Tests of specification in econometrics

This survey of recent developments in testing for misspecification of econometric models reviews procedures based on a method due to Hausman. Particular attention is given to alternative forms of the test, its relationship to classical test procedures, and its role in pre-test estimation.     

Amemiya's generalized least squares and tests of overidentification in simultaneous equation models with qualitative or limited dependent variables

Amemiya's generalized least squares method for the estimation of simultaneous equation modeis with qualitative or limited dependent variables is known to be efficient relative to many popular two stage estimators. This note points out that test statistics for overidentification restrictions can be obtained as by-products of Amerniya's generalized least squares procedure. Amemiya's procedure is shown to be a minimum chisquare method. The Amemiya procedure is valuable both for efficient estimation and for model evaluation of such models.     

Robustness of MML estimators based on censored samples and robust test statistics

We investigate the efficiences of Tiku's (1967) modified maximum likelihood estimators μ_c and σ_c (based on symmetrically censored normal samples) for estimating the location and scale parameters μ and σ of symmetric non-normal distributions. We show that μ_c and σ_c are jointly more efficient than x? and s for long-tailed distributions (kurtosis $\text{β}{}_2{}^1\text{=}\text{μ}{}_4\text{μ}{}_2{}^2\text{>4.2, β}{}_2{}^1\text{= 4.2}$ for the Logistic), and always more efficient than the trimmed mean μT and the matching sample estimate σ_T of σ. We also show that μ_c and σ_c are jointly at least as efficient as some of the more prominent “robust” estimators (Gross, 1976). We show that the statistic $\text{t}{}_{\mathrm{c}}\text{= μ}{}_{\mathrm{c}}\text{m}\text{σ}{}_{\mathrm{c}}\text{, m = n ?2r + 2rβ}$ (r is the number of observations censored on each side of the sample and β is a constant), is robust and powerful for testing an assumed value of μ. We define a statistic T_c (based on μ_c andσ_c) for testing that two symmetric distributions are identical and show that T_c is robust and generally more poweerful than the well-known nonparametric statistics (Wilcoxon, normal-score, Kolmogorov-Smirnov), against the important location-shift alternatives. We generalize the statistic T_c to test that k symmetric distibutions are identical. The asymptotic distributions of t_c and T_c are normal, under some very general regularity conditions. For small samples, the upper (lower) percentage points of t_c and T_c are shown to be closely approximated by Student's t-distributions. Besides, the statistics μ_c and σ_c (and hence t_c and T_c) are explicit and simple functions of sample observations and are easy to compute.     

Amemiya‘s generalized least squares and tests of overidentification in simultaneous equation models with qualitative or limited dependent variables

Amemiya's generalized least squares method for the estimation of simultaneous equation modeis with qualitative or limited dependent variables is known to be efficient relative to many popular two stage estimators. This note points out that test statistics for overidentification restrictions can be obtained as by-products of Amerniya's generalized least squares procedure. Amemiya's procedure is shown to be a minimum chisquare method. The Amemiya procedure is valuable both for efficient estimation and for model evaluation of such models.     

基于多重抽样框的连续性抽样估计方法研究

多重抽样框可以解决单一抽样框难以完整覆盖流动性目标总体的难题,连续性抽样调查则可以获取变量的时序观测数据,对总体现象进行追踪调查。本文将多重抽样框调查与连续性抽样调查两种方法结合在一起进行研究,深入分析基于多重抽样框的连续性抽样估计方法。文章首先设计了连续性调查环境下总体结构变动表;然后,在简单随机抽样假定下的轮换样本调查情形开展研究,设计了14种参数缩减方法对构建的似然函数进行估计求解,并给出了估计量的迭代计算过程;最后,对本文的研究内容进行了总结与展望。     

