Papers

I study randomization inference for dynamic causal effects in panels with many units and few periods when treatment is endogenous and an instrument is as good as randomly assigned only through the innovations of a first-order autoregressive assignment mechanism with unknown persistence. The persistence is a nuisance parameter in two senses: it determines which weighted average of heterogeneous causal effects the instrumented local projection estimand measures, and it governs the randomization distribution of any statistic built from the instrument. I propose tests that never estimate it. For each candidate value the innovations are recovered, rerandomized under a group that leaves their joint law invariant, and a randomization p-value is formed; the reported p-value is the supremum over candidate values or over an exact confidence set. Under a sharp null on the path of lag-specific effects the tests have level at most $\alpha$ for every persistence in finite samples, including the unit root, and the supremum is a maximum over finitely many points. Under a weak null on the heterogeneity-weighted estimand a studentized version is uniformly asymptotically valid.

The most widely used investment risk measures - variance, standard deviation, and tracking error - treat upside deviations as equally undesirable as downside losses. In stable markets with assumed symmetric return distributions, this simplification is potentially harmless. In the climate transition age, it is not. Climate risk is two-dimensionally asymmetric, across assets and over time. Both dimensions are negatively skewed against investors. Hence, climate transition investment strategies deliberately deviate from benchmarks that reflect an insufficiently decarbonising global economy. When fiduciaries enforce tracking error budgets that penalise outperformance just as heavily as underperformance, they inadvertently constrain exactly the portfolio return opportunities that climate-aware investing seeks. We argue that replacing symmetric deviation-based risk measures with their downside-only counterparts - semi-variance, standard risk and trailing error - resolves this conflict without sacrificing any fiduciary discipline. The distinction is not merely semantic: as the gap between climate transition trajectories and market benchmarks widens over the coming decades, symmetric risk budgets will become binding constraints on transition strategies well before actual investment risk warrants it. We propose specific changes to mandate design that would allow institutional investors to pursue climate transition opportunities within genuinely risk-aware (rather than deviation-averse) frameworks.

This paper provides moment conditions for dynamic multinomial logit panel data models with individual specific fixed effects. The moment conditions do not depend on the fixed effects and thus form the basis for generalized method of moments estimation. For a leading case, we provide sufficient conditions under which the moment conditions identify the common parameters, and we illustrate their use in an empirical application to household soft drink purchases. The construction of moment conditions is based on transformed models obtained by permuting outcomes across time periods. For any cyclic permutation, the ratio of the transformed model probability to the true model probability is free of the fixed effects, and comparing two such ratios yields restrictions on the common parameters of interest. This construction is not specific to the multinomial logit. It applies to any dynamic panel data model whose static counterpart admits a symmetric sufficient statistic for the fixed effects. This unifies our main result with analogous results for other models.

Event studies with panel data are widely used to estimate treatment effects. With repeated cross-sections, future treatment dates are unobserved for untreated individuals. Pseudo-panel event studies impute pre-treatment outcomes of the treated using matched untreated individuals. This paper establishes identification in such designs and characterizes bias when identification conditions fail. I show that the pseudo-panel regression is equivalent to weighted least squares with group means. This representation simplifies computation and yields analytical inference. In simulations, analytical confidence intervals attain near-nominal coverage, whereas conventional intervals substantially undercover. I also develop a doubly robust estimator using richer covariates, a symmetric matching design with synthetic type fixed effects, and a fully nonparametric estimator that accommodates heterogeneous treatment effects. In a Korean panel survey, the pseudo-panel regression yields an employment child penalty of 42.1%, close to 46.9% in the actual panel. Applications to repeated cross-sections yield employment penalties of about one-third.

This paper develops likelihood-based estimation for parametric rational inattention–additive random utility models. We establish consistency and asymptotic normality of the exact maximum likelihood estimator and provide conditions under which the simulated estimator shares its asymptotic distribution. To implement estimation, we develop Newton–BA, a KKT-guided hybrid of Newton–Raphson and Blahut–Arimoto (BA). The algorithm accommodates both interior and boundary solutions and substantially improves computational efficiency relative to direct BA while preserving numerical accuracy. Monte Carlo simulations show that parameter recovery improves with sample size and that confidence-interval coverage is generally close to the nominal $95$ percent level. Finally, we compare our model with no- and perfect-information logit benchmarks in an empirically calibrated ModeCanada experiment. Our model achieves similar in-sample likelihood fit to perfect-information logit but more accurately recovers key preference parameters, choice probabilities, and responses to travel-time changes.

