A Note on Specification Testing in Some Structural Regression Models

There exists a useful framework for jointly implementing Durbin–Wu–Hausman exogeneity and Sargan–Hansen overidentification tests, as a single artificial regression. This note sets out the framework for linear models and discusses its extension to nonlinear models. It also provides an empirical example and some Monte Carlo results.     

Testing for Heteroskedasticity and Predictive Failure in Linear Regression Models*

It is argued that, when researchers wish to carry out a Chow test of the significance of prediction errors, it is necessary to assume homoskedasticity because standard results on heteroskedasticity‐robust tests are not available. The effects of heteroskedasticity on the Chow prediction error test are examined. The implementation of tests for heteroskedasticity is discussed, with the case in which the regressors include dummy variables for prediction error tests receiving special attention. Monte Carlo results are reported.     

A Note on the Selection of Time Series Models

We consider issues related to the order of an autoregression selected using information criteria. We study the sensitivity of the estimated order to (i) whether the effective number of observations is held fixed when estimating models of different order, (ii) whether the estimate of the variance is adjusted for degrees of freedom, and (iii) how the penalty for overfitting is defined in relation to the total sample size. Simulations show that the lag length selected by both the Akaike and the Schwarz information criteria are sensitive to these parameters in finite samples. The methods that give the most precise estimates are those that hold the effective sample size fixed across models to be compared. Theoretical considerations reveal that this is indeed necessary for valid model comparisons. Guides to robust model selection are provided.     

基于回归模型的企业供给分析

本文借助成本函数和价格的回归模型在价格随机的假设条件下进行了企业供给分析，旨在对本量利分析做一些有益的探讨。     

A Note on Estimated Coefficients in Random Effects Probit Models

This note points out to applied researchers what adjustments are needed tothe coefficient estimates in a random effects probit model in order to make valid comparisons in terms of coefficient estimates and marginal effects across different specifications. These adjustments are necessary because of the normalization that is used by standard software in order to facilitate easyestimation of the random effects probit model.     

Laboratory Testing of Spurious Spatial Structure in Trip Distribution Models

Abstract

In this paper we examine the risk of reporting spurious relationships in trip distribution models. We show how to make synthetic data sets that (by construction) are neutral with respect to clustering effects. We study a particular case with two non-interacting groups of jobs/workers. A competing destinations model is applied to 100 randomly drawn data sets of this type. Quite disturbingly, the loglikelihood ratio test reported a significant clustering effect in all of these data sets. This shows that statistical tests based on likelihood values may not be the right tool to examine the effect of such model extensions.     

Non-Parametric Regression Models of Deviations from Othogonality in the Expectations Theory of the Term Structure

Regression tests of the expectations theory of the term structure typically reject the null hypothesis of orthogonality between implied forecast errors and the yield spreads. In the statistical literature on the term structure, these rejections are sometimes attributed to time-varying liquidity premia, and Engle et al . (1987) suggest that the ARCH-M model of time-variation in the liquidity premium may be sufficient to account for rejections of the expectations theory. We use non-parametric (kernel) regression to explore the regression test results on a number of data sets, and find some evidence of a persistent deviation from orthogonality for large absolute values of the spread. Incorporating ARCH-in-mean into models of the term premium indicates that this specification does explain significant time variation in liquidity premia, but the effect does not apepar to be sufficient to account for all of the deviations from orthogonality of forecast errors and spreads.     

指数自回归条件异方差模型的检验

本文在达尼艾尔松(1994)定义的随机波动模型(SV)的基础上,借用迪拉克.德鲁塔函数的思想,提出检验指数自回归条件异方差(EGARCH)模型的拉格朗日乘数检验统计量。该检验统计量的提出预示着一定条件下EGARCH模型为SV模型的一种特例。最后通过蒙特卡罗计算机仿真实验验证该检验统计量的检验能力。     

A New Measure of Multicollinearity in Linear Regression Models

Databases with a lot of data very often mean little information. It is because of the collinearity of variables which consist of the data of the database. This collinearity is in fact a kind of redundancy of the database.
In the study a new indicator is given. With this indicator, which contains the eigenvalues of the variables' correlation matrix, it is possible to quantify the percentage of collinearity: from 0% (all the eigenvalues are equal to 1) to 100% (all the eigenvalues, except the first, are equal to 0).     

Solving Multicollinearity in the Process of Fitting Regression Model Using the Nested Estimate Procedure

In the practical cases, we are usually faced with the more difficult problem of multicollinearity in our fitted regression model. Multicollinearity will arise when there are approximate linear relationships between two or more independent variables. It may cause some serious problems in validation, interpretation, and analysis of the model, such as unstable estimates, unreasonable sing, high-standard errors, and so on. Although there are some methods to solve or avoid this problem, we will propose another alternative from the practical view in this paper, called nested estimate procedure. The first half of the paper explains the concept and process of this procedure, and the second half provides two examples to illustrate this procedure’s suitability and reliability.     

A Note on the Identification of Dynamic Economic Models with Generalized Shock Processes

Dynamic stochastic general equilibrium (DSGE) models with generalized shock processes, such as shock processes which follow a vector autoregression (VAR), have been an active area of research in recent years. Unfortunately, the structural parameters governing DSGE models are not identified when the driving process behind the model follows an unrestricted VAR. This finding implies that parameter estimates derived from recent attempts to estimate DSGE models with generalized driving processes should be treated with caution, and that there always exists a tradeoff between identification and the risk of model misspecification. However, these results also make it easier to address the issue of model misspecification by making it computationally easier to check the validity of cross‐equation restrictions.     

