Papers

When producers in a network compete in quantities, an innovator's profit contains none of the change in allocative efficiency that its innovation causes, whether a gain or a loss, because its own choices are optimal and other effects on its profit are transfers. A process innovator also forgoes its own and downstream markups on the output its innovation adds at a fixed allocation, worth 14 to 26 percent of its cost saving for U.S. public firms in 2015. For innovators accounting for 68 percent of sales, the change in allocative efficiency exceeds a tenth of the private return. In a Markov R&D game, reallocation of R&D across firms is likewise external to the innovator. Rivals' profits and market values can misstate the welfare cost of business stealing from them even in sign. With estimated spillovers, the social return to R&D is 5.39 times the private return, against 2.53 in output-based accounting with estimated business stealing, mainly because that accounting credits the innovator with its rivals' lost sales.

Invasive alien species (IAS) generate substantial ecological and economic damages that often transcend political boundaries, creating strong incentives for coordinated management. We develop a two-region ecological-economic model of IAS control that integrates prevention and eradication measures with population dynamics characterized by logistic growth and an Allee effect. We derive analytical results on the interaction between ecological thresholds and strategic behaviour and compare outcomes under cooperation (central planner) and non-cooperation (open loop Nash equilibrium and Markovian Nash equilibrium). We show that, under realistic control costs, neither prevention nor eradication can eliminate invasive populations in finite time, and complete prevention of cross-border spread is generally not optimal. In the absence of an Allee effect, the zero-population equilibrium is unstable, implying long-run persistence of the invasive species. By contrast, the presence of an Allee effect fundamentally alters system dynamics by making extinction locally stable and creating a basin of attraction within which eradication becomes feasible. This finding highlights the economic significance of ecological thresholds and demonstrates how delays in management can shift populations beyond critical levels, after which eradication is unlikely regardless of subsequent control efforts. Numerical simulations further show that cooperative management expands the set of initial conditions leading to eradication and consistently reduces aggregate social costs relative to decentralized management. The results provide a formal rationale for rapid intervention, precautionary regulation, and stronger multilateral cooperation in IAS management, particularly in jurisdictions such as the European Union where listing and control actions may be delayed pending evidence of harm.

We build a labor market in which AI systems enter as workers: they apply for jobs, pass screenings, get hired, and get dismissed, alongside humans. Firms post vacancies, workers search with friction, and product demand slopes downward. Across 30 seeded runs per configuration, AI entry at 70% of the human wage raises unemployment by 4.1 percentage points (95% CI 3.5 to 4.6) and leaves 12.2 fewer humans employed (CI 10.5 to 13.9). Layoffs dominate when AI is much cheaper than humans: the layoff margin accounts for 7.2 of the lost jobs and reduced hiring for 5.0, though most dismissed workers find work again. A wider price gap reduces displacement, because cheap AI makes firms expand: at price parity, with zero dismissals, the unemployment effect is largest at 9.2 points (CI 8.6 to 9.9), all of it through hiring. That parity result survives cutting AI applications from five per period to one. Demand elasticity decides how many workers AI displaces. Screening changes who gets hired and leaves the displacement total unchanged.

Bus operations are inherently unstable—buses initially dispatched at equal headways will inevitably end up bunching up. This issue exacerbates passenger waiting times, creates load imbalances between buses, and undermines service reliability. Reinforcement learning (RL) has proven highly effective for mitigating bus bunching and outperforms traditional model-based approaches. However, existing RL approaches require agents to continuously interact with the environment, which potentially disrupts the bus system before effective policies are learned. This paper proposes an Offline Graph-based Multi-agent Actor-Critic (Offline-GMAC) method that trains bus holding policies using only readily available logged GPS data collected during normal uncontrolled operations, thereby eliminating the need for disruptive online interaction or exploration. The method employs general graph neural networks for multi-agent credit assignment. A key innovation of our method is a data augmentation scheme that synthesizes unperformed holding actions from historical uncontrolled bus trajectories. The scheme exploits the equivalence between stochastic link travel time delays and deliberate holding interventions. Under mild assumptions, we prove that the 1-Wasserstein distance between synthesized and target state transition distributions is bounded above by a term that scales linearly with the standard deviation of link travel times plus a tunable synthesis-dependent term. Evaluations using real-world bus data demonstrate that the proposed offline method achieves performance comparable to, and in some cases, even better than its online counterpart.

