6,588 research outputs found
Randomization tests for peer effects in group formation experiments
Measuring the effect of peers on individual outcomes is a challenging
problem, in part because individuals often select peers who are similar in both
observable and unobservable ways. Group formation experiments avoid this
problem by randomly assigning individuals to groups and observing their
responses; for example, do first-year students have better grades when they are
randomly assigned roommates who have stronger academic backgrounds? Standard
approaches for analyzing these experiments, however, are heavily
model-dependent and generally fail to exploit the randomized design. In this
paper, we extend methods from randomization-based testing under interference to
group formation experiments. The proposed tests are justified by the
randomization itself, require relatively few assumptions, and are exact in
finite samples. First, we develop procedures that yield valid tests for
arbitrary group formation designs. Second, we derive sufficient conditions on
the design such that the randomization test can be implemented via simple
random permutations. We apply this approach to two recent group formation
experiments
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
A Statistical View of Learning in the Centipede Game
In this article we evaluate the statistical evidence that a population of
students learn about the sub-game perfect Nash equilibrium of the centipede
game via repeated play of the game. This is done by formulating a model in
which a player's error in assessing the utility of decisions changes as they
gain experience with the game. We first estimate parameters in a statistical
model where the probabilities of choices of the players are given by a Quantal
Response Equilibrium (QRE) (McKelvey and Palfrey, 1995, 1996, 1998), but are
allowed to change with repeated play. This model gives a better fit to the data
than similar models previously considered. However, substantial correlation of
outcomes of games having a common player suggests that a statistical model that
captures within-subject correlation is more appropriate. Thus we then estimate
parameters in a model which allows for within-player correlation of decisions
and rates of learning. Through out the paper we also consider and compare the
use of randomization tests and posterior predictive tests in the context of
exploratory and confirmatory data analyses
Improved Error Bounds Based on Worst Likely Assignments
Error bounds based on worst likely assignments use permutation tests to
validate classifiers. Worst likely assignments can produce effective bounds
even for data sets with 100 or fewer training examples. This paper introduces a
statistic for use in the permutation tests of worst likely assignments that
improves error bounds, especially for accurate classifiers, which are typically
the classifiers of interest.Comment: IJCNN 201
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