estimation of cross sectional and panel data censored regression models with endogeneity it is very difficult to deal with endogeneity in limited dependent variables models unless strong assumptions are made on the exact relationship between the endogenous regressors and the instruments it is generally not possible to apply instrumental variable type techniques this paper derives moment conditions that are useful in estimating censored regression models with endogenous regressors these moment conditions are motivated by panel data censored regression models with predetermined but not strictly exogenous explanatory variables but the main insight is also applicable to cross sectional models with endogenous explanatory variables

orthogonality conditions for tobit models with fixed effects and lagged dependent variables abstract this paper presents orthogonality conditions for censored regression models with fixed effects and lagged dependent variables the orthogonality conditions can be used to construct method of moments estimators of the parameters of the model nonlinear fixed effects models are usually estimated by maximum likelihood with the fixed effects treated as parameters to be estimated monte carlo results indicate that in a tobit model with fixed effects and lagged dependent variables the maximum likelihood estimator of the effect of the lagged dependent variable performs poorly the method of moments estimator based on the orthogonality conditions presented here however performs quite well

symmetrically trimmed least squares estimation for tobit models this paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models known to economists as tobit models the proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable unlike methods based on the assumption of identically distributed gaussian errors the estimators are semiparametric in the sense that they are consistent and asymptotically normal for a wide class of symmetric error distributions with heteroskedasticity of unknown form the paper gives the regularity conditions and proofs of these large sample properties demonstrates how to construct consistent estimators of the asymptotic covariance matrices and presents the results of a simulation study for the censored case extensions and limitations of the approach are also considered

saddlepoint approximations for regression models summary this paper uses the techniques of saddlepoint or tilted exponential approximation to develop an approximation to the small sample distribution of estimators defined by a system of estimating equations when observations are independently but not identically distributed this allows for the explicit treatment of models with explanatory variables the approximation is applied to l1 regression and the accuracy of the approximation is demonstrated in a case in which the usual normal approximation is very poor an analysis of the example indicates the usefulness of a new variant of exponential tilting in calculating the transformation measure a quantity which plays an important role in assuring the accuracy of the approximation

semiparametric and nonparametric estimation of sample selection models under symmetry this paper considers the semiparametric estimation of binary choice sample selection models under a joint symmetry assumption our approaches overcome various drawbacks associated with existing estimators in particular our method provides root n consistent estimators for both the intercept and slope parameters of the outcome equation in a heteroscedastic framework without the usual cross equation exclusion restriction or parametric specification for the error distribution and or the form of heteroscedasticity our two step estimators are shown to be consistent and asymptotically normal a monte carlo simulation study indicates the usefulness of our approaches

pairwise difference estimators of censored and truncated regression models abstract this paper proposes a class of estimators of the semiparametric censored regression model under the assumption that the error terms are i i d and independent of the covariates the estimators exploit the fact that for a pair of observations a particular transformation of the censored variables depending upon the parameter vector and both covariate vectors will be identically distributed therefore the difference in the transformed dependent variables will be symmetrically distributed around zero when the transformation is evaluated at the true parameter vector an analogous class of estimators for the truncated regression model includes the bhattacharya chernoff and yang 1983 estimator as a special case the estimators are defined as minimizers of u processes so the large sample theory for classical m estimators is extended to this case conditions are given to ensure root n consistency and asymptotic normality of the estimators and a small scale simulation study for the censored regression estimator suggest that it will be well behaved in finite samples

a pseudo r2 measure for limited and qualitative dependent variable models abstract a pseudo r 2 measure for limited and qualitative dependent variable models is proposed a consistent estimator of the variance of the disturbance term is also suggested the pseudo r 2 measure is shown to have the same asymptotic limit as the conventional r 2 the measure is adapted to the logit model in an empirical example of female car ownership modeling the pseudo r 2 is applicable to a wide set of limited and qualitative dependent variable models and offers a valuable tool for model evaluation

rank estimation of a location parameter in the binary choice model abstract this paper proposes a rank based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition given an initial n consistent estimator for the slope parameter the estimator converges at the usual parametric rate compared with existing estimators no nonparametric smoothing is needed here a small monte carlo study illustrates the usefulness of the estimator we also point out that the location and slope parameters can be jointly estimated

