Nonstationary regression models with a lagged dependent variable

This paper studies regression models with a lagged dependent variable when both the dependent and independent variables are nonstationary, and the regression model is misspecified in some dimension. In particular, we discuss the limiting properties of leastsquares estimates of the parameters in such regression models, and the limiting distributions of their test statistics. We show that the estimate of the lagged dependent variable tends to unity asymptotically independent of its true value, while the estimates of the independent variables tend to zero. The limiting distributions of their test statistics are shown to diverge with sample size.     

Testing for Serial Independence: Beyond the Portmanteau Approach

Portmanteau tests are typically used to test serial independence even if, by construction, they are generally powerful only in presence of pairwise dependence between lagged variables. In this article, we present a simple statistic defining a new serial independence test, which is able to detect more general forms of dependence. In particular, differently from the Portmanteau tests, the resulting test is powerful also under a dependent process characterized by pairwise independence. A diagram, based on p-values from the proposed test, is introduced to investigate serial dependence. Finally, the effectiveness of the proposal is evaluated in a simulation study and with an application on financial data. Both show that the new test, used in synergy with the existing ones, helps in the identification of the true data-generating process. Supplementary materials for this article are available online.     

Inferences for a Partially Varying Coefficient Model With Endogenous Regressors

In this article, we propose a new class of semiparametric instrumental variable models with partially varying coefficients, in which the structural function has a partially linear form and the impact of endogenous structural variables can vary over different levels of some exogenous variables. We propose a three-step estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic normality of these proposed estimators are established. Moreover, a generalized F-test is developed to test whether the functional coefficients are of particular parametric forms with some underlying economic intuitions, and furthermore, the limiting distribution of the proposed generalized F-test statistic under the null hypothesis is established. Finally, we illustrate the finite sample performance of our approach with simulations and two real data examples in economics.     

Use of non-normality in structural equation modeling: Application to direction of causation

Structural equation modeling (SEM) typically utilizes first- and second-order moment structures. This limits its applicability since many unidentified models and many equivalent models that researchers would like to distinguish are created. In this paper, we relax this restriction and assume non-normal distributions on exogenous variables. We shall provide a solution to the problems of underidentifiability and equivalence of SEM models by making use of non-normality (higher-order moment structures). The non-normal SEM is applied to finding the possible direction of a path in simple regression models. The method of (generalized) least squares is employed to estimate model parameters. A test statistic for examining a fit of a model is proposed. A simulation result and a real data example are reported to study how the non-normal SEM approach works empirically.     

Best subset selection of autoregressive models with exogenous variables and generalized autoregressive conditional heteroscedasticity errors

Summary.  We develop an efficient way to select the best subset autoregressive model with exogenous variables and generalized autoregressive conditional heteroscedasticity errors. One main feature of our method is to select important autoregressive and exogenous variables, and at the same time to estimate the unknown parameters. The method proposed uses the stochastic search idea. By adopting Markov chain Monte Carlo techniques, we can identify the best subset model from a large of number of possible choices. A simulation experiment shows that the method is very effective. Misspecification in the mean equation can also be detected by our model selection method. In the application to the stock-market data of seven countries, the lagged 1 US return is found to have a strong influence on the other stock-market returns.     

中国农村居民的健康动态研究

 利用四轮中国健康与营养状况调查构成的面板数据（1997-2006）,本文研究了中国农村居民的健康动态决定过程及健康持续性。我们使用动态随机效应probit模型控制了个体的不可观测异质性。同时,为了避免状态依赖效应的估计偏差,本文分别采纳了Heckman(1981)和Wooldridge(2005)提出的估计方法来处理“初始条件问题”。结论表明：在控制了其他因素之后,状态依赖效应对中国农村居民健康状况具有显著的影响;此外,那些年龄较大、教育水平较低、收入水平较低的农村弱势群体陷入持续性健康问题的可能性更大。     

Iterated Feasible Generalized Least-Squares Estimation of Augmented Dynamic Panel Data Models

This article provides the large sample distribution of the iterated feasible generalized least-squares (IFGLS) estimator of an augmented dynamic panel data model. The regressors in the model include lagged values of the dependent variable and may include other explanatory variables that, while exogenous with respect to the time-varying error component, may be correlated with an unobserved time-invariant component. The article compares the finite sample properties of the IFGLS estimator to that of GMM estimators using both simulated and real data and finds that the IFGLS estimator compares favorably.     

