micro-to-macro projection

This paper addresses the nonparametric partial identification of linear combinations of individual-level conditional means using only marginal distributions of covariates—without access to their joint distribution—from aggregate data. Methodologically, it departs from conventional joint-distribution assumptions and instead develops a novel theoretical framework grounded in set identification and marginal-constrained optimization within a fully nonparametric setting, yielding sharp identification sets. Theoretically, the width of the identification set is shown to be determined precisely by the extent of missing marginal information; empirically, these sets are typically extremely wide, underscoring that practical inference from purely aggregate data necessitates substantive structural assumptions. The main contribution is the first systematic development of a marginal-distribution-driven nonparametric partial identification theory, which explicitly characterizes the fundamental limits of identification and provides a foundational diagnostic tool for micro-inference from macro-level data.

This paper addresses the challenge of identifying and estimating impulse response functions (IRFs) in nonlinear dynamic systems. Methodologically, it establishes, for the first time, theoretical equivalence between IRFs and nonlinear local projections (NLP) within a nonlinear Markov process framework. It introduces a nonparametric NLP estimator and rigorously proves its consistency for estimating nonlinear IRFs. Furthermore, it characterizes identifiability of multivariate IRFs under non-Gaussian innovations, showing that it hinges on the uniqueness of deconvolution, and provides explicit sufficient conditions for identification. The study extends beyond the limitations of conventional linear local projections, offering a novel nonparametric toolkit and rigorous theoretical foundation for quantifying the effects of non-Gaussian shocks in macro-finance applications.

Identifying counterfactual joint distributions (i.e., couplings) is essential for personalized decision-making and risk assessment, yet existing approaches—bijective structural causal models (SCMs) and optimal transport (OT)—suffer from sensitivity to noise misspecification and inability to identify higher-order couplings, respectively. This paper introduces a novel framework grounded in *cocycles*—a concept from dynamical systems theory newly imported into causal inference—to characterize invariant structures via local symmetries under intervention-induced transformations. Our approach enables nonparametric, model-free identification of counterfactual distributions without relying on parametric or semiparametric assumptions. Crucially, it is inherently robust to latent variable misspecification. We develop an efficient semiparametric cocycle estimator, demonstrating both robustness and state-of-the-art performance in simulations. Applied to 401(k) policy evaluation, our method accurately quantifies the causal effect of pension eligibility on household asset accumulation.

Multi-source short time-series data suffer from limited per-sequence length, hindering accurate modeling of complex dynamical mechanisms. Method: We propose the first hierarchical unsupervised generative framework that jointly learns population-level shared priors and domain-specific dynamics. Our approach integrates variational inference, multi-domain dynamical system reconstruction (DSR), and interpretable latent-space learning to construct a linearly controllable, low-dimensional feature space—enabling cross-parameter-domain transfer and fundamental dynamical modeling. Contributions/Results: (1) First automatic discovery of interpretable dynamical features under a hierarchical structure; (2) High-fidelity single-domain reconstruction on standard DSR benchmarks and real-world neuroscience/clinical datasets; (3) Significantly improved generalization to unseen parameter regimes and modeling robustness in few-shot settings.

Existing random-effects estimators—such as James–Stein and empirical Bayes—optimize overall (population-level) risk, often at the expense of individual prediction accuracy. This paper addresses micro-panel data and proposes an Individual Weighting (IW) shrinkage estimator: it replaces conventional cross-sectional information with each unit’s own time-series history for shrinkage, thereby overcoming the “majority-dominates” limitation inherent in standard approaches. IW constructs feasible weights guided by the minimax regret criterion, ensuring individual-risk optimality under weaker assumptions than traditional methods. Theoretically, the IW estimator achieves asymptotic individual-level optimality and substantially reduces systematic bias. Empirically, it delivers superior individual-level predictive accuracy compared to leading alternatives. Crucially, this work is the first to endogenize temporal structure directly into the shrinkage mechanism—yielding a more interpretable and practically useful framework for micro-level decision-making.

This study addresses the limitations of high-resolution proxies—such as nighttime lights—in capturing unobserved local economic activity after aggregation to administrative units, a constraint rooted in aggregation bias. The authors develop an inverse regression framework and introduce a triple decomposition theorem for predictive elasticity, revealing for the first time that this bias is jointly driven by administrative unit size and internal economic heterogeneity, while also clarifying the conditions under which cross-regional transferability holds. Leveraging VIIRS nighttime lights and subnational GDP or income data across Brazil, Italy, the United States, Indonesia, and Kenya, they combine elasticity decomposition, Monte Carlo simulations, and empirical validation to demonstrate that nighttime lights reliably predict economic activity only in relatively affluent regions and only after local calibration.

This study addresses the challenge of modeling insurance claims when payouts depend on unobservable micro-level states, while only macro-level states and realized payments are observable. Focusing on aggregated multi-state systems subject to left truncation and right censoring, the authors propose an inverse probability weighted estimator for state-specific cumulative payment processes within a micro-to-macro state projection framework. They establish, for the first time under this complex censoring mechanism, the strong consistency and weak convergence of the proposed estimator, rigorously deriving its asymptotic properties. This theoretical foundation enables reliable inference and modeling of latent risks in actuarial practice, where direct observation of underlying risk states is unavailable.

This study addresses the lack of a clear causal interpretation in existing state-dependent local projection (LP) methods when estimating heterogeneous responses of microeconomic agents to macroeconomic shocks. We demonstrate that, under linearity of the conditional mean in the macro shock, state-dependent LP identifies causal impulse responses, thereby providing the first rigorous causal foundation for this approach. To operationalize this insight, we develop a sieve-based nonparametric LP estimator that enables both consistent estimation and valid pointwise inference. Empirical application reveals that incorporating nonparametric state dependence substantially alters the estimated heterogeneous responses of firm investment to monetary policy shocks and reshapes the implied macroeconomic transmission mechanism.

This study addresses the estimation of state occupation probabilities in multistate processes when right censoring and baseline exposure coexist. Under a coarsening-at-random assumption, the proposed approach abandons the conventional Markov assumption and accommodates time-varying confounding. It introduces an augmented inverse probability weighting (AIPW) semiparametric estimator grounded in causal inference and missing data methodology. The method enjoys double robustness and statistical efficiency, ensuring reliable performance even under complex coarsening mechanisms. Both theoretical analysis and simulation studies demonstrate that the estimator yields robust and efficient inference for state occupation probabilities in non-Markov multistate processes.

This study addresses the structural identifiability of model parameters in partially observed stochastic processes, focusing on parameter uniqueness from two data modalities: single-particle trajectories and population density measurements. For spatiotemporal stochastic dynamics, the authors employ individual-based stochastic models to analyze trajectory data and partial differential equation (PDE)-based density evolution models for population-level observations. They innovatively extend differential algebraic methods to PDE models of stochastic processes and introduce a novel framework based on characteristic equations to construct Taylor expansions that explicitly account for the influence of initial conditions on identifiability. Their results demonstrate that parameters are globally identifiable from trajectory data, whereas only local identifiability can be achieved using density data alone, thereby highlighting the critical role of initial condition information in structural identifiability analysis.