This thesis builds a rich life-cycle model that considers optimal individual decisions on
consumption, leisure and portfolio choices under the Australian social security frame work. More specifically, we consider the Australia-specific policy details relating to in dividual income tax, the superannuation system, and the means-tested Age Pension in
the model. Then the model is solved with the Endogenous Grid-point Method (EGM).
We handle the model parsimoniously and solve the optimal individual decisions for all
possible scenarios. The corner solutions raised by the non-concave regions of the value
function, non-differentiable income tax function, and borrowing constraint of the decision
variables are also discussed in detail. For example, the Upper Envelope Algorithm is ap plied when there are multiple local optimal solutions. As for the non-differentiability
of the function, we simplify the problem to be a discrete-continuous problem and solve
for the optimal decisions with the Discrete-Continuous generalization of the Endogenous
Grid-point Method (DC-EGM). We gain enormously from the EGM solutions in terms of
robustness and computing speed, compared to the traditional Value Function Iteration
(VFI) method.
Moreover, we compare this model with empirical data from the Household, Income
and Labour Dynamics in Australia (HILDA) Survey. We first calculate the data variables
from the HILDA Survey and discuss their differences with the model variables. This
is also in preparation for the later model estimation. Secondly, we verify the model
mechanism by comparing the model outputs and empirical data observations for several
policy experiments. From the data visualisation and regression results, we find that the
interactions between the policy changes and the individual decisions are consistent with
the model implication. Therefore, we conclude that the model is appropriate in terms
of predicting the directional change of individuals’ decisions with respect to different
governmental policy changes.
Finally, we estimate the model with the data variables calculated from HILDA Survey
and obtain an Australia-specific set of parameters. We contribute to the literature by
estimating the age-varying endogenous parameters in the model in the Australian context.
We also explicitly show that compared to constant parameters, the age-varying setting
improves the goodness of fit significantly. In addition, the optimal model outputs fit
well with the empirical data. However, the model outputs and the HILDA data do not
match perfectly, which suggests that the estimation results can be further improved by
considering a more complex age-varying function form of the model parameters. Another
challenge is that the parameters are defined specifically in our model with the Cobb Douglas utility function. The individual preference parameters, such as the coefficient of
relative risk aversion, are interpreted differently than in other studies. In future research,
it could be valuable to investigate the same individual parameters under different utility
assumptions and evaluate the differences between the parameter estimation results.