Regret is the cost of uncertainty in algorithmic decision-making. Quantifying regret typically requires computationally expensive simulation via Sample Average Approximation (SAA), with complexity $\mathcal{O}(Bn^{2}d^{3})$ in the number of scenarios $B$, variables $n$, and constraints $d$. % This paper proves that expected regret in any stochastic optimization problem admits the exact decomposition % \begin{equation*} \mathrm{Regret}(c) = \mathrm{Cov}(c,\,\pi^{*}(c)) + R(c), \end{equation*} % where $c$ is the vector of uncertain parameters, $\pi^{*}(c)$ is the optimal decision, and $R(c)$ is a residual whose magnitude we bound explicitly under Lipschitz, smooth, and strongly convex conditions. % For linear programs and unconstrained quadratic programs, including the classical Markowitz portfolio problem, we prove $R(c)=0$ exactly, so that $\mathrm{Regret}(c) = \mathrm{Cov}(c,\pi^{*}(c))$ holds without approximation. % When historical cost-decision pairs $\{(c_i, \pi^*(c_i))\}$ are available, the covariance can be estimated in $\mathcal{O}(nd^{2})$ time, which is orders of magnitude faster than SAA. The estimation is performed by a single pass through the data. % We derive concentration bounds, a central limit theorem, and an asymptotically unbiased residual estimator, and we validate all results on synthetic LP, QP, and integer programming instances and on a rolling-window portfolio experiment using ten years of CRSP equity data.

This paper extends the incomplete model of Haile and Tamer (2003) from static English auctions to sequential English auctions. Because bidders may wait for future opportunities, the static condition that bidders do not let rivals win at beatable prices need not hold. We replace it with a dynamic opportunity-cost restriction, yielding nonparametric valuation bounds without solving a dynamic equilibrium. Sharp bounds are also characterized. We propose a novel moment-condition inversion estimator that pools auctions with heterogeneous bidder counts, mitigating finite-sample instability of order statistics approaches and admitting analytical standard errors and smooth confidence intervals. Applications to Korean wholesale used-car auctions and Cars and Bids online auctions deliver informative bounds. Counterfactual analyses show that the option to wait lowers first-period revenue by 8--11% in the Korean market, that increasing effective competition from 8 to 20 serious bidders in Cars and Bids raises seller revenue by 40--65%, and that maximin reserve prices vary substantially across vehicle clusters.

We study a model in which shocks propagate along a path chosen by agents embedded in a network. When a shock hits an agent, the affected agent cancels one of her outgoing edges. This cancellation cascades sequentially along a chosen path until reaching a terminal agent, resulting in a systemic cost equal to the sum of individual cancellation losses. A liability rule determines agent payments for realized losses, and we seek to implement efficient path selection in the induced sequential-move game. Our main axiomatic result characterizes a family of rules, which set each agent's liability to be proportional to the system's total realized losses with agent weights depending only on the network structure. We propose a way to set such weights based on a simple path-based procedure that assigns equal importance to all non-sink agents along each path and then aggregates these contributions across paths. These weights coincide with the Shapley value of an associated "path-counting" cooperative game and can be computed in polynomial time. A simulation study illustrates the mechanics of our approach.

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on.

The aim of this study is to empirically investigate the existence of a sectoral asset price channel of monetary policy in the region of the six republics of former Yugoslavia. The study constructs sectoral indices for the entire region, building on the idea that one regional stock exchange may provide more efficiency for the listed companies in the region, while monetary policy relevance for it may be sector-specific. We employ panel vector autoregressive model to observe impulse responses of sectoral indices to innovations in monetary policy, while then disentangle the long- from the short-run relationships per index through a Pooled Mean Group estimation. Overall, we document presence of the asset price channel in the finance and telecom sectors, likely driven by the established multinational corporate networks fostering sub-market regionalization. Yet, this is not the case for the manufacturing and electricity sectors, which may imply that local stock markets are yet too fragmented and space for a more efficient regional stock market, either in the true sense of the word or, more realistically, though enhanced regional cooperation of the stock exchanges certainly exists.

News media coverage of monetary policy is not a passive transcript of central-bank communication: it filters announcements, macroeconomic news, and editorial choices into narratives that move expectations and policy decisions. We embed media sentiment into a behavioral New-Keynesian model in which the central bank reacts to sentiment and sentiment follows an explicit law of motion. We construct monetary-policy sentiment indicators from more than 50,000 Canadian newspaper articles using dictionary methods, transformer models, and a generative-AI framework. Media sentiment shifts household inflation and wage expectations, improves out-of-sample forecasts of GDP growth and inflation, and loads positively on the Bank of Canada's estimated Taylor rule once treated as endogenous. A Bayesian SVAR identifies anticipated and unanticipated monetary-policy shocks together with a narrative shock; the narrative shock contributes a non-trivial share of medium-horizon macroeconomic variance, and a counterfactual that shuts down the dynamic feedback from media sentiment attenuates the propagation of monetary policy to output and prices. %The results suggest that media narratives are an integral part of monetary-policy transmission, not merely an additional source of information.

