The game theory of land value taxes
Microeconomics and game theory help us evaluate the game of land taxation, speculation, and rent.
The land value tax has been touted by urbanists, environmentalists, and economists of all political leanings for its efficiency and fairness, but it has yet to gain traction in 99.99% of US cities. I’ve wanted to do an in-depth Complex Effects post about land value taxes, and the reasons it may be an underutilized policy tool, and this grad school game theory assignment gave me the perfect opportunity to do so. While this essay is quite academic in nature and longer than my average post, I hope you enjoy it.
The land value tax (LVT) is a land taxation scheme where the government collects taxes levied from the value of land. This is in contrast to the property tax, which has won out in modern US cities, where the government taxes the value of the land and all improvements made upon the land. Unlike the property tax, the LVT does not tax improvements made to a piece of land, therefore incentivizing landowners to make their property productive by building housing and discouraging land speculation.
19th-century American political economist Henry George was a staunch supporter of the LVT, advocating that the LVT should be the primary means in which government revenue is derived. The LVT is a popular tax among economists as it creates positive externalities: more housing, improved infrastructure, higher property values in surrounding areas, and a strong tax base for the government. Even libertarian economists like it as Milton Friedman famously called it “the least bad tax.” Despite its popularity among economists, just over a dozen cities in the United States operate with some form of LVT - all of which are in Pennsylvania - and most of them still operate with a proportion of land taxes being derived from property taxes.
The game I’m arguing exists here involves three players: the policymaker, the landowner, and the renter. This is a sequential game that shows two things: 1) Why land value taxes would be an efficient and progressive form of land taxation, and 2) the equilibriums currently perceived and the reasons why property taxes are much more popular. Before I get to the game, I will first explain the economics of the LVT, which is necessary to understand the payoffs and strategies within the game.
The Economics of the Land Value Tax
Land taxes in the United States are used to fund schools, public infrastructure projects like roads and trains, sports stadiums, and much more. 99% of these funds are derived via property taxes, which includes the value of the land and all improvements made to the land. Land value taxes, on the other hand, are levied only on the value of the land.
Land taxation has some unique economic implications given that the supply of land on Earth cannot be changed. Of course, artificial land can be made on the coastal boundaries of places like New York City, but for the most part, land is a fixed asset that cannot practically be created or destroyed - making its supply curve a vertical line (Figure 1). Demand for land follows a typical curve - as the price of land increases (y-axis), the quantity demanded decreases (x-axis).
Figure 1
Let’s focus on the two graphs above. Figure 1 panel A depicts the supply and demand curves of most “normal” taxed goods - like Coca-Cola. As prices increase, Coca-Cola Inc. is more willing to supply higher quantities of the drink. Furthermore, as the price of Coke increases, demand for it decreases. Now suppose the government imposes a tax on Coca-Cola, and the cost of the product increases. The cost of the tax is shared by Coca-Cola and the consumer, with the consumer’s tax burden represented as the portion of the green “Tax revenue” box above the dotted line labeled P*, and Coca-Cola pays the portion below P*. The red triangle represents the “Deadweight Loss,” or the value lost by the consumer and supplier as a result of the market distortion caused by the tax. Policymakers are meant to try to avoid such market inefficiencies whenever possible.
Like Coca-Cola, land improvements (like housing, shops, and any other building or improvement) have a similar upward-sloping supply curve, meaning the same deadweight loss is present when it is taxed. In the case of housing, renters and landlords share the cost of property taxes.
Figure 1 panel B depicts the vertical supply curve of land. There is a fixed amount of land - creating perfect inelasticity. When land is taxed, notice there is not only zero deadweight loss, but the entire tax burden must be borne by the landowner according to the theory made famous by political economist Henry George, and empirical evidence showcased by Hoj et al. in their paper Land Taxes and Housing Prices.
Furthermore, the price of land and housing would decrease under an LVT. The economic rent produced by the land remains unchanged, but more of the economic rent is captured by the government, decreasing the profits of the landowner - making the land less valuable to potential investors and cheaper for the renter. Of course, long term, the incentives landowners would have to improve their land would increase the value of surrounding land and vice versa.
