Papers

We present a methodology for analyzing node-level outcomes while experimenting with edge-level treatments in a population connected by an undirected graph. Under our design, nodes are randomly assigned to test or control, and each edge inherits the treatment of its endpoints, with conflicts resolved by randomization. We use each node's assigned status as an instrument for its treatment exposure. We show that the Wald estimator is consistent for the global average treatment effect (GATE), even when the edge weights used to construct the exposure are misspecified. We formalize the assumptions needed both in terms of the linearity of potential outcomes and the sparsity of the graph, and prove the asymptotic normality of the Wald estimator. The estimator is straightforward to implement, requiring no assignment simulations over the graph. Our Monte Carlo study demonstrates the strong performance of our approach in the context of a social platform.

Trade-sign errors can change measured trading costs even when classification accuracy is high. We validate the side of Polymarket's public trade prints against the taker leg of each print's on-chain settlement. On twelve selected days between April and August 2026, spanning both exchange generations, 92.1% to 100.0% of prints match a settled taker leg, with exact side and token agreement on all 24.5 million matched pairs. Mint-and-merge settlement makes that taker leg essential: pooling maker and taker legs changes the measured buy share. Signing the full cached tape before settlement selection yields 16.6 million prints signed by every rule; equal-day balanced accuracy is 0.942 for Lee-Ready, 0.768 for the tick test and 0.670 for retrospective bulk volume classification. On 16.4 million identical eligible fills, Lee-Ready raises effective spread by 0.429 cents per share under equal-fill weights; its realised-spread difference is -0.209 cents. Under share-volume weights, taker five-minute midpoint impact is 0.689 cents, while tick and bulk classifications give -0.374 and -0.119 cents. That aggregate sign reversal disappears when tied print rows are excluded. Distortion depends on error-weighted signed outcomes, sample selection and weighting. Receipt-time ordering and unobserved future-quote age limit these delivered-quote accounting quantities; they do not identify causal impact or private information. Supporting venue and collector analyses provide descriptive diagnostics.

Quadratic-form test statistics are widely used in econometrics, and their performance depends on accurate variance estimation. Conventional plug-in estimators are consistent under the null hypothesis, but under alternatives the drift in the residuals inflates them and the test loses power. We develop a general framework for variance estimation in such statistics, replacing one of the two squared-residual factors by an auxiliary linear combination of the residuals (“cross-fitting”) chosen to annihilate the drift. We characterize the conditional bias of each estimator exactly. The drift enters the plug-in estimator squared, multiplied by quantities bounded away from zero, so its bias is positive whenever the drift is non-degenerate. It reaches the cross-fit estimator only through the part that survives the cross-fitting, and then only through off-diagonal entries of a residual-maker matrix. From this calculation we obtain conditions under which the cross-fit estimator remains consistent under alternatives while the plug-in estimator does not. At a common critical value the cross-fit test therefore rejects whenever the plug-in test does, and against distant alternatives the plug-in statistic converges to a finite limit, small when few observations carry the departure: its power can tend to zero where the cross-fit test's tends to one. We verify the conditions under primitive assumptions in nonparametric specification testing, overidentification testing, and testing many linear restrictions, and illustrate the procedure on the Oregon Health Insurance Experiment.

We study difference-in-differences (DID) estimation of average treatment effects on the treated when the researcher is uncertain about which pre-treatment periods satisfy the parallel trends assumption. Roth (2022) shows that pre-trend testing can induce bias, complementing the statistical literature on post-selection inference. We propose the model averaged difference-in-differences (MADID) estimator, a weighted average of the candidate $2\times2$ DID estimators. The weights are normalized exponential functions of the candidate residual sums of squares, so implementation requires no specification test. We derive MADID's asymptotic properties under conditions that make invalid comparisons detectably more variable than at least one valid comparison. Under these conditions, MADID is consistent when the parallel trends assumption holds for at least one pre-treatment period. Although its joint limiting distribution across post-treatment periods is generally non-Gaussian, inference can be conducted by subsampling or simulation.