A dimensionality reduction method of continuous dependent variables based supervised Laplacian eigenmaps

Dimensionality reduction is one of the important preprocessing steps in high-dimensional data analysis. In this paper we propose a supervised manifold learning method, it makes use of the information of continuous dependent variables to distinguish intrinsic neighbourhood and extrinsic neighbourhood of data samples, and construct two graphs according to these two kinds of neighbourhoods. Following the idea of Laplacian eigenmaps, we reveal that on the low-dimensional manifold the neighbourhood structure can be preserved or even improved. Our approach has two important characteristics: (i) it uses dependent variables to find an informative low-dimensional projection which is robust to noisy independent variables and (ii) the objective function simultaneously enlarges the distance between dissimilar samples and pushes similar samples close to each other according to the graph constructed with the help of continuous dependent variables. Our experiments demonstrate that the effectiveness of our method is over their traditional rivals.     

An Alternative to Transfer Function Forecasting Based on Subspace Methods

In the time series literature, recent interest has focused on the so-called subspace methods. These techniques use canonical correlations and linear regressions to estimate the system matrices of an ARMAX model expressed in state space form. In this article, we use subspace methods to forecast two series with the help of some exogenous variables related to them. We compare the results with those obtained using traditional transfer function models and find that the forecasts obtained with both methods are similar. This result is very encouraging because, in contrast to transfer function models, subspace methods can be considered as almost automatic.     

Identification of vector AR models with recursive structural errors using conditional independence graphs

In canonical vector time series autoregressions, which permit dependence only on past values, the errors generally show contemporaneous correlation. By contrast structural vector autoregressions allow contemporaneous series dependence and assume errors with no contemporaneous correlation. Such models having a recursive structure can be described by a directed acyclic graph. We show, with the use of a real example, how the identification of these models may be assisted by examination of the conditional independence graph of contemporaneous and lagged variables. In this example we identify the causal dependence of monthly Italian bank loan interest rates on government bond and repurchase agreement rates. When the number of series is larger, the structural modelling of the canonical errors alone is a useful initial step, and we first present such an example to demonstrate the general approach to identifying a directed graphical model.     

Maximum likelihood estimation for bivariate SUR Tobit modeling in presence of two right-censored dependent variables

This article extends the analysis of the Seemingly Unrelated Regression (SUR) Tobit model for two right-censored dependent variables by modeling its nonlinear dependence structure through the rotated by 180 degrees version of the Clayton copula. An advantage of our approach is to provide unbiased point estimates of the marginal and copula parameters. Moreover, we discuss the construction of confidence intervals using bootstrap resampling procedures. The results of the performed simulation study demonstrate the good performance of the proposed methods. We illustrate our procedures using bivariate customer churn data from a Brazilian commercial bank.     

Copula-based predictions in small area estimation

Unit-level regression models are commonly used in small area estimation (SAE) to obtain an empirical best linear unbiased prediction of small area characteristics. The underlying assumptions of these models, however, may be unrealistic in some applications. Previous work developed a copula-based SAE model where the empirical Kendall's tau was used to estimate the dependence between two units from the same area. In this article, we propose a likelihood framework to estimate the intra-class dependence of the multivariate exchangeable copula for the empirical best unbiased prediction (EBUP) of small area means. One appeal of the proposed approach lies in its accommodation of both parametric and semi-parametric estimation approaches. Under each estimation method, we further propose a bootstrap approach to obtain a nearly unbiased estimator of the mean squared prediction error of the EBUP of small area means. The performance of the proposed methods is evaluated through simulation studies and also by a real data application.     

Regularized receiver operating characteristic-based logistic regression for grouped variable selection with composite criterion

It is well known that statistical classifiers trained from imbalanced data lead to low true positive rates and select inconsistent significant variables. In this article, an improved method is proposed to enhance the classification accuracy for the minority class by differentiating misclassification cost for each group. The overall error rate is replaced by an alternative composite criterion. Furthermore, we propose an approach to estimate the tuning parameter, the composite criterion, and the cut-point simultaneously. Simulations show that the proposed method achieves a high true positive rate on prediction and a good performance on variable selection for both continuous and categorical predictors, even with highly imbalanced data. An illustrative example of the analysis of the suboptimal health state data in traditional Chinese medicine is discussed to show the reasonable application of the proposed method.     

Heterogeneous credit union production technologies with endogenous switching and correlated effects

Credit unions differ in the types of financial services they offer to their members. This article explicitly models this observed heterogeneity using a generalized model of endogenous ordered switching. Our approach captures the endogenous choice that credit unions make when adding new products to their financial services mix. The model that we consider also allows for the dependence between unobserved effects and regressors in both the selection and outcome equations and can accommodate the presence of predetermined covariates in the model. We use this model to estimate returns to scale for U.S. retail credit unions from 1996 to 2011. We document strong evidence of persistent technological heterogeneity among credit unions offering different financial service mixes, which, if ignored, can produce quite misleading results. Employing our model, we find that credit unions of all types exhibit substantial economies of scale.     