Before we move onto the game theory, the economic implication important to highlight here is that the introduction of an LVT would drastically shift economic power away from landowners. Landowners practicing land speculation, i.e. investors holding onto unproductive land waiting for it to appreciate, would suddenly either want to sell their land to avoid the LVT, make their land more productive in order to afford the tax, or lobby their City Council to get them to reverse the policy. This would cause a sudden change in how real estate investors, typically very influential people, operate in the area - putting the political feasibility of the LVT into question. More on that later.
Game Theory of Land Taxation
The three players in this game: the policymaker, landowner, and renter, all have decisions to make in this sequential game, so let’s inspect each of their decisions one by one based on the game payoffs depicted in Figure 2.
Figure 2
First, the policymaker needs to impose a tax on the citizens of the land in order to pay municipal bills, build infrastructure, and provide services to its citizens. They’re considering two options: the property tax and the land value tax. For results sake, we will assume that the tax revenue for each of these options will be similar. In reality, this may be true in the short term, but not in the long term. Increased land improvements would ensue under the land value tax, and would increase the value of surrounding land in the future, likely giving the city more property taxes.
While we're assuming the municipal government would receive the same amount of taxes from the land value and property taxes, we’re also going to assume that the policymaker wants its citizens to not move away. Therefore, the payoffs for the policymaker are lower in scenarios where the renter moves out of the city.
Second, the landowner must make decisions based on the decisions made by the policymaker. Under either the property tax or the land value tax, they must decide to sell their land, rent their land, or speculate on it. Depending on the tax scheme, the potential payoffs vary, with the property tax being their preferred situation. With this in mind, they would likely threaten to the policymaker, and renters who vote for the policymaker, that they will simply pass the new LVT on to the renters if the policymaker decides on the LVT. If all of the players in this game knew there was no deadweight loss with pure land value taxes, they would know that that is a threat that cannot be backed up. It’s cheap talk.
Third, the renter must decide whether to rent from the landowner, look in another neighborhood, or move to a different city. The renter does not want to move out of the city because it’s expensive to do so, but they will if it means they can find cheaper rent.
Now, let’s consider the main scenarios.
If the policymaker chooses to impose a property tax on its citizens, the landowner has several good options. They could sell their property for a decent profit, try to rent it for as much as possible, or they could speculate on it and hold it for a while. Perhaps the land is raw, unimproved land near the city center and it’s expected to double in price over the next 15 years. There’s little incentive to build because any improvements made to the property will be taxed, and the construction process is costly and stressful. Sitting on the land for a while is a great option.
Now let’s say the land near the city center already has a building on it but it’s in bad shape. It’s really old, needs a lot of improvements, and currently has no tenants. They could try to fix it up and make it rentable, but again, any improvement made to the land would increase the property value, and increase their taxes, and it could be costly and stressful to renovate. Furthermore, if the landowner is an experienced real estate investor, there are huge tax incentives for holding onto vacant land. Whatever their reason is to speculate instead of sell or rent, the landowner gets a good payoff. There is little incentive to deviate from this position unless they are motivated to receive rental payments.
Let’s now consider the case where the landowner has a property that they want to rent out. They are now in a two-by-two game with the renter. The landowner has two choices: absorb the cost of the property tax, or pass it on to the renter. Under the property tax scheme, the landowner knows they can get away with passing on at least part of the cost of the tax to the renter. Whether the landlord passes on the cost to the renter or not, the renter would rather rent than move. The landlord knows this and decides to pass on the cost of the tax to the renter, thus implementing a dominant strategy in the game under a property tax scheme and deciding the payoff of the renter. Furthermore, the landowner and the renter know that even if this game was repeated many times, the result of the game would always turn out the same.
Furthermore, this branch of the game has an interesting twist in that as it is repeated N times, the quality of the building deteriorates. As mentioned before, there is little incentive for the landowner to make repairs and increase the quality of their building. So, over time, the building becomes worse and worse, eventually degrading into an unrentable vacant building in which the landowner can hold onto and use for tax deductions. In reality, this phenomenon results in high vacancy rates in what used to be productive areas of a city.
