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PARIS-JOURDAN SCIENCES ECONOMIQUES

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WORKING PAPER N° 2006 - 15

Ricardian equivalence and the intertemporal

Keynesian multiplier

Jean-Pascal Bénassy

JEL Codes : E62, E63, E12

Keywords : multiplier, Ricardian equivalence,

non-Ricardian economies, price rigidities, Keynesian

multiplier.

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE – ÉCOLE DES HAUTES ÉTUDES EN SCIENCES SOCIALES

ÉCOLE NATIONALE DES PONTS ET CHAUSSÉES – ÉCOLE NORMALE SUPÉRIEURE

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Ricardian Equivalence

and the Intertemporal

Keynesian Multiplier

Jean-Pascal Bénassy∗†

December 2005

Revised February 2006

Abstract

We show that Keynesian multiplier effects can be obtained in dy-

namic optimizing models if one combines both price rigidities and a

“non Ricardian” framework where, due for example to the birth of

new agents, Ricardian equivalence does not hold.

JEL Codes: E62, E63, E12

Keywords: Multiplier, Ricardian equivalence, Non Ricardian economies,

Price rigidities, Keynesian multiplier.

∗Address: CEPREMAP-ENS, 48 Boulevard Jourdan, Bâtiment E, 75014, Paris, France.

Telephone: 33-1-43136338. Fax: 33-1-43136232. E-mail: benassy@pse.ens.fr

†I wish to thank Fabrice Collard and Harris Dellas, but retain responsibility for all

remaining deficiencies.

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1Introduction

One of the most intriguing features of traditional Keynesian theory (Keynes,

1936, Hicks, 1937) is the so called “multiplier effect” by which an increase

in governement spending can create an increase in consumption, whereas in

Walrasian models it leads to a decrease, via the usual “crowding out” effect.

This multiplier effect is customarily attributed to price or wage rigidities.

Now in the recent evolution of macroeconomic modelling most macroe-

conomic issues are reexamined within the rigorous framework of dynamic

intertemporal maximizing models à la Ramsey (1928). The typical model

depicts consumers as one single dynasty of infinitely lived agents. This model

has notably the property of “Ricardian equivalence” (Barro, 1974), accord-

ing to which, in a nutshell, the distribution of taxes across time is irrelevant

as long as the government balances its budget intertemporally. The model

has been extended to a monetary framework (Sidrauski, 1969, Brock, 1975),

where Ricardian equivalence also holds.

In line with this recent evolution, a natural question to ask is whether

a multiplier effect will arise in these dynamic models. The result has been

actually disappointing: crowding out occurs in the usual DSGE model (see

for example Fatas and Mihov, 2001), and even in models with price rigidities

under standard parameterizations (see for example Collard and Dellas, 2005).

What we want to show in this paper is that, in order to obtain a strong

enough multiplier effect, another ingredient, in addition to price rigidities,

has to be introduced in dynamic models. Namely one should not only have

price rigidities, but also model the economy as “non Ricardian”. By non Ri-

cardian economies we mean, as in Barro (1974), economies like overlapping

generations (OLG) economies à la Samuelson (1958), where Ricardian equiv-

alence does not hold. The non Ricardian economy we shall work with is due

to Weil (1987, 1991). It is a monetary economy where, as in the Ricardian

model, agents have an infinite life but, as in the OLG model, new agents

arrive over time.

We shall call n the rate of growth of the population. In a nutshell the

results are: If n > 0, there is a multiplier1, and government spending leads

to an increase in private consumption. This multiplier is larger, the higher

n is, i.e. the more “non Ricardian” the economy is.

1By this we mean more precisely that the income multiplier is greater than one, so that

there is no crowding out.

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2The model

We shall thus use the model of Weil (1987, 1991), which has the great ad-

vantage of having the Ricardian model as a particular case. Each household

lives forever, but new “generations” are born every period. Denote as Nt

the number of households alive at time t. We will work below with a con-

stant rate of growth of the population n ≥ 0, so that Nt= (1 + n)tN0. The

Ricardian model corresponds to the special limit case n = 0.

2.1 Households

Consider a household born in period j. We denote by cjt, yjtand mjthis

consumption, endowment and money holdings at time t ≥ j. This household

maximizes the following utility function:

Ujt=

∞

X

s=t

βs−tLogcjs

(1)

and is submitted in period t to a “cash in advance” constraint:

Ptcjt≤ mjt

(2)

Household j begins period t with a financial wealth ωjt. First the bond

market opens, and the household lends an amount bjtat the nominal interest

rate it. The rest is kept under the form of money mjt, so that:

ωjt= mjt+ bjt

(3)

Then the goods market opens, and the household sells his endowment yjt,

pays taxes τjtin real terms and consumes cjt, subject to the cash constraint

(2). Consequently, the budget constraint for household j is:

ωjt+1= (1 + it)ωjt− itmjt+ Ptyjt− Ptτjt− Ptcjt

(4)

2.2Aggregation, endowments and taxes

Aggregate quantities are obtained by summing the various individual vari-

ables. There are Nj−Nj−1agents in generation j, so for example aggregate

taxes Ttare given by:

X

Tt=

j≤t

(Nj− Nj−1)τjt

(5)

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The other aggregate quantities, Yt,Ct,Ωt,Mtand Bt, are deduced through

similar formulas from the individual variables, yjt,cjt,ωjt,mjtand bjt.

We now have to describe the distribution of endowments and taxes among

households. We assume that all households have the same income and taxes:

yjt= yt=Yt

Nt

τjt= τt=Tt

Nt

(6)

3The dynamic equations

3.1Taxes and government budget constraint

The dynamics of government liabilities Ωtis:

Ωt+1= (1 + it)Ωt− itMt+ PtGt− PtTt

Government budget balance corresponds to Ωt+1= Ωt, i.e. since Ωt=

Mt+ Bt:

(7)

PtGt= PtTt− itBt

(8)

We would like to have a tax index Ttsuch that budget balance is achieved

under the traditional condition:

Gt= Tt

(9)

This will be the case if we define Ttthrough:

PtTt= PtTt− itBt

(10)

Budget balance now corresponds to (9), and the government budget con-

straint (7) is rewritten as:

Ωt+1= Ωt+ PtGt− PtTt

(11)

3.2Consumption dynamics

The dynamics of consumption is given by (see the appendix):

Pt+1Ct+1= β (1 + n)(1 + it)PtCt− (1 − β)nΩt+1

The dynamic system consists of equations (11) and (12).

(12)

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