Public Choice 78: 103-114, 1994.
© 1994Kluwer Academic Publishers. Printed in the Netherlands.
An analysis of Dr. Sun Yat-sen's self-assessment scheme for
land taxation*
EMERSON M.S. NIOU
Department of Political Science, Duke University, Durham, ArC 27706
G U O F U TAN
Department of Economics, University of British Columbia, Vancouver, B.C., Canada V6T 1 W5
Dr. Sun Yat-sen 1 proposed a method of self-assessment of land value in 1905.
Under his scheme, each owner submits his own valuation but the state reserves
the right to purchase the land at the self-assessed value. Sun claimed that this
scheme would deter landowners from under-assessing their property, and the
annual tax would discourage them from over-valuation. The origin of Sun's
self-assessment method is not clear. 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" (Condliffe 1930: 182). Although remarkably similar to Sun's
proposal, no evidence indicates a connection between the two.
Others have argued for similar schemes for the taxation of economic rent.
Harberger (1965), in his study o f Latin America tax reform, proposed a variation of Sun's scheme. Under his scheme, each property owner publicly declares
the value of his own property, and is required to sell his property to any bidder
who is willing to pay, say, 20 per cent more than the declared value. He argues
that this simple scheme is self-enforcing, allows no scope for corruption, has
negligible costs o f administration, and creates incentives for efficient allocation of each property. Nuti (1988) recently suggests a procedure for capital
valuation and interfirm mobility in Soviet-style enterprises. He argues that the
investment miscalculation and mismanagement created by the lack o f a stock
market in planned economies can be eradicated only if enterprises are penalized
for their failure to maintain the market value of the investment and for their
inability to utilize it better than other enterprises. He proposed that enterprise
managers assess the current value of their productive assets and register it with
a central public record office. Subsequently, any other state enterprise can bid
for the enterprise's productive assets. The challenged enterprise either revises
the valuation of its assets to equal the highest bid or it has to sell the assets at
* The authors thank William Bernhard and Peter Ordeshook for their helpful comments.
104
the highest bid. Nuti pointed out that this scheme performs some of the tasks
usually expected of a capital market.
An interesting aspect of these self-assessment schemes is that it depends on
the voluntary actions and truthful reports of the property owners. This paper
analyzes the properties of this type of truth-revelation mechanism, with emphasis on the scheme proposed by Sun Yat-sen. In Section 1, we review some
historical accounts of Sun's land policy and formulates his scheme as a
principal-agent model, with government as the principal and each landowner
the agent. We examine whether truth-telling is the best strategy for the landowners under his scheme. In Section 2, we modify Sun's scheme by incorporating auditing and more severe penalty. Section 3 makes further modifications,
creating a scheme that always induces truthful reporting of land value. In Section 4, we make some concluding comments.
1. Sun Yat-sen's land policy
After observing the seamier side of the industrial revolution during his European exile of 1896-98, Sun began to pay attention to socio-economic problems
and their possible solutions. Sun believed that the reason the West has been
burdened with social problems is because it has not solved the land problem.
He cited England, where a few wealthy individuals monopolized large tracts
of urban land for speculative purposes. This inequality in land ownership
created great disparities in the distribution of wealth. To overcome this inequality without infringing on landowner's currently held wealth, Sun proposed
a unique land policy.2 In his own words:
The prosperity resulting from civilization should be equally enjoyed by the
entire population. We should reform our social and economic structure and
assess the value of all the land in the country. Its present value shall still be
considered the property of the owner, but all increases in value resulting
from social reform and progress after the revolution shall belong to the state,
to be enjoyed by all the people . . . " (Hu, 1957, Vol. 1: 289).
