  This paper experimentally studies whether individuals hold a first-order
belief that others apply Bayes' rule to incorporate private information into
their beliefs, which is a fundamental assumption in many Bayesian and
non-Bayesian social learning models. We design a novel experimental setting in
which the first-order belief assumption implies that social information is
equivalent to private information. Our main finding is that participants'
reported reservation prices of social information are significantly lower than
those of private information, which provides evidence that casts doubt on the
first-order belief assumption. We also build a novel belief error model in
which participants form a random posterior belief with a Bayesian posterior
belief kernel to explain the experimental findings. A structural estimation of
the model suggests that participants' sophisticated consideration of others'
belief error and their exaggeration of the error both contribute to the
difference in reservation prices.
