An OLG Model with Stochastic Dynamics an
An OLG Model with Stochastic Dynamics and
Matching in the “Old Keynesian” Tradition
Marco Guerrazzi∗
Department of Economics
University of Pisa
(Preliminary Draft: October, 2008)
Abstract
This paper proposes a dynamic 2-period OLG model inspired to the “Old Keynesian” tradition. Specifically, following the microfoundation of the General Theory
(1936) recently provided by Farmer (2006, 2007), we build a competitive search
model in which nominal output and employment are driven by effective demand
and prices are not sticky. In our theoretical proposal, old households consumption
is financed by young households savings and investments are financed with realized
profits. Moreover, we formalize the “animal spirits” hypothesis by assuming that
the nominal expenditure in investments follows a stochastic process. Finally, calibrating the model in order to match the first-moments of US data, we show that
our framework can provide a rationale for the so-called Shimer’s (2005) puzzle, i.e.,
the relative stability of real wages in spite of the large volatility of labour market
tightness.
JEL Classification: E12, E24, J63, J64
Keywords: OLG Model, Stochastic Dynamics, Old Keynesian Tradition, DemandConstrained Equilibrium, Search Theory and Animal Spirits
Research Fellow, Department of Economics, University of Pisa, via F. Serafini n. 3, 56126 Pisa
(Italy), phone +39 050 2212434, e-mail [email protected].
∗
1
1
Introduction
In addressing some criticisms raised after the publication of the General Theory (1936),
Keynes (1937) stated: “I’m more attached to the comparatively simple fundamental ideas
which underlie my theory than to the particular forms in which I have embodied them, and
I have no desire that the latter should be crystallized at the present stage of the debate.
If the simple basic ideas can become familiar and acceptable, time and experience and the
collaboration of a number of minds will discover the best way of expressing them”.
An influential evaluation of the circulation of the Keynesian legacy in the economic
profession is given by Leijonhufvud (1966) in On Keynesian Economics and the Economics
of Keynes. By “Keynesian Economics” Leijonhufvud (1966) meant the interpretation of
the General Theory (1936) incorporated into the IS-LM apparatus and more recently
into the new-Keynesian paradigm. This kind of modeling has a Neo-classical core and
deviations from the “natural” rate of unemployment are assumed to be the (optimal)
reaction to different kind of rigidities.
In this paper we take a different perspective. Following the microfoundation of the
General Theory (1936) recently provided by Farmer (2006, 2007), we build a 2-period
OLG competitive search model in which nominal output and employment are driven by
effective demand and prices are not sticky. In our theoretical proposal, old households
consumption is financed by young households savings and investments are financed with
realized profits. Moreover, we formalize the “animal spirits” hypothesis by assuming that
the nominal expenditure in investments follows a stochastic AR(1) process.
Finally, calibrating the model in order to match the first-moments of the US data, we
show that our framework can provide a rationale for the so-called Shimer’s (2005) puzzle,
i.e., the relative stability of the real wage in spite of the large volatility of labour market
tightness. In fact, this striking feature of the US business cycle can hardly be explained
by using the standard Pissarides’s (2000) matching model.
The paper is arranged as follows. Section 2 describes the model. Section 3 provides
some numerical simulations. Finally, section 4 concludes.
2
The Model
We consider a 2-period OLG model in which the old households consumption is financed
by young households savings. In other words, we assume the existence of a contributory
pension scheme. Only young households are allowed to work and they supply inelastically
2
their labour services by tacking as given labour demand. Thereafter, young households
decide their contribution to the pension scheme according to their inter-temporal preferences.
On the other side, firms produce a perishable-homogeneous good by mean of the labour
supplied by the young households and a fixed capital factor that accumulates according
to the usual dynamic law. Labour demand is derived from the classical assumption of
profit maximization. By contrast, in each firm, nominal expenditure in investments is
assumed to follow a stochastic AR(1) process that formalizes the Keynesian “animal
spirits” hypothesis. Finally, that nominal expenditure is financed by the firm’s profits.
Therefore, the profit rate implicitly defines the real interest rate.
In our framework, the matching technology combines searching worker and recruiters
and enters the model as an externality because we assume that moral hazard factors
prevents the creation of markets for the search inputs. Therefore, even if agents are
price-takers, the equilibrium allocation is not - in general - Pareto optimal.
Finally, we show how to tune an optimal fiscal policy that implements the social
optimum level of employment.
