Title

Monotonicity Conditions and Inequality Imputation for Sample-Selection and Non-Response Problems

Publication Type

Journal Article

Publication Date

2005

Abstract

Under a sample selection or non-response problem, where a response variable y is observed only when a condition ? = 1 is met, the identified mean E ( y |? = 1) is not equal to the desired mean E ( y ). But the monotonicity condition E ( y |? = 1) ? E ( y |? = 0) yields an informative bound E ( y |? = 1) ? E ( y ), which is enough for certain inferences. For example, in a majority voting with ? being the vote-turnout, it is enough to know if E ( y ) > 0.5 or not, for which E ( y |? = 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 |? = 1) ? P ( y , z |? = 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. [ABSTRACT FROM AUTHOR]

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

Publisher

Taylor and Francis

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=17658797&site=ehost-live

This document is currently not available here.

Share

COinS