Determinants
of Prices of Agricultural
and Mineral Commodities
Jeffrey Frankel,
Harvard University, &
Andrew Rose,
University of California, Berkeley
First draft of a paper for the Reserve Bank of Australia.
To be presented at pre

conference, 16 June, 2009,
Westfälische Wilhelms University Münster, Germany;
Co

sponsored also by CAMA, Australia,
& VERC, Wilfred Laurier University, Canada
2
The determination of prices for oil and
other mineral & agricultural commodities
falls predominantly in the province of
microeconomics.
But in periods when many commodity
prices are moving far in the same
direction at the same time, it becomes
difficult to ignore the influence of
macroeconomics.
The decade of the 1970s.
The decade of the 2000s.
3
►
A rise in the price of oil
might be explained by
“peak oil” fears, a risk
premium on Gulf instability,
or political developments in
Russia, Nigeria or
Venezuela.
►
Some farm prices
might be explained by
drought in Australia,
shortages in China, or
ethanol subsidies in the US.
4
But it cannot be coincidence that
almost all commodity prices rose
together during much of the decade,
and peaked abruptly in mid

2008.
5
Three theories competed to explain the
ascent of commodity prices in 2003

08.
1.
Most standard: the
global demand growth
explanation
, emphasizing especially
growth in China, India, etc.
2.
Also highly popular:
destabilizing speculation
.
1.
Storability & homogeneity
=> asset

like speculation.
2.
But destabilizing?
3.
Expansionary monetary policy
1.
low
real interest rates
2.
expected
inflation
.
6
Counter

evidence to claims of
destabilizing speculation
1. Futures price of oil initially lagged behind
spot price.
2. High volume of trading
≠
net short position
3. Commodities that lack futures markets are
as volatile as those that have them.
4. Historical efforts to ban speculative futures
markets have failed to reduce volatility.
7
The real interest rate explanation
1.
Some argue that high prices for oil & other
commodities in the 1970s were not exogenous,
but rather a result of easy monetary policy.
[1]
2.
Conversely, a rise in US real interest rates in the
early 1980s
.
helped drive commodity prices down
.
[2]
3.
The Fed cut real interest rates sharply,2001

04,
and again in 2008

09.
My claim: it helped push up commodity prices.
[3]
[1]
Barsky & Killian (2001).
[2]
Frankel (1985).
[3]
Frankel (2008).
8
High interest rates
Lower inventory demand;
and
encourage faster pumping of oil,
mining of deposits, harvesting of crops, etc.,
because owners can invest the proceeds at interest rates higher
than the return to saving the reserves.
Both channels
–
fall in demand & rise in supply
–
work to lower the commodity price.
A 3
rd
channel goes the same direction

trading in contracts (“the carry trade”):
Low interest rates induce a “search for yield”
among investors, who go long in commodities
(just as FX, emerging markets.,
etc.)
9
Inverse correlation between
real interest rate and real
commodity price index
(DJ, 1950

2008)
10
Counter

argument that applies to both
the destabilizing

speculation & easy

money theories
(Krugman
, 2008
, & Kohn
, 2008
):
Inventories of oil & other commodities were
said to be low in 2008, contrary to the theory.
Perhaps inventory numbers
do not capture all inventories, or
are less relevant than (larger) reserves.
King of Saudi Arabia (2008):
“we might as well leave the reserves
in the ground for our grandchildren.”
11
But in 2008, enthusiasm for theories (2) & (3),
the speculation & interest rate theories, rose,
at the expense of theory (1), the global boom.
The sub

prime mortgage crisis
hit the US in August 2007.
Thereafter, forecasts of growth fell, not just
for the US but globally, including China.
Meanwhile commodity prices, far from
declining as one might expect from the global
demand hypothesis, accelerated.
For the year following August 2007, at least,
the global boom theory was not relevant.
That left explanations (2) and (3).
12
Definitions
s
≡ the spot price,
S ≡ its long run equilibrium,
p
≡ the economy

wide price index,
q ≡ s

p
, the real price of the commodity,
and
Q
≡
the long run equilibrium real price of
the commodity;
all in log form.
13
Derive the relationship between
q
&
r
from two equations:
Regressive expectations:
E (Δs) =

θ (q

Q)
+
E(Δp
).
(2)
Arbitrage condition between inventories & bonds:
E Δs + c = i,
(3)
where
c ≡ cy
–
sc
–
rp .
cy
≡
convenience yield from holding the stock (e.g., the
insurance value of having an assured supply of a critical input in
the event of a disruption)
sc
≡
storage costs (e.g., rental rate on oil tanks, etc.)
rp
≡
E Δs
–
(f

s)
≡
risk premium,
>0 if being long in commodities is risky, and
i
≡
the interest rate
14
Combining (2) & (3)
gives the relationship:
q

