I suggest that the underlying value of the land is zero, or so close to it as to be statistically insignificant. The market value of land is overwhelmingly dominated by proximity to improvements. If you subtract the value of improvements on the land itself from the market value, you are still left with the value of being near the improvements on all surrounding properties.
The true underlying value is the value it would have if you picked up the land with a god's hand and plopped it down in the middle of nowhere, in a land devoid of people and far from roads or rivers. Does it have valuable natural or mineral resources on or under it? Does it have energy production potential? Fresh water? Historical significance?
No? It's worth zero. People drive the economy. Land only has value to the extent that it does not present barriers between you and your trade partners. No one wants to live atop the mountain if the funicular is not built. No one wants to live across the lake if there are no boats, docks, and piers. No one wants to live deep in the forest if the road into it has not yet been cleared.
How then do you calculate a land tax fairly? Surface area alone? Population density data from the census?
Actually it isn't that hard. The land value is simply the property value minus the value of the depreciated physical capital (buildings etc.) on it (LV = PV - K). This calculation is already done in the market in order to determine the size of a home owners insurance policy. Property tax values aren't ideally precise, but are already common enough that replacing them with and land value tax wouldn't greatly impact tax code precision.
To address your more general critique, it might be better said that you are paying a location tax as opposed to a land tax. Specific locations have particular value and until we develop hand of god technology, putting multiple units of land in a given location will be impossible. So land vs. location is really just a semantic difference.
You either didn't read my entire comment or chose to talk past it. I said that the result of your calculation (LV = PV - K) actually still includes the value of improvements adjacent to or near the property. The value of some improvements bleed across property lines.
As such, that result still represents the improved value of land.
Roads increase the value of lands adjacent to the road, even if they are not on the land itself. Parks and greenways increase the value of land within a certain distance. Schools increase value. Shopping centers increase value. Police stations, fire protection stations, restaurants, theaters, museums, public transportation, and other improvements all affect the value of living near those improvements. There is even some value in living next door to an expensive-looking house rather than a shabby one, or an abandoned, empty lot.
I contend that if you factor out all those improvements-by-proximity--if you erect a magical barrier that prevents all human influence from passing it--the inherent value of a hectare in a city or suburb is about the same, or perhaps less, than a hectare in the middle of a cornfield--a field without an irrigation system, and far from any roads.
For the most part, the inherent value in land is as a place to put the improvements.
A location tax does not encourage efficient land use (by discouraging inefficient use). It discourages living closer to other people, which itself is a more efficient use of land. When home is where you hang your hat, people gather around the hatracks. As long as you are taxing desirable location rather than land area, you are addressing the movement of the people rather than the use of the limited resource.
If high-density housing is a more efficient use of land than low-density housing (a rhetorical conditional), then it is counterproductive to tax people for being closer together in more efficient cities, rather than less-efficient suburbs.
The true underlying value is the value it would have if you picked up the land with a god's hand and plopped it down in the middle of nowhere, in a land devoid of people and far from roads or rivers. Does it have valuable natural or mineral resources on or under it? Does it have energy production potential? Fresh water? Historical significance?
No? It's worth zero. People drive the economy. Land only has value to the extent that it does not present barriers between you and your trade partners. No one wants to live atop the mountain if the funicular is not built. No one wants to live across the lake if there are no boats, docks, and piers. No one wants to live deep in the forest if the road into it has not yet been cleared.
How then do you calculate a land tax fairly? Surface area alone? Population density data from the census?