regife：面板交互固定效应模型-Interactive Fixed Effect

发布时间：2021-04-07 阅读 19095

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王晓娟 (吉林大学)，594806861@qq.com
甘徐沁 (厦门大学)，1072759894@qq.com

今天要给大家分享一篇发表于 2009 年，但目前引用率已经超过 1000 次的重磅文章：

Bai, J. S., 2009, Panel data models with interactive fixed effects, Econometrica, 77 (4): 1229-1279. -Link-, -PDF-, -Cited-

文中介绍的「面板交互固定效应」在近十年中得到的广泛的应用，在控制遗漏变量 (内生性问题的一个主要来源)、捕捉时变特征、提高拟合优度等方面都有重要的用途。以至于在合成控制法的改进模型中，也有「交互固定效应」的身影，如：

Xu, Y., 2017, Generalized synthetic control method: Causal inference with interactive fixed effects models, Political Analysis, 25 (01): 57-76. -PDF-

1. 交互固定效应简介

一般而言，面板数据模型误差项由以下几部分组成：

一是随个体变化但不随时间变化的个体效应；
二是随时间变化但不随个体变化的时间效应；
三是随截面和时间而变化的不可观测因素。

面板数据模型的好处之一是，在模型中引入个体和时间固定效应，并通过去均值处理把不可观测因素差分掉，从而可以减少由于不随时间或个体变化的遗漏变量与解释变量相关导致的内生性问题。

传统的面板固定效应模型中，个体效应和时间效应都是以加法形式进入模型，进而控制样本中不随时间变化的个体差异和不随个体变化的时间差异。然而，时间上的冲击可能是多维的，即同一种冲击对于不同国家的影响可能并不相同。

因此，传统固定效应模型无法解决那些既随时间变化又随个体变化的不可观测变量带来的内生性问题。Bai (2009) 在线性面板模型中引入了个体和时间的交互效应，来反映共同因素对不同个体影响的差异。与传统的面板固定效应模型相比，交互固定效应 (interactive fixed effect) 模型在具体问题中能更好地反映现实，它充分考虑到现实经济中存在的多维冲击，以及不同个体对这些冲击反应力度的异质性，并将传统的双向固定效应进一步拓展为更一般的形式。

Y_{i t} = X_{i t}^{'} β + u_{i t}, u_{i t} = λ_{i}^{'} F_{t} + ϵ_{i t} (1)

其中， $λ_{i}^{'} F_{t}$ 为交互固定效应，它可视为多维个体效应与多维时间效应的乘积， $F_{t}$ 为共同因子， $λ_{i}$ 为因子载荷。显然，常见的双向固定效应模型只是交互固定效应模型的特例。假设有 2 个共同因子：

F_{t} = [\begin{matrix} 1 \\ ξ_{t} \end{matrix}], λ_{i} = [\begin{matrix} α_{i} \\ 1 \end{matrix}] (2)

则：

λ_{i}^{'} F_{t} ＝ α_{i} ＋ ξ_{t} (3)

此时，(1) 式就是我们平时所使用的「双向固定效应模型」：

Y_{i t} = X_{i t}^{'} β + α_{i} ＋ ξ_{t} + ϵ_{i t} (4)

更一般化的包含交互固定效应的模型通常表述为 (参见 Bai (2009), Eq. (4), p.1233)：

Y_{i t} = X_{i t}^{'} β + α_{i} + δ_{t} + λ_{i}^{'} F_{t} + ε_{i t} (4)

因此，「交互固定效应模型」是对「双向固定效应模型」的重要推广，是当前面板数据研究最活跃的研究前沿之一，参见 Bai, 2009, Cited。

相对于传统固定效应模型，交互固定效应模型具有更普遍的现实意义。例如，在研究收入时，固定效应通常捕获了无法观测的能力因素。而现有研究表明，其他个人习惯或特征，如动机、奉献精神、毅力、努力工作、甚至自尊心都是决定收入的重要因素 (Cawley 等，2003；Carneiro 等，2003)。但是，这些特征对收入的影响可能会随着时间发生变化。