estimation of type 3 tobit models using symmetric trimming and pairwise comparisons abstract this paper considers estimation of the semiparametric type 3 tobit model we construct two step estimators that use the ideas of symmetric trimming and pairwise comparisons which have been proposed for the censored regression model by powell 1986 and honore and powell 1994 the estimators are consistent and asymptotically normal under two identifying assumptions conditional symmetry and independence between the errors and regressors the ideas and techniques are also implementable in other selection models that are variations of the basic type 3 tobit model we demonstrate this by applying the proposed method in estimating an empirical model considered by udry 1994

semiparametric robust estimation of truncated and censored regression models many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares scls are sensitive to outliers and data contamination as we document therefore we propose a semiparametric general trimmed estimator gte of truncated and censored regression which is highly robust but relatively imprecise to improve its performance we also propose data adaptive and one step trimmed estimators we derive the robust and asymptotic properties of all proposed estimators and show that the one step estimators e g one step scls are as robust as gte and are asymptotically equivalent to the original estimator e g scls the finite sample properties of existing and proposed estimators are studied by means of monte carlo simulations

moment inequalities and their application this paper provides conditions under which the inequality constraints generated by either single agent optimizing behavior or by the nash equilibria of multiple agent problems can be used as a basis for estimation and inference we also add to the econometric literature on inference in models defined by inequality constraints by providing a new specification test and methods of inference for the boundaries of the model s identified set two applications illustrate how the use of inequality constraints can simplify the problem of obtaining estimators from complex behavioral models of substantial applied interest

quantile regression under random censoring censored regression models have received a great deal of attention in both the theoretical and applied econometric literature most of the existing estimation procedures for either cross sectional or panel data models are designed only for models with fixed censoring in this paper a new procedure for adapting these estimators designed for fixed censoring to models with random censoring is proposed this procedure is then applied to the clad and quantile estimators of powell j econom 25 1984 303 32 1986a 143 to obtain an estimator of the coefficients under a mild conditional quantile restriction on the error term that is applicable to samples exhibiting fixed or random censoring the resulting estimator is shown to have desirable asymptotic properties and performs well in a small scale simulation study

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

on the choice between sample selection and two part models abstract this paper resolves the vigorous debates between advocates of the sample selection model and the two part model recent monte carlo studies by hay leu and rohrer 1987 and manning duan and rogers 1987 find that the two part model performs better than the sample selection model even when the latter is the true model we show that manning duan and rogers negative results regarding the sample selection model are caused by a critical design problem we demonstrate that their data generating process produces serious collinearity problems that bias against the sample selection model once the design problem is rectified the poor performance of the sample selection model evaporates our monte carlo results offer a more balanced view on the relative merits of the two models as each model performs well under different conditions in particular the sample selection model is susceptible to collinearity problems and a t test can be used to distinguish between the two models as long as there are no collinearity problems as an example we employ mroz s 1987 labor supply data to illustrate how his tests for selectivity bias might have been affected by collinearity problems

the effect of truncation on the identifiability of regression coefficients abstract when data are truncated and hence partly unobservable parameters identifiable under the complete observation may not be identifiable a class of distributions is characterized under which regression coefficients are unidentifiable by truncation of a dependent variable in the regression model in a class of strongly unimodal densities regression coefficients are shown to be unidentifiable only when the underlying distribution is proportional to the exponential distribution in support of the truncated observation the exponential double exponential and huber s least informative distribution for a location parameter are apparent examples of the distributions under which the unidentifiability can occur in a more restrictive class of symmetric and strongly unimodal densities the unidentifiability arises only when the error distribution has exponential tails and the degree of truncation is at least 50 the likelihood function becomes completely flat with respect to the regression coefficients and

adaptive estimation in time series regression models this work develops adaptive estimators for a linear regression model with serially correlated errors we show that these results continue to hold when the order of the arma process characterizing the errors is unknown the finite sample results are promising indicating that substantial efficiency gains may be possible for samples as small as 50 observations we use these estimators to investigate the behavior of the forward foreign exchange market

semiparametric estimation of the type 3 tobit model abstract this paper considers estimation of the type 3 tobit model with only some weak restrictions imposed on the distribution of the error terms two least squares type estimation approaches are proposed under the condition that the error terms and regressors are independent consistent estimators for the asymptotic covariance matrices are proposed to facilitate large sample inference and a small monte carlo simulation is performed to investigate the finite sample behavior of the proposed estimators also the semiparametric efficiency bound is derived for the type 3 tobit model under the independence restriction

distribution free estimation of the random coefficient dummy endogenous variable model this paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution we follow a two step approach the selection equation is estimated first in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method our approach can be readily extended to the general switching regression model in constrast to the existing literature on sample selection models the exclusion restriction is not needed here for model identification furthermore the intercept term for the outcome equation can be estimated at the usual parametric rate