How indeed can the price of the land be determined? I would advocate that
the landowner himself should fix the price. The landowner reports the value
of his land to the government and the government levies a land tax accordi n g l y . . . [T]he government makes two regulations: first, that it will collect
taxes according to the declared value of the land; second, that it can also buy
back the land at the same p r i c e . . . According to my plan, if the landowner
makes a low assessment, he will be afraid lest the government buy back his
land at that value and make him lose his property; if he makes too high an
assessment, he will be afraid of the government taxes according to this value
serious possibilities, he will certainly not want to report the value of his land
105
too high or too low; he will strike a mean and report the true market price
to the government (Sun, t924: 177-178).
Sun's land policy has three main features. First, the government appropriates
all future increments in land value. Second, land values, exclusive of improvement, are self-assessed. The government retains the right to purchase any piece
of land at any time according to its original reported value. Third, it is easy
to implement. Sun's program, no doubt, was, in part, derived from John
Stuart Mill and Henry George. 3 While Sun was in England near the turn of the
century, the influence of Henry George's book, Progress and Poverty, had
already left its mark on the British socialist and liberal labor movements.
However, John Stuart Mill (1874) exerted the strongest influence on preGeorge land reform movements in Britain, popularizing the term "future unearned increment." His organization's program called for state appropriation,
by taxation, of the "Future Unearned Increment Increase of the Rent of the
Land . . . or a great part of that increase, which is continually taking place,
without any effort or outlay by the proprietors, merely through the growth of
population and wealth . . . " (V: 225).
Although Sun received his ideas on land value taxation and the unearnedincrement concept from Mill and George, the tax legislation of the German
leased territory of Kiaochow in 1898 showed him how that theory could be put
into practice (Schiffrin, 1957: 561). The Kiaochow legislation called for a 6%
tax on land values and a 331,4% levy on future increases, the first recorded
occasion in which a future unearned increment tax was invoked. Sun's predilection for the programs of Mill and George was also reinforced by the Lloyd
George Budget (Finance Act 1909-10), which, among other measures, instituted a future unearned increment tax on land values and government royalties
on mine production (Schiffrin, 1957: 562).
After the passage of the Lloyd George Budget, Sun observed that the British
government required the services of thousands of valuers to assess approximately eleven million holdings in Great Britain. The administrative costs of the
Lloyd George Budget helped Sun realize the advantages of a self-assessment
method.
To specify Sun's scheme formally, we begin by assuming that (1) each
landowner can costlessly observe his land value, v. However, the government can only observe this value if it performs an audit; (2) Although the
government does not know the true land value, it can make an estimate,
9, of v; (3) The government does not reveal the estimated value to the
landowner; (4) The government requires each landowner to report the value of
his land, denoted by R. Sun's scheme, denoted by S0, can be summarized
thus:
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If R > 0, then the landowner pays taxes proportional to his reported land
value, t.R, 0 < t < 1.
If R < ~7, then the government buys the land from the landowner at price R.
According to Sun's scheme, the government does not necessarily have to purchase the land at the self-assessed value if the government detects an underreport - the government has the option to purchase the land at the self-assessed
value. Without loss of generality though, we assume that if the government detects an underreport, the government buys the land at the reported value with
certainty. We also assume that the government's objective is to induce truthtelling, or, equivalently, to minimize the difference between reported value and
true value of the land. On the other hand, the landowner's objective is to maximize their monetary payoffs.
1.1. A n ideal case
We first consider an ideal case. Suppose it is common knowledge that the
government knows the market value of the land. Hence, 9 = v. Because the
land policy implies:
if R < v, then the government buys the land at price R,
if R > v, then the government collects tax t . R , t > 0,
the landowner has the following profit function,
f
R
if R < v,
v-t.R
i f R > v.
II(R,v)
Therefore, it is in the landowner's interest to underreport if
II(R,v) = R > v - tv = II(v,v)
That is, it is optimal for the landowner to report less than the land's true market
value, and the landowner's optimal strategy is R = v - E, where E > 0 is arbitrarily small. Because we assume that the government will buy the land with
certainty if the landowner underreports, the landowners try to have the government buy their lands by underreporting just a little bit below the market value.
