Monotonicity conditions and inequality imputation for sample-selection and non-response problems

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)175-194
Number of pages20
JournalEconometric Reviews
Volume24
Issue number2
DOIs
Publication statusPublished - 2005 Aug 8
Externally publishedYes

Fingerprint

Monotonicity
Sample selection
Imputation
Non-response
Query
Voter turnout
Proxy variables
Majority voting
Inference
Voting
Presidential elections

Keywords

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

ASJC Scopus subject areas

  • Economics, Econometrics and Finance(all)

Cite this

Monotonicity conditions and inequality imputation for sample-selection and non-response problems. / Lee, Myoung-jae.

In: Econometric Reviews, Vol. 24, No. 2, 08.08.2005, p. 175-194.

Research output: Contribution to journalArticle

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