We propose a heteroskedasticity-robust and dimention-adaptive test for multiple linear restric- tions in sparse high-dimensional linear regression models. It combines desparsified LASSO estimation with a ridge-regularized quadratic form statistic and critical values that adapt to the restriction dimension. Under stated regularity conditions, our approach is asymptotically valid under a fixed or diverging number of restrictions without specifying the asymptotic regime in advance. Our random-design theory allows independent non-identically distributed covari- ate rows with marginal sub-Weibull tails and heteroskedastic errors satisfying finite polynomial moments. Monte Carlo simulations demonstrate improved finite-sample size control relative to conventional Wald tests, particularly as the number of restrictions increases.

In this paper, we develop an asymptotically normal estimator for the value of policy improvement (VPI) under adaptively collected data. This value, which is defined as the gap between the value of the best treatment policy in a class and that of a baseline policy, gauges whether or not it is worth deploying a personalized treatment policy. Building an estimator for the VPI is naturally more difficult than estimating the value of a fixed policy. This is because, in addition to contending with the correlated data and decaying propensities associated with adaptive experiments, any estimator must also handle the non-regularity, or lack of pathwise differentiability, of the underlying estimand when the optimal policy is non-unique. Our proposed estimator works by sequentially fitting a weighted empirical welfare maximizing policy on historical data and then evaluating it using inverse propensity weighting on future samples. We neither assume that the optimal policy is unique nor make a margin assumption on the underlying heterogeneous treatment effects. A key difficulty in analyzing our estimator is showing that the regret incurred through policy learning is asymptotically smaller than the standard error of the estimator. We accomplish this by showing faster regret rates for policy learning under decaying propensities, which may be of independent interest. We not only evaluate the coverage of our estimator on a mix of synthetic and semi-synthetic data, but also employ it to estimate the VPI in an adaptive experiment evaluating the efficacy of job assistance programs in Jordan due to Caria et al. Although our estimates are generally more conservative than their hierarchical Bayesian analysis, which assumes that the optimal policy is unique, we still corroborate the benefits of personalization amongst Syrian refugees.

Researchers and policymakers frequently make a large number of decisions simultaneously over many units using noisy estimates of unit-level effects. Researchers often assume that unit-level effects are drawn from a common effect distribution, allowing for optimal decision-making. In applications, however, this effect distribution is unknown to the econometrician, introducing uncertainty in the ultimate decision-making problem. This paper considers the problem of quantifying this uncertainty. For instance, researchers may seek to understand how an oracle decision maker with knowledge of the effect distribution would compare different feasible decisions, or understand which decisions an oracle would plausibly make. Analyzing these questions from the perspective of an oracle decision maker involves comparing the conditional means of unit-level effects given estimates thereof, suggesting a sufficient inferential objective of uniform coverage of these conditional means. Based on an equivalence between uniform coverage of conditional means and multiple testing, I develop methods that satisfy this coverage. Finally, I consider an application to the problem of identifying high-economic-mobility neighborhoods. My methods sharpen inference relative to existing methods and identify units that can be confidently included in oracle selections.

This paper examines the use of recurrent neural networks and their extensions for forecasting autoregressive causal-noncausal processes, characterized by local explosive patterns such as bubbles and spikes. We study the recurrent neural networks (RNN), long short-term memory networks (LSTM), gated recurrent unit (GRU), bidirectional LSTM, and also a simple feed-forward network (FNN) to reveal the difficulty of forecasting extreme values depending on the type of network and the length of the training set. We show that FNN outperforms other networks in predicting extreme values of a univariate noncausal time series during a bubble. We also examine the improvements of point predictions of extreme values resulting from pooling and a modified loss function.

