solve the dynamic non-linear forward looking model by Newton-Raphson. The simulation horizon
must, however, be chosen long enough such that the solution is close to the steady state at the final
date. We set the simulation horizon to 500 years. Roeger and In’t Veld (1999) provide a more
detailed technical discussion of this solution method as well as some sensitivity analysis in the
context of permanent shocks.
2. Model Calibration
We select parameters such that the model fits some basic economic ratios both within and across
regions. The objective of this exercise is to limit the international variation of structural parameters
as much as possible and to explain divergences of economic development by the exogenous
shocks and institutional differences. To select parameter values we largely follow standard
procedures, i.e. we base these values on evidence from growth observations and some
microeconometric evidence.
Demographics: We calibrate the model such that it can closely replicate the most recent
EUROSTAT projections until 20509. Because we make some simplifying assumptions on the
evolution of the birth rate and life expectancy and because we do not consider migration our
demographic projections in the model are not identical to the EUROSTAT projection. However, as
can be seen from Table 1, using the old age dependency ratio as a summary measure of the
demographic trend, the model projections follow the fundamental trends of the EUROSTAT
projection. The survival probabilities in the three age groups are chosen such that the mean
duration in each group is consistent with the age classification (0-14), (15-64) and (65-life
expectancy). The demographic trend is fundamentally determined by two features, namely a
decline in the fertility rate from 2.4 in 1970 to 1.6 in 1990. Since 1990 the decline has slowed
down and has reached a value of 1.3 in 2004. The projections assume that it will slightly increase
to 1.6 in 2050. More important for the dependency ratio is the development of life expectancy,
which is supposed to increase from currently 81.7 to 86.7 for women and from 76.0 to 86.7 for
men.
Table 1: Old Age Dependency Ratio
|
2004 |
2010 |
2020 |
2030 |
2040 |
2050 | |
|
EUROSTAT |
24.5 |
26.2 |
31.9 |
39.7 |
47.4 |
51.4 |
|
Model_______ |
25.5 |
27.3 |
31.4 |
38.1 |
45.7 |
52.0________ |
Preferences: Consumption and savings behaviour is characterised by three parameters, the
intertemporal elasticity of substitution, the rate of time preference and the elasticity of substitution
between domestic and foreign assets. Most studies using household survey data (see e.g. Attanasio
and Weber (1993), Attanasio and Browning (1995)) tend to find estimates for sigma which are
below one. We choose a value of .5 which is compromise between a value of one which is often
used in the business cycle literature and smaller values often used in micro simulation studies. For
the rate of time preference we choose a value of 1% per year. This is at the lower end compared to
existing studies. This value is necessary for the model to generate a realistic level of the real
interest rate. As discussed above, the effective rate of time preference is higher since it is a
function of financial wealth. In selecting values for the rate of time preference we also take into
9 We use United Nations (2000) and US Census (2001) data for the other regions.
79