Papers

When do text embeddings work as inputs to empirical analysis? Their use rests on an assumption: that we can trade text for its low-dimensional embedding, and lose little in doing so. I make that assumption precise under a generative model in which documents are mixtures of latent topics. I study two uses—clustering units in embedding space and controlling for high-dimensional text. A cluster of embeddings is a set of documents with similar topic mixtures; controlling for the embedding is equivalent to controlling for the topic mixture, so validity reduces to whether that mixture captures the confounding. In an application to 363 U.S. metropolitan areas, embedding-based clusters of LLM-generated economic descriptions recover interpretable economic archetypes and separate local employment dynamics more sharply than clustering on model residuals, or on a curated set of industry and demographic covariates.

Stablecoins, typically pegged to fiat currencies, cannot achieve true stability because they inherit fluctuations in the underlying unit of account. To overcome this limitation, we introduce a stablecoin pegged to the Maximum Likelihood Value (MLV), a newly defined unit of account derived as the most probable configuration of latent real-value movements that explains observed nominal-value (price) changes. Grounded in inferential statistics and modern portfolio theory, MLV represents the most stable unit of account, as it enforces a zero real return on the minimum-variance portfolio. Empirical results confirm the operational viability of an MLV-pegged stablecoin: MLV can be computed in real time from 500 asset price series and improves annualized returns and Sharpe ratios while substantially reducing turnover in portfolio optimization.

Industrial recommenders give new content initial views through budgeted exploration, then use early performance to decide further delivery. On many short-video platforms, exploration is the primary way new videos reach viewers. Viewer-side tests measure consumption; the published budget objectives we review omit creator response. We analyze four experiments on a major short-video platform. An eight-month creator ablation finds production exploration raises videos posted per creator by 8.55% and creators posting at least once by 7.10% relative to a minimal floor. A budget-matched reallocation raises creator participation with no detectable short-run viewer-side change. A year-long viewer ablation finds 1.74% more video views but 2.13% less view time. A delivered view creates immediate feed value, can trigger organic take-up, and can induce creator supply. Take-up and supply replenish a shared corpus, creating two measurement limits. Viewer-side A/B tests cancel the corpus effect when both arms consume the same corpus. Giving each arm its own corpus avoids cancellation, but turnover still controls the horizon. If the corpus turns over at rate w per posting cycle, a t-cycle experiment expresses at most wt of the eventual corpus effect. More users reduce noise but do not speed turnover. Before the corpus path visibly bends, data cannot distinguish a modest fast effect from an arbitrarily large slow one, so a valid confidence interval may lack a finite upper endpoint. As predicted, the three-week co-diverted experiment cannot determine the sign of the eventual corpus effect. Within the window, it identifies the direct feed effect, and an exploratory cohort analysis detects organic lift after exploration ends. The experiments establish a positive creator response, measure the gross corpus flow visible within three weeks, and show the design and duration needed to identify total value.

In this paper, we study causal non-causal state space models to model time series characterised by a local explosive increase followed by a sharp decrease such as stock prices. To motivate the use of causal non-causal state space models, we show that the causal non-causal convolution autoregressive model introduced by Gourieroux and Zakoian (2017) can be consistent with the rational expectations stock price model. As in a causal state space model, a central question is how to perform state and parameter inference in the causal non-causal state space model, which we discuss in the paper. We also study the causal non-causal convolution autoregressive model in more detail, providing some new results for the model. To illustrate the usefulness of causal non-causal state space models, we use the causal non-causal convolution autoregressive model to estimate the size of the dot-com bubble in both real time and a posteriori with the stable non-causal autoregressive model considered also by Gourieroux and Zakoian (2017) as a benchmark.

We present a suite of R packages for macroeconomic forecasting that leverages advanced Bayesian, structural, multivariate, dynamic, hierarchical, non-linear, and non-Gaussian models. The suite enables both structural and predictive analyses, and is adapted to time series data across various types, dimensions, and sampling frequencies. Each additional feature increases computational complexity. To address this challenge, our software design incorporates a carefully curated selection of models, efficient algorithms implemented in C++, advanced econometric and numerical methods, robust handling of complex input and output objects, and standardised workflows. This approach combines the computational efficiency of C++ with the convenience of working with data in R. We demonstrate that our packages facilitate original research contributions in forecasting, as illustrated by our example in which vector autoregressions with non-centred stochastic volatility enhance density and point predictions relative to models with centred stochastic volatility.

