Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2106.00788

Retrospective causal inference via matrix completion, with an evaluation of the effect of European integration on cross-border employment

Jason Poulos·Andrea Albanese·Andrea Mercatanti·Fan Li
View original source ↗Read source document ↗Export metadata ↓

Abstract

We propose a method of retrospective counterfactual imputation in panel data settings with later-treated and always-treated units, but no never-treated units. We use the observed outcomes to impute the counterfactual outcomes of the later-treated using a matrix completion estimator. We propose a novel propensity-score and elapsed-time weighting of the estimator's objective function to correct for differences in the observed covariate and unobserved fixed effects distributions, and elapsed time since treatment between groups. Our methodology is motivated by studying the effect of two milestones of European integration -- the Free Movement of persons and the Schengen Agreement -- on the share of cross-border workers in sending border regions. We apply the proposed method to the European Labour Force Survey (ELFS) data and provide evidence that opening the border almost doubled the probability of working beyond the border in Eastern European regions.

Explore related subjects

stat.MEecon.EMecon.GNq-fin.ECstat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jason Poulos, Andrea Albanese, Andrea Mercatanti, Fan Li. 2021-06-01. Retrospective causal inference via matrix completion, with an evaluation of the effect of European integration on cross-border employment. https://arxiv.org/abs/2106.00788

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Switchback Experiments under Geometric Mixing

The switchback is an experimental design that measures treatment effects by repeatedly turning an intervention on and off for a whole system. Switchback experiments are a robust way to overcome cross-unit spillover effects; however, they are vulnerable to bias from temporal carryovers. In this paper, we consider properties of switchback experiments in Markovian systems that mix at a geometric rate. We find that, in this setting, standard switchback designs suffer considerably from carryover bias: Their estimation error decays as $T^{-1/3}$ in terms of the experiment horizon $T$, whereas in the absence of carryovers a faster rate of $T^{-1/2}$ would have been possible. We also show, however, that judicious use of burn-in periods can considerably improve the situation, and enables errors that decay as $\log(T)^{1/2}T^{-1/2}$. Our formal results are mirrored in an empirical evaluation.

stat.ME↗
arXiv2026

Saddlepoint approximations for plug-in resampling

Resampling-based procedures can improve on normal approximations in sparse, large-scale testing problems, but their computational cost can be prohibitive. We recognize that several existing procedures belong to a faster plug-in resampling subclass, fixing fitted nuisance parameters during resampling. When the resampled statistic is a sum of conditionally independent terms, the saddlepoint approximation (SPA) for the resampling $p$-value offers further acceleration, replacing resampling with an analytical tail approximation. However, standard Edgeworth-based approximation-error bounds impose regularity conditions that are hard to verify for plug-in resampling laws. We use an alternative approach to establish a finite-sample relative-error bound for the Lugannani-Rice approximation under more tractable conditions, which we apply in two contexts. In statistical genetics, we identify response resampling procedures as the targets of existing SPAs and establish guarantees in a representative setting. In conditional independence testing, we introduce spaCRT, an SPA for the distilled conditional randomization test (dCRT), which has been applied successfully in biology. Our rates quantify the effects of sparsity and signal strength, with matching lower bounds in special cases. We additionally establish asymptotic Type-I error control of the corresponding plug-in resampling procedures under growing sparsity. In simulations and single-cell CRISPR data analysis, spaCRT closely approximates dCRT $p$-values and preserves its statistical performance while accelerating computation by up to 250-fold.

stat.ME↗
arXiv2026

NIRVAR: Network Informed Restricted Vector Autoregression

High-dimensional panels of time series often arise in finance and macroeconomics, where co-movements within groups of panel components occur. Extracting these groupings from the data provides a coarse-grained description of the complex system in question and can inform subsequent prediction tasks. We develop a novel methodology to model such a panel as a restricted vector autoregressive process, where the coefficient matrix is the weighted adjacency matrix of a stochastic block model. This network time series model, which we call the Network Informed Restricted Vector Autoregression (NIRVAR) model, yields a coefficient matrix that has a sparse block-diagonal structure. We propose an estimation procedure that embeds each panel component in a low-dimensional latent space and clusters the embedded points to recover the blocks of the coefficient matrix. Crucially, the method allows for network-based time series modelling when the underlying network is unobserved. We derive the bias, consistency and asymptotic normality of the NIRVAR estimator. Simulation studies suggest that the NIRVAR estimated embedded points are Gaussian distributed around the ground truth latent positions. On three applications to finance, macroeconomics, and transportation systems, NIRVAR outperforms competing models in terms of prediction and provides interpretable results regarding group recovery.

stat.ME↗