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Statistical inference for the low dimensional parameters of linear regression models in the presence of high-dimensional data: An orthogonal projection approach

高维线性回归中低维参数推断的正交投影方法

We consider the estimation and statistical inference for low dimensional parameters for a regression model with covariates whose dimension increases with sample size. We suggest a computationally simple one stage orthogonal projection approach to estimate the low dimensional parameters under strict or approximate sparsity conditions. The orthogonal projection approach is simple to implement and the inference for the low dimensional parameters is straightforward to derive…

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Panel treatment effects measurement: Factor or linear projection modelling?

面板处理效应测量:因子模型还是线性投影?

Summary We discuss methods of measuring the treatment effects of a unit through the use of other units in panel data by either the factor‐based (FB) approach or the linear projection (LP) approach under different sample configurations of cross‐sectional dimension and time series dimension . We show that the LP approach in general yields smaller mean square prediction error than the FB approach when either both and are large or fixed and or fixed and large. The Monte Carlo…

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Transformed Estimation for Panel Interactive Effects Models

交互效应面板模型的变换估计

We propose a transformed estimator for the slope coefficients of panel models with interactive effects. The transformed estimation method does not require the prior knowledge of the dimension of factor structure. It is consistent and asymptotically normally distributed under fairly general conditions when N is fixed and T→∞ or T is fixed and N→∞, or when both N and T are large and NT→a≠0<∞. Moreover, because the transformation is equivalent to aggregating cross-sectional…

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Economic impact of the most drastic lockdown during COVID‐19 pandemic—The experience of Hubei, China

新冠疫情期间严厉封锁的经济影响:中国湖北的经验

Summary This paper uses a panel data approach to assess the evolution of economic consequences of the drastic lockdown policy in the epicenter of COVID‐19—the Hubei Province of China during worldwide curbs on economic activity. We find that the drastic 76‐day COVID‐19 lockdown policy brought huge negative impacts on Hubei's economy. In 2020:q1, the lockdown quarter, the treatment effect on GDP was about 37% of the counterfactual. However, the drastic lockdown also brought…

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Recursive estimation in large panel data models: Theory and practice

大型面板数据模型的递归估计:理论与实践

Bai (2009) proposes recursive estimation for panel data models with interactive effects. We study the behaviours of this recursive estimator. The recursive formula is established that shows the behaviours of recursive estimators depend on the initial estimator, the population structure and the iterative steps. Under some general scenarios, we find that the recursive estimator becomes consistent after the first iteration from any initials. We also obtain the optimal number of…

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Panel parametric, semiparametric, and nonparametric construction of counterfactuals

面板反事实的参数、半参数与非参数构造

Summary We consider panel parametric, semiparametric and nonparametric methods of constructing counterfactuals. We show through extensive simulations that no method is able to dominate other methods in all circumstances, since the true data‐generating process is typically unknown. We therefore also suggest a model‐averaging method as a robust method to generate counterfactuals. As an illustration of the sensitivity of counterfactual construction, we reexamine the impact of…

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JIVE FOR PANEL DYNAMIC SIMULTANEOUS EQUATIONS MODELS

面板动态联立方程模型的刀切工具变量估计

We consider the method of moments estimation of a structural equation in a panel dynamic simultaneous equations model under different sample size combinations of cross-sectional dimension, N , and time series dimension, T . Two types of linear transformation to remove the individual-specific effects from the model, first difference and forward orthogonal demeaning, are considered. We show that the Alvarez and Arellano (2003) type GMM estimator under both transformations is…

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Incidental parameters, initial conditions and sample size in statistical inference for dynamic panel data models

动态面板推断中的附带参数、初始条件与样本规模

We use a quasi-likelihood function approach to clarify the role of initial values and the relative sample size of the cross-section dimension N and the time series dimension T on the asymptotic properties of estimators for dynamic panel data models with the presence of individual-specific effects. We show that a properly specified quasi-likelihood estimator (QMLE) that uses the Mundlak–Chamberlain approach to condition the unobserved effects and initial values on the…

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Panel models with interactive effects

具有交互效应的面板模型

The multiplication of individual specific effects, ▪ and time-specific effects, ▪ provides a more general formulation than the traditionally used additive form to capture the unobserved heterogeneity in panel data modeling. It is also a useful approach for dimension reduction for modeling cross-section dependence. However, ▪ and ▪ are unobservable. We explore the implications for econometric modeling under various formulations of the interactive effects models and suggest a…

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Statistical inference for panel dynamic simultaneous equations models

面板动态联立方程模型的统计推断

We study the identification and estimation of panel dynamic simultaneous equations models. We show that the presence of time-persistent individual-specific effects does not lead to changes in the identification conditions of traditional Cowles Commission dynamic simultaneous equations models. However, the limiting properties of the estimators depend on the way the cross-section dimension, N, or the time series dimension, T, goes to infinity. We propose three limited…

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Testing error serial correlation in fixed effects nonparametric panel data models

