Publications

Empirical models of multi-product demand rely on low-dimensional product representations to capture substitution patterns, increasingly using proxies built from unstructured data. When proxies are imperfect, standard workflows yield biased counterfactuals and invalid inference. We develop a practical toolkit to address these issues. Our methods apply to market-level and/or individual data, require minimal additional computation, provide simple standard-error formulas, and accommodate proxies from fine-tuned models. Further, we propose diagnostics to assess proxy quality. Our methods yield meaningful improvements in predicting substitution in empirically calibrated simulations and in an application where we assess counterfactual prediction performance against a ground truth.

Divorce reshapes family life, yet little is known about one of its most consequential features: the allocation of child custody. We study the impact of joint versus sole custody on both parents and children using rich administrative data from Sweden linked to over 25 years of newly-collected court custody rulings. To address selection concerns, we exploit random assignment of custody disputes to judges who differ sharply in their propensity to grant joint custody. For fathers, joint custody substantially raises earnings and improves mental health, consistent with sustained paternal involvement enhancing labor market attachment and psychological well-being. In contrast, there are no measurable labor market or mental health effects for mothers. Turning to children, joint custody increases standardized test scores and school quality without affecting mental health outcomes. Joint custody increases fathers’ chances of remarriage, keeps separated parents in closer geographic proximity, and has no effect on intimate partner violence allegations against either partner. These findings inform longstanding debates over the role of child custody in shaping post-divorce family life.

With uncertainty about persistence, we show that forecasts necessarily become more persistent and over-react at long horizons. For these reasons, correctly specified and Bayesian forecasts may under-react at short horizons and over-react at long horizons. These results provide a unified explanation for several asset pricing and forecasting puzzles, including: (i) the excess responsiveness of long-horizon rates to short rates, (ii) the dominance of apparent term premia for long-term rates, (iii) the ex post predictability of bond yields, (iv) the excess volatility of long-horizon forward prices, (v) the excess persistence of long-horizon forecasts, and (vi) the over-reaction of long-horizon forecasts.

Conversational recommender systems powered by generative AI can enhance personalization by facilitating information elicitation through follow-up questions. However, engaging in these conversations imposes a communication cost on users. As platforms with different objectives and monetization models deploy these systems, a central question is: how does the platform’s objective and sellers’ strategic response shape the design of these systems in terms of their elicitation strategy? We develop a parsimonious model of conversational elicitation in which interaction generates noisy preference information and imposes a communication cost borne by the user. A user-welfare-maximizing platform elicits more information when accurate niche matching yields large gains, even when niche users are rare. In contrast, under a conversion objective, for the same setting, the optimal strategy is to immediately recommend the same mainstream option to all users with no or minimal preference elicitation because the incremental conversion benefit from improved matching is bounded, while communication costs are borne by all users. When prices are endogenous and the platform earns a commission, increased elicitation is again optimal because improved screening raises equilibrium prices and platform revenue; however, these price responses can counteract consumer benefits and reduce user welfare. The model also highlights that the optimal elicitation intensity increases with preference heterogeneity, helping explain why conversational systems ask more in highly differentiated categories than in low-heterogeneity ones. We complement the theory with a dataset of long-form product queries that vary in length and informational content. Using our dataset and LLM-based user simulation, we quantify how additional information impacts user decisions and demonstrate that the magnitude of this impact depends on the degree of preference heterogeneity. Additionally, this dataset provides a testbed for measuring the (incremental) value of preference elicitation and may be of independent interest.

We study efficient dynamic mechanism design with independent private values when agents do not share a common prior over the stochastic environment. Each agent privately observes the stochastic kernel governing the evolution of her own type and may hold arbitrary beliefs about the kernels of others. We extend the agents’ type space to include the kernel itself and show that the dynamic team mechanism of Athey and Segal (2013) and the dynamic pivot mechanism of Bergemann and Välimäki (2010) implement the socially efficient allocation in periodic ex-post equilibrium. We further show that kernels can be elicited only once, at the outset, and that the same mechanisms induce the efficient private acquisition of the stochastic kernels.