We study identification of two-way unobserved heterogeneity in the nonparametric panel regression $G_{it}=g(\alpha_i,\gamma_t)+\varepsilon_{it}$, where identification of the latent types reduces to constructing identified, injective proxies for them. To this end we consider the singular value decomposition (SVD) of the bivariate regression function $g(\alpha,\gamma)$ on a product domain $\Omega_\alpha\times\Omega_\gamma$, whose left singular functions $\{u_r\}$ serve as proxies for the unobserved heterogeneity parameter $\alpha$. The arguments are symmetric for $\{v_r\}$ vis-à-vis $\gamma$. We work under an observational-equivalence simplification: two values of $\alpha$ that induce the same conditional response $g(\alpha,\cdot)$ are identified, so that the response map $\alpha\mapsto g(\alpha,\cdot)$ is injective by construction. We show two things. First, this reduction is equivalent to injectivity of the full collection of left singular eigenfunctions, so no further condition is needed over the infinite collection $\{u_r\}_{r\ge1}$. Second, under a single additional local injectivity condition, a finite collection of leading eigenfunctions $U_R=(u_1^{\top},\dots,u_R^{\top})^{\top}$ is injective for all sufficiently large $R$. The proof reduces a global univalence question to a local first-order condition plus a topological compactness argument, bypassing the global Jacobian conditions usually required.

Recent work encourages political scientists to move from post-only toward within-subject designs for improved precision from repeated measurements. We formalize a potential-outcomes framework for two-period within-subject designs that allows for unequal allocation and heterogeneous treatment and carryover effects. We characterize the pooled estimator and evaluate the carryover test used to justify pooling. We find: first, pooling identifies the average treatment effect only when the gap in the average carryover effects is zero across the two treatment sequences. The unit-clustered standard error for the pooled estimator is identical to its design-based counterpart. Second, under mild conditions, the carryover test has strictly less power than the average-treatment-effect test with post-only data. The resulting two-step procedure, which pools only after a nonrejected test, produces confidence intervals that typically undercover. When the gap is zero, undercoverage occurs if and only if pooling is more efficient than post-only analysis, precisely when the within-subject design is worthwhile. When the gap is nonzero, undercoverage is typical unless the gap or sample size is large. Third, we derive a sensitivity analysis and find published conclusions robust to plausible carryover gaps. We therefore endorse within-subject designs but recommend justifying a zero carryover gap substantively and reporting sensitivity to departures.

Which visual choices make a post perform better? A growing literature answers this question with pooled coefficients estimated across many creators, which platforms translate into creative recommendations. We show that these coefficients blend two distinct patterns that can point in opposite directions for the same attribute. The first, audience preference, arises because creators who favor a style attract differently composed audiences, so their posts perform differently because of who is watching, not what any single post does. The second, creative effect, captures how a creator's audience responds when she departs from her usual look. Pooled estimation averages the two, and audience preference can be large enough to reverse the signal that creative direction requires. We propose DIRECT (Decomposed Identification of Response Effects via Causal Tools), a panel-based causal-inference framework that separates them, combining the Mundlak between-within decomposition with double machine learning over latent vision-language treatments that co-vary within a creator. We apply it to 232,088 sponsored Instagram beauty posts across 1,527 creators and 11 CLIP-derived visual style axes. The two carry opposite signs on 4 of 11 attributes, and on 2 of 11 the pooled coefficient itself recommends the wrong creative direction: on skin tone, it favors lighter representations while the creative effect points the other way, since a creator's audience engages more with tones darker than her baseline. On held-out creators, prescribing from the pooled coefficient forgoes 31% of the achievable engagement gain. We contribute a diagnosis of estimand mismatch in visual content analytics, a framework that recovers the decision-relevant estimand from observational panel data, and three portable diagnostics for auditing whether pooled estimates support the decisions they inform.

