Papers

This paper studies the nonparametric identification and estimation of additively separable triangular models with continuous endogenous and instrumental variables, allowing for a nonseparable first-stage equation. Under the independence of instrumental variables and unobservables, we show that the outcome function possesses a closed-form expression as a functional of conditional cumulative distribution functions. The resulting plug-in estimators require no regularization and converge at the rate $n^{-m/(2m+1)}$, where $m$ is the order of smoothness the model imposes. Also, no estimator of the outcome function converges faster. We use the empirical bootstrap to construct a uniform confidence band that covers the outcome function at every point of a compact set simultaneously.

We study a dynamic spatial panel model with observed regressors, interactive effects, and contemporaneous and lagged dependence in a large-$N$, fixed-$T$ framework. The spatial model constitutes an $N$-dimensional simultaneous-equations system. In this $N$-equation view, the interactive effects introduce $N$ unit-specific loading vectors. Estimating them individually when $T$ is fixed creates the type of incidental-parameters problem underlying Nickell bias. We use the $N$-equation view to account for spatial simultaneity through the spatial Jacobian. Crucially, however, we view the same model as a $T$-equation system with $N$ observations. Together with a spatially enriched random-loadings (SERL) specification, this $T$-equation view yields a quasi-likelihood without unit-specific incidental parameters. We propose a computationally tractable block-coordinate algorithm. Simulations show small estimation errors and generally near-nominal coverage probabilities. Applying the method to U.S. county female labor-force participation, we find substantial dynamic and spatial dependence and an important role for education in explaining the rise in female labor-force participation.

Consider the problem of designing a revenue-optimal auction mechanism when two heterogeneous items are sold to a single buyer having independent valuations over the items. The distributions of the buyer's valuation for the items are assumed to have densities that are positive, nondecreasing, and continuously differentiable on their support sets $[c_i,c_i+b_i]$ in the positive axis. I prove that the optimal mechanism is deterministic if at least one of the minimum valuations (i.e., either $c_1$ or $c_2$) is sufficiently high. I provide a method to calculate the threshold of $(c_1,c_2)$ beyond which the optimal mechanism is deterministic. I also provide a sufficient condition on the distributions of buyer's valuations for which the individual sale mechanism is optimal. I show that when $c_1$ is low and $c_2$ is high, it is optimal for the seller to sell item $2$ at the minimum valuation $c_2$, thus effectively reducing the problem to finding the optimal mechanism in the one-dimensional setting only for item $1$. I conjecture with promising preliminary results that this result can be extended to the three-item setting. Specifically, I conjecture that when $c_1$ and $c_2$ are low but $c_3$ is high, it is optimal for the seller to sell item $3$ at the minimum valuation $c_3$, thus effectively reducing the problem to finding the optimal mechanism in the two-dimensional setting for items $1$ and $2$.

This paper studies quantile treatment and spillover effects in network experiments. Average spillover effects reveal how treating a unit's neighbors affects its outcome on average, but mask the heterogeneity of these effects across the outcome distribution. We define structural quantile effects that compare outcome quantiles between exposure states, characterizing how own treatment and exposure to treated neighbors affect different parts of the outcome distribution. Building on \citet{leung2020treatment}, we first establish the weak convergence of the estimated quantile-effect process under conditions requiring the stabilization of the degree distribution and the network-dependent covariance structure. Our main contribution is to propose uniform confidence bands (UCBs) based on Gaussian approximations conditional on the realized network, avoiding these stabilization requirements. The proposed method is evaluated through extensive simulation studies and an empirical application to a randomized savings-account experiment in Nepal \citep{prina2015banking}.

We characterize the communication networks that ensure consensus in rational social learning under the sure-thing principle. A network ensures consensus if and only if it is pseudo-reciprocal, a property under which reciprocity may fail between individuals but holds at a coarser group level. Prior work has assumed message exchange to be bidirectional, yet such pairwise reciprocity proves largely dispensable. We show that a single bidirectional link can suffice, however large the population.

Staggered distributional difference-in-differences produces cohort-specific potential-outcome distributions, but applied work typically wants one overall quantile treatment effect. Two natural summaries—averaging cohort quantile treatment effects (QTTs) and mixing cohort distributions before inversion—use the same policy weights yet answer different target-population questions and can disagree even in sign. We derive the exact sharp interval for their gap conditional on cohort quantiles and weights, a globally sharp range-only envelope, and a locally sharp density-tilt representation. We develop joint smooth and mass-point-safe inference and show that neither estimator is uniformly more precise, even when the estimands coincide. In a same-object reconstruction of a public staggered-QTT application, holding data, identification, distributions, and weights fixed while changing only aggregation order reverses reported signs at several quantiles. Aggregation order is therefore part of the estimand and must be chosen before inversion.

