# Risk Premium (UIP) Shocks in a Flexible Price Economy

Dear all,

As in Adolfon et al. (2007), I am using a debt-elastic interest rate rule with a risk premium shock. UIP is given by

\Delta e_{t+1} = (r_t - r^*_t) + \Gamma a_t - v_t

where e denotes the nominal interest rate (positive means depreciation), r and r^* is domestic and foreign interest rates, respectively, a is the net foreign assets and v is the risk premium. An increase in v yields an immediate depreciation of the domestic nominal currency.

A way to achieve this equation is to modify the price of foreign bonds such that the price of the foreign bond (P_t B_{F,t}) is now written as

P_t \frac{B_{F,t}}{e^{\upsilon_t} e^{-\Gamma a_t}}

In the flexible price equilibrium, UIP is written as

\Delta q^n_{t+1} = r^n_t - r^{n,*}_t + \Gamma a^n_t - v_t

where q^n denotes the flexible price eq. real exchange rate and r^n_t denotes the domestic neutral interest rate at time t. An increase in q^n implies a real depreciation in the domestic currency.

In the flexible price equilibrium (FPE), an increase in v yields real depreciation and output increase. The problem is, I am not sure if I want the risk premium to have real effects on output in the FPE. I can avoid this problem by switching the risk premium to the price of the domestic bonds, such that the price of the domestic bond is given by

e^{v_t} P_t B_{H,t}

\lambda_t = \lambda_{t+1} + r_t - \pi_{t+1} - v_t

\lambda^n_t = \lambda^n_{t+1} + r^n_t - v_t

However, this completely changes the model. With this specification

• In the FPE: an increase in the risk premium is completely offset by an increase in the domestic neutral rate, hence the risk premium has no effect on the real exchange rate and on output.

• In the sticky price equilibrium: an increase in the risk premium now shifts the IS curve, e.g. makes the monetary policy less tight. I don’t think that this particular outcome is desirable.

I think I need a setup where I don’t want the risk premium to have real effects on FPE, but only to have real effects on the sticky price equilibrium.

1. Do you think such a framework would be unreasonable?
2. What is the correct way to achieve this result?
3. Do you think that changes in the risk premium should affect the real variables in the FPE?

Any help is much appreciated.
Yakup.

I don’t think it makes sense to not have the risk premium affect real variables in the FPE. If people require more compensation to hold a given amount of risk, which is real consumption risk, then this will cause adjustments, regardless of whether prices are sticky. Take the current Corona shock. Risk premia have spiked and capital is fleeing to safe havens. That does not depend in prices being sticky.

Thank you @jpfeifer.