IV估计的大样本性质——基于二维参数空间的研究

存在很多个工具变量或工具变量为弱工具变量时,IV估计的大样本性质是近年来IV估计研究的新方向。本文提出了一种新的研究思路,从参数空间的角度重新剖析了IV估计在大样本下的各种收敛情况。借鉴Rothenberg(1984)的研究方法,我们将IV估计的结果表示为参数δ(工具变量个数的阶数)和λ(工具变量解释强度的阶数)的函数;根据IV估计量收敛情况的不同,我们对参数δ和λ的可行性区域进行对应的划分,将IV估计的研究划分为6种情形,涵盖了传统理论、Bekker(1994)、Staiger和Stock(1997)以及Chao和Swanson(2003b)的研究结论。     

层级数据空间误差自回归模型的估计方法研究

本文建立同时考虑空间误差自回归和嵌套随机效应误差分量的层级数据空间误差自回归模型,并推导最优权重GMM估计量,对空间自回归系数和误差项的方差进行估计。然后,定义对应的FGLS估计量,对层级数据空间误差自回归模型的总体回归系数进行估计。通过蒙特卡洛模拟,验证了所提出模型估计量的有限样本性质。模拟结果表明,本文提出的最优权重GMM估计量以及总体回归系数的GMM FGLS估计量有很好的小样本性质。     

Logistic回归的ArctanLASSO惩罚似然估计及应用

Logistic回归是计量经济学中应用最广的离散选择模型。当变量个数较多时,极大似然估计解释性较差,为此本文基于新的惩罚函数ArctanLASSO,给出Logistic回归的一种非凸惩罚似然估计进行参数估计和变量选取,并证明了估计量的n1/2相合性和Oracle性质。本文结合二阶近似处理、LLA方法和梯度下降法给出估计算法,并通过最小化BIC准则对正则化参数进行选取。模拟数据分析显示,当样本量较大时,该方法在参数估计和变量选取两个方面都优于传统的LASSO、SCAD和MCP方法,样本量较小时,该方法同样具有很大优势。实际数据分析表明,该方法很好地权衡了拟合程度和非零系数的选择,是最优的备选模型,具有重要的实际意义。     

非等间隔动态面板数据模型：估计方法与应用实例

非等间隔动态面板数据模型由于相邻两期观测之间的时间长度不尽相同使得传统动态面板数据模型的估计方法失效,本文提出使用非线性最小二乘、最短距离以及它们的一步估计量对该模型进行估计,证明了这四个估计量的一致性和渐进正态性,同时借助蒙特卡洛模拟的方法验证了它们在有限样本中的估计精度,并且进一步使用所提出的估计量讨论了以往文献由于缺乏相应的估计方法而没有被研究或者充分讨论的问题,得到了一些新的结论。     

分整阶数半参数估计的有限样本性质研究

随着对经济和金融时间序列长记忆性的研究,分整阶数估计已成为当前理论研究的焦点问题。以对数周期图回归和局部Whittle方法为代表的半参数分整阶数估计方法在实践中得到广泛应用,但对这两类半参数估计方法的有限样本性质的比较则鲜有涉及,影响了在实践中对估计方法的选择。利用蒙特卡洛模拟方法,在不同数据产生的过程下,这两种半参数估计方法有限样本性质的研究结果表明：在ARFIMA(0, d, 0)过程下,LW类估计量具有较好的小样本性质;在平稳ARFIMA(1, d, 0)过程下,本文建议的QGPH估计量的有限样本性质要优于其他对数周期图估计量;在非平稳过程下,MGPH的偏差最小。     

Ⅳ估计的大样本性质——基于二维参数空间的研究

存在很多个工具变量或工具变量为弱工具变量时,Ⅳ估计的大样本性质是近年来Ⅳ估计研究的新方向.本文提出了一种新的研究思路,从参数空间的角度重新剖析了Ⅳ估计在大样本下的各种收敛情况.借鉴Rothenberg(1984)的研究方法,我们将Ⅳ估计的结果表示为参数δ(工具变量个数的阶数)和λ(工具变量解释强度的阶数)的函数;根据Ⅳ估计量收敛情况的不同,我们对参数δ和λ的可行性区域进行对应的划分,将Ⅳ估计的研究划分为6种情形,涵盖了传统理论、Bekker(1994)、Staiger和Stock(1997)以及Chao和Swanson(2003b)的研究结论.     

