Page 336 - Contributed Paper Session (CPS) - Volume 7

CPS2120 Grażyna Trzpiot et al.
2. Methodology
Our research proceeds with the three main steps. For each task proper method
is applied.
1. First step: selection of the European countries to the analysis. The cluster
analysis is applied to choose representative countries from each cluster of
countries due to the macroeconomic variables. Hierarchical method allows
determining the best number of clusters as well as to see the hierarchical
relations between obtained groups of countries. Steps 2 and 3 are
conducted for each of the selected countries.
2. Second step: identification factors that could have influence on the long-
term investment return. Dimension reduction by PCA is used for
transformation of highly correlating variables into set of uncorrelated
latent variables, and combination of several variables that characterize
demographic changes and economic development into uncorrelated
factors. Factors are associated with risks related with investments.
3. Third step: Simulation of three investment portfolios with different risk
level (low, medium and high) as a particularly possibly investments. The
level of the risk for long-term investment is determined by fixed
percentage share of stocks and bonds. The investment rates of return were
modeled through the PCR: risk factors – obtained in the step 2 – were used
as predictors in a regression model fitted using the least squares
procedure. There are two main reasons for regressing the investment
return on the risk factors rather than directly on the explanatory variables.
Firstly, the explanatory variables are often highly correlated
(multicollinearity) which may cause inaccurate estimations of the least
squares regression coefficients. Secondly, the dimensionality of the
regressors is reduced by taking only a subset of PCs for prediction. A
method does not require uncorrelated variables or normal distribution of
the residuals.
PCR and PCA are both well now techniques for dimensionality reduction when
modelling, and are especially useful when the independent variables are highly
multicollinear (Jolliffe, 1982).
The selection of variables was preceded by an analysis of literature in the
field of research on determinants of macroeconomic and financial implications
of ageing. In the process of identification of risk factors the following variables
are taken into consideration:
1. Demographic old-age dependency ratio – traditionally seen as an
indication of the level of support available to older persons (those aged 65
or over, i.e. age when they are generally economically inactive) by the
working age population (those aged between 15 and 64) [expressed per
100 persons of working age (15-64)].

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