Estimating Fixed Effects: Perfect Prediction and Bias in Binary Response Panel Models, with an Application to the Hospital Readmissions Reduction Program

44 Pages Posted: 22 Nov 2017

See all articles by Johannes Kunz

Johannes Kunz

Monash University - Centre for Health Economics; University of Zurich - Department of Economics

Kevin E. Staub

University of Melbourne - Department of Economics; IZA Institute of Labor Economics

Rainer Winkelmann

University of Zurich - Statistics and Empirical Economic Research; IZA Institute of Labor Economics; Centre for Economic Policy Research (CEPR)

Multiple version iconThere are 2 versions of this paper

Date Written: November 20, 2017

Abstract

The maximum likelihood estimator for the regression coefficients, β, in a panel binary response model with fixed effects can be severely biased if N is large and T is small, a consequence of the incidental parameters problem. This has led to the development of conditional maximum likelihood estimators and, more recently, to estimators that remove the O(T−1) bias in βˆ. We add to this literature in two important ways. First, we focus on estimation of the fixed effects proper, as these have become increasingly important in applied work. Second, we build on a bias-reduction approach originally developed by Kosmidis and Firth (2009) for cross-section data, and show that in contrast to other proposals, the new estimator ensures finiteness of the fixed effects even in the absence of within-unit variation in the outcome. Results from a simulation study document favourable small sample properties. In an application to hospital data on patient readmission rates under the 2010 Affordable Care Act, we find that hospital fixed effects are strongly correlated across different treatment categories and on average higher for privately owned hospitals.

Keywords: Perfect prediction, Bias reduction, Penalised likelihood, Logit, Probit, Affordable Care Act

JEL Classification: C23, C25, I18

Suggested Citation

Kunz, Johannes S and Staub, Kevin E. and Winkelmann, Rainer, Estimating Fixed Effects: Perfect Prediction and Bias in Binary Response Panel Models, with an Application to the Hospital Readmissions Reduction Program (November 20, 2017). Available at SSRN: https://ssrn.com/abstract=3074193 or http://dx.doi.org/10.2139/ssrn.3074193

Johannes S Kunz

Monash University - Centre for Health Economics ( email )

Building 75, 15 Innovation Walk
Monash University
Clayton, Victoria 3800
Australia

University of Zurich - Department of Economics ( email )

Zürich
Switzerland

Kevin E. Staub (Contact Author)

University of Melbourne - Department of Economics ( email )

Melbourne, Victoria 3010
Australia

IZA Institute of Labor Economics ( email )

P.O. Box 7240
Bonn, D-53072
Germany

Rainer Winkelmann

University of Zurich - Statistics and Empirical Economic Research ( email )

Raemistrasse 62
CH-8001 Zurich
Switzerland
++41 1 634 2292 (Phone)
++41 1 634 4996 (Fax)

HOME PAGE: http://www.unizh.ch/sts/

IZA Institute of Labor Economics ( email )

P.O. Box 7240
Bonn, D-53072
Germany
+49 228 3894 503 (Phone)
+49 228 3894 510 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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