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on Econometrics |
| By: | Masahiro Kato |
| Abstract: | This study proposes Riesz representer estimation methods based on score matching. The Riesz representer is a key component in debiased machine learning for constructing $\sqrt{n}$-consistent and efficient estimators in causal inference and structural parameter estimation. To estimate the Riesz representer, direct approaches have garnered attention, such as Riesz regression and the covariate balancing propensity score. These approaches can also be interpreted as variants of direct density ratio estimation (DRE) in several applications such as average treatment effect estimation. In DRE, it is well known that flexible models can easily overfit the observed data due to the estimand and the form of the loss function. To address this issue, recent work has proposed modeling the density ratio as a product of multiple intermediate density ratios and estimating it using score-matching techniques, which are often used in the diffusion model literature. We extend score-matching-based DRE methods to Riesz representer estimation. Our proposed method not only mitigates overfitting but also provides insights for causal inference by bridging marginal effects and average policy effects through time score functions. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.20523 |
| By: | Marc-Oliver Pohle; Jan-Lukas Wermuth; Christian H. Wei{\ss} |
| Abstract: | Kendall's tau and Spearman's rho are widely used tools for measuring dependence. Surprisingly, when it comes to asymptotic inference for these rank correlations, some fundamental results and methods have not yet been developed, in particular for discrete random variables and in the time series case, and concerning variance estimation in general. Consequently, asymptotic confidence intervals are not available. We provide a comprehensive treatment of asymptotic inference for classical rank correlations, including Kendall's tau, Spearman's rho, Goodman-Kruskal's gamma, Kendall's tau-b, and grade correlation. We derive asymptotic distributions for both iid and time series data, resorting to asymptotic results for U-statistics, and introduce consistent variance estimators. This enables the construction of confidence intervals and tests, generalizes classical results for continuous random variables and leads to corrected versions of widely used tests of independence. We analyze the finite-sample performance of our variance estimators, confidence intervals, and tests in simulations and illustrate their use in case studies. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.14609 |
| By: | Domenico Giannone; Michele Lenza; Giorgio Primiceri |
| Abstract: | It is well known that standard frequentist inference breaks down in IV regressions with weak instruments. Bayesian inference with diffuse priors suffers from the same problem. We show that the issue arises because flat priors on the first-stage coefficients overstate instrument strength. In contrast, inference improves drastically when an uninformative prior is specified directly on the concentration parameter—the key nuisance parameter capturing instrument relevance. The resulting Bayesian credible intervals are asymptotically equivalent to the frequentist confidence intervals based on conditioning approaches, and remain robust to weak instruments. |
| JEL: | C01 C11 C12 C26 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34648 |
| By: | Daniel Czarnowske; Amrei Stammann |
| Abstract: | Inference for fixed effects estimators of linear and nonlinear panel models is often unreliable due to Nickell- and/or incidental parameter biases. This article develops new inferential theory for (non)linear fixed effects M-estimators with data featuring a three-dimensional panel structure, such as sender x receiver x time. Our theory accommodates bipartite, directed, and undirected network panel data, integrates distinct specifications for additively separable unobserved effects with different layers of variation, and allows for weakly exogenous regressors. Our analysis reveals that the asymptotic properties of fixed effects estimators with three-dimensional panel data can deviate substantially from those with two-dimensional panel data. While for some specifications the estimator turns out to be asymptotically unbiased, in other specifications, it suffers from a particularly severe inference problem, characterized by a degenerate asymptotic distribution and complex bias structures. We address this atypical inference problem, by deriving explicit expressions to debias the fixed effects estimators. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.18678 |
| By: | Daniel Lewis; Karel Mertens |
| Abstract: | We approximate the finite-sample distribution of impulse response function (IRF) estimators that are just-identified with a weak instrument using the conventional local-to-zero asymptotic framework. Since the distribution lacks a mean, we assess bias using the mode and conclude that researchers prioritizing robustness against weak instrument bias should favor vector autoregressions (VARs) over local projections (LPs). Existing testing procedures are ill-suited for assessing weak instrument bias in IRF estimates, and we propose a novel simple test based on the usual first stage F-statistic. We investigate instrument strength in several applications from the literature, and discuss to what extent structural parameters must be restricted ex-ante to reject meaningful bias due to weak identification. |
| Date: | 2026–01–05 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:01/26 |
| By: | Brigham R. Frandsen; Lars J. Lefgren; Emily C. Leslie; Samuel P. McIntyre |
