Almost Consistent Estimation of Panel Probit Models with “Small” Fixed Effects

We propose four different GMM estimators that allow almost consistent estimation of the structural parameters of panel probit models with fixed effects for the case of small Tand large N. The moments used are derived for each period from a first order approximation of the mean of the dependent variable conditional on explanatory variables and on the fixed effect. The estimators differ w.r.t. the choice of instruments and whether they use trimming to reduce the bias or not. In a Monte Carlo study, we compare these estimators with pooled probit and conditional logit estimators for different data generating processes. The results show that the proposed estimators outperform these competitors in several situations.     

二元选择面板模型的设定检验

 本文将RESET检验扩展到二元选择面板数据模型的设定,考察了固定效应Probit模型和Logit模型的设定检验,包括异方差、遗漏变量和分布误设的检验。模拟结果表明Logit模型的RESET设定检验显示良好的水平和功效,而Probit模型的RESET检验可能由于估计方法的选择导致在某些方面的功效表现不好。但总体说来,在二元选择面板数据模型的设定检验上,RESET检验仍然是一个较好的选择。     

A Monte Carlo study of bias corrections for panel probit models

We examine bias corrections which have been proposed for the fixed effects panel probit model with exogenous regressors, using several different data generating processes to evaluate the performance of the estimators in different situations. We find a best estimator across all cases for coefficient estimates, but when the marginal effects are the quantity of interest no analytical correction is able to outperform the uncorrected maximum-likelihood estimator.     

On probit versus logit dynamic mixed models for binary panel data

In this paper, we consider inferences in a binary dynamic mixed model. The existing estimation approaches mainly estimate the regression effects and the dynamic dependence parameters either through the estimation of the random effects or by avoiding the random effects technically. Under the assumption that the random effects follow a Gaussian distribution, we propose a generalized quasilikelihood (GQL) approach for the estimation of the parameters of the dynamic mixed models. The proposed approach is computationally less cumbersome than the exact maximum likelihood (ML) approach. We also carry out the GQL estimation under two competitive, namely, probit and logit mixed models, and discuss both the asymptotic and small-sample behaviour of their estimators.     

带异质线性趋势的动态二元选择面板模型估计

本文提出了带异质线性趋势的动态二元面板模型的极大似然偏误纠正估计量和近似条件Logit估计量。我们给出了通常极大似然估计量偏误的解析形式,并提供了相应的估计方法。小样本实验表明近似条件似然函数可以很好的消除异质性参数的影响,而偏误纠正估计量可以显著的修正极大似然估计量的偏误。最后我们将本文提出的方法应用到现金红利支付模型。     

Two-parameter ridge estimator in the binary logistic regression

The binary logistic regression is a commonly used statistical method when the outcome variable is dichotomous or binary. The explanatory variables are correlated in some situations of the logit model. This problem is called multicollinearity. It is known that the variance of the maximum likelihood estimator (MLE) is inflated in the presence of multicollinearity. Therefore, in this study, we define a new two-parameter ridge estimator for the logistic regression model to decrease the variance and overcome multicollinearity problem. We compare the new estimator to the other well-known estimators by studying their mean squared error (MSE) properties. Moreover, a Monte Carlo simulation is designed to evaluate the performances of the estimators. Finally, a real data application is illustrated to show the applicability of the new method. According to the results of the simulation and real application, the new estimator outperforms the other estimators for all of the situations considered.     

Evaluating the performance of simple estimators for probit models with two dummy endogenous regressors

This study considers the small sample performance of approximate but simple two-stage estimators for probit models with two endogenous binary covariates. Monte Carlo simulations show that all the considered estimators, including the simulated maximum-likelihood (SML) estimation, of the trivariate probit model are biased in very small samples (N=100). With moderately small samples (N=500), some of the approximations perform as well as the SML estimator when the degree of endogeneity is not very large. Some of the approximations seem robust with higher correlations and are also promising for testing the exogeneity of binary covariates. The methods are used to estimate the impact of employment-based health insurance and health care (HC) on HC use, where the approximations seem to work at least as well as the SML and in some cases better.     