具体来看，雇主对劳动者个人能力的准确评估需要一定的时间，而工作收入取决于雇主对这些个人能力和特征的评估。因此 $F_{t}$ 可以视为雇主雇佣劳动者 $T$ 期后对劳动者个人特征的评价。在宏观上， $F_{t}$ 可以视为共同冲击， $λ_{i}$ 代表对这些共同冲击的异质性反应 (Bai，2009)。

2. 交互固定效应模型的估计方法

由于交互固定效应的特殊形式，传统的静态面板估计方法 (组内估计量、差分估计量、以及 LSDV 方法) 一般都不能得到一致性的估计，因此需要寻求更加有效的估计方法。交互固定效应的估计思路大致可以分为两类：一类是尝试消去交互固定效应，如 Holtz-Eakin 等 (1988)，Ahn 等 (2001)；另一类的基本思想则是控制或估计，如 Pesaran (2006)，Bai (2009)。下面简要介绍其中四种方法：

2.1 准差分法

Holtz-Eakin 等 (1988) 提出对只含有一个共同因子的模型，使用准差分的方法消去交互固定效应。假设共同因子 $f_{t}$ 是外生的 (如宏观经济冲击)，因子载荷 $b_{i}$ 内生。

y_{i t} = β x_{i t} + b_{i} f_{t} + ϵ_{i t}

减去滞后一期的 $r_{t}$ 倍， $r_{t} = f_{t} / f_{t - 1}$ ：

r_{t} y_{i, t - 1} = r_{t} β x_{i, t - 1} + b_{i} r_{t} f_{t - 1} + r_{t} ϵ_{i, t - 1}

得到：

\begin{aligned} y_{i t} & = r_{t} y_{i, t - 1} + β x_{i t} - β r_{t} x_{i, t - 1} + (ϵ_{i t} - r_{t} ϵ_{i, t - 1}) \\ = r_{t} y_{i, t - 1} + β x_{i t} - β r_{t} x_{i, t - 1} + ϵ_{i t}^{*} \end{aligned}

这样就消掉了内生的因子载荷 $b_{i}$ 。对于准差分后的模型:

\begin{aligned} y_{i t} & = r_{t} y_{i, t - 1} + β x_{i t} - β r_{t} x_{i, t - 1} + (ϵ_{i t} - r_{t} ϵ_{i, t - 1}) \\ = r_{t} y_{i, t - 1} + β x_{i t} - β r_{t} x_{i, t - 1} + ϵ_{i t}^{*} \end{aligned}

可以将 ${r_{1}, r_{2}, r_{3}, . . .}$ 作为待估参数，用更高阶的滞后项作为工具变量，使用 GMM 方法进行估计 (详见 Holtz 等，1988)。然而，这种准差分的方法引入了因变量的滞后项以及随时间变化的参数，仅仅方便用于估计一个共同因子的情况，对于含有多个共同因子的模型，必须经过多次准差分。

2.2 广义组内去心法

Ahn 等 (2001) 提出可以进行广义组内去心法。

2.3 主成分法

主成分法由 Coakey 等 (2002) 提出，其基本思想是先估计被遗漏的因子，然后作为控制变量加入回归方程。对于交互固定效应模型：

Y_{i t} = X_{i t}^{'} β + λ_{i}^{'} F_{t} + ϵ_{i t}

若给定 $β$ ，则可以得到因子模型：

Y_{i t} - X_{i t}^{'} β = λ_{i}^{'} F_{t} + ϵ_{i t}

用主成分法可以估计出方程右边的因子 $F_{t}$ 。具体来看 Coakey 等 (2002) 主成分法的基本步骤是：先使用 OLS 估计原方程，得到 $T \times N$ 的残差矩阵，将其视为 $N$ 个残差变量，每个个体有 $T \times 1$ 的残差序列。假设共同因子为 $r$ 个，提取 $N$ 个残差变量的前 $r$ 个主成分作为对共同因子 $F_{t}$ 的估计量 ${\hat{F}}_{t}$ ，然后再进行 OLS 回归：