| Abstract: | In instrumental variables (IV) estimation with many instruments, such as judge fixed effects designs, the precision of the jackknife-estimated first stage can vary widely across observations. When such variability exists, we show that the precision of JIVE second-stage estimates is meaningfully improved by shrinking judge propensities towards their conditional means, where the shrinkage factor depends on the precision of the first-stage fitted value. Doing so requires no further assumptions and identifies the same local average treatment effect as the usual (unshrunken) JIVE estimator. We illustrate the precision gains from using a Shrunken JIVE estimator (SJIVE) in an application from the literature studying pre-trial detention of defendants in criminal cases. |
| JEL: | C1 C11 C21 K14 |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34634 |
| By: | Stephane Bonhomme |
| Abstract: | Many popular estimation methods in panel data rely on the assumption that the covariates of interest are strictly exogenous. However, this assumption is empirically restrictive in a wide range of settings. In this paper I argue that credible empirical work requires meaningfully relaxing strict exogeneity assumptions. Econometricians have developed methods that allow for sequential exogeneity, which in contrast with strict exogeneity allows for the presence of feedback from past outcomes to future covariates or treatments. I review some of the classic work on linear models with constant coefficients, and then describe some approaches that allow for coefficient heterogeneity in models with feedback. Finally, in the last two parts of the paper I review recent work that allows for sequential exogeneity in nonlinear panel data models, and mention possible extensions to network settings. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.17576 |
| By: | Hiroaki Kaido; Kirill Ponomarev |
| Abstract: | Exclusion and shape restrictions play a central role in defining causal effects and interpreting estimates in potential outcomes models. To date, the testable implications of such restrictions have been studied on a case-by-case basis in a limited set of models. In this paper, we develop a general framework for characterizing sharp testable implications of general support restrictions on the potential response functions, based on a novel graph-based representation of the model. The framework provides a unified and constructive method for deriving all observable implications of the modeling assumptions. We illustrate the approach in several popular settings, including instrumental variables, treatment selection, mediation, and interference. As an empirical application, we revisit the US Lung Health Study and test for the presence of spillovers between spouses, specification of exposure maps, and persistence of treatment effects over time. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.20851 |
| By: | Ian Xu |
| Abstract: | Randomization-based inference commonly relies on grid search methods to construct confidence intervals by inverting hypothesis tests over a range of parameter values. While straightforward, this approach is computationally intensive and can yield conservative intervals due to discretization. We propose a novel method that exploits the algebraic structure of a broad class of test statistics--including those with variance estimators dependent on the null hypothesis--to produce exact confidence intervals efficiently. By expressing randomization statistics as rational functions of the parameter of interest, we analytically identify critical values where the test statistic's rank changes relative to the randomization distribution. This characterization allows us to derive the exact p-value curve and construct precise confidence intervals without exhaustive computation. For cases where the parameter of interest is a vector and a confidence region is needed, our method extends by calculating and storing the coefficients of the polynomial functions involved. This approach enables us to compute approximate p-value functions and confidence regions more efficiently than traditional grid search methods, as we avoid recalculating test statistics from scratch for each parameter value. We illustrate our method using tests from Pouliot (2024) and extend it to other randomization tests, such as those developed by DiCiccio and Romano (2017) and D'Haultf{\oe}uille and Tuvaandorj (2024). Our approach significantly reduces computational burden and overcomes the limitations of traditional grid search methods, providing a practical and efficient solution for confidence interval and region construction in randomization-based inference. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.14024 |
| By: | Yue Fang; Geert Ridder; Haitian Xie |
| Abstract: | Recent literature on policy learning has primarily focused on regret bounds of the learned policy. We provide a new perspective by developing a unified semiparametric efficiency framework for policy learning, allowing for general treatments that are discrete, continuous, or mixed. We provide a characterization of the failure of pathwise differentiability for parameters arising from deterministic policies. We then establish efficiency bounds for pathwise differentiable parameters in randomized policies, both when the propensity score is known and when it must be estimated. Building on the convolution theorem, we introduce a notion of efficiency for the asymptotic distribution of welfare regret, showing that inefficient policy estimators not only inflate the variance of the asymptotic regret but also shift its mean upward. We derive the asymptotic theory of several common policy estimators, with a key contribution being a policy-learning analogue of the Hirano-Imbens-Ridder (HIR) phenomenon: the inverse propensity weighting estimator with an estimated propensity is efficient, whereas the same estimator using the true propensity is not. We illustrate the theoretical results with an empirically calibrated simulation study based on data from a job training program and an empirical application to a commitment savings program. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.19230 |
| By: | Agust\'in Garc\'ia-Garc\'ia; Pablo Hidalgo; Julio E. Sandubete |