Asymptotic normality approximations often fail to hold for extremum estimators when the true value of the parameter is at or close to the boundary of a parameter space. I analyze and develop tests using a quasi-unconstrained estimator, which is asymptotically normal even when the true parameter vector is near or at the boundary. These results generalize previous work with this estimator by allowing for more types of constraints and showing how the method can naturally be modified when a nuisance parameter is also high-dimensional. I show that variations of Wald, Likelihood Ratio, and Lagrange Multiplier tests can control size in a uniform sense, provided the initial constrained estimator is sufficiently accurate. Lastly, I apply the method to an application involving network estimation with panel data.

In 2025, bilateral foreign aid was reduced by 23%, affecting more than 130 aid recipient countries. We assess whether debt service relief or remittance increases can match the USD 26 billion in aid losses. Using a network-shock model calibrated to bilateral donors' individual cuts, we estimate recipient-country aid losses and evaluate compensation feasibility in terms of annual debt service payments that would need to be cancelled and remittance capacity (the headroom between flows and a theoretical maximum in which every working-age migrant sends funds) mobilised to financially offset them. We find that 18% external debt service relief and 10% of remittance mobilisation could compensate half of the affected countries. However, some countries remain locked out of either or both mechanisms. A fundamental trade-off in the global financial architecture emerged for large aid-cut losers: countries positioned to benefit from debt service relief lack large international diaspora networks (limiting their capacity to increase remittances), while those with established diaspora channels face structural exclusion of traditional debt markets, rendering debt service relief ineffective. These insights introduce nuance in how alternative finance sources can replace foreign aid.

Global forecasting models pool many series and learn one shared function. Gradient-boosted trees are their most common form. We measure a failure of this design that has not, to our knowledge, been documented. Train a global tree on the individual series of a hierarchy, then ask it for the hierarchical aggregate. The aggregate sits far outside the model's training range, and the forecast collapses. The model under-predicts the total by 30-50x in our production deployment, and by up to 496x in a public M5 reconstruction. The mechanism is known: beyond its training range, a tree predicts a constant. It surfaces at the aggregate because the total dwarfs every training series. The cure is not new. Per-series scaling, the preprocessing step that Montero-Manso and Hyndman (2021) recommend, prevents the collapse. So do a weighted aggregate-level training row and seasonal differencing. Our contribution is the characterization. The collapse reproduces on five panels: a production business-to-business marketplace, a synthetic hierarchy, M5, Australian Tourism, and a public business-buyer panel. It holds on three tree libraries, is invariant across training seeds, and is statistically significant. Its onset is immediate and tracks a simple support bound: a scale gap of only 1.15x already costs a third of the total. No standard configuration change prevents it: pooling every hierarchy level into training fails at scale, and the one knob that fits linear models in the leaves softens it without curing it. Rolling the forecasts forward recursively separates the cures: the aggregate-row cure re-collapses, per-series scaling degrades but stays low, and only seasonal differencing keeps its one-step accuracy unchanged. We close with a three-step procedure for diagnosing and preventing the failure in deployed systems.

In online product search, returned alternatives often look alike. We investigate when a product's visual separation from its closest look-alike in a returned set increases its choice probability. We introduce two occasion-level constructs: contextual visual distinctiveness (image distance from the nearest similar alternative in the consideration set) and relative fit (compatibility with the search query). We hypothesize that distinctiveness favors selection and is highly contextual, yields a premium that rises with relative fit, and matters most when text descriptions fail to differentiate options. Analyzing over 800,000 e-commerce search events using dense representations, we apply search-event and product fixed effects to evaluate the exact same product alongside varying visual neighbors. Results show a product is significantly more likely to be clicked when it lacks a close look-alike. This distinctiveness premium increases with relative fit and roughly doubles when competing descriptions are highly similar. Consistent with a model where distinctiveness aids in standing out pre-evaluation rather than increasing inherent utility, the extra clicks distinctiveness recruits convert 5-7% less often downstream. Ultimately, the evidence characterizes visual differentiation as a local attention allocation mechanism whose value depends on query fit and information from competing cues.

