can one measure the temperature of a curve the entropy of a plane curve is defined in terms of the number of intersection points with a random line the gibbs distribution which maximizes the entropy enables one to define the temperature of the curve at 0 temperature the curve reduces to a straight segment at high temperature the curve is somewhat chaotic and behaves like a perfect gas we attempt to show that thermodynamic formalism can be used for the study of plane curves the curves we discuss have finite length unlike mandelbrot s fractal curves 1 yet we feel our approach to the mathematics is not far from his

development of special finite elements for free boundaries a modified two dimensional quadrilateral plane stress element and a modified three dimensional brick element have been developed to eliminate the weakness of the conventional finite elements in determining the stress distributions along free boundaries the results obtained by the said modified elements are in good agreement with the theoretical and experimental results and are superior to the conventional finite element results a comparison is made between the proposed approach of improving stress calculations and another approach which employs the least square fitting method the comparison shows that the two approaches provide comparable accuracy but the latter is more difficult to implement

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

isoperimetric phase transitions of two dimensional droplets we consider two dimensional assemblies of particles governed by hamiltonians depending on the area and the perimeter of their convex hull provided the hamiltonian is quadratically homogeneous in the coordinates we find an exact formula for the free energy phase transitions resulting from the competition between area and perimeter can easily be produced and explicitly dealt with we illustrate those features by a simple example undergoing a second order transition

the droplet in the tube a case of phase transition in the canonical ensemble we consider the 2 dimensional ising model with ferromagnetic nearest neighbour interaction at inverse temperature lets n t be the total magnetization inside ann n square box per be the gibbs state in with periodic b c andm be the spontaneous magnetization we show the existence of the limit psi varrho mathop lim limits n to infty left frac 1 beta n right ln mu lambda per s n n varrho for m provided is large enough it turns out that the quantity is closely related to the wulf construction and the dependence of the function on is singular

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

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

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

toward a hybrid trefftz element with a hole for elasto plasticity the paper deals with the modelling of riveted assemblies for full scale complete aircraft crashworthiness many comparisons between experiments and fe computations of bird impacts onto aluminium riveted panels have shown that macroscopic plastic strains were not sufficiently developed and localised in the riveted shell fe in the impact area consequently fe models never succeed in initialising and propagating the rupture in the sheet metal plates and along rivet rows as shown by experiments without calibrating the input data especially the damage and failure properties of the riveted shell fe to model the assembly correctly it appears necessary to investigate on fe techniques such as hybrid trefftz finite element method h t fem indeed perforated fe plates developed for elastic problems based on a hybrid trefftz formulation have been found in the open literature our purpose is to find a way to extend this formulation so that the super element can be used for crashworthiness to reach this aim the main features of an elastic hybrid trefftz plate are presented and are then followed by a discussion on the possible extensions finally the interpolation functions of the element are evaluated numerically

a high precision element with a central circular hole an eight node rectangular membrane element with a central circular hole has been developed using complex potentials to define stress and strain functions this new element type can be combined with the conventional elements e g isoparametric elements with no modifications required two numerical examples were employed to illustrate the superiority and versatility of the proposed element type the results obtained using the said element type are closer to the theoretical results as compared with those obtained by similar types of elements

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

adjoint transform overconvexity and sets of constant width the properties of the adjoint transform associating to a set the in tersection of all disks of given radius centered in the set are systematically in vestigated in particular its relationship with the overconvex the parallelisation and completion of sets sets conjugate by the transform can be characterised in a new way as the union or the intersection of all completions of the reference body new relationships satisfied by their areas and perimeters are derived two applications in problems of random intersection of disks are finally treated

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

partial identification of functionals of the joint distribution of potential outcomes in this paper we present a systematic study of partial identification of two general classes of functionals of the joint distribution of two potential outcomes when a bivariate sample from the joint distribution is not available to the econometrician assuming the identification of the conditional marginal distributions of potential outcomes and the distribution of the covariate vector we show that the identified sets for functionals in both classes are intervals and provide conditions under which the identified sets point identify the true value of the functionals in addition we establish sufficient and necessary conditions for the covariate information to be informative in the sense of shrinking the identified sets we focus on the application of our general results to evaluating distributional treatment effects of a binary treatment in two commonly used frameworks in the literature for evaluating average treatment effects the selection on observables framework and a latent threshold crossing model we characterize the role of the propensity score in the selection on observables framework and the role of endogenous selection in the latent threshold crossing model examples of policy parameters that our results apply include the correlation coefficient between the potential outcomes many inequality measures of the distribution of treatment effects and median of the distribution of the individual treatment effect