Instrumental variables (IV) methods are central to applied microeconomics. While classical approaches assume linear models with constant effects, recent literature has shifted toward the local average treatment effect (LATE) framework to accommodate heterogeneous treatment effects. This paper provides a practical guide to aligning empirical practice with recent theory. We first examine how different specifications with covariates lead to distinct weighted averages of covariate-specific LATEs. We then discuss how parametric misspecification can undermine the causal interpretation of these estimands and suggest flexible specifications as essential robustness checks. Finally, we review formal tests for LATE assumptions and methods robust to monotonicity violations. We provide a guide to software implementations to help researchers apply the methods in practice.

This paper develops a difference-in-differences framework for staggered policy adoption when units can be affected by other units' adoption. For each treated cohort and event time, the framework separates the effect of own adoption, the spillover effect generated by other adopters, and the total effect under the realized rollout. Identification uses a prespecified summary of spillover exposure and parallel trends comparisons among units with the same exposure at the baseline and target dates. Spillover effects are learned from never-treated units and evaluated for treated cohorts under the exposure distribution they face. We construct estimators for these effects and an inference procedure that allows for spatial dependence. Monte Carlo simulations illustrate that standard DID estimators that ignore spillovers can miss the total effect, whereas the proposed estimators have small bias for these effects and the associated confidence intervals have coverage close to the nominal level. In an empirical study of the Community Health Centers rollout, estimated spillovers account for a substantial share of the effect on older-adult mortality.

Humans increasingly delegate decisions to language models, yet whether these systems reproduce or reshape human patterns of discrimination remains unclear. Here we run a large-scale study to analyse whether language models use demographic information in hiring decisions. We show, across 27 models and 177 occupations, that language models give female and Black candidates hiring advantages relative to otherwise-comparable male and white candidates, while giving disabled candidates disadvantages. The differences are meaningful in magnitude: the role of race, gender, and disability status is comparable to six months to one year of additional education. Post-training alignment is the primary driver: relative to matched pre-trained models, alignment amplifies advantages for female and Black candidates by 325% and 330%, and disadvantages for disabled candidates by 171%. Compared with previous human correspondence studies, language models reverse the direction of racial discrimination, attenuate the disability penalty, and amplify the female advantage by 190%. Alignment changes how models use qualification signals: alignment increases returns to skills and work experience overall, but relatively more so for female and Black candidates. Meanwhile, the absence of qualification signals harms marginalised groups more, particularly for disabled candidates, differences that may explain the asymmetry of alignment effects across groups we observe.

This paper studies Markov-switching (MS) models with time-varying transition probabilities (TVTP) under various specifications of the transition probability matrix. Especially, we extend the two-regime common-variance setting of the Generalized Autoregressive Score (GAS) model from (Bazzi et al., 2017) to the general $K$-regime case with regime-specific means and variances. Our study contains comprehensive Monte Carlo simulations and we developed an open-source R package, \texttt{multiregimeTVTP}, for data simulation and parameter estimation. We find that the regime means, variances, and transition probabilities are reliably recovered, whereas the TVTP driving coefficients are harder to identify. Another finding from our paper is that the GAS score coefficient appears to be statistically non-identifiable, due to a ridge in the joint likelihood surface $(\sigma^2,A)$. In addition, we find that one-step point forecasts are remarkably robust to TVTP misspecification, but filtered regime probabilities are not, so correct specification matters most for characterizing regime dynamics rather than short-horizon forecasting. An empirical application to U.S. Treasury zero-coupon yield changes at four maturities (1961-2024) shows that an exogenous specification driven by the lagged yield level dominates the constant and lagged-change models in fit, while the GAS specification fails to converge, with $\hat{A}$ collapsing to zero, reflecting the same identifiability issue observed in simulation.

We study a dynamic model in which a principal monitors agents based on historical data of infractions. This data informs when and at what intensity to monitor; the monitoring decision, in turn, selects the collected data, shaping the principal's future learning. We analyze this feedback loop using a bandit model in which the underlying monitoring environment evolves according to a hidden Markov process. Because data collection is endogenous, how the principal uses this information is critical: surprisingly, a myopic approach renders historical data completely valueless. By endogenizing the agent's incentives, we demonstrate that the principal's purely informational motive to explore serves as an endogenous commitment device. This inherent drive to gather data compels persistent vigilance, strictly lowering the equilibrium infraction rate and restoring the power of deterrence.