Y_{i t} = X_{i t}^{'} β + λ_{i}^{'} {\hat{F}}_{t} + ϵ_{i t}

2.4 主成分迭代法

Pesaran (2004) 指出，采用 Coakey 等（2002) 的两阶段估计法得到的估计量是不一致的。Bai (2009) 提出的主成分迭代法，将 Coakey 等 (2002) 的两步法不断迭代，直到收敛，最终可得一致估计量。主成分迭代法要求面板数据为大 $N$ 和大 $T$ 的结构，同时因子与因子载荷都可以是内生的。

3. 交互固定效应模型的 Stata 实现

3.1 regife 命令

安装命令如下：

. ssc install regife, replace

输入 help regife 可以查看其语法：


Syntax

    regife depvar [indepvars] [if] [in] [weight] , factors(idvar timevar, dimensionint) [options]

Description

    regife fits a model with interactive fixed effects following Bai (2009). Optionally, it saves the estimated factors. Errors are computed following the
    regressions indicated in Section 6, but Monte Carlo evidence suggest bootstraps performs n finite sample. The program requires reghdfe and hdfe to be installed
    (both are available on SSC).

Options
    options                         Description
    ----------------------------------------------------------------------------------------------------------------------------------------------------------------
      factors(idvar timevar, dimensionint)
                                      id variable, time variable, and factor dimension. To save the estimates for the factor model, write newvar=factorvar.
      absorb(absvar[...])            identifiers of the fixed effects that will be absorbed. To save the estimates for the fixed effect, write newvar=absvarvar.
      vce(vcetype[, opt])           vcetype} is unadjusted/ols (default), robust, bootrap or cluster clustervars. Monte carlo evidence suggests that bootstrap
                                      performs better in finite sample
      tolerance(#)                   specifies the tolerance criterion for convergence; default is tolerance(1e-9)
      maxiterations(#)               specifies the maximum number of iterations; default is maxiterations(5000). 0 corresponds to an illimited number of iterations
      residuals(newvar)              save residuals
      bstart(matrix)                 start the iteration algorithm at a given value for b
    ----------------------------------------------------------------------------------------------------------------------------------------------------------------
    fweights, aweights and pweights are allowed but should be constant within idvar; see weight.

其中，factors(idvar timevar, dimensionint) 用于指定个体变量、时间变量以及共同因子的个数；
absorb(absvar[...]) 表示加入个体或时间效应；
vce(vcetype[, opt]) 指定对标准误调整方法。

3. Stata 操作实例

. webuse nlswork, clear  
* 数据地址2: https://gitee.com/lianxh/data/raw/master/data01/nlswork.dta
. keep if id <= 100      
. regife ln_w tenure, f(id year, 1)                   //考虑一维交互固定效应
. regife ln_w tenure, a(id) f(id year, 1)             //加入个体固定效应
. regife ln_w tenure, a(id year) f(id year, 1)        // 加入个体和时间固定效应
. regife ln_w tenure, f(fid = id fyear = year, 1)     //生成因子载荷和共同因子并保存在新变量fid、fyear中
. regife ln_w tenure, f(id year, 1) residuals(newvar) //保存残差项

比较单向固定效应、双向固定效应以及交互固定效应的结果：

qui:xtreg ln_w tenure, fe         //只考虑地区固定效应
est store idfe
qui:xtreg ln_w tenure i.year, fe  //只考虑时间和地区固定效应
est store idyearfe
regife ln_w tenure, a(id year) f(id year, 1) //考虑时间、地区固定效应和一维交互效应
est store idyearinterfe
esttab idfe idyearfe idyearinterfe, drop(*.year) nogap  //输出结果


. esttab idfe idyearfe idyearinterfe, drop(*.year) nogap  //输出结果

------------------------------------------------------------
                      (1)             (2)             (3)   
                  ln_wage         ln_wage         ln_wage   
------------------------------------------------------------
tenure             0.0394***       0.0258***       0.0118*  
                   (8.47)          (4.65)          (2.02)   
_cons               1.755***        1.649***        1.837***
                  (99.41)         (30.68)         (94.79)   
------------------------------------------------------------
N                     570             570             561   
------------------------------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001

