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Register a new userVarying Coefficient Panel Data Model with Interactive Fixed Effects
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Added by
Gaorong Li
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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In this paper, we propose a varying coefficient panel data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function by B-spline, and propose a robust nonlinear iteration scheme based on the least squares method to estimate the coefficient functions of interest. We also establish the asymptotic theory of the resulting estimators under certain regularity assumptions, including the consistency, the convergence rate and the asymptotic distribution. Furthermore, we develop a least squares dummy variable method to study an important special case of the proposed model: the varying coefficient panel data model with additive fixed effects. To construct the pointwise confidence intervals for the coefficient functions, a residual-based block bootstrap method is proposed to reduce the computational burden as well as to avoid the accumulative errors. Simulation studies and a real data analysis are also carried out to assess the performance of our proposed methods.
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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 of the estimation procedure are studied under certain conditions. A Monte Carlo simulation study is used to illustrate the advantages of the proposed method. Further considerations for the situations that the number of subspaces for factors, the dimension of factors and the dimension of subspaces are unknown are also discussed. For illustrative purposes, the proposed method is applied to study the linkage between income and democracy across countries while subspace patterns of unobserved factors and factor loadings are allowed.
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This paper investigates the integration of gradient boosted decision trees and varying coefficient models. We introduce the tree boosted varying coefficient framework which justifies the implementation of decision tree boosting as the nonparametric effect modifiers in varying coefficient models. This framework requires no structural assumptions in the space containing the varying coefficient covariates, is easy to implement, and keeps a balance between model complexity and interpretability. To provide statistical guarantees, we prove the asymptotic consistency of the proposed method under the regression settings with $L^2$ loss. We further conduct a thorough empirical study to show that the proposed method is capable of providing accurate predictions as well as intelligible visual explanations.
We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences transformation identifies the effect. We show that analogous, albeit more complex, transformations exist in the more general linear factor model, providing a new means to identify the effect in that model. In fact many such transformations exist, called bridge functions, all identifying the same causal effect estimand. This poses a unique challenge for estimation and inference, which we solve by targeting the minimal bridge function using a regularized estimation approach. We prove that our resulting average causal effect estimator is root-N consistent and asymptotically normal, and we provide asymptotically valid confidence intervals. Finally, we provide extensions for the case of a linear factor model with time-varying unmeasured confounders.
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