Q =

(1/
θ
) (i

E(
Δ
p
)
–
c) .
(5)
This inverse relationship between q & r
has been supported by:
Event studies
(monetary announcements)
The graphs
Regressions of
q
against
r
in Frankel (2008):
Significant for half of the individual commodities
and in a panel study
and for various aggregate commodity price indices
But much is left out of this equation. Esp. variation in
c.
15
Inverse correlation between real
interest rate and real commodity
price index
(Moody’s,
1950

2008
)
16
Translate convenience yield, storage
costs, & risk premium from equation
(6) into empirically usable form,
with 4 or 5 measurable factors:
1. Inventories.
Storage costs rise with the extent to which
inventory holdings strain existing storage
capacity:
sc = Φ (INVENTORIES).
Can estimate an inventory equation:
INVENTORIES
= Φ

1
(sc) = Φ

1
(cy

i
–
(s

f))
(8)
17
Two more measurable
determinants
2. Real GDP
or industrial production,
representing the transactions demand for
inventories, is a determinant of the convenience
yield
cy
. Call the relationship γ (
Y
).
3. The spot

futures spread,
s

f
.
A higher spot

futures spread (normal
backwardation) signifies a low speculative
return and should have a negative effect on
inventory demand and on prices.
18
The last two are uncertainy
measures
4. Medium

term volatility
(σ), measured
either as the standard deviation of the spot
price or as the implicit forward

looking
expected volatility that can be extracted from
options prices.
Volatility is a determinant of convenience yield,
cy;
and so of commodity prices
It may also be a determinant of the risk
premium.
19
5. Risk
(political, financial, & economic),
in the case of oil,
e.g.,
is measured by a weighted
average of
(inverse)
political risk
for 12 top oil producers.
The theoretical sign is ambiguous:
Risk is another determinant of
cy
(esp. fear of
disruption of availability), whereby it should have a
positive effect on commodity prices.
But it is also a determinant of the risk premium
rp
,
whereby it should have a negative effect on prices.
20
The equation works for oil inventories:
INVENTORIES
= Φ

1
(cy

i
–
(s

f)
)

log_inventories  Coef. Std. Err. t
P>t

+

Real interest rate

.00056
.00033

1.71
0.09
Oil spot

forward 

.00079
.00013

5.98
0.00
Log industr.prod.  .05222
.01968 2.65
0.01
risk
 .00013
.00018 0.69
0.491
Lag log inv
 .93105
00976 95.39
0.000
counter


.00003
.00001

2.21
0.027
counter2


2.78e

09 5.13e

09

0.54
0.588
_constant  .18380
.09458 1.94
0.052

21
The same macro variables work
to determine real oil price:

Log real oil p  Coef. Std. Err. t P>t

+

Log ind.prod.  3.445 .239
14.44 0.00
log inventory  .455
.119
3.82 0.00
Real int.rate 

.052
.004

13.24 0.00
Oil risk  .037 .002 16.25 0.00
s

f spread  .026 .002
15.94 0.00 .
counter 

.006 .0002

34.82 0.00
counter2 
2.84e

06 6.23e

08
45.52 0.00
constant 

19.673 1.143

17.21 0.00

22
Complete equation,
from (5) and (8):
q = Q

(1/
θ
) r
+
(1/
θ
)
γ
(Y) + (1/
θ
)Ψ
(
σ
)

(1/
θ
)
Φ
(INVENTORIES)
(9)
We now test it on 12 commodities,
with data from 1960s to 2008.
23
Booms around 1974

75 and 2008
24
Table 3b

Panel Results,
for
ln
of real commodity prices,
with risk included. Annual data.
Ln(G

7
Real
GDP)
Volatility
Risk
Spot

Futures
Spread
Inven

tories
Real
interest
rate
.82*
2.24
.21

.021**

.16**
.02
(.38)
(1.57)
(.11)
(.006)
(.04)
(.04)
.57*
1.75*

.06

.003*

.15**
.00
(.21)
(.58)
(.04)
(.001)
(.03)
(.01)
Pooled
Commodity
effects
** (*) => significantly different from zero at .01 (.05) significance level.
Robust standard errors in parentheses; Intercept & trend included, not reported.
25
Other tests
6 Major commodity price indices.
Unit root tests
Philips

Perron on individual commodities
& panel
Co

integration tests
Johanson on individual commodities
Panel
Vector error correction
26
Overall conclusions
(as of now)
The commodity

specific explanatory factors
work surprisingly well:
Inventory holdings
Spot

futures spread
Volatility
In the latest results, the macroeconomic
variables work surprisingly poorly:
Economic activity
Real interest rates
27
Possible extensions
Explore other measures of real interest
rate and economic activity.
Try survey data as a direct measure of
expectations.
Estimate simultaneous system
in inventories, expectations or spread,
and commodity prices,
tied directly to the theory.
28
Appendix
Graphs of data
29
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