Tax policy with uncertain future costs: Some simple models

Abstract

This paper considers the extent to which the standard argument, that the disproportionate excess burden of taxation suggests the use of tax smoothing in the face of future cost increases, is modified by uncertainty regarding the future. The role of uncertainty and risk aversion is examined using several highly simplified models involving a possible future contingency requiring an increase in tax-financed expenditure.

Keywords:

• tax smoothing
• uncertainty
• risk aversion
• excess burden

JEL Classification:

• D81
• D90
• H20

Acknowledgements

We have benefited from discussions with Ross Guest, Omar Aziz and Andrew Coleman. We are grateful to Bob Buckle, Norman Gemmell, Hemant Passi, Michael Reddell and Paul Rodway for comments on an earlier version.

Notes

1. An early modern discussion of tax smoothing is Barro (1979). Armstrong, Draper, Nibbelink, and Westerhout (2007) also highlight the concave nature of the government’s revenue function, arising from adverse incentive effects. However, these are not modelled here. Davis and Fabling (2002) stress the ability of the government to obtain a rate of return in excess of the cost of borrowing. Again, this feature is not examined here.

2. See, for example, Dixit and Pindyck (1994) and Pindyck (2008). Auerbach and Hassett (2002) illustrate the potential benefits from waiting.

3. In the context of health and long-term care under demographic uncertainty, Lassila and Valkonen (2004, p. 637) find that the longer the time horizon, ‘the virtues of using continuously updated demographic information to evaluate future expenditures become evident’.

4. The danger that a precautionary fund will be raided by a future government, stressed long ago by Ricardo in the context of the British Sinking Fund, is not considered here. Davis and Fabling (2002) model ‘expenditure creep’ and report that it can completely erode the efficiency gains from tax smoothing. They conclude that, ‘strong fiscal institutions are a prerequisite for achieving the welfare gains from tax smoothing’ (2002, p. 16).

5. Furthermore, in practice different cohorts of taxpayers may be affected.

6. A different aspect of decision-making under uncertainty is considered by Auerbach and Hassett (1998), who discuss the effects of policy variability itself in increasing uncertainty in the economy.

7. The term ‘two-period model’ need not be taken literally, since the periods can consist of multiple sub-periods, in which case care is needed in specifying interest and growth rates.

8. The fact that labour supply is not modelled means that a rather ‘mechanical’ approach is taken regarding the excess burden of taxation. In a more complex model, it would be desirable to allow the tax rate to affect the growth rate of income, thereby contributing an additional component of sunk cost. Other individual behaviour is ignored, such as saving, which may be affected by uncertainty and views about how the government responds to it.

9. Tax smoothing under certainty within this simple framework is examined in Ball and Creedy (2013).

10. Constraints on flexibility of government policy, such as the ability to change tax rates and expenditure, are ignored here. Such constraints are examined by Auerbach and Hassett (1998), who suggested that, faced with uncertainty, the inability to have frequent changes suggests early action but on the other hand inaction may be chosen because of the inability to reverse any adverse effects on particular groups. They concluded (p. 23) that, ‘the optimal policy response over time might best be characterized by great caution in general, but punctuated by occasional periods of apparent irresponsibility’.

11. As the values of are fixed, it is not necessary here to allow for any benefits arising from this form of tax-financed expenditure. This is discussed further in Section 4.

12. However, this standard approximation strictly applies to small tax rates or small increases in rates: see Creedy (2004). The term, , involves income and the (compensated) labour supply elasticity, but these need not be considered explicitly here as, to keep the model as simple as possible, income is assumed to be exogenous.

13. The certainty case does not imply complete tax smoothing, as the optimal rates in the two periods are 0.435 and 0.46, respectively.

14. The certainty equivalent is the value that, if know for certain, would give the same welfare as the uncertain prospect. An early proposal to have one concave function to generate the certainty equivalent and another concave function to describe intertemporal substitution between current consumption and the certainty equivalent was made by Selden (1978). For a review of a range of ‘exotic’ preference functions, see Backus, Routledge, and Zin (2004).

15. The analysis has not restricted the two probabilities to sum to 1. A modification is to suppose that an event will certainly happen in period two, giving rise to an uncertain cost. Results (again not shown here) are, perhaps not surprisingly, similar to the case of a single cost above, except that is optimal for all combinations. Risk aversion has little effect and dominates.

16. Such an approach would also need to allow for the fact that, at any date, the population consists of overlapping generations of voters.