This paper develops 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 approach can be used to estimate the parameters of the opinion formation process from aggregate data on its average realization. Our application to a well-known business climate index provides strong indication of social interaction as an important element in respondents' assessment of the business climate.