Quantile regression for panel data models with fixed effects under random censoring

Abstract

The locally weighted censored quantile regression approach is proposed for panel data models with fixed effects, which allows for random censoring. The resulting estimators are obtained by employing the fixed effects quantile regression method. The weights are selected either parametrically, semi-parametrically or non-parametrically. The large panel data asymptotics are used in an attempt to cope with the incidental parameter problem. The consistency and limiting distribution of the proposed estimator are also derived. The finite sample performance of the proposed estimators are examined via Monte Carlo simulations.     

Exponential class of dynamic binary choice panel data models with fixed effects

ABSTRACT

This paper proposes an exponential class of dynamic binary choice panel data models for the analysis of short T (time dimension) large N (cross section dimension) panel data sets that allow for unobserved heterogeneity (fixed effects) to be arbitrarily correlated with the covariates. The paper derives moment conditions that are invariant to the fixed effects which are then used to identify and estimate the parameters of the model. Accordingly, generalized method of moments (GMM) estimators are proposed that are consistent and asymptotically normally distributed at the root-N rate. We also study the conditional likelihood approach and show that under exponential specification, it can identify the effect of state dependence but not the effects of other covariates. Monte Carlo experiments show satisfactory finite sample performance for the proposed estimators and investigate their robustness to misspecification.     

Response shrinkage estimation in multinomial logit models

A shrinkage estimation method for multinomial logit models is developed. The proposed method is based on shrinking the responses for each category towards the underlying probabilities. The estimator is also used in combination with Pregibon's resistant fitting. The resulting estimator can also be used to control the over-estimation of Pregibon's resistant estimator. The proposed method handles not only the problem of separation in multinomial logit models but estimates also exist when the number of covariates is large relative to the sample size. Estimates exist even when the MLE does not exist. Estimates can be easily computed with all commonly used statistical packages supporting the fitting procedures with weights. Estimates are compared with the usual MLE and Firth's bias reduction technique in a simulation study and an application.     

C335. Some numerology for the mass ratio of proton to electron,and a partially Bayesian evaluation

Recent small sample studies of estimators for the shape parameter a of the negative binomial distribution (NBD) tend to indicate that the choice of estimator can be reduced to a choice between the method of moments estimator, maximum likelihood estimator (MLE), maximum quasi-likelihood estimator and the conditional likelihood estimator (CLE). In this paper the results of a comprehensive simulation study are reported to assist with the choice from these four estimators. The study includes a traditional procedure for assessing estimators for the shape parameter of the NBD and in addition introduces an alternative assessment procedure. Based on the traditional approach the CLE is considered to perform the best overall for the range of parameter values and sample sizes considered. The alternative assessment procedure indicates that the MLE is the preferred estimator.     

A two-stage estimation for panel data models with grouped fixed effects

ABSTRACT

This paper considers panel data models with fixed effects which have grouped patterns with unknown group membership. A two-stage estimation (TSE) procedure is developed to improve the properties of the GFE estimators of common parameters when the time span is small. Firstly, the common parameters are estimated. Subsequently, the optimal group assignment and the estimators of group effects are obtained by the K-means algorithm. Monte Carlo results reveal that the TSE estimator has a much smaller bias than the GFE estimator when the values of difference between effects are moderately small or at high variance of the idiosyncratic error.     

Modified Profile Likelihood for Fixed-Effects Panel Data Models

We show how modified profile likelihood methods, developed in the statistical literature, may be effectively applied to estimate the structural parameters of econometric models for panel data, with a remarkable reduction of bias with respect to ordinary likelihood methods. Initially, the implementation of these methods is illustrated for general models for panel data including individual-specific fixed effects and then, in more detail, for the truncated linear regression model and dynamic regression models for binary data formulated along with different specifications. Simulation studies show the good behavior of the inference based on the modified profile likelihood, even when compared to an ideal, although infeasible, procedure (in which the fixed effects are known) and also to alternative estimators existing in the econometric literature. The proposed estimation methods are implemented in an R package that we make available to the reader.     