In a parallel universe, the policymaker decides to implement a pure land value tax. Again, we’re assuming their payoff is the same as under a property tax and they only care about keeping citizens from moving out of their town.
The landowner is now in a much different position. It is suddenly much less beneficial for them to speculate on their land. Under the LVT scheme, unproductive land is taxed at a relatively higher amount than under the property tax. They still may be able to generate tax deductions from owning vacant land, but their incentives have drastically changed. If their land is raw or has a vacant building on it, they are now better off either making it productive and renting it, or selling it. Notice now that the payoff for selling land is also less because a higher proportion of the economic rent generated by the land is being captured by the government. This isn’t because the government is earning more, necessarily, it’s just that the landowner is earning less.
Under the LVT, the best option for the landowner is to either sell their land to someone who plans on making it productive or make it productive on their own. After all, any improvements made to the land will not be taxed, but will generate more rental income. Let’s finally look at the two-by-two game between the landowner and the renter under the LVT scheme.
The landowner would love to pass the cost of the LVT on to the renter, but unlucky for them, the renter sees that the apartment buildings across town are much cheaper because that landlord is absorbing the cost of the tax themselves. So, if the landowner passes the cost of the tax onto the renter, the renter’s best move is to either move across town or move out of the city. Perhaps the landowner can get away with this initially, but over the long term they will continue to lose out to the competition.
If the landowner chooses to absorb the cost of the tax as LVT theory suggests, the renter’s best response is to rent from the landowner. Notice this is the most evenly distributed payoff between all of the scenarios.
The Subgame Perfect Nash Equilibria
Now that we understand the incentives behind the game, we can observe the Nash Equilibria of the game. As this is a sequential game, we have five important Subgame Perfect Nash Equilibria (SPNE) - two under the property tax and three under the land value tax. In other words, using backward induction, we can deduce the most likely outcomes within each subgame, or branch, of the game.
Looking at the property tax side of the game, there are two SPNEs: (PT, Rent, Pass, Rent), and (PT, Speculate, Pass, Rent). In the first one, the landowner and renter agree to rent with the property taxes passed onto the renter. The landlord holds the dominant strategy, and therefore the power, in this game. The second equilibrium is where the landowner chooses to speculate on their land. This is the best payoff for the landowner in many cases and there is nothing the renter can do to change this. The policymaker, on the other hand, can do something about it.
This brings us to the three important SPNE on the LVT branch of the game: (LVT, Sell, Absorb, Rent), (LVT, Rent, Absorb, Rent), and (LVT, Rent, Pass, Move). The policymaker can incentivize the landowner to choose an option outside of speculation by adopting the LVT. The landowner has no incentive to speculate and would much rather sell or make their land productive.
The next SPNE is where the landowner tries to pass the cost of the tax onto the renter so the renter chooses to move somewhere else. This is only an equilibrium because the landlord is indifferent between their two options when the renter is deciding to move. The last SPNE is where the renter rents and the landowner offers fair rent - bearing the cost of the LVT.
Now that we have the entire game analyzed and the equilibriums identified, we can speculate on why only about a dozen US cities have adopted the LVT. Obviously, real-life US policymakers are not indifferent between the property tax and the LVT - they strongly prefer the property tax. This could mean two things - either we have not properly identified the correct payoffs within the game for the policymaker, or the policymaker is unaware of all of the payoffs within the game. The latter could be a fair description of the discrepancy as land value taxes are a rather unknown policy tool. Though the former, that we have misidentified the payoffs, seems to be a likely cause as well.
We could argue that the payoffs should reflect the policymaker’s preference for the land value tax as maybe they understand the importance of reducing deadweight loss and housing prices. But, adding a point to all of the policymaker payoffs on the LVT side of the game feels wrong given the fact that the real world shows the most-likely equilibrium obviously lies on the property tax side of the game.
This means either the policymaker perceives or receives more utility by opting for the property tax. Perhaps they themselves are landowners and know that profits are easily extracted through a property tax. Perhaps a majority of political donors request the property tax in exchange for their ongoing campaign contributions. While this is all speculation, the motivations that keep property taxes the status quo in 99.99% of US cities likely have something to do with the shift in landowner incentives that would result from adopting a land value tax.