Executive Summary
Governments are often faced with the possibility that higher public expenditure may be needed in the future, although much uncertainty is involved. For example there may be a risk of an earthquake, though the timing and cost implications are subject to considerable uncertainty. A different context is that of population ageing, which is being experienced by most developed economies. While the time profile of the population age distribution in a country can be predicted with a reasonable amount of confidence, it is difficult to know how markets will respond. The question therefore arises of how much, if any, tax smoothing to use, by raising current taxes to build up a fund.
Faced with uncertainty, it is not clear whether governments should take immediate action or wait to collect useful information. Decision makers are more likely to take immediate and larger action, the higher the perceived probability of the contingency arising, the larger the potential cost, and the higher their degree of risk aversion. The aim of this paper is to clarify the precise nature of the relationships, and the orders of magnitude involved, in the context of simple models.
The tax policy choices facing a decision-maker in a multi-period framework, in which a future contingency may or may not arise, are examined. The possible higher future expenditure may be financed using some form of tax smoothing, by increasing the present tax rate.
The incentive for tax smoothing arises from the nature of the excess burden arising from taxation, which depends on the square of the tax rate. It is also thought to depend on the decision-maker's attitude towards risk, as reflected in the degree of risk aversion. If the extra revenue turns out not to be needed, the future tax rate can be reduced accordingly. However, the higher future net income and lower excess burden may not compensate for the initial tax increase.
The models examined in this paper are highly simplified, involving the choice by a single policy-maker or judge faced with information about the probability of a future event and its associated cost. The judge is considered to maximise a welfare or evaluation function that depends on present and future net incomes, associated probabilities and risk aversion. However, the models help to highlight some of the important inter-relationships and trade-offs involved in making policy choices. The value of not acting immediately and waiting until further information becomes available is referred to as the option value.
Numerical illustrations show that the potential future expenditure must be relatively large (as a proportion of income) before it becomes worthwhile to act immediately, that is to sacrifice the option value of waiting to see what the actual outcome will be. In cases where some pre-funding is favoured, the optimal policy does not imply complete smoothing of tax rates.
The degree of risk aversion of the hypothetical judge is found to have little effect on the optimal degree of tax smoothing. In the case of constant relative risk aversion, the effect of varying the degree of risk aversion is found to be negligible; in this case a single parameter affects both risk aversion and the inter-temporal elasticity of substitution of the judge. The alternative case of Epstein-Zin preferences, where the link between risk aversion and inter-temporal substitution is broken, is also considered. With this form of preferences, 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.
