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Simple differences between reports from self and proxy respondents from non-experimental studies can not be taken as evidence of differential reporting behavior. Both groups are to some extent self-selected and mean reports will contain selectivity bias. In this paper, a traditional response error model is modified to incorporate selectivity bias explicitly. The model is estimated on monthly earnings data for prime-age males from SIPP. The results suggest the existence of substantial selectivity and differential reporting biases as well as differential reporting error variance.
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