Industry-academia ML collaborations routinely fail to launch -- not for scientific reasons, but because academics must publish while companies must protect models trained on proprietary data, and no standard contract framework resolves this tension. Because contracts are negotiated by legal departments alone, many apparent legal disputes are incentive misalignment problems that only scientists at the table can correctly diagnose. We propose PBOS (Protect-the-Business / Open-Source-the-Science), a community-adoptable contract template anchored to a single technically-grounded boundary: pre-training artifacts (architectures, training code, benchmarks, untrained weights) are open science; post-training artifacts (weights trained on proprietary data) are business IP. This boundary is technically meaningful, legally clean, and auditable -- and could not have been drawn correctly without scientists at the negotiating table. We argue the ML community should adopt PBOS as its default contract for such collaborations.

The emergence of large language models (LLMs) has spurred economists to study how humans and LLMs behave in strategic settings. We organized a series of round-robin tournaments in the Colonel Blotto game. This game attracts game theorists' attention due to high-dimensional action space and the absence of pure strategy Nash equilibria. In the first tournament, more than 200 human participants competed against one another. In the second tournament, several popular LLMs were invited to submit strategies. In the third tournament, we matched the number of LLM strategies to the number submitted by humans. We find that humans more often employ better-calibrated intermediate-level allocation heuristics and outperform the simpler, more stereotyped strategies submitted by LLMs. Strategic sophistication is key to success if and only if the necessary level of reasoning depth is reached, while lower and higher levels of reasoning offer no clear advantage over the primitive strategies. Among humans, field of study weakly predicts success: participants with STEM backgrounds perform better in the first tournament. Surprisingly, humans almost do not adjust their strategies across tournaments with different sets of opponents. This result suggests that humans base their choices primarily on the game's rules rather than on the identity of their opponents, treating LLMs much like human competitors.

We propose a new approach to inference in tightly identified and large-scale structural vector autoregressions based on a reparameterization that enables imposing identifying inequality restrictions through continuously differentiable mappings. Permitted inequality restrictions include shape and ranking restrictions as well as bounds on economically relevant elasticities, and the approach is also able to accommodate zero restrictions in a straightforward manner. We implement a Hamiltonian Monte Carlo algorithm and show how the posterior density can be rapidly evaluated under the reparameterization, thus facilitating inference in high-dimensional settings. Two empirical applications demonstrate that our approach tends to result in lower serial dependence in Markov chains, larger effective sample sizes and reduced computation time relative to existing methods.

We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria are characterized as follows: In equilibrium, the optimal indemnity function exhibits a layer-type structure, providing full insurance over any loss layer on which the policyholder is more pessimistic than the insurer's pricing functional about tail losses; and no insurance coverage over loss layers on which the policyholder is less pessimistic than the insurer's pricing functional about tail losses. In equilibrium, the optimal pricing distortion function is determined by the policyholder's degree of risk aversion, whereby prices never exceed the policyholder's marginal willingness to insure tail losses. Moreover, we show that both the insurance coverage and the insurer's expected profit increase with the policyholder's degree of risk aversion. Additionally, and echoing recent work in the literature, we show that equilibrium contracts are Pareto efficient, but they do not induce a welfare gain to the policyholder. Conversely, any Pareto-optimal contract that leaves no welfare gain to the policyholder can be obtained as an equilibrium contract. Finally, we consider a few examples of interest that recover some existing results in the literature as special cases of our analysis.

Recent developments in causal machine learning methods have made it easier to estimate flexible relationships between confounders, treatments and outcomes, making unconfoundedness assumptions in causal analysis more palatable. How successful are these approaches in recovering ground truth baselines? In this paper we analyze a new data sample including an experimental rollout of a new feature at a large technology company and a simultaneous sample of users who endogenously opted into the feature. We find that recovering ground truth causal effects is feasible -- but only with careful modeling choices. Our results build on the observational causal literature beginning with LaLonde (1986), offering best practices for more credible treatment effect estimation in modern, high-dimensional datasets.

A principal contracts with an agent through an informed delegate. Although the principal cannot directly mediate the interaction, she can restrict the menus of contracts the delegate may offer. We characterize the outcomes implementable through delegated contracting: they are exactly those achievable by a centralized Bayesian mechanism that is dominant-strategy incentive compatible and ex-post individually rational for the agent. We use this result to identify the optimal contractual restrictions in several settings. First, an organization that procures through a budget-indulgent agency should grant full flexibility below an expected spending cap. Second, unlike centralized mechanisms, delegated contracting can never dissolve partnerships efficiently, highlighting a limit to delegated authority. Finally, a seller can entrust sales to an intermediary without revenue loss by combining a resale price agreement with a buyback policy.

