Post-Randomization Under Test: Estimation of the Probit Model

Ronning Gerd (), Rosemann Martin () and Harald Strotmann ()
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Ronning Gerd: Department of Economics, University of Tuebingen, Mohlstrasse 36, D-72074 Tuebingen, Germany
Rosemann Martin: Institut for Applied Economic Research (IAW) Tuebingen, Ob dem Himmelreich 1, D-72074 Tuebingen, Germany

Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), 2005, vol. 225, issue 5, 544-566

Abstract: The paper analyzes effects of randomized response with respect to some binary dependent variable on the estimation of the probit model. This approach is used in interviews when asking sensitive questions or if a respondent erroneously chooses the wrong category in an interview leading to ‘misdassification’. Alternatively, randomization can be used for statistical disclosure control and then is called ‘post randomization method’ (PRAM). We consider two variants which are termed ‘ordinary’ and ‘invariant’ PRAM the latter being of importance mainly in descriptive analysis. Maximum likelihood estimation of the corrected likelihood results in consistent estimates although variances increase considerably for ‘strong’ randomization. Moreover a finite sample bias has been observed in the simulation study, but it is much less pronounced than the bias implied from use of the ‘naive’ probit estimator when the binary dependent variable has been randomized. Effects of randomization on the probit estimates are also illustrated by an empirical study using cross-section data from the German ‘ΑΒ establishment panel’ (IAB Betriebspanel). The decision of firms to accept a collective bargaining agreement (‘Tarifvertrag’) is analyzed in a binary probit model using both original data and data masked by ordinary and invariant PRAM. Here, too, a remarkable bias is observed in case of ‘strong’ randomization.

Keywords: Asymptotic efficiency; collective bargaining; finite sample bias; maximum likelihood; misdassification; statistical disclosure (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:jns:jbstat:v:225:y:2005:i:5:p:544-566

DOI: 10.1515/jbnst-2005-0505

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