通过比较三种回归结果可以发现，考虑的固定效应越多，系数的值越来越小，显著性越来越弱，说明因变量受到时间、地区以及两者交互效应的影响较大。

4. 交互固定效应在文献中的应用

下面我们以 Hagedorn 等 (2015) 的文章为例，来看一下这个命令在实际研究中的应用场景和结果。

4.1 问题背景

Hagedorn 等 (2015) 的目标在于研究美国 2013 年末所执行的一项法规——失业补偿救济金期限缩短，对劳动力市场的影响。

从 2008 年 6 月开始，为了应对美国国内逐渐恶化的劳动力市场环境，政府实施了联邦紧急失业救助法案 (Emergency Unemployment Compensation Act, EUC08)。该法案同意所有州将其原本的失业救助期限额外延长 13 个月。随着政策的演化，政策逐渐调整为四层分级，提供了最多潜在 53 周的联邦财政失业救济支持。作为结果，到 2013 年 12 月末美国各州的失业救济时长各不相同，最长的有 73 周，最短的为 19 周。这一法案在 2013 年末，被美国国会决定结束，统一地将其所有州的失业救济时长缩短为 26 周。

在经济理论中，失业救济对劳动力市场的影响是相当模糊的。本文相当于从实证数据中给出了答案，研究结果显示，失业救济缩短使得劳动力市场更加繁荣。具体而言，在失业救济原本更长的州 (意味着被缩短到 26 周，被砍掉的时间更长)，就业率的增长要比失业救济原本更短的州高出 25%。

4.2 识别策略和模型设定

作者所用的衡量劳动力市场情况的数据满足 border counties 特征，即 county a 和 county b 为一组，且 a 和 b 相邻并属于不同州。由于相邻两个县在地理位置上毗邻，拥有十分类似的环境、自然资源、劳动力市场和产业布局，因此它们的潜在的经济指标很可能会具有相同的随时间演化的趋势。但由于两个 counties 在法律上属于不同的州，因此其原本的失业救济时长不同，这使得其失业救济缩短的程度不同，由此造成干预强度的差异。

这样的研究设计类似于配对化随机试验，即在一对十分类似的个体中，随机地选取其中一个进行干预来检验作用效果。

本文的主要模型采取 Diff-in-Diff 形式，设定如下：失业救济补偿政策 $b_{i, t}$ 对于就业 $e_{i, t}$ 的影响以系数 $α$ 来衡量。其中 $I_{t \geq 2013 / Q 4}$ 表示时间点是否处于 EUC08 法案取消之后。

e_{i, t} = κ I_{t \leq 2013 / Q 3} b_{p, t} + α I_{t \geq 2013 / Q 4} b_{i, t} + ϵ_{i, t}

为了能够保证一致性地估计事前趋势，识别方程中同样加入了事前的失业救济时长，用一个不同的系数 $κ$ 来捕捉其效应。

e_{i, t} = κ I_{t \leq 2013 / Q 3} b_{p, t} + α I_{t \geq 2013 / Q 4} b_{i, t} + ϵ_{i, t}

考虑在一对 border counties 之间，称这组为 p ，将上述等式进行事前事后的一阶差分。两个 border counties 由于所处不同州，EUC08 法案取消对其带来的失业救济期限缩短程度不同，即干预强度不同，以此识别失业救济对就业增长的影响。

Δ e_{p, t} = κ I_{t \leq 2013 / Q 3} Δ b_{p, t} + α I_{t \geq 2013 / Q 4} Δ b_{p, t} + Δ ϵ_{p, t},

而我们可以将上式中的误差项假定为不同的形式，从而得到不同灵活度的模型。例如我们可以将其设置为：

常规的时间和个体固定效应 (individual and time fixed effect)；
因子模型 (Factor model)，即本文所介绍的交互固定效应模型。其设定如下：

Δ ϵ_{p, t} = (λ_{i}^{'} - λ_{j}^{'}) F_{t} + ν_{p, t}

其中， $λ_{i}$ 是一组 county-specific factor loading， $F_{t}$ 是时间变异的 common factor，这样模型就变成了：