Finding which variables cause which others in multivariate time series, and at what lags, is central to science and policy, yet existing methods force a choice between flexible confounder adjustment, data-driven lag selection, and inference that controls the false discovery rate (FDR). ORACLE-VARX does all three in one pipeline. First, double/debiased machine learning (DML) removes nonlinear confounder effects from the outcomes and the lagged series. Second, adaptive causal lag estimation (ACLE) picks the lag order at each time step by sequential significance tests, tracking regime changes. Third, entry-wise $z$-tests with Benjamini–Hochberg correction select directed edges at a target FDR. We prove that in each rolling window, the debiased coefficients are asymptotically normal around a window-averaged target, so their $z$-tests are asymptotically valid. On a synthetic benchmark with time-varying structure and nonlinear confounding, ORACLE-VARX (LightGBM) tracks the true lag order best (RMSE $0.96$ vs $1.1$–$1.5$), has edge FDR $0.047$, close to PCMCI ($0.045$) and below VAR ($0.129$) and VAR-LiNGAM ($0.187$), and forecasts better than all three. On nine U.S. sector ETFs with macroeconomic confounders, it yields interpretable causal graphs whose lag order rises in high-volatility regimes.

Synthetic control relies on pre-treatment fit to balance the unobserved factors that drive untreated outcomes. The argument fails when an observed common shock, such as a commodity price, moves with the latent factors before treatment and departs from them afterwards and pre-treatment fit then says almost nothing about the synthetic unit's exposure to the shock. I derive a period-specific bound that links the post-treatment bias of any weighting estimator to pre-treatment misfit through a leverage statistic, and show that the statistic decomposes exactly into a latent-factor component and the partial leverage of the observed shock. The decomposition yields a diagnostic for such silent factor that uses no post-treatment outcome of the treated unit. Balancing an observed exposure index removes the problem, but simplex weights can achieve balance only when the treated unit lies inside the donors' exposure hull. Outside the hull, every simplex-weighted estimator carries an exposure imbalance with an explicit lower bound. For that case I propose an exposure-augmented synthetic control that corrects the remaining imbalance with a cross-donor regression, characterise what the correction identifies and when it fails, and derive bias-aware confidence intervals with a breakdown value. Monte Carlo experiments, including designs in which the correction's assumptions fail, map its gains and its limits. Iran's 2012 sanctions coincided with the 2014 oil collapse, and Iran is more oil-dependent than any of its natural comparators. The 2012-15 output loss of about 12 percent survives every adjustment. The persistent loss that standard synthetic control reports after 2016 does not. Any adjustment for oil exposure removes it, and the long-run effect is not identified with these comparators.

Clinical trials with survival endpoints lose information when participants are censored before death is observed. We develop target-preserving estimators that use posttreatment disease history, such as recurrence or progression, to recover information lost to censoring for marginal survival and restricted mean survival effects. The difficulty is that the intermediate event is downstream of treatment: naive adjustment can change the causal estimand, and the useful information enters only through the observed coarsening. We derive observed-data influence functions with and without recurrence history and obtain an exact gain identity. The identity shows that efficiency improvement is driven by the censoring hazard, the split of the alive risk set into recurrence states, and the residual-survival separation between those states. In the no-covariate illness-death model, the Aalen-Johansen estimator realizes the recurrence-augmented efficient score after standardization to the marginal target. With covariates, correctly specified Cox-Breslow transition hazards provide a root-N plug-in benchmark, while a hazard-induced one-step estimator gives rate robustness and, under primitive transition and censoring learner rates, canonical inference with a second-order product remainder. A semi-synthetic metastatic breast cancer study calibrated from digitized progression-free survival and overall survival curves illustrates the gain identity. The framework applies broadly to censored time-to-event studies with informative intermediate histories.

