1. Redistributive land taxation
Alain Trannoy
Canazei Winter school January 2017

2. Modern public economics
When we think nowadays about redistributive taxation
Progressive income tax
Capital tax, inheritance tax

3. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Georgism
Single tax movement: Henry George is best known for his argument that the economic rent of land (location) should be shared by society
George proposed to create a pension and disability system, and an unconditional basic income from surplus land rents. It would be distributed to residents "as a right" instead of as charity.
Georgists often refer to this policy as a citizen’s dividend in reference to a similar proposal by Thomas Paine
Bonnet, Bono, Chapelle, Trannoy, Wasmer

4. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Letter to Gorbatchev
November 7, 1990
Mikhail Gorbachev, President Union of Soviet Socialist Republics
Dear Mr. Gorbachev:
The movement of the Soviet Union to a market economy will greatly enhance the prosperity of your citizens. Your economists have learned much from the experience of nations with economies based in varying degrees on free markets…
It is important that the rent of land be retained as a source of government revenue. While the governments of developed nations with market economies collect some of the rent of land in taxes, they do not collect nearly as much as they could, and they therefore make unnecessarily great use of taxes that impede their economies--taxes on such things as incomes, sales and the value of capital.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

5. 30 economists among whom
William Vickrey, Jacques Thisse, Tibor Scitovsky, James Tobin, Richard Musgrave, Franco Modigliani, Zvi Griliches, William Baumol, Robert Solow
“In my opinion, the least bad tax is the property tax on the unimproved value of land, the Henry George argument of many, many years ago.” Milton Friedman

6. Henry Georges’ Theorem
Arnott and Stiglitz (1979)
Under some conditions, it is optimal to finance local public infrastructures and utilities with a tax on rents or tax on real estate”
Different perspective, not local public finance, but nationwide public finance.

7. Outline Why a revival of Georgism?
Is it possible to fund a basic income with a property tax on land which correct both inequalities in ownership of land and capital?
In the likely case where the level of tax rate on the real estate cannot be politically accepted by landowners, is a tax on rents (without including imputed rents) second best?
The actual world is quite different from that of Henry George with the emergence of a vast middle class which becomes homeowner when people are sufficiently old. Should the property tax also be borne by the “old middle class”?

8. Based on forthcoming WP
Land is back…and it must be taxed
Odran Bonnet, Guillaume Chapelle, Alain Trannoy, Etienne Wasmer

9. 1. Aftermath of Piketty’s book
The impetus: “Capital in the twenty-First Century”
Piketty did three things:
From an empirical view point: new series about 𝐾/𝑌
From a theoretical view point: exploding accumulation of capital and linkage with growing inequality
From a policy view point: a world tax on capital
Bonnet, Bono, Chapelle, Trannoy, Wasmer

10. Housing land: main source of divergence of K/Y (France)
Bonnet, Bono, Chapelle, Trannoy, Wasmer

11. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Housing price indices
Bonnet, Bono, Chapelle, Trannoy, Wasmer

12. Residential-structure price indices
Bonnet, Bono, Chapelle, Trannoy, Wasmer

13. Housing Land prices indices
Bonnet, Bono, Chapelle, Trannoy, Wasmer

14. Share of land in housing capital
Bonnet, Bono, Chapelle, Trannoy, Wasmer

15. Why increasing housing land prices/income ratio ?
Credit
Population growth
Land regulation
Bonnet, Bono, Chapelle, Trannoy, Wasmer

16. Credit exuberance (Robert Shiller)
Credit exuberance during the beginning of this millenium.
Lower interest rates
Longer mortgage maturity
Lower downpayment or higher loan-to-value ratio
Higher cap for debt-to-income ratio
Bonnet, Bono, Chapelle, Trannoy, Wasmer

17. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Credit exuberance
Bonnet, Bono, Chapelle, Trannoy, Wasmer

18. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Real causes
Growth of population
“The value and thus economic rent of land, which is permanently inelastic in supply, is governed by the growth in demand for land for purposes of food production and housing, which in turn is driven by population growth. The increasing value and rent is, in the Ricardo-George context, entirely due to the growth of population” Warren Samuel
You don’t need sunspots to trigger a housing land bubble
Bonnet, Bono, Chapelle, Trannoy, Wasmer

19. Housing land regulation
Three different periods for France
: the influence of Le Corbusier
Social housing and large housing estates
Relatively « land use saving »
: Middle class left large housing estates for new houses in suburbs.
Urban sprawn, « land use augmenting »
: « Greenness » more respectful of agricultural land and recreative areas.
Restrictive zoning
Local political equilibrium (because it will increase the price of housing land for already homeownert)
Bonnet, Chapelle, Trannoy, Wasmer

20. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Paris Le Corbusier 1937
Bonnet, Bono, Chapelle, Trannoy, Wasmer

21. Credit maybe not the original cause
Suppose that bankers are smart.
They remember the Ricardo-George result for countries with growing population or shift to smaller household’size
They expect land regulation to be a political equilibrium
They deduce that on the long run the value of the mortgage collateral will be pushed up.
They will be very friendly when new mortgages are asked.
Credit lines up with the fundamentals
And people are just bayesians with respect to the evolution of housing land prices.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

22. Bonnet, Chapelle, Trannoy, Wasmer
Our reading of Piketty
Empirical side
The evolution of 𝐾/𝑌 is mainly governed by housing
The evolution of the market value of housing is mainly driven by land price for both real, policy and financial reasons
Policy side
Suppose that we can tax housing land separately from structures.
(Example of Pittsburgh of “two rates” or “Split-rates” from 1913 to ) see Oates and Wallace 1997 NTJ)
Bonnet, Chapelle, Trannoy, Wasmer

23. 2. Macroeconomic foundation of Neogeorgism
Is it possible to fund a basic income with a property tax on land which correct both inequalities in ownership of land and capital?
Judd’s model (close but a bit different from Chamley)
Bonnet, Bono, Chapelle, Trannoy, Wasmer

24. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Judd’s model
Two types of agents, one type of capital, one aggregate consumption good
Capitalists optimally choose capital and intertemporally allocate consumption 𝐶 𝑡 , and capital investment 𝐼 𝑡
Workers consume their wages 𝑐 𝑡 = 𝑤 𝑡
Capital taxation is not first best, and not even second best.
Judd = Negative Ramsey result.
Still some mathematical pbs (Straub & Werning (2015))
Bonnet, Bono, Chapelle, Trannoy, Wasmer

25. Extension to land use and property
Two classes: capitalists and landlords vs workers and tenants.
Benchmark: Housing = Land housing
The capitalists own all land 𝐻
For their housing use, 𝐻 𝑡 , and they rent the remaining to workers ℎ 𝑡
Purely redistributive aim of taxation to redistribute welfare from capitalists to workers. (No public expenditure)
Link with equality of opportunity
Bonnet, Bono, Chapelle, Trannoy, Wasmer

26. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Model (I)
Capital investment equation: 𝐾 𝑡+1 = 𝐾 𝑡 1−𝛿 + 𝐼 𝑡 Utility of capitalists-landowners: 𝑡=0 ∞ 𝛽 𝑡 𝑈( 𝐶 𝑡 , 𝐻 𝑡 ) Utility of workers-tenants: 𝑡=0 ∞ 𝛽 𝑡 𝑢( 𝑐 𝑡 , ℎ 𝑡 )
Bonnet, Bono, Chapelle, Trannoy, Wasmer

27. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Model (2)
Ressource constraint of the economy: 𝑐 𝑡 + 𝐶 𝑡 + 𝐾 𝑡+1 ≤𝑓 𝐾 𝑡 + 1−𝛿 𝐾 𝑡 Factor’s returns: 𝑤 𝑡 =𝑓 𝐾 𝑡 − 𝑓 ′ 𝐾 𝑡 𝐾 𝑡 𝑅 𝑡 𝐾 𝑔𝑟𝑜𝑠𝑠 = 𝑓 ′ 𝐾 𝑡 +1−𝛿 Tax on capital: 𝜏 𝐶𝑎𝑝𝑖𝑡𝑎𝑙,𝑡 Net return on capital : 𝑅 𝑡 𝐾𝑛𝑒𝑡 =(1− 𝜏 𝑐𝑎𝑝𝑖𝑡𝑎𝑙,𝑡 ) 𝑅 𝑡 𝐾 𝑔𝑟𝑜𝑠𝑠 Tax rate of the rent: 𝜏 𝑅𝑒𝑛𝑡,𝑡
Bonnet, Bono, Chapelle, Trannoy, Wasmer

