🤖 AI Summary
This study addresses the incidental parameter problem arising in two-way fixed effects network models when the outcome variable is sparse or observed at extreme quantiles. The authors propose a distributional regression approach based on multi-threshold binarization combined with conditional maximum likelihood estimation, which effectively eliminates fixed effects through pairwise differencing to identify structural parameters. They innovatively derive the joint asymptotic distribution of estimators across different thresholds, enabling the construction of simultaneous confidence bands and the development of cross-threshold equality tests for coefficients. Monte Carlo simulations demonstrate that the method exhibits low bias and accurate coverage even under sparsity. An application to bilateral trade data reveals significant heterogeneity in the impact of key trade barriers across the conditional distribution of trade flows.
📝 Abstract
I develop an estimation and inference framework for distribution regression in dyadic network settings with two-way fixed effects that vary across thresholds of the outcome. I show that identification of the structural parameters is achieved through binarization of the outcome at each threshold, and estimate the model by conditional maximum likelihood, which "differences out" the fixed effects and circumvents the incidental parameter problem. The estimator remains asymptotically unbiased under sparsity, whether from the network structure or binarization at extreme thresholds. The second novelty is to establish the joint asymptotic distribution of the estimators across multiple thresholds with different convergence rates, and to develop simultaneous confidence bands and tests for equality of coefficients across thresholds. Monte Carlo simulations confirm small bias, valid inference, and correct simultaneous coverage under sparsity. An application to bilateral trade finds that coefficients vary substantially across the distribution, with equality rejected for key trade barriers.