instrumental variable estimation of nonlinear models with nonclassical measurement error using control variables we consider nonlinear models with an independent variable that is measured with error the measurement error can be correlated with the true value i e the measurement error is allowed to be nonclassical we show that we can use a control variate estimator to estimate the parameters of interest if we are prepared to make an assumption of the joint distribution of the rst stage

lyapunov based boundary feedback design for parabolic pdes this paper presents a methodology for the construction of simple control lyapunov functionals clfs for boundary controlled parabolic partial differential equations pdes the proposed methodolog

time dependent transformations in deformation quantization we study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics we extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time dependent coordinate transformations this result considerably enlarges the set of possible phase space representations of quantum mechanics and makes it possible to construct a causal representation for the distributional sector of wigner quantum mechanics

estimation and inference with weak semi strong and strong identification this paper analyzes the properties of standard estimators tests and confidence sets cs s for parameters that are unidentified or weakly identified in some parts of the parameter space the paper also introduces methods to make the tests and cs s robust to such identification problems the results apply to a class of extremum estimators and corresponding tests and cs s that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification this covers a class of models estimated using maximum likelihood ml least squares ls quantile generalized method of moments generalized empirical likelihood minimum distance and semi parametric estimators the consistency lack of consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions the asymptotic sizes in a uniform sense of standard and identification robust tests and cs s are established the results are applied to the arma 1 1 time series model estimated by ml and to the nonlinear regression model estimated by ls in companion papers the results are applied to a number of other models

correlated probit analysis of repeatedly measured ordinal and continuous outcomes with application to the health and retirement study the health and retirement study was designed to evaluate changes in health and labor force participation during and after the transition from working to retirement every 2 years participants provided information about their self rated health srh body mass index bmi smoking status and other characteristics our goal was to assess the effects of smoking and gender on trajectories of change in bmi and srh over time joint longitudinal analysis of outcome measures is preferable to separate analyses because it allows to account for the correlation between the measures to test the effects of predictors while controlling type i error and potentially to improve efficiency however because srh is an ordinal measure while bmi is continuous formulating a joint model and parameter estimation is challenging a joint correlated probit model allowed us to seamlessly account for the correlations between the measures over time established estimating procedures for such models are based on quasi likelihood or numerical approximations that may be biased or fail to converge therefore we proposed a novel expectation maximization algorithm for parameter estimation and a monte carlo bootstrap approach for standard errors approximation expectation maximization algorithms have been previously considered for combinations of binary and or continuous repeated measures however modifications were needed to handle combinations of ordinal and continuous responses a simulation study demonstrated that the algorithm converged and provided approximately unbiased estimates with sufficiently large sample sizes in the health and retirement study male gender and smoking were independently associated with steeper deterioration in self rated health and with lower average bmi copyright 2016 john wiley sons ltd

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

mixed h2 h sampled data output feedback control design for a semi linear parabolic pde in the sense of spatial l norm abstract this paper addresses distributed mixed h 2 h sampled data output feedback control design for a semi linear parabolic partial differential equation pde with external disturbances in the sense of spatial l norm under the assumption that a finite number of local piecewise measurements in space are available at sampling instants a static sampled data output feedback controller is suggested where the sampling interval in time is bounded the local piecewise measurements bring additional difficulty for the exponential stability and performance analysis since the existing poincare wirtinger inequality in 1d spatial domain is not applicable by constructing an appropriate lyapunov krasovskii functional candidate and employing wirtinger s inequalities a variant of poincare wirtinger inequality in 1d spatial domain as well as agmon s inequality it is shown that the suggested static sampled data output feedback controller not only guarantees the output exponential stability of the resulting closed loop pde in the spatial l norm but also ensures the mixed h 2 h performance index defined in the spatial l norm if the sufficient conditions presented in terms of standard linear matrix inequalities lmis are fulfilled the satisfactory and better performance of the suggested sampled data feedback controller is demonstrated by numerical simulation results of an illustrative example

