The dynamics of unobservable short rate are frequently estimated directly by using a proxy. We estimate the biases resulting from this practice (proxy problem). To solve this problem, State-Space models have been proposed by many researchers. State-Space models have been used to estimate the unobservable variables from the observable variables in econometrics. However, applications of State-Space models often result in a misleading interpretation of the underlying processes especially when the observability of the State-Space model and the assumption of noise processes in the state vector are not properly considered. In this study, we propose the exact State-Space model that properly considers the faults of previous researchers to solve the proxy problem.