Working Papers

2023 - 2026

Abstract Neyman-orthogonal moments underpin debiased and double machine learning, yet their existence and informativeness are typically presumed. We characterize two oracle properties that orthogonal inference presupposes for a target--model pair: existence and relevance. Under conditions ensuring attainability by valid moment functions, nontrivial orthogonal moments exist when fixing the target restricts the observed-data distribution to first order---\emph{restricted local overidentification}. Under suitable target coordinates, informative moments exist when effective Fisher information is nonzero. Its rank---the \emph{relevance rank}---counts informative target directions: orthogonalization isolates information but cannot create it. Moment Jacobians give lower bounds on this rank; target changes offset by nuisance adjustments give upper bounds. When these bounds coincide, they identify the relevance rank without efficiency bounds calculations. Two examples illustrate the feasibility frontier. In sample selection without covariate exclusions, we characterize all orthogonal moments and obtain identification-robust inference under rank deficiency. In latent-variable models, an exact RKHS representation reveals why important distributional and threshold-policy targets admit no informative orthogonal moments.
Abstract Developing robust inference for models with nonparametric Unobserved Heterogeneity (UH) is both important and challenging. We propose novel Debiased Machine Learning (DML) procedures for valid inference on functionals of UH, allowing for partial identification of multivariate target and high-dimensional nuisance parameters. Our main contribution is a full characterization of all relevant Neyman-orthogonal moments in models with nonparametric UH, where relevance means informativeness about the parameter of interest. Under additional support conditions, orthogonal moments are globally robust to the distribution of the UH. They may still involve other high-dimensional nuisance parameters, but their local robustness reduces regularization bias and enables valid DML inference. We apply these results to: (i) common parameters, average marginal effects, and variances of UH in panel data models with high-dimensional controls; (ii) moments of the common factor in the Kotlarski model with a factor loading; and (iii) smooth functionals of teacher value-added. Monte Carlo simulations show substantial efficiency gains from using efficient orthogonal moments relative to ad-hoc choices. We illustrate the practical value of our approach by showing that existing estimates of the average and variance effects of maternal smoking on child birth weight are robust.
Abstract We consider treatment-effect estimation using a first-difference regression of an outcome evolution $\Delta Y$ on a treatment evolution $\Delta D$. Under a causal model in levels with a time-varying effect, the regression residual is a function of the period-one treatment $D_1$. Then, researchers should test if $\Delta D$ and $D_1$ are correlated: if they are, the regression may suffer from an omitted variable bias. To solve it, researchers may control nonparametrically for $\mathbb{E}\left[\Delta D|D_1\right]$. We use our results to revisit first-difference regressions estimated on the data of Acemoglu et al. (2016), who study the effect of imports from China on US employment. $\Delta D$ and $D_1$ are strongly correlated, thus implying that first-difference regressions may be biased if the effect of Chinese imports changes over time. The coefficient on $\Delta D$ is no longer significant when controlling for $\mathbb{E}\left[\Delta D|D_1\right]$.
Abstract This paper proposes a method to automatically construct or estimate Neyman-orthogonal moments in general models defined by a finite number of conditional moment restrictions (CMRs), with possibly different conditioning variables and endogenous regressors. CMRs are allowed to depend on non-parametric components, which might be flexibly modeled using Machine Learning tools, and non-linearly on finite-dimensional parameters. The key step in this construction is the estimation of Orthogonal Instrumental Variables (OR-IVs)—"residualized" functions of the conditioning variables, which are then combined to obtain a debiased moment. We argue that computing OR-IVs necessarily requires solving potentially complicated functional equations, which depend on unknown terms. However, by imposing an approximate sparsity condition, our method finds the solutions to those equations using a Lasso-type program and can then be implemented straightforwardly. Based on this, we introduce a GMM estimator of finite-dimensional parameters (structural parameters) in a two-step framework. We derive theoretical guarantees for our construction of OR-IVs and show √n-consistency and asymptotic normality for the estimator of the structural parameters. Our Monte Carlo experiments and an empirical application on estimating firm-level production functions highlight the importance of relying on inference methods like the one proposed.
Abstract Models with Conditional Moment Restrictions (CMRs) are popular in economics. These models involve finite and infinite dimensional parameters. The infinite dimensional components include conditional expectations, conditional choice probabilities, or policy functions, which might be flexibly estimated using Machine Learning tools. This paper presents a characterization of locally debiased moments for regular models defined by general semiparametric CMRs with possibly different conditioning variables. These moments are appealing as they are known to be less affected by first-step bias. Additionally, we study their existence and relevance. Such results apply to a broad class of smooth functionals of finite and infinite dimensional parameters that do not necessarily appear in the CMRs. As a leading application of our theory, we characterize debiased machine learning for settings of treatment effects with endogeneity, giving necessary and sufficient conditions. We present a large class of relevant debiased moments in this context. We then propose the Compliance Machine Learning Estimator (CML), based on a practically convenient orthogonal relevant moment. We show that the resulting estimand can be written as a convex combination of conditional local average treatment effects (LATE). Altogether, CML enjoys three appealing properties in the LATE framework: (1) local robustness to first-stage estimation, (2) an estimand that can be identified under a minimal relevance condition, and (3) a meaningful causal interpretation. Our numerical experimentation shows satisfactory relative performance of such an estimator. Finally, we revisit the Oregon Health Insurance Experiment, analyzed by Finkelstein et al. (2012)}. We find that the use of machine learning and CML suggest larger positive effects on health care utilization than previously determined.