Depreciating Licenses

An overview of a useful property ownership mechanism

Published in
8 min readAug 3, 2021


This post by Daniel Firebanks-Quevedo and Charles Cui is a summary of Anthony Lee Zhang’s talk on Depreciating Licences, given at the MD4SG Environment and Climate working group. Anthony Lee Zhang is an Assistant Professor of Finance at the University of Chicago Booth School of Business, studying questions in market design. His work covers topics including financial derivatives, housing markets, and the allocation of natural resources such as land and the electromagnetic spectrum. Zhang has received a number of honors and awards, including the 2019 AQR Top Finance Graduate Award and the 2018 Facebook Fellowship. This series of blog posts represent our members’ reflections on the various MD4SG activities related to mechanism design and access to opportunity. Our previous talks can be found on our Youtube channel.

Disclaimer: This article does not represent the viewpoints of Prof. Zhang; all errors belong to the authors.

Many natural resources like water and timber are scarce, because they are highly demanded for human consumption and limited in supply. The property rights of such scarce resources, such as fishing rights and land use, have to be allocated for a variety of uses. Given the scarcity and importance of such resources, it is essential that they are allocated properly, to avoid waste and make the best use of them. Currently, the most widely adopted approach to sell property rights uses licenses via market mechanisms like auctions. A central question for policy-makers and market designers is the design of such licences and mechanisms. Different mechanisms provide different incentives for potential users, which in turn stipulate their strategies for competing to use these resources, and consequently affect the sustainability and welfare of the resources.

Figure 1. Resources that a license gives the right to. Top left: Land, Top Right: Spectrum, Bottom left: Oil drilling, Bottom right: Domain names

Tradeoffs when assigning property rights

The strength of property rights is at the heart of this mechanism design problem. Strong property rights often come in the form of perpetual ownership, while term-limited leases reflect weak property rights.

On the one hand, offering weak property rights induces strong allocative efficiency, as the people who value the property the most will be able to own it during every time period t. However, weak property rights discourage investment because investors won’t have enough time to enjoy the fruits of their assets. Even if they do invest, they may act myopically and exploit the resource in the short term of their rental license. For example, if one wishes to use the land for agricultural purposes, one will need to spend money in maintenance for soil fertility; however, if they cannot own the land in the long term, they will not be incentivized to take proper care of the land, and instead cash in on what they can.

On the other hand, strong property rights inhibit the efficient allocation of the resource because potential owners of the land with more resources to invest in it will not have access to it. Nevertheless, they provide strong investment incentives, as the owners will be the sole beneficiaries of their investment.

This fundamental tradeoff between allocative welfare and investment welfare is often referred to as the “hold-out problem” in economics and finance literature. Standard property rights systems do not offer great schemes to maneuver the trade-offs between investment and allocative efficiency. How can we do better? Professor Anthony Zhang’s paper offers a promising solution.

Figure 2. Property rights over time: perpetual ownership (left), term-limited rental (center), and depreciating licenses (right)

Depreciating licenses for property rights

The solution Anthony Zhang and his coauthor E. Glen Weyl designed is called depreciating licenses. Instead of granting perpetual ownership or providing only a term-limited lease, depreciating licenses allow investors to have the resource for an extended period of time with diminishing property rights.

For instance, at the start of the licensing period, the investor may have 100% of ownership over the property, but the ownership/property rights gradually decrease over the years, and the investor will only have 5% of property rights near the end of the license. You might ask: what does owning 20% of a piece of land mean? Does it mean owning 20% of it in terms of area or time? This is indeed a tricky question, and the answer seems to vary for different types of natural resources. Taking into account that an owner needs to have 100% of an asset to keep using it, Zhang and Weyl propose a universal solution that leverages a government-enforced payment scheme to resolve this issue.

In their paper, Zhang and Weyl propose the following: initially, the administrator of a divisible asset — usually governments — would hold all the asset, which gets sold in an auction. After the asset is sold to the winner of the auction, they will hold 100% of the asset. Then, every time period t, a share τ of this asset gets sold in another auction by the government; this gives the current license owner the opportunity to keep this portion of its asset by winning the new auction, and it also allows other bidders to obtain a percentage of ownership of the asset if they win.