| Abstract: | Explainable Artificial Intelligence (XAI) is increasingly required in computational economics, where machine-learning forecasters can outperform classical econometric models but remain difficult to audit and use for policy. This survey reviews and organizes the growing literature on XAI for economic time series, where autocorrelation, non-stationarity, seasonality, mixed frequencies, and regime shifts can make standard explanation techniques unreliable or economically implausible. We propose a taxonomy that classifies methods by (i) explanation mechanism: propagation-based approaches (e.g., Integrated Gradients, Layer-wise Relevance Propagation), perturbation and game-theoretic attribution (e.g., permutation importance, LIME, SHAP), and function-based global tools (e.g., Accumulated Local Effects); (ii) time-series compatibility, including preservation of temporal dependence, stability over time, and respect for data-generating constraints. We synthesize time-series-specific adaptations such as vector- and window-based formulations (e.g., Vector SHAP, WindowSHAP) that reduce lag fragmentation and computational cost while improving interpretability. We also connect explainability to causal inference and policy analysis through interventional attributions (Causal Shapley values) and constrained counterfactual reasoning. Finally, we discuss intrinsically interpretable architectures (notably attention-based transformers) and provide guidance for decision-grade applications such as nowcasting, stress testing, and regime monitoring, emphasizing attribution uncertainty and explanation dynamics as indicators of structural change. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.12506 |
| By: | Shunsuke Imai |
| Abstract: | Uniform confidence bands for functions are widely used in empirical analysis. A variety of simple implementation methods (most notably multiplier bootstrap) have been proposed and theoretically justified. However, an implementation over a literally continuous index set is generally computationally infeasible, and practitioners therefore compute the critical value by evaluating the statistic on a finite evaluation grid. This paper quantifies how fine the evaluation grid must be for a multiplier bootstrap procedure over finite grid points to deliver valid uniform confidence bands. We derive an explicit bound on the resulting coverage error that separates discretization effects from the intrinsic high-dimensional bootstrap approximation error on the grid. The bound yields a transparent workflow for choosing the grid size in practice, and we illustrate the implementation through an example of kernel density estimation. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.18627 |
| By: | Philipp Ketz; Adam McCloskey; Jan Scherer |
| Abstract: | In nonstandard testing environments, researchers often derive ad hoc tests with correct (asymptotic) size, but their optimality properties are typically unknown a priori and difficult to assess. This paper develops a numerical framework for determining whether an ad hoc test is effectively optimal - approximately maximizing a weighted average power criterion for some weights over the alternative and attaining a power envelope generated by a single weighted average power-maximizing test. Our approach uses nested optimization algorithms to approximate the weight function that makes an ad hoc test's weighted average power as close as possible to that of a true weighted average power-maximizing test, and we show the surprising result that the rejection probabilities corresponding to the latter form an approximate power envelope for the former. We provide convergence guarantees, discuss practical implementation and apply the method to the weak instrument-robust conditional likelihood ratio test and a recently-proposed test for when a nuisance parameter may be on or near its boundary. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.19843 |
| By: | Li, Mengchu; Chen, Yudong; Wang, Tengyao; Yi, Yu |
| Abstract: | We study mean change point testing problems for high-dimensional data, with exponentially- or polynomially-decaying tails. In each case, depending on the ℓ0-norm of the mean change vector, we separately consider dense and sparse regimes. We characterise the boundary between the dense and sparse regimes under the above two tail conditions for the first time in the change point literature and propose novel testing procedures that attain optimal rates in each of the four regimes up to a poly-iterated logarithmic factor. To be specific, when the error distributions possess exponentially-decaying tails, a near-optimal CUSUM-type statistic is considered. As for polynomially-decaying tails, admitting bounded α-th moments for some α ≥ 4, we introduce a median-of-means-type test statistic that achieves a near-optimal testing rate in both dense and sparse regimes. Our investigation in the even more challenging case of 2 ≤ α |
| Keywords: | change points; heavy-tailed error; minimax testing; high-dimensional data; robustness |
| JEL: | C1 |
| Date: | 2026–01–05 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:130166 |
| By: | Neville Francis; Peter Reinhard Hansen; Chen Tong |
| Abstract: | We take a new perspective on identification in structural dynamic models: rather than imposing restrictions, we optimize an objective. This provides new theoretical insights into traditional Cholesky identification. A correlation-maximizing objective yields an Order- and Scale-Invariant Identification Scheme (OASIS) that selects the orthogonal rotation that best aligns structural shocks with their reduced-form innovations. We revisit a large number of SVAR studies and find, across 22 published SVARs, that the correlations between structural and reduced-form shocks are generally high. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.17005 |
| By: | Fabio Canova; Luca Fosso |
