Abstract
The Kitagawa-Oaxaca-Blinder decomposition splits the difference in means between two groups into an explained part, due to observable factors, and an unexplained part. In this paper, we reformulate this framework using potential outcomes, highlighting the critical role of the reference outcome. To address limitations like common support and model misspecification, we extend Neumark's (1988) weighted reference approach with a doubly robust estimator. Using Neyman orthogonality and double machine learning, our method avoids trimming and extrapolation. This improves flexibility and robustness, as illustrated by two empirical applications. Nevertheless, we also highlight that the decomposition based on the Neumark reference outcome is particularly sensitive to the inclusion of irrelevant explanatory variables.

AI Summary

• The paper reformulates the Kitagawa-Oaxaca-Blinder (KOB) decomposition using potential outcomes, highlighting the critical role of the reference outcome in defining explained and unexplained components. [3]
• Crucially, the equilibrium reference outcome eliminates the need for trimming or extrapolation, which are common practices in standard KOB decompositions to address common support issues, thereby improving robustness and data utilization. [3]
• The new construction of the unexplained part, based on the equilibrium reference outcome, is not analogous to Average Treatment Effect on the Treated (ATT) or Untreated (ATU), requiring specific orthogonality conditions to be verified for DML application. [3]
• While offering significant advantages, the decomposition based on the Neumark reference outcome is shown to be particularly sensitive to the inclusion of irrelevant explanatory variables, which is an important consideration for model specification. [3]
• The paper demonstrates that the common support assumption, often required for IPW and AIPW estimators in standard KOB, is not necessary when using the equilibrium reference outcome because the propensity score does not appear in the denominator of the identification equations. [3]
• Kitagawa-Oaxaca-Blinder (KOB) decomposition: A method to split the observed difference in means between two groups into an 'explained' part (due to observable characteristics) and an 'unexplained' part (due to differences in returns to characteristics or discrimination). [3]
• It extends Neumark's (1988) weighted reference approach by defining an 'equilibrium reference outcome' as a propensity score-weighted combination of potential outcomes, which intrinsically avoids the common support assumption. [2]
• The proposed method integrates a doubly robust estimator with Double Machine Learning (DML) and Neyman orthogonality to achieve root-n consistent and debiased estimation of decomposition components, even with high-dimensional covariates and potential model misspecification. [2]
• Reference outcome (Y(r)): A counterfactual outcome representing what an individual would receive under a specific hypothetical scenario (e.g., if paid according to the wage model of another group). [2]
• Common support assumption: The condition that for every combination of covariates observed in one group, there must be individuals with similar covariates in the other group, ensuring comparable 'alter egos'. [2]

Abstract
This paper investigates how market competition influences poverty dynamics using a functional econometric framework that captures both contemporaneous and lagged effects. Using annual data for 48 countries from 1991-2017, we estimate function-on-function regressions linking poverty headcount ratios to market concentration and other macroeconomic indicators. The results show that, based on the entire sample, stronger competition initially increased poverty during structural adjustment phases, but its adverse impact weakened after 2010 as economies adapted and efficiency gains emerged. The estimated bivariate surfaces reveal that the effect of competition on poverty often persists over multiple years (around 5 years), highlighting the importance of intertemporal transmission. Then, functional clustering based on market capitalization (MCAP) uncovers strong heterogeneity: pro-poor 5-years lagged effect of competition in low- and medium-MCAP economies, while it remains insignificant to weakly negative in high-MCAP countries. Overall, the findings underscore the value of functional data methods in uncovering evolving and lag-dependent poverty-competition linkages that static panel models fail to capture.

Abstract
In this work, we prove a critical version of a Hardy-Rellich type inequality. We show that for $N\geq 1$ there exists a constant $C_N>0$ such that \[ \int_{\mathbb R^N}\left|\nabla\left(\frac{u(x)}{|x|}\right)\right|^N\,\mathrm{d}x\leq C_N\int_{\mathbb R^N}\left|Δu(x)\right|^N\,\mathrm{d}x, \] for any $u\in C^\infty_c(\mathbb R^N\setminus\left\{0\right\})$.

Abstract
We propose a new approach to estimate selection-corrected quantiles of the gender wage gap. Our method employs instrumental variables that explain variation in the latent variable but, conditional on the latent process, do not directly affect selection. We provide semiparametric identification of the quantile parameters without imposing parametric restrictions on the selection probability, derive the asymptotic distribution of the proposed estimator based on constrained selection probability weighting, and demonstrate how the approach applies to the Roy model of labor supply. Using German administrative data, we analyze the distribution of the gender gap in full-time earnings. We find pronounced positive selection among women at the lower end, especially those with less education, which widens the gender gap in this segment, and strong positive selection among highly educated men at the top, which narrows the gender wage gap at upper quantiles.

Abstract
I introduce heterogeneity into the analysis of peer effects that arise from conformity, allowing the strength of the taste for conformity to vary across agents' actions. Using a structural model based on a simultaneous network game with incomplete information, I derive conditions for equilibrium uniqueness and for the identification of heterogeneous peer-effect parameters. I also propose specification tests to determine whether the conformity model or the spillover model is consistent with the observed data in the presence of heterogeneous peer effects. Applying the model to data on smoking and alcohol consumption among secondary school students, I show that assuming a homogeneous preference for conformity leads to biased estimates.