Simple subvector inference on sharp identified set in affine models
Conditionally Accepted, Journal of Econometrics , 2024 (subsumes
"Inference in high-dimensional set-identified linear models")
Arxiv version
This paper studies a regularized support function estimator for bounds on components of the
parameter vector in the case in which the identified set is a polygon. The proposed regularized
estimator has three important properties: (i) it has a uniform asymptotic Gaussian limit in the
presence of flat faces in the absence of redundant (or overidentifying) constraints (or vice
versa); (ii) the bias from regularization does not enter the first-order limiting
distribution;(iii) the estimator remains consistent for sharp identified set for the individual
components even in the non-regualar case. These properties are used to construct uniformly valid
confidence sets for an element theta_1 of a parameter vector θ∈ℝd that is partially identified
by
affine moment equality and inequality conditions. The proposed confidence sets can be computed
as a solution to a small number of linear and convex quadratic programs, which leads to a
substantial decrease in computation time and guarantees a global optimum. As a result, the
method provides uniformly valid inference in applications in which the dimension of the
parameter space, d, and the number of inequalities, k, were previously computationally
unfeasible (d,k=100). The proposed approach can be extended to construct confidence sets for
intersection bounds, to construct joint polygon-shaped confidence sets for multiple components
of θ, and to find the set of solutions to a linear program. Inference for coefficients in the
linear IV regression model with an interval outcome is used as an illustrative example.
On model selection criteria for climate change impact studies
Climate change impact studies inform policymakers on the estimated damages of future climate
change on economic, health and other outcomes. In most studies, an annual outcome variable is
observed, e.g. agricultural yield, annual mortality or gross domestic product, along with a
higher-frequency regressor, e.g. daily temperature. While applied researchers tend to consider
multiple models to characterize the relationship between the outcome and the high-frequency
regressor, a choice between the damage functions implied by the different models has to be made
to inform policy. This paper formalizes the model selection problem and the policy objective in
this empirical setting in light of current empirical practice. We then show that existing model
selection criteria are only suitable for the policy objective under specific conditions. These
conditions include a requirement that one of the models under consideration nests the true
model. To overcome this restriction, we propose a new criterion, the proximity-weighted
mean-squared error (PWMSE) of predicting climate change impacts. The PWMSE targets the policy
objective of predicting the impact of projected climate change directly by giving higher weight
to prior years with weather closer to the projected scenario. We show that our approach selects
the best approximate regression model that has the smallest weighted error of predicted impacts
for a future climate scenario. A simulation study and an application revisiting the impact of
climate change on agricultural production illustrate the empirical relevance of our theoretical
analysis.
Time Consistency and Duration of Government Debt: A Model of Quantitative Easing∗
All finite single-agent choice problem with ordinal preferences admit a compatible utility
function such that: strict dominance by pure or mixed actions coincides with dominance by pure
actions in the sense of Börgers (1993). With asymmetric preferences, Börgers’ notion of
dominance reduces to the classical notion of strict dominance by pure strategies. The result
extends to some infinite environments satisfying different assumptions. In all cases, the
equivalence holds whenever the agent is sufficiently risk averse.
Other publications
What Price is Right? Cigarette Demand Has Become More Responsive to Prices
This paper studies small sample properties and bias of just-identified instrumental variable
quantile regression (IVQR) estimators, nesting order statistics and classical quantile
regression. We propose a theoretical framework for analyzing small sample properties based on a
novel approximation of the discontinuous sample moments with a Hölder continuous process. Using
this approximation, we derive remainder bounds for the asymptotic linear expansions of exact and
k-step estimators of IVQR models. Furthermore, we derive a bias formula for exact IVQR
estimators up to order o(1/n). The bias contains components that cannot be consistently
estimated and depend on the particular numerical estimation algorithm. To circumvent this
problem, we propose a novel 1-step adjustment of the estimator, which admits a feasible bias
correction. Monte Carlo evidence suggests that our formula removes a substantial portion of the
bias for sample sizes as small as n=50. We suggest using exact estimators, when possible, to
achieve the smallest bias. Otherwise, applying 1-step corrections may improve the higher-order
bias and MSE of any consistent estimator.
Secular rise and pro-cyclical variation in markups: Evidence from US grocery stores
We study the properties of projection inference for set-identified Structural Vector
Autoregressions. A nominal 1-alpha projection region collects the structural parameters that are
compatible with a 1-alpha Wald ellipsoid for the model's reduced-form parameters (autoregressive
coefficients and the covariance matrix of residuals). We show that projection inference can be
applied to a general class of stationary models, is computationally feasible, and it produces
regions for the structural parameters and their identified set with both frequentist coverage
and robust Bayesian credibility of at least 1- alpha.
A drawback of the projection approach is that both coverage and robust credibility may be
strictly above their nominal level. Following the work of Kaido, Molinari, and Stoye (2016), we
calibrate the radius of the Wald ellipsoid to guarantee that the robust Bayesian credibility of
the projection method is exactly 1 - alpha. If the bounds of the identified set are
differentiable, our calibrated projection also covers the identified set with probability 1 -
alpha. We illustrate the main results of the paper using the demand/supply-model for the U.S.
labor market in Baumeister and Hamilton (2015).
2015 11th World Congress Econometric Society, Montreal, Canada
2015 22nd International Symposium on Mathematical Programming, Pittsburgh, USA
2015 PSU-Cornell Macro Workshop, Pennsylvania State University, State College, USA
2015 Annual Conference of the Royal Economic Society, University of Manchester, UK
2015 Higher School of Economics, Moscow, Russia
2014 Latin American Meeting of The Econometric Society, University of São Paulo, Brazil
Identification in dynamic models using sign restrictions
Sign restrictions on impulse response functions are used in the literature to identify
structural vector autoregressions and structural factor models. I extend the rank condition used
for exclusion restrictions and provide a necessary and sufficient conditions for point
identification for sign restrictions in this class of models. The necessary condition for point
identification implies that as the number of sign restrictions grows a subset with sufficient
number of sign restrictions becomes binding in the limit. However, one does not need to possess
information about this subset to achieve point identification. So when exclusion restrictions
are not justified by theory, sign restrictions can provide an alternative way to get
point-identified impulse response functions. Also further, I present a closed form
representation of the set of all impulse response functions satisfying a set of sign
restrictions. I demonstrate that restrictions on responses to all shocks can dramatically shrink
this set when compared to restrictions only on a small number of shocks.
2013 23rd Annual Meeting of the Midwest Econometrics Group, Indiana University,
Bloomington