Rejection sampling requires a proposal that dominates the target by a known constant, generally unavailable for non-Gaussian state space models. We construct such a proposal for the latent state path, yielding independent exact smoothing draws and an unbiased likelihood estimator whose relative variance is at most $1/p-1$ per draw at acceptance probability $p$. The method covers scalar states with affine Gaussian dynamics and log-concave observation densities, including multivariate observations. Transition twisting makes the log target-to-proposal ratio separable, and tangent-line twists make each term nonpositive, producing an attained, sharp dominating constant. With a companding node placement, the accumulated envelope error is $O(T/G^2)$ for a sample of length $T$ with $G$ nodes per date, so $G\propto\sqrt{T}$ keeps acceptance bounded away from zero; for stochastic volatility, the required conditions hold almost surely. A simpler mode-centered grid shows the same scaling empirically. At $T=2{,}000$, acceptance is $75\%$, versus roughly $10^{-16}$ for the Gaussian envelope.

Short observational pricing panels often contain many data points but very few actual price changes. This paper shows that this sparsity creates a hidden source of error that standard statistical methods miss. When estimating price effects, most of the uncertainty does not come from sample size within a panel, but from the specific history of price movements observed. Standard confidence intervals fail because they only measure variation within the panel, ignoring this broader design-level error. Using simulations, we find that this cross-design variation accounts for most of the estimation error, causing standard methods to significantly understate uncertainty. First, we show that cross-design error decreases predictably as the total volume of price variation increases. Second, adding more data from regions that share the same price trends does not fix the issue; true precision improves only when combining data across units with independent price trajectories. Third, applying a simple variance-component adjustment across independently priced units restores accurate statistical coverage. We confirm these findings in real-world store scanner data, showing that products and pricing zones behave as if they have far fewer independent price movements than their raw counts suggest. Ultimately, reliable inference in passive pricing data requires genuine, independent variation, which can be achieved through controlled regional price testing.

We study an experiment with 8.5 million users on Netflix's recommender system to measure how improvements in recommendation technology affect the set of products that get consumed. Improvements increase total consumption and users' reliance on recommendations while diffusing recommendations and consumption away from the most popular titles (“superstars") toward a larger number of moderately popular titles (“middle-tail"), with minimal effects on the most niche titles (“long-tail"). Our results challenge the notion that recommender systems polarize consumption – raising the consumption shares of the head and tail at the expense of the middle – and suggest that the returns to investing in middle-tail products grow as algorithms improve and platforms scale.

Marketing Mix Models (MMMs) estimate the incremental sales effect of advertising from observational time series, yet they are rarely validated against ground truth, because ground truth is unobservable in real data. Synthetic data closes that gap in principle, but existing generators produce marketing spend exogenously - omitting the central difficulty of the estimation problem, since real budgets are planned around promotional calendars, seasons, and recent performance. This paper presents a parameterized generator, and a fixed reference instance, of a synthetic weekly retail dataset (156 weeks, three media channels) in which spend arises from four documented coordination mechanisms - quarterly budget feedback, anticipatory spending ahead of a promotional calendar, scheduled TV bursts, and algorithmic performance chasing - on a demand baseline with seasonal, quality, price, and unobserved sentiment components. Spend translates into incremental sales through two transformations, carryover and diminishing returns, instantiated here as geometric adstock and logistic saturation with known parameters; the true causal decomposition of every week's sales is recorded alongside the error-contaminated variables a practitioner would observe. Every mechanism is a parameter that can be varied or switched off, and a companion procedure simulates go-dark geo-experiments with exact treatment effects. The seeded generator and reference instance are publicly released with notebooks that reproduce every number in this paper.

Marketing Mix Models (MMMs) are widely used for marketing measurement and budget allocation, but face fundamental identification challenges: due to endogenous marketing spend decisions, MMM estimation on observational time-series data cannot recover the true causal effects of marketing. On the other hand, geo-experiments provide causal identification through randomization, but it is not clear how to use them efficiently to calibrate marketing mix models. We propose a novel structural estimation approach that recovers the complete set of MMM parameters - adstock decay ($\alpha$), saturation ($\lambda$), and effectiveness ($\beta$) - directly from geo-experimental time-series. By differencing outcomes between treatment and control regions, our method eliminates observed and unobserved confounding factors while preserving the temporal variation that identifies each parameter. We demonstrate on synthetic data that this approach recovers the true ROAS and the response curve over the range of spending covered by the experiments, together with credible estimates of the underlying parameters. Our framework enables efficient pooling across multiple experiments and provides a principled foundation for MMM calibration that fully utilizes the information experiments contain.