Matrix autoregressive (MAR) models offer a parsimonious framework for modeling matrix-valued time series, yet tools for estimation and inference for their impulse response functions are lacking. We develop asymptotic and bootstrap-based inference for impulse responses of stable MAR($p$) models. We derive the joint asymptotic distribution of the coefficient and covariance estimators, which permits closed-form delta-method standard errors. To address finite-sample bias, we propose ProBAB-MAR, a bias-corrected bootstrap that projects the corrected coefficients back onto the Kronecker parameter space, and prove that it attains asymptotically correct coverage. Monte Carlo simulations show that delta-method intervals undercover in small samples, while ProBAB-MAR achieves near-nominal coverage with intervals considerably narrower than those from an unrestricted VAR. An application to euro area inflation illustrates how shocks transmit across countries and inflation categories.

A new form of the fiscal multiplier suited to data expressed as gross growth rates is proposed, together with a structural vector autoregression that isolates discretionary fiscal policy from regime and rule-based components. Because cumulating growth-rate responses over a horizon involves a product rather than a sum, the proposed multiplier is multiplicative: both numerator and denominator are polynomials in the size of the fiscal impulse, so the multiplier varies nonlinearly with the scale of the expenditure programme – a dependence that conventional additive multipliers cannot capture. The multiplier requires no discounting, no ad hoc conversion factor, and no auxiliary estimate of an average expenditure share of output, and it is computed directly from nominal, non-seasonally-adjusted data, matching the terms in which government budgets are actually expressed. A version of the narrative approach to identification is introduced. It allows to decompose the influence of fiscal policy into a regime component, a standard policy rule embedded in the autoregressive structure, and discretionary shocks. Removing the regime component from the residuals yields smaller identified shocks, and correspondingly smaller multipliers, than found in SVARs not controlling for regime changes – closing much of the gap between SVAR- and DSGE-based estimates. It is found that multipliers vary substantially across countries and across types of government expenditure, that regime volatility itself differs markedly by country, and that several economies display cyclicality in spending and multiplier paths that only becomes visible once responses are cumulated multiplicatively. The resulting multipliers are nominal, derived from unadjusted data, proven to be sensitive to shock size, and purged of regime effects, offering a tool with direct relevance for budget planning and fiscal policy evaluation.

A common empirical strategy in triple-differences (DDD) is to include either covariate trends or covariate levels to a three-way fixed effects (3WFE) regression. This strategy is typically motivated by the conditional parallel gaps assumption which assumes that deviations from parallel trends are similar among units with comparable observed covariates. We formally study both 3WFE specifications and show that, in general, neither consistently estimates the average treatment effect on the treated (ATT). Our diagnosis has two parts. First, we show that the OLS estimands of both specifications fail to satisfy the covariate balancing condition that is sufficient for them to equal the ATT. Second, we characterize the additional assumptions for each OLS estimand to equal the ATT. To address these limitations, we propose a matched triple-differences framework that accommodates a general class of matching procedures, including nearest-neighbor matching and kernel matching. Within this framework, we construct a class of consistent matching estimators, establish their asymptotic normality, and provide a consistent variance estimator that accounts for the variability introduced by the matching step. Our empirical application shows that the proposed matched triple-differences estimator can yield estimates and qualitative conclusions that differ from those obtained using the 3WFE regression.

Random assignment can make ordinary least squares (OLS) inference insensitive to outcome dependence, yet iid resampling can still fail because assignment and resampling need not remove the same covariance terms. With binary treatment, the iid variance target differs from the sampling variance by exactly minus aggregate cross-unit covariance of treatment effects. Under a Gaussian first-order limit, positive covariance leads to over-rejection and negative covariance to under-rejection. Two designs can generate the same distribution for each observation but require variance corrections of opposite signs, so no marginal-only variance correction is first-order exact for both. For first-order Gaussian inference, only one covariance component—the covariance carried by the randomized-regressor score—must be recovered. Standard dependence estimators on that score restore validity under suitable ordered or grouped dependence conditions. In simulations with ordered data, fixed-bandwidth calibration reduces several large-bandwidth size distortions.

