The Relative Performance of Poisson and Negative Binomial Regression Estimators

Negative binomial estimators are commonly used in estimating models with count‐data dependent variables. In this paper, sampling experiments are used to evaluate the performance of these estimators relative to the simpler Poisson estimator in finite‐sample situations. The results do not suggest a clear preference for negative binomial estimators in situations in which the underlying dependent variables are overdispersed, unless the researcher is comfortable in assumptions about the precise form of the overdispersion.     

Dynamic Panel Data Models With Irregular Spacing: With an Application to Early Childhood Development

With the increased availability of longitudinal data, dynamic panel data models have become commonplace. Moreover, the properties of various estimators of such models are well known. However, we show that these estimators break down when the data are irregularly spaced along the time dimension. Unfortunately, this is an increasingly frequent occurrence as many longitudinal surveys are collected at non‐uniform intervals and no solution is currently available when time‐varying covariates are included in the model. In this paper, we propose two new estimators for dynamic panel data models when data are irregularly spaced and compare their finite‐sample performance to the näive application of existing estimators. We illustrate the practical importance of this issue in an application concerning early childhood development. Copyright © 2016 John Wiley & Sons, Ltd.     

A Comparative Analysis of Different IV and GMM Estimators of Dynamic Panel Data Models

It is well known that the usual procedures for estimating panel data models are inconsistent in the dynamic setting. A large number of consistent estimators however, have been proposed in the literature. This paper provides a survey of the majority of mainstream estimators, which tend to consist of IV and GMM ones. It also considers a newly proposed extension to the promising Wansbeek–Bekker estimator (Harris & Mátyás, 2000). To provide guidance to the applied researcher working on micro-datasets, the small sample performance of these estimators is evaluated using a set of Monte Carlo experiments.     

Partial rank estimation of duration models with general forms of censoring

In this paper we propose estimators for the regression coefficients in censored duration models which are distribution free, impose no parametric specification on the baseline hazard function, and can accommodate general forms of censoring. The estimators are shown to have desirable asymptotic properties and Monte Carlo simulations demonstrate good finite sample performance. Among the data features the new estimators can accommodate are covariate-dependent censoring, double censoring, and fixed (individual or group specific) effects. We also examine the behavior of the estimator in an empirical illustration.     

Estimation strategies for the regression coefficient parameter matrix in multivariate multiple regression

We consider improved estimation strategies for the parameter matrix in multivariate multiple regression under a general and natural linear constraint. In the context of two competing models where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information, there is a need of combining two estimation techniques in an optimal way. In this scenario, we suggest some shrinkage estimators for the targeted parameter matrix. Also, we examine the relative performances of the suggested estimators in the direction of the subspace and candidate subspace restricted type estimators. We develop a large sample theory for the estimators including derivation of asymptotic bias and asymptotic distributional risk of the suggested estimators. Furthermore, we conduct Monte Carlo simulation studies to appraise the relative performance of the suggested estimators with the classical estimators. The methods are also applied on a real data set for illustrative purposes.     

A new class of asymptotically efficient estimators for moment condition models

In this paper, we propose a new class of asymptotically efficient estimators for moment condition models. These estimators share the same higher order bias properties as the generalized empirical likelihood estimators and once bias corrected, have the same higher order efficiency properties as the bias corrected generalized empirical likelihood estimators. Unlike the generalized empirical likelihood estimators, our new estimators are much easier to compute. A simulation study finds that our estimators have better finite sample performance than the two-step GMM, and compare well to several potential alternatives in terms of both computational stability and overall performance.     

Blockwise bootstrap wavelet in nonparametric regression model with weakly dependent processes

In this paper, we suggest a blockwise bootstrap wavelet to estimate the regression function in the nonparametric regression models with weakly dependent processes for both designs of fixed and random. We obtain the asymptotic orders of the biases and variances of the estimators and establish the asymptotic normality for a modified version of the estimators. We also introduce a principle to select the length of data block. These results show that the blockwise bootstrap wavelet is valid for general weakly dependent processes such as α-mixing, φ-mixing and ρ-mixing random variables.     

