This paper studies the impact of generative AI on U.S. households' task allocation at home, using detailed Internet browsing data from a large sample of home devices between 2021 and 2024. Leveraging pre-ChatGPT browsing patterns, we measure households' exposure to ChatGPT and use it as an instrument for ChatGPT adoption during the post-release period. Our IV estimates show that adopting generative AI substantially increases leisure browsing on home devices while leaving time spent on productive digital tasks unchanged. To examine mechanisms, we infer the purpose of households' ChatGPT use from surrounding internet activity and find that households primarily employ it for productive non-market tasks. Together, these results suggest that generative AI frees up leisure time by raising the efficiency of productive digital activities. Interpreting these findings through a standard time-allocation model implies economically large productivity gains from generative AI at home.

We propose a focused weighted-average least squares (FWALS) estimator that addresses the computational burden of focused model averaging. By semi-orthogonalizing auxiliary regressors, the weighting problem is reduced from $2^{k_2}$ sub-models to at most $k_2$ regressor-wise weights, yielding a tractable sub-optimal procedure. Under local-to-zero conditions, we derive the limiting distribution of FWALS for smooth focused functions and provide a plug-in AMSE criterion for data-driven weight selection. Simulations show that FWALS closely matches the focused information criterion (FIC) benchmark and delivers stable performance when focused function is designed for impulse response function. Prior-based WALS can be competitive in some settings, but its performance depends on the signal regime and the design of focused parameter. Overall, FWALS offers a practical and robust alternative with substantial computational savings.

As AI systems enter institutional workflows, workers must decide whether to delegate task execution to AI and how much effort to invest in verifying AI outputs, while institutions evaluate workers using outcome-based standards that may misalign with workers' private costs. We model delegation and verification as the solution to a rational worker's optimization problem, and define worker quality by evaluating an institution-centered utility (distinct from the worker's objective) at the resulting optimal action. We formally characterize optimal worker workflows and show that AI induces *phase transitions*, where arbitrarily small differences in verification ability lead to sharply different behaviors. As a result, AI can amplify workers with strong verification reliability while degrading institutional worker quality for others who rationally over-delegate and reduce oversight, even when baseline task success improves and no behavioral biases are present. These results identify a structural mechanism by which AI reshapes institutional worker quality and amplifies quality disparities between workers with different verification reliability.

Range-based volatility estimators are widely used in financial econometrics to quantify risk and market stress, yet their application to local commodity markets remains limited. This paper shows how open-high--low-close (OHLC) volatility estimators can be adapted to monitor localized market distress across diverse development contexts, including conflict-affected settings, climate-exposed regions, remote and thinly traded markets, and import- and logistics-constrained urban hubs. Using monthly food price data from the World Bank's Real-Time Prices dataset, several volatility measures -- including the Parkinson, Garman-Klass, Rogers-Satchell, and Yang-Zhang estimators -- are constructed and evaluated against independently documented disruption timelines. Across settings, elevated volatility aligns with episodes linked to insecurity and market fragmentation, extreme weather and disaster shocks, policy and fuel-cost adjustments, and global supply-chain and trade disruptions. Volatility also detects stress that standard momentum indicators such as the relative strength index (RSI) can miss, including symmetric or rapidly reversing shocks in which offsetting supply and demand disturbances dampen net directional price movements while amplifying intra-period dispersion. Overall, OHLC-based volatility indicators provide a robust and interpretable signal of market disruptions and complement price-level monitoring for applications spanning financial risk, humanitarian early warning, and trade.

These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit combining probability theory, statistics, numerical methods, and empirical modeling, with a strong emphasis on implementation in Python. Core topics include random variables and distributions, moments and dependence, simulation and Monte Carlo methods, numerical optimization, root-finding, and time-series models commonly used in finance and macro-finance. Particular attention is paid to translating theoretical concepts into reproducible code, emphasizing vectorization, numerical stability, and interpretation of outputs. The notes progressively bridge theory and practice through worked examples and exercises covering asset pricing intuition, risk measurement, forecasting, and empirical analysis. By focusing on clarity, minimal prerequisites, and hands-on computation, these lecture notes aim to serve both as a pedagogical entry point for non-programmers and as a practical reference for applied researchers seeking transparent and replicable quantitative methods in finance.

Standard methods for determining the number of factors often overestimate the true number when data exhibit heavy-tailed randomness, misinterpreting noise-induced outliers as genuine factors. This paper addresses this challenge within the framework of Elliptical Factor Models (EFM), which accommodate both heavy tails and potential non-linear dependencies common in real-world data. We demonstrate, both theoretically and empirically, that heavy-tailed noise generates spurious eigenvalues that mimic true factor signals. To distinguish these, we propose a novel methodology based on a fluctuation magnification algorithm. Under mild conditions, we show that, by magnifying perturbations, the eigenvalues associated with real factors exhibit significantly less fluctuation (stabilizing asymptotically) than spurious eigenvalues arising from heavy-tailed effects. We develop a formal testing procedure based on this principle and apply it to the problem of accurately selecting the number of common factors in heavy-tailed EFMs. Simulation studies and real data analysis confirm the effectiveness of our approach, particularly in scenarios with pronounced heavy-tailedness.

We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have potentially heterogeneous risk preferences modeled by risk measures on a separable probability space. We derive the dual representation of the value function using a Strassen-type theorem for the weak-star topology and provide a characterization of the acceptance set using Aumann integration. These results are illustrated by explicit formulas when risk preferences are within the family of entropic and expected shortfall risk measures, and applications to Pareto efficiency in large markets.

