_{1}

^{*}

Carlstrom and Fuerst [“Asset Prices, Nominal Rigidities, and Monetary Policy,” Review of Economic Dynamics, Vol. 10, 2007, pp. 256-275] find that a positive monetary policy response to share prices is a source of equilibrium indeterminacy. In this note, we investigate the negative response of a central bank to share prices. We find that a negative monetary policy response to share prices is also a source of equilibrium indeterminacy.

Should monetary policy respond to asset price fluctuations? To this classic monetary policy question, a recent paper by Carlstrom and Fuerst [

The intuition of Carlstrom and Fuerst’s [

To address this question, we extend the model of [

The rest of this paper is organized as follows. Section 2 introduces our model. Section 3 presents the main results and their interpretation. Section 4 discusses the robustness of the results. Finally, Section 5 presents our concluding remarks.

Our model is the same as that of [

The linearized equilibrium system is given as follows:

where

As shown by [

where

We employ an assumption on

Assumption 1.

Under this assumption, an increase in the real marginal cost decreases the dividend.

The equilibrium system is reduced to the following matrix form:

where

The first equation is the consumption Euler equation (2); the second, the New Keynesian Phillips curve (6); and the third, the Euler equation for share (3).

For the analysis, we transform this system as follows:

where

A necessary and sufficient condition for the equilibrium determinacy of this three-dimensional system is as follows

Proposition 1. Suppose that

where

Proof. A necessary and sufficient condition for equilibrium determinacy is that all roots of

where

Necessary and sufficient conditions for equilibrium determinacy are

Q.E.D.

Since

Corollary 1. Suppose that

central bank’s stance on inflation

The existence of the upper bound of

Why is there a lower bound,

In the case where wages are also sticky a la [

and the following two equations are introduced to the log-linearized equilibrium system:

where

In this case, it is difficult to derive an analytical condition for equilibrium determinacy. Then, we calculate the determinacy region by numerical simulations.

In this paper, the effects of monetary policy responses to asset prices are investigated. [

all overreaction to inflation. We have found that negative monetary policy response is also a source of indeterminacy. This is because an increase in asset prices generates further increases in asset prices through monetary policy. Therefore, the central bank should not respond to asset prices both positively and negatively from the viewpoint of equilibrium indeterminacy.

I would like to thank Keiichiro Kobayashi for their helpful comments and suggestions. Of course, the remaining errors are mine. This work was funded by a Senshu University research grant (“Equilibrium Indeterminacy, Share Prices, and Monetary Policy”) in 2012.