We develop a novel method of inference for network-dependent high-dimensional random vectors. Dependence is characterized via a functional dependence measure based on graph distance, allowing the approximation theory to capture the interaction between the decay of dependence and the growth of network neighborhoods. We establish Gaussian approximation results for the maximum norm under finite-moment and sub-Weibull conditions, providing explicit conditions under which the dimension may increase with the network size. We also propose a high-dimensional network HAC covariance estimator and establish its convergence properties, yielding a feasible procedure for simultaneous inference. Simulation studies demonstrate favorable finite-sample performance of the proposed method. We apply the procedure to study how spillover effects vary with an index of network homophily by constructing confidence bands for the conditional spillover-effect function. The application reveals heterogeneity and local significance that would be obscured by conventional low-dimensional inference.

In this study, we construct the first orthogonal basis for additively consistent subspace in pairwise comparisons theory. This construction is based on our representation of additively consistent best approximations of skew-symmetric matrices with respect to a tensor basis having minimal support. The orthogonal basis establishes the logarithmic consistent projection for the orthogonal windowing of pairwise comparisons matrices. It is compared with the windowing of the Saaty and SVD types. These comparisons resulted in new composite formulae for logarithmic, Saaty, and SVD projections. The theoretical considerations presented in the paper are accompanied by numerous examples.

Many empirical investigations of long-run relations are based on cross-section regressions in averaged or long differenced data that effectively have the time dimension of a $T\times N$ panel compressed. We analyze a class of time-compressed I(1) data and show that they have magnified variability stemming from the fact that the cross-section variance of a non-stationary panel `fans out' with time. Cross-section regressions in time compressed data can potentially yield estimates that are super-consistent and asymptotically normal, whether the regressors are stationary, non-stationary, or highly persistent. The fastest convergence rate of $\sqrt{N}T$ requires a compression scheme that not only magnifies the non-stationary signal, but also dilutes the regression noise. Omitted fixed effects preclude noise dilution but the estimates remain super-consistent. However, the fanning out effect can be weakened when the data have a strong force for mean-reversion or convergence, a problem that seems relevant for temperature data. We consider three applications and find that the long-run relation between consumption and income, and between growth/inflation and demographic variables are reasonably well determined, but the estimated relation between growth and warming temperature is fragile.

This paper proposes a nonparametric Bayesian inference framework for partially identified discrete response models. The key observation is that these models map a reduced-form conditional choice probability to an identified set. Consequently, nonparametric Bayesian inference for the conditional probability mass function leads to Bayesian inference for the identified set. The inference framework nests conditional moment inequalities and linear systems with unknown coefficients as special cases. Importantly, our proposal does not require converting conditional moments into unconditional moments or discretizing covariates. We show that the posterior is consistent for the true identified set when the model is correctly specified, show that the posterior can consistently detect model misspecification, and show posterior consistency for a pseudo-identified set that is valid under misspecification. We also verify the assumptions for a class of priors based on Gaussian processes that we use to implement our proposal. These priors offer similar flexibility to frequentist partial identification methods, and are computationally attractive because posterior sampling can be performed in closed-form. We also show that many of the ideas in this paper extend to continuous responses and aggregated discrete responses (e.g., market shares).

This paper develops a new econometric framework to identify and estimate policy-relevant causal effects in contexts with endogenous selection into treatment and spillovers within single large networks or spatial settings. Conventional causal inference methods relying on either unconfoundedness or no-interference assumptions are generally inadequate in these scenarios. We introduce a Spillover Roy model that jointly models endogenous treatment selection and potential outcomes while allowing spillovers through a low-dimensional exposure mapping of neighbors' treatments. The model captures heterogeneous treatment responses across levels of latent resistance to treatment and neighborhood exposure. Within this framework, we define policy-relevant direct, spillover, and total effects under feasible policy changes and show that the total effect decomposes into a direct component from policy-induced participation and a spillover component from policy-induced changes in neighborhood treatment exposure. For estimation and inference, we develop a Bayesian data-augmentation algorithm with parameter expansion that enables efficient posterior computation and coherent uncertainty quantification for heterogeneous causal effects and policy counterfactuals. An application to the U.S. Opportunity Zones program finds positive direct effects on housing development but limited spillover benefits, while counterfactual policy analysis reveals diminishing returns from program expansion.

