5 Conclusions
This paper has examined the extent to which the standard tax smoothing argument, arising from the disproportional excess burden of taxation, is modified by the existence of uncertainty both about whether the need for extra expenditure will arise, and about the level of expenditure if the need arises. This is important in view of the fact that considerable uncertainty regarding future expenditure requirements exists in practice. A range of simple two-period models has been examined in which a single decision maker decides on the level of tax smoothing, and associated precautionary fund, which maximises an objective function, or ‘social welfare function', expressed in terms of net income and the excess burden of taxation in each period.
Although these are highly simplified models, they do help to highlight some of the important inter-relationships and trade-offs involved. Numerical illustrations showed that the potential future expenditure must be relatively large (as a proportion of income) before the 'option value', the cost of waiting to see what the actual outcome will be, is sacrificed. In cases where some pre-funding is favoured, the optimal policy does not imply complete smoothing of tax rates. Importantly, the degree of risk aversion of the judge was found to have little effect on the optimal degree of smoothing. In the case of the standard iso-elastic welfare function (where the same parameter affects risk aversion and the inter-temporal elasticity of substitution), the effect of varying risk aversion was negligible. In the case of Epstein-Zin preferences, where the link between risk aversion and inter-temporal substitution is broken, slightly more sensitivity was found for high potential future (uncertain) costs and low substitution elasticities. In general, the size of the potential future tax-financed cost and its associated probability were found to be the major determinants of the optimal policy.
The simple models examined here are concerned only with aggregate values, using proportional income taxation, and therefore no consideration has been given to distributional issues. It would be of interest to consider the possible effects of using a progressive income tax structure where, in addition, the decision maker has some concern for inequality. Allowing for income inequality would also allow consideration of 'political economy' approaches to decision making, such as the use of majority choice by members of the population, rather than decision making by a disinterested judge. [18] Further complications could be introduced by allowing explicitly for incentive effects of income taxation.
Notes
- [18] Such an approach would also need to allow for the fact that, at any date, the population consists of overlapping generations of voters.