This paper extends the finite-population asymptotic framework of Abadie et al. (2014,2020) to the generalized method of moments (GMM) estimator for moment condition models. Motivating examples include instrumental variable regressions and regression adjustments under randomized controlled trials. We establish consistency and asymptotic normality of the GMM estimator and propose conservative variance estimators. We also study GMM weighting, misspecification, and over-identification testing under finite-population asymptotics. Notably, even though the optimally weighted GMM estimator is infeasible under finite-population asymptotics, the regression adjustment estimator in a randomized controlled trial is shown to be asymptotically equivalent to the optimally weighted GMM estimator. A simulation study and real data application illustrate the usefulness of our GMM theory.

Randomized experiments are often linked to administrative data to measure outcomes, but coarse identifiers can leave multiple administrative records consistent with each experimental unit. We show that unbiased estimation of the sample average treatment effect is possible without resolving these ambiguous links or specifying an outcome model. Our key linkage requirement is that the true administrative outcome is contained among the candidate outcomes for each experimental unit. We characterize the precision cost of linkage ambiguity and study two complementary ways to mitigate it: regression adjustment and reweighting based on observed linkage characteristics. We establish finite-sample and asymptotic properties of these estimators and develop valid randomization-based and large-sample inference.

We introduce the balanced correlation parametrization (BCP), which maps positive-definite correlation matrices one-to-one onto the set of symmetric hollow matrices. A key feature of the parametrization is that both the transformation and its inverse are available in closed form. It combines marginal and partial correlations, is inverse-consistent and equivariant under variable permutations and sign changes, and preserves block structure. A novel property of BCP is that it preserves correlation sparsity as the dimension tends to infinity under suitable factor conditions, providing a basis for sparse high-dimensional correlation modeling. An empirical illustration using standardized idiosyncratic daily stock returns for 1,765 equities over 15 years shows that BCP retains the approximate sparsity pattern and magnitudes of shock correlations, and that it yields accurate positive-definite reconstructions under sparse coordinate restrictions.

A realized tail-risk conditional autoregressive expectile (RTCARE) model is proposed for joint forecasting of value-at-risk (VaR) and expected shortfall (ES). Realized tail measures such as the realized quantile and the realized ES, constructed from intraday high-frequency returns, are incorporated into the dynamics and measurement equations of the conditional expectile, allowing information about lower-tail risk to enter the forecasts. The parameters are estimated by Markov chain Monte Carlo, and we evaluate the resulting VaR-ES forecasts in numerical examples and in an empirical application using U.S. stock-return data. Across the considered tail levels, the RTCARE models deliver competitive and often superior forecasting performance relative to existing alternatives, with stable results across Monte Carlo replications and rolling forecast evaluations.

Local projections (LPs) have become a standard tool for estimating dynamic effects in macroeconomics and are typically implemented using ordinary least squares (OLS) for a given lag order. We propose an alternative approach that exploits additional lags as excluded instrumental variables (IVs). Under a finite-order model with martingale-difference shocks, the resulting (optimally weighted) IV estimator is never asymptotically less efficient than OLS and, as we show, can deliver substantial efficiency gains when data are persistent. For the unit-root AR(1) data with i.i.d. errors, our baseline IV estimator (with one overidentifying restriction) has asymptotic variance $2-h^{-1}$, compared with $h$, the asymptotic variance of the OLS lag-augmented estimator in Montiel Olea and Plagborg-Møller (2021), for an integer propagation horizon $h$. We then develop IV-based LP inference that is robust to unknown persistence and moderate local model misspecification, whereas the recursive VAR-based inference is generally not robust to the latter. We also characterize the trade-off between the degree of misspecification and the number of additional lag controls. Through simulations and an empirical application, we demonstrate that the proposed method can yield meaningfully shorter confidence intervals for impulse responses than OLS in finite samples.