Multinomial choice models allow flexible substitution patterns but become computationally demanding with many alternatives or observations. With a fixed per-observation simulation budget, simulated maximum likelihood introduces simulation bias, while each optimization step requires a full-sample likelihood evaluation. We propose Stochastic Approximation with Unbiased Simulated Scores (SAUSS), an averaged stochastic approximation based on conditionally unbiased mini-batch score estimates. Each iteration uses a fixed mini-batch regardless of sample size. For multinomial probit, accept-reject sampling provides exact conditional draws and unbiased score estimates for any fixed number of accepted draws. Under local conditions, asymptotic theory for the averaged estimator and the partial-sum process of the SAUSS iterates incorporates mini-batch and simulation variability and supports random-scaling and plug-in inference. In simulations and an application, SAUSS gives comparable results in less than 1% of the computation time of simulated maximum likelihood. SAUSS extends to limited dependent variable models with conditional-expectation score representations and exact conditional sampling.

We introduce a network realized GARCH-Itô model in which volatility transmission is a dynamic relation among the latent daily integrated volatilities of multiple assets. An unknown directed and signed network is embedded in a continuous-time variance process and appears in the resulting exponential daily recursion. Intraday returns identify integrated volatility and hence the network that governs its propagation. For a fixed network template, feasible estimation based on realized volatility is first-order equivalent to estimation based on latent integrated volatility. For an unknown network, regularization selects the relevant structure, and, under oracle conditions, a fixed-rank local refit provides conditional inference for model-implied response-based connectedness. In an application to nine U.S. sector ETFs from 2007 to 2025, the model attains the lowest average out-of-sample QLIKE among the reported recursive forecasts, although its advantage over HAR is not statistically significant. In the full sample the weighted LASSO selects an empty sparse support, so inference concerns the rank-one projected factor component; this conditional analysis identifies Energy as a net volatility transmitter. Aggregate connectedness is more stable across volatility measures than individual sparse channels.

Comparing economic models requires balancing fit against flexibility. Yet standard selection criteria often proxy flexibility using parameter counts, overlooking differences due to functional form and experimental design. This paper introduces a data compression approach for evaluating economic models. Following the Minimum Description Length principle, models are interpreted as codes and evaluated by how effectively they compress data. This perspective yields compression-based analogues of Selten's predictive success and Fudenberg et al.'s completeness and restrictiveness. Unlike Selten's measure, its analogue unifies deterministic and stochastic models in a likelihood framework; unlike Fudenberg et al.'s measures, the proposed framework provides a complete selection criterion. Applications to social preferences, risky choice, and intertemporal choice illustrate the relevance of the approach. In simulations, accounting for flexibility differences due to functional form and experimental design improves model recovery relative to AIC, BIC, and cross-validation. In empirical reanalyses, MDL changes model rankings in favor of more parsimonious specifications.

Natural hazards are a nonmarket disamenity that affects an individual's search for employment resulting in a negative environmental impact that produces an economic inefficiency. We develop a seek-and-screen job search approach that uses a discrete choice simulation to examine how salary, crime, and natural hazard risk influence job choice. We model the job decision process as a series of elimination events using a Cox hazard model grounded in a Random Utility Model. We use data from the discrete choice simulation to estimate both a standard proportional hazards model and an extended specification that allows the effect of natural hazard risk to vary across decision rounds. Individuals are exposed to the dynamics of a simulated job search as they make decisions between pairs of job offers in an adaptive learning process based on income, geography, crime level, and natural hazard attributes. The results of the job choice decisions provide the input to a statistical survival analysis. The results indicate that salary and crime exert stable and economically intuitive effects on job elimination, with higher salary reducing and higher crime increasing the likelihood of removal. In contrast, natural hazard risk exhibits a time-varying effect that increases the probability of elimination in early rounds but becomes neutral or favorable in later stages of the decision process. These findings suggest that environmental risk is evaluated differently as individuals transition from initial screening to final job selection, highlighting the importance of modeling job choice as a multi-stage process.

