NBER WORKING PAPER SERIES

COMMODITY PRICES AS A LEADING INDICATOR OF INFLATION

James K. Boughton
William H. Branson

Working Paper No. 2750

NATIONAL BUREAU OF ECONOMIC RESEARCH

1050 Massachusetts Avenue
Cambridge, MA 02138
October 1988

Mr. Branson's work on this paper was completed in part while he was a
Visiting Scholar at the IMF, and in part while a Visiting Scholar at the
Banca d'Italia. We are grateful to Tom Walter, who carried out the empirical
tests for this paper; to a number of colleagues at the IMF, especially Blair
Rourke and Alphecca Muttardy, who helped prepare and interpret the data; to
Mark Watson for a number of suggestions; and to participants at seminars at
the IMF and the Banca d'Italia. The views expressed herein are those of the
authors and should not be attributed to any institution.
 NBER Working Paper #2750
October 1988

COMMODITY PRICES AS A LEADING INDICATOR OF INFLATION

ABSTRACT

This paper studies the value of broad commodity price indexes as

predictors of consumer price inflation in the G-7 industrial countries.
After an introduction, the paper discusses the theoretical relationship
between commodity and consumer prices and the conditions under which, in
general, one would expect commodity prices to be a leading indicator of
inflation. It then presents tests of the relationships between
conventiomal broad indexes of commodity prices and consumer prices, and
uses the data on individual commodities to generate the optimum weights in
a commodity price index for forecasting G-7 inflation. We find that
commodity and consumer prices are not co-integrated; the hypothesis that
there is a reliable long-run relationship between the level of commodity
prices and the level of consumer prices may be rejected. There is a
tendency for changes in commodity prices to lead those in consumer prices,
at least when the data are denominated in a broad index of major-country
currencies. However, although the inclusion of commodity prices
significantly improves the in-sample fit of regressions of an aggregate
(multi-country) consumer price index, the results may not be sufficiently
stable to improve post-sample forecasts. Estimated alternative commodity-
price indexes, in which the weights are chosen so as to minimize the
residual variance in aggregate inflation regressions, track the behavior
of the aggregate CPI reasonably well in-sample. However, the estimated
indexes work only moderately well in post-sample predictions, and they do
not appear to offer significant advantages over the conventional export-
weighted index. Perhaps the most important result is that turning points
in commodity-price inflation frequently precede turning points in
consumer-price inflation for the large industrial countries as a group.

James M. Boughton William H. Branson

Research Department Woodrow Wilson School
IMP Princeton University
Washington, DC 20431 Princeton, NJ 08544
 -1-

I. Introduction

Changes in commodity prices have long played an important indicative

role in analyses of global economic conditions, principally because of

their importance for developing countries. More than 70 countries derive

at least 50 percent of their export earnings from nonfuel primary

commodities; another 20 derive the majority of their export earnings from

fuels (see IMF, 1988, pp. 104-105). Changes in the terms of trade for

these countries typically arise largely from changes in world commodity

prices. Recently, however, attention has also been drawn to the

importance of changes in commodity prices as indicators of changes in

inflationary conditions affecting industrial countries. For example, the

World Economic Outlook recently began to include an analysis comparing

percentage changes in an index of 40 primary commodity prices with the

aggregate inflation rate of the seven largest industrial countries (see

IMF, 1988, p. 11). The task of this paper is to examine the usefulness of

commodity prices as a leading indicator of inflation in the large

industrial countries as a group.

An early exponent of focusing on commodity prices in this context

was Robert Hall. In his 1982 book, Hall argued in favor of basing U.S.

monetary policy on a commodity standard, with the commodities chosen on

the basis of the closeness of their historical fit against the cost of

living. j,J Bosworth and Lawrence (1982) also emphasized the role of

commodity prices as a contributor to the rise in inflationary pressures

j,J The index favored by Hall at that time was limited to four
commodities: ammonium nitrate, copper, aluminum, and plywood (p. 112).
Hall later (1987) emphasized the limitations of that index.
 -2-

during the 1970s. More recently, Federal Reserve Board Governor Wayne

Angell (1987) noted the close qualitative link between turning points in

a broad index of commodity prices and turning points in the U.S. CPI.