We study the asymptotic properties of the nonlinear stochastic GMM algorithm proposed by Chen, Lee, Liao, Seo, Shin and Song for recursively estimating parameters defined by possibly nonlinear and overidentified moment restrictions $\E[g(X,\beta^*)]=0$. Each observation updates estimates of the moment Jacobian, inverse covariance matrix and Gauss–Newton preconditioner at a cost independent of sample size. For linear and nonlinear instrumental-variable moments, we derive an exact rank-two Sherman–Morrison–Woodbury update. The algorithm combines preconditioned stochastic approximation with iterate averaging. Under a preconditioned monotonicity condition, satisfied globally in linear models and locally around a consistent pilot estimate in general, we establish almost sure convergence and rates, as well as a functional central limit theorem with the efficient GMM variance. These results require four moments of the moment function and its Jacobian when the step exponent exceeds $2/3$. The inverse Gauss–Newton matrix consistently estimates this variance, and a projected linearised statistic enables online testing of overidentifying restrictions. We extend the results to $L$-dependent data with long-run variance weights under stronger moment assumptions. Simulations show that the averaged estimator approaches offline two-step GMM in accuracy and coverage at $10^6$ observations, while requiring a fraction of its computing time and fixed memory at up to $10^7$ observations. The online test achieves correct size and comparable power. In an application estimating the effect of a third child on weeks worked using $254{,}654$ women from the 1980 US Census, single-pass estimates agree with offline GMM within a fraction of a standard error on average across data orderings, and both methods yield the same overidentification-test conclusion in most orderings.

This paper develops a smoothed generalized method of moments (GMM) framework for panel quantile models with individual-specific fixed-effects and endogenous regressors. By smoothing the indicator in the quantile moment conditions and profiling out the individual effects through smoothed individual quantile restrictions, the proposed estimator can be implemented using standard GMM algorithms. We establish consistency, asymptotic normality, and feasible inference under weak time dependence as both panel dimensions diverge. This dependence structure accommodates dynamic panel specifications, serially dependent disturbances, lagged instruments, and within-individual heteroskedasticity and autocorrelation consistent inference. Monte Carlo simulations show that the estimator is nearly unbiased under endogeneity and yields generally accurate inference while remaining computationally tractable. An application to OECD inflation dynamics suggests asymmetric inflation propagation: under the structural IVQR interpretation, the response of current inflation to lagged inflation is substantially larger at the lower structural quantile than at the upper structural quantile.

We develop standard errors for estimates of causal effects in settings where the distribution of treatment exposures is known but potentially exhibits complicated dependence patterns across units. Such dependence arises, for example, in settings with spillovers/interference across units or when the treatment assignment is spatially correlated. Our variance estimator generalizes several properties of the Neyman variance estimator for completely randomized experiments to general designs: it is unbiased for an upper bound on the variance from the design-based perspective; the conservativeness of this upper bound depends on the heterogeneity of treatment effects; and it is also valid under certain forms of super-population sampling of the potential outcomes. Our estimator reduces to standard approaches in simple designs, such as the Neyman variance estimator in completely randomized experiments and the cluster-robust variance estimator in cluster-randomized experiments. We show that the proposed estimator is admissible among the class of quadratic-form variance estimators, and derive asymptotic conditions under which it is consistent for an upper bound on the asymptotic variance of the treatment effect estimator. In simulations and applications based on two empirical studies, one with peer effects and another with a spatially correlated treatment, we find that the proposed variance estimator performs well, and in some cases yields standard errors that are 2-3 times shorter than those of existing alternatives.

The Information Matrix (IM) test is a natural specification check for likelihood-based models, yet cross-sectional implementations are often badly sized, confound neglected heterogeneity with distributional misspecification, and require third derivatives. We develop the panel information matrix (PIM) test for models with fixed effects. Explicit fixed effects isolate functional-form misspecification from time-invariant unobserved heterogeneity. Although the profile maximum likelihood estimator inherits incidental-parameter bias of order $O(1/T)$, the leading bias of the profile PIM is of order $\sqrt{n}/T$, so it is asymptotically negligible whenever $n/T^2\to 0$, which includes the rectangular regime $n/T\to\mathrm{const}$, and stabilizes under parabolic asymptotics $n/T^2\to\rho\in(0,\infty)$. This robustness arises because the indicator fluctuates at rate $\sqrt{n}$ rather than $\sqrt{nT}$. The same rate argument makes third-derivative corrections asymptotically unnecessary, so the test uses only first- and second-order likelihood derivatives. Simulations confirm that asymptotic PIM critical values suffice in moderately long panels, even when Wald tests for $\theta$ are badly sized, while a parametric bootstrap largely removes size distortions when $\rho>0$.

