Indirect inference in incomplete and partially identified econometric models

Lixiong Li; Marc Henry

Home/Archive/arXiv

arXiv · 2610.36206

Indirect inference in incomplete and partially identified econometric models

Lixiong Li·Marc Henry

View original source ↗Read source document ↗Export metadata ↓

Abstract

We extend the indirect inference principle to structural econometric models that are incomplete, in the sense that a single value of the structural parameter may be compatible with multiple distributions of the observed endogenous variables, so that the structural parameter is typically only partially identified. We define the binding function as the smallest norm of the auxiliary estimating equations over the set of data generating processes compatible with the structural model. Hence, we obtain a confidence region by inverting a test of the hypothesis that the binding function vanishes at the pseudo-true value. A dual characterization based on random set theory makes the binding function computationally tractable. We define the auxiliary model conditionally on the covariates to remove its dependence on the unknown covariate distribution and we show that the binding function is Lipschitz and Hadamard directionally differentiable, so that the numerical delta method delivers valid critical values. We show that the method provides significant computational advantages without relinquishing informativeness in a simulation experiment based on an entry game with 100 potential entrants.

Explore related subjects

econ.EM

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Lixiong Li, Marc Henry. 2026-10-26. Indirect inference in incomplete and partially identified econometric models. https://arxiv.org/abs/2610.36206

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Valid Post-Contextual Bandit Inference

Contextual multi-armed bandits (CMAB) are increasingly used as adaptively sampled experiments, after which researchers test hypotheses about treatment effects. We derive the Hájek-Le Cam limit experiment for multi-armed contextual bandits under equal-arms (weak-signal) asymptotics. It is Locally Asymptotically Quadratic, but not a (mixed) Gaussian shift experiment. Girsanov's theorem gives it a structural representation in stochastic differential equations. Together with a general weak convergence result, this yields the asymptotic null distribution and local asymptotic power of often-used test statistics. Two kinds of nuisance parameters threaten size control: the common reward level of the arms of interest and the rewards of the arms not of interest. The first threat is removed by translation-invariant sampling. We propose Regularized Translation-Invariant (RTI) versions of Thompson, tempered-greedy, tempered-(Lin)UCB, and exploration sampling. The second threat calls for appropriate pivots. The structural representation of the limit experiment is key to overcome the inferential challenges arising from adaptive sampling. Simulations corroborate the theory.

econ.EM↗

arXiv2026

Bias Correction and Inference for Panel Quantile Regression

We develop a large-$n$, large-$T$ theory for the unsmoothed fixed-effects quantile regression estimator, paralleling Hahn and Newey (2004) for smooth nonlinear panel models. An exact rank-score identity for the profiled criterion, with a convexity argument, delivers the leading incidental parameter bias of the slope estimator, of order $T^{-1}$, in closed form. When $n$ and $T$ grow at the same rate, the estimator is asymptotically normal but in general not centred, and conventional intervals are invalid. Admissible growth of $n$ relative to $T$, up to $n=o(T^3)$, depends on the regularity of the conditional error densities. A split-panel jackknife removes the leading bias throughout this range and yields valid inference. In serially dependent panels whose dependence decays geometrically or polynomially, the bias acquires a term from the dependence between regressors and errors of different periods, the jackknife remains valid with contiguous but not with interleaved half-panels, and clustered standard errors are valid.

econ.EM↗

arXiv2026

Time-Varying Quantile VAR Models: Estimation and Inference

We study time-varying quantile VAR models in which the conditional quantile does not propagate linearly through the recursion, and develop a toolkit for impulse response analysis, which to the best of our knowledge has not been established elsewhere. For example, we establish Bahadur representation for quantile VAR regression, infer model parameters via smoothed check function, and define and investigate the best linear projection of the time-varying tau-quantile impulse response via local projections. An application to U.S. industrial production growth and credit spreads from 1919-2025 uncovers structural shifts in tail relationships, demonstrating downside asymmetry diminishes at longer forecast horizons.

econ.EM↗