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lianxh
命令发布了:
随时搜索推文、Stata 资源。安装命令如下:
. ssc install lianxh
详情参见帮助文件 (有惊喜):
. help lianxh
⛳ Stata 系列推文:
王晓娟 (吉林大学),594806861@qq.com
甘徐沁 (厦门大学),1072759894@qq.com
目录
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:
一般而言,面板数据模型误差项由以下几部分组成:
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。
其中,
则:
此时,(1) 式就是我们平时所使用的「双向固定效应模型」:
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):
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
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:
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
减去滞后一期的
得到:
这样就消掉了内生的因子载荷
可以将
Ahn 等 (2001) 提出可以进行广义组内去心法。
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:
若给定
用主成分法可以估计出方程右边的因子
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
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.
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。. 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。
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。
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%。
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
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
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。
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:
其中,
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
在交互固定效应模型下,本文作者又使用了两种设定方法:
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。
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。
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Milda Norkutė, Joakim Westerlund, The factor analytical approach in near unit root interactive effects panels, Journal of Econometrics, (2020) -Link-, -PDF-
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Liangjun Su, Xia Wang, Sainan Jin, Sieve Estimation of Time-Varying Panel Data Models With Latent Structures, Journal of Business & Economic Statistics, 37, 2, (334-349), (2017) -Link-, -PDF-
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-
Liangjun Su, Xia Wang, On time-varying factor models: Estimation and testing, Journal of Econometrics, 198, 1, (84-101), (2017) -Link-, -PDF-
Badi H. Baltagi, Chihwa Kao, Fa Wang, Identification and estimation of a large factor model with structural instability, Journal of Econometrics, 197, 1, (87-100), (2017) -Link-, -PDF-
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-
Yunus Emre Ergemen, Carlos Velasco, Estimation of fractionally integrated panels with fixed effects and cross-section dependence, Journal of Econometrics, 196, 2, (248-258), (2017) -Link-, -PDF-
Wei Shi, Lung-fei Lee, Spatial dynamic panel data models with interactive fixed effects, Journal of Econometrics, 197, 2, (323-347), (2017) -Link-, -PDF-
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-.
Evan Totty, THE EFFECT OF MINIMUM WAGES ON EMPLOYMENT: A FACTOR MODEL APPROACH, Economic Inquiry, (2017) 55, 4, 1712-1737, -Link-
Degui Li, Junhui Qian, Liangjun Su, Panel Data Models With Interactive Fixed Effects and Multiple Structural Breaks, Journal of the American Statistical Association, 111, 516, (1804-1819), (2017) -Link-, -PDF-
Christopher A. Candelaria, Kenneth A. Shores, Court-Ordered Finance Reforms in the Adequacy Era: Heterogeneous Causal Effects and Sensitivity, Education Finance and Policy, (1-30), (2017) -Link-, -PDF-
Tomohiro Ando, Jushan Bai, Selecting the regularization parameters in high-dimensional panel data models: Consistency and efficiency, Econometric Reviews, 37, 3, (183-211), (2016) -Link-, -PDF-
Xun Lu, Liangjun Su, Shrinkage estimation of dynamic panel data models with interactive fixed effects, Journal of Econometrics, 190, 1, (148-175), (2016) -Link-, -PDF-
Iván Fernández-Val, Martin Weidner, Individual and time effects in nonlinear panel models with large , Journal of Econometrics, 192, 1, (291-312), (2016) -Link-, -PDF-
Jushan Bai, Peng Wang, Econometric Analysis of Large Factor Models, Annual Review of Economics, 8, 1, (53-80), (2016) -Link-, -PDF-
Sunghoon Chung, Joonhyung Lee, Thomas Osang, Did China tire safeguard save U.S. workers?, European Economic Review, 85, (22-38), (2016) -Link-, -PDF-
Laurent Gobillon, Thierry Magnac, Regional Policy Evaluation: Interactive Fixed Effects and Synthetic Controls, Review of Economics and Statistics, 98, 3, (535-551), (2016) -Link-, -PDF-
Qiu-Hua Xu, Zong-Wu Cai, Ying Fang, Panel data models with cross-sectional dependence: a selective review, Applied Mathematics-A Journal of Chinese Universities, 31, 2, (127-147), (2016) -Link-, -PDF-
Lajos Horváth, Lorenzo Trapani, Statistical inference in a random coefficient panel model, Journal of Econometrics, 193, 1, (54-75), (2016) -Link-, -PDF-
Jianqing Fan, Yuan Ke, Yuan Liao, Robust Factor Models with Explanatory Proxies, SSRN Electronic Journal, (2016) -Link-.
Hyungsik Roger Moon, Martin Weidner, DYNAMIC LINEAR PANEL REGRESSION MODELS WITH INTERACTIVE FIXED EFFECTS, Econometric Theory, 33, 1, (158-195), (2015) -Link-, -PDF-
Yinchu Zhu, Uniform Estimation and Inference of Time-Heterogeneous Panel Data Models with Interactive Fixed Effects, SSRN Electronic Journal, (2015) -Link-.
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