conditions for the convolution of two wigner distributions to be itself a wigner distribution the convolution of two wigner distribution functions wdf s is always non negative but not always a wdf as jagannathan et al phys lett a 120 161 1987 have shown in this paper conditions are given that are sufficient and probably necessary for such a convolution to be a wdf and a new characterization of gaussian wdf s is obtained as a by product

when is the wigner function of multidimensional systems nonnegative it is shown that for systems with an arbitrary number of degrees of freedom a necessary and sufficient condition for the wigner function to be nonnegative is that the corresponding state wavefunction is the exponential of a quadratic form this result generalizes the one obtained by hudson rep math phys 6 249 1974 for one dimensional systems

sampled data observers for semilinear damped wave equations under spatially sampled state measurements abstract sampled data observers controllers under the sampled in space and time measurements were suggested in the past for parabolic systems in the present paper for the first time a sampled data observer is constructed for a hyperbolic system governed by 1d semilinear wave equation with either viscous or boundary damping the measurements are sampled in space and time sufficient conditions for the exponential stability of the estimation error are derived by using the time delay approach to sampled data control and appropriate lyapunov krasovskii functionals the dual sampled data controller problems are formulated numerical examples including observer design for unstable damped sine gordon equation illustrate the efficiency of the method

panel data methods for fractional response variables with an application to test pass rates we revisit the effects of spending on student performance using data from the state of michigan in addition to exploiting a dramatic change in funding in the mid 1990s and subsequent nonsmooth changes we propose nonlinear panel data models that recognize the bounded nature of the pass rate importantly we show how to estimate average partial effects which can be compared across many different models linear and nonlinear under different assumptions and estimated using many different methods we find that spending has nontrivial and statistically significant effects although the diminishing effect is not especially pronounced

efficient estimation of limited dependent variable models with endogenous explanatory variables abstract this paper discusses asymptotically efficient estimation of the parameters of limited dependent variable models with endogenous explanatory variables general results on asymptotic efficiency of two stage and amemiya gls estimators are derived and used to obtain a simple asymptotically efficient estimator of the structural coefficients this estimator can be calculated by applying gls to estimates of the reduced form coefficients that are obtained by using reduced form residuals as additional explanatory variables it is also shown that it is possible to obtain asymptotically efficient estimators of the other coefficients by a modified minimum chi square method

quantum symmetries and the weyl wigner product of group representations in the usual formulation of quantum mechanics groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex hilbert space in accordance with wigner s theorem in the phase space formulation they have real true unitary representations in the space of square integrable functions on phase space each such phase space representation is a weyl wigner product of the corresponding hilbert space representation with its contragredient and these can be recovered by factorizing the weyl wigner product however not every real unitary representation on phase space corresponds to a group of automorphisms so not every such representation is in the form of a weyl wigner product and can be factorized the conditions under which this is possible are examined examples are presented

a symplectic extension map and a new shubin class of pseudo differential operators for an arbitrary pseudo differential operator a s rn s rn with weyl symbol a s r2n we consider the pseudo differential operators a s rn k s rn k associated with the weyl symbols a a 12k s where 12k x 1 for all x r2k and s is a linear symplectomorphism of r2 n k we call the operators a symplectic dimensional extensions of a in this paper we study the relation between a and a in detail in particular their regularity invertibility and spectral properties we obtain an explicit formula allowing to express the eigenfunctions of a in terms of those of a we use this formalism to construct new classes of pseudo differential operators which are extensions of the shubin classes hg m1 m0 of globally hypoelliptic operators we show that the operators in the new classes share the invertibility and spectral properties of the operators in hg m1 m0 but not the global hypoellipticity property finally we study a few examples of operators that belong to the new classes and which are important in mathematical physics

bias corrections for two step fixed effects panel data estimators this paper introduces large t bias corrected estimators for nonlinear panel data models with both time invariant and time varying heterogeneity these models include systems of equations with limited dependent variables and unobserved individual effects and sample selection models with unobserved individual effects our two step approach first estimates the reduced form by fixed effects procedures to obtain estimates of the time varying heterogeneity underlying the endogeneity selection bias we then estimate the primary equation by fixed effects including an appropriately constructed control variable from the reduced form estimates as an additional explanatory variable the fixed effects approach in this second step captures the time invariant heterogeneity while the control variable accounts for the time varying heterogeneity since either or both steps might employ nonlinear fixed effects procedures it is necessary to bias adjust the estimates due to the incidental parameters problem this problem is exacerbated by the two step nature of the procedure as these two step approaches are not covered in the existing literature we derive the appropriate correction thereby extending the use of large t bias adjustments to an important class of models simulation evidence indicates our approach works well in finite samples and an empirical example illustrates the applicability of our estimator

