478 research outputs found
The Augmented Synthetic Control Method
The synthetic control method (SCM) is a popular approach for estimating the
impact of a treatment on a single unit in panel data settings. The "synthetic
control" is a weighted average of control units that balances the treated
unit's pre-treatment outcomes as closely as possible. A critical feature of the
original proposal is to use SCM only when the fit on pre-treatment outcomes is
excellent. We propose Augmented SCM as an extension of SCM to settings where
such pre-treatment fit is infeasible. Analogous to bias correction for inexact
matching, Augmented SCM uses an outcome model to estimate the bias due to
imperfect pre-treatment fit and then de-biases the original SCM estimate. Our
main proposal, which uses ridge regression as the outcome model, directly
controls pre-treatment fit while minimizing extrapolation from the convex hull.
This estimator can also be expressed as a solution to a modified synthetic
controls problem that allows negative weights on some donor units. We bound the
estimation error of this approach under different data generating processes,
including a linear factor model, and show how regularization helps to avoid
over-fitting to noise. We demonstrate gains from Augmented SCM with extensive
simulation studies and apply this framework to estimate the impact of the 2012
Kansas tax cuts on economic growth. We implement the proposed method in the new
augsynth R package
Using Multiple Outcomes to Improve the Synthetic Control Method
When there are multiple outcome series of interest, Synthetic Control
analyses typically proceed by estimating separate weights for each outcome. In
this paper, we instead propose estimating a common set of weights across
outcomes, by balancing either a vector of all outcomes or an index or average
of them. Under a low-rank factor model, we show that these approaches lead to
lower bias bounds than separate weights, and that averaging leads to further
gains when the number of outcomes grows. We illustrate this via simulation and
in a re-analysis of the impact of the Flint water crisis on educational
outcomes.Comment: 36 pages, 6 figure
A Random Walk to a Non-Ergodic Equilibrium Concept
Random walk models, such as the trap model, continuous time random walks, and
comb models exhibit weak ergodicity breaking, when the average waiting time is
infinite. The open question is: what statistical mechanical theory replaces the
canonical Boltzmann-Gibbs theory for such systems? In this manuscript a
non-ergodic equilibrium concept is investigated, for a continuous time random
walk model in a potential field. In particular we show that in the non-ergodic
phase the distribution of the occupation time of the particle on a given
lattice point, approaches U or W shaped distributions related to the arcsin
law. We show that when conditions of detailed balance are applied, these
distributions depend on the partition function of the problem, thus
establishing a relation between the non-ergodic dynamics and canonical
statistical mechanics. In the ergodic phase the distribution function of the
occupation times approaches a delta function centered on the value predicted
based on standard Boltzmann-Gibbs statistics. Relation of our work with single
molecule experiments is briefly discussed.Comment: 14 pages, 6 figure
Estimating Racial Disparities in Emergency General Surgery
Research documents that Black patients experience worse general surgery
outcomes than white patients in the United States. In this paper, we focus on
an important but less-examined category: the surgical treatment of emergency
general surgery (EGS) conditions, which refers to medical emergencies where the
injury is "endogenous," such as a burst appendix. Our goal is to assess racial
disparities for common outcomes after EGS treatment using an administrative
database of hospital claims in New York, Florida, and Pennsylvania, and to
understand the extent to which differences are attributable to patient-level
risk factors versus hospital-level factors. To do so, we use a class of linear
weighting estimators that re-weight white patients to have a similar
distribution of baseline characteristics as Black patients. This framework
nests many common approaches, including matching and linear regression, but
offers important advantages over these methods in terms of controlling
imbalance between groups, minimizing extrapolation, and reducing computation
time. Applying this approach to the claims data, we find that disparities
estimates that adjust for the admitting hospital are substantially smaller than
estimates that adjust for patient baseline characteristics only, suggesting
that hospital-specific factors are important drivers of racial disparities in
EGS outcomes
Anomalous biased diffusion in a randomly layered medium
We present analytical results for the biased diffusion of particles moving
under a constant force in a randomly layered medium. The influence of this
medium on the particle dynamics is modeled by a piecewise constant random
force. The long-time behavior of the particle position is studied in the frame
of a continuous-time random walk on a semi-infinite one-dimensional lattice. We
formulate the conditions for anomalous diffusion, derive the diffusion laws and
analyze their dependence on the particle mass and the distribution of the
random force.Comment: 19 pages, 1 figur
Two-Scale Annihilation
The kinetics of single-species annihilation, , is investigated in
which each particle has a fixed velocity which may be either with equal
probability, and a finite diffusivity. In one dimension, the interplay between
convection and diffusion leads to a decay of the density which is proportional
to . At long times, the reactants organize into domains of right- and
left-moving particles, with the typical distance between particles in a single
domain growing as , and the distance between domains growing as .
The probability that an arbitrary particle reacts with its
neighbor is found to decay as for same-velocity pairs and as
for pairs. These kinetic and spatial exponents and their
interrelations are obtained by scaling arguments. Our predictions are in
excellent agreement with numerical simulations.Comment: revtex, 5 pages, 5 figures, also available from
http://arnold.uchicago.edu/~eb
- …