Xunkang Tian, Nan Zhi
arXiv 11 Sep 2026 · Econometrics
arXiv:2609.13026 · PDF · Extracted main text
This paper studies identification and inference in a triangular system with an endogenous regressor when exclusion restrictions are unavailable and the dependence between structural disturbances is modeled through an unrestricted control function. In this setting, standard orthogonality conditions do not deliver point identification, as the unknown control function can rationalize a wide range of structural coefficients. We show that identifying information can be extracted from distributional shifts in the first-stage disturbance induced by an auxiliary variable that may directly affect the outcome. Imposing a local restriction on the log density ratio, together with an explicit bound on the sieve approximation error of the control function, we derive moment inequalities that restrict the structural parameter. We develop a practical inference procedure based on test inversion and multiplier bootstrap that accommodates generated regressors, cross-fitted sieve estimation, and locally estimated density-ratio nuisances. The results clarify how identification can be recovered from weak local distributional structure in the absence of classical instruments.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Klein, Roger and Vella, Francis (2010) Estimating a class of triangular simultaneous equations models without exclusion restrictions | 0.405 | 1 | 1 | 100% |
| 2 | Lewbel, Arthur (2012) Using heteroscedasticity to identify and estimate mismeasured and endogenous regressor models | 0.405 | 1 | 1 | 100% |
Showing the top 2 of 2 scored citations.