Δ e_{p, t} = α I_{t \geq 2013 / Q 4} Δ b_{p, t} + (λ_{i}^{'} - λ_{j}^{'}) F_{t} + ν_{p, t}

之所以采用交互固定效应，是由于在 border counties 之间也可能出现潜在经济趋势的异质性。具体而言，这些趋势反映了拥有不同的失业补偿救济时长的 county 对于各种加总冲击 $F_{t}$ 的异质性反应，而这种异质性反应本质上是由于对于冲击的不同暴露程度所引起的。这种异质性的反应使用因子载荷 (factor loading) $λ_{i}$ 来捕捉。

在交互固定效应模型下，本文作者又使用了两种设定方法：

潜在因子模型 (Latent Factor Model)，将共同冲击 $F_{t}$ 设定为不可观测，而使用数据驱动的方法来估计，这种情况下需要设定因子个数。
“自然” 因子模型 ("Natural" Factor Model)，这里作者将 $F_{t}$ 设定为可观测的一个向量，其包含 3 个宏观经济变量的时间序列，分别为石油价格、建筑业就业、联邦银行储备余额的货币指标。

需要注意的是，使用交互固定效应模型可以更大化模型的灵活度，但是模型的灵活度的增加需要以可解释程度的下降作为代价。第二种设定方法中尽管丢失了一些灵活性，但是却增加了模型的可解释性。