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

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

spatially piecewise fuzzy control design for sampled data exponential stabilization of semilinear parabolic pde systems this paper employs a takagi sugeno t s fuzzy partial differential equation pde model to solve the problem of sampled data exponential stabilization in the sense of spatial l infty norm vert cdot vert infty for a class of nonlinear parabolic distributed parameter systems dpss where only a few actuators and sensors are discretely distributed in space initially a t s fuzzy pde model is assumed to be derived by the sector nonlinearity method to accurately describe complex spatiotemporal dynamics of the nonlinear dpss subsequently a static sampled data fuzzy local state feedback controller is constructed based on the t s fuzzy pde model by constructing an appropriate lyapunov krasovskii functional candidate and employing vector valued wirtinger s inequalities a variation of vector valued poincare wirtinger inequality in one dimensional spatial domain as well as a vector valued agmon s inequality it is shown that the suggested sampled data fuzzy controller exponentially stabilizes the nonlinear dpss in the sense of vert cdot vert infty if sufficient conditions presented in term of standard linear matrix inequalities lmis are fulfilled moreover an lmi relaxation technique is utilized to enhance exponential stabilization ability of the suggested sampled data fuzzy controller finally the satisfactory and better performance of the suggested sampled data fuzzy controller are demonstrated by numerical simulation results of two examples

bayesian inference in a simultaneous equation model with limited dependent variables abstract this paper develops a bayesian approach for inference in a simultaneous equation model with limited dependent variables sldv by employing a combination of gibbs sampling and data augmentation we can draw from the exact posterior of this sldv model and avoid direct evaluation of the non trivial likelihood function a by product from our posterior simulation is the savage dickey density ratio which is used for computing the bayes factor the practicality and efficiency of the proposed method are illustrated through an example in corporate finance

two step estimation of panel data models with censored endogenous variables and selection bias this paper presents some two step estimators for a wide range of parametric panel data models with censored endogenous variables and sample selection bias our approach is to derive estimates of the unobserved heterogeneity responsible for the endogeneity selection bias to include as additional explanatory variables in the primary equation these are obtained through a decomposition of the reduced form residuals the panel nature of the data allows adjustment and testing for two forms of endogeneity and or sample selection bias furthermore it incorporates roles for dynamics and state dependence in the reduced form finally we provide an empirical illustration which features our procedure and highlights the ability to test several of the underlying assumptions

estimating derivatives in nonseparable models with limited dependent variables we present a simple way to estimate the effects of changes in a vector of observable variables x on a limited dependent variable y when y is a general nonseparable function of x and unobservables and x is independent of the unobservables we treat models in which y is censored from above below or both the basic idea is to first estimate the derivative of the conditional mean of y given x at x with respect to x on the uncensored sample without correcting for the effect of x on the censored population we then correct the derivative for the effects of the selection bias we discuss nonparametric and semiparametric estimators for the derivative we also discuss the cases of discrete regressors and of endogenous regressors in both cross section and panel data contexts

sampled data relay control of diffusion pdes we consider a vector reaction advection diffusion equation on a hypercube the measurements are weighted averages of the state over different subdomains these measurements are asynchronously sampled in time subject to matched disturbances the discrete control signals are applied through shape functions and zero order holds the feature of this work is that we consider generalized relay control the control signals take their values in a finite set this allows for networked control through low capacity communication channels first we derive linear matrix inequalities lmis whose feasibility guarantees the ultimate boundedness with a limit bound proportional to the sampling period then we construct a switching procedure for the controller parameters that ensures semi global practical stability for an arbitrarily large domain of initial conditions the trajectories converge to a set whose size does not depend on the domain size for the disturbance free system this procedure guarantees exponential convergence to the origin the results are demonstrated by two examples 2d catalytic slab and a chemical reactor