The paper develops a theory for selecting the rolling window when generating out-of-sample forecasts with factor-augmented regression (FAR) models in the presence of structural instabilities. It shows how to select a rolling window by minimizing the conditional mean squared forecast error (MSFE) while accounting for uncertainty in factor estimation. Because the conditional MSFE is unobserved and the factors are latent, this paper proposes a feasible version of the criterion and derives conditions under which the new method is asymptotically loss-efficient. A simulation experiment documents the procedure's performance.

We develop inference for heterogeneous panel vector autoregressive (VAR) models and their structural impulse response functions, where the error terms are dependent in the cross-sectional and time dimensions (two-way dependence). For proxy-identified structural VARs, we first adapt mean-group estimation and construct a closed-form pooled identification. Considering the reduced-form VAR dynamics, residual covariances, and structural parameters, we derive a joint central limit theorem under joint limits in the cross-sectional and time dimensions. We then propose a recursive-design panel moving-block bootstrap that resamples the estimated error terms in (i) the temporal, (ii) the cross-sectional, or (iii) both dimensions jointly, and prove consistency of the joint panel-block scheme under two-way dependence. Simulations show coverage close to the nominal level for the joint scheme but severe undercoverage for cross-sectional resampling.

One-to-one matching without replacement is a classical approach to constructing comparable treated and control samples in the design of observational studies. It pairs each treated unit with a distinct control while minimizing a covariate distance objective. With continuous covariates, the matched pairs generally remain inexact, which contributes to bias in downstream analysis. Its key theoretical properties, such as the resulting imbalance between matched pairs and when it is negligible to support valid inference, remain unclear. In this paper, we analyze one-to-one matching based on $d$-dimensional, continuous covariates with a quadratic covariate-distance objective. First, we find that when $d\leq 3$, under standard conditions on the propensity score ensuring abundant control samples near each treated sample, the imbalance (difference between within-group averages) is root-$n$ negligible uniformly over the family of smooth functions with a common first- and second-order derivative bound. However, such balance is subject to a dimension restriction, as we construct examples in which the imbalance is root-$n$ non-negligible when $d=4$ and dominates root-$n$ rate when $d>4$. Second, we show that when $d\leq 3$, the matched design allows valid Wald-type and bootstrap inference for the average treatment effect on the treated, distributional treatment effects, and quantile treatment effects. Thus, the same outcome-blind matched design supports various downstream inferences without having to tailor the design to the targets. Finally, paired randomization inference based on the matched design is asymptotically valid in the super-population sense for $d\leq 3$ but can fail when $d=4$. We corroborate the theoretical results with numerical experiments.

We introduce a mean-reverting stochastic differential equation with a three-component stochastic term and show that it generates a hierarchy of steady-state (stationary) distributions. At the top level, the hierarchy is described by a modified-Beta distribution, while one- and two-parameter reductions produce compact-support, power-law-tailed, and exponential-type limiting families within a single stochastic framework. We then construct two generalized extensions of this hierarchy. In the first, the power transformation is applied directly at the level of the stochastic differential equation; in the second, the same transformation is applied only after the stationary modified-Beta hierarchy has been obtained. While these two procedures agree on important lower branches and limiting cases they generally differ at the top level. The generalized hierarchy is therefore not unique: nonlinear transformation and stationary-state reduction do not commute. For both routes, we derive the probability density and cumulative distribution functions, express their parameters in terms of the underlying stochastic dynamics, clarify the relations among their limiting cases, and compare the resulting families with the traditional Generalized Beta framework.

What should a macroeconomically relevant climate index contain? The composition is inherently ambiguous, and aggregation choices affect structural inference. We introduce the Assemblage VAR, which jointly estimates nonnegative aggregation weights and VAR parameters by maximizing the system likelihood-gain criterion, effectively outsourcing aggregation to observed macroeconomic dynamics. Two variants operate in component-space and rank-space, reweighting named subcomponents or emphasizing regions of the cross-sectional distribution. Applied to disaggregated U.S. climate data from the Actuaries Climate Index and NOAA, VARs using the assembled climate measures yield contractionary impulse responses that are substantially larger than those estimated using fixed-weight benchmarks. Weights emphasize high-wind variables and distributional tails over slow-moving components such as sea level.