In this paper, we construct an analytical model of the data economy with empirical evidence to explain the nexus between dataization and technological progress in general equilibrium. Data originates from the dataization of firm total output and contributes to the formation and enhancement of technology. Firms use the production function with data to solve the optimal investment, while households use the endogenous interest rate from the firm problem to solve the optimal consumption. We find that dataization has a negative moderating effect on the transition of general equilibrium affected by technological progress. Policy can only facilitate a positive transition in general equilibrium by simultaneously encouraging dataization and technological progress. Furthermore, when equilibrium capital stock is in a stationary state, dataization enhances technological progress at high levels. However, when equilibrium consumption is in a stationary state, dataization enhances technological progress at low levels while weakening it at high levels. Our empirical analysis uses macroeconomic data and policy from Chinese cities between 2000 and 2021 to verify the theories proposed in this paper. We further apply the Mean Field Games in a continuous-time framework to provide an extended explanation for the nexus between dataization and technological progress in partial equilibrium.

Difference-in-Differences designs with staggered treatment adoption are widely used to study heterogeneous treatment effects across cohorts and time periods. We develop a probabilistic framework for estimating potentially high-dimensional ATT arrays that vary across cohorts, periods, and strata defined by baseline covariates. The framework jointly estimates subgroup-specific treatment effects through a unified likelihood-based model, stabilizing inference in sparse cohort-by-time-by-stratum settings. We establish a Bernstein-von Mises theorem for the ATT array, implying asymptotically valid frequentist coverage of posterior credible intervals. Simulations and an application to minimum wage increases and teen employment demonstrate meaningful finite-sample improvements and important subgroup heterogeneity.

We study relationships between dynamic programs by applying conjugacy methods from dynamical systems theory. When two dynamic programs are connected by an order isomorphism, we show that optimality properties transmit from one formulation to the other. We apply these results to Epstein--Zin preferences with time preference shocks, obtaining a sharp characterization of when optimality holds. We also show that multiplicative Kreps--Porteus preferences and risk-sensitive preferences are isomorphic, so that well-known results for the latter carry over to the former. Finally, we demonstrate how isomorphic transformations can improve the numerical accuracy of value function approximations, with gains of two orders of magnitude in a multisector real business cycle model.

Why do societies remain stuck in inferior institutions even when superior al ternatives are widely recognized? This paper develops a model in which agents choose not only actions within a game but also transformations of the game it self. Transformations may be soft, changing payoffs through taxes or subsidies, or hard, changing feasibility through deletion or replacement of actions. Within a coordination model with status-quo bias (switching cost) and boundedly rational play (logit quantal response), we show that these interventions are qualitatively different: finite taxes shift behavior continuously but cannot eliminate residual use of the inherited action, whereas deletion bypasses inertia by removing the action from the feasible set. We further characterize how antagonistic social preferences at the meta level can block reforms that are individually beneficial for every player. The framework provides a formal rationale for why hard feasibility restrictions of ten dominate soft price incentives under inertia, with direct applications to climate transition (carbon tax vs. fossil-fuel phase-out) and platform regulation (fines vs. deletion of addictive features).

Why do inefficient practices, technologies, or institutions persist even when su perior alternatives are available? This paper introduces a quantal response equilib rium with status-quo bias (QRE-SB) in which each player incurs a fixed switching cost when deviating from an inherited default action. In a binary coordination game, we compare two policy interventions: a tax on the default action (price-only reform) versus deleting the default action entirely (ban). We prove that there exists a threshold tax below which the status quo persists and above which a transition occurs; notably, this threshold does not depend on the degree of bounded ratio nality. Deleting the default action always forces play to the superior equilibrium, irrespective of switching costs or rationality. Moreover, when the superior equilib rium is Pareto-dominant, deletion yields strictly higher expected welfare than any finite tax that leaves the old action feasible. Numerical simulations illustrate the theoretical predictions. The framework provides a formal foundation for the policy principle that sometimes you must ban, not just tax, with direct applications to climate policy, social media regulation, and international sanctions.

The impact of rising consumption on wealth inequality remains an open question. Here we revisit and extend the Social Architecture of Capitalism agent-based model proposed by Ian Wright, which reproduces stylized facts of wealth and income distributions. In a previous study, we demonstrated that the macroscopic behavior of the model is predominantly governed by a single dimensionless parameter, the ratio between average wealth per capita and mean salary, denoted by R. The shape of the wealth distribution, the emergence of a two-class structure, and the level of inequality - summarized by the Gini index - were found to depend mainly on R, with inequality increasing as R increases. In the present work, we examine the robustness of this result by relaxing some simplifying assumptions of the model. We first allow transactions such as purchases, salary payments, and revenue collections to occur with different frequencies, reflecting the heterogeneous temporal dynamics of real economies. We then impose limits on the maximum fractions of wealth that agents can spend or collect at each step, constraining the amplitude of individual transactions. We find that the dependence of the inequality on R remains qualitatively robust, although the detailed distribution patterns are affected by relative frequencies and transaction limits. Finally, we analyze a further variant of the model with adaptive wages emerging endogenously from the dynamics, showing that self-organized labor-market feedback can either stabilize or amplify inequality depending on macroeconomic conditions.

