There are a number of assets where determining the value for purposes of taxation may be difficult to check or uncertain. For example, I know generally what my house is worth, but for purposes of property taxation, whether that estimate is, say, 20% high or low makes a meaningful difference to my tax bill.

At various times and places, a proposed solution has been that the owner of the asset declares a certain value for purposes of taxation–and if that valuation seems too low, the government reserves the right to buy that asset at the owner’s declared value. Marco A. Haan, Pim Heijnen, Lambert Schoonbeek, and Linda A. Toolsema explored the incentives of this approach about ten years ago in “Sound taxation? On the use of self-declared value” (European Economic Review, 2012, 56: 205-215). They begin with some historical examples:

In the 16th century, the Kingdom of Denmark controlled both sides of the Sound (Øresund), an important waterway situated between present-day Denmark and Sweden. All foreign ships passing through this strait had to make a stop in Helsingør (known in English as Elsinore, the stage for Shakespeare’s Hamlet) and pay taxes to the Danish Crown, which varied between some 1% and 5% of the value of the cargo. These taxes are often referred to as the Sound Dues. Although obviously unfamiliar with the concept of incentive compatibility, the Danish Crown was fully aware that such a tax would give skippers a strong incentive to cheat and declare a value much lower than the true one. It came up with an intriguing solution. The Crown reserved the right to purchase the cargo at the value declared by the skipper. Thus, a Skipper who declared a value that was too low ran the risk of losing his cargo at a price below market value. But a Skipper who declared a value that was too high ran the risk of paying too much in taxes.

This mechanism is clearly ingenious, but it does raise a number of questions. First, what is the optimal confiscation strategy for the tax authority? Obviously, it cannot be part of a Nash equilibrium to never purchase the cargo. Then, the threat of confiscation would simply be empty. Second, does this mechanism induce truth-telling? That is, does it give skippers the incentive to always declare the true value of their cargo? Third, does it allow the tax authority to effectively raise the tax rate that it desires? Put differently, did this mechanism really amount to sound taxation or was there something rotten in the state of Denmark? …

There are numerous instances where a similar tax has either been proposed or implemented. In 1891, New Zealand passed a Land and Income Tax act, based on a ‘‘self-assessment with the shrewd device of making Government’s purchase at the tax value an effective check on the owner’s assessment’’… Dr. Sun Yat-sen, the first provisional president when the Republic of China was founded in 1912, proposed a land tax using the exact same mechanism: landowners are taxed according to their declared value of the land, and the government can also buy the land at the same price. Anyone buying a house in southern Europe may face property taxes based on self-declared value. Other examples include land tax in India around 1900 as well as in present-day Taiwan, taxes on works of art leaving Mussolini’s Italy, and British taxes on imported American Jerome clocks …

(I had to look up “Jerome clocks.” It refers to clocks made by the American clockmaker Chauncey Jerome (1793-1868), who revolutionized the clock-making business by using metal rather than wood for the inner workings, thus allowing the firm to sell millions of long-lasting and inexpensive clocks around the world.)

The paper by Haan, Heijnen, Schoonbeek, and Toolsema applies mathematical game theory tools to describe various outcomes. In intuitive terms, start by imagining that the King can seize and resell the cargo with zero cost of effort or transaction. However, a King who seizes and resells the cargo does not receive tax payments! The Skipper of this ship, knowing this, will have an incentive to understate the value of the ship slightly, knowing that the King has a preference against the seize-and-resell option.

If the King does face transactions costs of seizing and reselling, the Skipper knows that the King will be even less eager to choose the seize-and-resell option, and has an additional incentive to understate the value of the ship by an additional amount.

However, the King must sometimes choose the seize-and-resell option, just to keep the estimates of the skippers within a reasonable distance of actual values. One can then imagine a King who looks at the estimated values received from Skippers, and think about whether it’s more useful just to seize at random a certain percentage of ship cargoes, or whether certain kinds of ship cargoes might be more prone to cheating–or more likely to cover the costs of the seize-and-resell option.

As the authors point out, this problem is quite similar to the question of government choosing who to audit for income tax purposes: some degree of randomness seems desireable, but also some focus on those where the returns from doing the audit are more likely to be larger.

Another aspect of the situation that occurs to me is that government may act for reasons other than tax revenue. For example, say that the King was an enemy of certain Skippers for political reasons, or perhaps an enemy of some customers who were originally scheduled to receive the cargo. The King might want to give the Skipper a reputation as “that captain who never actually manages to deliver the cargo,” or delay and disrupt the ability of the final customer to get their delivery. (The power to audit tax returns has sometimes been wielded as a political weapon in this way, too.) If you are a Skipper in this situation, you may find yourself overstating the value of the cargo, knowing that you will pay higher taxes, but also viewing that as a cost to be paid for dissuading the King from choosing the seize-and-resell option.