Abstract
This paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete outcome variables. The method is based upon projection of simultaneous confidence bands for distribution functions constructed from fixed effects distribution regression estimators. These fixed effects estimators are debiased to deal with the incidental parameter problem. Under asymptotic sequences where both dimensions of the data set grow at the same rate, the confidence bands for the quantile functions and effects have correct joint coverage in large samples. An empirical application to gravity models of trade illustrates the applicability of the methods to network data.
Highlights
Standard regression analyzes average effects of covariates on outcome variables
In this paper we develop inference methods for distributional effects in nonlinear models with two-way unobserved effects
We show that the fixed effects distribution regression (FE-distribution regression (DR)) estimator can be obtained as a sequence of binary response fixed effects estimators where the binary response is an indicator of the outcome passing some threshold
Summary
Standard regression analyzes average effects of covariates on outcome variables. In many applications it is important to consider distributional effects. In the same framework, Kato, Galvao, and Montes-Rojas (2012), Galvao, Lamarche and Lima (2013), Galvao and Kato (2016) and Arellano and Weidner (2016) considered fixed effects quantile regression estimators without shrinkage and developed bias corrections All these papers require that T pass to infinity faster than N , making it difficult to extend the theory to models with two-way individual and time effects. These include Charbonneau (2017), Cruz-Gonzalez, Fernandez-Val and Weidner (2016), Dzemski (2017), Fernandez-Val and Weidner (2016), Graham (2016, 2017), Jochmans (2018), and Yan, Jiang, Fienberg and Leng (2016), which developed methods for models of network formation with unobserved sender and receiver effects for directed and undirected networks None of these papers consider estimation of quantile effects as the outcome variable is binary, whether or not a link is formed between two agents. For a set A, |A| denotes the cardinality or number of elements of A
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