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

reply to comments by r piltner on development of two dimensional elements with a central circular hole comput methods appl mech engrg 188 2000 431 440

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

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

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

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

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

on the microscopic validity of the wulff construction and of the generalized young equation for a large class of 1 1 dimensional interfaces of the solid on solid type we prove on a microscopic basis the validity of the wulff construction and of the generalized young equation which gives the contact angle of a sessile drop on a wall our proof relies on a new method to treat random walks with a finite number of global constraints

local model uncertainty and incomplete data bias with discussion problems of the analysis of data with incomplete observations are all too familiar in statistics they are doubly difficult if we are also uncertain about the choice of model we propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation the increase in variance when an assumed model is correct the bias in estimation when the model is incorrect examples include non ignorable missing data hidden confounders in observational studies and publication bias in meta analysis doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model the problem of assessing the risk of lung cancer from passive smoking is used as a motivating example

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

about the lipschitz property of the metric projection in the hilbert space abstract we consider the metric projection operator from the real hilbert space onto a strongly convex set we prove that the restriction of this operator on the complement of some neighborhood of the strongly convex set is lipschitz continuous with the lipschitz constant strictly less than 1 this property characterizes the class of strongly convex sets and to a certain degree the hilbert space we apply the results obtained to the question concerning the rate of convergence for the gradient projection algorithm with differentiable convex function and strongly convex set

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

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

semiparametric identification and heterogeneity in discrete choice dynamic programming models abstract empirical discrete choice dynamic programming models have become important empirical tools a question that arises in estimation and interpretation of the results from these specifications is which combination of data and assumptions are needed to overcome problems of heterogeneity selection and omited variables bias this paper addresses this question by considering nonparametric identification of a version of the model that allows for quite general forms of unobservable and information structures i show that the model can be identified under conditions similar to a static polychotomous choice model using a stochastic version of an identification of infinity argument utility can be identified up to a monotonic transformation of the observables under strong support conditions and two types of exclusion restriction the first type is similar to a standard static exclusion restriction a variable that influences the first period decision but does not enter the second period decision directly the second type requires a variable that does not affect the utility of the first option directly but is known during the first period and has predictive power on the choice during the second i also provide two specifications under which the full error structure can be identified this requires the additional assumption of stochastic innovations in the observables i then use the model to estimate schooling decisions in which students deciding whether to drop out of high school account for the option value of attending college

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

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

bayesian inference in a correlated random coefficients model modeling causal effect heterogeneity with an application to heterogeneous returns to schooling abstract we consider the problem of causal effect heterogeneity from a bayesian point of view this is accomplished by introducing a three equation system similar in spirit to the work of heckman and vytlacil 1998 describing the joint determination of a scalar outcome an endogenous treatment variable and an individual specific causal return to that treatment we describe a bayesian posterior simulator for fitting this model which recovers far more than the average causal effect in the population the object which has been the focus of most previous work parameter identification and generalized methods for flexibly modeling the outcome and return heterogeneity distributions are also discussed combining data sets from high school and beyond hsb and the 1980 census we illustrate our methods in practice and investigate heterogeneity in returns to education our analysis decomposes the impact of key hsb covariates on log wages into three parts a direct effect and two separate indirect effects through educational attainment and returns to education our results strongly suggest that the quantity of schooling attained is determined at least in part by the individual s own return to education specifically a one percentage point increase in the return to schooling parameter is associated with the receipt of approximately 0 14 more years of schooling furthermore when we control for variation in returns to education across individuals we find no difference in predicted schooling levels for men and women however women are predicted to attain approximately 1 4 of a year more schooling than men on average as a result of higher rates of return to investments in education

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

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

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

improved estimation of controlled direct effects in the presence of unmeasured confounding of intermediate variables adjusting for a causal intermediate is a common analytic strategy for estimating an average causal direct effect acde the acde is the component of the total exposure effect that is not relayed through the specified intermediate even if the total effect is unconfounded the usual acde estimate may be biased when an unmeasured variable affects the intermediate and outcome variables using linear programming optimization to compute non parametric bounds we develop new acde estimators for binary measured variables in this causal structure and use root mean square confounding bias rmsb to compare their performance with the usual stratified estimator in simulated distributions of target populations comprised of the 64 possible potential response types as well as distributions of target populations restricted to subsets of 18 or 12 potential response types defined by monotonicity or no interactions assumptions of unit level causal effects we also consider target population distributions conditioned on fixed outcome risk among the unexposed or fixed true acde in one stratum of the intermediate results show that a midpoint estimator constructed from the optimization bounds has consistently lower rmsb than the usual stratified estimator both unconditionally and conditioned on any risk in the unexposed when conditioning on true acde this midpoint estimator performs more poorly only when conditioned on an extreme true acde in one stratum of the intermediate yet outperforms the stratified estimator in the other stratum when interaction is permitted an alternate limit modified crude estimator can never perform less favourably than the stratified estimator and often has lower rmsb

