Comparison of optimal and empirical consumption, portfolio selection and labour–leisure choice in Australia

Abstract

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.