28. Capitalists/landlords program
Maximisation program: Max 𝐶 𝑡 , 𝐻 𝑡 , 𝐾 𝑡+1 𝑡=0 ∞ 𝛽 𝑡 𝑈( 𝐶 𝑡 , 𝐻 𝑡 ) 𝑠.𝑡. 𝐶 𝑡 + 𝐾 𝑡+1 = 𝑅 𝑡 𝐾 𝑔𝑟𝑜𝑠𝑠 1− 𝜏 𝐶𝑎𝑝𝑖𝑡𝑎𝑙,𝑡 𝐾 𝑡 + 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 (1− 𝜏 𝑅𝑒𝑛𝑡,𝑡 )( 𝐻 − 𝐻 𝑡 ) Euler equation: 𝑈 𝐶 ′ 𝐶 𝑡 , 𝐻 𝑡 =𝛽 𝑅 𝑡+1 𝐾 𝑔𝑟𝑜𝑠𝑠 1− 𝜏 𝐶𝑎𝑝𝑖𝑡𝑎𝑙,𝑡 𝑈 𝐶 ′ ( 𝐶 𝑡+1 , 𝐻 𝑡+1 ) Intra-period allocation: 𝑈 𝐻 ′ 𝐶 𝑡 , 𝐻 𝑡 = 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 1− 𝜏 𝑅𝑒𝑛𝑡,𝑡 𝑈 𝐶 ′ ( 𝐶 𝑡 , 𝐻 𝑡 ) Transversality condition: 𝛽 t 𝑈 𝐶 ′ ( 𝐶 𝑡 , 𝐻 𝑡 )→0
Bonnet, Bono, Chapelle, Trannoy, Wasmer

29. Workers/tenants program
Worker does not save. Live in ℎ units of rented housing and consume from their wage and of a government transfer 𝑇 Maximization program: Max 𝑐 𝑡 , ℎ 𝑡 𝑡=0 ∞ 𝛽 𝑡 𝑢( 𝑐 𝑡 , ℎ 𝑡 ) 𝑠.𝑡. 𝑐 𝑡 + ℎ 𝑡 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 = 𝑤 𝑡 + 𝑇 𝑡 First order condition: 𝑢 ℎ ′ 𝑐 𝑡 , ℎ 𝑡 = 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 𝑢 𝑐 ′ 𝑐 𝑡 , ℎ 𝑡
Bonnet, Bono, Chapelle, Trannoy, Wasmer

30. Bonnet, Bono, Chapelle, Trannoy, Wasmer
First best setting
The Gvt is able to commit to future tax policies
In a model without land, we already know that the first best can be implemented through
constant tax on consumption for all periods (Coleman (2000) JpubE) or
tax on capital with tax credit on new capital = tax rate (Abel (2007 JPubE)
Way to tax initial capital
No restrictions on instruments
Tax on land
Tax on rents including imputed rents
Bonnet, Bono, Chapelle, Trannoy, Wasmer

31. Program of the social planner
Max 𝑐 𝑡 , 𝐶 𝑡 , 𝐻 𝑡 , 𝐾 𝑡+1 𝑡=0 ∞ 𝛽 𝑡 𝑢 𝑐 𝑡 , 𝐻 − 𝐻 𝑡 +𝛾𝑈( 𝐶 𝑡 , 𝐻 𝑡 ) 𝑠.𝑡. 𝑐 𝑡 + 𝐶 𝑡 + 𝐾 𝑡+1 =𝑓 𝐾 𝑡 + 1−𝛿 𝐾 𝑡
𝛾 𝑈′ 𝐶 ( 𝐶 𝑡 , 𝐻 𝑡 ) = 𝑢′ 𝑐 ( 𝑐 𝑡 , 𝐻 - 𝐻 𝑡 )= λ 𝑡
𝛾 𝑈′ 𝐻 ( 𝐶 𝑡 , 𝐻 𝑡 ) = 𝑢′ ℎ ( 𝑐 𝑡 , 𝐻 - 𝐻 𝑡 )
λ 𝑡 / λ 𝑡+1 =𝛽( 𝑓 ′ 𝐾 𝑡+1 +1−𝛿))
At the steady state: 𝑅 𝐾𝑔𝑟𝑜𝑠𝑠 = 1 𝛽
Bonnet, Bono, Chapelle, Trannoy, Wasmer

32. First-best taxation Results
A tax on land or a tax on rents including imputed rents decentralizes the first best
Taxation of capital or rents are not first-best optimal
Bonnet, Bono, Chapelle, Trannoy, Wasmer

