followed by a section discussing the calibration of the most crucial structural parameters. Section 3
presents standard simulations on debt and pension reforms in order to show the basic magnitudes
of crucial multipliers in the model. Section 4 compares the alternative scenarios to each other and
the paper ends with some concluding remarks.
1. The Model
An identical good is produced in each region with a constant returns to scale production function.
The technology in each region is identical up to the level of TFP. We allow for capital mobility
across regions but restrict international migration to zero. In order to allow for demographic effects
on savings within a life cycle framework and at the same time keep the model tractable we
distinguish three age groups in each region and adopt the Gertler (1999) specification of consumer
preferences and make similar assumptions concerning population dynamics, insurance
arrangements and preferences.
Individuals go through three distinct stages of life: youth (0 - 14 years), work (15years - retirement
age), and retirement (retirement age+1 - expected end of life). The number of children in period t
is given by N' . Each period bNy children are born and average duration in childhood is 1/λ
where λy is the fraction of young people turning age 15. Child population dynamics is given by
Nt'+1 = bNt' +λt'Nt' . (1)
The working age population in period t is given by Nw . Each period λ'N' children enter the
working age population cohort. The mean duration of staying in this cohort is 1/ λw where λw is
the fraction of the population in working age which goes into retirement in the current period.
Thus the population of working age evolves over time as follows
Ntw+1 =λt'Nt' +(1-λtw)Ntw. (2)
There are Nr pensioners at date t. they are joined by λwNw new retirees, while a fraction (1-λr )
incumbent retirees survive to the next period. This gives the following law of motion for the retiree
population
Ntr+1 =λtwNtw+(1-λtr)Ntr. (3)
Population dynamics imply that individuals face certain probabilities of switching into different
stages of their lives. Each child faces a probability λ' of becoming a worker, each worker has a
probability λw of becoming a retiree and each retiree faces an uncertain time of death. Following
Yaari (1965) and Blanchard (1985) a perfect annuities market is introduced which provides life
insurance for retirees. Each worker faces an idiosyncratic income risk each period of loosing wage
income and receiving pension income for the rest of his life. This type of uncertainty is dealt with
analytically by restricting preferences, i. e. by employing a special class of nonexpected utility
functions proposed by Farmer (1990). The so called risk neutral constant elasticity of substitution
(RINCE) preferences separate a household’s attitude toward income risk from its intertemporal
elasticity of substitution. In particular they restrict individuals to be risk neutral with respect to
income risk but allow for an arbitrary intertemporal elasticity of substitution. Notice, income risk
is introduced artificially because it allows to simplify the analysis and not because there is a real
72