Valid tests when instrumental variables do not perfectly satisfy the exclusion restriction
Andrés Riquelme
North Carolina State University
Department of Economics
Raleigh, NC
[email protected]
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Daniel Berkowitz
University of Pittsburgh
Department of Economics
Pittsburgh, PA
[email protected]
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Mehmet Caner
North Carolina State University
Department of Economics
Raleigh, NC
[email protected]
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Abstract. There is a growing consensus that it is difficult to pick instruments
that perfectly satisfy the exclusion restriction. Drawing on results from
Berkowitz, Caner, and Fang (2012, Journal of Econometrics 166: 255–266), we
provide in this article a nontechnical summary of how valid inferences can be
made when instrumental variables come close to satisfying the exclusion restriction.
Although the Anderson–Rubin (1949, Annals of Mathematical Statistics
20: 46–63) test statistic is robust to weak identification, it assumes that the instruments
are perfectly orthogonal to the structural error term and is therefore
oversized under mild violations of the orthogonality condition. The fractionally
resampled Anderson–Rubin (FAR) test is a modification of the Anderson–Rubin
test that accounts for violations of the orthogonality condition. We show that in
small samples, the size of the resampling block of the FAR test can be modified to
obtain valid critical values and analyze its size and power properties. We focus on
power and not on size-adjusted power because the FAR test uses only one critical
value in its application. We also describe user-written commands to implement
the Anderson–Rubin and FAR tests in Stata.
View all articles by these authors:
Andrés Riquelme, Daniel Berkowitz, Mehmet Caner
View all articles with these keywords:
far, fractionally resampled Anderson–Rubin test, exclusion restriction, instrumental variables, near exogeneity
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