Understanding the causal effects of text on downstream outcomes is a central task in many applications. Estimating such effects requires researchers to run controlled experiments that systematically vary textual features. While large language models (LLMs) hold promise for generating text, producing and evaluating controlled variation requires more careful attention. In this paper, we present an end-to-end pipeline for the generation and causal estimation of latent textual interventions. Our work first performs hypothesis generation and steering via sparse autoencoders (SAEs), followed by robust causal estimation. Our pipeline addresses both computational and statistical challenges in text-as-treatment experiments. We demonstrate that naive estimation of causal effects suffers from significant bias as text inherently conflates treatment and covariate information. We describe the estimation bias induced in this setting and propose a solution based on covariate residualization. Our empirical results show that our pipeline effectively induces variation in target features and mitigates estimation error, providing a robust foundation for causal effect estimation in text-as-treatment settings.

Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly subsidies are commonly required. We propose a new pricing scheme for nonconvex markets with both discreteness and nonlinearity, by convexifying nonconvex structures through a semidefinite programming (SDP) relaxation and deriving prices from the relaxation's dual variables. When the choice set is bounded, we establish strong duality for the SDP, which allows us to extend the envelope theorem to the value function of the relaxation. This extension yields a marginal price signal for demand, which we use as our pricing mechanism. We demonstrate that under certain conditions-for instance, when the relaxation's right hand sides are linear in demand-the resulting lost opportunity cost is bounded by the relaxation's optimality gap. This result highlights the importance of achieving tight relaxations. The proposed framework applies to nonconvex electricity market problems, including for both direct current and alternating current UC. Our numerical experiments indicate that the SDP relaxations are often tight, reinforcing the effectiveness of the proposed pricing scheme. Across a suite of IEEE benchmark instances, the lost opportunity cost under our pricing scheme is, on average, 46% lower than that of the commonly used fixed-binary pricing scheme.

Minimizing volatility and adjustment costs is of central importance in many economic environments, yet it is often complicated by evolving feasibility constraints. We study a decision maker who repeatedly selects an action from a stochastically evolving interval of feasible actions in order to minimize either average adjustment costs or variance. We show that for strictly convex adjustment costs (such as quadratic variation), the optimal decision rule is a reference rule in which the decision maker minimizes the distance to a target action. In general, the optimal target depends both on the previous action and the expectation of future constraints; but for the special case where the constraints follow a random walk, the optimal mechanism is to simply target the previous action. If the decision maker minimizes variance, the optimal policy is also a reference rule, but the target is a constant, which is not necessarily equal to the long-term average action. Compared to mid-point heuristics, these optimal rules may substantially reduce quadratic variation and variance, in natural environments by $50\%$ or more. Applied to stock market auctions, our results provide an explanation for the wide-spread use of reference price rules. We also apply our results to bilateral trade in over-the-counter markets, capacity planning in supply chains, and positioning in political agenda setting.

This article investigates the causal antecedents of conflictual language and the geometry of interaction in online threaded conversations related to climate change. We employ three annotation dimensions, inferred through LLM prompting and averaging, to capture complementary aspects of discursive conflict (such as stance: agreement vs disagreement; tone: attacking vs respectful; and emotional versus factual framing) and use data from a threaded online forum to examine how these dimensions respond to temporal, conversational, and arborescent structural features of discussions. We show that, as suggested by the literature, longer delays between successive posts in a thread are associated with replies that are, on average, more respectful, whereas longer delays relative to the parent post are associated with slightly less disagreement but more emotional (less factual) language. Second, we characterize alignment with the local conversational environment and find strong convergence both toward the average stance, tone and emotional framing of older sibling posts replying to the same parent and toward those of the parent post itself, with parent post effects generally stronger than sibling effects. We further show that early branch-level responses condition these alignment dynamics, such that parent-child stance alignment is amplified or attenuated depending on whether a branch is initiated in agreement or disagreement with the discussion's root message. These influences are largely additive for civility-related dimensions (attacking vs respectful, disagree vs agree), whereas for emotional versus factual framing there is a significant interaction: alignment with the parent's emotionality is amplified when older siblings are similarly aligned.

