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Selectivity Bias June 8, 2007

Posted by jyu in Qualifying.
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There are basically two versions of the selection bias problem:

(1) In the standard case of selection bias, information on the dependent variable for part of the respondents is missing

(2) In the other version of the selection bias problem, information on the dependent variable is available for all respondents, but the distribution of respondents over categories of the independent variable we are interested in has taken place in a selective way

In brand choice, there might be high correlations between the consumer’s probability distributions for buying, for buying the specific brand, and for buying greater quantities of the brand.  The nature and extent of these corrleations across purchase decisions are not obvious, a priori.  A model that does not accommodate these correlations in a flexible manner is likely to be mis-specified for purchase situations and will render biased parameter estimates that are inappropriate for policy making.

Qin (2005) adopted a recently proposed econometric technique to deal with selectivity in count data and account for two sources of selectivity bias in their simultaneous incidence, brand choices, and quantity model:

(1) unobserved correlations between quantity and incidence outcomes

(2) unobserved correlations between quantity and brand choice outcomes

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