4.3 估计结果

可以看到，失业救济时长和就业增长呈现反向变化关系，即 EUC08 法案的取消促进了劳动力就业的增长。

5. 相关文献

Bai J. Panel data models with interactive fixed effects[J]. Econometrica, 2009, 77(4): 1229-1279. -PDF-
Bai, J. S., 2013, Fixed-effects dynamic panel models, a factor analytical method, Econometrica, 81 (1): 285-314. -Link-, -PDF1-, PDF2
Hagedorn M, Manovskii I, Mitman K. The impact of unemployment benefit extensions on employment: the 2014 employment miracle?[R]. National Bureau of Economic Research, 2015. -PDF-
Jushan Bai, Kunpeng Li, Dynamic spatial panel data models with common shocks, Journal of Econometrics, (2021) -Link-, -PDF-
Cheng Hsiao, Yimeng Xie, Qiankun Zhou, Factor dimension determination for panel interactive effects models: an orthogonal projection approach, Computational Statistics, (2021) -Link-, -PDF-
Stephen O'Neill, Noemi Kreif, Matt Sutton, Richard Grieve, A comparison of methods for health policy evaluation with controlled pre‐post designs, Health Services Research, 55, 2, (328-338), (2020) -Link-
Matthew Harding, Carlos Lamarche, M. Hashem Pesaran, Common correlated effects estimation of heterogeneous dynamic panel quantile regression models, Journal of Applied Econometrics, 35, 3, (294-314), (2020) -Link-
Joakim Westerlund, A cross‐section average‐based principal components approach for fixed‐T panels, Journal of Applied Econometrics, 35, 6, (776-785), (2020) -Link-
Yana Petrova, Joakim Westerlund, Fixed effects demeaning in the presence of interactive effects in treatment effects regressions and elsewhere, Journal of Applied Econometrics, 35, 7, (960-964), (2020) -Link-
Jianqing Fan, Yuan Ke, Yuan Liao, Augmented factor models with applications to validating market risk factors and forecasting bond risk premia, Journal of Econometrics, (2020) -Link-, -PDF-
Otilia Boldea, Bettina Drepper, Zhuojiong Gan, Change point estimation in panel data with time‐varying individual effects, Journal of Applied Econometrics, 35, 6, (712-727), (2020) -Link-
Ke Miao, Kunpeng Li, Liangjun Su, Panel threshold models with interactive fixed effects, Journal of Econometrics, (2020) -Link-, -PDF-
Zongwu Cai, Ying Fang, Qiuhua Xu, Testing capital asset pricing models using functional-coefficient panel data models with cross-sectional dependence, Journal of Econometrics, (2020) -Link-, -PDF-
Guido M. Kuersteiner, Ingmar R. Prucha, Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity, Econometrica, 88, 5, (2109-2146), (2020) -Link-
Hanchao Wang, Bin Peng, Degui Li, Chenlei Leng, Nonparametric estimation of large covariance matrices with conditional sparsity, Journal of Econometrics, (2020) -Link-, -PDF-
Patrick Gagliardini, Elisa Ossola, Olivier Scaillet, Estimation of large dimensional conditional factor models in finance, (2020) -Link-, -PDF-
Ryan Rafatya, Geoffroy Dolphin, Felix Pretis, Carbon Pricing and the Elasticity of CO2 Emissions, Institute for New Economic Thinking Working Paper Series, (1-84), (2020) -Link-, -PDF-
Bin Jiang, Yanrong Yang, Jiti Gao, Cheng Hsiao, Recursive estimation in large panel data models: Theory and practice, Journal of Econometrics, (2020) -Link-, -PDF-
Milda Norkutė, Vasilis Sarafidis, Takashi Yamagata, Guowei Cui, Instrumental variable estimation of dynamic linear panel data models with defactored regressors and a multifactor error structure, Journal of Econometrics, (2020) -Link-, -PDF-
Mingli Chen, Iván Fernández-Val, Martin Weidner, Nonlinear factor models for network and panel data, Journal of Econometrics, (2020) -Link-, -PDF-
Artūras Juodis, Hande Karabiyik, Joakim Westerlund, On the robustness of the pooled CCE estimator, Journal of Econometrics, (2020) -Link-, -PDF-
José Diogo Barbosa, Marcelo J. Moreira, Likelihood inference and the role of initial conditions for the dynamic panel data model, Journal of Econometrics, (2020) -Link-, -PDF-
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Xi Qu, Lung-fei Lee, Chao Yang, Estimation of a SAR model with endogenous spatial weights constructed by bilateral variables, Journal of Econometrics, (2020) -Link-, -PDF-
Lei Hou, Kunpeng Li, Qi Li, Min Ouyang, Revisiting the location of FDI in China: A panel data approach with heterogeneous shocks, Journal of Econometrics, (2020) -Link-, -PDF-
Milda Norkutė, Joakim Westerlund, The factor analytical approach in near unit root interactive effects panels, Journal of Econometrics, (2020) -Link-, -PDF-