VaR样本分位数估计的偏差改进

本文指出了人们通常所使用的VaR样本分位数估计量会产生高估或低估的现象,并分析了产生这些现象的原因,提出在样本较大的情况下利用加权样本分位数估计量去估计VaR,在样本较小的情况下用基于Bootstrap方法的样本分位数估计量去估计VaR。数值模拟的结果表明,这些估计方法的估计精度得到了较好地改进。最后,运用这两种分位数估计量来估计两支股票(招商银行、中国石化)的日对数回报序列的VaR值,并比较它们的风险估计量的大小。     

非线性动态面板模型的条件GMM估计

基于时间序列的实证分析已经证实,很多经济变量的动态调整过程都存在非线性的平滑转换机制.本文将传统的线性动态面板模型扩展为平滑转换的非线性动态面板模型,并基于对非线性参数的格点搜索,提出了一种简便易行的非线性动态面板模型估计程序--条件GMM估计,其估计量具有一致性.仿真实验结果显示,条件GMM估计量在有限样本下具有良好表现.同时,非线性动态面板模型的条件GMM估计还为在非线性框架下检验面板单位根创造了条件.     

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。     

线性模型参数的最优估计——基于对最小P乘估计的研究

本文通过随机模拟计算研究了线性回归模型参数的LP估计量的一些特性,当误差项服从不同的分布时,在LP估计量中寻找最优或接近最优的估计。     

Jackknife instrumental variables estimation

Two-stage-least-squares (2SLS) estimates are biased towards the probability limit of OLS estimates. This bias grows with the degree of over-identification and can generate highly misleading results. In this paper we propose two simple alternatives to 2SLS and limited-information-maximum-likelihood (LIML) estimators for models with more instruments than endogenous regressors. These estimators can be interpreted as instrumental variables procedures using an instrument that is independent of disturbances even in finite samples. Independence is achieved by using a ‘leave-one-out’ jackknife-type fitted value in place of the usual first stage equation. The new estimators are first-order equivalent to 2SLS but with finite-sample properties superior, in terms of bias and coverage rate of confidence intervals, compared to those of 2SLS and similar to those of LIML, when there are many instruments. Copyright © 1999 John Wiley & Sons, Ltd.     

Improved instrumental variables estimation of simultaneous equations under conditionally heteroskedastic disturbances

In this paper we develop estimation techniques and a specification test for the validity of instrumental variables allowing for conditionally heteroskedastic disturbances. We propose modified two‐stage least squares (2SLS) and modified 3SLS procedures where the conditional heteroskedasticity is taken into account, which are natural extensions of the traditional 2SLS and 3SLS estimators and which achieve a lower variance. We recommend the use of these modified 2SLS and 3SLS procedures in practice instead of alternative estimators like limited‐information maximum likelihood/full‐information maximum likelihood, where the non‐existence of moments leads to extreme values, and also for ease of computation. It is shown theoretically and with simulation that in some cases 2SLS, 3SLS and our modified 2SLS and 3SLS procedures can have very severe biases (including the weak instruments case), and we present bias correction procedures to apply in practice along the lines of Flores‐Lagunes ( 2007 ). Our new estimation procedures can also be used to extend the test for weak instruments of Stock and Yogo ( 2005 ) and to allow for conditional heteroskedasticity. Finally, we show the usefulness of our estimation procedures with an application to the demand and supply of fish. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficiency of iterative estimators in the regression model with AR(1) disturbances

The mean square error approximation method of Nagar is applied to the iterated Prais-Winsten and (iterated) maximum likelihood estimators of regression coefficients in the model with AR(1) disturbances. Their mean square errors are found to equal that of the two-stage Prais-Winsten estimator at the second-order level of approximation.     