Others, notably Klein (1986) and Roth (1988), have examined the

performance of commodity prices as one component of overall predictions of

inflation.
Chart 1 presents inflation rates for the U.S. CPI and a world

export-weighted index of commodity prices; this chart is similar to one

presented by Angell. Two stylized facts emerge clearly. First, there is

a similarity in the cycles for commodity and consumer prices, with the

commodity-price cycles often turning ahead of those in the CPI. Second,

the amplitudes of these cycles are very different (note the differences

in the two scales). There is thus a presumption that the relationship is

more qualitative than quantitative. Chart 2 presents the same type of

information except that CPI inflation is a weighted average of inflation

rates in the seven largest industrial countries, as in the World Economic

Outlook. The qualitative relationships are generally similar in the two

sets of data. These stylized facts are discussed more critically in the

empirical sections that follow.

This paper begins (Section II) by discussing the theoretical

relationship between commodity and consumer prices and the conditions

under which, in general, one would expect commodity prices to be a

leading indicator of inflation. Section III then presents some tests of

the relationships between conventional broad indexes of commodity prices

and consumer prices. In Section IV, the question of using the data to
 CHART 1
RATES OF CHANGE OF COMMODITY PRICES AND
U.S. CONSUMER PRICES, IN U.S. DOLLARS, 1960—87 1
(In percent)
15

12

60 62 64 66 68 70 72 74 76 78 80 82 84 86

60 62 64 66 68 70 72 74 76 78 80 82 84 86

1 Three—month centered moving overage of 12—month inflation rate..

T and P denote trough. and peaks reepectively; In the CP1.
 CHA 2
RATES OF CHANGE OF COMMODITY PRICES AND INDUSTRIAL—
COUNTRY CONSUMER PRICES, IN AN AGGREGATE CURRENCY BASKET,
1960—87 1
(In percent)
15 15
P
AGGREGATE CPI
P

12 12

9. 9

6 6

3 3

0 0
60 62 64 66 68 70 72 74 76 78 80 82 84 86

60 62 64 66 68 70 72 74 76 78 80 82 84 86

Three—month centered moving average of 12—month Inflation rote,.

T and P denote trough. and peak., respectively, In the CP1.
 -3-

generate the optimum weights in a commodity price index is taken up.

Conclusions are summarized in Section V.

II. A Dynamic Model of Commodity and Industrial Prices

This section presents a dynamic model of the relationship between

commodity and industrial prices as a theoretical motivation for the idea

of movements in commodity prices as a leading indicator of general price

level fluctuations. The model treats commodities as either final goods

or inputs, and emphasizes the role of expectations in determining

movements of commodity prices.

An important feature of the model is that commodity prices are

determined in "auction" markets, actually financial markets that trade

commodity contracts, while industrial prices are set by sellers and

adjusted gradually. This permits commodity prices to react immediately

to "news" about future inflation, and to lead adjustment of industrial

prices. The two cases of commodities as final goods or as inputs are

treated separately, but the basic results are the same in both cases.

With unanticipated monetary disturbances, commodity prices overshoot and

lead industrial prices, but with real disturbances the relationship is

less clear. For example, with a supply shock and no monetary accommo-

dation, commodity prices would lead industrial prices, but the two would

move in opposite directions.

1. Commodities as final goods

This subsection discusses a basic dynamic model of the interaction

of commodity and industrial prices in which the two are final goods

entering the CPI, and commodity prices are determined in flexible markets
 -4-

with forward-looking expectations. The model can be interpreted as one

country with two sectors, or as two countries, one producing commodities

and the other a perishable industrial output. The model includes a

monetary sector, in which expectations of commodity price movements are

important, and an industrial sector, in which prices adjust gradually

following excess demand. To focus attention on price dynamics, the level

of real output in the industrial sector is held constant. The model is

an extension of Frankel (1986), which applies the Dornbusch (1976) over-

shooting model to the case of commodity price dynamics.