weyl wigner formulation of noncommutative quantum mechanics we address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension displaying both spatial and momentum noncommutativities by resorting to a covariant generalization of the weyl wigner transform and to the darboux map we construct an isomorphism between the operator and the phase space representations of the extended heisenberg algebra this map provides a systematic approach to derive the entire structure of noncommutative quantum mechanics in phase space we construct the extended star product and moyal bracket and propose a general definition of noncommutative states we study the dynamical and eigenvalue equations of the theory and prove that the entire formalism is independent of the particular choice of the darboux map our approach unifies and generalizes all the previous proposals for the phase space formulation of noncommutative quantum mechanics for concreteness we rederive these proposals by restricting our formalism to some two dimensional spaces

homogeneous fedosov star products on cotangent bundles i weyl and standard ordering with differential operator representation in this paper we construct homogeneous star products of weyl type on every cotangent bundle t q by means of the fedosov procedure using a symplectic torsion free connection on t q homogeneous of degree zero with respect to the liouville vector field by a fibrewise equivalence transformation we construct a homogeneous fedosov star product of standard ordered type equivalent to the homogeneous fedosov star product of weyl type representations for both star product algebras by differential operators on functions on q are constructed leading in the case of the standard ordered product to the usual standard ordering prescription for smooth complex valued functions on t q polynomial in the momenta where an arbitrary fixed torsion free connection 0 on q is used motivated by the flat case t n another homogeneous star product of weyl type corresponding to the weyl ordering prescription is constructed the example of the cotangent bundle of an arbitrary lie group is explicitly computed and the star product given by gutt is rederived in our approach

semiparametric estimation of binary response models with endogenous regressors abstract in this paper we propose a two step semiparametric maximum likelihood sml estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach the first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals in the second step the latter are added as control variates to the outcome equation which is in turn estimated by sml we establish the estimator s n consistency and asymptotic normality in a simulation study we compare the properties of our estimator with those of existing alternatives highlighting the advantages of our approach

three stage semi parametric inference control variables and differentiability abstract we show the usefulness of the path derivative calculations that were introduced in econometrics by newey 1994 for multi step semi parametric estimators these estimators estimate a finite dimensional parameter using moment conditions that depend on nonparametric regressions on observed and estimated regressors that are estimated in the second and first step of the estimation procedure respectively our earlier paper showed that newey s calculations can be extended to three step estimators in the current paper we consider the control variable cv estimator and related statistics in semi parametric econometric models with non separable errors and regressors that are correlated with these errors non separable econometric models with endogenous regressors are often identified by average moment restrictions that average over control variables and these control variables are estimated in a first stage by non parametric regression we study aspects of inference for such estimators where we focus on a finite dimensional parameter vector or statistic the asymptotic distribution and a closed form expression for the asymptotic variance of the cv estimator were not available until now our path derivative calculations are much simpler than the derivation of the asymptotic distribution by a stochastic expansion that is particularly complicated for multi step semi parametric estimators we also consider just and overidentification of the parameters and we propose a diagnostic test for overidentifying restrictions in models with non separable errors and endogenous regressors finally the path derivative calculation breaks down if the moment condition is not differentiable in an example we show that non differentiability is associated with irregular behavior of the estimator

brief paper wirtinger s inequality and lyapunov based sampled data stabilization discontinuous lyapunov functionals appeared to be very efficient for sampled data systems fridman 2010 naghshtabrizi hespanha teel 2008 in the present paper new discontinuous lyapunov functionals are introduced for sampled data control in the presence of a constant input delay the construction of these functionals is based on the vector extension of wirtinger s inequality these functionals lead to simplified and efficient stability conditions in terms of linear matrix inequalities lmis the new stability analysis is applied to sampled data state feedback stabilization and to a novel sampled data static output feedback problem where the delayed measurements are used for stabilization

constrained control of 1 d parabolic pdes using sampled in space sensing and actuation abstract we consider distributed control of a class of 1 d parabolic pdes under distributed in domain point actuation and measurements in the presence of control constraints this class includes unstable diffusion reaction equations as well as stable burgers equations where we aim to locally improve the convergence we suggest an observer based control law that employs the averaged values of the observer state this allows to regionally stabilize the system we derive linear matrix inequalities lmis conditions that provide an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero a numerical example validates the efficiency of the method

