Theoretical work on contracts often identifies an "optimal" contract as a function of the characteristics of the principal and agent who are contracting. Correspondingly, empirical work on contracts often regresses contract form on observed (by the econometrician) characteristics of the principal and agent. This paper examines the econometric implications when some of the theoretically relevant characteristics are partially observed (e.g. proxied) or unobserved. We show that if there are incentives wehreby particular types of agents end up contracting (i.e. matching) with particular types of principals (and we argue that there are), one may end up with estimated co-efficients on the observed characteristics that are misleading. The problem is that this matching generates correlation between observable characteristics of one party and proxy errors of the other party, causing biases in many or all coefficients of interest. We then suggest a number of solutions to this problem, applying these solutins to a historical dataset on agricultural contracts between landlords and tenants in 15th Century Tuscany.