arXiv subjects

Songnian Chen

Publications and source records attributed to Songnian Chen.

5 recordsLinked to original sources

arXiv2025

Universal Factor Models

We propose a new factor analysis framework and estimators of the factors and loadings that are robust to certain weak factors in a large $N$ and large $T$ setting. Our framework, by simultaneously considering all quantile levels of the outcome variable, induces standard mean and quantile factor models, but the factors can have an arbitrarily weak influence on the outcome's mean or quantile at most quantile levels. Our method estimates the factor space at the $\sqrt{N}$-rate as long as each factor is strong at some unknown quantile level, and achieves $\sqrt{N}$- and $\sqrt{T}$-asymptotic normality for the factors and loadings based on a novel sample splitting approach that handles incidental nuisance parameters. We also develop a weak-factor-robust estimator of the number of factors and consistent selectors of factors of any tolerated level of influence on the outcome's mean or quantiles. Monte Carlo simulations demonstrate the effectiveness of our method.

econ.EM↗

arXiv2023

Group-Heterogeneous Changes-in-Changes and Distributional Synthetic Controls

We develop new changes-in-changes (CIC) and distributional synthetic controls (DSC) types of methods when there exists group-level heterogeneity. For CIC, we allow individuals to belong to heterogeneous groups, extending Athey and Imbens (2006) by finding appropriate control groups that share similar group-level unobserved characteristics to the treatment groups. For DSC, we show that the synthetic control units are not necessarily from the same period as in Gunsilius (2023); they may come from different periods in which they have comparable group-level heterogeneity to the treatment group. Implementation of these new methods is briefly discussed.

econ.EM↗

arXiv2022

Endogeneity in Weakly Separable Models without Monotonicity

We identify and estimate treatment effects when potential outcomes are weakly separable with a binary endogenous treatment. Vytlacil and Yildiz (2007) proposed an identification strategy that exploits the mean of observed outcomes, but their approach requires a monotonicity condition. In comparison, we exploit full information in the entire outcome distribution, instead of just its mean. As a result, our method does not require monotonicity and is also applicable to general settings with multiple indices. We provide examples where our approach can identify treatment effect parameters of interest whereas existing methods would fail. These include models where potential outcomes depend on multiple unobserved disturbance terms, such as a Roy model, a multinomial choice model, as well as a model with endogenous random coefficients. We establish consistency and asymptotic normality of our estimators.

econ.EM↗

arXiv2020

Identification and Estimation of Weakly Separable Models Without Monotonicity

We study the identification and estimation of treatment effect parameters in weakly separable models. In their seminal work, Vytlacil and Yildiz (2007) showed how to identify and estimate the average treatment effect of a dummy endogenous variable when the outcome is weakly separable in a single index. Their identification result builds on a monotonicity condition with respect to this single index. In comparison, we consider similar weakly separable models with multiple indices, and relax the monotonicity condition for identification. Unlike Vytlacil and Yildiz (2007), we exploit the full information in the distribution of the outcome variable, instead of just its mean. Indeed, when the outcome distribution function is more informative than the mean, our method is applicable to more general settings than theirs; in particular we do not rely on their monotonicity assumption and at the same time we also allow for multiple indices. To illustrate the advantage of our approach, we provide examples of models where our approach can identify parameters of interest whereas existing methods would fail. These examples include models with multiple unobserved disturbance terms such as the Roy model and multinomial choice models with dummy endogenous variables, as well as potential outcome models with endogenous random coefficients. Our method is easy to implement and can be applied to a wide class of models. We establish standard asymptotic properties such as consistency and asymptotic normality.

econ.EM↗

arXiv2007

Local partial likelihood estimation in proportional hazards regression

Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] considered the estimation of the risk function $ψ(x)$ in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large sample properties of the estimator for the risk function itself were not established. In this paper, we consider direct estimation of the relative risk function $ψ(x_2)-ψ(x_1)$ for any location normalization point $x_1$. The main novelty in our approach is that we select observations in shrinking neighborhoods of both $x_1$ and $x_2$ when constructing a local version of the partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] only concentrated on a single neighborhood, resulting in the cancellation of the risk function in the local likelihood function. The asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated. The idea behind our approach is extended to estimate the differences between groups. A simulation study is carried out.

math.ST↗