Adaptive randomized experiments update treatment probabilities as data accrue, but still require an end-of-study interval for the average treatment effect (ATE) at a prespecified horizon. Under adaptive assignment, propensities can keep changing, so the predictable quadratic variation of AIPW/DML score increments may remain random. When no deterministic variance limit exists, Wald statistics normalized by a single long-run variance target can be conditionally miscalibrated given the realized variance regime. We assume no interference, sequential randomization, i.i.d. arrivals, and executed overlap on a prespecified scored set, and we require two auditable pipeline conditions: the platform logs the executed randomization probability for each unit, and the nuisance regressions used to score unit $t$ are constructed predictably from past data only. These conditions make the centered AIPW/DML scores an exact martingale difference sequence. Using self-normalized martingale limit theory, we show that the Studentized statistic, with variance estimated by realized quadratic variation, is asymptotically N(0,1) at the prespecified horizon, even without variance stabilization. Simulations validate the theory and highlight when standard fixed-variance Wald reporting fails.

The stable unit treatment value (SUTVA) is a crucial assumption in the Difference-in-Differences (DiD) research design. It rules out hidden versions of treatment and any sort of interference and spillover effects across units. Even if this is a strong assumption, it has not received much attention from DiD practitioners and, in many cases, it is not even explicitly stated as an assumption, especially the no-interference assumption. In this technical note, we investigate what the DiD estimand identifies in the presence of unknown interference. We show that the DiD estimand identifies a contrast of causal effects, but it is not informative on any of these causal effects separately, without invoking further assumptions. Then, we explore different sets of assumptions under which the DiD estimand becomes informative about specific causal effects. We illustrate these results by revisiting the seminal paper on minimum wages and employment by Card and Krueger (1994).

We consider an agent with a rationally inattentive preference over menus of acts, as in de Oliveira et al (2017). We show that two axioms, Independence of Irrelevant Alternatives and Ignorance Equivalence, are necessary and sufficient for this agent to have a posterior-separable cost satisfying a mild smoothness condition, called joint-directional differentiability. Viewing the decision-maker's problem as a Bayesian persuasion problem, we also show that these axioms are necessary and sufficient for solvability by a unique hyperplane. When the cost function remains invariant for different priors, we show that these axioms imply uniformly posterior separable costs that are differentiable.

We develop a resource-efficient methodology for measuring economic outlook in news text that combines document embeddings with synthetic training data generated by large language models. Applied to 27 million news articles, the resulting indicator significantly improves GDP growth forecast accuracy and captures sentiment shifts weeks before official releases, proving particularly valuable during crises. The indicator outperforms both survey-based benchmarks and traditional dictionary methods and is interpretable, allowing identification of specific drivers of economic sentiment. Our approach addresses key institutional constraints: it performs sentiment classification locally, enabling analyses of proprietary news content without transmission to external services while requiring minimal computational resources compared to direct large language model classification.

I study peer effects that arise from irreversible decisions in the absence of a standard social equilibrium. I model a latent sequence of decisions in continuous time and obtain a closed-form expression for the likelihood, which allows to estimate proposed causal estimands. The method avoids linear-in-means regression by modeling the (possibly unobserved) realized direction of causality, whose probability is identified. I provide identification and estimation results under two settings, several networks and one large network, while allowing for various forms of peer effect heterogeneity. Under (strong) data requirements, it is possible to separate endogenous, contextual, and correlated effects while allowing for full heterogeneity and maximum likelihood methods where parameters lend themselves to standard inference.

In this paper, we review modern approaches to building interpretable models of property markets using machine learning on the base of mass valuation of property in the Primorye region, Russia. There are numerous potential difficulties one could encounter in the effort to build a good model. Their main source is the huge difference between noisy real market data and ideal data usually used in tutorials on machine learning. This paper covers all stages of modeling: collection of initial data, identification of outliers, search and analysis of patterns in the data, formation and final choice of price factors, building of the model, and evaluation of its efficiency. For each stage, we highlight potential issues and describe sound methods for overcoming emerging difficulties on actual examples. We show that the combination of classical linear regression with kriging (interpolation method of geostatistics) allows to build an effective model for land parcels. For flats, when many objects are attributed to one spatial point, the application of geostatistical methods becomes problematic. Instead, we suggest linear regression with automatic generation and selection of additional rules on the base of decision trees, so called the RuleFit method. We compare the performance of our inherently interpretable models with well-proven "black-box" Random Forest method and demonstrate similar results. Thus we show, that despite such a strong restriction as the requirement of interpretability which is important in practical aspects, for example, legal matters, it is still possible to build effective models of real property markets.