Chaohua Dong, Jiti Gao, Bin Peng, Varying-Coefficient Panel Data Models With Nonstationarity and Partially Observed Factor Structure, Journal of Business & Economic Statistics, (1-12), (2020) -Link-, -PDF-
Artūras Juodis, Vasilis Sarafidis, A Linear Estimator for Factor-Augmented Fixed-T Panels With Endogenous Regressors, Journal of Business & Economic Statistics, (1-15), (2020) -Link-, -PDF-
Johannes Boehm, Ezra Oberfield, Misallocation in the Market for Inputs: Enforcement and the Organization of Production*, The Quarterly Journal of Economics, (2020) -Link-, -PDF-
Mustafa Tuğan, Panel VAR models with interactive fixed effects, The Econometrics Journal, (2020) -Link-, -PDF-
Jianqing Fan, Yuan Liao, Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors, Journal of the American Statistical Association, (1-42), (2020) -Link-, -PDF-
Hande Karabiyik, Joakim Westerlund, Forecasting using cross-section average–augmented time series regressions, The Econometrics Journal, (2020) -Link-, -PDF-
Liangjun Su, Xia Wang, TESTING FOR STRUCTURAL CHANGES IN FACTOR MODELS VIA A NONPARAMETRIC REGRESSION, Econometric Theory, (1-32), (2020) -Link-, -PDF-
Jörg Breitung, Philipp Hansen, Alternative estimation approaches for the factor augmented panel data model with small T, Empirical Economics, (2020) -Link-, -PDF-
Markus Eberhardt, Francis Teal, The Magnitude of the Task Ahead: Macro Implications of Heterogeneous Technology, Review of Income and Wealth, 66, 2, (334-360), (2019) -Link-
Hande Karabiyik, Franz C. Palm, Jean-Pierre Urbain, Econometric Analysis of Panel Data Models with Multifactor Error Structures, Annual Review of Economics, 11, 1, (495-522), (2019) -Link-, -PDF-
Patrick Gagliardini, Elisa Ossola, Olivier Scaillet, A diagnostic criterion for approximate factor structure, Journal of Econometrics, (2019) -Link-, -PDF-
Tingting Cheng, Jiti Gao, Yayi Yan, Regime switching panel data models with interactive fixed effects, Economics Letters, 177, (47-51), (2019) -Link-, -PDF-
Hao Liu, The communication and European Regional economic growth: The interactive fixed effects approach, Economic Modelling, (2019) -Link-, -PDF-
Ignace De Vos, Joakim Westerlund, On CCE estimation of factor-augmented models when regressors are not linear in the factors, Economics Letters, 178, (5-7), (2019) -Link-, -PDF-
Marco Avarucci, Paolo Zaffaroni, Robust Nearly-Efficient Estimation of Large Panels With Factor Structures, SSRN Electronic Journal, (2019) -Link-.
Simon C. Smith, Allan Timmermann, Yinchu Zhu, Variable selection in panel models with breaks, Journal of Econometrics, (2019) -Link-, -PDF-
Patrick Gagliardini, Elisa Ossola, Olivier Scaillet, Estimation of Large Dimensional Conditional Factor Models in Finance, SSRN Electronic Journal, (2019) -Link-.
Edith Aguirre, Do changes in divorce legislation have an impact on divorce rates? The case of unilateral divorce in Mexico, Latin American Economic Review, 28, 1, (2019) -Link-, -PDF-
Joakim Westerlund, Yana Petrova, Milda Norkute, CCE in fixed‐T panels, Journal of Applied Econometrics, 34, 5, (746-761), (2019) -Link-
Jia Li, Viktor Todorov, George Tauchen, Jump factor models in large cross‐sections, Quantitative Economics, 10, 2, (419-456), (2019) -Link-
Kunpeng Li, Guowei Cui, Lina Lu, Efficient estimation of heterogeneous coefficients in panel data models with common shocks, Journal of Econometrics, (2019) -Link-, -PDF-
Ruiqi Liu, Zuofeng Shang, Yonghui Zhang, Qiankun Zhou, Identification and estimation in panel models with overspecified number of groups, Journal of Econometrics, (2019) -Link-, -PDF-
Jianqing Fan, Yuan Liao, Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors, SSRN Electronic Journal, (2019) -Link-.
Sanying Feng, Gaorong Li, Tiejun Tong, Shuanghua Luo, Testing for heteroskedasticity in two-way fixed effects panel data models, Journal of Applied Statistics, (1-26), (2019) -Link-, -PDF-
John Inekwe, Elizabeth Ann Maharaj, Mita Bhattacharya, Drivers of carbon dioxide emissions: an empirical investigation using hierarchical and non-hierarchical clustering methods, Environmental and Ecological Statistics, (2019) -Link-, -PDF-
Shou-Yung Yin, Chu-An Liu, Chang-Ching Lin, Focused Information Criterion and Model Averaging for Large Panels With a Multifactor Error Structure, Journal of Business & Economic Statistics, (1-30), (2019) -Link-, -PDF-