identifying dynamic discrete decision processes in this paper we analyze the nonparametric identification of dynamic discrete choice models our methodology is based on the insight of hotz and miller 1993 that bellman equations can be interpreted as moment conditions we consider cases with and without unobserved heterogeneity not only do we show that these models are not identified rust 1994 we are also able to determine their exact degree of underidentification we begin with the case without correlated unobserved heterogeneity using bellman equations as moment conditions we show that utility functions in each alternative cannot be nonparametrically identified as long as the following structural parameters are not set the distribution function of unobserved preference shocks the discount rate and the current and future preferences in one reference alternative we also investigate how exclusion or parametric restrictions can provide identifying restrictions as the identification proof is constructive a simple method of moment estimator can be derived and overidentifying restrictions can be tested provided that one is willing to make stronger identifying assumptions dynamic discrete choice modelling is thus little different from the continuous case bellman equations can be used to recover deep structural parameters as are euler equations we continue by exploring a case where the unobserved component of preferences is correlated over time even if the functional degree of underidentification of this model is larger we present reasonable identifying assumptions that lead to the same identification results as without unobserved heterogeneity the same methodology using moment conditions is applied this paper expands upon the work in rust 1994 where the generic nonidentification result is stated we use a slightly different model in our case agents preferences have unobservable and possibly persistent components the constructive aspect of our proof allows us to interpret rust s underidentification result and to propose identifying restrictions on the technical side the insights for our identification strategy are borrowed from the works of hotz and miller 1993 hotz et al 1994 and altug and miller 1998 we

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

swapping the nested fixed point algorithm a class of estimators for discrete markov decision models this paper proposes a new nested algorithm npl for the estimation of a class of discrete markov decision models and studies its statistical and computational properties our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities when the npl algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities successive iterations return a sequence of estimators of the structural parameters which we call k stage policy iteration estimators we show that the sequence includes as extreme cases a hotz miller estimator for k 1 and rust s nested fixed point estimator in the limit when k furthermore the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator we illustrate the performance of our method with several examples based on rust s bus replacement model monte carlo experiments reveal a trade off between finite sample precision and computational cost in the sequence of policy iteration estimators

lipschitz selections of the diametric completion mapping in minkowski spaces we develop a constructive completion method in general minkowski spaces which successfully extends a completion procedure due to buckner in two and three dimensional euclidean spaces we prove that this generalized buckner completion is locally lipschitz continuous thus solving the problem of finding a continuous selection of the diametric completion mapping in finite dimensional normed spaces the paper also addresses the study of an elegant completion procedure due to maehara in euclidean spaces the natural setting of which are the spaces with a generating unit ball we prove that in these spaces the maehara completion is also locally lipschitz continuous besides establishing other geometric properties of this completion the paper contains also new estimates of the local lipschitz constants for the wide spherical hull

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

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

comments on development of two dimensional elements with a central circular hole a k soh z f long comput methods appl mech engrg 188 2000 431 440

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

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

a characterization of monotone unidimensional latent variable models recently the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by ellis and van den wollenberg and by junker we generalize their work with a de finetti like characterization of the distribution of repeated measures x x 1 x 2 that can be represented with mixtures of likelihoods of independent but not identically distributed random variables where the data satisfy a stochastic ordering property with respect to the mixing variable the random variables x j may be arbitrary real valued random variables we show that the distribution of x can be given a monotone unidimensional latent variable representation that is useful in the sense of junker if and only if this distribution satisfies conditional association ca and a vanishing conditional dependence vcd condition which asserts that finite subsets of the variables in x become independent as we condition on a larger and larger segment of the remaining variables in x it is also interesting that the mixture representation is in a certain ordinal sense unique when ca and vcd hold the characterization theorem extends and simplifies the main result of junker and generalizes methods of ellis and van den wollenberg to a much broader class of models exchangeable sequences of binary random variables also satisfy both ca and vcd as do exchangeable sequences arising as location mixtures in the same way that de finetti s theorem provides a path toward justifying standard i i d mixture components in hierarchical models on the basis of our intuitions about the exchangeability of observations this theorem justifies one dimensional latent variable components in hierarchical models in terms of our intuitions about positive association and redundancy between observations because these conditions are on the joint distribution of the observable data x they may also be used to construct asymptotically power 1 tests for unidimensional latent variable models