33. Bonnet, Bono, Chapelle, Trannoy, Wasmer
3. Second best setting
The set of available distortionary tax instruments is given and the optimal tax system within this set is explored
Not possible to confiscate initial capital
Three constraints on land tax instruments
No land register
Only 50 countries have one (over 200) (Van der Molen et Al 2014)
The most hated tax: in the US (Cabral-Hoxby (2012)), among the Swedes (Hammar and al.(2008))
Cap on the property tax as in California proposition 13 (June 6, 1978).
Not possible any more to tax imputed rent
Likely because ownership becomes widespread (up to 1963 in France)
Bonnet, Bono, Chapelle, Trannoy, Wasmer

34. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Ramsey problem
Tax on “new” capital vs tax on housing rents
Gvt finances redistribution by a flat tax either on rents or capital
Maximize social welfare under constraints
Resource constraint of the economy for each period
FOCs of the capitalist (Euler, intraperiod allocation between consumption and housing, transversality)
FOC of the worker
Bonnet, Bono, Chapelle, Trannoy, Wasmer

35. Without Housing: Planner Program
Max 𝑐 𝑡 , 𝐶 𝑡 , 𝐾 𝑡 𝑡=0 ∞ 𝛽 𝑡 𝑢 𝑐 𝑡 +𝛾𝑈( 𝐶 𝑡 )
𝑐 𝑡 + 𝐶 𝑡 + 𝐾 𝑡+1 =𝑓 𝐾 𝑡 + 1−𝛿 𝐾 𝑡 Mutiplier 𝜆
𝛽 𝑈 ′ 𝐶 𝑡 𝐶 𝑡 + 𝐾 𝑡+1 − 𝑈 ′ 𝐶 𝑡−1 𝐾 𝑡 Mutiplier 𝜇
𝛽 𝑡 𝑈 ′ 𝐶 𝑡 𝐾 𝑡+1 →0
Bonnet, Bono, Chapelle, Trannoy, Wasmer

36. Statement of Judd’s result
(Version of Straub & Werning (2015)
Theorem: Suppose quantities and multipliers converge to an interior steady state, i-e, 𝑐 𝑡 , 𝐶 𝑡 , 𝐾 𝑡 converge to positive values and 𝜇 𝑡 converges. Then the tax on capital is zero in the limit.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

37. Completing Judd’s statement
We define 𝛾 𝑈 ′ (𝐶) 𝑢 ′ (𝑐) =𝛼 𝑈 𝐶 = 𝐶 1−𝜎 1−𝜎 Proposition: Suppose quantities converge to an interior steady state. Then The mutiplier 𝜇 𝑡 converge iff 1−𝛼 1−𝜎 >0. More specifically, if 𝛼<1 then the convergence of mutipliers occurs iff 𝜎<1.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

38. The case of separable preferences
𝑈 𝐶 𝑡 , 𝐻 𝑡 = 𝑈 1 𝐶 𝑡 + 𝑈 2 ( 𝐻 𝑡 ) 𝑢 𝑐 𝑡 , 𝐻 − 𝐻 𝑡 = 𝑢 1 𝑐 𝑡 + 𝑢 2 ℎ 𝑡 𝑢 1 ∙ = 𝑈 1 ∙ = 𝑥 1−𝜎 1−𝜎 𝑢 2 ∙ and 𝑈 2 ∙ unspecified
Bonnet, Bono, Chapelle, Trannoy, Wasmer

39. The optimization pb with housing
Max 𝑐 𝑡 ,𝐶 𝑡 , 𝐻 𝑡 , 𝐾 𝑡+1 , 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 𝑡=0 ∞ 𝛽 𝑡 𝑢 𝑐 𝑡 , 𝐻 − 𝐻 𝑡 +𝛾𝑈( 𝐶 𝑡 , 𝐻 𝑡 ) C1 𝑐 𝑡 + 𝐶 𝑡 + 𝐾 𝑡+1 =𝑓 𝐾 𝑡 +1−𝛿 mutiplier 𝜆 C2 𝛽 𝑈 1 ′ 𝐶 𝑡 𝐶 𝑡 + 𝐾 𝑡+1 − 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 𝐻 − 𝐻 𝑡 − 𝑈 1 ′ 𝐶 𝑡−1 𝐾 𝑡 =0 multiplier 𝜇 C3 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 𝑢 1 ′ 𝑐 𝑡 − 𝑢 2 ′ 𝐻 − 𝐻 𝑡 ≥0 multiplier 𝜂 1 ≥0 C4 𝑅 𝑡 𝐻 𝑔𝑟𝑜𝑠𝑠 𝑈 1 ′ 𝐶 𝑡 − 𝑈 2 ′ 𝐻 𝑡 ≥0 multiplier 𝜂 2 ≥0 C5 𝛽 𝑡 𝑈 1 ′ 𝐶 𝑡 𝐾 𝑡+1 →0
Bonnet, Bono, Chapelle, Trannoy, Wasmer

40. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Two parameters
𝛾 the relative social welfare weight of capitalists ≤ 1 𝛼= 𝛾 𝑈 1 ′ 𝐶 𝑡 𝑢 1 ′ 𝑐 𝑡 𝛼 ℎ = 𝛾 𝑈 2 ′ 𝐻 𝑡 𝑢 2 ′ ℎ 𝑡
Distance to first best
Bonnet, Bono, Chapelle, Trannoy, Wasmer

41. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Local result
Proposition Consider the steady state of the second best optimum when 𝛼<1 and 𝜎<1 and the tax on capital is zero in the limit. If we consider a small pertubation around the steady state with a small rent tax financing a lump sum benefit to the worker, then social welfare is improving at the margin.
However, we do not know whether a zero tax on capital is still optimal in the limit in the economy with a rent tax as an additional instrument.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

42. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Main result
Proposition
Assume that the following instruments are available to the decision-maker: tax on capital, lump sum benefit to workers, tax on rents.
Consider an economy where the preferences of both the capitalist and worker are separable, with a CRRA subutility of consumption.
Suppose that quantities converges to an interior steady state and that 𝜎,𝛼 and 𝛼 ℎ < 1.
Then the optimal tax on capital is 0 and the optimal tax on rents is positive in the limit.
the stock of capital = the stock of capital in the first best.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

43. The second best optimal housing rent tax
Proposition: The optimal rent tax is given by 𝜏∗ 1−𝜏∗ = 1−𝛼 𝜖 𝑠 where 𝜖 𝑠 the supply elasticity of rental housing land wrt to net rent With CRRA sub-utility of housing 𝜖 𝑠 = 1/ 𝜎 𝐻 𝜏∗ 1−𝜏∗ = 𝜎 𝐻 (1−α)
Bonnet, Bono, Chapelle, Trannoy, Wasmer

44. Interpretation of the result
In a static setting, Diamond&Mirrlees (1971) shows that it is better not to tax production. Depending on the context, it may be second best optimal to tax consumption.
In a dynamic setting, not optimal to tax capital because it is productive.
Housing is a consumption good and under some conditions it can be optimal to tax it.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

45. Bonnet, Bono, Chapelle, Trannoy, Wasmer
4. Middle class
Karl Marx’s description of 19th century England : 36,000 homeowners
Alternative to Henry Georges, dissemination of property thanks to mortgage
Mortgage might be partially responsible for housing land inflation (a bad thing) but also for a good thing (reducing wealth inequality)
Life-cycle savers. They rent when young and accumulate savings for the downpayment. They become homeowners when old.
Bonnet, Bono, Chapelle, Trannoy, Wasmer

46. Only 3 meaningful wealth classes
Bonnet, Bono, Chapelle, Trannoy, Wasmer

47. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Main Issue
In that context, is George’s idea useless?
Or should we just exempt the (old) middle class from the property tax? (in that case, we are almost back to the previous model)
Dilemma: Housing Land is more evenly distributed than financial capital but the deadweight loss to tax housing land is lower
Bonnet, Bono, Chapelle, Trannoy, Wasmer

48. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Three class model
Capitalists: as previously + they can sell land instead of renting it to life-cycle savers
Workers-tenants
Life-cycle savers (live two periods)
They have a higher productivity and then wages than workers
They are workers-tenants-savers when young
They buy land (no credit) at the end of their working time period.
When they retired they sell their house and consume hand to mouth until they died. No bequest.
Housing Land market between the capitalists and young life-cyle savers during the transition period
Housing land market between young and old life-cycle savers at the steady state
Bonnet, Bono, Chapelle, Trannoy, Wasmer

49. Bonnet, Bono, Chapelle, Trannoy, Wasmer
Discussion
If you do not exempt the old life-cycle savers
Transfer to the young
Transfer to the tenant-worker
Transfer to the young vs gifts
Transfer to the tenant-worker: does the inequality of opportunity argument works?
Bonnet, Bono, Chapelle, Trannoy, Wasmer

50. Global new Georgian view
Two-tier property tax
Property tax to finance local public goods (à la Arnott-Stiglitz) on all owners
Additional property tax at the national or federal level on homeowners whose wealth is above some threshold to finance means of fight against poverty.
Bonnet, Bono, Chapelle, Trannoy, Wasmer