Rising interest rates can expose life insurers to surrender risk by reducing the market value of their assets and raising policyholders' outside returns. This paper develops a minimal model of an insurance-specific run mechanism in which strategic interaction arises because early surrenders can deplete the asset pool backing continuation values. We analyze a strategic surrender game in which a run is an equilibrium outcome determined jointly by asset values, contractual surrender claims, and payoff-dependent continuation benefits. The model yields closed-form interest-rate thresholds for fundamentals-driven and self-fulfilling runs. Thinner capitalization weakly lowers the joint-surrender cutoff. Continuation benefits raise surrender thresholds but can also create strategic complementarity.

We study causal moderation when treatment assignment is randomized but the moderator is not. We combine the parallel estimation framework with front-door adjustment to identify an average mediated treatment moderation effect. We apply this approach to 165 municipal assembly elections in Tokyo (1987-2023), where pamphlet positions are assigned by lottery and total pamphlet pages are mechanically determined by candidate set size and fixed municipal rules. One additional candidate increases the front-page effect on winning probability by 0.322 percentage points through the page-count channel, 8.0% of its baseline magnitude, while the back-page effect does not increase significantly.

As an extension of existing Bayesian persuasion framework with inadequate message mechanism, we study direct recommendation when a sender is bound by an installed information policy only with probability $\rho$, the realization of binding is hidden, and the receiver does not observe the persistent structural environment. The receiver first sees a payoff-neutral, nonmanipulable calibration sample and then faces a fresh, non-certified deployment interaction. In common, the calibration law identifies only the receiver-facing reduced form, not the latent binding and discretionary kernels. We characterize type-wise $\rho$-implementability, construct the receiver's posterior over the full deployment node, and prove a static direct-following implementation theorem. After every calibration history that passes a posterior-predictive obedience test, the deployment assessment is an exact perfect Bayesian equilibrium: Bayes consistency, receiver sequential rationality, sender sequential rationality, and off-path completion are all verified. Under finite-type separation, common recommendation support, and a positive obedience margin, the test activates such an equilibrium with high probability. Our results keep statistical failure probability distinct from equilibrium approximation. Finally, we embed the original robust value frontier, support-wise linear-programming algorithm, and binary-action fractional-knapsack specialization into this implementation framework

We study, theoretically and experimentally, how transparency about students' priorities and admission chances shapes their incentives to acquire information about their own preferences in school choice and college admissions. In the model, uninformed students choose schools based on a common prior. When they learn their own preferences, their choices become more heterogeneous, which frees up seats at popular schools. Students who know they have high priority have stronger incentives to learn because they can more readily act on what they learn, whereas students who know they have low priority are discouraged. Full priority disclosure concentrates learning among high-priority students. By pooling priorities, partial disclosure spreads learning incentives to pooled students and yields higher welfare. In the laboratory, however, full disclosure yields the highest welfare instead, followed by partial disclosure, and then no disclosure, because greater transparency improves subjects' understanding of the strategic environment, leading to fewer mistakes. These findings support full disclosure of priorities or admission chances to guide information acquisition. However, deviations in learning remain even under greater priority transparency, partly because subjects respond suboptimally to admission chances when these are provided directly rather than inferred. Students' ability to interpret and use them is therefore itself a policy concern.

Objective functions (goodness criteria which have to be optimized) that are considered, for instance, in cluster analysis, factor analysis, (linear) structural equation modeling, (linear) regression, multidimensional scaling, choice theory, and utility theory, must be adequate, i.e. carefully adapted to the structure of the observed data. Adequateness of an objective function means, in our terminology, that (certain) transformations of its arguments, e.g. changes in the unit measures of the quantities involved, do not influence the solutions of the optimization procedure. In this paper we concentrate our attention on affine strictly increasing transformations and we also incorporate the case of continuous adequate objective functions accordingly. The characterization of adequate dissimilarity coefficients for interval scaled data shows the appropriateness of the concept of adequateness that is developed in this paper.