Equilibrium in the money market is described in the standard form of

equation (1):

(1) m - apm -
(1 -
)Pc — y - U.

Here , p, Pc' and are the logarithms of nominal money, the price of

manufactures, the price of commodities, and real output; j is the nominal

short-term interest rate; and a is the share of manufactures in the CPI.

Commodity price inflation and the interest rate are related by an

arbitrage condition:

(2) i.c+b,

where k is the real return to holding commodities for final use, net of

storage costs, and c is the exDected rate of change of the commodity

price.
 -5-

Substitution of equation (2) into (1) yields the first dynamic

equation:

(3) m - Piu -
(1 -
)pc — - A(pc + b).

The locus of points where — 0 is shown in Figure 1; its slope is

-(1 -

For a point above the ic — 0 line to be consistent with money market

equilibrium, P must be expected to rise. This is because above the line

the CPI is higher, and real balances lower, than on it. This makes the

interest rate higher than k above the — 0 line, so commodity prices

must be expected to rise. If expectations exhibit perfect foresight, c

must actually be rising above the c — 0 line. In other words, a

commodity price level above that consistent with zero expected inflation

must be supported by a positive rate of commodity price inflation.

Similarly, at any point below the c — 0 line, commodity prices would be

falling. These dynamics of c are shown by the horizontal arrows in

Figure 1.

The supply of the industrial good (ym) is assumed to be constant.

Demand is assumed to be an increasing function of the price of

commodities relative to industrial goods, c/m' and a decreasing

function of the real interest rate in terms of the industrial good. Thus

demand is given by

(4) d — 6(pc -
Pm)
-
a(i -
 FIGURE 1
COMMODITY AND
MANUFACTURES PRICES: MARKET
EQUILIBRIUM AND DYNAMICS

S\__ Pm°
N

PC
 -6-

The price of the industrial good is assumed to adjust slowly to

eliminate excess demand:

(5) m — w[S(Pc -
pm)
- o(i -
bin) -
Ym].

The terms on can be consolidated to yield the second dynamic equation:

(6) j — [6(Pc -
Pm)
- ai -
Ym]'

where , — ,r/(l - ira). This term must be positive if a positive shock to

excess demand is to raise the price of industrial goods.

The positively sloped — 0 line in Figure 1 shows the relationship

between the two prices that would maintain zero excess demand in the

market for industrial goods for a given value of the money stock. The

slope of the line is positive because an increase in the commodity price

creates excess demand for industrial output, requiring an increase in the

industrial price to eliminate it. The slope is less than unity because

as prices rise, the interest rate also rises, reducing the demand for

industrial goods. / So as the price of commodities rises, the increase

in industrial goods prices needed to eliminate excess demand is less than

proportional. At points above the m — 0 line, there is excess supply of

industrial goods and the price is falling, assuming 'i > 0. Below the

line, there is excess demand and the price is rising. The dynamics of

adjustment of the industrial price are summarized by the vertical arrows

in Figure 1.

),,/ Upward movement along the m — 0 locus implies > 0; from

equation (2), this requires a rise in the interest rate.
 -7-

The two equilibrium lines in Figure 1 show the equilibrium pair of

prices at E0 for a given money stock and real commodity supply

conditions. The dynamic adjustment to equilibrium is along the stable

saddle path ss. This path has two essential properties. It leads to the

equilibrium, and along it the expected rate of change of the commodity

price is realized. All other paths explode away from the equilibrium;

they are speculative bubbles. The assumption that the market seeks out

the stable ss path is equivalent to assuming that speculative bubbles are

unsustainable. Eventually they collapse, and the market moves back to the

stable path.

The model of Figure 1 can be used to illustrate two properties of

commodity price behavior that are important for constructing a leading

indicator for inflation: following an unanticipated increase in the

money supply, commodity prices overshoot, and they lead the adjustment in

prices of industrial goods. In a situation in which the signals from the

various monetary aggregates are unclear, the movements in commodity

prices can be interpreted as distilling the information in the aggregates

into a clearer signal.

