We present a new estimator for causal effects with panel data that builds on insights behind the widely used difference-in-differences and synthetic control methods. Relative to these methods we find, both theoretically and empirically, that this “synthetic difference-in-differences” estimator has desirable robustness properties, and that it performs well in settings where the conventional estimators are commonly used in practice. We study the asymptotic behavior of the estimator when the systematic part of the outcome model includes latent unit factors interacted with latent time factors, and we present conditions for consistency and asymptotic normality. (JEL C23, H25, H71, I18, L66)

No abstract

At least one co-author has disclosed a financial relationship of potential relevance for this research. Further information is available online at http://www.nber.org/papers/w25532.ack NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

Abstract. Three-dimensional (3D) shape models are powerful because they enable the inference of object shape from incomplete, noisy, or ambiguous 2D or 3D data. For example, realistic parameterized 3D human body models have been used to infer the shape and pose of people from images. To train such models, a corpus of 3D body scans is typically brought into registration by aligning a common 3D human-shaped template to each scan. This is an ill-posed problem that typically involves solving an optimization problem with regularization terms that penalize implausible deformations of the template. When aligning a corpus, however, we can do better than generic regularization. If we have a model of how the template can deform then alignments can be regularized by this model. Constructing a model of deformations, however, requires having a corpus that is already registered. We address this chicken-and-egg problem by approaching modeling and registration together. By minimizing a single objective function, we reliably obtain high quality registration of noisy, incomplete, laser scans, while simultaneously learning a highly realistic articulated body model. The model greatly improves robustness to noise and missing data. Since the model explains a corpus of body scans, it captures how body shape varies across people and poses.

Adaptive experimental designs can dramatically improve efficiency in randomized trials. But with adaptively collected data, common estimators based on sample means and inverse propensity-weighted means can be biased or heavy-tailed. This poses statistical challenges, in particular when the experimenter would like to test hypotheses about parameters that were not targeted by the data-collection mechanism. In this paper, we present a class of test statistics that can handle these challenges. Our approach is to adaptively reweight the terms of an augmented inverse propensity-weighting estimator to control the contribution of each term to the estimator’s variance. This scheme reduces overall variance and yields an asymptotically normal test statistic. We validate the accuracy of the resulting estimates and their CIs in numerical experiments and show that our methods compare favorably to existing alternatives in terms of mean squared error, coverage, and CI size.