Econometric inference allows an analyst to back out the values of agents in a mechanism from the rules of the mechanism and bids of the agents. This paper proposes the problem of inferring the values of agents in a mechanism from the social choice function implemented by the mechanism and the mechanism's outcome (specially: per-unit prices) when the actions are not observed. For single-dimensional agents, this inference problem is a multi-dimensional inversion of the payment identity and is feasible only if the payment identity is uniquely invertible. The inversion is unique for single- and multi-unit proportional weights social choice functions (common, for example, in the bandwidth allocation); and its inverse can be found efficiently. This inversion is not unique for social choice functions that exhibit complementarities.