Notice also that if the government buys the land with probability p, then the
higher the probability, the closer is the landowner's report to the true value o f
the land. In other words, with perfect information, Sun's scheme cannot induce truth-telling. Landowners always have an incentive to underreport.
107
1.2. A general case
In reality, the government must pay a cost to learn the true value of the land.
The government usually begins only with an estimate ~, o f the land value. So
assume that although landowners do not know the value o f 0, they do know
that ~ is drawn f r o m a cumulative distribution function F(~) with the density
function f(~) and support [0,9], and that v belongs to the support [0,9].4 One
example is the degenerate distribution
F(~) = 0 if ¢¢ E [0,v),
= 1 if f, E [v,9].
That is, the landowner believes that ~ = v with probability one. This is the case
discussed in Section 1. Another example is the uniform distribution
F(~7) = ,~/9
for all ¢" E [0,-~].
That is, the landowner believes that the government's estimate has an equal
chance to take any point between 0 and 9, when 9 is the m a x i m u m possible
value of the land and is c o m m o n knowledge. A third example is the truncated
normal distribution with the mean E~ = v and variance Var(¢¢) = a 2.
In this paper, we only consider the distribution with positive continuous density function f(f0 and assume both ~¢ + [F(~)/f(,~)] and ~ - [1 - F(~)/f(¢,)] are
strictly increasing in f~. Given Sun's scheme, we can write the landowner's
profit function as the following:
II(R,v) = ( v - tR)prob(R > 0) + R . p r o b ( R < 0)
= ( v - t R ) F ( R ) + R [ 1 - F ( R ) ] , VvE[0,,~], R E [0,9].
F(R) is the probability that the reported value is greater than or equal to
government's estimated value. The landowner selects R E [0,9] to maximize his
profit function II(R,v) that depends on his true value v. The first-order condition gives the following:
OII
- -
=
l
=
O.
OR
- F(R) - Rf(R) - tF(R) - tF(R) + ( v - t R ) f ( R )
That is,
f(R)-[v-(l+t)R
+
1 - (1 +t)F(R)
f(R)
] = 0.
108
Since f(R) > 0, the l a n d o w n e r ' s o p t i m a l reporting strategy R*(v) is determined
by the equation
1 v
=
(l+t)R*
(I+t)F(R*)
-
(1)
fiR*)
1
-
Let ~t(R) = (1 + t ) R -
(I+t)F(R)
f(R)
Then, based on the regularity condition, ~t(R) is strictly increasing in R. It has
inverse function q t 1(.) = R. Thus, equation (1) can also be written as R*(v)
= 'I,t- l(v). It is easy to see that
0II
OR
f(R)(v - ~t(R))
L_
> 0 when R < xIttl(v )
= 0 when R = xIttl(v )
< 0 when R > x I ' t l ( v )
Thus, II(R,v) is globally m a x i m i z e d at R = 9 t l ( v ) "
We can show that the l a n d o w n e r ' s best reporting strategy 9~'(v) = ,I,t l(v)
has the following properties:
1.
2.
3.
4.
R t is increasing in v;
R t is decreasing in t;
Ro(V) > v for all v E [0,~];
if t > 0 and t . ( v + F(v)/f(v)) - (1 - F ( v ) ) / f ( v ) is strictly increasing in v,
then there exists a v o E [0,?] such that
,I,~(v)
~
> v if v < v o
= vifv = vo
< vifv > vo
P r o p e r t y (1) says that for any tax rate t _> 0, the higher the true m a r k e t value
o f the land, the m o r e the landowner reports. P r o p e r t y (2) implies that the landowner is likely to report less when tax rate is higher. P r o p e r t y (3) m e a n s that
if there is not tax, the landowner will always report higher than the true value
o f the land. M o r e interestingly, when tax rate is positive, for a general class o f
distribution F(9), there exists only one value v o at which the landowner will
report the truth. W h e n the value is lower, the landowner will overreport, and
when the true value is higher, the landowner will underreport. Therefore, the
chance that the landowner reports the truth is close to zero.