The role of commodity prices as a leading indicator of the infla-

tionary effects of a monetary disturbance is illustrated in panel (a) of

Figure 2, which shows the effects of an unanticipated increase in the

money supply. If the model is interpreted as representing two countries,

this would involve a proportional increase in both countries' money

supplies. The original equilibrium from Figure 1 is at E0 in Figure 2.

An increase in the money supply shifts both the c — 0 and — 0 lines,

and the new long-run equilibrium moves proportionately out to E1. In the
 FIGURE 2
PRICE ADJUSTMENTS WITH
COMMODITIES AS FINAL GOODS

/
,
/ / E0 — —

/
//
$

/ /
/
/ 'C

(a) Monetary Disturbance (Overshooting)

$
/ /
/
/ /
/
// —
=0

/—-- S

PC

(b) Real Disturbance (Undershooting)

 -8-

long run, both prices rise by the same proportion as the money supply.

In the short run, the gradually adjusting industrial price does not move,

but the flexible commodity price jumps to the new ss path at E0'. Then

gradually the industrial price rises and the commodity price falls along

the ss path to the new equilibrium at E1.

The initial jump in the commodity price is consistent with an

initial decline in the interest rate. In the original equilibrium at E0,

the expected rate of commodity price increase is zero, and the interest

rate is equal to . The rise in the money supply increases real balances

initially, reducing the interest rate below . This is consistent with

equilibrium only if commodity prices are expected to fall. So initially

the commodity price must rise by enough to create the expectation that it

will fall during the adjustment period. This generates the jump onto the

new ss path, along which the commodity price falls as expected as the

economy moves toward E1. At that point, real balances and the interest

rate are back to their original levels, and the expected rate of commodity

price inflation is again zero.

The reaction of the model to a real disturbance that alters the

equilibrium relative price of commodities is shown in panel (b) of

Figure 2. As one would expect, it is substantially different from the

reaction to a monetary disturbance. Suppose that a supply shock raises

the equilibrium relative price of commodities. This shifts the 0

line down along the — 0 line to a new long-run equilibrium at

which lies on a ray from the origin that characterizes the new higher

ratio of commodity prices to industrial prices. With no monetary

accommodation, the c — 0 line does not move. The result is that

 -9-

commodity prices jump onto the new ss path at E0' and then continue to

rise, gradually, as industrial prices fall toward the new equilibrium E2.

As is usual in this type of model, the commodity price undershoots in

response to a real disturbance. The industrial price must fall if there

is no monetary accommodation. So in this case commodity prices lead, but

industrial prices move in the opposite direction.

It appears that commodity prices would not be a reliable indicator

of future price developments in the presence of unaccomniodated supply

shocks, unless reliable information were available about the nature and

the effects of those shocks. This problem can be minimized, although

probably not eliminated, by using an index of commodity prices that are

subject to supply shocks from different, preferably independent, sources.

Such an index would resemble a portfolio of commodities with a minimum

aggregate variance from supply disturbances, since at any point in time

positive and negative disturbances would be offsetting. Presumably

movements in this index would be dominated by demand disturbances, actual

or expected, which would be a desirable property of an inflation

indicator.

2. Commodities as inDuts

The case of commodities as inputs can be discussed more briefly,

since only two minor modifications need to be made to the model, and the

results are essentially the same. In the money market, the deflator is

now simply the price of industrial goods, so the dynamic equation (3)

reduces to

(3') m - Pm — y - + b).
 - 10 -

This change makes the c — 0 line in the top panel of Figure 3 horizontal

at the level of the industrial price that clears the money market with

zero expected commodity price inflation. )/ At points above the c 0

line, real balances are lower than on it, so the -interest rate is higher

than k and commodity prices are expected to rise. Below the c — 0

line, commodity prices are falling. These dynamics are illustrated by

the horizontal arrows in the top panel of Figure 3.

The market for industrial output is slightly more complicated. The

demand for industrial goods is a decreasing function of the real interest

rate. The supply of industrial goods is an increasing function of their

price relative to commodities. Therefore, excess demand is a decreasing

function of the relative price of industrial goods and the real interest

rate. This gives a new equation for m:

(6') m — 'i((Pc - Pm) au.