直角边回归建模技术

在实际应用回归模型中，最重要也是最难的是确定建模技术。最小二乘建模技术实现了残差平方和最小，而不是残差绝对值和最小。本文认为，建模技术应追求残差绝对值和最小，从而追求拟合度最高。本文提出了一种新的回归建模技术——直角边法，可以降低残差绝对值和，提高拟合度。     

New Multicollinearity Indicators in Linear Regression Models

Correlation is an important statistical issue for the Ordinary Least Squares estimates and for data‐reduction techniques, such as the Factor and the Principal Components analyses. In this paper we propose new indicators for the multicollinearity problem in the multiple linear regression model.     

A Note on the Importance of Testing for Regularities for Estimated Flexible Functional Forms

In empirical productivity analysis it has become customary to use flexible functional forms to represent a firm's production technology by estimating cost functions. In this note we suggest a procedure to calculate the region where an estimated translog cost function meet the required regularities (positive cost, positive marginal cost, homogeneous, monotonicity and concavity in input prices). We calculate this region for the US Bell cost function as reported by Evans and Heckman (1984, 1986), and show that the estimated cost function had negative marginal cost in most of the test region.     

Robust Hierarchical Bayes Small Area Estimation for the Nested Error Linear Regression Model

Standard model‐based small area estimates perform poorly in presence of outliers. Sinha & Rao ( 2009 ) developed robust frequentist predictors of small area means. In this article, we present a robust Bayesian method to handle outliers in unit‐level data by extending the nested error regression model. We consider a finite mixture of normal distributions for the unit‐level error to model outliers and produce noninformative Bayes predictors of small area means. Our modelling approach generalises that of Datta & Ghosh ( 1991 ) under the normality assumption. Application of our method to a data set which is suspected to contain an outlier confirms this suspicion, correctly identifies the suspected outlier and produces robust predictors and posterior standard deviations of the small area means. Evaluation of several procedures including the M‐quantile method of Chambers & Tzavidis ( 2006 ) via simulations shows that our proposed method is as good as other procedures in terms of bias, variability and coverage probability of confidence and credible intervals when there are no outliers. In the presence of outliers, while our method and Sinha–Rao method perform similarly, they improve over the other methods. This superior performance of our procedure shows its dual (Bayes and frequentist) dominance, which should make it attractive to all practitioners, Bayesians and frequentists, of small area estimation.     

Varying Coefficient Regression Models: A Review and New Developments

Varying coefficient regression models are known to be very useful tools for analysing the relation between a response and a group of covariates. Their structure and interpretability are similar to those for the traditional linear regression model, but they are more flexible because of the infinite dimensionality of the corresponding parameter spaces. The aims of this paper are to give an overview on the existing methodological and theoretical developments for varying coefficient models and to discuss their extensions with some new developments. The new developments enable us to use different amount of smoothing for estimating different component functions in the models. They are for a flexible form of varying coefficient models that requires smoothing across different covariates' spaces and are based on the smooth backfitting technique that is admitted as a powerful technique for fitting structural regression models and is also known to free us from the curse of dimensionality.     

A General Approach to Testing Volatility Models in Time Series

Volatility models have been playing important roles in economics and finance. Using a generalized spectral second order derivative approach, we propose a new class of generally applicable omnibus tests for the adequacy of linear and nonlinear volatility models. Our tests have a convenient asymptotic null N(0,1) distribution, and can detect a wide range of misspecifications for volatility dynamics, including both neglected linear and nonlinear volatility dynamics. Distinct from the existing diagnostic tests for volatility models, our tests are robust to time-varying higher order moments of unknown form (e.g., time-varying skewness and kurtosis). They check a large number of lags and are therefore expected to be powerful against neglected volatility dynamics that occurs at higher order lags or display long memory properties. Despite using a large number of lags, our tests do not suffer much from the loss of a large number of degrees of freedom, because our approach naturally discounts higher order lags, which is consistent with the stylized fact that economic or financial markets are affected more by the recent past events than by the remote past events. No specific estimation method is required, and parameter estimation uncertainty has no impact on the convenient limit N(0,1) distribution of the test statistics. Moreover, there is no need to formulate an alternative volatility model, and only estimated standardized residuals are needed to implement our tests. We do not have to calculate tedious and model-specific score functions or derivatives of volatility models with respect to estimated parameters, which are required in some existing popular diagnostic tests for volatility models. We examine the finite sample performance of the proposed tests. It is documented that the new tests are rather powerful in detecting neglected nonlinear volatility dynamics which the existing tests can easily miss. They are useful diagnostic tools for practitioners when modelling volatility dynamics.     

混合地理加权回归模型中的空间相关性检验和参数估计研究

对混合地理加权回归模型,提出新的空间相关性检验统计量,利用三阶矩?2逼近方法导出了其检验p-值的近似计算公式,模拟结果显示该检验统计量在检测空间相关性方面具有满意的功效。为了处理数据中可能同时存在的空间相关性和空间异质性,引入一类新的混合地理加权空间滞后回归模型,模拟结果表明该估计方法具有较高的可靠性和稳健性,与全局空间滞后回归模型比较,混合地理加权空间滞后回归模型在处理空间异质性方面具有更优良的表现。