Self‐fulfilling regression and statistical discrimination

• Date: 01 September 2019
• Published date: 01 September 2019
• Author: Takashi Hayashi
• DOI: http://doi.org/10.1111/ijet.12190

doi: 10.1111/ijet.12190

Self-fulfilling regression and statistical discrimination

Takashi Hayashi∗

This paper provides a simple model which explains that statistical discrimination can arise in a

purely self-fulfilling manner. The story is as follows. (i) Atthe point of hiring , employerscannot

observe workers’ productivities but can observe only their signals, such as test scores, and under

perfect competition they pay for expected labor productivity conditional on signal observation,

based on their belief about return to signal. (ii) Given the employers’ belief, workers choose an

effort level, which affects the joint probability distribution over productivity–signal pairs. (iii)

In equilibrium, the employers’ belief proves to be statistically consistent. We show that there

may be multiple equilibria, and that equilibrium selection has nothing to do with economic

fundamentals.

Key wor ds statistical discrimination, self-fulfilling prophecy, signaling, hidden action

JEL classification J71, D82

Accepted 11 May2017

1 Introduction

This paper provides a simple model which explains that statistical discrimination can arise in a purely

self-fulfilling manner, that is, as a multiple-equilibrium phenomenon.

The story is at follows. (i) At the point of hiring, employers cannot observe workers’ produc-

tivities but can observe only their signals, such as test scores, and under perfect competition they

pay for expected labor productivity conditional on signal observation, based on their belief about

return to signal. (ii) Workers choose an effort level, which affects the joint probability distribution

over productivity–signal pairs, and such effort is high (low) when the employers’ belief about return

to signal is high (low). (iii) In equilibrium, the employers’ belief proves to be statistically consistent,

as one can observe the statistical relationship between signal and productivity ex post. We show that

there may be multiple equilibria, and different groups of workers may fall into different equilibria

even when they have exactly the same fundamentals.

Statistical discrimination as a self-fulfilling prophecy phenomenon has been widely studied. The

idea of the self-fulfilling prophecy in the context of discrimination dates back to Merton (1948) and

Myrdal (1944). Prominent among the works in economic theory are Arrow (1973) and Coate and

Loury (1993). The basic story throughout is that as employers have a belief that a given group has

high (low) productivity,it encourages (discourages) the workers in that group to spend effort on skill

formation in some way, and its consequenceverifies the employers’ belief in a self-fulfilling manner,

while the precise driving-force of this cycle differs across the workers.

Arrow (1973) considers that there are two kinds of jobs, skilled and unskilled, and in or-

der to be qualified for skilled jobs workers need to incur some cost, which is drawn from a

∗Adam Smith Business School, Universityof Glasgow, Glasgow, UK. Email: takashi.hayashi@glasgow.ac.uk

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International Journal of Economic Theory

International Journal of Economic Theory 15 (2019) 289–295 © IAET 289