We study capital budgeting when a manager privately knows project productivity and her empire-building benefits, while headquarters lacks credible priors. Headquarters minimizes maximum regret relative to informed investment. Without compensation, the optimal policy is a spending cap balancing empire-building overinvestment against profitable investment forgone. Compensation helps when empire-building incentives are weak. The optimal payment incentivizes restraint, declines with investment, and reaches zero at the spending cap, supporting greater managerial discretion. When empire-building incentives are strong, compensation cannot distinguish productive investment from biased expansion; therefore, a spending cap alone is optimal.

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.

We study the optimal sequential aggregation of randomly arriving votes from a finite population to identify an unknown majority preference before a fixed deadline, trading off decision accuracy against the cost of delay. The optimal policy is a dynamic majority-quorum rule: a joint, time-varying threshold on vote lead and count, in which quorum and supermajority requirements emerge as the solution to an inference problem about non-participants' preferences. At each date, the continuation region is lens-shaped: the lead required to stop grows with turnout until too few voters remain to overturn it, and it vanishes at the deadline. We characterize conditions under which the boundary is monotone in the stakes, the arrival process, and time. Because the exact boundary admits no closed form, we derive a large-population approximation that reduces the two-dimensional rule onto a single sufficient statistic, and express the rule as a sequential significance test set by a single error tolerance. Calibrated on Polkadot governance data, an out-of-sample evaluation finds that our rule with a 2% error tolerance halves decision times relative to the incumbent mechanism.

Pregnancy can disrupt schooling before infant care begins. We use monthly histories from the National Longitudinal Survey of Youth 1997 to study school interruptions during pregnancy and after childbirth and whether students later return to school or earn a diploma or GED. We jointly model conception and sustained interruptions in enrollment, allowing persistent unobserved differences to affect both processes. Under the timing-of-events identifying assumptions, pregnancy raises the monthly interruption rate to nearly four times the rate without pregnancy. Interruption rates are elevated before delivery and remain elevated afterward. After an interruption, students already exposed to pregnancy return to school and earn a diploma or GED less often within two years. These findings show that schooling disruption is already present during pregnancy, before the additional demands of infant care begin.

Who should give up compute for AI safety research: customers or capability research? Safety paid for by customers delays no capability. Safety paid for by research slows the frontier, which gives knowledge more time to accumulate but postpones what a finished frontier provides. In a frontier-takeoff model, the cheaper source at a given allocation is set by a threshold in demand capacity. Demand capacity is the share of compute customers can use once the frontier is finished. Research should pay too only when demand capacity lies below the threshold. Where the threshold sits depends on how fast the value of customer services diminishes. In the calibration it rises with the service budget, because each further unit taken from customers costs them more. Safety paid for by customers should come early: its ratio to customer compute falls over the takeoff unless safety productivity rises fast. In a calibration with a tight service budget, early customer-funded safety lowers the probability of catastrophe from 75 to 51 percent. That is within one point of the best rule found that may also slow research.

How should consumers learn when a seller chooses a menu of product qualities and prices? We study information design when the seller observes the learning policy, but not consumers' private signals, before choosing its menu. Under cost-curvature conditions, we characterize optimal learning when consumer surplus receives greater weight than profit. Even with two valuations, every optimal posterior distribution combines an interval of posterior types with an efficiently served atom at the highest valuation. The induced menu features a continuum of differentiated products. Strikingly, optimal learning can also induce a lower posterior atom, separated from this interval by a support gap. Buyers in this atom either purchase an isolated low-quality product or are excluded, even when trade with every buyer creates gains. Both configurations can be optimal for the same prior and welfare weight. Served buyers with distinct posterior types are never bunched at the same quality. General finite priors can yield several separating regions and trading atoms. We also characterize the optimal joint design of learning and valuation-dependent segmentation, showing, among other results, that every posterior type with positive gains from trade must be served. Joint design can raise both consumer surplus and profit relative to buyer-optimal private learning alone. Even random assignment to segments with different learning policies and separate menus can give consumers more surplus than any single market yielding the same profit. Additional price discrimination can therefore benefit consumers, even when privacy restrictions require segmentation to reveal nothing about valuations to the seller.

We examine business models that could support frontier AI companies' valuations and the public evidence of plans to earn income beyond selling model access. Reverse cash-flow calculations for OpenAI and Anthropic yield combined year-ten revenue requirements of \$2.79 trillion or \$733 billion, depending on financial assumptions. Public documents identify proposed payments and ownership interests that could supply additional income, such as through partnerships on pharmaceuticals, robotics, or materials science. We discuss how these arrangements relate to firm boundaries and value capture.