Using 380 trillion tokens of realized AI consumption across more than four hundred large language models from the licensed proprietary OpenRouter dataset covering approximately 2 percent of current global monthly AI token consumption, we analyze how AI affects firms, markets, and workers. Leveraging the unprecedented size, scope and granularity data, we construct the AI Factor from growth in tokens, dollars, and users, estimate firm-level AI Betas from stock return comovement, and characterize the AI Premium. First, we build a high-frequency AI factor and decompose it into salient components. Second, we show that firms whose returns covary more positively with the AI factor—high AI beta firms—earn higher subsequent returns, and the AI premium is large and heterogeneous. A value-weighted long-short strategy earns 64.1 basis points per week, and the premium is large for loadings on the intensive, frontier-oriented margin of AI consumption—closed-source models, paying and seasoned users, and long prompts—but not on casual or open-weight use. Third, the premium reaches beyond technology firms into consumer-facing and capital-heavy parts of the economy, but is absent in emerging markets, including China. Fourth, the AI exposure is more positive in nonroutine interactive work and more negative in analytical, scientific, and operations-control skills—an occupation one standard deviation higher in interaction-and-communication content has 0.36-standard-deviation higher market-implied AI exposure. Additionally, we provide early evidence of the rise of the agentic economy.

Between 1880 and 1920, more than 20 million immigrants settled in the United States. We study how this migration wave affected innovation and growth. Using a newly constructed dataset linking individual census records to historical immigration records and the universe of US patents, we highlight a new channel through which immigrants contributed to growth: they disproportionately settled in urban innovation hubs. To quantify the aggregate and regional effects of this mass migration episode, we develop a new spatial growth model in which skilled workers have a comparative advantage in innovation and sort endogenously across space. We find that international arrivals after 1880 raised US income per capita by 8.2% by 1940. Removing the subsequent immigration restrictions of the 1920s would have raised income per capita by a further 1.7% by 2000. Immigrants’ skill composition and their concentration in urban hubs are key drivers of these effects.

Originally the author envisioned this book as an exposition of some asymptotic methods used for developing statistical and econometric theory. However, over the years the focus shifted towards the inequalities and approximations at the core of those methods. In part, the book evolved into an attempt to explain how tricks invented to solve specific problems in one area can turn into general tools applicable in many areas; it attempts to shed light on the mystery of how anyone could come up with such clever ideas. As the book tries to explain, the story often starts from a small insight that slowly gets transformed into an imposing theory where motivating ideas lie hidden behind clever definitions. (Sometimes, plain old Calculus plus a smidgen of convexity magic are at work behind the scenes.) The main topics are: exponential inequalities for both sums of independent random variables and martingales; path methods for gaussian processes; maximal inequalities, with their extension via chaining arguments to uniform bounds for large (or infinite) index sets; symmetrization and the combinatorial methods initiated by Vapnik and Chervonenkis; and concentration inequalities. The final chapters also describe some ways to handle dependence.

We analyze consumer surplus when a monopolist can adjust both prices and prod-uct qualities across segments, engaging in second- and third-degree price discrimination simultaneously. We characterize the consumer-optimal segmentation and show that it has a striking structure: consumers with the same value receive the same quality in every segment, though prices differ. Under mild conditions, any segmentation harms consumers if and only if demand is sufficiently more elastic than supply. Hence, po-tential benefits for consumers depend critically on demand and supply elasticities. These findings have implications for regulatory policy regarding price discrimination and market segmentation.

The "deep learning revolution" has led to remarkable success of neural networks in applications across a wide range of fields, such as computer vision, speech recognition, natural language processing, code generation, protein structure prediction, image and video generation, and dynamic control. This review introduces neural networks to economists. Recent advances and challenges in approximation theory, neural network architecture, computation, econometric theory and practice are presented. Finally, we survey the rapidly evolving applications of modern neural networks and Large Language Models in economic research.

This paper proposes a semi-endogenous growth theory that incorporates technology vintages and the endogenous evolution of multiple technological paradigms through innovation. It provides a characterization of both balanced growth equilibrium and transitional dynamics in an environment where new technologies continuously emerge. From a positive perspective, the model rationalizes two distinct empirical patterns. Using two centuries of US patent data, I first document that the age profile of patents has a pronounced hump shape: most contemporary patents build upon technologies that are between 50 and 100 years old. Second, this age profile has remained stable throughout the past century. From a normative standpoint, the theory underscores a misallocation of research effort induced by the tendency among profit-maximizing firms to overinvest in further developing mature technologies. This yields a suboptimally slow development of emerging technologies. According to a calibrated version of the model, correcting such misallocation could generate welfare gains of 7%.