固定效应非参数面板模型中的误差序列相关检验

In this paper we consider the problem of testing serial correlation in fixed effects panel data model in a nonparametric framework. Using asymptotic results developed in Su and Lu (2013), we show that our test statistic has a standard normal distribution under the null hypothesis of zero serial correlation. The test statistic diverges to infinity at the rate of N under the alternative hypothesis that error is serially correlated, where N is the cross sectional sample size.…

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IV, GMM or likelihood approach to estimate dynamic panel models when either N or T or both are large

不同面板维度渐近框架下动态面板的 IV、GMM 与似然估计

We examine the asymptotic properties of IV, GMM or MLE to estimate dynamic panel data models when either NorT or both are large. We show that the Anderson and Hsiao (1981, 1982) simple instrumental variable estimator (IV) or maximizing the likelihood function with initial value distribution properly treated (quasi-maximum likelihood estimator) is asymptotically unbiased when either N or T or both tend to infinity. On the other hand, the QMLE mistreating the initial value as…

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Is there an optimal forecast combination?

是否存在最优的预测组合?

We consider several geometric approaches for combining forecasts in large samples—a simple eigenvector approach, a mean corrected eigenvector and trimmed eigenvector approach. We give conditions where geometric approach yields identical result as the regression approach. We also consider a mean and scale corrected simple average of all predictive models for finite sample and give conditions where simple average is an optimal combination. Monte Carlos are conducted to compare…

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Model specification test with correlated but not cointegrated variables

相关但不协整变量的模型设定检验

Many macroeconomic and financial variables show highly persistent and correlated patterns but are not necessarily cointegrated. Recently, Sun et al. (2011) propose using a semiparametric varying coefficient approach to capture correlations between integrated but non cointegrated variables. Due to the complication arising from the integrated disturbance term and the semiparametric functional form, consistent estimation of such a semiparametric model requires stronger…

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Forecasting a long memory process subject to structural breaks

存在结构突变的长记忆过程预测

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids…

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A PANEL DATA APPROACH FOR PROGRAM EVALUATION: MEASURING THE BENEFITS OF POLITICAL AND ECONOMIC INTEGRATION OF HONG KONG WITH MAINLAND CHINA

项目评估的面板数据方法:衡量香港与内地政治及经济融合的收益

SUMMARY We propose a simple‐to‐implement panel data method to evaluate the impacts of social policy. The basic idea is to exploit the dependence among cross‐sectional units to construct the counterfactuals. The cross‐sectional correlations are attributed to the presence of some (unobserved) common factors. However, instead of trying to estimate the unobserved factors, we propose to use observed data. We use a panel of 24 countries to evaluate the impact of political and…

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MEASUREMENT ERRORS AND CENSORED STRUCTURAL LATENT VARIABLES MODELS

含测量误差的删失结构潜变量模型

We consider censored structural latent variables models where some exogenous variables are subject to additive measurement errors. We demonstrate that overidentification conditions can be exploited to provide natural instruments for the variables measured with errors, and we propose a two-stage estimation procedure. The first stage involves substituting available instruments in lieu of the variables that are measured with errors and estimating the resulting reduced form…

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Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models

半参数非线性变量测量误差模型的矩估计与可识别性

This paper deals with a nonlinear errors-in-variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric. Using the instrumental variable approach, we propose method of moments estimators for the unknown parameters and simulation-based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals. Both estimators are consistent and…

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Measuring correlations of integrated but not cointegrated variables: A semiparametric approach

单整但不协整变量相关性的半参数度量

Many macroeconomic and financial variables are integrated of order one (or I(1)) processes and are correlated with each other but not necessarily cointegrated. In this paper, we propose to use a semiparametric varying coefficient approach to model/capture such correlations. We propose two consistent estimators to study the dependence relationship among some integrated but not cointegrated time series variables. Simulations are used to examine the finite sample performances…

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Decriminalization and Marijuana Smoking Prevalence: Evidence From Australia

大麻非刑罪化与吸食率:来自澳大利亚的证据

This article uses the 2001 National Drug Strategy Household Survey to assess the impact of marijuana decriminalization policy on marijuana smoking prevalence in Australia. Both parametric and nonparametric methods are used. The parametric approach includes endogenous probit switching, two-part, sample selection, and standard dummy variable models, while the nonparametric approach uses propensity score stratification matching. Specification analyses are also conducted. A…

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Two‐stage estimation of limited dependent variable models with errors‐in‐variables

This paper deals with censored or truncated regression models where the explanatory variables are measured with additive errors. We propose a two-stage estimation procedure that combines the instrumental variable method and the minimum distance estimation. This approach produces consistent and asymptotically normally distributed estimators for model parameters. When the predictor and instrumental variables are normally distributed, we also propose a maximum likelihood based…

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Lag‐augmented two‐ and three‐stage least squares estimators for integrated structural dynamic models

We consider a lag-augmented two- or three-stage least-squares estimator for a structural dynamic model of non-stationary and possibly cointegrated variables without the prior knowledge of unit roots or rank of cointegration. We show that the conventional two-and three-stage least-squares estimators are consistent but contain non-standard distributions without the strict exogeneity assumption; hence the conventional Wald type test statistics may not be chi-square distributed.…

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