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Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
Interlinked Contracts: An Empirical
Study
Hui-wen Koo, Chen-ying Huang and
Kamhon Kan
March 26, 2015
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Conclusions
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Interlinkage is a contractual arrangement between
two parties that combines transactions across
multiple markets.
Example prevalent in a developing country:
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A monopsonist middleman buys crops from a
farmer at price P .
The middleman also provides the farmer a
production loan with interest rate i.
The middleman will decide {P, i}.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Conclusions
Definition of interlinkage
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Literature
Where to find data to test the theory?
Model modification
Conclusions
Q: Why should the middleman offer a loan to his
farmers? What is the interest rate, i, the
middleman will charge?
Traditional wisdom: i is a usurious rate
Gangopadhyay and Sengupta (1987):
i ≤ the middleman’s cost of capital
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
Gangopadhyay and Sengupta (1987):
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L: production loan a farmer takes
f (L): an increasing and concave production
function
Given the middleman’s terms {P, i}, the farmer
will decide how much to borrow:
maxL πf = P f (L) − (1 + i)L.
F OC : f ′(L) = (1 + i)/P
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
The middleman sells crops in a competitive market
at price v, and his cost of capital is r. He wishes to:
max{P,i} πm = vf (L) − (1 + r)L − P f (L) + (1 + i)L
s.t. f ′ (L) = (1 + i)/P (IC)
P f (L) − (1 + i)L ≥ A (IR),
where A is the farmer’s opportunity cost.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
The middleman’s optimal strategy:
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Choose {P, i} to induce the farmer to borrow L
so that the joint surplus,
S(L) ≡ πf + πm = vf (L) − (1 + r)L,
is maximized.
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Then suppress the farmer’s profit, πf , to his
opportunity cost, A.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
To achieve the maximum joint surplus S ∗, the
optimal L∗ satisfies:
f ′ (L∗) = (1 + r)/v,
while the IC constraint is:
f ′ (L∗) = (1 + i)/P.
Any {P, i} satisfying
(1+i)/P = (1+r)/v or P/v = (1+i)/(1+r) ≡ α.
yields the maximum joint surplus.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
The farmer’s share of surplus is:
πf /S ∗ = (P f (L∗)−(1+i)L∗)/(vf (L∗)−(1+r)L∗) = α.
To choose α = A/S ∗ makes the farmer receives A.
In sum, in the optimal interlinked contracts,
P/v = (1 + i)/(1 + r) = A/S ∗.
The middleman will provide loan to the farmer only
when the farmer’s opportunity cost is less than the
maximal joint surplus. So, A/S ∗ ≤ 1 and it implies
that i ≤ r.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
◮
Literature
Where to find data to test the theory?
Model modification
Conclusions
It is difficult to collect the terms of trade
between the middleman and the farmer.
This paper uses the contracts between Taiwanese
cane farmers and Japanese sugar mills in the
colonial era to test the theory, because the
situation fits the theory’s framework.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
◮
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Literature
Where to find data to test the theory?
Model modification
Conclusions
Each sugar mill was a monopsonist in its local
region thanks to regulation. Before the planting
season, mills would announce their future
contracts for cane. Considering the terms,
farmers were free to choose cane or other crops
to plant.
Most sugar produced in Taiwan was exported to
Japan, where the Japanese and other foreign
manufacturers competed to sell it.
Mills provided their cane farmers with loans.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
300
250
sum
200
150
fertilizers
100
working capital
50
others
seeds
9
0
8
1
9
3
9
/4
8
/3
7
/3
9
3
9
3
1
1
6
7
6
/3
5
/3
9
3
9
3
1
1
4
5
4
/3
3
/3
9
3
9
3
1
1
2
3
2
/3
1
/3
9
3
9
3
1
1
0
1
0
/3
9
/3
9
3
9
2
1
1
8
9
9
2
8
/2
7
/2
1
9
2
6
/2
9
2
1
1
6
7
5
9
2
1
9
2
5
/2
4
4
/2
1
1
9
2
3
/2
3
2
/2
9
2
1
9
2
1
1
9
2
0
/2
1
/2
1
2
0
Figure: Average Loan (yuan/chia)
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
We have to modify the model to fit the data.
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Price discrimination between paddy farmers (rice
growers) and dry-field farmers (potato growers)
because of their different opportunity costs to
plant cane (A1 < A2 ).
The interest rate was not differentiated among
farmers. Otherwise farmers qualifying for the
lowest rate would borrow and then transfer their
loans to other farmers.
A mill’s contract is: {i, P1, P2 }.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
1.2
village credit unions’ average
1
mills’ average
0.8
0.6
0.4
0.2
0
1930/31
1931/32
1932/33
1933/34
1934/35
1935/36
1936/37
1937/38
1938/39
1939/40
Figure: Monthly Interest Rate (%)
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
◮
Literature
Where to find data to test the theory?
Model modification
Conclusions
v/P2 > (1 + r)/(1 + i)?
1930/31 橋仔頭, units = yuan/1000gin
Ps = 121.7 (the 1928 future price of sugar)
c = 25.58 (production cost)
φ = 0.1519 (the conversion ratio)
v = (Ps − c)φ = 14.6
P2 = 5
For r < 192%, the inequality holds only if i < 0.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
◮
◮
Literature
Where to find data to test the theory?
Model modification
Conclusions
Why not negative interest rate?
Loans on fertilizers were probably interest free.
While the stated interest rate was said clearly to
apply to loans on working capital and tenants’
rent payments, no contract ever discussed how to
calculate interest payments for fertilizer loans.
《農業基本調查書》: 28.98% of mills’ loans were
free of interest.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
◮
Literature
Where to find data to test the theory?
Model modification
Conclusions
All contracts stated that fertilizer loans were
given out in-kind, and mills would charge farmers
no more than the cost.
1930/31 台東, the aboriginal cane farmers
received 20% of their ammonium sulfate and
50% of their calcium superphosphate for free.
This in fact made interest rates negative.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
Literature
Where to find data to test the theory?
Model modification
Conclusions
Working capital loans, unlike fertilizer loans, were
lent in cash. If working capital loans were free of
interest, or if the mill subsidized working capital
loans, farmers would be induced to borrow to
finance other needs as well.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
◮
Literature
Where to find data to test the theory?
Model modification
Conclusions
To control for farmer’s moral hazard: In the case
that i was lower than the market rate, cane
farmers would use a mill’s loan to finance their
other needs, or even take the arbitrage
opportunity to lend money from the mill to
others at the market rate.
Mills were apparently aware of this problem and
their contracts stipulated that if a farmer was
caught using the loan for other purposes, he was
subject to a fine two to three times the amount
of his loan.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
Literature
Where to find data to test the theory?
Model modification
Conclusions
Conclusions:
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Our findings support Gangopadhyay and
Sengupta (1987) who proposed that when a
production loan is interlinked with other trade,
the creditor is willing to ask for an interest rate
lower than its cost of capital, and the loss in
lending will be more than compensated by profit
in the other trade.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study
Definition of interlinkage
◮
◮
Literature
Where to find data to test the theory?
Model modification
Conclusions
The interest rate is not as low as their model
predicts. We conjecture that it is because too
low an interest rate would encourage farmers to
borrow more than their investment needs.
The terms in the contracts are largely consistent
with the second best interest rate and the
optimal cane price.
Hui-wen Koo, Chen-ying Huang and Kamhon Kan
Interlinked Contracts: An Empirical Study