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2. The first modification, S 1
Thus far, we have shown that the self-assessment scheme proposed by Sun
generally does not induce landowners to reveal land value truthfully. Landowners with higher land values have a tendency to underreport and landowners
with lower values to overreport. To remedy Sun's policy, punishments need to
be incorporated into the land policy to deter underreporting, assuming that the
government can audit and learn about the true value at some costs. Again, let
v denote the true value of the land, 0, the government's estimate value, and R,
the reported value. We can modify Sun's scheme thus:
If R >
If R <
If R
If R
price
0, then the government does not audit. Landowner pays tax tR.
0, then the government audits and learns about the true value, v.
>_ v, the landowner pays tax tv, instead of tR.
< v, the landowner pays tv and the government buys the land at
R.
Thus, with this modified scheme, the landowner's expected p a y o f f is:
II(R,v) = F ( R ) ( v - t R ) + ( 1 - F ( R ) ) ( 1 - t ) v , if R _> v,
II(R,v) = F ( R ) ( v - t R ) + ( 1 - F ( R ) ) ( R - t v ) , if R < v.
Again, we first consider the case that the government knows the market
value of the land. That is, 0 = v. Landowners know this and thus each landowner has the following profit function:
R - tvifR
< v,
II(R,v) =
v - tv i f R >_ v.
Obviously, the landowner never profits f r o m underreporting with this modified scheme and under the assumption that the government knows the true land
value.
Next, we consider the case that the government only has an estimate of the
land value. First, the landowner will never overreport because II(R,v) is
decreasing in R,
3II
OR
( v - R ) t f ( R ) - tF(R) < O.
Second, for R < v,
110
II(R,v) - II(v,v) = ( v - R)[(1 + t)F(R) - 1].
Then,
II(R,v) > II(v,v) ~
F(R) > t/1 + t.
This expression implies that if v is close to the upper bound, 9, of the support
[0,~], there always exists an R < v such that 1 > F(R) > 1/1 + t. Then underreporting is better than telling truth. In other words, under the modified
scheme, a landowner whose land value is high compared to the government's
estimate 9 is more likely to underreport. The intuition is that the landowner believes that the value of his land is higher than the government's estimate on
average (i.e. v > Eg) and thus the probability that the land will be audited
(1 - F(R)) is very small if he underreports. Therefore, for any landowner whose
land value satisfies F(v) > 1/1 + t, he will always choose R < v such that F(R)
> 1/1 + t. The optimal R* for the landowner is determined by
0II
-- = (v-R)(I+0f(R)
OR
+ 1 - ( I + 0 F ( R ) = 0.
and
1
F(R)
>
-
-
l+t
F r o m the government's point of view, the probability of underreporting is
t/1 + t. So, for example, if the tax rate is 1%0, the probability o f underreporting is about 0.9%. Although the modified scheme significantly improves
Sun's original scheme, it still does not always induce truth-telling. In the next
section, we propose another modification to perfect the scheme by introducing
additional penalty on the landowners who underreport.
3. The second modification, S 2
The new scheme is a triple S 2 = [t, R o, P(R,v)], where t is the tax rate, t > 0,
R o is the report cutoff level, and P(R,v) is the penalty. This scheme works as
follows:
I f R > 9, then the government does not audit and the landowner pays tax tR.
I f R < 9, the government audits, and learns the true value, v.
I f R > v, then the landowner pays tax tv, instead of tR.
111
I f R < m i n [ Ro,V }, then the landowner pays tv and the g o v e r n m e n t buys
the land at price R.
I f R o ___ R < v, the g o v e r n m e n t buys the land at price R and the landowner pays tax tv and fine P(R,v) as well. P is p r o p o r t i o n a l to the a m o u n t
o f tax evasion, tv - tR.
T h a t is, the g o v e r n m e n t sets a c u t o f f point R o. I f R is lower t h a n R o and v,
then the g o v e r n m e n t buys the land at the reported value and collects tax, tv.