Shunan Zhao, Ruiqi Liu, Zuofeng Shang, Statistical Inference on Panel Data Models: A Kernel Ridge Regression Method, Journal of Business & Economic Statistics, (1-13), (2019) -Link-, -PDF-
Christian Hansen, Yuan Liao, THE FACTOR-LASSO AND K-STEP BOOTSTRAP APPROACH FOR INFERENCE IN HIGH-DIMENSIONAL ECONOMIC APPLICATIONS, Econometric Theory, 35, 03, (465-509), (2018) -Link-, -PDF-
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Joakim Westerlund, On Estimation and Inference in Heterogeneous Panel Regressions with Interactive Effects, Journal of Time Series Analysis, 40, 5, (852-857), (2018) -Link-
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Simon Smith, Forecasting Panel Data with Structural Breaks and Regime-Specific Grouped Heterogeneity, SSRN Electronic Journal, (2018) -Link-.
Liangjun Su, Gaosheng Ju, Identifying latent grouped patterns in panel data models with interactive fixed effects, Journal of Econometrics, 206, 2, (554-573), (2018) -Link-, -PDF-
Chaoxing Dai, Kun Lu, Dacheng Xiu, Knowing factors or factor loadings, or neither? Evaluating estimators of large covariance matrices with noisy and asynchronous data, Journal of Econometrics, (2018) -Link-, -PDF-
Hyungsik Roger Moon, Matthew Shum, Martin Weidner, Estimation of random coefficients logit demand models with interactive fixed effects, Journal of Econometrics, 206, 2, (613-644), (2018) -Link-, -PDF-
Marc K. Chan, Simon Kwok, Difference-in-Differences When Trends are Uncommon and Stochastic, SSRN Electronic Journal, (2018) -Link-.
Isamu Ginama, Kazuhiko Hayakawa, Takahiro Kanmei, Examining the Feldstein–Horioka puzzle using common factor panels and interval estimation, Japan and the World Economy, (2018) -Link-, -PDF-
Tingting Cheng, Jiti Gao, Yayi Yan, Regime Switching Panel Data Models with Interactive Fixed Effects, SSRN Electronic Journal, (2018) -Link-.
Simon Smith, Allan Timmermann, Yinchu Zhu, Variable Selection in Panel Models with Breaks, SSRN Electronic Journal, (2018) -Link-.
Shujie Ma, Liangjun Su, Estimation of large dimensional factor models with an unknown number of breaks, Journal of Econometrics, 207, 1, (1-29), (2018) -Link-, -PDF-
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Joachim Freyberger, Non-parametric Panel Data Models with Interactive Fixed Effects, The Review of Economic Studies, 85, 3, (1824-1851), (2017) -Link-, -PDF-
Jiaolong Li, Zhiqin Yang, A panel data model with interactive effects characterized by multilevel non-parallel factors, Applied Economics Letters, 25, (707-712), (2017) -Link-, -PDF-
Wei Shi, Lung-fei Lee, The effects of gun control on crimes: a spatial interactive fixed effects approach, Empirical Economics, 55, 1, (233-263), (2017) -Link-, -PDF-
Artūras Juodis, Pseudo Panel Data Models With Cohort Interactive Effects, Journal of Business & Economic Statistics, 36, 1, (47-61), (2017) -Link-, -PDF-
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Jushan Bai, Yuan Liao, Inferences in panel data with interactive effects using large covariance matrices, Journal of Econometrics, 200, 1, (59-78), (2017) -Link-, -PDF-
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Liu Hao, The Communication and European Regional Economic Growth: The Interactive Fixed Effects Approach, SSRN Electronic Journal, (2017) -Link-.
Bin Jiang, Yanrong Yang, Jiti Gao, Cheng Hsiao, Recursive Estimation in Large Panel Data Models: Theory and Practice, SSRN Electronic Journal, (2017) -Link-.
Shou-Yung Yin, Chu-An Liu, ChanggChing Lin, Focused Information Criterion and Model Averaging for Large Panels with a Multifactor Error Structure, SSRN Electronic Journal, (2017) -Link-.
Cheng Hsiao, Panel Models with Interactive Effects, SSRN Electronic Journal, (2017) -Link-.
Jesse Wursten, The Employment Elasticity of the Minimum Wage: Is It Just Politics after All?, SSRN Electronic Journal, (2017) -Link-.
Hyungsik Roger Moon, Matthew Shum, Estimation of Random Coefficients Logit Demand Models with Interactive Fixed Effects, SSRN Electronic Journal, (2017) -Link-.
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Jianqing Fan, Yuan Ke, Yuan Liao, Robust Factor Models with Explanatory Proxies, SSRN Electronic Journal, (2016) -Link-.
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