Imperfect measurements allow different underlying distributions to generate the same observations. Restrictions linking unobserved components can make it difficult to characterize all compatible distributions and compute the resulting range of parameter values. We ask how to construct computable parameter bounds and tighten them without additional data or stronger assumptions. We develop a general framework for partial identification under imperfect measurement based on distributionally robust optimization. We use measurement restrictions to construct a neighborhood around a benchmark distribution, ensuring that every compatible distribution lies within it. Optimizing over this neighborhood gives parameter bounds through a common procedure that can be adapted to different measurement problems. The choice of benchmark affects how informative these bounds are. We establish conditions under which changing it can tighten the bounds while preserving every parameter value consistent with the same data and assumptions. Applications to networks, missing outcomes, and regression illustrate how the framework tightens bounds and can recover the full range of compatible values.

This study develops a survey-calibrated, path-dependent agent-based microsimulation for evaluating crime and violence reduction policies in Bolivia. A synthetic population is constructed from the 2025 Household Survey and the fourth-quarter 2025 Continuous Employment Survey using official expansion weights and cross-survey donor matching. The model combines heterogeneous agents, place-based risk, criminal adaptation, institutional capacity, community organization, and multiple policy channels. Uncertainty is propagated through adaptive Gaussian-process and tree-ensemble emulators, global sensitivity analysis, tempered ensemble MCMC, and predictive meta-calibration. Simulated portfolios include focused policing, community control, Guardabosques-type incentives, social prevention, environmental interventions, justice reforms, investigation, rehabilitation, and financial-network disruption. Results are interpreted as structural policy scenarios rather than causal forecasts, with explicit attention to displacement, distributional effects, implementation capacity, and multi-objective trade-offs.

Cross-fitting is routine in much of applied research. While conventional confidence intervals that ignore cross-fold dependence are asymptotically valid in several settings, they undercover in many applications that share a common form of nonregularity: from the classic cross-validation problem of testing whether a fitted model outperforms another, to testing for heterogeneous treatment effects with machine learning, to estimating the value of a potentially non-unique optimal treatment regime. Exploiting a new locality condition, I show that a large class of cross-fitting estimators still satisfies a central limit theorem despite the nonregularity, but with an asymptotic variance that must be adjusted for the cross-fold correlation. Then, I propose a method for estimating this correlation and construct new confidence intervals that attain asymptotically nominal coverage. Finally, I show that the proposed confidence intervals attain approximately nominal coverage in a simulation study with random forests and neural networks.

Many policies assign treatment according to whether a score crosses a cutoff. Regression discontinuity (RD) designs identify the effect of treatment assignment, but the threshold policy itself may also reshape individuals' incentives, inducing behavioral responses that affect outcomes even holding treatment status fixed—a channel that conventional RD designs cannot capture. We develop a framework that exploits randomized variation in policy thresholds, together with rank-invariance-type restrictions, to identify the treatment-assignment and incentive-response effects. We illustrate the empirical relevance of this distinction using data from a merit-based scholarship experiment in Malawi. In this illustration, the conventional RD estimate is positive, while the incentive-response effect is negative and more than twice as large in magnitude. These findings suggest that threshold policies may generate unintended adverse behavioral responses, potentially reflecting discouragement induced by demanding thresholds, and caution against relying solely on conventional RD estimates when evaluating threshold policies.

This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean–variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean–variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide.

Text, images, and other rich covariates are increasingly compressed into AI-learned representations and then used as controls in causal analysis. We study when this approach is valid and develop a practical framework for causal inference with learned representations. For a broad class of estimands, an imperfect representation distorts the target causal parameter by the product of two representation errors: one in the outcome regression and one in the balancing weight (or Riesz representer). This yields three constructive results. First, cross-fitted double machine learning (DML) provides valid Wald inference for the representation-dependent target. When representation errors are small, the same interval covers the causal parameter, and it can even attain the semiparametric efficiency bound. Second, fold-wise representation learning (or fine-tuning) is compatible with DML inference for the causal parameter. To this end, we develop convex- and star-aggregation pipelines for learning and combining representations. Third, when representation errors are substantial, we can provide interpretable sensitivity regions and root-$n$ inference for their endpoints. In a multi-modal demand application, seven representation-specific estimates and their star aggregate all imply a negative near-unit elasticity for rank-based price response, and the result remains robust over the reported sensitivity grid.