Data collection is often costly or logistically demanding, limiting both the questions researchers can pursue and how precisely they can answer them. Prediction-powered inference (PPI) can reduce the amount of data needed for precise parameter estimation by combining labeled data with machine learning predictions. However, ignoring dependence within clusters can produce confidence intervals that cover the true parameter less often than their nominal rate. We introduce Cluster-Robust PPI++, which provides standard errors in closed form and asymptotically valid confidence intervals under arbitrary dependence within independent clusters, requiring no bootstrap or resampling. Our central contribution is to accommodate partially labeled clusters, a common empirical setting in which clusters contain both labeled and unlabeled units. As units are dependent within clusters, partially labeled clusters violate the independence assumption of PPI++. We also show how precision increases depend on the labeling design, and derive a cluster-aware power tuning rule that minimizes asymptotic variance. In an application to television news, standard PPI++ confidence intervals have coverage below 60%, whereas Cluster-Robust PPI++ can achieve nominal 95% coverage.

This paper develops novel smooth tests for structural changes in the innovation copula of multivariate dynamic models. We characterize deviations from copula constancy through a collection of generalized Fourier coefficients and test their joint significance. Under the null hypothesis, estimation of the dynamic parameters and the unknown marginals has no first-order estimation effect on the proposed statistics. Consequently, the feasible tests based on estimated residuals are asymptotically equivalent to their infeasible counterparts based on the unobserved innovations, yielding a desirable oracle property. Our proposed tests are asymptotically $\chi^2$-distributed and possess nontrivial power against local alternatives that approach the null at the parametric rate. To enhance the practicability of our methods, we further develop a data-driven procedure that automatically selects the truncation orders of the basis expansions. Unlike existing methods based on empirical copula processes or kernel smoothing, our tests require neither computationally intensive bootstrap procedures nor bandwidth selection. Extensive simulations demonstrate the satisfactory empirical size and power of our proposed tests. In particular, the data-driven test delivers substantial power gains under sparse alternatives, while remaining competitive under dense alternatives. Applications to exchange rates and stock returns further illustrate the practical usefulness of the proposed methods.

Program evaluations routinely find larger returns to investment in low-skill children, while structural models of skill formation typically find that skill and investment are complements. I show that these findings are not in tension: they measure different objects. The Beckerian schedule of returns (BSR) is the elasticity of output with respect to an input, holding all inputs at fixed values; average marginal returns (AMR) average that elasticity over the joint distribution of inputs. Revisiting Cunha, Heckman, and Schennach (2010)'s model of child skill formation on the Children of the NLSY79, I find that skill and investment are complements, but that low-skill children receive so much less investment that their AMR to investment is higher in early childhood — a pattern that reverses at later ages. The framework also provides a natural way to sign bias from curvature in log-linear models with interaction terms, which conflate the BSR and AMR and accurately estimate neither; adding quadratic terms both reduces this bias and often strengthens estimated interaction effects. Methodologically, I model discrete proxies with an ordered probit measurement system — treating them as continuous biases AMR estimates and fails to detect that low-skill children have higher AMR than high-skill children in early childhood — and introduce effective factors, a scaling system that allows latent factors to take different effective scales when producing different skills in the same period. Finally, conditional on maternal permanent income, current household income has no predictive power for parental investment, undermining the exogenous variation on which the standard control-function approach relies and cautioning a descriptive interpretation of my estimates.