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

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

uniformly convex subsets of the hilbert space with modulus of convexity of the second order we prove that in the hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius we also obtain an estimate of this radius

development of two dimensional elements with a central circular hole abstract two new two dimensional 2d elements one is a eight node rectangular and the other is a eight node circular element each with a central circular hole have been developed using complex potentials to define stress and strain functions these new elements can be combined with the conventional elements e g isoparametric elements with no modifications required two numerical examples were employed to illustrate the potential accuracy and versatility of the proposed elements the results obtained using these two elements are in good agreement with the theoretical results moreover the proposed rectangular element performs better than the proposed circular element

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

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

porosity and unique completion in strictly convex spaces we are concerned in this paper with topological and stochastic properties of the family mathcal g of all closed convex sets with a unique extension to a complete set with the help of a strengthened version of a lemma by groemer we show that in minkowski spaces with a strictly convex norm mathcal g is lower porous this improves a previous result from groemer geom dedicata 20 319 334 1986 where in the same context mathcal g was proved to be nowhere dense in contrast to this fact we show that in these spaces there is a stochastic construction procedure which provides a complete set with probability one this generalizes an earlier result of bavaud trans amer math soc 333 1 315 324 1992 proved for the particular case of the euclidean plane

a flexible parametric approach for estimating switching regime models and treatment effect parameters in this paper we propose a flexible parametric class of switching regime models allowing for both skewed and fat tailed outcome and selection errors specifically we model the joint distribution of each outcome error and the selection error via a newly constructed class of multivariate distributions which we call generalized normal mean variance mixture distributions we extend heckman s two step estimation procedure for the gaussian switching regime model to the new class of models when the distributions of the outcome errors are asymmetric we show that an additional correction term accounting for skewness in the outcome error distribution besides the analogue of the well known inverse mill s ratio needs to be included in the second step regression we use the two step estimators of parameters in the model to construct simple estimators of average treatment effects and establish their asymptotic properties simulation results confirm the importance of accounting for skewness in the outcome errors in estimating both model parameters and the average treatment effect and the treatment effect for the treated

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

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

a hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions a hybrid finite element approach is proposed for the mechanical response of two dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes in conventional finite element methods many elements must be used to represent one inclusion in this work each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion in numerically approximating stress and displacement distributions around the inclusion classical elasticity solutions for a multiply connected region are employed a modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense the accuracy and efficiency of the proposed method are demonstrated by two boundary value problems in one example the results based on the proposed method with only 64 hybrid elements 450 degrees of freedom are shown to be almost identical to those based on the traditional method with 2928 conventional elements 5526 degrees of freedom

statistical mechanics of convex bodies the difficulties inherent in the construction of two dimensional pressure ensembles are discussed and are tackled by defining an energy cost depending on the convex hull of the set of particles an energy proportional to the area of the convex hull is not able to prevent evaporation of the system whereas an energy proportional to the area of the circumcircle of the convex hull ensures a thermodynamic behavior in the latter model which turns out to be exactly solvable various characterizations are given of the geometry of a typical state

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

hybrid trefftz plane elasticity elements with p method capabilities a family of p method plane elasticity elements is derived based on the hybrid trefftz formulation 1 exact solutions of the lame navier equations are used for the intra element displacement field together with an independent displacement frame function field along the element boundary the final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid side nodes since the element matrices do not involve integration over the element area the elements have a polygonal contour with an optional number of curved sides the quadrilateral element has the same external appearance as the conventional p method plane elasticity element 2 3 but unlike in the conventional p method approach suitable special purpose trefftz functions are generally used to handle the singularity and or stress concentration problems rather than a local mesh refinement the practical efficiency of the new elements is assessed through a series of examples

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

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

stress analysis around holes or notches by special finite elements in this paper three special elements for stress concentration analysis around holes or notches are presented one is based on a variational principle involving displacements unsymmetric stresses and rotations as independent variables the other two on the classical hellinger reissner principle the new elements are designed to be used in a single layer along the cavity rim where enhanced properties are needed to get a satisfactory level of accuracy special properties are obtained by enforcing the stress approximation to satisfy a priori the traction free boundary condition on the element side positioned along the cavity rim and by properly enriching the displacement interpolation the proposed elements are applicable to geometries of arbitrary shape easy to use low cost and readily implementable into existing finite element codes copyright 2005 john wiley sons ltd

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