance parameters these results are applied to several econometric problems inference in simultaneous equations instrumental variables iv regressions linear regressions with autoregressive errors inference about long run multipliers and cointegrating vectors for example it is shown that standard asymptotically justified confidence intervals based on iv estimators such as two stage least squares and the associated standard errors have zero coverage probability and the corresponding t statistics have distributions which cannot be bounded by any finite set of distribution functions a result of interest for interpreting iv regressions with weak instruments furthermore expansion methods e g edgeworth expansions and bootstrap techniques cannot solve these difficulties finally in a number of cases where wald type methods are fundamentally flawed e g iv regressions with poor instruments it is observed that likelihood based methods e g likelihood ratio tests and confidence sets combined with projection techniques can easily yield valid tests and confidence sets

instrumental variable methods for recovering continuous linear functionals abstract this paper develops methods for estimating continuous linear functionals in nonparametric instrumental variable problems examples of such functionals include consumer surplus and weighted average derivatives the estimation procedure is robust to a setting where the underlying model is not identified but the linear functional is in order to attain such robustness it is necessary to employ a partially identified nuisance parameter we address this problem by consistently estimating a unique element of the identified set for nuisance parameters which we then use to construct a n asymptotically normal estimator for the desired linear functional

modeling heaped duration data an application to neonatal mortality in 2005 the indian government launched a conditional cash incentive program to encourage institutional delivery this paper studies the effects of the program on neonatal mortality using district level household survey data we model mortality using survival analysis paying special attention to substantial heaping a form of measurement error present in the data the main objective of this paper is to provide a set of sufficient conditions for identification and consistent estimation of the discretized baseline hazard accounting for heaping and unobserved heterogeneity our identification strategy requires neither administrative data nor multiple measurements but a correctly reported duration point and the presence of some flat segment s in the baseline hazard we establish the asymptotic properties of the maximum likelihood estimator and derive a set of specification tests that allow among other things to test for the presence of heaping and to compare different heaping mechanisms our empirical findings do not suggest a significant reduction of mortality in treated districts however they do indicate that accounting for heaping matters for the estimation of the hazard parameters

a class of partially adaptive one step m estimators for the non linear regression model with dependent observations in this paper we consider a class of partially adaptive one step m estimators for the non linear regression model with dependent observations those estimators adapt themselves with respect to a measure of the tailthickness of the disturbance distribution as well as to a measure of the scale the large sample behavior of those estimators is examined theoretically for general disturbance distributions and numerically for various specific ones the estimators considered are motivated by the student r maximum likelihood estimator given appropriate specifications of the adaptation parameter the estimators are asymptotically efficient on the family of student t distributions including the normal distribution