A ridge-like method for simultaneous estimation of simultaneous equations

In the context of full information estimation in a linear simultaneous equations model, this paper considers a ridge-like modification of the 3SLS estimator. The proposed method is particularly desirable where the square matrix of the 3SLS normal equationsis singular (or near-singular) leading to non-existence (or poor performance) of the estimator. Furthermore, the type of solution suggested here does seem to result in the existence of the finite sample moments of the estimator even when the degrees of over identification are as low as zero (just identified models). This paper considers only a simple scalar form of the ‘ridge-matrix” with a relatively simple choice of the modifying scalar that preserves the asymptotic properties of the 3SLS estimator. A value of this scalar is derived which minimizes an appropriatequadratic risk criterion. The approximate quadratic risk function is based upon the asymptotic approximation of the relevant moments in the manner of Nagar (1959). A range of risk reducing values of the ‘ridge-scalar” is also given.     

GMM estimation of social interaction models with centrality

This paper considers the specification and estimation of social interaction models with network structures and the presence of endogenous, contextual, correlated, and group fixed effects. When the network structure in a group is captured by a graph in which the degrees of nodes are not all equal, the different positions of group members as measured by the Bonacich (1987) centrality provide additional information for identification and estimation. In this case, the Bonacich centrality measure for each group can be used as an instrument for the endogenous social effect, but the number of such instruments grows with the number of groups. We consider the 2SLS and GMM estimation for the model. The proposed estimators are asymptotically efficient, respectively, within the class of IV estimators and the class of GMM estimators based on linear and quadratic moments, when the sample size grows fast enough relative to the number of instruments.     

A regularization approach to the many instruments problem

This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation. We show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound. Higher-order analysis of the MSE reveals that the bias of the modified estimators does not depend on the number of instruments. Finally, we suggest a data-driven method for selecting the regularization parameter. Interestingly, our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument.     

Estimation of models with grouped and ungrouped data by means of “2SLS”

This paper deals with a special case of estimation with grouped data, where the dependent variable is only available for groups, whereas the endogenous regressor(s) is available at the individual level. By estimating the first stage using the available individual data, and then estimating the second stage at the aggregate level, it might be possible to gain efficiency relative to the OLS and 2SLS estimators that use only grouped data. We term this the mixed-2SLS estimator (M2SLS). The M2SLS estimator is consistent and asymptotically normal. We also provide a test of efficiency of M2SLS relative to OLS and “2SLS” estimators.     

The case against JIVE

We perform an extensive series of Monte Carlo experiments to compare the performance of two variants of the ‘jackknife instrumental variables estimator’, or JIVE, with that of the more familiar 2SLS and LIML estimators. We find no evidence to suggest that JIVE should ever be used. It is always more dispersed than 2SLS, often very much so, and it is almost always inferior to LIML in all respects. Interestingly, JIVE seems to perform particularly badly when the instruments are weak. Copyright © 2006 John Wiley & Sons, Ltd.     

GMM and 2SLS estimation of mixed regressive,spatial autoregressive models

The GMM method and the classical 2SLS method are considered for the estimation of mixed regressive, spatial autoregressive models. These methods have computational advantage over the conventional maximum likelihood method. The proposed GMM estimators are shown to be consistent and asymptotically normal. Within certain classes of GMM estimators, best ones are derived. The proposed GMM estimators improve upon the 2SLS estimators and are applicable even if all regressors are irrelevant. A best GMM estimator may have the same limiting distribution as the ML estimator (with normal disturbances).     

A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments

The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the ‐norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The ‐norm regularization with a regularized parameter O(n) allows us to obtain the Rothenberg (1984) type of higher‐order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter O(n), which is used as a standardized factor in the higher‐order approximation. We also show that the proposed ‐norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.