Can random taxes be desirable?

Can random taxes be desirable?

One of Adam Smith’s principles of taxation is that ‘‘the tax which each individual is bound to pay ought to be certain.”[1] And his maxim still resonates, not least with a focus of the G-20 in recent years on strengthening ‘tax certainty.’[2] Reasonable though all this sounds, however, the desirability of complete tax certainty is not as obvious as it may seem.


Suppose, for instance, that you are choosing how much of some item of machinery to import. Would you rather face a 10 percent tariff for sure, or the toss of a fair coin to determine whether the tariff will be 5 or 15 percent (and so expected also to be that same 10 percent)? So long as you learn what the tariff rate is before deciding how much to import,[3] it is the coin toss that gives you higher expected profits: if the tariff rate turns out to be the high 15 percent, you can cut back on the number of machines imported and maybe use them more intensively; and if the tariff turns out to be the low 5 percent you can import more machines and use less labour.
That insight is well-known. (Formally, it is a consequence of convexity of the profit function). But it is only part of the story, and two further lessons emerge from our paper.

First, in the tariff story just told the randomization of the tariff rate through the coin toss, while good for the taxpayer, is bad for the government: the higher expected profit comes at the cost of lower expected tax revenue. A better basis for deciding whether randomization is in the public interest is to ask whether it can increase the firm’s expected profit while holding expected tax revenue constant. (That might require, for instance, a coin toss between tariff rates of not 5 and 15 percent but of 5 and 17 percent).

The answer, we show, is that randomization can indeed achieve this—if (a slightly cumbersome condition) a higher tariff rate makes the demand for those machines less elastic. (Under somewhat weaker but even more cumbersome conditions, such randomization can also increase output and the total demand for machines). And then it is also possible, by setting slightly higher tax rates, for randomization to increase both expected tax revenue and expected profits.

The conclusion that government and firm can both benefit from randomization is very striking. The explanation is that the cumbersome condition means that the firm’s ability to respond to the tariff is less at higher tariff rates, which reduces the expected deadweight loss from the tariff. As a result, imposing high tariff rates then makes the tax system more efficient.

The second lesson is that heterogeneity among firms makes it substantially more likely that randomization can increase expected profits without reducing the government’s expected tax revenue. Even if all firms have unchanging elasticities of demand for those machines, for example (so that the cumbersome condition above is not satisfied), then, so long as those elasticities of demand differ, such a randomization is sure to increase expected profits. The reason for this is closely related to the ‘Ramsey rule’: that efficiency requires heavier taxation of commodities in less elastic demand. For with heterogeneous firms, a higher tariff reduces the demand for machines least by firms that have the less elastic demand, and a lower tariff increases the demand from such firms least. And so, in aggregate, randomization shifts the tax burden towards less elastic activities. In effect, randomization acts as a device to implicitly tax as Ramsey taught us that we should.

All this may sound very abstract. But situations of the kind just described are commonplace in practice. Imagine, for example, a government that has a fixed budget which it wants to spend so as to stimulate employment as much as possible—perhaps to support activity during a pandemic. Is it better to spread that spending equally over all firms, or to randomize in the sense of giving more to some than to others? The analysis suggests that, if firms differ in their (more or less) elasticities of demand for labour, randomization is the more efficient approach. Sometimes, moreover, governments deliberately create situations of the kind we analyze. Advance tax rulings, for instance, allow firms to know what the tax treatment of alternative actions would be before they decide which action to take—just like the importer above. So the analysis helps understand when it may be good policy to offer such rulings.

All this is not to say that random taxation is always a good thing. The conditions for randomization to be efficient may not be satisfied. And even when they are, randomization might be unacceptably inequitable. Rather the point is that the instinctive appeal of ‘tax certainty’ as a principle should not in itself be decisive for policy making, as there are some beneficial features of randomization. In evaluating tax alternatives, it is important to look beyond slogans to understand more deeply what good policy actually requires.


[1] Adam Smith (1802), An Inquiry into the Nature and Causes of the Wealth of Nations, vol. III, 10th ed. (Cadell and Davies, London); p.256.
[2] See for instance IMF and OECD (2017), Tax certainty: IMF/OECD report for the G-20 finance ministers.
[3] This is important to the analysis: things are different if decisions must be made before their tax implications are known.