Testing exogeneity in overidentified models

Summary In this paper we analyse the consequences of model overidentification on testing exogeneity, when maximum likelihood techniques for estimation and inference are used. This situation is viewed as a particular case of the more general problem of considering how restrictions on nuisance parameters could help in making inference on the parameters of interest. At first a general model is considered. A suitable likelihood function factorization is used which allows a simple derivation of the information matrix and others tools useful for building up joint tests of exogeneity and overidentifying restrictions both of Wald and Lagrange Multiplier type. The asymptotic local power of the exogeneity test in the justidentified model is compared with that in the overidentified one, when we assume that the latter is the true model. Then the pseudo-likelihood framework is used to derive the consequences of working with a model where overidentifying restrictions are erroneously imposed. The inconsistency introduced by imposing false restrictions is analysed and the consequences of the misspecification on the exogeneity test are carefully examined.     

中国利率期限结构与货币政策联合建模的实证研究

本文采用卡尔曼滤波和极大似然函数估计方法对中国无套利利率期限结构与货币政策联合建模进行估计,实证结果显示通货膨胀目标值对利率期限结构的冲击是扩张性和持续性的,对于所有到期期限都是持续上升的;货币政策冲击对利率期限结构冲击的效应则是递减的,对利率期限结构曲线的斜率影响较显著;通货膨胀冲击对利率期限结构曲线的曲度影响较显著。模型样本外预测大大优于VAR模型。研究结果表明,本文构建模型一方面有助于对利率期限结构的预测,另一方面有助于央行制定前瞻有效的货币政策。     

面板数据单位根似然比检验研究

本文采用似然比类检验统计量进行面板单位根检验（简称为LR检验）研究,在局部备择假设成立的条件下,推导了其在无确定项、仅含截距项以及存在线性时间趋势项三种模型下所对应的渐近分布与局部渐近势函数。Monte Carlo模拟结果显示,当面板数据中含确定项（截距项或时间趋势项）时,LR检验水平比LLC和IPS检验水平更接近于给定的显著性检验水平;此外,当面板数据中包含发散个体时,经水平修正后的LR检验势要远远高于经水平修正后的LLC与IPS检验势,其中,经水平修正后的LLC与IPS检验势接近于零。     

空间滞后分位数回归模型的工具变量估计及参数检验

本文提出一种遵循空间数据分布特征的空间分位数回归模型,并着重探讨该模型的估计方法和参数检验问题。本文构建了上述模型的一个工具变量估计法,通过数理证明建立了估计量的大样本理论,并基于估计量的渐近分布构造了模型的参数检验方法。本文还通过数值模拟方法和应用实例考察估计方法和参数检验方法的实际应用效果,数值模拟结果显示,估计方法和参数检验方法在有限样本条件下均可以达到较高的精确度和稳定性。在应用实例中,本文利用所构建的理论方法重新检验我国“资源诅咒”效应的存在性,实证结果体现了理论方法的应用价值。     

时变系数空间自回归面板数据模型的极大似然估计

本文对扰动项存在跨时期的异方差、但不存在序列相关的时变系数空间自回归模型提出了极大似然的估计方法,并证明了该估计量的一致性,同时,证明了该估计量渐进服从正态分布,由此说明该估计量具有优良的大样本性质。同时,我们还对本文所提出估计量的小样本性质进行了数值模拟。本文研究表明,估计量虽然在N较小时偏差较大,但是随着N的不断增加,估计量偏差减小,体现了比较优良的渐进性质。同时,估计量的偏差会随着时期数的增加而变大,这说明本文所提出的估计方法适用于个体数较多、时期数较少的短面板数据。     

Maximum likelihood revisited under a semi-parametric context - estimation of the tail index

In this paper, and in a context of regularly varying tails, we study computationally the classical Maximum Likelihood (ML) estimator based on the Paretian behaviour of the excesses over a high threshold, denoted PML-estimator, a type II Censoring estimator based specifically on a Fréchet parent, denoted CENS-estimator, and two ML estimators based on the scaled log-spacings, and denoted SLS-estimators. These estimators are considered under a semi-parametric set-up, and compared with the classical Hill estimator and a Generalized Jackknife (GJ) estimator, which has essentially in mind a reduction of the bias of Hill's estimator.     