Aggregate linear demand systems can be micro-founded by a population of heterogeneous consumers making discrete choices. They can also be extended to incorporate income effects. I prove these results and show how to structurally estimate this class of models using only market-level data. The distribution of consumer preferences is recovered by disciplining the corner solutions with aggregate terms only. This approach allows for the same richness of Berry, Levinsohn, and Pakes (1995) [BLP] while retaining the analytical and computational advantages of linear demand: it does not require exogenously fixing market size, allows for heterogeneity in choice sets, and results in a flexible substitution matrix which varies endogenously as different consumers enter/exit the market. The discrete-choice microfoundation facilitates welfare analysis and the flexible measurement of markups an cost pass-throughs, among a wide range of other applications.

A sender with commitment provides additional information to an already informed receiver. Final posterior means must be more dispersed than initial means and less dispersed than the state, in convex order. We characterize when these two plausibility constraints are also sufficient, so that every distribution satisfying them can be induced. If the state has a positive density, they are sufficient exactly under interval-partition information: the receiver learns which interval of a partition contains the state and nothing more, where an interval may be a single point. Otherwise, a nonempty open set of distributions satisfying both constraints cannot be induced, even when the sender observes the receiver's information. We use the sufficient case to derive an optimal symmetric disclosure rule in a second-price auction where bidders initially know valuation intervals.

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 stochastic dynamic matching with abandonment, a fundamental model in which agents of different types arrive over time, may abandon the market while waiting, and can be matched in pairs for rewards that depend on their types. No online policy can guarantee more than $0.5$ of the omniscient benchmark, which knows all arrival and departure times. Whether this guarantee is achievable has been a central open problem, even in special cases. We resolve this problem by showing that, on every instance, a simple static priority policy, which is computable in polynomial time, earns at least $0.5$ of the omniscient benchmark. This establishes that the optimal competitive ratio is exactly $0.5$, improving the previous best guarantee of 0.192 for the general model [Li et al. 2026; Collina et al. 2020] Our analysis rests on a key stochastic result, which is a new lower bound on the probability that some agent from a given set of types is available. Building on this bound, we develop two approaches: a primal approach that reads the priorities from an optimal solution of a novel linear program, and a dual approach that assigns a “value” to each type, and prioritizes matches with high “surplus” (reward minus value of involved agents). These values are the unique solution of a fixed-point equation derived from linear programming duality. We also show that the two approaches are closely connected.

AI shopping assistants increasingly influence which products consumers consider. We study retail assortment planning under AI mediation, where a retailer chooses a catalog, an AI intermediary forms a customer-facing shortlist, and the customer chooses from that shortlist according to a multinomial logit model. We consider both deterministic mediation, in which the AI follows a fixed segment-specific ranking, and stochastic mediation based on the Plackett-Luce model. Empirically, we construct a dataset of product rankings from leading AI models, estimate Plackett-Luce ranking models, and evaluate their predictive performance on held-out assortments. Combining these estimates with synthetic customer preferences, we find that accounting for AI mediation can materially change optimal assortments and revenue. Across the tested capacity configurations, ignoring mediation yields mean revenue losses between 2.52% and 11.37% relative to the PL optimum. A much simpler deterministic plug-in, based only on the ordering of fitted AI utilities, performs substantially better, with mean losses of at most 0.53%. Motivated by this performance, we study assortment optimization under deterministic mediation. We characterize its computational complexity and show that, for any fixed number of customer segments, the problem admits a fully polynomial-time approximation scheme.

I study how intermediary liquidity affects mortgage resolution using 1.9 million Ginnie Mae buyout options from 2019 to 2022. When funding markets froze in 2020, nonbank issuers repurchased far fewer delinquent loans than depositories servicing loans in the same pools and, within the same issuer and month, shifted repurchases away from large balances, the loans that require the most cash. About $19 billion of repurchases were delayed, and most were completed later. A model of rationing by value per dollar of cash explains this pattern and shows that borrower information is most valuable when funding is intermediate.

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.

"Security by obscurity," or the idea that hiding how a system works helps protect it from adversaries, has long been poorly regarded in the security community. Yet its intuitive appeal persists, and it has resurfaced repeatedly in industry practices and public debates over the years. The logic, on the one hand, is that open scrutiny of systems is the best way to find and respond to problems; and on the other hand, that too much openness can increase risk by giving adversaries a roadmap for attack. This isn't purely a technical question, but a human one: it's about how attackers and good-faith security researchers respond to openness in the real world. As such, security experts base their stance on decades of community experience; however, the field lacks empirical or theoretical foundations to back up these long-standing beliefs. We provide the first rigorous modeling of "security by obscurity," aiming to capture how rational actors will respond to openness or obscurity in fallible systems. We prove that in equilibrium under realistic model conditions, "obscured" systems are more likely to suffer successful attacks than "open" systems — establishing theoretical support for the longstanding received wisdom.