I f R is greater t h a n Ro, then a direct penalty, P, will be imposed. Thus, u n d e r
S 2, landowners w h o o w n m o r e valuable land are punished m o r e severely if
they u n d e r r e p o r t t h a n landowners w h o o w n less valuable land. Next, in p r o p o sition 1, we show t h a t S 2 always induces truth-telling.
Proposition 1: S 2 = [t, R o, P] always induces truth-reporting, where R o a n d
P are chosen such that
1. F(Ro) _ 1/1 + t, and
2. P = o f f t v - t R ) , where a > F ( R ) / 1 - F ( R ) .
Proof." Given S2, the l a n d o w n e r ' s expected profits are:
II(R,v) = F ( R ) ( v - t R )
II(R,v) = F ( R ) ( v - t R )
II(R,v) = F ( R ) ( v - t R )
+ (1 - F ( R ) ) ( 1 - t)v, if R >_ v,
+ ( 1 - F ( R ) ) ( R - t v ) , if R < min(R o, v),
+ (1-F(R))[R-tv-P],
if R o _ R < v.
To show that Scheme S 2 induces truth-reporting, we need to consider three
cases:
Case 1: R >_ v
IIs2(R,v ) is decreasing in R a n d hence II(R,v) < II(v,v) v R > v.
Case 2: R < min(Ro,V)
II(R,v) - II(v,v) = ( v - R ) [ ( 1 + t ) F ( R ) - 11
< ( v - R ) [ ( 1 + t ) F ( R o ) - 1]
_<0.
Case 3 : R o _ R < v
II(R,v) - II(v,v) = - (1 - F(R))[P - t ( v - R)
F(R)
1 -
_< - [1 - F ( R ) ] ( v - R) < 0.
F(R)
+ ( v - R)]
112
In all three cases, II(R,v) < II(v,v) for all R ~ v.
QED.
Proposition 1 shows that S2 always induces truth-telling. The amount of direct
penalty needed to ensure truth-telling is proportional to the government's tax
revenue loss and also depends on the landowner's report.
4. Conclusion
Sun designed his land program to create a more equitable distribution of wealth
among citizens. To equalize wealth the government appropriates, by taxation,
the future unearned increment increase in land value. To implement this program, the government must first assess the present land value. Sun believed
that his self-assessment scheme would induce reporting of true market value
by the landowner. Sun's scheme has one form of penalty - the government
buys the land at the reported value if the landowner nnderreports. Thus, the
government need not worry whether landowners who nnderreport have enough
income to pay for a penalty. The government would simply buy the land from
landowners at the reported value of the land. However, in Section 1, we show
that, first, with perfect information, landowners will not report land truthfully
- the reported land value will be less than the market price. Second, if the
government does not know the market value of the land, the probability that
the landowners report truthfully is still close to zero.
In Section 2, we modify Sun's scheme by imposing an additional cost on
the landowners in the calculation o f their expected profits. Under the modified
scheme, government not only purchases the land at the underreported value,
but also collects taxes bases on the true land value. With the additional penalty
under S 1, with perfect information, landowners will report land value truthfully; but with asymmetric information, a small probability exists that some
landowners will still underreport (especially those whose land values are closer
to the upper bound of government's estimated value). To prevent underreporting, a more severe punishment must be used. Under scheme S2, if the
government sets a cutoff point o f the land value, then if the reported value is
less than the cutoff point, S 1 still applies. If the reported value is above the
cutoff point but still underreported, the landowner must pay an additional
fine. The cutoff point is a function of the tax rate, and the fine is proportional
to the amount o f tax evasion. Under this scheme, the landowners will always
report land value truthfully.