This article surveys two deeply connected literatures that approach the same fundamental problem from different disciplinary traditions: dynamic discrete choice (DDC) in structural econometrics and inverse reinforcement learning (IRL) in machine learning. Both seek to infer the preferences of decision makers from observed sequential behavior, assuming that individuals act to maximize an expected reward function within a dynamic, uncertain environment formalized as a Markov decision process (MDP). Despite independent origins, the two fields have converged on similar mathematical formulations. We show that the (soft Q-learning) framework now prevalent in IRL is closely related to DDC models under additive extreme value preference shocks, yielding the same softmax (multinomial logit) choice probabilities and smooth Bellman equations that underpin structural estimation in economics. We compare the estimation and computational methods developed in each field. DDC has emphasized maximum likelihood estimation, conditional choice probability estimators, and policy iteration methods. IRL has developed scalable alternatives, including maximum entropy methods, adversarial approaches, and model-free temporal difference estimators that extend to high-dimensional state spaces using deep neural networks. Model-free IRL estimators that combine temporal difference learning with classical two-step methods from econometrics represent a promising direction for bridging the two literatures. Both fields confront shared foundational challenges: the identification problem, whereby multiple reward functions can rationalize the same observed behavior, and the curse of dimensionality in solving the underlying MDP. We believe that cross-fertilization offers substantial opportunities for methodological progress in both fields.

We study dynamic linear panel data models in which the lagged outcomes and strictly exogenous covariates carry individual-specific coefficients and the time-varying errors have a flexible covariance structure. With a fixed number of time periods, we point-identify the joint distribution of the random coefficients and the structural errors under a distributional form of strict exogeneity, and propose a closed-form, multi-step estimator based on the inverse Radon transform. We establish a uniform convergence rate for the estimator of the random coefficient density, as well as uniform consistency of the estimator for the conditional density of the time-varying structural errors. Monte Carlo simulations demonstrate good finite-sample performance of the estimators.

Econometric models offer parsimonious but inexact approximations to data-generating processes. This paper studies the generalized method of moments (GMM) when exchangeable specification errors of order $n^{-1/2}$ contaminate the moment conditions. I develop estimators for the mean and variance of these specification errors, establishing their consistency in an asymptotic framework where the number of overidentifying restrictions grows with the sample size. These hyperparameter estimates are used to develop a feasible bias-corrected estimator of target parameters. I also propose an empirical Bayes estimator that weakly improves precision by subtracting a best linear predictor of the first-order estimation error from the bias-corrected estimator. Using a combinatorial central limit theorem, I establish asymptotic normality of both estimators and provide variance estimators that enable misspecification-aware frequentist inference. Simulation exercises indicate the procedures can meaningfully improve on standard two-stage least squares estimation when exclusion violations are present. Revisiting the influential study of Angrist and Krueger (1991), I consider an instrument set where exchangeable excludability violations are plausible. Repairing the two-stage least squares estimates of the returns to schooling moves them in the direction of ordinary least squares and reduces sensitivity to the specification of controls.

Problem definition: Solar electricity generation is a strategic component of energy portfolios designed to meet growing demand and reduce carbon emissions. Governments and municipalities encourage household photovoltaic (PV) adoption through upfront rebates and tax credits. Limited budgets require principled, data-driven policies that account for the drivers of adoption and the effects of incentives on adoption rates. Methodology/results: We develop a dynamic structural model of residential PV diffusion based on adoption decisions by forward-looking households that weigh the economic trade-offs between installing now and later. Adoption depends on return on investment and influence from neighboring adopters. The model segments households by home value and urbanization level, incorporates unobserved heterogeneity, and captures spatiotemporal installation dynamics. We estimate the model using Bayesian methods and detailed household-level data from Austin, Texas. In out-of-sample tests, it predicts installations more accurately than contemporary alternatives. We simulate counterfactual policies within the dynamic equilibrium of PV diffusion to evaluate rebate designs. The framework can also be adapted to study the adoption of other durable technologies. Managerial implications: A rebate offered for a limited period generates more adoption and emissions reductions than a prolonged, costlier program. This counterintuitive result arises from forward-looking behavior, neighbor influence, and accelerated adoption before the rebate expires. We also evaluate phased reductions and rebates differentiated by household segment. A two-step reduction outperforms multiple small reductions. Geographic differentiation improves policy performance, whereas differentiation by home value offers little advantage over a uniform rebate.

This paper develops a procedure for uncovering the common cyclical factors that drive a mix of stationary and nonstationary variables. The method does not require knowing which variables are nonstationary or the nature of the nonstationarity. An application to the FRED-MD macroeconomic dataset demonstrates that the approach offers similar benefits to those of traditional principal component analysis with some added advantages.