We consider voting rules in settings where voters' identities are difficult to verify. Voters can manipulate the process by casting multiple votes under different identities or abstaining from voting. Immunities to such manipulations are called \emph{false-name-proofness} and \emph{participation}, respectively. For the universal domain of (strict) preferences, these properties together imply \emph{anonymity} and are incompatible with \emph{neutrality}. For the domain of preferences defined over all subsets of a given set of objects, both \emph{false-name-proofness} and \emph{participation} cannot be met by rules that are also \emph{onto}, \emph{object neutral}, and \emph{tops-only}. However, when preferences over subsets of objects are restricted to be separable, all these properties can be satisfied. Furthermore, the domain of separable preferences is maximal for these properties.

Boundary discontinuity designs are used to learn about causal treatment effects along a continuous assignment boundary that splits units into control and treatment groups according to a bivariate location score. We analyze location-based local polynomial treatment effect estimators that directly employ the bivariate score of each unit. We develop pointwise and uniform estimation and inference methods for the \textit{Boundary Average Treatment Effect Curve} (BATEC), as well as for two aggregated causal parameters: the \textit{Weighted Boundary Average Treatment Effect} (WBATE) and the \textit{Largest Boundary Average Treatment Effect} (LBATE). Our results cover both sharp and fuzzy (imperfect compliance) designs. We illustrate the methods with an empirical application, and provide companion general-purpose software. The supplemental appendix includes additional substantive theoretical results, methodological details, and simulation evidence.

A well-known feature of overlapping generations economies is that the First Welfare Theorem fails and equilibrium may be inefficient. The Cass (1972) criterion furnishes a necessary and sufficient condition for efficiency, but it does not address the existence of efficient equilibria, and Cass, Okuno, and Zilcha (1979) provide nonexistence examples. A closely related question (known as the Hahn (1965) problem) deals with the existence of monetary equilibria. In this paper, I provide sufficient conditions for the existence of optimal monetary equilibria on consumption-loan, non-stationary overlapping generations economies without durable, dividend-paying assets, cash-in-advance constraints, wealth-transfer mechanisms, or transaction costs. Essentially, the economy must be prone to savings. Furthermore, I develop an algorithm to find these optimal monetary equilibria as the limit of nested compact sets. These compact sets are the result of a backward calculation through equilibrium equations departing from the set of optimal monetary equilibria of well-behaved tail economies.

Consider a social-choice function (SCF) is chosen to decide votes in a formal system, including votes to replace the voting method itself. Agents vote according to their ex-ante belief over what decisions are considered, and whether they prefer them to be decided by the incumbent SCF or the suggested replacement. The existing SCF then aggregates the agents' votes and arrives at a decision of whether it should itself be replaced. An SCF is self-maintaining if it can not be replaced in such fashion by any other SCF. Our focus is on the implications of self-maintenance for centralization. For this purpose, unlike [Barbera and Jackson, 2004], we do not generally restrict attention to anonymous SCFs. We also do not restrict attention to neutral SCFs, unlike [Koray, 2000]. We present results considering optimistic, pessimistic and i.i.d. approaches with respect to agent beliefs, different tie-breaking rules, and different SCF domains. To highlight two of the results, (i) for the i.i.d. unbiased case with arbitrary tie-breaking and general Boolean functions, we prove an Arrow-Style Theorem for Dynamics: We show that only a dictatorship is self-maintaining, and any other SCF has a path of changes that arrives at a dictatorship. (ii) With a pessimistic approach, tie-breaking that prefers the status quo, and WMGs, we provide a tight characterization of the self-maintaining rules, which are exactly all games with minimal winning coalitions of size at most 2. We then consider two extensions, (i) forward-looking voters, (ii) Where the voter utility depends on wisdom of the crowd effects. In both cases, less centralized SCFs become self-maintaining. All in all we provide a basic framework and body of results for centralization dynamics and stability, applicable for institution design, especially in formal De-Jure systems, such as Blockchain Decentralized Autonomous Organizations (DAOs).

On platforms where time-to-contract is itself payoff-relevant--Aalsmeer's flower auctions, ride-hailing dispatch, on-demand-labor matching--the textbook revenue equivalence between Dutch and first-price formats holds the trading outcome fixed. Once participation is endogenous and both sides bear waiting costs, the trading format directly shapes who enters, market thickness, volume, and platform revenue. The platform's ranking of the descending clock against immediate and batched posted-price benchmarks is decided by two estimable primitives on each side of the market: an earnings gap and a timing gap. A bidirectional four-case classification identifies when the descending clock dominates at every level of waiting costs, only above a floor, only below a ceiling, or not at all; the last case is unconditional -- when the descending clock charges no more per trade and contracts no faster than the posted-price benchmark, it cannot win. No format admits a universal ranking. The local verdict propagates through endogenous entry, and cross-side complementarity amplifies shared local advantages into joint dominance. A conditional revenue theorem converts entry and volume gains into a platform-revenue ranking. In calibrated parameterizations the revenue-ranking switching boundary lies near $p_0/\bar v\approx 1$, inside the empirical range for ride-hailing platforms. A measurement protocol provides explicit nonparametric estimators for the six reduced-form objects and a test statistic for the dominance condition, and a Lean~4 formalization audits the algebraic and order-theoretic content. In markets where goods or services cannot wait, the speed of the trading mechanism is a primitive of market design.