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

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

exogeneity tests incomplete models weak identification and non gaussian distributions invariance and finite sample distributional theory abstract we study the distribution of durbin wu hausman dwh and revankar hartley rh tests for exogeneity from a finite sample viewpoint under the null and alternative hypotheses we consider linear structural models with possibly non gaussian errors where structural parameters may not be identified and where reduced forms can be incompletely specified or nonparametric on level control we characterize the null distributions of all the test statistics through conditioning and invariance arguments we show that these distributions do not involve nuisance parameters in particular this applies to several test statistics for which no finite sample distributional theory is yet available such as the standard statistic proposed by hausman 1978 the distributions of the test statistics may be non standard so corrections to usual asymptotic critical values are needed but the characterizations are sufficiently explicit to yield finite sample monte carlo tests of the exogeneity hypothesis the procedures so obtained are robust to weak identification missing instruments or misspecified reduced forms and can easily be adapted to allow for parametric non gaussian error distributions we give a general invariance result block triangular invariance for exogeneity test statistics this property yields a convenient exogeneity canonical form and a parsimonious reduction of the parameters on which power depends in the extreme case where no structural parameter is identified the distributions under the alternative hypothesis and the null hypothesis are identical so the power function is flat for all the exogeneity statistics however as soon as identification does not fail completely this phenomenon typically disappears we present simulation experiments which confirm the finite sample theory the theoretical results are illustrated with an empirical example the relation between trade and economic growth

generalized weyl wigner map and vey quantum mechanics the weyl wigner map yields the entire structure of moyal quantum mechanics directly from the standard operator formulation the covariant generalization of moyal theory also known as vey quantum mechanics was presented in the literature many years ago however a derivation of the formalism directly from standard operator quantum mechanics clarifying the relation between the two formulations is still missing in this article we present a covariant generalization of the weyl order prescription and of the weyl wigner map and use them to derive vey quantum mechanics directly from the standard operator formulation the procedure displays some interesting features it yields all the key ingredients and provides a more straightforward interpretation of the vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the vey idiom these features are illustrated through a simple example

using lyapunov s direct method for wave suppression in reactive systems this paper proposes a new approach for stabilizing a homogeneous solution in reaction convection diffusion system with oscillatory kinetics in which moving or stationary patterns emerge in the absence of control specifically we aim to suppress patterns by using a spatially weighted finite dimensional feedback control that assures stability of the solution according to lyapunov s direct method a practical design procedure based on spectral representation of the system and the dissipative nature of parabolic pdes is presented 2006 elsevier b v all rights reserved

quasi maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables abstract i propose a quasi maximum likelihood framework for estimating nonlinear models with continuous or discrete endogenous explanatory variables joint and two step estimation procedures are considered the joint procedure is a quasi limited information maximum likelihood procedure as one or both of the log likelihoods may be misspecified the two step control function approach is computationally simple and leads to straightforward tests of endogeneity in the case of discrete endogenous explanatory variables i argue that the control function approach can be applied with generalized residuals to obtain average partial effects i show how the results apply to nonlinear models for fractional and nonnegative responses

mixed states with positive wigner functions the wigner distribution function of a pure quantum state is everywhere positive if and only if the state is coherent according to a result of hudson the characterization of mixed states with a positive wigner function is a special case of the problem of determining functions satisfying a twisted positive definiteness condition for a prescribed set of twisting parameters i e functions with given wigner spectrum in the sense of narcowich if a state is a convex combination of coherent states it has the property that the wigner spectrum contains the unit interval which in turn implies that the wigner function is positive it is shown by explicit examples that the converses of both implications are false the examples are taken from a low dimensional section of the state space in which all wigner spectra can be computed in this set counterexamples to a conjecture by narcowich concerning the wigner spectrum of products are also found as well as a state whose wigner spectrum is a convergent sequence of discrete points