2.1
The Households’ Sector
For sake of simplicity, we assume that for each generation there is large number of identical
households. Thereafter, the representative household chooses current (ct ) and future (ct+1 )
consumption by solving the following problem:
1−β
max cβt ct+1
0
Matching in the “Old Keynesian” Tradition
Marco Guerrazzi∗
Department of Economics
University of Pisa
(Preliminary Draft: October, 2008)
Abstract
This paper proposes a dynamic 2-period OLG model inspired to the “Old Keynesian” tradition. Specifically, following the microfoundation of the General Theory
(1936) recently provided by Farmer (2006, 2007), we build a competitive search
model in which nominal output and employment are driven by effective demand
and prices are not sticky. In our theoretical proposal, old households consumption
is financed by young households savings and investments are financed with realized
profits. Moreover, we formalize the “animal spirits” hypothesis by assuming that
the nominal expenditure in investments follows a stochastic process. Finally, calibrating the model in order to match the first-moments of US data, we show that
our framework can provide a rationale for the so-called Shimer’s (2005) puzzle, i.e.,
the relative stability of real wages in spite of the large volatility of labour market
tightness.
JEL Classification: E12, E24, J63, J64
Keywords: OLG Model, Stochastic Dynamics, Old Keynesian Tradition, DemandConstrained Equilibrium, Search Theory and Animal Spirits
Research Fellow, Department of Economics, University of Pisa, via F. Serafini n. 3, 56126 Pisa
(Italy), phone +39 050 2212434, e-mail [email protected].
∗
1
1
Introduction
In addressing some criticisms raised after the publication of the General Theory (1936),
Keynes (1937) stated: “I’m more attached to the comparatively simple fundamental ideas
which underlie my theory than to the particular forms in which I have embodied them, and
I have no desire that the latter should be crystallized at the present stage of the debate.
If the simple basic ideas can become familiar and acceptable, time and experience and the
collaboration of a number of minds will discover the best way of expressing them”.
An influential evaluation of the circulation of the Keynesian legacy in the economic
profession is given by Leijonhufvud (1966) in On Keynesian Economics and the Economics
of Keynes. By “Keynesian Economics” Leijonhufvud (1966) meant the interpretation of
the General Theory (1936) incorporated into the IS-LM apparatus and more recently
into the new-Keynesian paradigm. This kind of modeling has a Neo-classical core and
deviations from the “natural” rate of unemployment are assumed to be the (optimal)
reaction to different kind of rigidities.
In this paper we take a different perspective. Following the microfoundation of the
General Theory (1936) recently provided by Farmer (2006, 2007), we build a 2-period
OLG competitive search model in which nominal output and employment are driven by
effective demand and prices are not sticky. In our theoretical proposal, old households
consumption is financed by young households savings and investments are financed with
realized profits. Moreover, we formalize the “animal spirits” hypothesis by assuming that
the nominal expenditure in investments follows a stochastic AR(1) process.
Finally, calibrating the model in order to match the first-moments of the US data, we
show that our framework can provide a rationale for the so-called Shimer’s (2005) puzzle,
i.e., the relative stability of the real wage in spite of the large volatility of labour market
tightness. In fact, this striking feature of the US business cycle can hardly be explained
by using the standard Pissarides’s (2000) matching model.
The paper is arranged as follows. Section 2 describes the model. Section 3 provides
some numerical simulations. Finally, section 4 concludes.
2
The Model
We consider a 2-period OLG model in which the old households consumption is financed
by young households savings. In other words, we assume the existence of a contributory
pension scheme. Only young households are allowed to work and they supply inelastically
2
their labour services by tacking as given labour demand. Thereafter, young households
decide their contribution to the pension scheme according to their inter-temporal preferences.
On the other side, firms produce a perishable-homogeneous good by mean of the labour
supplied by the young households and a fixed capital factor that accumulates according
to the usual dynamic law. Labour demand is derived from the classical assumption of
profit maximization. By contrast, in each firm, nominal expenditure in investments is
assumed to follow a stochastic AR(1) process that formalizes the Keynesian “animal
spirits” hypothesis. Finally, that nominal expenditure is financed by the firm’s profits.
Therefore, the profit rate implicitly defines the real interest rate.
In our framework, the matching technology combines searching worker and recruiters
and enters the model as an externality because we assume that moral hazard factors
prevents the creation of markets for the search inputs. Therefore, even if agents are
price-takers, the equilibrium allocation is not - in general - Pareto optimal.
Finally, we show how to tune an optimal fiscal policy that implements the social
optimum level of employment.
2.1
The Households’ Sector
For sake of simplicity, we assume that for each generation there is large number of identical
households. Thereafter, the representative household chooses current (ct ) and future (ct+1 )
consumption by solving the following problem:
1−β
max cβt ct+1
0