We explore the behaviour emerging from learning agents repeatedly interacting strategically for a wide range of learning dynamics, including $Q$-learning, projected gradient, replicator and log-barrier dynamics. Going beyond the better understood classes of potential games and zero-sum games, we consider the setting of a general repeated game with finite recall under different forms of monitoring. We obtain a Folk Theorem-style result and characterise the set of payoff vectors that can be obtained by these dynamics, discovering a wide range of possibilities for the emergence of algorithmic collusion. Achieving this requires a novel technical approach, which, to the best of our knowledge, yields the first convergence result for multi-agent $Q$-learning algorithms in repeated games.

We study how market segmentation affects consumers when a monopolist can adjust both prices and product 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 more elastic than a cost-determined threshold. Hence, potential benefits for consumers depend critically on cost and demand elasticities. These findings have implications for regulatory policy regarding price discrimination and market segmentation.

The Reconstruction Finance Corporation and Public Works Administration loaned 50 U.S. railroads over $1.1 billion between 1932 and 1939. The government goal was to decrease the likelihood of bond defaults and increase employment. Bailouts had little effect on employment, instead they increased the average wage of their employees. Bailouts reduced leverage, but did not significantly impact bond default. Overall, bailing out railroads had little effect on their stock prices, but resulted in an increase in their bond prices and reduced the likelihood of ratings downgrades. We find some evidence that manufacturing firms located close to railroads benefited from bailout spillovers.

Digital advertising increasingly relies on visual content, yet marketers lack rigorous methods for understanding how specific visual attributes causally affect consumer engagement. This paper addresses a fundamental methodological challenge: estimating causal effects when the treatment, such as a model's skin tone, is an attribute embedded within the image itself. Standard approaches like Double Machine Learning (DML) fail in this setting because vision encoders entangle treatment information with confounding variables, producing severely biased estimates. We develop DICE-DML (Deepfake-Informed Control Encoder for Double Machine Learning), a framework that leverages generative AI to disentangle treatment from confounders. The approach combines three mechanisms: (1) deepfake-generated image pairs that isolate treatment variation; (2) DICE-Diff adversarial learning on paired difference vectors, where background signals cancel to reveal pure treatment fingerprints; and (3) orthogonal projection that geometrically removes treatment-axis components. In simulations with known ground truth, DICE-DML reduces root mean squared error by 73-97% compared to standard DML, with the strongest improvement (97.5%) at the null effect point, demonstrating robust Type I error control. Applying DICE-DML to 232,089 Instagram influencer posts, we estimate the causal effect of skin tone on engagement. Standard DML produces diagnostically invalid results (negative outcome R^2), while DICE-DML achieves valid confounding control (R^2 = 0.63) and estimates a marginally significant negative effect of darker skin tone (-522 likes; p = 0.062), substantially smaller than the biased standard estimate. Our framework provides a principled approach for causal inference with visual data when treatments and confounders coexist within images.

We develop a flexible neural demand system for continuous budget allocation that estimates budget shares on the simplex by minimizing KL divergence. Shares are produced via a softmax of a state-dependent preference scorer and disciplined with regularity penalties (monotonicity, Slutsky symmetry) to support coherent comparative statics and welfare without imposing a parametric utility form. State dependence enters through a habit stock defined as an exponentially weighted moving average of past consumption. Simulations recover elasticities and welfare accurately and show sizable gains when habit formation is present. In our empirical application using Dominick's analgesics data, adding habit reduces out-of-sample error by c.33%, reshapes substitution patterns, and increases CV losses from a 10% ibuprofen price rise by about 15-16% relative to a static model. The code is available at https://github.com/martagrz/neural_demand_habit .

The alignment tax is widely discussed but has not been formally characterized. We provide a geometric theory of the alignment tax in representation space. Under linear representation assumptions, we define the alignment tax rate as the squared projection of the safety direction onto the capability subspace and derive the Pareto frontier governing safety-capability tradeoffs, parameterized by a single quantity of the principal angle between the safety and capability subspaces. We prove this frontier is tight and show it has a recursive structure. safety-safety tradeoffs under capability constraints are governed by the same equation, with the angle replaced by the partial correlation between safety objectives given capability directions. We derive a scaling law decomposing the alignment tax into an irreducible component determined by data structure and a packing residual that vanishes as $O(m'/d)$ with model dimension $d$, and establish conditions under which capability preservation mediates or resolves conflicts between safety objectives.

We study allocation mechanisms that utilize costly signaling as a screening tool. A social planner aims to maximize social welfare, defined as the weighted sum of agents' utilities, while implementing a specific allocation rule. Within a broad class of agent preferences, we show that coordination mechanisms (where recommended signals depend on joint reports) can be outperformed by non-coordination mechanisms (where signals depend solely on individual reports). We formalize the conditions under which the optimal mechanism features no coordination and demonstrate that such mechanisms are implementable through coarse-ranking contests.

In an auction each party bids a certain amount and the one which bids the highest is the winner. Interestingly, auctions can also be used as models for other real-world systems. In an all pay auction all parties must pay a forfeit for bidding. In the most commonly studied all pay auction, parties forfeit their entire bid, and this has been considered as a model for expenditure on political campaigns. Here we consider a number of alternative forfeits which might be used as models for different real-world competitions, such as preparing bids for defense or infrastructure contracts.