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Licensed Unlicensed Requires Authentication Published by De Gruyter July 11, 2018

Signaling in monetary policy near the zero lower bound

Sergio Salas and Javier Nuñez

Abstract

What are the consequences of asymmetry of information about the future state of the economy between a benevolent Central Bank (CB) and private agents near the zero lower bound? How is the conduct of monetary policy modified under such a scenario? We propose a game theoretical signaling model, where the CB has better information than private agents about a future shock hitting the economy. The policy rate itself is the signal that conveys information to private agents in addition to its traditional role in the monetary transmission mechanism. We find that only multiple “pooling equilibria” arise in this environment, where a CB privately forecasting a contraction will most likely follow a less expansionary policy compared to a complete information context, in order to avoid making matters worse by revealing bad times ahead. On the other hand, a CB privately forecasting no contraction is most likely to distort its complete information policy rate, the consequences of which are welfare detrimental. However, this is necessary because deviating from the pooling policy rate would be perceived by private agents as an attempt to mislead them into believing that a contraction is not expected, which would be even more harmful for society.

JEL Classification: E58; C72

A Appendix

In this appendix I study a flexible price economy, where the CB maintains i0 throughout period 0 and there is no uncertainty, with θ0 and θ1 being the productivity levels for periods 0 and 1 respectively.

Environment

As in the main model, households are indexed by j and each produce a given variety ℓ. Taking as given Pt and i0, HH j maximize:

(50)uj=u(c0j)+βu(c1j)

subject to:

(51)P0c0j+Bj=P0()y0(),  y0()=θ0n0j
(52)P1c1j=(1+i0)Bj+P1()y1(),  y1()=θ1n1j.

Choosing Pt(),ctj,yt() and ntj, where the price level and demand for variety ℓ are given by:

(53)Pt=[01Pt()1ηd]11η,  ctj()=(Pt()Pt)ηctj

where ctj() is demand of variety ℓ by HH j.

Definition of equilibrium

A (monopolistic) competitive equilibrium is a price level Pt and an interest rate i0 such that:

  • HH maximize utility (50) subject to the constraints (51)

  • Markets clear:

    (54)Goods market clears:  ct()01ctj()dj=yt()
    (55)Bonds market clears:  01Bjdj=0

Solution

The intra-temporal problem of how to set prices can be written for HHs as maximizing real income from the production of variety ℓ:

(56)maxPt(),ntPt()Ptyt()

subject to:

(57)yt()=ct(),   yt()=θtntj,   0ntj1.

where ct(ℓ) is the market demand for variety ℓ:

(58)ct()01ctj()dj=(Pt()Pt)η01ctjdj(Pt()Pt)ηct

and 01ctjdjct is defined as aggregate consumption.

Using (58), HH’s problem can be written as:

(59)maxPt()(Pt()Pt)1ηct,  subject to:  ntj(Pt()Pt)ηctθt1

Let λt be the multiplier for the constraint in (59). The K-K-T conditions are:

(60)Pt()Pt=ηη1λtθt,  λt[1(Pt()Pt)ηctθt],  λt0

By way of contradiction it is straightforward to show that ntj<1 cannot be optimal. If λt = 0 then Pt(ℓ) = 0 but the iso-elastic demand for ℓ implies that demand for product ℓ is infinite at that price. This clearly violates the restriction that ntj1, hence ntj=1. Then with flexibility of prices Pt(ℓ) = Pt, and market clearing in the bond market implies ct = θt. It is also immediate that ct = θt = yt(ℓ) = ct(ℓ).

As for the intertemporal consumption decision, the Euler equation in its aggregate form is:

(61)u(θ0)=β(1+i0)P0P1u(θ1)

A.1 Money market clearing and price level determination

Here we show that by modelling money in a simple, ad-hoc fashion, we are able to anchor the price level. First, we assume that money Mtj by each HH is demanded each period for transaction purposes:

(62)Ptctj=Mtj

We assume a given supply of money Mts. Hence in both periods, money market clearing 01Mtjdj=Mts should satisfy:

(63)01Mtjdj=Ptθt=Mts

The stock of money anchors the price level P1 = 1, by assumption. In period 0 prices are determined by Euler’s equation (61):

(64)P0=u(θ0)β(1+i0)u(θ1)

And given the interest rate i0, money supply in period 0 adjusts to clear the money market, using (63):

(65)M0s=θ0u(θ0)β(1+i0)u(θ1)

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Published Online: 2018-07-11

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