Accurately measuring consumer emotions and evaluations from unstructured text remains a core challenge for marketing research and practice. This study introduces the Linguistic eXtractor (LX), a fine-tuned, large language model trained on consumer-authored text that also has been labeled with consumers' self-reported ratings of 16 consumption-related emotions and four evaluation constructs: trust, commitment, recommendation, and sentiment. LX consistently outperforms leading models, including GPT-4 Turbo, RoBERTa, and DeepSeek, achieving 81% macro-F1 accuracy on open-ended survey responses and greater than 95% accuracy on third-party-annotated Amazon and Yelp reviews. An application of LX to online retail data, using seemingly unrelated regression, affirms that review-expressed emotions predict product ratings, which in turn predict purchase behavior. Most emotional effects are mediated by product ratings, though some emotions, such as discontent and peacefulness, influence purchase directly, indicating that emotional tone provides meaningful signals beyond star ratings. To support its use, a no-code, cost-free, LX web application is available, enabling scalable analyses of consumer-authored text. In establishing a new methodological foundation for consumer perception measurement, this research demonstrates new methods for leveraging large language models to advance marketing research and practice, thereby achieving validated detection of marketing constructs from consumer data.

This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the proposed test and show that it can detect local alternatives at the parametric rate. Using the nonparametric orthogonal projection, we construct a computationally convenient multiplier bootstrap to obtain critical values from the case-dependent asymptotic null distribution. Compared with the existing literature, our approach overcomes the need for a stronger compact support assumption on the density of covariates arising from random denominators. We also extend the tailor-made projection procedure to test the conditional independence assumption. The simulation experiments further illustrate the advantages of our proposed method in testing significance and conditional independence in finite samples.

We study how a decision-maker (DM) learns from data of unknown quality to form robust, ''general-purpose'' posterior beliefs. We develop a framework for robust learning and belief formation under a minimax-regret criterion, cast as a zero-sum game: the DM chooses posterior beliefs to minimize ex-ante regret, while an adversarial Nature selects the data-generating process (DGP). We show that, in large samples of $n$ signal draws, Nature optimally induces ambiguity by choosing a process whose precision converges to the uninformative signals at the rate $1/\sqrt{n}$. As a result, learning against the adversarial DGP is nontrivial as well as incomplete: the DM's ex-ante regret remains strictly positive even with an infinite amount of data. However, when the true DGP is fixed and informative (even if only slightly), our DM with a robust updating rule eventually learns the state with enough data. Still, learning occurs at a sub-exponential rate -- quantifying the asymptotic price of robustness -- and it exhibits ''under-inference'' bias. Our framework provides a decision-theoretic dual to the local alternatives method in asymptotic statistics, deriving the characteristic $1/\sqrt{n}$-scaling endogenously from the signal ambiguity.

Travel time prediction is central to transport geography and planning's accessibility analyses, sustainable transportation infrastructure provision, and active transportation interventions. However, calculating accurate travel times, especially for driving, requires either extensive technical capacity and bespoke data, or resources like the Google Maps API that quickly become prohibitively expensive to analyze thousands or millions of trips necessary for metropolitan-scale analyses. Such obstacles particularly challenge less-resourced researchers, practitioners, and community advocates. This article argues that a middle-ground is needed to provide reasonably accurate travel time predictions without extensive data or computing requirements. It introduces a free, open-source minimally-congested driving time prediction model with minimal cost, data, and computational requirements. It trains and tests this model using the Los Angeles, California urban area as a case study by calculating naive travel times from open data then developing a random forest model to predict travel times as a function of those naive times plus open data on turns and traffic controls. Validation shows that this interpretable machine learning method offers a superior middle-ground technique that balances reasonable accuracy with minimal resource requirements.

This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and controls, inference on variance components, and testing multiple restrictions in a linear regression. Na\"ıve plug-in estimators are known to be biased. We study a leave-one-cluster-out estimator that is unbiased, and provide sufficient conditions for its asymptotic normality. For inference, we establish the consistency of a leave-three-cluster-out variance estimator under primitive conditions. In addition, we develop a novel leave-two-cluster-out variance estimator that is computationally simpler and guaranteed to be conservative under weaker conditions. Our analysis allows cluster sizes to diverge with the sample size, accommodates strong within-cluster dependence, and permits the dimension of the covariates to diverge with the sample size, potentially at the same rate.

Generative AI is directional: it performs well in some task directions and poorly in others. Knowledge work is directional and endogenous as well: workers can satisfy the same job requirements with different mixes of tasks. We develop a high-dimensional model of AI adoption in which a worker uses a tool when it raises their output. Both the worker and the AI tool can perform a variety of tasks, which we model as convex production possibility sets. Because the tool requires supervision from the worker's own time and attention budget, adoption is a team-production decision, similar to hiring a coworker. The key sufficient statistics are the worker's pre-AI shadow prices: these equal the output gain from a small relaxation in each task direction, and they generally differ from the worker's observed activity mix. As AI capability improves, the set of adopted directions expands in a cone centered on these autarky prices. Near the entry threshold, small capability improvements generate large extensive-margin expansions in adoption. The model also delivers a structured intensive margin: between the entry and all-in thresholds, optimal use is partial. We parametrize the model in a simple but flexible way that nests most existing task-based models of technical change.

