Expectation shocks and fiscal rules

Abstract

This paper discuss expectation (or news) shocks to government expenditures: consumption or investment spending in an otherwise standard RBC model of the U.S. economy. In addition, we study the differences emerging from modelling fiscal policy with and without fiscal rules. We find that news about future fiscal policy generate dramatically different effects, if fiscal policy follows a rule. Our findings have several implications for the design and the implementation of fiscal policy as well as the estimation of fiscal shocks.

Appendix

1.1 A.1 Solution algorithm

Here, we follow the exposition in Fujiwara and Kang (2006). The solution to a rational expectation model

$$\begin{array}{@{}rcl@{}} 0 &=&\alpha_{0}\mathbb{E}_{t}\left[ Z_{t+1}-Z^{\ast }\right] +\alpha_{1} \left[ Z_{t}-Z^{\ast }\right] +\alpha_{2}\left[ Z_{t-1}-Z^{\ast }\right]\\ &&\quad+\beta_{0}\left[ S_{t+1}-S^{\ast }\right] +\beta_{1}\left[ S_{t}-S^{\ast }\right] , \end{array} $$

(30)

$$\begin{array}{@{}rcl@{}} S_{t} &=&S^{\ast }+P\left[ S_{t-1}-S^{\ast }\right] +C\varepsilon_{t}, \end{array} $$

(31)

where Z gives the vector of endogenous variables and S is the vector of exogenous disturbances is given by

$$ Z_{t}=Z^{\ast }+A\left[ Z_{t-1}-Z^{\ast }\right] +B\left[ S_{t}-S^{\ast } \right] . $$

(32)

Combining those equations gives

$$\begin{array}{@{}rcl@{}} \alpha_{0}A^{2}+\alpha_{1}A+\alpha_{2} &=&0, \end{array} $$

(33)

$$\begin{array}{@{}rcl@{}} \left[ \beta_{0}+\alpha_{0}B\right] P+\left[ \beta_{1}+\alpha_{1}B+\alpha_{0}AB\right] &=&0. \end{array} $$

(34)

The expectation shock is introduced by modifying the B matrix. Suppose a shock process is given by

$$ \varphi_{t}=\rho_{\varphi }\varphi_{t-1}+\xi_{\varphi ,t-p}+\varepsilon_{\varphi ,t}, $$

(35)

where ξ_φ,t−p is the expectation shock that might occur in period p > 0. This shock can be introduced to the shock vector

$$ S_{t}^{\ast }= \left( \begin{array}{c} \varphi_{t} \\ \xi_{\varphi ,t} \\ \xi_{\varphi ,t-1} \end{array}\right) , $$

(36)

and by adjusting the following matrices

$$\begin{array}{@{}rcl@{}} \beta_{0}^{\ast } &=& \left( \begin{array}{ccc} & 0 & 0 \\ \beta_{0} & 0 & 0 \\ & 0 & 0 \end{array}\right) ,\end{array} $$

(37)

$$\begin{array}{@{}rcl@{}} \beta_{1}^{\ast } &=& \left( \begin{array}{ccc} & 0 & 0 \\ \beta_{1} & 0 & 0 \\ & 0 & 0 \end{array}\right) ,\end{array} $$

(38)

$$\begin{array}{@{}rcl@{}} P^{\ast } &=& \left( \begin{array}{ccc} \rho_{\varphi } & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 1 & 0 \end{array}\right) .\end{array} $$

(39)

Then, the new B^∗ can be computed and the system can be solved.

1.2 A.2 Technology shock with fiscal rule

In this section, agents receive a signal about a positive, one percent favorable technology shock and fiscal policy follows fiscal rules with endogenous feedback to macroeconomic variables. Figure 6 presents the impulse responses.

Fig. 6

Expectation shock to technology with fiscal rules. Horizontal axes measure quarters, vertical axes deviations from steady state. Two scenarios plotted: the shock materializes (black lines) and the shock does not materializes (red, dashed lines)

The response of the model economy with fiscal rules is very different to the exogenous fiscal policy scenario discussed before. In contrast, the announcement of an increase in technology decreases output on impact. The reason is the countercyclicality of fiscal variables. We have established that in the absence of fiscal rules output would increase. With fiscal rules this - ceteris paribus - effect triggers a decrease in government consumption, government investment, and an increase in tax rates. Overall, those three fiscal effects counter the positive effect from higher anticipated technology and lead to an initial decrease of output.

Further, this implies that consumption and labor supply decrease. With less government investment firms increase investment activities by more than in the exogenous fiscal policy scenario.

If the shock materializes, the positive effects of higher technology materialize: output expands driving up consumption and reducing labor supply. Investment is further increased. Still, fiscal policy creates adverse effect towards the real economy due to its countercyclicality. Government consumption and investment decrease, while taxes further increase.

If the shock does not materializes, agents reverse plans and start to consume more and work more. Firms reduce investment activities. The government increases expenditures and lowers taxes given the low level of output and the falling level of debt. Debt increased on impact because lower labor supply and lower wages reduced the tax base. The adjustment to the steady state is quite persistent and takes several years.