Adverse selection, efficiency and the structure of information
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Adverse selection, efficiency and the structure of information Heski Bar-Isaac1 · Ian Jewitt2
· Clare Leaver3
Received: 29 August 2019 / Accepted: 17 July 2020 © The Author(s) 2020
Abstract This paper explores how the structure of asymmetric information impacts on economic outcomes in Akerlof’s (Q J Econ 84(3):488–500, 1970) Lemons model applied to the labour market and extended to admit a matching component between worker and firm. We characterize the nature of equilibrium and define measures of adverse selection and efficiency. We then characterize the joint distribution of outcomes—adverse selection, probability of trade, efficiency, profits, and wage—for the class of Gaussian basic games and information, and perform comparative statics with respect to a parsimonious parameterization of the information structure. We use this framework to revisit the classic issue, first addressed by Roy (Oxford Econ Pap 3(2):135-146, 1951), of selection into different sectors. We identify conditions under which an effect reversal—adverse selection at any realisation of public information but, overall, positive selection into the outside sector—can and cannot arise, and note the implications for empirical work. We also explore the divisions of expected total surplus between worker and firm that can be achieved as information varies. We show that, if the distribution of worker types is non-singular, any point in the set of possible surplus divisions can be achieved as a limit of a PBE for some information structure with asymmetric information. Finally, re-interpreting the model in an insurance context, where the matching component becomes consumer risk aversion, we use our framework to highlight sources of advantageous selection.
We are grateful to very many people for helpful comments on earlier versions of this paper, in particular Ignacio Esponda, Paul Klemperer, Jonathan Levin, Alessandro Lizzeri, Margaret Meyer and Dan Quigley. We also thank participants at numerous conferences and seminars. Bar-Isaac thanks SSHRC (435-2014-0004) for financial support. Jewitt and Leaver are grateful for the hospitality of the Toulouse School of Economics, 2018–2019.
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Ian Jewitt [email protected]
1
University of Toronto, CEPR and CRESSE, Toronto, Canada
2
Nuffield College, University of Oxford and CEPR, Oxford, England
3
Blavatnik School of Government, University of Oxford and CEPR, Oxford, England
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H. Bar-Isaac et al.
Keywords Information design · Adverse selection · Asymmetric information JEL Classification D82 · J30
1 Introduction We aim to characterize how the structure of asymmetric information impacts economic outcomes in a natural generalization of Akerlof’s (1970) Lemons model. We couch our discussion in terms of an employer learning model of the labour market, giving a brief discussion of insurance. This model generalizes Akerlof (1970) in two main respects. First, the scalar type assumption is relaxed by introducing a match component between the good to be traded (a worker) and the seller (the current
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