217 research outputs found
Identification region of the potential outcome distributions under instrument independence
This paper examines identification power of the instrument exogeneity assumption in the treatment effect model. We derive the identification region: The set of potential outcome distributions that are compatible with data and the model restriction. The model restrictions whose identifying power is investigated are (i)instrument independence of each of the potential outcome (marginal independence), (ii) instrument joint independence of the potential outcomes and the selection heterogeneity, and (iii) instrument monotonicity in addition to (ii) (the LATE restriction of Imbens and Angrist (1994)), where these restrictions become stronger in the order of listing. By comparing the size of the identification region under each restriction, we show that the joint independence restriction can provide further identifying information for the potential outcome distributions than marginal independence, but the LATE restriction never does since it solely constrains the distribution of data. We also derive the tightest possible bounds for the average treatment effects under each restriction. Our analysis covers both the discrete and continuous outcome case, and extends the treatment effect bounds of Balke and Pearl(1997) that are available only for the binary outcome case to a wider range of settings including the continuous outcome case.
Instrumental Variables Before and LATEr
The modern formulation of the instrumental variable methods initiated the
valuable interactions between economics and statistics literatures of causal
inference and fueled new innovations of the idea. It helped resolving the
long-standing confusion that the statisticians used to have on the method, and
encouraged the economists to rethink how to make use of instrumental variables
in policy analysis. [arXiv:1410.0163]Comment: Published in at http://dx.doi.org/10.1214/14-STS494 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Mostly Harmless Simulations? Using Monte Carlo Studies for Estimator Selection
We consider two recent suggestions for how to perform an empirically
motivated Monte Carlo study to help select a treatment effect estimator under
unconfoundedness. We show theoretically that neither is likely to be
informative except under restrictive conditions that are unlikely to be
satisfied in many contexts. To test empirical relevance, we also apply the
approaches to a real-world setting where estimator performance is known. Both
approaches are worse than random at selecting estimators which minimise
absolute bias. They are better when selecting estimators that minimise mean
squared error. However, using a simple bootstrap is at least as good and often
better. For now researchers would be best advised to use a range of estimators
and compare estimates for robustness
Testing Instrument Validity with Covariates
We develop a novel specification test of the instrumental variable
identifying assumptions (instrument validity) for heterogeneous treatment
effect models with conditioning covariates. Building on the common empirical
settings of local average treatment effect and marginal treatment effect
analysis, we assume semiparametric dependence between the potential outcomes
and conditioning covariates, and show that this allows us to express the
testable implications of instrument validity in terms of equality and
inequality restrictions among the subdensities of estimable partial residuals.
We propose jointly testing these restrictions. To improve power of the test, we
propose distillation, a process designed to reduce the sample down to the
information useful for detecting violations of the instrument validity
inequalities. We perform Monte Carlo exercises to demonstrate the gain in power
from testing restrictions jointly and distillation. We apply our test procedure
to the college proximity instrument of Card1 (1993), the same-sex instrument of
Angrist and Evans (1998), the school leaving age instrument of Oreopoulos
(2006), and the mean land gradient instrument of Dinkelman (2011). We find that
the null of instrument validity conditional on covariates cannot be rejected
for Card (1993) and Dinkelman (2011), but it can be rejected at the 10% level
of significance for Angrist and Evans (1998) for some levels of a tuning
parameter, and it is rejected at all conventional levels of significance in the
case of Oreopoulos (2006)
Who Should Get Vaccinated? Individualized Allocation of Vaccines Over SIR Network
How to allocate vaccines over heterogeneous individuals is one of the
important policy decisions in pandemic times. This paper develops a procedure
to estimate an individualized vaccine allocation policy under limited supply,
exploiting social network data containing individual demographic
characteristics and health status. We model spillover effects of the vaccines
based on a Heterogeneous-Interacted-SIR network model and estimate an
individualized vaccine allocation policy by maximizing an estimated social
welfare (public health) criterion incorporating the spillovers. While this
optimization problem is generally an NP-hard integer optimization problem, we
show that the SIR structure leads to a submodular objective function, and
provide a computationally attractive greedy algorithm for approximating a
solution that has theoretical performance guarantee. Moreover, we characterise
a finite sample welfare regret bound and examine how its uniform convergence
rate depends on the complexity and riskiness of social network. In the
simulation, we illustrate the importance of considering spillovers by comparing
our method with targeting without network information
von Mises-Fisher distributions and their statistical divergence
The von Mises-Fisher family is a parametric family of distributions on the
surface of the unit ball, summarised by a concentration parameter and a mean
direction. As a quasi-Bayesian prior, the von Mises-Fisher distribution is a
convenient and parsimonious choice when parameter spaces are isomorphic to the
hypersphere (e.g., maximum score estimation in semi-parametric discrete choice,
estimation of single-index treatment assignment rules via empirical welfare
maximisation, under-identifying linear simultaneous equation models). Despite a
long history of application, measures of statistical divergence have not been
analytically characterised for von Mises-Fisher distributions. This paper
provides analytical expressions for the -divergence of a von Mises-Fisher
distribution from another, distinct, von Mises-Fisher distribution in
and the uniform distribution over the hypersphere. This paper
also collect several other results pertaining to the von Mises-Fisher family of
distributions, and characterises the limiting behaviour of the measures of
divergence that we consider.Comment: 28 pages, 2 figure
Individualized Treatment Allocation in Sequential Network Games
Designing individualized allocation of treatments so as to maximize the
equilibrium welfare of interacting agents has many policy-relevant
applications. Focusing on sequential decision games of interacting agents, this
paper develops a method to obtain optimal treatment assignment rules that
maximize a social welfare criterion by evaluating stationary distributions of
outcomes. Stationary distributions in sequential decision games are given by
Gibbs distributions, which are difficult to optimize with respect to a
treatment allocation due to analytical and computational complexity. We apply a
variational approximation to the stationary distribution and optimize the
approximated equilibrium welfare with respect to treatment allocation using a
greedy optimization algorithm. We characterize the performance of the
variational approximation, deriving a performance guarantee for the greedy
optimization algorithm via a welfare regret bound. We establish the convergence
rate of this bound. We demonstrate the performance of our proposed method in
simulation exercises
Mostly harmless simulations? Using Monte Carlo studies for estimator selection
We consider two recent suggestions for how to perform an empirically motivated Monte Carlo study to help select a treatment effect estimator under unconfoundedness. We show theoretically that neither is likely to be informative except under restrictive conditions that are unlikely to be satisfied in many contexts. To test empirical relevance, we also apply the approaches to a real-world setting where estimator performance is known. Both approaches are worse than random at selecting estimators which minimise absolute bias. They are better when selecting estimators that minimise mean squared error. However, using a simple bootstrap is at least as good and often better. For now researchers would be best advised to use a range of estimators and compare estimates for robustness
Treatment Choice, Mean Square Regret and Partial Identification
We consider a decision maker who faces a binary treatment choice when their
welfare is only partially identified from data. We contribute to the literature
by anchoring our finite-sample analysis on mean square regret, a decision
criterion advocated by Kitagawa, Lee, and Qiu (2022). We find that optimal
rules are always fractional, irrespective of the width of the identified set
and precision of its estimate. The optimal treatment fraction is a simple
logistic transformation of the commonly used t-statistic multiplied by a factor
calculated by a simple constrained optimization. This treatment fraction gets
closer to 0.5 as the width of the identified set becomes wider, implying the
decision maker becomes more cautious against the adversarial Nature
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