We derive the asymptotic theory of Bai (2009)'s interactive fixed effects estimator for unbalanced panels in which the source of attrition is conditionally random. For inference, we propose a method of alternating projections algorithm based on straightforward scalar expressions to compute the residualized variables required for bias correction and covariance matrix estimation. Simulation experiments confirm that our asymptotic results provide reliable finite-sample approximations. We also reassess Acemoglu et al. (2019). Allowing for a more general form of unobserved heterogeneity, we confirm significant effects of democratization on economic growth.
Empirical economists are often deterred from the application of fixed effects binary choice models mainly for two reasons: the incidental parameter problem and the computational challenge even in moderately large panels. Using the example of binary choice models with individual and time fixed effects, we show how both issues can be alleviated by combining asymptotic bias corrections with computational advances. Because unbalancedness is often encountered in applied work, we investigate its consequences on the finite sample properties of various (bias corrected) estimators. In simulation experi…
Many panel data sets used for pseudo-poisson estimation of three-way gravity models are implicitly unbalanced because uninformative observations are redundant for the estimation. We show with real data as well as simulations that this phenomenon, which we call latent unbalancedness, amplifies the inference problem recently studied by Weidner and Zylkin (2021).
This paper develops a new toolbox for multiple structural break detection in panel data models with interactive effects. The toolbox includes tests for the presence of structural breaks, a break date estimator, and a break date confidence interval. The new toolbox is applied to a large panel of US banks for a period characterized by massive quantitative easing programs aimed at lessening the impact of the global financial crisis and the COVID--19 pandemic. The question we ask is: Have these programs been successful in spurring bank lending in the US economy? The short answer turns out to be: `…
Threshold Regression for Fixed-T Panel Data with Interactive Fixed Effects
Free University of Bozen-Bolzanno（博尔扎诺自由大学）；Brunel University of London（伦敦布鲁内尔大学）；University of Birmingham（伯明翰大学）；Lund University（隆德大学）；Deakin University（迪肯大学）
In this paper, we investigate binary response models for heterogeneous panel data with interactive fixed effects by allowing both the cross-sectional dimension and the temporal dimension to diverge. From a practical point of view, the proposed framework can be applied to predict the probability of corporate failure, conduct credit rating analysis, etc. Theoretically and methodologically, we establish a link between a maximum likelihood estimation and a least squares approach, provide a simple information criterion to detect the number of factors, and achieve the asymptotic distributions accord…
We consider the construction of confidence intervals for treatment effects estimated using panel models with interactive fixed effects. We first use the factor-based matrix completion technique proposed by Bai and Ng (2021) to estimate the treatment effects, and then use bootstrap method to construct confidence intervals of the treatment effects for treated units at each post-treatment period. Our construction of confidence intervals requires neither specific distributional assumptions on the error terms nor large number of post-treatment periods. We also establish the validity of the proposed…
This paper studies the estimation of linear panel data models with interactive fixed effects, where one dimension of the panel, typically time, may be fixed. To this end, a novel transformation is introduced that reduces the model to a lower dimension, and, in doing so, relieves the model of incidental parameters in the cross-section. The central result of this paper demonstrates that transforming the model and then applying the principal component (PC) estimator of \cite{bai_panel_2009} delivers $\sqrt{n}$ consistent estimates of regression slope coefficients with $T$ fixed. Moreover, these e…
IV Estimation of Heterogeneous Spatial Dynamic Panel Models with Interactive Effects
University of Macau（澳门大学）；Huazhong University of Science and Technology（华中科技大学）；Brunel University London（布鲁内尔伦敦大学）；University of York（约克大学）；Tohoku University（东北大学）
In this paper, a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and the group membership can be unknown. The factor loadings are assumed to be in different subspaces and the subspace clustering for factor loadings are considered. A method called least squares subspace clustering estimate (LSSC) is proposed to estimate the model parameters by minimizing the least-square criterion and to perform the subspace clustering simultaneously. The consistency of the proposed subspace clustering is proved and the asymptotic properties …
This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano and Hahn 2007; a section in Arellano and Bonhomme 2011) we discuss models with both individual and time effects, sp…
Dealing with structural breaks is an important step in most, if not all, empirical economic research. This is particularly true in panel data comprised of many cross-sectional units, such as individuals, firms or countries, which are all affected by major events. The COVID-19 pandemic has affected most sectors of the global economy, and there is by now plenty of evidence to support this. The impact on stock markets is, however, still unclear. The fact that most markets seem to have partly recovered while the pandemic is still ongoing suggests that the relationship between stock returns and COV…
We study linear panel regression models in which the unobserved error term is an unknown smooth function of two-way unobserved fixed effects. In standard additive or interactive fixed effect models the individual specific and time specific effects are assumed to enter with a known functional form (additive or multiplicative). In this paper, we allow for this functional form to be more general and unknown. We discuss two different estimation approaches that allow consistent estimation of the regression parameters in this setting as the number of individuals and the number of time periods grow t…
Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer of incidental parameter bias. We show how models with factor structures can also be applied to capture impor…
This paper studies large $N$ and large $T$ conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of the) fixed effects. It also allows the number of covariates to grow slowly with $N$ and $T$. We derive an error bound on the estimator that holds uniformly in quantile level. The order of the bound implies uniform consistency of the estimator and is …
This paper considers identifying and estimating the Average Treatment Effect on the Treated (ATT) when untreated potential outcomes are generated by an interactive fixed effects model. That is, in addition to time-period and individual fixed effects, we consider the case where there is an unobserved time invariant variable whose effect on untreated potential outcomes may change over time and which can therefore cause outcomes (in the absence of participating in the treatment) to follow different paths for the treated group relative to the untreated group. The models that we consider in this pa…
In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We propose a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to impute the "missing" elements of the control outcome matrix, corresponding to treated units/periods. This leads to a matrix that well-approximates the original (incomplete) matrix, …
