Appendix A
One way of modeling the time-varying NRR is to use both short-term and long-term interest rates to estimate the unobserved NRR that are embedded in both of these market prices. Assuming that the short-term interest rate is mainly determined by the central bank, and that the long-term interest rates are determined by economic fundamentals, and further assuming that the different agents in the economy know the same NRR, the NRR can be estimated in the following way:
where 
are short-term interest rates, 
are long-term interest rates (5 year-government bond yield), 
is the unobserved neutral real interest rate, 
the expected inflation term is the expectations for the period t+1 formed at period t, and ω is the term premium. The term premium is assumed to be a constant, although there is international evidence that the term premium varies at business cycle frequency.
Equation 1 and 2 are the measurement equations. The state variable is assumed to follow the following:
Equations (1) - (3), once put in state-space representation, can be estimated with the Kalman filter via the maximum likelihood.
