Monotonicity Conditions and Inequality Imputation for Sample-Selection and Non-Response Problems
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]
Imputation; Monotonicity; Non-response; Orthant dependence; Sample selection
Taylor and Francis
Monotonicity Conditions and Inequality Imputation for Sample-Selection and Non-Response Problems. (2005). Econometric Reviews. 24, (2), 175-194. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/359
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