| Abstract: | This paper studies the consequences of using a deterministic steady state in Vector Autoregressive (VAR) models, when the data may display structural breaks, transitional dynamics or low-frequency fluctuations. We document substantial upward biases in the estimated coefficients, with distortions further amplified by the identification scheme. Allowing the steady state to be stochastic, however, reduces these distortions. To address this issue, we propose a spike-and-slab prior to differentiate between two alternative long-run specifications. Finally, we apply our empirical framework to revisit two well-known debates in macro: (i) the dynamics of hours in response to technology shocks; (ii) the habit formation hypothesis and the humpshaped response of consumption to business cycle shocks. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:bny:wpaper:0145 |
| By: | Fabrizia Mealli; Javier Viviens |
| Abstract: | 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). |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.21176 |
| By: | Jeff Dominitz; Charles F. Manski |
| Abstract: | We study the population limit maximum regret (MR) of plug-in prediction when the decision problem is to choose between two treatments for the members of a population with observed covariates x. In this setting, the optimal treatment for persons with covariate value x is B if the conditional probability P(y = 1|x) of a binary outcome y exceeds an x-specific known threshold and is A otherwise. This structure is common in medical decision making, as well as non-medical contexts. Plug-in prediction uses data to estimate P(y|x) and acts as if the estimate is accurate. We are concerned that the model used to estimate P(y|x) may be misspecified, with true conditional probabilities being outside the model space. In practice, plug-in prediction has been performed with a wide variety of prediction models that commonly are misspecified. Further, applications often use a conventional x-invariant threshold, whereas optimal treatment choice uses x-specific thresholds. The main contribution of this paper is to shed new light on limit MR when plug-in prediction is performed with misspecified models. We use a combination of algebraic and computational analysis to study limit MR, demonstrating how it depends on the limit estimate and on the thresholds used to choose treatments. We recommend that a planner who wants to use plug-in prediction to achieve satisfactory MR should jointly choose a predictive model, estimation method, and x-specific thresholds to accomplish this objective. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.19824 |
| By: | Carboni, Giacomo; Fonseca, Luís; Fornari, Fabio; Urrutia, Leonardo |
| Abstract: | We investigate the impact of structural shocks on the joint distribution of future real GDP growth and inflation in the euro area. We model the conditional mean of these variables, along with selected financial indicators, using a VAR and perform quantile regressions on the VAR residuals to estimate their time-varying variance as a function of macroeconomic and financial variables. Through impulse response analysis, we find that demand and financial shocks reduce expected GDP growth and increase its conditional variance, leading to negatively skewed future growth distributions. By enabling this mean-volatility interaction, demand and financial shocks drive significant time variation in downside risk to euro area GDP growth, while supply shocks result in broadly symmetric movements. For inflation, supply shocks drive instead a positive mean-volatility co-movement, where higher inflation is associated with increased uncertainty, causing time variation in upside risk. JEL Classification: C32, C58, E32, G17 |
| Keywords: | downside risk, euro area, mean-variance correlation, quantile regressions, stochastic volatility, structural shocks, tail risk, vector autoregression (VAR) |
| Date: | 2026–01 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263171 |
| By: | Siddhartha Chib; Fei Tan |
| Abstract: | We show how state-of-the-art large language models (LLMs), seemingly inapplicable to the small samples typical of macroeconomics, can be trained to learn the language of macroeconomy. We estimate a large-scale dynamic stochastic general equilibrium (DSGE) model on an initial segment of the data and obtain a posterior distribution over structural parameters. We sample from this posterior to generate millions of theory-consistent synthetic panels that, when mixed with actual macroeconomic data, form the training corpus for a time-series transformer with attention. The trained model is then used to forecast out-of-sample through 2025. The results show that this hybrid forecaster, which combines the theoretical coherence of DSGE models with the representational power of modern LLMs, successfully learns the macroeconomic language. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.21031 |
| By: | Pooyan Amir-Ahmadi; Marko Mlikota; Dalibor Stevanovi\'c |
| Abstract: | For a general class of dynamic and stochastic structural models, we show that (i) non-linearity in economic dynamics is a necessary and sufficient condition for time-varying parameters (TVPs) in the reduced-form VARMA process followed by observables, and (ii) all parameters' time-variation is driven by the same, typically few sources of stochasticity: the structural shocks. Our results call into question the common interpretation that TVPs are due to "structural instabilities". Motivated by our theoretical analysis, we model a set of macroeconomic and financial variables as a TVP-VAR with a factor-structure in TVPs. This reveals that most instabilities are driven by a few factors, which comove strongly with measures of macroeconomic uncertainty and the contribution of finance to real economic activity, commonly emphasized as important sources of non-linearities in macroeconomics. Furthermore, our model yields improved forecasts relative to the standard TVP-VAR where TVPs evolve as independent random walks. |
| Date: | 2025–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2512.20152 |