Stochastic Model Specification Search for Time-Varying Parameter VARs

This article develops a new econometric methodology for performing stochastic model specification search (SMSS) in the vast model space of time-varying parameter vector autoregressions (VARs) with stochastic volatility and correlated state transitions. This is motivated by the concern of overfitting and the typically imprecise inference in these highly parameterized models. For each VAR coefficient, this new method automatically decides whether it is constant or time-varying. Moreover, it can be used to shrink an otherwise unrestricted time-varying parameter VAR to a stationary VAR, thus providing an easy way to (probabilistically) impose stationarity in time-varying parameter models. We demonstrate the effectiveness of the approach with a topical application, where we investigate the dynamic effects of structural shocks in government spending on U.S. taxes and gross domestic product (GDP) during a period of very low interest rates.     

Empirical Performance of Cross-Validation With Oracle Methods in a Genomics Context

When employing model selection methods with oracle properties such as the smoothly clipped absolute deviation (SCAD) and the Adaptive Lasso, it is typical to estimate the smoothing parameter by m-fold cross-validation, for example, m = 10. In problems where the true regression function is sparse and the signals large, such cross-validation typically works well. However, in regression modeling of genomic studies involving Single Nucleotide Polymorphisms (SNP), the true regression functions, while thought to be sparse, do not have large signals. We demonstrate empirically that in such problems, the number of selected variables using SCAD and the Adaptive Lasso, with 10-fold cross-validation, is a random variable that has considerable and surprising variation. Similar remarks apply to non-oracle methods such as the Lasso. Our study strongly questions the suitability of performing only a single run of m-fold cross-validation with any oracle method, and not just the SCAD and Adaptive Lasso.     

Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain

We develop results for the use of Lasso and post‐Lasso methods to form first‐stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post‐Lasso in the first stage is root‐n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well‐approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic “beta‐min” conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso‐based IV estimator with a data‐driven penalty performs well compared to recently advocated many‐instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso‐based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post‐Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non‐Gaussian, heteroscedastic disturbances that uses a data‐weighted ℓ₁‐penalty function. By innovatively using moderate deviation theory for self‐normalized sums, we provide convergence rates for the resulting Lasso and post‐Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that logp = o(n^1/3). We also provide a data‐driven method for choosing the penalty level that must be specified in obtaining Lasso and post‐Lasso estimates and establish its asymptotic validity under non‐Gaussian, heteroscedastic disturbances.     

Bayesian adaptive Lasso for quantile regression models with nonignorably missing response data

Abstract

Handling data with the nonignorably missing mechanism is still a challenging problem in statistics. In this paper, we develop a fully Bayesian adaptive Lasso approach for quantile regression models with nonignorably missing response data, where the nonignorable missingness mechanism is specified by a logistic regression model. The proposed method extends the Bayesian Lasso by allowing different penalization parameters for different regression coefficients. Furthermore, a hybrid algorithm that combined the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simulate the parameters from posterior distributions, mainly including regression coefficients, shrinkage coefficients, parameters in the non-ignorable missing models. Finally, some simulation studies and a real example are used to illustrate the proposed methodology.     

Ordinal ridge regression with categorical predictors

In multi-category response models, categories are often ordered. In the case of ordinal response models, the usual likelihood approach becomes unstable with ill-conditioned predictor space or when the number of parameters to be estimated is large relative to the sample size. The likelihood estimates do not exist when the number of observations is less than the number of parameters. The same problem arises if constraint on the order of intercept values is not met during the iterative procedure. Proportional odds models (POMs) are most commonly used for ordinal responses. In this paper, penalized likelihood with quadratic penalty is used to address these issues with a special focus on POMs. To avoid large differences between two parameter values corresponding to the consecutive categories of an ordinal predictor, the differences between the parameters of two adjacent categories should be penalized. The considered penalized-likelihood function penalizes the parameter estimates or differences between the parameter estimates according to the type of predictors. Mean-squared error for parameter estimates, deviance of fitted probabilities and prediction error for ridge regression are compared with usual likelihood estimates in a simulation study and an application.     

Covariance structure approximation via gLasso in high-dimensional supervised classification

Recent work has shown that the Lasso-based regularization is very useful for estimating the high-dimensional inverse covariance matrix. A particularly useful scheme is based on penalizing the ?₁ norm of the off-diagonal elements to encourage sparsity. We embed this type of regularization into high-dimensional classification. A two-stage estimation procedure is proposed which first recovers structural zeros of the inverse covariance matrix and then enforces block sparsity by moving non-zeros closer to the main diagonal. We show that the block-diagonal approximation of the inverse covariance matrix leads to an additive classifier, and demonstrate that accounting for the structure can yield better performance accuracy. Effect of the block size on classification is explored, and a class of asymptotically equivalent structure approximations in a high-dimensional setting is specified. We suggest a variable selection at the block level and investigate properties of this procedure in growing dimension asymptotics. We present a consistency result on the feature selection procedure, establish asymptotic lower an upper bounds for the fraction of separative blocks and specify constraints under which the reliable classification with block-wise feature selection can be performed. The relevance and benefits of the proposed approach are illustrated on both simulated and real data.     

社会治理刑罚化的问题与症结

社会治理刑罚化是指刑罚权在社会治理进程中日益扩张与加重趋势,其问题症结在于错用社会控制论。具体表现为,社会治理理念的症结：强化刑罚工具主义,削弱刑罚人本主义;社会治理方式的症结：注重外在刑罚制裁,轻视内心道德约束;社会治理主体的症结：国家刑罚控制过多,社会公众参与不足。由此导致刑法价值理念存有偏差、刑法正性机能弱化、犯罪预防效果不彰。无疑,社会治理刑罚化不利于社会治理现代化与法治化进程,必须予以深刻反省与长久审思。     

嵌入网络舆情指数的中国金融机构系统性风险传染效应研究

首先基于文本挖掘技术构建反映投资者情绪的网络舆情指数,然后将所构建的网络舆情指数嵌入到系统性风险传染效应度量模型,得到修正的单指标非对称CoVaR模型,并运用线性分位数LASSO算法与局部多项式估计方法进行参数估计,以此为基础构建金融有向网络,进而对中国金融机构系统性风险传染效应进行实证分析。实证研究表明：(1)以单指标非对称CoVaR为代表的金融机构风险指标与网络舆情的协同变化趋势明显;(2)证券类和银行类金融机构对外部风险非常敏感,极易受到其他金融机构的影响,也极易影响其他金融机构;(3)非银行类机构在风险积累阶段占据重要位置,银行在风险爆发时刻占据重要位置;(4)相对于非银行类金融机构,银行类机构具有较强的传染能力。     

基于Lasso和支持向量机的粮食价格预测

首先利用Lasso方法在影响粮食价格波动的众多因素中选出了粮食储备、粮食生产成本、粮食产量、粮食政策、生产需求、贸易需求、心理预期等7个主要影响因素;然后在Lasso变量选择的基础上利用支持向量机进行粮食价格的回归与预测,同时,把Lasso、支持向量机、Lasso-支持向量机及ARIMA方法的拟合预测效果进行比较。实证结果表明：Lasso-支持向量机组合预测方法的拟合预测效果要优于另外三种预测方法。