Signal extraction: experimental evidence
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Signal extraction: experimental evidence Te Bao1 • John Duffy2 Accepted: 12 October 2020 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We report on an experiment examining whether individuals can solve a simple signal extraction problem of the type found in models with imperfect information. In one treatment, subjects must form point predictions based on observing both public and private signals, while in another they receive the same information but must decide on the weight to attach to each signal, which then determines their point prediction. We find that, at the aggregate level, signal extraction provides a good characterization of subjects’ behavior in both treatments, but at the individual level, there is considerable heterogeneity in subjects’ ability to perform signal extraction. Keywords Signal extraction model Belief updating Heterogeneous expectations Bayesian learning
1 Introduction The process of extracting signals corrupted by noise is known as the signal extraction problem. Signal extraction is a particular type of linear filtering, known as the Wiener–Kolmogorov filter, that is applicable to settings where the sources of noise follow stationary processes.1 1
This method was developed simultaneously by Wiener (1941) and Kolmogorov (1941) during the Second World War with the aim of targeting radar-assisted anti-aircraft guns on incoming enemy aircraft
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11238020-09785-x) contains supplementary material, which is available to authorized users. & John Duffy [email protected] Te Bao [email protected] 1
Division of Economics, School of Social Sciences, Nanyang Technological University, Singapore, Singapore
2
Department of Economics, University of California, Irvine, USA
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T. Bao, J. Duffy
In economics, signal extraction is an important micro building block in characterizing the equilibria of models of imperfect information. Perhaps the most famous application of signal extraction is found in Lucas’s (1972) ‘‘island model’’ where firms that are located on different islands (and thus lacking perfect information about the prices of other firms) have to determine the extent to which an increase in the price of their own product is due to an increase in the demand for their product or to a rise in the general level of prices.2 While the Lucas example is perhaps the most well-known application of signal extraction, there are many other economic applications involving the use of signal extraction problems. Fang and Moro (2011) show that statistical discrimination amounts to solving a signal extraction problem. Wolfers (2002) asks whether voters can assess the record of politicians apart from factors the politicians are unable to affect, which amounts to a signal extraction problem. Gabaix and Laibson (2017) show that agents can exhibit as-if discounting behavior when they face imperfect information and estimate the value of future
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