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.

Parents seeking childcare often face long waitlists. At the same time, vacancies at childcare centers can remain unfilled for extended periods. We trace this paradox to two persistent features of childcare services. First, families consider multiple child care options due to enrollment uncertainties, resulting in phantom listings that remain on waitlists even after families have found care elsewhere or no longer need a slot. Second, filling a slot is time-consuming: centers learn whether a family is actively seeking enrollment only after making an offer and waiting for a response. As families pursue alternatives while they wait and their children age, these delays and feedback effects amplify the mismatch between demand and available capacity. We study two operational remedies. First, we examine regular verification that removes phantom listings before offers are made, improving the efficiency of enrollment and reducing vacancies. Second, we study mixed-age classrooms, in which some slots designated for older children can be flexibly used by younger children. This flexibility increases utilization, shortens waits, and reduces wasted offers. Its benefits extend beyond conventional pooling: as children move between age groups, classrooms can be filled through internal flows rather than costly external search, further reducing enrollment delays. Together, verification and mixed use offer a way to expand effective capacity in early childhood classrooms, where regulatory and operational constraints make adding physical capacity particularly costly.

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.

Mental accounting is usually explained by self-control, and two-stage budgeting by separable preferences. We propose a third explanation based on sellers' market power. A consumer who commits to spend a fixed number of dollars in a category has unit-elastic demand, so a seller in that category gains nothing by restricting quantity. A consumer who instead targets a fixed physical quantity has perfectly inelastic demand, a case that a monopolist can exploit. We characterize the commitments that remove a seller's incentive to mark up prices, and show that the fixed dollar budget is the least restrictive. We then show that what matters is budget rigidity rather than separability of preferences. A consumer who re-optimizes her category budget when prices change is insulated from market power only if categories are substitutes; a rigid budget insulates her in every case. Mental accounting can therefore be read as a commitment device against markups, a rationale that is separate from the self-control motive in the existing literature.

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 $\rho>0$.

A second-price auction must determine its price but need not learn how far losing values lie below it. We show that protecting this information from the seller conflicts with auction credibility. In deterministic protocols with private communication, lower-tail privacy forces the first informative question to reveal whether a bidder has the highest possible value. The seller can then manipulate the winner's payment without any bidder detecting the deviation, increasing revenue at some valuation profiles and never reducing it. A descending protocol conceals losing values below the price but permits manipulation; with mandatory sale, a credible ascending protocol reveals them.

After decades of microfinance expansion and despite charging higher interest rates, moneylenders continue to exist alongside microfinance institutions (MFIs). We develop a dynamic model with ex post moral hazard, in which borrowers use MFI loans for production and can rely on moneylenders for bridge loans after shocks to repay MFIs and preserve future access to MFI credit. We then study how MFI competition shapes the coexistence between MFIs and moneylenders. The effect of competition on MFI credit is ambiguous: it may weaken repayment incentives or replace moneylenders as bridge lenders. By contrast, competition unambiguously reduces moneylender credit. In a village-level randomized expansion in Bangladesh, stratified by baseline MFI presence, one additional MFI reduces the number of moneylender loans by roughly 30-40% two to three years later, with no detectable effect on MFI or overall borrowing. This suggests that, in markets where MFIs rely primarily on the threat of exclusion to induce repayment and moneylenders provide emergency finance, gains from additional MFI entry may be greater in less saturated areas.

Employers in Germany argue that collective agreements restrict their flexibility concerning working hours. Using data from the IAB Establishment Panel for the years 2008 to 2024, we investigate working-time adjustments after exit from collective bargaining. We find that exit is associated with only a modest increase in weekly working hours of around 0.3 to 0.6 per cent using fixed-effects and event-study models, corresponding to eight to thirteen additional minutes per week. This adjustment occurs shortly after leaving collective bargaining coverage. We further find no evidence that other margins of working-time adjustment, such as Saturday or Sunday work, are used more extensively after exit. In contrast to previous survey evidence, our findings call into question that working-hours constraints are one of the main drivers of exit from collective bargaining coverage.

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.