In panels with sample selection (that may occur due to attrition, nonresponse, etc.), the assumption of selection on observables (missing at random, MAR) is commonly imposed despite often being implausible. However, this assumption becomes testable when a refreshment sample is available. We develop a statistical test of MAR based on a distance between two estimated distributions: one obtained using the standard inverse probability weighting (IPW) that is valid under MAR and the other obtained using an alternative weighting that is valid under a weaker assumption of additive nonignorability of Hirano et al. (2001). This test implicitly compares the distribution of the IPW-weighted sample in the attrition period with the distribution of the refreshment sample, which coincide if the MAR assumption holds. We establish that, when the input distributions are parametric, our test statistic converges to the generalized chi-squared distribution under the null of MAR. This limit distribution can be estimated using the recursive formulas derived by Franguridi et al. (2026). We illustrate the performance of our test in Monte Carlo simulations. Finally, we apply our test to an empirical example using a subsample of the Understanding America Study (UAS) dataset.

Research, policy, and capital rely on the Cooperative Patent Classification's Y02 tag to locate climate invention, yet whether Y02 measures what it is used to measure has never been tested at corpus scale. We ask three questions: what types of error does Y02 make, are those errors idiosyncratic, and what are their main causes? Because neither Y02 nor a text classifier trained on it is ground truth, our Error-as-Signal framework treats their disagreements as evidence, not model failure: in a construct-validity test, two independent large language models judge whether the primary function of each of 517,772 disputed inventions among 9,075,421 USPTO patents has a direct climate mechanism. Y02 makes two types of error, which we term False Green (180,384 inclusions) and Silent Green (29,465 omissions). The errors are not idiosyncratic but form a systematic bias: False Green concentrates in ICT, Silent Green in energy, transport, chemistry, and industrial engineering, so raw counts overstate ICT energy efficiency threefold. The evidence points away from applicant strategy, misclassification did not jump when green labels became salient, and toward bounded classification capacity. Yet complexity does not simply make classification harder; its two forms push errors in opposite directions, a complexity paradox. A one-standard-deviation increase in reflection complexity (capability scarcity) is associated with 2.45 times the odds that an error is an omission rather than an inclusion, whereas structural complexity (combinatorial diversity) tilts errors toward inclusion. What matters is not how complex an invention is but whether its complexity is legible to the taxonomy.

Social scientists rely on hypothesis testing to support their research conclusions, but the standard tests are designed for testing one hypothesis rather than adjudicating between rival possibilities. We develop a new framework, "classification testing", as an alternative. Instead of selecting one hypothesis to test, a researcher conducting a classification test decides what qualitative distinctions ("classes") are most substantively relevant; the test either assigns the estimand to a class with error control similar to that of a conventional hypothesis test, or declares the result inconclusive. We argue that classification testing is superior to current practice not just when the objective is to adjudicate between rival possibilities but also when there is one research hypothesis to be tested, because classification testing exposes that hypothesis to refutation. We illustrate the framework by applying it to a well-known media experiment and offer an R package to aid in implementation.

In the empirical sciences, significance thresholds often determine whether findings are treated as evidence of an effect. This paper studies how likely findings that just meet conventional significance thresholds are to remain significant in replications of the same sample size. To answer this question, we estimate the expected replication probability conditional on a given p-value among published studies for experimental economics, psychology, and social science. We validate this measure by showing it accurately predicts actual replication outcomes, outperforming prediction markets. A finding with a p-value of 0.05 has an expected replication probability ranging from 0.10 to 0.25 across fields. Low replicability reflects low power in original studies rather than publication bias. We then develop a nonparametric estimator and apply it to economics literatures that use larger samples, finding higher but still low replication probabilities. These results indicate that statistical significance in a single study provides only suggestive evidence of an effect. Stronger conclusions require cumulative evidence.