Firms perform online experiments with multi-armed bandits to personalize what consumers are shown while balancing exploration and exploitation. However, third-parties can infer consumers' underlying segments from observing which banners, ads, or recommendations consumers receive. To control this inference, we propose a privacy risk budget that firms can set ex ante to bound such third party belief updating using differential privacy. To spend this privacy risk budget, we propose two strategies: a constant privacy risk strategy and a dynamic privacy risk strategy that spend privacy risk differently across visitor. We study how privacy risk budgets affect experimentation performance in two applications–website design and a recommendation system–under these strategies. For both strategies, we analytically find privacy risk budgets that optimally balance exploration and exploitation. We then extend the idea of an experiment-level privacy risk budget to a firm-wide privacy risk budget. We apply this firm-wide privacy risk budget in an empirical setting with 78 experiments. We find that the dynamic strategy is particularly valuable in longer and more complex experiments, and that optimizing the allocation of a firm-wide privacy risk budget across experiments substantially improves learning performance.

We compare statistical experiments when observations are inexpensive and can be acquired sequentially until the decision maker chooses to stop. We introduce two orders. Small-cost decision dominance asks which of two equally priced experiments is eventually preferred in every decision problem as the per-observation cost vanishes; large-budget stopping dominance asks which experiment can reproduce every terminal experiment attainable from the other under all sufficiently large expected-sample budgets. Our main result shows that, for generic pairs, the two orders coincide and are both characterized by strict dominance of every pairwise Kullback–Leibler divergence. The key step is a uniform exact-conversion theorem: any finite-output stopping policy based on one experiment can be reproduced exactly using another, with first-order expected-sample requirements determined by pairwise KL rates and a square-root remainder that is uniform over policies.

Are simple delegation rules optimal under ambiguity? We study delegation when the principal knows the mean, but not the distribution, of the agent's private information. In a parsimonious quadratic constant-bias environment, the robustly optimal randomized mechanism is a random cap: the principal draws and reveals an upper bound, below which the agent chooses freely. Randomization strictly outperforms every deterministic cap by hedging against cap-specific worst-case distributions. We characterize random caps through a nondecreasing and concave expected-action rule and construct the solution using a saddle-point approach. The worst-case distribution features an exponential survival function over its continuous region and an atom at the upper endpoint. Under regularity conditions, the result extends to convex-order ambiguity. Moreover, when the mean is below the agent's bias, an optimum can be implemented by supplementing the random cap with an incentive-neutral outcome lottery, while pure random caps are strictly suboptimal.

Moment restrictions provide a flexible basis for quasi-Bayesian inference when a full likelihood is unavailable, but the weighting matrix in a quadratic moment criterion determines both the relative importance of the moments and the information scale of posterior updating. We propose curvature-calibrated quasi-Bayesian updating, which uses the inverse of the covariance (or long-run covariance) of the moment conditions evaluated at a self-consistent quasi-posterior center. The resulting fixed-point procedure alternates between covariance estimation and simulation from a fixed-weight quasi-posterior, thereby avoiding parameter-dependent weighting during each simulation run. Under a Bernstein-von Mises condition for the fixed-weight quasi-posterior at the efficient population weight, we show that the calibration map is locally contractive, that its fixed point is consistent at the standard parametric rate, and that the Gaussian approximation continues to hold under the calibrated data-dependent weight, with covariance given by the inverse Godambe information matrix. Under a uniform fourth-moment condition, the scaled quasi-posterior covariance converges to the same matrix, so quasi-posterior and repeated-sampling uncertainty agree to first order. Simulations show improved covariance calibration and interval coverage after a few updates. An application to longitudinal binary-response data illustrates the method with within-subject dependence and overidentified residual moments.

We study one-dimensional screening when the Spence-Mirrlees condition fails along a monotone dividing curve, on which all types value marginal output equally. A single ratio, marginal distortion over marginal rent, governs the problem. When the relaxed solution stays in the positive region, non-decreasing optima in the positive single-crossing region are continuous if the ratio increases in the decision. When it crosses a flat curve and marginal rents are separable, every continuous contract is improved by a jump. When it crosses a strictly monotone curve, a contract that pools and jumps continues along the mirror of the pool if the ratio does not increase along it. Optimality among all implementable allocations, deterministic or random, is proved by a measure on the binding constraints whose weights are the same ratio; with constant curvatures and no crossing, it is also necessary. As applications, we solve problems of procurement and nonlinear pricing.

