In this paper, we extend the Riesz representation framework to causal inference under sample selection, where both treatment assignment and outcome observability are non-random. Formulating the problem in terms of a Riesz representer enables stable estimation and a transparent decomposition of omitted variable bias into three interpretable components: a data-identified scale factor, outcome confounding strength, and selection confounding strength. For estimation, we employ the ForestRiesz estimator, which accounts for selective outcome observability while avoiding the instability associated with direct propensity score inversion. We assess finite-sample performance through a simulation study and show that conventional double machine learning approaches can be highly sensitive to tuning parameters due to their reliance on inverse probability weighting, whereas the ForestRiesz estimator delivers more stable performance by leveraging automatic debiased machine learning. In an empirical application to the gender wage gap in the U.S., we find that our ForestRiesz approach yields larger treatment effect estimates than a standard double machine learning approach, suggesting that ignoring sample selection leads to an underestimation of the gender wage gap. Sensitivity analysis indicates that implausibly strong unobserved confounding would be required to overturn our results. Overall, our approach provides a unified, robust, and computationally attractive framework for causal inference under sample selection.

One thread of empirical work in social science focuses on decomposing group differences in outcomes into unexplained components and components explained by observable factors. In this paper, we study gender wage decompositions, which require estimating the portion of the gender wage gap explained by career histories of workers. Classical methods for decomposing the wage gap employ simple predictive models of wages which condition on a small set of simple summaries of labor history. The problem is that these predictive models cannot take advantage of the full complexity of a worker's history, and the resulting decompositions thus suffer from omitted variable bias (OVB), where covariates that are correlated with both gender and wages are not included in the model. Here we explore an alternative methodology for wage gap decomposition that employs powerful foundation models, such as large language models, as the predictive engine. Foundation models excel at making accurate predictions from complex, high-dimensional inputs. We use a custom-built foundation model, designed to predict wages from full labor histories, to decompose the gender wage gap. We prove that the way such models are usually trained might still lead to OVB, but develop fine-tuning algorithms that empirically mitigate this issue. Our model captures a richer representation of career history than simple models and predicts wages more accurately. In detail, we first provide a novel set of conditions under which an estimator of the wage gap based on a fine-tuned foundation model is $\sqrt{n}$-consistent. Building on the theory, we then propose methods for fine-tuning foundation models that minimize OVB. Using data from the Panel Study of Income Dynamics, we find that history explains more of the gender wage gap than standard econometric models can measure, and we identify elements of history that are important for reducing OVB.

Women have faced gender-based discrimination in the workforce throughout history, denied employment in all but a handful of subservient roles, regularly ignored for promotions and pay raises -- and rarely ever compensated at the same rates as their male peers. This long and storied socioeconomic tradition of financially screwing over half the population continues largely unabated into the 21st century where women still make 84 cents on the dollar that men do. In her new book, The Equality Machine: Harnessing Digital Technology for a Brighter, More Inclusive Future, Professor of Law and founding member of the Center for Intellectual Property Law and Markets at the University of San Diego, Dr. Orly Lobel, explores how digital technologies, often maligned for their roles in exacerbating societal ills, can be harnessed to undo the damage they've caused. This article has been excerpted from The Equality Machine: Harnessing Digital Technology for a Brighter, More Inclusive Future by Orly Lobel. For years, the double standard was glaring: employers demanded secrecy about salaries while asking prospective employees for their salary histories.

As we saw in Minding the Gender Gap, women still lag far behind men in the tech field, both in terms of representations (which hovers around 25% in the United States), and in terms of pay, where the gap between men and women is close to 12%. While figures for pay disparity in tech don't focus on specialists in artificial intelligence (AI), female representation there is even lower. According to the report, Discriminating Systems: Gender, Race, and Power, conferences women make up only 18% of the represented authors at AI conferences and less than 20% of AI professors. They fare even worse in corporations where they make up only 15% of research staff positions at Facebook and a mere 10% at Google. Join nearly 200,000 subscribers who receive actionable tech insights from Techopedia.

In 2016, the majority of full-time employed women in the U.S. earned significantly less than comparable men. The extent to which women were affected by gender inequality in earnings, however, depended greatly on socio-economic characteristics, such as marital status or educational attainment. In this paper, we analyzed data from the 2016 American Community Survey using a high-dimensional wage regression and applying double lasso to quantify heterogeneity in the gender wage gap. We found that the gap varied substantially across women and was driven primarily by marital status, having children at home, race, occupation, industry, and educational attainment. We recommend that policy makers use these insights to design policies that will reduce discrimination and unequal pay more effectively.