Heterogeneous skewness in binary choice models: predicting outcomes in the men's NCAA basketball tournament

Several authors have recently explored the estimation of binary choice models based on asymmetric error structures. One such family of skewed models is based on the exponential generalized beta type 2 (EGB2). One model in this family is the skewed logit. Recently, McDonald (1996, 2000) extended the work on the EGB2 family of skewed models to permit heterogeneity in the scale parameter. The aim of this paper is to extend the skewed logit model to allow for heterogeneity in the skewness parameter. By this we mean that, in the model developed, here the skewness parameter is permitted to vary from observation to observation by making it a function of exogenous variables. To demonstrate the usefulness of our model, we examine the issue of the predictive ability of sports seedings. We find that we are able to obtain better probability predictions using the skewed logit model with heterogeneous skewness than can be obtained with logit, probit, or skewed logit.     

The estimation of multidimensional fixed effects panel data models

This article introduces the appropriate within estimators for the most frequently used three-dimensional fixed effects panel data models. It analyzes the behavior of these estimators in the cases of no self-flow data, unbalanced data, and dynamic autoregressive models. The main results are then generalized for higher dimensional panel data sets as well.     

Aalen's linear model for doubly censored data

Double censoring often occurs in registry studies when left censoring is present in addition to right censoring. In this work, we examine estimation of Aalen's nonparametric regression coefficients based on doubly censored data. We propose two estimation techniques. The first type of estimators, including ordinary least squared (OLS) estimator and weighted least squared (WLS) estimators, are obtained using martingale arguments. The second type of estimator, the maximum likelihood estimator (MLE), is obtained via expectation-maximization (EM) algorithms that treat the survival times of left censored observations as missing. Asymptotic properties, including the uniform consistency and weak convergence, are established for the MLE. Simulation results demonstrate that the MLE is more efficient than the OLS and WLS estimators.     

Inferences in dynamic logit models in semi-parametric setup for repeated binary data

Binary dynamic fixed and mixed logit models are extensively studied in the literature. These models are developed to examine the effects of certain fixed covariates through a parametric regression function as a part of the models. However, there are situations where one may like to consider more covariates in the model but their direct effect is not of interest. In this paper we propose a generalization of the existing binary dynamic logit (BDL) models to the semi-parametric longitudinal setup to address this issue of additional covariates. The regression function involved in such a semi-parametric BDL model contains (i) a parametric linear regression function in some primary covariates, and (ii) a non-parametric function in certain secondary covariates. We use a simple semi-parametric conditional quasi-likelihood approach for consistent estimation of the non-parametric function, and a semi-parametric likelihood approach for the joint estimation of the main regression and dynamic dependence parameters of the model. The finite sample performance of the estimation approaches is examined through a simulation study. The asymptotic properties of the estimators are also discussed. The proposed model and the estimation approaches are illustrated by reanalysing a longitudinal infectious disease data.     

Norm restricted maximum likelihood estimators for binary regression models with parametric link

Parametric link transformation families have shown to be useful in the analysis of binary regression data since they avoid th? problem of link misspecifaction. Inference for these models are commonly based on likelihood methods. Duffy and Santner (1988, 1989) however showed that ordinary logistic maximum likelihood estimators (MLE) have poor mean square error (MSE) behavior in small samples compared to alternative norm restricted estimators. This paper extends these alternative norm restricted estimators to binary regression models with any specified parametric link family. These extended norm restricted MLE's are strongly consistent and efficient under regularity conditions. Finally a simulation study shows that an empiric version of norm restricted MLE's exhibit superior MSE behavior in small samples compared to MLE's with fixed known link.     

On improved estimation of a gamma shape parameter

This paper deals with improved estimation of a gamma shape parameter from a decision-theoretic point of view. First we study the second-order properties of three estimators – (i) the maximum-likelihood estimator (MLE), (ii) a bias corrected version of the MLE, and (iii) an improved version (in terms of mean squared error) of the MLE. It is shown that all the three estimators mentioned above are second-order inadmissible. Next, we obtain superior estimators which are second order better than the above three estimators. Simulation results are provided to study the relative risk improvement of each improved estimator over the MLE.     

On second-order admissibilities of the estimators of gamma shape vector

Simultaneous estimation problem of gamma shape vector is considered.First, it is shown that the maximum likelihood estimator (MLE), the bias corrected MLE, and the conditional MLE of shape vector are second-order inadmissible. Second, these estimators are improved up to the second order. Finally, we identify whether these improved estimators are second-order admissible or not. Simulation studies are also given.