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《误差可预测时的反事实结果插补》作者回应
We thank Bruno Ferman (BF), Marcelo Medeiros (MM), Yuya Sasaki (YS), and Kaspar Wüthrich (KW) for their constructive comments on our paper. Below are some further thoughts.1 The discussants offered...
误差可预测时的反事实结果插补
A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information not captured by the model. While the literature has focused on sampling uncertainty, it vanishes with the sample size. Often overlooked is the possibility that the out-of-sample error can be informative about the missing counterfactual…
具有较弱载荷的近似因子模型
Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where Λ0′Λ0/Nα is positive definite in the limit when α=1, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal…
灾难型冲击动态效应的时间序列估计
This paper provides three results for SVARs under the assumption that the primitive shocks are mutually independent. First, a framework is proposed to accommodate a disaster-type variable with infinite variance into a SVAR. We show that the least squares estimates of the SVAR are consistent but have non-standard asymptotics. Second, the disaster shock is identified as the component with the largest kurtosis. An estimator that is robust to infinite variance is used to recover…
高维面板数据缺失值与协方差的因子插补
Economists are blessed with a wealth of data for analysis, but more often than not, values in some entries of the data matrix are missing. Various methods have been proposed to handle missing observations in a few variables. We exploit the factor structure in panel data of large dimensions. Our tall-project algorithm first estimates the factors from a tall block in which data for all rows are observed, and projections of unit specific sample size are then used to estimate…
分类调查回答的潜在狄利克雷分析
Beliefs are important determinants of an individual’s choices and economic outcomes, so understanding how they comove and differ across individuals is of considerable interest. Researchers often rely on surveys that report individual beliefs as qualitative data. We propose using a Bayesian hierarchical latent class model to analyze the comovements and observed heterogeneity in categorical survey responses. We show that the statistical model corresponds to an economic…
矩阵补全、反事实与缺失数据的因子分析
This paper proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the…
时变参数高维预测回归的 Boosting 估计
High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for parameter instability in economic time series, but theories for parameter instability are mainly developed for models with a small number of covariates. In this paper, we present two L2 boosting algorithms for estimating high dimensional…
近似因子模型的秩正则化估计
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares with ridge regressions turns out to have the effect of removing the contribution of factors associated with small singular values from the common component. The method has been used in the machine learning literature to recover low-rank…
基于辅助统计量的模拟估计：ABC与模拟最小距离的联系
The frequentist method of simulated minimum distance (SMD) is widely used in economics to estimate complex models with an intractable likelihood. In other disciplines, a Bayesian approach known as Approximate Bayesian Computation (ABC) is far more popular. This paper connects these two seemingly related approaches to likelihood-free estimation by means of a Reverse Sampler that uses both optimization and importance weighting to target the posterior distribution. Its hybrid…
含变量测量误差动态模型的模拟最小距离估计
Empirical analysis often involves using inexact measures of the predictors suggested by economic theory. The bias created by the correlation between the mismeasured regressors and the error term motivates the need for instrumental variable estimation. This paper considers a class of estimators that can be used in dynamic models with measurement errors when external instruments may not be available or are weak. The idea is to exploit the relation between the parameters of the…
可能不可逆的移动平均模型的最小距离估计
This article considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the MA(1) model is classical root-T consistent and asymptotically normal when the MA root is inside, outside, and on the unit circle. For more general models where the dependence of the…
动态模型中的测量误差
Static models that are not identifiable in the presence of white noise measurement errors are known to be potentially identifiable when the model has dynamics. However, few results are available for the plausible case of serially correlated measurement errors. This paper provides order and rank conditions for “limited information” identification of parameters in dynamic models with measurement errors where some aspects of the probability model are not fully specified or…
静态因子的主成分估计与识别
It is known that the principal component estimates of the factors and the loadings are rotations of the underlying latent factors and loadings. We study conditions under which the latent factors can be estimated asymptotically without rotation. We derive the limiting distributions for the estimated factors and factor loadings when N and T are large and make precise how identification of the factors affects inference based on factor augmented regressions. We also consider…
具有经典渐近性质的持久性及可能非平稳数据估计量
This paper considers a moments-based nonlinear estimator that is $\root \of T $ -consistent and uniformly asymptotically normal irrespective of the degree of persistence of the forcing process. These properties hold for linear autoregressive models, linear predictive regressions, and certain nonlinear dynamic models. Asymptotic normality is obtained because the moments are chosen so that the objective function is uniformly bounded in probability and so that a central limit…
数据丰富环境中的工具变量估计
We consider estimation of parameters in a regression model with endogenous regressors. The endogenous regressors along with a large number of other endogenous variables are driven by a small number of unobservable exogenous common factors. We show that the estimated common factors can be used as instrumental variables and they are more efficient than the observed variables in our framework. Whereas standard optimal generalized method of moments estimator using a large number…
存在截面依赖的面板单位根检验：进一步研究
An effective way to control for cross-section correlation when conducting a panel unit root test is to remove the common factors from the data. However, there remain many ways to use the defactored residuals to construct a test. In this paper, we use the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) residuals to form two new tests. One estimates the pooled autoregressive coefficient, and one simply uses a sample moment. We establish their…
扩散指数预测中的提升法
Abstract In forecasting and regression analysis, it is often necessary to select predictors from a large feasible set. When the predictors have no natural ordering, an exhaustive evaluation of all possible combinations of the predictors can be computationally costly. This paper considers ‘boosting’ as a methodology of selecting the predictors in factor‐augmented autoregressions. As some of the predictors are being estimated, we propose a stopping rule for boosting to prevent…
含全球随机趋势的面板协整
This paper studies estimation of panel cointegration models with cross-sectional dependence generated by unobserved global stochastic trends. The standard least squares estimator is, in general, inconsistent owing to the spuriousness induced by the unobservable I(1) trends. We propose two iterative procedures that jointly estimate the slope parameters and the stochastic trends. The resulting estimators are referred to respectively as CupBC (continuously-updated and…
使用定向预测变量预测经济时间序列
This paper studies two refinements to the method of factor forecasting. First, we consider the method of quadratic principal components that allows the link function between the predictors and the factors to be non-linear. Second, the factors used in the forecasting equation are estimated in a way to take into account that the goal is to forecast a specific series. This is accomplished by applying the method of principal components to 'targeted predictors' selected using…
混合面板非平稳性的简单检验
This article proposes a simple estimator that is consistent for the fraction of a panel that has an autoregressive unit root. Given such an estimate, , we can test the null hypothesis that θ = θ0 for any value of θ0 ϵ (0, 1]. The test is asymptotically standard normal and is valid whether or not the panel is cross-sectionally correlated. The main insight is that in a panel in which some units are stationary and some have unit roots, the cross-sectional variance of the mixed…
因子模型中原始冲击数量的确定
A widely held but untested assumption underlying macroeconomic analysis is that the number of shocks driving economic fluctuations, q, is small. In this article we associate q with the number of dynamic factors in a large panel of data. We propose a methodology to determineq without having to estimate the dynamic factors. We first estimate a VAR in r static factors, where the factors are obtained by applying the method of principal components to a large panel of data, then…
扩散指数预测的置信区间与因子增强回归推断
We consider the situation when there is a large number of series, N, each with T observations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors. In this paper, we show that the least squares estimates obtained from these factor-augmented…