Publication Type

Journal Article

Version

submittedVersion

Publication Date

2-2007

Abstract

Under a sample selection or non-response problem, where a response variable y is observed only when a condition δ = 1 is met, the identified mean E(y|δ = 1) is not equal to the desired mean E(y). But the monotonicity condition E(y|δ = 1) ≤ E(y|δ = 0) yields an informative bound E(y|δ = 1) ≤ E(y), which is enough for certain inferences. For example, in a majority voting with δ being the vote-turnout, it is enough to know if E(y) > 0.5 or not, for which E(y|δ = 1) > 0.5 is sufficient under the monotonicity. The main question is then whether the monotonicity condition is testable, and if not, when it is plausible. Answering to these queries, when there is a ‘proxy’ variable z related to y but fully observed, we provide a test for the monotonicity; when z is not available, we provide primitive conditions and plausible models for the monotonicity. Going further, when both y and z are binary, bivariate monotonicities of the type P(y, z|δ = 1) ≤ P(y, z|δ = 0) are considered, which can lead to sharper bounds for P(y). As an empirical example, a data set on the 1996 U.S. presidential election is analyzed to see if the Republican candidate could have won had everybody voted, i.e., to see if P(y) > 0.5, where y = 1 is voting for the Republican candidate.

Keywords

Imputation, Monotonicity, Non-response, Orthant dependence, Sample selection

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometric Reviews

Volume

24

Issue

2

First Page

175

Last Page

194

ISSN

0747-4938

Identifier

10.1081/ETC-200067910

Publisher

Taylor and Francis

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1081/ETC-200067910

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