We develop a methodology for estimating the parameters of dynamic opinion or expectation formation processes with social interactions. We study a simple stochastic framework of a collective process of opinion formation by a group of agents who face a binary decision problem. The aggregate dynamics of the individuals’ decisions can be analyzed via the stochastic process governing the ensemble average of choices. Numerical approximations to the transient density for this ensemble average allow the evaluation of the likelihood function on the base of discrete observations of the social dynamics. This generic approach can be used to estimate the parameters of various opinion formation processes from a variety of available aggregate data. Our applications include: (i) identification of interaction effects in a well-known business climate index as well as (ii) analysis of sentiment data from the German stock market. In both cases we find strong evidence of strong social interactions with the potential of generating abrupt swings in the average mood of respondents. In this way, the psychological component or the imprints of animal spirits in economic data can be identified.