I study why some groups—polities and organizations alike—sustain independent judgment while others fall into conformity traps. Social approval can suppress not only the expression of independent judgment but also the upstream practice that keeps such judgment available: maintaining judgment generates visible questioning, and observers cannot distinguish diligence from opposition. Because suspicion falls when questioning is common, the same desire for approval can sustain a questioning culture or a conformity trap. The model separates maintaining judgment from acting on it when novelty arrives. When the decision to act is uniquely determined, I give primitive conditions for coexistence; in a logit–proportional benchmark, a single inequality is necessary and sufficient. The principal contribution is dynamic. Under staggered revision the stock of judgment is inherited: protecting dissent releases existing judgment at once—with negative expected adaptive value on impact in a stationary culture below a break-even competence threshold—whereas rebuilding the stock is constrained by turnover. A monotone operator constructs the extremal perfect-foresight paths from every inherited state. When recovery under every admissible continuation is attainable, two cutoffs classify inherited states—recovery impossible, expectation-dependent, or assured—and a focus condition at the unstable culture strictly separates them, opening a band of states where expectations select the long-run culture. Turnover then yields sharp physical duration bounds, within temporary direct formation support, for making recovery possible or robust. A fully coupled interval-certified example verifies coexistence, the band, and the distinct output and welfare implications.

Pairwise randomization can yield substantial efficiency gains in experiments. Yet methodological guidance cautions against pairwise randomization, especially in settings with attrition, partly because common practices for estimation (i.e., pair fixed effects) imply discarding data from incomplete pairs thus exacerbating data loss from attrition. This practice of dropping incomplete pairs reduces statistical power of tests as well as precision of estimates, in paired experiments, compared to designs with less finely stratified treatment assignment. We argue that this concern is misplaced if attrition is independent of treatment status and potential outcomes, and that these issues follow from an inefficient use of the data that remains post-attrition. First, we show how, by using a specific permutation test, it is possible to use all observed units for inference (complete pairs and incomplete pairs where one unit attrits) while still exploiting the pairwise randomization design structure. The test procedure we suggest provides exact size control under the sharp null. Second, we study an optimally weighted estimator that efficiently combines within-pair and across-pair comparisons. Finally, we show that combining these two insights yields a test procedure that dominates the two commonly used inference methods (a paired $t$-test and the two-sample $t$-test) in power, for any level of attrition. Usefully for applied researchers, we show that the efficient procedure can be implemented via a weighted fixed effects regression, straightforward in standard software. In sum, our results provide researchers with practical tools for conducting experiments with pairwise randomization without sacrificing observations or statistical power when facing independent attrition.

The Plurality rule is vulnerable to vote splitting between similar alternatives. Defying conventional wisdom, we characterize the Plurality rule through a specific type of clone independence condition. We further introduce the notion of a one-parameter family of $p$-Clone Resistance ($p$-CR), and examine the property within the class of scoring rules. For $p \in (0,1)$, nontrivial rules exist with at most three alternatives, but only the Trivial rule generally satisfies the condition.

We study coalitional manipulation of interval-valued social choice correspondences on the single-peaked domain. In the single-valued model, strategy-proofness and group strategy-proofness coincide within the standard class of peaks-only social choice functions, so generalized median voter rules retain their robustness to coalitional manipulation. This equivalence breaks down once the outcome is allowed to be set-valued: generalized median correspondences may be strategy-proof while remaining vulnerable to coordinated deviations. We show that, among generalized median correspondences allowing genuine set-valued choice, pairwise strategy-proofness already forces anonymity. With voter sovereignty, this restriction becomes sharp and characterizes target set correspondences. Thus, the target-set structure emerges as the form of set-valued flexibility compatible with pairwise coalitional robustness.

The European Union has committed to reducing greenhouse gas emissions 55% below 1990 levels by 2030, but whether current trends are compatible with this ambition remains uncertain. We apply deep learning to high-resolution socioeconomic and sectoral data across EU27 member states till 2023 to project sectoral CO$_2$ trajectories under current trends, extrapolating observed sectoral momentum without assuming changes in the pace or effectiveness of the policy environment beyond what is already reflected in historical data. We project that EU27 emissions will exceed the 2030 target by 35% (620 Mt CO$_2$ shortfall), with only a small minority of countries on trajectories consistent with the bloc's commitments. While the Power sector achieves target-consistent reductions driven by the renewable transition, Mobility shows minimal progress and accounts for over a third of total emissions by 2030, reflecting a structural inertia across member states rather than geographically concentrated lag. Our findings indicate that substantial additional intervention is required to close Europe's ambition-implementation gap, and call for establishing up-to-date energy information in Europe.