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over-accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is above the bubbleless interest rate (the steady-state interest rate in the economy without the asset) but below the population growth rate, then bubbles are necessary in the sense that there exists no bubbleless equilibrium but there exists a unique bubbly equilibrium. We show that this result (as stated) is incorrect by presenting an example economy that satisfies all assumptions of Proposition 1(c) but its unique equilibrium is bubbleless. We also restore Proposition 1(c) under the additional assumptions that initial capital is sufficiently large and dividends are sufficiently small. We show through examples that these conditions are essential.

Priority-based allocation of individuals to positions are pervasive, and elimination of justified envy is often, an absolute requirement. This leaves serial dictatorship (SD) as the only rule that avoids justified envy under standard direct mechanisms. What if SD outcomes are undesirable from a designer's perspective? We propose visible fairness, which demands fairness relative to the (potentially purposefully incomplete) preference information the mechanism elicits. Visibly fair mechanisms generalize SD; we fully characterize them and provide necessary and sufficient conditions for strategy-proofness. We show how to apply these results to design strategy-proof visibly fair rules that satisfy a broad class of distributional objectives. Visible fairness, however, results in a new information-efficiency trade-off: meeting distributional goals leads to the avoidance of eliciation of information about preferences that could prevent inefficiencies.

In many causal inference applications, only one or a few units (or clusters of units) are treated. An important challenge in such settings is that standard inference methods relying on asymptotic theory may be unreliable, even with large total sample sizes. This survey reviews and categorizes inference methods designed to accommodate few treated units, considering cross-sectional and panel data methods. We discuss trade-offs and connections between different approaches. In doing so, we propose slight modifications to improve the finite-sample performance of some methods, and we also provide theoretical justifications for existing heuristic approaches that have been proposed in the literature.

I study dynamic contracting where Sender privately observes a Markovian state and seeks to motivate Receiver, who acts. Sender provides incentives in two ways: payments, which alter payoffs ex-post, and (Bayesian) persuasion, which shapes Receiver interim beliefs about payoffs. For all stage game payoffs, discount rates, and Markov transition rules, transfers are a last resort--there is an optimal contract where payments occur only after Sender commits to reveal the state at every continuation history. In an example, the optimal contract is a loyalty program: Sender chooses the static optimal information structure until a random promotion time, after which Sender reveals the state and pays Receiver.

This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant challenges due to the non-standard limiting behaviors of the corresponding estimator, which arise in settings with increasing dimension of parameters, non-smooth objectives, or constraints. We propose a simple and unified method that guarantees validity in both regular and irregular cases. We provide a unified treatment of validity, conservativeness, and the size of the resulting confidence sets. In particular, the presented width analysis demonstrates the adaptive behavior of the confidence set to the unknown degree of instance-specific regularity. We apply the proposed method to several high-dimensional and irregular statistical problems. Numerical results for all statistical applications are provided.

Applied Difference-in-Differences studies often involve outcomes that are discrete, mixed, censored, or otherwise non-continuously distributed, while policy questions frequently concern distributional effects rather than mean effects alone. This paper develops a distributional DiD framework for identifying and conducting uniform inference on distribution and quantile treatment effects on the treated in such settings under stated identifying and regularity conditions. Identification is based on distributional parallel trends and no-anticipation assumptions, illustrated through an economic model of crime that generates count-valued untreated potential outcomes. The identification and asymptotic theory accommodate staggered treatment adoption and a general sampling scheme encompassing repeated cross-sections, unbalanced panels, rotating panels, and balanced panels. The paper also proposes a test of functional over-identifying restrictions as a diagnostic for the identifying assumptions and working-CDF specification. An empirical application to the effect of police on crime illustrates the practical relevance of the approach and shows how distributional effects can be interpreted as event-probability effects for count outcomes.

This paper investigates how productivity dispersion relates to input misallocation in European manufacturing. The model features staggered productivity shocks that create wedges between anticipated and realized productivity for any production input. Using European firm-level data from 2001-2017, I show that, under the maintained model, shocks realized after inputs are committed are the largest contributor to marginal revenue product dispersion for every input, accounting for 75% of the variance for materials, 37% for labor, and 18% for capital. These results are consistent with input misallocation in European manufacturing reflecting post-commitment productivity shocks more than persistent heterogeneity across firms.