The importance of default risk awareness in conducting monetary and fiscal policies

Abstract

We developed a class of dynamic stochastic general equilibrium models with nominal rigidities to investigate the importance of default risk awareness in developing and implementing monetary and fiscal policies. We introduced default risk in the model and analyzed two policies: exact policies and false policies. The exact policy includes optimal monetary and fiscal policies as well as policy authorities who are aware of default risk. The false policy includes optimal monetary and fiscal policies as well as policy authorities who are unaware of default risk. We calculated the coefficients of simple rules that are a class of Taylor rules and a class of the Bohn rule. We found that there is no distinction on simple rules between the exact and false policies if the interest spread in the steady state is low. However, if the interest spread is high, policy authorities should not stabilize inflation and minimize the premium difference. We calculated welfare costs under the two policies. If the interest spread is low, there is a large difference in welfare costs between the two policies, and if the spread is high, the difference between the welfare costs is further increased. If policy authorities are unaware of the default risk, they introduce a stricter policy that generates significant welfare costs. If the interest spread is high, policy authorities should be aware of the default risk.

Appendices

Appendices

1.1 A nonstochastic steady state

We focus on equilibria in cases that the state variables follow paths that reflect a deterministic stationary equilibrium in which $\Pi _t = 1$ and $\frac{{{\tilde{P}}}_t}{P_t} = 1$. Because this steady state is nonstochastic, productivity is expressed with unit values; i.e., $A = 1$.

In this steady state, the gross nominal interest rate is equal to the inverse of the subjective discount factor, denoted by

$$\begin{aligned} R = \beta ^{-1}. \end{aligned}$$

$\Gamma \left( 0 \right) = 1$, which is the definition of the government debt coupon rate, may be simplified to

$$\begin{aligned} R^G = R. \end{aligned}$$

Notice that $sp_t = 0$ in the steady state.

Equation (23) can be rewritten as:

$$\begin{aligned} \frac{{{\tilde{P}}}_t}{P_t} = \text {E}_t \left( \frac{K_t}{F_t} \right) , \end{aligned}$$

(A.1)

with:

$$\begin{aligned} K_t \equiv \frac{\varepsilon }{\varepsilon - 1} \sum ^\infty _{k =0} \left( P_{t+k} C_{t+k} \right) ^{-1} {{\tilde{Y}}}_{t+k} MC^n_{t+k} \,\,\, ; \,\,\, \ F_t \equiv P_t \sum ^\infty _{k =0} \left( P_{t+k} C_{t+k} \right) ^{-1} {{\tilde{Y}}}_{t+k}, \end{aligned}$$

which may be simplified in the steady state to

$$\begin{aligned} K = \frac{\frac{\varepsilon }{\varepsilon - 1} Y MC^n}{\left( 1 - \alpha \beta \right) \left( P C \right) }\,\,\, ; \,\,\, F = \frac{P Y}{\left( 1 - \alpha \beta \right) \left( P C \right) }. \end{aligned}$$

Entering those equalities into the steady state condition of Eq. (A.1)—namely, $K = F$—yields

$$\begin{aligned} P = \frac{\varepsilon }{\varepsilon - 1} MC^n, \end{aligned}$$

which can be rewritten as

$$\begin{aligned} MC = \left( \frac{\varepsilon }{\varepsilon - 1} \right) ^{-1}. \end{aligned}$$

(A.2)

Furthermore, Eqs. (25) and (A.2) imply that

$$\begin{aligned} \frac{U_N}{U_C} = \frac{1 - \tau }{\left( \frac{\varepsilon }{\varepsilon - 1} \right) \mu ^w} = 1 - \Phi , \end{aligned}$$

with $U_C = C^{-1}$ and $U_N = N^\psi$. Note that because $\tau \in \left( 0, 1 \right)$ and $\varepsilon > 1$, this steady state is distorted.

In the steady state, the definition of $R^H_t$ may be simplified to

$$\begin{aligned} R^S = \left[ 1 + \frac{B}{SP} \Gamma ^\prime \left( 0 \right) \right] . \end{aligned}$$

(A.3)

In the steady state, Eq. (13) may be simplified to

$$\begin{aligned} R^S = \left( 1 - \delta \right) ^{-1} \end{aligned}$$

(A.4)

By entering Eqs. (A.4) into (A.3) and rearranging the terms, we obtain

$$\begin{aligned} \delta = \frac{\phi \varsigma _\tau \sigma _B}{\tau + \phi \varsigma _\tau \sigma _B}, \end{aligned}$$

where we use $\frac{B}{SP} = \left( \frac{SP}{Y} \right) ^{-1} \frac{B}{Y}$.