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WORKING PAPER N° 2006 - 15
Ricardian equivalence and the intertemporal
JEL Codes : E62, E63, E12
Keywords : multiplier, Ricardian equivalence,
non-Ricardian economies, price rigidities, Keynesian
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE – ÉCOLE DES HAUTES ÉTUDES EN SCIENCES SOCIALES
ÉCOLE NATIONALE DES PONTS ET CHAUSSÉES – ÉCOLE NORMALE SUPÉRIEURE
and the Intertemporal
Revised February 2006
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: email@example.com
†I wish to thank Fabrice Collard and Harris Dellas, but retain responsibility for all
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.
2 The 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.
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:
and is submitted in period t to a “cash in advance” constraint:
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
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
2.2 Aggregation, 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:
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:
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=
PtGt= PtTt− itBt
We would like to have a tax index Ttsuch that budget balance is achieved
under the traditional condition:
This will be the case if we define Ttthrough:
PtTt= PtTt− itBt
Budget balance now corresponds to (9), and the government budget con-
straint (7) is rewritten as:
Ωt+1= Ωt+ PtGt− PtTt
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).