I study a decentralized marriage market with search frictions, costly pre-marital skill investments, and non-transferable utility. Despite a symmetric environment, the market can exhibit asymmetric equilibria, with one gender investing more in skills than the other; in some environments, the asymmetric equilibrium is unique. A microfounded model of household utility maximization shows that this transition from a unique symmetric equilibrium to a unique asymmetric equilibrium can be driven by rising labor-market wages for high-skilled workers: as the skill premium rises, one gender ends up fully investing while the other invests substantially less.

Generative artificial intelligence (AI) facilitates content production and enhances ideation capabilities, which can significantly influence developer productivity and participation in software development. To explore its impact on collaborative open-source software (OSS) development, we investigate the role of GitHub Copilot, a generative AI pair programmer, in OSS development where multiple distributed developers voluntarily collaborate. Using GitHub's proprietary Copilot usage data, combined with public OSS project data obtained from GitHub, we find that Copilot use increases project-level code contributions by 5.9%. This gain is driven by a 3.4% rise in developer coding participation and a 2.1% increase in individual productivity. However, Copilot use also leads to an increase in coordination time by 8% due to more code discussions. This reveals an important tradeoff: While AI expands who can contribute and how much they contribute, it slows coordination in collective development efforts. Despite this tension, the combined effect of these two competing forces remains positive, indicating a net gain in overall project-level timely merge of code contributions from using AI pair programmers. Interestingly, we also find the effects differ across developer roles. Peripheral developers show relatively smaller increases in project-level code contributions and experience larger increases in coordination time than core developers. In summary, our study underscores the dual role of AI pair programmers in affecting project-level code contributions and coordination time in OSS development. Our findings on the differential effects between core and peripheral developers also provide important implications for the structure of OSS communities in the long run.

We study a canonical multi-task demand-learning problem motivated by retail pricing, where a firm seeks to estimate heterogeneous linear price-response functions across multiple decision contexts. Each context is described by rich covariates but exhibits limited price variation, motivating transfer learning across tasks. A central challenge in leveraging cross-task transfer is endogeneity: prices may be arbitrarily correlated with unobserved task-level demand determinants across tasks. We propose a new meta-learning framework that identifies the conditional mean of task-specific causal demand parameters given a subset of task-specific observables despite such confounding, assuming that each task contains at least two distinct locally exogenous price points. This subset is carefully designed to include all of the prices to address cross-task confounding, while masking two demand outcomes that provide randomized supervision to address identifiability issues arising from the inclusion of all prices. We show that this information design is maximally uniformly valid, in that any refinement of the conditioning set that reveals withheld-outcome information is not guaranteed to identify the conditional mean causal target. We validate our method on real and synthetic data, demonstrating improved recovery of demand responses relative to standard transfer-learning baselines.

Reinforcement-learned reasoning has powered recent AI leaps on verifiable tasks, including mathematics, code, and structure prediction. The harder bottleneck is evaluative judgment in low-verifiability domains, where no oracle anchors reward and the core question is which untested ideas deserve attention. We test whether institutional traces, the record of what fields published, where, and at which tier, can serve as a training signal for AI evaluators. Across eight social science disciplines (psychology, economics, communication, sociology, political science, management, business and finance, public administration), we built held-out four-tier research-pitch benchmarks and supervised-fine-tuned (SFT) LLMs on field-specific publication outcomes. The fine-tuned models cleared the 25 percent chance baseline and exceeded frontier-model performance by wide margins, with best single-model accuracy ranging from 55.0 percent in public administration to 85.5 percent in psychology. In management, evaluated against 48 expert gatekeepers, 174 junior researchers, and 11 frontier reasoning models, the best single fine-tuned model (Qwen3-4B) reached 59.2 percent, 17.6 percentage points above expert majority vote (41.6 percent, non-tied) and 28.1 percentage points above the frontier mean (31.1 percent). The fine-tuned models also showed calibrated confidence: confidence rose when predictions were correct and fell when wrong, mirroring how a skilled reviewer can say "I'm sure" versus "I'm guessing." Selective triage on this signal reached very high accuracy on the highest-confidence subsets in every field. Institutional traces, we conclude, encode a scalable training signal for the low-verifiability judgment on which science depends.