Roughly one-third of U.S. households rent their homes, yet measuring who owns rental property is difficult: ownership is frequently obscured by LLCs, partnerships, and other intermediary entities that separate legal from economic control. We develop a method that traces ownership through administrative records—combining deeds and property assessments with the Census Bureau’s Business Register, IRS Schedule K-1 filings, and SEC filings on REITs—to identify ultimate owners and construct property portfolios across the full landlord size distribution. Applying the method to 11 large CBSAs, we find that individual landlords own a large majority of rental units, though their share varies meaningfully across markets. We also show that the widely used mailing-address aggregation approach both under- and over-states portfolio size in systematic ways. The method is designed to scale to national coverage and to support measurement of landlord identity, portfolio composition, and ownership concentration in U.S. rental markets. We also discuss the method’s current limitations and outline directions for refinement and validation.

This paper develops and applies new asymptotic theory for estimation and inference in parametric autoregression with function valued cross section curve time series. The study provides a new approach to dynamic panel regression with high dimensional dependent cross section data. Here we deal with the stationary case and provide a full set of results extending those of standard Euclidean space autoregression, showing how function space curve cross section data raises efficiency and reduces bias in estimation and shortens confidence intervals in inference. Methods are developed for high-dimensional covariance kernel estimation that are useful for inference. The findings reveal that function space models with wide-domain and narrow-domain cross section dependence provide insights on the effects of various forms of cross section dependence in discrete dynamic panel models with fixed and interactive fixed effects. The methodology is applicable to panels of high dimensional wide datasets that are now available in many longitudinal studies. An empirical illustration is provided that sheds light on household Engel curves among ageing seniors in Singapore using the Singapore life panel longitudinal dataset.

To meet voluntary climate targets, firms often complement internal decarbonization efforts by purchasing carbon credits in the voluntary carbon market (VCM), which finance projects that reduce emissions elsewhere. However, these emissions reductions are difficult to verify, and growing evidence of overcrediting has cast doubt on the VCM's potential to genuinely offset emissions. We investigate how the VCM's defining features shape its climate effectiveness. Our model captures three central elements: adverse selection, as high-quality projects that truly reduce emissions are costlier yet difficult to distinguish from low-quality ones; imperfect third-party certification, as projects are screened based on a noisy signal of quality; and buyer preferences for non-carbon attributes, as some firms value credits that generate observable social or economic co-benefits beyond reducing emissions. We show that the market fails to sustain trade if certification is sufficiently noisy, as quality uncertainty erodes buyer confidence and triggers a market-for-lemons collapse. However, demand for co-benefits can sustain markets that would otherwise collapse. Yet in such cases, the market remains active but yields limited carbon abatement, as most traded credits are low-quality. We then examine policy and market design interventions reflecting recent developments in practice, such as penalizing buyers for greenwashing and offering credit portfolios. We show that these measures can be counterproductive for carbon mitigation if certification remains inaccurate. Accordingly, we demonstrate that the certifier’s incentives for accuracy can be strengthened by modifying its fee structure so that its revenue is tied to the market value rather than the volume of credits.

We document and explain the gap between measures of AI exposure and measures of AI adoption in the workplace. This leads us to propose a new AI adoption index based on comparative advantage. Using the representative German DiWaBe employee survey linked to worker and establishment information, we compare worker-reported AI use to prominent exposure measures and find that the relationship is weak. Motivated by this gap, we develop a framework in which adoption depends not only on technical feasibility—AI’s absolute advantage measured by exposure—but on profitability—AI’s comparative (dis)advantage relative to a specific worker—balancing AI productivity against AI user costs and worker productivity against wages. We operationalize this framework at the task level by (i) estimating worker productivity relative to pay, (ii) mapping exposure indices into AI productivity, and (iii) inferring task-specific AI user costs from revealed-preference adoption. The resulting occupation-level index accounts for 60% of cross-occupation variation in observed AI adoption, compared to 14% for an exposure-only model. The two approaches diverge substantially for approximately 30% of workers, highlighting that comparative advantage—not exposure alone—is crucial for assessing AI’s labor-market impact.