具有异质性非参数时间趋势的面板数据模型的估计

本文为一类具有异质性非参数时间趋势的面板数据模型提出了一种简单估计方法。基于局部多项式回归的思想,首先去除数据中的时间趋势成分,然后由最小二乘法来估计公共系数,同时得到时间趋势函数的非参数估计。在一些正则条件下,研究了这些估计量的渐近性质,即在时间维度T和横截面维度n同时趋向无穷时,建立了各个估计量的渐近相合性和渐近正态性。最后通过蒙特卡洛模拟,考查了这种估计方法的有限样本性质。     

Empirical implementation of nonparametric first-price auction models

Nonparametric estimators provide a flexible means of uncovering salient features of auction data. Although these estimators are popular in the literature, many key features necessary for proper implementation have yet to be uncovered. Here we provide several suggestions for nonparametric estimation of first-price auction models. Specifically, we show how to impose monotonicity of the equilibrium bidding strategy; a key property of structural auction models not guaranteed in standard nonparametric estimation. We further develop methods for automatic bandwidth selection. Finally, we discuss how to impose monotonicity in auctions with differing numbers of bidders, reserve prices, and auction-specific characteristics. Finite sample performance is examined using simulated data as well as experimental auction data.     

Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility

In this paper, we propose two estimators, an integral estimator and a discretized estimator, for the wavelet coefficient of regression functions in nonparametric regression models with heteroscedastic variance. These estimators can be used to test the jumps of the regression function. The model allows for lagged-dependent variables and other mixing regressors. The asymptotic distributions of the statistics are established, and the asymptotic critical values are analytically obtained from the asymptotic distribution. We also use the test to determine consistent estimators for the locations of change points. The jump sizes and locations of change points can be consistently estimated using wavelet coefficients, and the convergency rates of these estimators are derived. We perform some Monte Carlo simulations to check the powers and sizes of the test statistics. Finally, we give practical examples in finance and economics to detect changes in stock returns and short-term interest rates using the empirical wavelet method.     

Asymptotic theory for heterogeneous dynamic pseudo-panels

Dynamic pseudo-panel models with inter-cohort parameter heterogeneity are studied. The population is divided into cohorts and the cohort sample means are used as a heterogeneous panel. Least squares and instrumental variables estimators are considered. Multidimensional limits are analyzed as the cross-sectional and temporal dimensions of the data pass to infinity, allowing for both stationary and nonstationary cases. Monte-Carlo simulations on the finite-sample performance of the estimators in these two dimensions are conducted and these, in conjunction with the asymptotic results, are used to make recommendations for practical implementation of the techniques. An empirical illustration finds heterogeneity in consumption growth rates among Taiwanese birth cohorts.     

Mixing of direct, ratio, and product method estimators

In a paper by S rivenkataramana T racy [4], four methods of estimating a population total Y with the use of an auxiliary variable were introduced, given a random sample without replacement from that population. These methods were "built around the idea that estimating the population total is essentially equivalent to estimating the total corresponding to the non-sample units, since that corresponding to the sample units is known once the sample is drawn and measurements are made on it."
However, in the case of small sampling fractions the nonsample units constitute most of the population and no great improvement over the traditional estimators is to be expected. Therefore the methods are compared with the existing estimators and it turns out that they are special cases of the "mixing estimators", introduced in this paper. The latter estimators can be made asymptotically equivalent to the regression estimator and are therefore asymptotically superior to all other estimators. An exact comparison is carried out on the artificial example given in [4]. The statement in this paper that "the proposed estimators are to be preferred to the regression estimator for., superiority of performance in the case of small samples" is evidently misleading. Finally a comparison is made with other "mixing-type" estimators, that can prove very useful in practice.     

Nonparametric estimators of the bivariate survival function under random censoring

A large number of proposals for estimating the bivariate survival function under random censoring have been made. In this paper we discuss the most prominent estimators, where prominent is meant in the sense that they are best for practical use; Dabrowska's estimator, the Prentice–Cai estimator, Pruitt's modified EM-estimator, and the reduced data NPMLE of van der Laan. We show how these estimators are computed and present their intuitive background. The asymptotic results are summarized. Furthermore, we give a summary of the practical performance of the estimators under different levels of dependence and censoring based on extensive simulation results. This leads also to a practical advise.     