Refreshment samples are the standard remedy for panel attrition, and the identification results behind them maintain that participation does not change measurement. We characterize what a refreshment sample identifies about panel conditioning, modelled as a deterministic monotone map at reinterview, when attrition is unrestricted. A candidate map is consistent with the data if and only if the retention-scaled distribution of the stayers' implied latent outcomes is setwise dominated by the refreshment distribution; every such map is rationalized by an explicit attrition process. Without attrition the map is identified on the latent-outcome support; with attrition, a density-ratio condition governs the identified set, and tail behaviour alone does not determine it. For an unrestricted map the survivors' mean effect has the familiar trimming bounds; for an item with all categories reported, the model reduces to a test of no conditioning. Within a cohort, other waves, dropout patterns and entry-wave items leave the set unchanged unless restrictions link selection across waves. Under explicit selection restrictions, survival matching, symmetric matching and entry-wave correction identify survivor effects. We derive their biases and give rank conditions under which refreshment schedules identify curvature in the conditioning path. A Japanese panel illustrates the results.

The increasing volatility of electricity prices driven by renewable energy integration, market shocks, and regulatory changes has reinforced the need for forecasting methods that go beyond point predictions and accurately describe the full conditional price distribution. This paper applies the Generalised Additive Models for Location, Scale and Shape (GAMLSS) framework to forecast Spanish day-ahead electricity prices using hourly data from 2020 to 2024. Alternative specifications based on Normal, Johnson's SU (JSU), and Sinh-Arcsinh (SHASH) distributions are considered, allowing the location, scale, and shape parameters to vary with market fundamentals, including electricity demand, renewable generation, seasonal effects, and regulatory and geopolitical risk factors. Forecasts are generated using a rolling-window approach and evaluated through the mean absolute error (MAE), pinball loss, and Diebold-Mariano tests. The results show that flexible distributional specifications improve forecasting performance relative to a naive benchmark and the standard normal specification. While SHASH and JSU specifications provide the lowest point forecasting errors, the hourly analysis reveals substantial intraday variation in relative performance across specifications. JSU specification with all four parameters driven by covariates achieves the best probabilistic forecasting performance, particularly in the tails of the distribution. Diebold-Mariano tests confirm the statistical significance of these improvements. These findings highlight the importance of modelling time-varying shape distributional parameters and demonstrate the value of GAMLSS models for forecasting and risk management in increasingly volatile electricity markets.

We develop the first empirically implementable selective-inference framework for difference-in-differences with controls selected by pre-treatment fit. We construct confidence intervals for the average treatment effect on the treated (ATT), incorporating that selection and estimating the unknown full covariance from the same observations. Counterexamples establish undercoverage from Roth's fixed-comparison pretest adjustment and direct Gaussian-score application of Andrews–Kitagawa–McCloskey to this selection, despite parallel trends for every candidate. Retaining the actual polynomial or piecewise-polynomial event, we establish uniform validity at perfect fit and population ties, endpoint equivalence with known-covariance inference, and unequal-sample guarantees. We accommodate staggered adoption, reused observations, and fitting-rule choice. In police-deployment and minimum-wage reanalyses, we find changes in significance and economically relevant effect ranges while retaining the selected comparison. For a smooth randomized test, we obtain higher-order accuracy through stabilized joint mean–covariance correction preserving normal-sampling baseline rejection probabilities. Researchers should disclose selection rules alongside ATT uncertainty.

We study the anatomy of commodity risk by distinguishing micro, market-level, and economy-wide sources. We develop a two-stage "divide-and-conquer" framework that allows sensitivities to these risk sources to vary across commodities while treating economy-wide risk as latent. The first stage uses defactored instrumental-variable estimation to recover commodity-specific sensitivities to micro and market conditions. The second combines principal components with high-dimensional variable selection to identify an observable representation of macro-financial risk. We then construct Risk Intensity Indices (RIIs), which combine estimated sensitivities with prevailing risk conditions to quantify the relative importance of each risk source on a common scale. Market risk is the largest component on average, accounting for about two fifths of total risk intensity and more than half for energy commodities. Risk intensity is also highly concentrated across individual commodities: the top 20% account for approximately half of micro and market risk intensity, whereas macro risk is more broadly dispersed. The composition of risk varies substantially across sectors and over time, with market risk becoming particularly prominent during episodes of commodity-market stress. Micro and market RIIs also contain information about future volatility and absolute returns. These findings provide investors, risk managers, and policymakers with a diagnostic of where commodity risk is concentrated, which risk layers are most important, and how their importance changes over time. More broadly, our divide-and-conquer framework provides a flexible approach to decomposing layered risk in settings where common risk is latent.