Traditional statistical tests are poorly suited for the sequential evaluation of probabilistic forecast calibration. We address this limitation in macroeconomic forecasting by applying a new sequential testing method based on e-values. The e-value-based methodology enables anytime-valid inference. It allows practitioners to test against calibration continuously without invalidating statistical guarantees. To illustrate the framework's practical value, we apply it to probabilistic inflation forecasts for the United States, the Euro Area, and Switzerland. Our analysis shows that the sequential approach gives detailed insights into the timing and nature of forecast misspecification. We find these diagnostics are particularly insightful during major structural breaks. During these events, we find evidence against calibration that static, full-sample tests often miss. Therefore, this work shows that e-value-based tests are a practical method for the evaluation of forecast calibration in empirical macroeconomics.

Understanding the propagation of extreme events is important in many economic and environmental applications, yet most econometric methods for causal inference focus on average effects rather than tail behavior. This paper studies the identification of causal relations in extremes and derives resulting estimators and their asymptotic inference. As measure of causal dependence between extreme realizations of variables, we analyze the asymptotic behavior of the Causal Tail Coefficient (CTC) within a linear structural causal model with heavy-tailed regularly varying innovations. In contrast to the existing literature, we allow the variables in the system to exhibit heterogeneous tail indices and consider the presence of potentially heavy-tailed confounders. We derive theoretical results assessing the limiting behavior of the CTC under these conditions and show how differences in tail behavior can help to reach identification of the causal structure. Light-tailed confounders are asymptotically negligible, but sufficiently heavy-tailed confounders can induce extremal dependence patterns that are observationally indistinguishable from direct causal effects. When suitable proxy information is available, identification can be recovered using an adjusted Causal Tail Coefficient. Based on these results, we develop estimation and inference procedures for causal relations in extremes under general conditions. We establish asymptotic properties of the proposed estimators and derive tests for the causal direction and heavy-tailed confounding. Simulation evidence examines their finite-sample performance and provides guidance on their implementation. Applications to climate and financial extremes illustrate how the proposed methods can uncover causal relations that may remain undetected by approaches targeting average dependence.

Analysis of experimental data becomes challenging when the underlying population is connected by a network. Exposure mapping is a common tool in the literature for defining and estimating spillover effects. These mappings reduce the dimensionality of the estimand, thereby facilitating identifiability. It is assumed that this mapping is correctly specified, leaving the choice of the exposure mapping to the analyst. This makes estimators of the spillover effect, such as the Horvitz-Thompson estimator, vulnerable to bias from model misspecification. Although these estimators have been shown to be robust to certain forms of controlled misspecification, there has been relatively little methodological progress in empirically investigating appropriate exposure mappings. In this paper, we propose a novel design-based model specification framework for causal inference. Building on this, we develop a randomization-testing procedure to assess the correct specification of an exposure-mapping model in the presence of network interference. We provide theoretical guarantees for the asymptotic validity of the proposed testing procedure. We establish the favorable power properties of our method through an extensive simulation study and illustrate it in a field experiment investigating the effect of anti-conflict norms among adolescents.

Spatial autoregressive inference is typically conditional on the spatial weights matrix, W, even though the underlying interaction structure is often unknown and empirical conclusions can be sensitive to its specification. This paper develops double/debiased machine learning inference for low-dimensional SAR parameters when the spatial interaction operator is learned flexibly from potentially endogenous characteristics. Within a maintained admissible support, interaction strength is generated by an unknown function of geographic and socioeconomic characteristics, making inference robust to functional form specification of the weights within that support. Endogeneity in the characteristics generating W is addressed through a nonlinear control function based on locally relevant first-stage residual information. Because the learned operator enters both the spatial lag and spatially transformed instruments, treating the estimated W as known generally leaves a first-order generated-W effect. I construct an operator-orthogonal SAR-IV/GMM score that removes this leading sensitivity and combine it with buffered spatial cross-fitting that separates evaluation-score footprints from nuisance-training observations. Under near epoch dependence on a spatially mixing innovation field and target-relevant nuisance rate and regularity conditions, the estimator is asymptotically linear and root-n normal. Monte Carlo simulations show improved finite-sample inference relative to nonorthogonal alternatives when the interaction function is misspecified, weight generating characteristics are endogenous, and observations are spatially dependent. In a U.S. application, diabetes estimates vary with the choice of W, showing the sensitivity of SAR inference to the interaction structure. Even for the same learned W, results differ across inferential methods, highlighting the importance of inference when W is learned.