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

a nonparametric approach to the truncated regression problem abstract a description is given of a new method of estimating the regression parameters in the linear regression model from data where the dependent variable is subject to truncation the residual distribution is allowed to be unspecified the method is iterative and involves estimation of the residual distribution under the truncated sampling scheme the technique can be interpreted as an iterative bias adjustment of the observations in order to correct the regression relationship in the sampled population to match that of the model a simulation study compares the performance of various estimators including one suggested by bhattacharya chernoff and yang 1983 this truncation regression problem arises in many contexts of scientific and social research in economics tobin 1958 analyzed household expenditure on durable goods using a regression model that took account of the fact that the expenditure is always nonnegative a more general situation was studied by hausman and wise 1976 1977 in conn

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

semiparametric models and inference for the effect of a treatment when the outcome is nonnegative with clumping at zero the outcome in a randomized experiment is sometimes nonnegative with a clump of observations at zero and continuously distributed positive values one widely used model for a nonnegative outcome with a clump at zero is the tobit model which assumes that the treatment has a shift effect on the distribution of a normally distributed latent variable and the observed outcome is the maximum of the latent variable and zero we develop a class of semiparametric models and inference procedures that extend the tobit model in two useful directions first we consider more flexible models for the treatment effect than the shift effect of the tobit model for example our models allow for the treatment to have a larger in magnitude effect for upper quantiles second we make semiparametric inferences using empirical likelihood that allow the underlying latent variable to have any distribution unlike the original tobit model that assumes the latent variable is normally distributed we apply our approach to data from the rand health insurance experiment we also extend our approach to observational studies in which treatment assignment is strongly ignorable

a simple consistent test of conditional symmetry in symmetrically trimmed tobit models we propose a weighted and sample size adjusted kolmogorov smirnov type statistic to test the assumption of conditional symmetry maintained in the symmetrically trimmed least squares stls approach of powell 1986b which is widely used to estimate censored or truncated regression models without making distributional assumptions our statistic is consistent and does not require any nonparametric smoothing although we test the validity of a conditional feature we also propose a bootstrap procedure to obtain the p values and critical values that are required to carry out the test in practical applications results from a simulation study suggest that our test can work very well even in small to moderately sized samples as an empirical illustration we apply our test to two datasets that have been used in the literature to estimate censored regression models using powell s stls approach to check whether the assumption of conditional symmetry is supported by these datasets

bounded influence estimators for the tobit model abstract this paper introduces a class of bounded influence estimators for the gaussian censored regression or tobit model these estimators can be interpreted as weighted ml estimators with weights chosen to attain the best trade off between efficiency and robustness an empirical example illustrates the feasibility and usefulness of these estimators as well as their performance vis a vis the tobit ml clad and scls estimators

estimation of panel data partly specified tobit regression with fixed effects this paper presents an estimation of a partly specified tobit model with fixed effects by extending the symmetric trimming procedure proposed in honore 1992 under some sufficient conditions we present conditions to identify both the parametric and the nonparametric component of the unknown parameter under some sufficient conditions we establish that the proposed estimates are consistent and the estimates of the parametric component are asymptotically normally consistent finally we present some consistent covariance matrix for the estimates of the parametric component

trimmed lad and least squares estimation of truncated and censored regression models with fixed effects this paper considers estimation of truncated and censored regression models with fixed effects up until now no estimator has been shown to be consistent as the cross section dimension increases with the time dimension fixed trimmed least absolute deviations and trimmed least squares estimators are proposed for the case where the panel is of length two and it is proven that they are consistent and asymptotically normal it is not necessary to maintain parametric assumptions on the error terms to obtain this result a small scale monte carlo study demonstrates that these estimators can perform well in small samples copyright 1992 by the econometric society

a polynomial membership function approach for stability analysis of fuzzy systems for the stability analysis of a polynomial fuzzy system a new polynomial membership function approach is proposed to reduce the conservatism based on a state feedback closed loop system a polynomials fitting method is utilized and an improved membership functions transformation technique are proposed to approximate the membership functions of fuzzy system then the membership function dependent polynomials form stability conditions are derived the obtained polynomial membership functions and approximation errors will be involved in the stability analysis process based on the sum of squares optimization technique the polynomials conditions can be directly solved finally by several numerical and practical examples the conservatism reduction effects are shown by comparisons with existing methods