We examine the robustness of information cascades in laboratory experiments. Apart from the situation in which each player can obtain a signal for free (as in the experiment by Anderson and Holt, 1997, American Economic Review), the case of costly signals is studied where players decide whether to obtain private information or not, at a small but positive cost. In the equilibrium of this game, only the first player buys a signal and chooses an urn based on this information whereas all following players do not buy a signal and herd behind the first player. The experimental results show that too many signals are bought and the equilibrium prediction performs poorly. To explain these observations, the depth of the subjects' reasoning process is estimated, using a statistical error-rate model. Allowing for different error rates on different levels of reasoning, we find that the subjects' inferences become significantly more noisy on higher levels of the thought process, and that only very short chains of reasoning are applied by the subjects.