A simpler approach for mediation analysis for dichotomous mediators in logistic regression

Mediation is a hypothesized causal chain among three variables. Mediation analysis for continuous response variables is well developed in the literature, and it can be shown that the indirect effect is equal to the total effect minus the direct effect. However, mediation analysis for categorical responses is still not fully developed. The purpose of this article is to propose a simpler method of analysing the mediation effect among three variables when the dependent and mediator variables are both dichotomous. We propose using the latent variable technique which in turn will adjust for the necessary condition that indirect effect is equal to the total effect minus the direct effect. An intensive simulation study is conducted to compare the proposed method with other methods in the literature. Our theoretical derivation and simulation study show that the proposed approach is simpler to use and at least as good as other approaches provided in the literature. We illustrate our approach to test for the potential mediators on the relationship between depression and obesity among children and adolescents compared to the method in Winship and Mare using National children health survey data 2011–2012.     

Flexible Bivariate Count Data Regression Models

The article develops a semiparametric estimation method for the bivariate count data regression model. We develop a series expansion approach in which dependence between count variables is introduced by means of stochastically related unobserved heterogeneity components, and in which, unlike existing commonly used models, positive as well as negative correlations are allowed. Extensions that accommodate excess zeros, censored data, and multivariate generalizations are also given. Monte Carlo experiments and an empirical application to tobacco use confirms that the model performs well relative to existing bivariate models, in terms of various statistical criteria and in capturing the range of correlation among dependent variables. This article has supplementary materials online.     

Threshold negative binomial autoregressive model

This article studies an observation-driven model for time series of counts, which allows for overdispersion and negative serial dependence in the observations. The observations are supposed to follow a negative binomial distribution conditioned on past information with the form of thresh old models, which generates a two-regime structure on the basis of the magnitude of the lagged observations. We use the weak dependence approach to establish the stationarity and ergodicity, and the inference for regression parameters are obtained by the quasi-likelihood. Moreover, asymptotic properties of both quasi-maximum likelihood estimators and the threshold estimator are established, respectively. Simulation studies are considered and so are two applications, one of which is the trading volume of a stock and another is the number of major earthquakes.     

Some state space models of hiv epidemic and its applications for the estimation of hiv infection and incubation

In this paper we have developed some state space models for the HIV epidemic for populations at risk for AIDS. By using these state space models, we have developed a general Bayesian procedure for estimating simultaneously the unknown parameters and the state variables. The unknown parameters include the immigration and recruitment rates, the death and retirement rates, the incidence of HIV infection ( and hence the HIV infection distribution ) and the incidence of HIV incubation ( and hence the HIV incubation distribution). The state variables are the numbers of susceptible people (S people), HIV-infected people (I people) and AIDS incidence over time. The basic approach is through multi-level Gibbs sampler combined with the weighted bootstrap method. We have applied the methods to the Swiss AIDS homosexual and IV drug data to estimate simultaneously the unknown parameters and the state variables. Our results show that in both populations, both the HIV infection and HIV incubation have multi-peaks indicating the mixture nature of these distributions. Our results have also shown that the estimates of the death and retirement rates for I people are greater than those of S people, suggesting that the infection by HIV may have increased the death and retirement rates of the individuals.     

Quantile regression based on a weighted approach under semi-competing risks data

In this article, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. Due to the dependent censoring, the estimation of quantile regression coefficients on the non-terminal event becomes difficult. In order to handle this problem, we assume Archimedean Copula to specify the dependence of the non-terminal event and the terminal event. Portnoy [Censored regression quantiles. J Amer Statist Assoc. 2003;98:1001–1012] considered the quantile regression model under right-censoring data. We extend his approach to construct a weight function, and then impose the weight function to estimate the quantile regression parameter for the non-terminal event under semi-competing risks data. We also prove the consistency and asymptotic properties for the proposed estimator. According to the simulation studies, the performance of our proposed method is good. We also apply our suggested approach to analyse a real data.     

On the use of the Box-Cox transformation in a linear regression with a lagged dependent variable

In this paper, we show a maximum likelihood estimation procedure in the Box-Cox model when a lagged dependent variable is included among explanatory variables and the first observation of the dependent variable is random. It is shown in a numerical example that a test of a coefficientof the lagged dependent variable is sensitive to whether the first observation of the dependentvariable is random or not.