Semiparametric time series regression modeling with a diverging number of parameters

Variable selection and error structure determination of a partially linear model with time series errors are important issues. In this paper, we investigate the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation penalty for a partially linear model with a divergent number of covariates and finite order autoregressive time series errors. Both consistency and asymptotic normality of the proposed penalized estimators are derived. The oracle property of the resultant estimators is proved. Simulation studies are carried out to assess the finite‐sample performance of the proposed procedure. A real data analysis is made to illustrate the usefulness of the proposed procedure as well.     

Break Date Estimation for Models with Deterministic Structural Change

In this article, we consider estimating the timing of a break in level and/or trend when the order of integration and autocorrelation properties of the data are unknown. For stationary innovations, break point estimation is commonly performed by minimizing the sum of squared residuals across all candidate break points, using a regression of the levels of the series on the assumed deterministic components. For unit root processes, the obvious modification is to use a first differenced version of the regression, while a further alternative in a stationary autoregressive setting is to consider a GLS‐type quasi‐differenced regression. Given uncertainty over which of these approaches to adopt in practice, we develop a hybrid break fraction estimator that selects from the levels‐based estimator, the first‐difference‐based estimator, and a range of quasi‐difference‐based estimators, according to which achieves the global minimum sum of squared residuals. We establish the asymptotic properties of the estimators considered, and compare their performance in practically relevant sample sizes using simulation. We find that the new hybrid estimator has desirable asymptotic properties and performs very well in finite samples, providing a reliable approach to break date estimation without requiring decisions to be made regarding the autocorrelation properties of the data.     

Data Dependent Endogeneity Correction in Cointegrated Panels*

This paper examines the small‐sample performance of several information based criteria that can be employed to facilitate data dependent endogeneity correction in estimation of cointegrated panel regressions. The Monte Carlo evidence suggests that the criteria generally perform well but that there are differences of practical importance. In particular, the evidence suggests that, although the estimators of the cointegration vectors generally perform well, the criterion with best small‐sample performance also leads to the best performing estimator.     

Multiplicative-error models with sample selection

This paper presents a simple approach to deal with sample selection in models with multiplicative errors. Models for non-negative limited dependent variables such as counts fit this framework. The approach builds on a specification of the conditional mean of the outcome only and is, therefore, semiparametric in nature. GMM estimators are constructed for both cross-section data and for panel data. We derive distribution theory and present Monte Carlo evidence on the finite-sample performance of the estimators.     

Robust linear static panel data models using ε-contamination

The paper develops a general Bayesian framework for robust linear static panel data models using$\epsilon$-contamination. A two-step approach is employed to derive the conditional type-II maximum likelihood (ML-II) posterior distribution of the coefficients and individual effects. The ML-II posterior means are weighted averages of the Bayes estimator under a base prior and the data-dependent empirical Bayes estimator. Two-stage and three stage hierarchy estimators are developed and their finite sample performance is investigated through a series of Monte Carlo experiments. These include standard random effects as well as Mundlak-type, Chamberlain-type and Hausman–Taylor-type models. The simulation results underscore the relatively good performance of the three-stage hierarchy estimator. Within a single theoretical framework, our Bayesian approach encompasses a variety of specifications while conventional methods require separate estimators for each case.     

Small Area Quantile Estimation

Sample surveys are widely used to obtain information about totals, means, medians and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio‐demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit‐level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise.     

Small sample properties of LIML and jackknife IV estimators: experiments with weak instruments

Using Monte Carlo simulations we study the small sample performance of the traditional TSLS, the LIML and four new jackknife IV estimators when the instruments are weak. We find that the new estimators and LIML have a smaller bias but a larger variance than the TSLS. In terms of root mean square error, neither LIML nor the new estimators perform uniformly better than the TSLS. The main conclusion from the simulations and an empirical application on labour supply functions is that in a situation with many weak instruments, there still does not exist an easy way to obtain reliable estimates in small samples. Better instruments and/or larger samples is the only way to increase precision in the estimates. Since the properties of the estimators are specific to each data-generating process and sample size it would be wise in empirical work to complement the estimates with a Monte Carlo study of the estimators' properties for the relevant sample size and data-generating process believed to be applicable. Copyright © 1999 John Wiley & Sons, Ltd.