We develop a computationally efficient framework for quasi-Bayesian inference based on linear moment conditions. The approach employs a delayed acceptance Markov chain Monte Carlo (DA-MCMC) algorithm that uses a surrogate target kernel and a proposal distribution derived from an approximate conditional posterior, thereby exploiting the structure of the quasi-likelihood. Two implementations are introduced. DA-MCMC-Exact fully incorporates prior information into the proposal distribution and maximizes per-iteration efficiency, whereas DA-MCMC-Approx omits the prior in the proposal to reduce matrix inversions, improving numerical stability and computational speed in higher dimensions. Simulation studies on heteroskedastic linear regressions show substantial gains over standard MCMC and conventional DA-MCMC baselines, measured by multivariate effective sample size per iteration and per second. The Approx variant yields the best overall throughput, while the Exact variant attains the highest per-iteration efficiency. Applications to two empirical instrumental variable regressions corroborate these findings: the Approx implementation scales to larger designs where other methods become impractical, while still delivering precise inference. Although developed for moment-based quasi-posteriors, the proposed approach also extends to risk-based quasi-Bayesian formulations when first-order conditions are linear and can be transformed analogously. Overall, the proposed algorithms provide a practical and robust tool for quasi-Bayesian analysis in statistical applications.

In the context of macroeconomic/financial time series, the FARS package provides a comprehensive framework in R for the construction of conditional densities of the variable of interest based on the factor-augmented quantile regressions (FA-QRs) methodology, with the factors extracted from multi-level dynamic factor models (ML-DFMs) with potential overlapping group-specific factors. Furthermore, the package also allows the construction of measures of risk as well as modeling and designing economic scenarios based on the conditional densities. In particular, the package enables users to: (i) extract global and group-specific factors using a flexible multi-level factor structure; (ii) compute asymptotically valid confidence regions for the estimated factors, accounting for uncertainty in the factor loadings; (iii) obtain estimates of the parameters of the FA-QRs together with their standard deviations; (iv) recover full predictive conditional densities from estimated quantiles; (v) obtain risk measures based on extreme quantiles of the conditional densities; and (vi) estimate the conditional density and the corresponding extreme quantiles when the factors are stressed.

Motivated by applications such as cloud computing, gig platforms, and blockchain auctions, we study optimal selling mechanisms for dynamic markets with stochastic supply and demand. In our model, buyers with private valuations and homogeneous goods arrive stochastically and can be held in queues at a cost. The optimal mechanism pairs allocative efficiency with dynamic admission control: goods are assigned to the highest-value buyer, while entry is restricted by value thresholds that strictly increase with the queue length and decrease with available inventory. This policy smooths competitive pressure across time and is implemented in dominant strategies via auctions with dynamic reserve prices.

Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains why Smithson's argument is invalid. It also contains new results on the structure of the set of fixed points and monotone comparative statics.

Contractual relationships between the state and private firms involving large irreversible investments are vulnerable to sovereign hold-up risk: anticipating that the state can unilaterally revise terms once capital is sunk, firms may underinvest. Causal evidence on this mechanism is scarce because sovereign commitment is typically bundled with broader institutional quality. We overcome this identification challenge by exploiting a natural experiment in the North Sea oil and gas industry. In 1985, a Norwegian Supreme Court ruling declared retroactive changes to petroleum licenses unconstitutional, while the UK retained the discretion to revise contracts. Using granular data on the universe of fields and firms from 1975 to 1995, we estimate the impact of this strengthening of sovereign commitment on the adoption of Enhanced Oil Recovery (EOR), a major extraction technology requiring large irreversible investments. Firms exposed to the ruling sharply increased EOR adoption and productivity, gaining market share through aggressive portfolio expansion. We find that private firms with preexisting EOR expertise -- rather than state-owned enterprises -- drove this transformation, leveraging this expertise to diversify into riskier geologies and adopt complementary technologies. These findings establish sovereign commitment as a primary determinant of investment and technology adoption. By tying the state's hands, the ruling transformed promises into credible commitments, effectively functioning as an industrial policy that unlocked a trajectory of technological deepening. While such constitutional protections are critical for investment, a global survey of constitutions reveals that only 30.6% of countries prohibit retroactive legislation beyond criminal law.