How serious is the measurement-error problem in risk-aversion tasks?

Abstract

This paper analyzes within-session test/retest data from four different tasks used to elicit risk attitudes. Maximum-likelihood and non-parametric estimations on 16 datasets reveal that, irrespective of the task, measurement error accounts for approximately 50% of the variance of the observed variable capturing risk attitudes. The consequences of this large noise element are evaluated by means of simulations. First, as predicted by theory, the coefficient on the risk measure in univariate OLS regressions is attenuated to approximately half of its true value, irrespective of the sample size. Second, the risk-attitude measure may spuriously appear to be insignificant, especially in small samples. Unlike the measurement error arising from within-individual variability, rounding has little influence on significance and biases. In the last part, we show that instrumental-variable estimation and the ORIV method, developed by Gillen et al. (2019), both of which require test/retest data, can eliminate the attenuation bias, but do not fully solve the insignificance problem in small samples. Increasing the number of observations to N=500 removes most of the insignificance issues.