stabilization of well posed infinite dimensional systems by dynamic sampled data feedback it is shown that a set of six natural conditions is necessary and sufficient for the existence of a finite dimensional stabilizing sampled data controller for a well posed infinite dimensional system the underlying stability concept for the sampled data system is reminiscent of the notion of input to state stability from nonlinear control theory

wigner measures in noncommutative quantum mechanics we study the properties of quasi distributions or wigner measures in the context of noncommutative quantum mechanics in particular we obtain necessary and sufficient conditions for a phase space function to be a noncommutative wigner measure for a gaussian to be a noncommutative wigner measure and derive certain properties of the marginal distributions which are not shared by ordinary wigner measures moreover we derive the robertson schrodinger uncertainty principle finally we show explicitly how the set of noncommutative wigner measures relates to the sets of liouville and commutative wigner measures

stability analysis of a text 2 times text 2 linear hyperbolic system with a sampled data controller via backstepping method and looped functionals this paper is concerned with the global exponential stability of a 2 times 2 linear hyperbolic system with a sampled data boundary feedback control designed by means of the backstepping method for a nominal continuous input we show that there exists a sufficiently small intersampling time that encompasses both periodic and aperiodic sampling for which the global exponential stability of the closed loop system is guaranteed in addition we provide easily tractable sufficient stability conditions that can be used to find an upper bound of the maximum intersampling time the results rely on the combination of the lyapunov method and looped functionals the effectiveness of the proposed results is illustrated with a numerical example

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

estimating probit models with self selected treatments outcomes research often requires estimating the impact of a binary treatment on a binary outcome in a non randomized setting such as the effect of taking a drug on mortality the data often come from self selected samples leading to a spurious correlation between the treatment and outcome when standard binary dependent variable techniques like logit or probit are used intuition suggests that a two step procedure analogous to two stage least squares might be sufficient to deal with this problem if variables are available that are correlated with the treatment choice but not the outcome this paper demonstrates the limitations of such a two step procedure we show that such estimators will not generally be consistent we conduct a monte carlo exercise to compare the performance of the two step probit estimator the two stage least squares linear probability model estimator and the multivariate probit the results from this exercise argue in favour of using the multivariate probit rather than the two step or linear probability model estimators especially when there is more than one treatment when the average probability of the dependent variable is close to 0 or 1 or when the data generating process is not normal we demonstrate how these different methods perform in an empirical example examining the effect of private and public insurance coverage on the mortality of hiv patients

exogeneity tests in a truncated structural equation abstract two bayesian and one non bayesian test statistics are derived to test the hypothesis that stochastic regressors in a truncated structural equation are independent of the error term the truncation is caused by an indicator function sampling experiments are conducted to examine sizes and powers of the test statistics and to compare them with those of the mroz test the tests are also applied to a labor supply equation for married women to see whether the wage variable is exogenous the michigan panel study of income dynamics data for 1976 are used

approximate generalized extreme value models of discrete choice abstract estimation of generalized extreme value gev models of discrete choice is hampered by computational complexity and convergence problems however if the model deviates only modestly from standard multinomial logit a first order approximation may be useful this paper presents three tests each based on such an approximation for the null hypothesis of multinomial logit against any particular gev model as an alternative hypothesis one test applies the universal logit concept of mcfadden train and tye the second is the usual lagrange multiplier test and the third generalizes a regression based test developed by mcfadden 1987 all three begin with a logit estimation followed by one further computational step which also produces an approximate estimate of the gev model these estimates as well as the test statistics are asymptotically equivalent under the null hypothesis monte carlo data generated alternatively by logit and by three different gev models provide evidence on the small sample properties of both the test statistics and the approximate estimators these properties are found to be superior in important respects to maximum likelihood estimation of the gev model