The estimation of principal agent models is a subset of inverse optimal problems. As of now there is no consistent method of estimating all its parameters. In general, some proxies for the parameters have been utilized to test plausible economic implications of such models. This study develops a method of estimation for all the parameters using a very limited time series data for one contracting pair. Progress towards empirical reality, based on stylized facts, has been achieved by iteratively modifying the theoretical models and econometric methods. One of these results provides a theoretical justification for the econometric tools utilized in practice as well. However, a fundamental modification of the underlying assumptions is necessary. Given the emphasis on contracts in economic exchange it is necessary to develop the methods further. The study also outlines some of the pertinent issues.