Scheme S2, is essentially an auditing scheme combined with a specific
penalty structure. The probability of auditing depends on the report, R, and
is given by 1 - F(R). Even though it is optimal for the landowner to report
truthfully, the government still has to audit randomly in order to build up the
113
a u d i t i n g r e p u t a t i o n . Since a u d i t i n g is costly, S 2 i n d u c e s t r u t h r e p o r t i n g at
s o m e costs. A n interesting p r o b l e m is t o design a s c h e m e t h a t i n d u c e s t r u t h r e p o r t i n g at n o costs. U n f o r t u n a t e l y , such a s c h e m e d o e s n o t exist. T h e best
we c a n d o is t o design a s c h e m e t h a t m i n i m i z e s t h o s e costs. This is b e c a u s e w h e n
we t r y t o solve t h e r e s o u r c e a l l o c a t i o n p r o b l e m s b y designing a m e c h a n i s m t o
elicit t r u t h f u l i n f o r m a t i o n f r o m i n f o r m e d agents, i f t h e i n f o r m a t i o n to b e
elicited is n o t verifiable, agents d o n o t h a v e incentives to r e p o r t t r u t h f u l l y a n d
n o a u d i t i n g p o l i c y is h e l p f u l . T h u s , s o m e f o r m s o f policies o r i n s t i t u t i o n s h a v e
to be c r e a t e d t o p r o v i d e agents sufficient incentives to reveal their i n f o r m a t i o n
t r u t h f u l l y . U n f o r t u n a t e l y , except for special cases, efficient r e s o u r c e a l l o c a t i o n
a n d incentive c o m p a t i b i l i t y are n o t c o m p a t i b l e . O u r m o d i f i e d scheme induces
t r u t h - r e p o r t i n g is b e c a u s e we a s s u m e t h a t t h e t r u e value o f l a n d is v e r i f i a b l e
a n d can be l e a r n e d b y t h e g o v e r n m e n t t h r o u g h a u d i t i n g at certain cost. I n this
way, o u r s o l u t i o n is a s e c o n d best s o l u t i o n . 5
I n t e r m s o f the a p p l i c a b i l i t y o f the self-assessment scheme, Sun discussed
o n l y t h e a p p l i c a t i o n o f his scheme to l a n d . But it s h o u l d n o t b e difficult to imagine the a p p l i c a t i o n o f a self-assessment scheme to o t h e r m a r k e t a b l e sources
o f rent, e.g., m i n e r a l rights, b r a n d n a m e s , a n d p a t e n t s . 6 T h e t a x system c o u l d ,
for e x a m p l e , r e q u i r e t h a t every p r o p e r t y o w n e r d e c l a r e his v a l u a t i o n f o r t a x a t i o n at s t a t e d intervals, s a y a n n u a l l y , a n d m u s t t h e n a c c e p t a n y b o n a fide o f f e r
a b o v e his v a l u a t i o n d u r i n g this p e r i o d . T h e incentive to u n d e r v a l u e is to a v o i d
t a x a t i o n ; the p r o s p e c t i v e p e n a l t y is t a k e - o v e r .
Notes
1. Dr. Sun Yat-sen (1866-1925) and his followers toppled the Manchu government and established the Republic of China in 1911. His political ideals are summarized in a set of doctrines
called the Three Principles of the People - Nationalism, Democracy, and the People's
Well-Being.
2. The government's option to purchase land, however, is not related to agrarian land, but is
limited to urban land. Sun proposed a different land policy in 1924 - "land to the tiller" to deal with the excesses of rural landownerism and the maldistribufion of landholdings.
3. For a detail discussion of this issue, see Schiffrin (1957: 549-564).
4. The distribution F('~)can be interpreted in two ways. First, it may be the case that the government has an estimate which is not observed by the landowner, but the landowner formulates
a belief, F(f0, about "~. Second, it may be the case that the government randomly chooses any
number according to a cumulative distribution, F('~).
5. For a general discussion of the issue of incentive comparability, see Ledyard (1987).
6. Archibald (1978) develops a set of criteria to evaluate the effectiveness of self-assessment
scheme when applied to different sources of rent.
114
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