Businesses regularly offer gift card programs to drive customer spending and increase engagement. A central question is how much incremental revenue these programs generate, and which channels drive it most efficiently. Measuring the incremental revenue associated with a gift card program is a challenging problem in causal inference, requiring a firm to infer how much each customer would have spent if they never received a gift card. Observational data on past customer purchasing behavior reveal possession of a gift card only when a customer makes a purchase, thus leaving a customer's treatment status systematically censored. In this paper, we develop a novel data fusion approach to overcome this missing data challenge. We identify and estimate incrementality by combining a large observational dataset with a smaller experimental dataset from a different population. Our approach relies on a mild transferability condition, which posits that the conditional relative treatment effect of gift card receipt on the decision to purchase is invariant across the two populations. We develop a flexible, machine learning-based estimator for the incremental revenue and establish its asymptotic normality. We apply our estimator across both first- and third-party channels through which Airbnb distributes gift cards, finding heterogeneity in incrementality across segments of the population. In particular, we find not only that third-party channels are more incremental than first-party ones, but also that "self-gifters" (i.e., customers likely to have purchased their own gift cards) are more incremental than the broader population.

This work studies how Bayesian machine learning methods can be used for large-scale demand estimation with many product categories. I compare two model classes, a latent factorization model and a mixed logit model and two Bayesian estimation approaches, Markov Chain Monte Carlo (MCMC) and Variational Inference (VI). The analysis combines a simulation study with an application to supermarket scanner data. The results show that the latent factorization model benefits from information across categories and improves its predictive performance as the dimensionality of the choice environment increases, whereas the mixed logit model does not exhibit the same pattern. MCMC delivers the highest predictive accuracy but is computationally intensive. VI achieves slightly lower predictive performance while substantially reducing runtime. In the empirical application, VI also outperforms the mixed logit benchmark. These findings highlight a trade-off between accuracy and computational feasibility in multi-category demand estimation.

North-star metrics such as customer lifetime value are often too slow and noisy to decide a short A/B test. Teams therefore rely on a proxy metric, commonly chosen by how closely its effects tracked the north star's across past experiments. Validating that choice, or any method for making it, is hard: the only benchmark is the noisy north star, and the number of available past experiments is limited. In addition, proxy and north-star effects are estimated on the same customers, so their sampling errors are correlated. Recent work at major experimentation platforms removes this shared error as contamination, improving estimates of the true-effect covariance. Choosing a proxy, however, is a ranking problem, and a better estimate need not give a better ranking. We measure agreement free of shared error by estimating the two effects on disjoint random halves of each experiment's customers. In an archive of 262 experiments and 69 candidate proxies, the shared error ranks the candidates in a similar order to this agreement (Spearman correlation 0.65): it carries information about proxy quality. The more of it a correction removes, the worse the ranking because removal discards part of the signal but leaves the main sources of ranking noise, the noisy north star and the limited number of experiments, untouched. Archive-calibrated simulations, in which the correct ranking is known, confirm this even when every correction receives the true sampling covariance. Held-out real experiments, evaluated on disjoint customer halves so that shared error cannot bias the comparison, closely reproduce the predicted ordering (Spearman correlation 0.93). Correction can still pay off with more experiments, but the number needed rises steeply with the north star's noise. We map this crossover and give platform teams three inexpensive checks for deciding from their own archive whether and how strongly to correct.

Joint-event forecasts combine an estimated dependence model with current marginal forecasts. Retaining historical transforms at the marginal fits available when each outcome arrived creates overlapping estimation errors. We derive their joint influence with the terminal estimates in a stable Vine Copula VAR with normal innovation margins and a fixed, correctly specified Gaussian or positive Clayton vine. An intercept identity and the stable VAR filter reduce the historical correction to harmonically weighted innovation moments. Terminal slope uncertainty remains in the forecast gradient. A feasible covariance estimator yields asymptotically valid repeated-sample intervals for fixed one-sided event probabilities at the realized forecast state. A same-family terminal refit provides the efficiency comparison. Retaining dated transforms adds a positive semidefinite limiting covariance term, whose event-level cost depends on dependence sensitivity and forecast-state leverage. Monte Carlo comparisons show a small accuracy cost of retaining the transforms and a larger inferential role for current marginal estimation. Allowing Clayton dependence improves downside forecasts relative to Gaussian dependence under each transform rule. A fourteen-variable U.S. real-time forecasting application and simulations with twenty and fifty variables illustrate feasible joint-event estimation and analytic inference for fixed-depth vines.