In many statistical settings, the available data and maintained assumptions do not suffice to uniquely identify the model parameters of interest. In such cases, one can only identify sets which are guaranteed to contain the true parameters. These are often characterized through linear programs that optimize over models compatible with the observed data. These programs can be infinite-dimensional in the optimizer and the number of constraints. We provide a unified way to characterize and solve such optimization problems by phrasing them as optimal transport problems on path spaces. This allows us to regularize the problem with an entropy penalty, recasting it as a multi-marginal entropic optimal transport problem, which can be solved efficiently via Sinkhorn iterations. In addition, it allows us to establish convergence of the regularized value to the sharpest bound, derive consistency rates for a plug-in estimator, and obtain asymptotic distribution for approximate bounds. The method is general and accommodates settings ranging from instrumental variable models with continuous variables to welfare estimation in heterogeneous demand models. We verify the statistical and computational properties in simulations and provide an application to demand estimation.

This paper develops a framework for estimation and inference on the volumes of sets that are projections of critical function sets, focusing particularly on the convex body beneath the optimal receiver operating characteristic (ROC) surface. Specifically, we propose a volume calculation method that first uses an Aumann expectation representation and then applies Minkowski mixed volumes. Using this framework, we show that the population volume under the ROC surface (VUS) is proportional to the expectation of a symmetric U-statistic kernel. We then propose a double/debiased machine learning estimator of the VUS, derive its asymptotic properties, and develop an inference procedure. Further applications of this framework include an analysis of the feasible error set across pre-defined groups and a natural generalization of the Gini coefficient for measuring inequality.

Imputation-based causal estimation is typically viewed as relying exclusively on an outcome model, in contrast to augmented inverse-probability weighting, whose consistency is protected by fitting two nuisance models. This paper argues that this view can be misleading by highlighting a hidden dual weighting structure in least-squares sieve regression imputation. Although only outcome regressions are explicitly fitted, the resulting imputation estimator admits an exact weighting representation whose induced weights balance every function in the sieve space and the corresponding population weighting functions are the $L^2$ projections of the inverse propensity scores onto the same sieve space. This projection structure yields an implicit form of double robustness and, under standard sieve approximation and growth conditions, asymptotic linearity with the efficient influence function. Thus, weighting, covariate balance, double robustness, and semiparametric efficiency can all emerge from imputation alone through the geometry of least-squares projection.

We study estimation and inference for a partially identified parameter whose identified set depends on a first-stage nuisance parameter that must itself be estimated. Combining the criterion-function approach with the theory of Neyman-orthogonal moments that underlies double/debiased machine learning, we propose a two-step procedure: the point-identified nuisance is estimated by flexible machine-learning methods, and the set-identified target is recovered as a level set of a sample criterion built from orthogonal moment inequalities with cross-fitting. When the contour level is bounded, we show that the resulting set estimator converges in Hausdorff distance at the parametric rate of the infeasible criterion built on the true nuisance. We further develop a subsampling procedure that delivers asymptotically valid coverage, provided the product of the first-stage estimation errors is $o(N^{-1/2})$. We illustrate the method on bounds for the wage distribution and the interquantile range under selection into employment and on the gender wage gap with an interval-censored wage. The empirical application studies the gender wage gap using the March supplement of the 2015 Current Population Survey.

We answer the question posed in the title with a nonlinear mixed-frequency vector autoregression, estimated with Bayesian additive regression trees. The model combines monthly macro-financial variables with quarterly bank lending survey data, and identifies the dynamic responses from high-frequency policy surprises. Sign asymmetry dominates; a tightening produces monetary policy transmission mostly in line with the theoretical predictions, whereas easing of any size produces mostly insignificant responses. Peak effects vary with initial conditions, while several common, predefined regime splits do not yield considerable differences in the propagation of the shocks.