The government will always start these auctions with a share τ of the asset, whereas the current license owner will be holding (1-τ) of it. The current owner would be able to keep the license at a cost proportional to τ if they win to reclaim the share, or get a payment proportional to (1-τ) if they lose, as this is the share which was not already forfeited to the government.

It is worth noting that this mechanism interpolates between perpetual ownership and rental auctions. When τ=0, that means that the government never forces the company to auction any portion of their asset at all; therefore, the current license owner maintains full ownership perpetually. However, at the other extreme, when depreciation rate τ is 1 and the incumbent loses the auction, they’d lose all of the asset without any compensation; if they win, they would regain the entire asset at full price.

Finally, a key property of the proposed mechanism is that the depreciation rate τ doesn’t have to be constant over time. For instance, τ could be very close to 0 (i.e. an almost-full property rights license that depreciates slowly) for the first few years, and then the ownership starts diminishing faster via a larger τ (i.e. higher depreciation rate). This is beneficial when using an asset that requires large investment during the initial period of ownership, after which the asset requires little maintenance and investment, as it is with the case of the electromagnetic spectrum (e.g. commercial AM/FM radio, television, and cellular networks).

Before we introduce the main result of the paper, we need to define two important concepts that measure how good the license is: allocative welfare and investment welfare. Allocative welfare is high when a resource is assigned to a user that has a high value for it, and low otherwise. Investment welfare is high if the user of the resource chooses to invest in preserving or improving the resource, so that it becomes more valuable for everyone. For example, oil leaseholders can drill exploratory wells to gauge the value of a given oilfield, gaining more information that could benefit future leaseholders. The main result from this paper is that the administrator of the asset can always increase the total welfare (allocative welfare + investment welfare) by increasing the value of τ slightly from 0, and decreasing it from 1, as seen in the figure below. This represents an optimal tradeoff between both investment and allocative welfare. Therefore, an optimal depreciation rate τ is always between 0 and 1 (i.e. not at 0 or 1), and adding a small amount of depreciation (τ > 0) will improve allocative welfare, whereas reducing it from 1 (increasing property rights) will improve investment welfare.

Figure 3. Tradeoff between allocative and investment welfare: welfare against depreciation rate

Other benefits of depreciating licenses

In addition to the benefits explained above, depreciating licenses come with two extra advantages over the traditional licensing schemes. Firstly, they discourage speculation. Normally, asset prices can reach a bubble as perpetual holders speculate over its true price, the goal being that at some point the owners will be able to sell it for a much higher price than its true value. Alternatively, owners may search for assets at a discounted price and then sell them at a higher price — something known as “flipping”. With depreciating licenses, since there is a cost to maintaining ownership over the land, the owners are less incentivized to hold it unnecessarily for extended periods of time. In addition, the license price is much lower than what it would be in other schemes, and therefore not much profit can be made out of flipping assets.

The second benefit of depreciating licenses is that they encourage risk-sharing. In rental licenses, the government bears the short-term risk, while for perpetual licenses, the buyer bears all the risk. Going back to our land-use case, if the land gets exploited for short term profit without any maintenance, then the government ends up being the one that is the most negatively affected because they still own the land after the current lease ends; whereas if the land is owned perpetually by an entity, then they are the sole benefactors of their profit and the only ones affected by negative consequences. In depreciating licenses, since the government would now be a partial owner of the properties by selling a percentage of the licenses, they would share the risk with the owners of the property and the rest of the market players. Generally, governments have higher risk capacities than private firms/owners, which is why it is good that they share some of the risk in terms of the asset value.

Depreciating licenses have large implications and applications in the areas of emissions permits, fishing rights, congestion control, electromagnetic spectrum, and land use. There still remain challenges to be addressed; for instance, the presence of information asymmetry on the value of the asset and the strategic behavior between market agents.

The design of licenses that balance allocative and investment welfare still has unexplored potential, which is why the development of depreciating licenses represents a promising outset for future work, encouraging better mechanism design for licensing rights.



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