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Identification of Economic Models

Paper Session

Sunday, Jan. 7, 2018 1:00 PM - 3:00 PM

Marriott Philadelphia Downtown, Meeting Room 410
Hosted By: Econometric Society
  • Chair: Francesca Molinari, Cornell University

Partial Independence in Nonseparable Models

Matthew A. Masten
,
Duke University
Alexandre Poirier
,
University of Iowa

Abstract

We analyze identification of nonseparable models under three kinds of exogeneity assumptions weaker than full statistical independence. The first is based on quantile independence. Selection on unobservables drives deviations from full independence. We show that such deviations based on quantile independence require non-monotonic and oscillatory propensity scores. Our second and third approaches are based on a distance-from-independence metric, using either a conditional cdf or a propensity score. Under all three approaches we obtain simple analytical characterizations of identified sets for various parameters of interest. We do this in three models: the exogenous regressor model of Matzkin (2003), the instrumental variable model of Chernozhukov and Hansen (2005), and the binary choice model with nonparametric latent utility of Matzkin (1992).

Optimal Invariant Tests in an Instrumental Variables Regression With Heteroskedastic and Autocorrelated Errors

Marcelo J. Moreira
,
Getulio Vargas Foundation (FGV)
Geert Ridder
,
University of Southern California

Abstract

This paper uses model symmetries in the instrumental variable (IV) regression to derive an invariant test for the causal structural parameter. Contrary to popular belief, we show there exist model symmetries when equation errors are heteroskedastic and autocorrelated (HAC). Our theory is consistent with existing results for the homoskedastic model (Andrews, Moreira and Stock(2006} and Chamberlain (2007}), but in general uses information on the structural parameter beyond the Anderson-Rubin, score, and rank statistics. This suggests that tests based only the Anderson-Rubin and score statistics discard information on the causal parameter of interest. We apply our theory to construct designs in which these tests indeed have power arbitrarily close to size. Other tests, including other adaptations to the CLR test, do not suffer the same deficiencies. Finally, we use the model symmetries to propose novel weighted-average power tests for the HAC-IV model.

Robust Likelihood-ratio Tests for Incomplete Economic Models

Hiroaki Kaido
,
Boston University
Yi Zhang
,
Boston University

Abstract

This paper develops a framework for testing hypotheses on structural parameters in incomplete economic models. Examples of hypotheses include those on the presence of strategic interaction in discrete games of complete information. Incomplete economic models make set-valued predictions and hence do not generally yield a unique likelihood. The model structure, however, allows to construct tests based on least favorable pairs of likelihoods using the theory of Huber and Strassen (1973). Building on this, we develop likelihood-ratio tests that are robust to model incompleteness. The tests can be implemented in a computationally tractable manner by solving convex programs.
We further consider hypothesis tests in the presence of nuisance parameters and develop a likelihood-ratio test that minimizes a certain risk function. We then establish a minimax theorem for this setting.

Interpretation of Point Forecasts with Unknown Directive

Patrick W. Schmidt
,
Heidelberg Institute for Theoretical Studies (HITS)
Matthias Katzfuss
,
Texas A&M University

Abstract

Point forecasts can be interpreted as functionals (i.e., point summaries) of predictive distributions. We consider the situation of unknown directives and show how to identify the functional based on point forecasts and associated realizations. Focusing on state-dependent quantiles and expectiles, we construct a generalized method of moments estimator for the functional, along with tests of optimality and more specific hypotheses. Using simulations, we demonstrate that our optimality test is better calibrated and more powerful than existing solutions. In a data example, we show that the gross domestic product (GDP) Greenbook forecasts of the U.S. Federal Reserve can be interpreted as state-dependent quantiles.
JEL Classifications
  • C14 - Semiparametric and Nonparametric Methods: General
  • C30 - General