Ignoring unobserved heterogeneity in duration models biases parameter estimates and invalidates inference, but testing for it is non-regular: the null hypothesis lies on the boundary of the parameter space and some parameters are unidentified under the null. These features render standard asymptotic theory inapplicable. This paper develops an EM test for unobserved heterogeneity in censored Weibull duration models, building on the EM approach of Li, Chen, and Marriott (2009). The test statistic has an asymptotic null distribution equal to the square of max{0, N(0,1)}, hence critical values require neither simulation nor bootstrap, and the test accommodates covariate-dependent censoring of arbitrary form. Monte Carlo simulations compare the EM test with the likelihood ratio test (LRT) of Cho and White (2010), information matrix tests, and Lagrange multiplier tests. The EM test has empirical size close to the nominal level for sample sizes of 500 or more, where the LRT remains markedly conservative and the other tests over-reject. Its size-adjusted power is comparable to that of the LRT and higher than that of the other tests. Because size adjustment requires knowledge of the data-generating process and is unavailable in practice, the EM test attains higher power than the LRT in most designs as the tests would actually be applied. In an application to the Stanford Heart Transplant data, the EM test rejects homogeneity in every covariate specification, whereas the LRT's conclusion depends on a user-chosen set of admissible parameter values and on the specification.

This paper characterizes the global minimum of the continuously updating generalized method of moments (CU-GMM) objective in linear instrumental variables models. We allow optimal weighting matrices under heteroskedasticity, autocorrelation, or clustering. We show that the objective is a ratio of polynomials. For one endogenous regressor, stationary points of CU-GMM objective function are real eigenvalues of a companion matrix. Comparing their objective values with the value at infinity gives the global minimum, extending the classical eigenvector approach to limited information maximum likelihood. With multiple endogenous regressors, algebraic elimination and checks for real solutions identify the minimum among finitely many candidate objective values, including boundary values. Galois theory rules out general formulas by radicals even with one endogenous regressor and two instruments, while numerical root finding remains possible. Finding the global minimum allows us to compute overidentification and likelihood ratio tests, including the conditional likelihood ratio (CLR) test.

Seasonal adjustment is fundamental to economic analysis, but uncertain because seasonal components are inherently latent. This article introduces a probabilistic model discovery method that decomposes a time series into seasonal and nonseasonal components. The method returns a posterior distribution over the structure and parameters of a seasonal component. In simulation studies, the method can improve point forecasts, interval predictions, and recovery of seasonal components relative to X-13ARIMA-SEATS. In a study of eight U.S. macroeconomic series during the COVID-19 recession, the method surfaces significant ex-ante uncertainty about current seasonal adjustments in real time, well before many X-13 revisions reach their eventual peaks.

Price stability remains a pillar in monetary policy practices and carries a special importance within monetary unions. Mainstream economics tried to leverage price stability using price indices and several metrics to shed light on specific dynamics and optimal macroeconomic levels. The wide availability of data led researchers to consider the study of systems using Random Matrix Theory, based on inner correlation patterns. This aims to enhance the multivariate analysis by removing noisy patterns from the signal and improve data quality for further inferences. This work considers the collection of monthly inflation indices in the Eurozone as a system of prices to analyze its eigenvalues' statistical and asymptotic properties and uncover inner country-level insights. Results confirm the system cannot assumed to be randomly generated, and the data exhibit noise-dominated patterns, due to small and persistent variations at the country-level. The latter make the inter-country correlations more dynamic and the separation of the signal from the noise quiet difficult. Findings identified two countries as distorting inflation dynamics besides three other distinct, regional-based groups of countries. Variability sources might stem from economic episodes fueling inflation spikes in some countries, as well as methodological aspects used to ensure data quality and representativeness in the European Union. Despite being complex, the system demonstrates a certain stability, in terms of self-organization; while large monthly fluctuations cannot be considered as rare events, but part of the data-generating process.