Estimation of weibull parameters for grouped data with competing risks

We consider the problem of estimating Weibull parameters for grouped data when competing risks are present. We propose two simple methods of estimation and derive their asymptotic properties. A Monte Carlo study was carried out to evaluate the performance of these two methods.     

A consistency result in general censoring models

In this paper we prove a consistency result for sieved maximum likelihood estimators of the density in general random censoring models with covariates. The proof is based on the method of functional estimation. The estimation error is decomposed in a deterministic approximation error and the stochastic estimation error. The main part of the proof is to establish a uniform law of large numbers for the conditional log-likelihood functional, by using results and techniques from empirical process theory.     

LSTAR-GARCH模型的单位根检验

LSTAR模型的单位根检验往往易忽视其条件方差的时变性,实际上,对许多经济变量尤其是金融变量建立LSTAR模型后,经常发现其条件方差存在GARCH效应。针对LSTAR-GARCH模型的平稳性检验,本文构建了检验统计量tNG,之后在极大似然估计的基础上,推导出tNG的渐近分布,通过蒙特卡洛模拟方法得到该统计量的渐近临界值,并在此基础上研究了tNG检验的检验功效。在与刘雪燕和张晓峒(2009)提出的tNL检验、Ling等(2003)提出的tLG检验以及DF单位根检验进行比较后,发现tNG检验具备明显优势。     

具有组群异方差结构的面板数据模型及其应用研究

面板数据由不同个体的时间序列数据汇聚而成。已有大量研究表明面板数据个体之间存在组群结构,并且普遍存在模型的异方差现象。本文借鉴组群异质性的研究成果,构建模型误差项组群结构的面板数据模型,基于模型假定条件,提出惩罚伪最大似然函数估计法(PQMLE),该方法能够同时进行结构识别和参数估计;证明了估计量具有Oracle渐近性质;蒙特卡洛模拟验证了该方法有效的样本性质;进一步应用该方法对我国股市进行Fama-French三因子模型的实证分析,验证了理论模型的应用效果。     

三个多元正态总体在简单半序约束下均值估计

 多元保序回归理论对统计学中研究多维参数在序约束下的估计理论起着关键性作用。本文讨论了当协方差矩阵已知,在简单半序约束下,对三个多元正态总体均值的估计问题,给出了估计的算法。并证明了在多元均方损失条件下,给出的均值估计优于无序约束的均值估计。     

A comparison of various methods for estimating the parameters in mixtures of von mises distributions

In this paper we compare five methods for estimating the unknown parameters in a mixture of two von Mises distributions. We propose a new method based on the characteristic function and compare it with the classical methods based on maximum likelihood and moments. Thus far these methods have been successfully applied only to linear data. Here we show that the application to circular data is reasonably straightforward and that convergence to the final estimates is fairly rapid. For various simulated known mixtures the results obtained are satisfactory. Finally, we introduce a modification of the method of moments which is considerably faster in CPU time than any of the other methods used and gives good results.     

Tests of hypotheses on concomitant variables in linear models

The likelihood ratio test for the equality of k univariate normal populations is extended to include the case in which the means are expressed as simple linear regression functions involving two parameters, The moments of the likelihood ratio statistic are derived, and an approximation to the null distribution is obtained.     

Finite sample properties of ml and reml estimators in time series regression models with long memory noise

Finite sample properties of ML and REML estimators in time series regression models with fractional ARIMA noise are examined. In particular, theoretical approximations for bias of ML and REML estimators of the noise parameters are developed and their accuracy is assessed through simulations. The impact of noise parameter estimation on performance of t -statistics and likelihood ratio statistics for testing regression parameters is also investigated.     

A test of the normality assumption in ordered probit model

This paper presents a Lagrange multiplier test of the normality assumption underlying the ordered probit model. The test is presented both for the standard ordered probit model and a version in which censoring is present in the dependent variable. The test is then compared to normality tests proposed here compares favorably to tests based on artificial regression techinques.