Here fi represents the supply effect, and t is defined as before.

The — 0 locus is the positively sloped line in the top panel of

Figure 3. To hold excess demand equal to zero in the market for

industrial goods with a given increase in the commodity price, the

industrial price would increase less than proportionately because the

interest rate rises. Thus, the — 0 line along which excess demand for

the industrial good is zero has a slope less than unity in the top panel

/ Movement to the right along the c — 0 line in Figure 3 implies

falling value added in the industrial sector, since input prices are
rising against constant output prices. Therefore, if the vertical axis
in Figure 3 measured the price of industrial-sector value added instead
of the price of final output, the Pc — 0 line would be downward-sloping,
as before.
 FIGURE 3
PRICE ADJUSTMENTS WITH
COMMODITIES AS INPUTS

Pm

\
Ic = 0

PC

(a) Market Equilibrium

Pm

, ,
, /
, ,
'2 .
,,
=0

/ , —
,—
,—
, 6,—
—
'-I
PC

(b) Real Disturbance

 - 11 -

of Figure 3. Above this line, there is excess supply and Pm is falling.

elow it, P is rising. The stable dynamic adjustment path is ss in

Figure 3, as in the case of commodities as final goods.

The analysis following an unanticipated increase in the money supply

is the same as that in panel (a) of Figure 2, discussed above. Adjust-

ment to a supply shock that raises the equilibrium price of commodities

relative to that of industrial output is illustrated in the bottom panel

of Figure 3. The m — 0 line shifts out to intersect the c — 0 line at

the new equilibrium price ratio. The commodity price rises, but, with no

monetary accommodation, the price of industrial goods remains unchanged.

The price of value added in the industrial sector or country falls. As

before, it may be noted that a broad index of commodity prices might

essentially average out supply shocks, leaving monetary disturbances to

dominate movements of the index.

In these two models, commodity prices play the role of an inflation

hedge. With gradual adjustment of industrial prices, agents can protect

themselves against an anticipated inflation by buying commodities or,

more generally, commodity futures contracts. The result falls naturally

out of an analysis with two prices, one that adjusts gradually and one

that can jump. The latter becomes the hedge against inflation in the

former. A richer model would include more prices, such as foreign

exchange or domestic equities, that can adjust instantaneously to

inflationary expectations. In such a model, several variables can play

the role of inflation hedge, with a wide variety of over-shooting and

under-shooting behavior. This was shown in Frenkel and Rodriguez (1982).

Then which price is the best indicator of future inflation becomes an

 12 -

empirical question. The conclusion to be drawn from the analysis in this

section is that commodity prices are a reasonable candidate.

III. Emt,irical Tests Usina Conventional Indexes

This section evaluates the empirical relationships between commodity

prices and general price movements in industrial countries. In order to

simplify the discussion, tests will be presented only for consumer rather

than output prices as the objective variable, and only for the large

industrial countries as a group. 1,1 These decisions are somewhat

arbitrary, but there is likely to be a stronger empirical link from

commodity prices to consumer prices than to output prices, especially in

countries that are net importers of primary commodities. Focusing on the

aggregate inflation rate for a broad group of countries may also enhance

the measured importance of commodity prices as a leading indicator;

changes in inflation in individual countries may be relatively more

affected by policy actions and exogenous domestic events and less by

international variables.

1. Construction of data

The first empirical task is to construct a data series for the

aggregate CPI for the large industrial countries. How best to do this is

not obvious, because national price data are in different currencies.

One approach would be to convert the time series data on price levels

into a common currency (say, U.S. dollars or SDRs) and then construct an

average index using GNP, consumption, or some other set of weights. One

./ The countries are the United States, Japan, the Federal Republic of
Germany, France, the United Kingdom, Italy, and Canada.
 - 13 -

would then have a direct estimate of the aggregate price level measured
in that currency. An alternative would be to average the logarithms of

the price levels in local-currency terms. This procedure would give a

more accurate measure of the average inflation experience in the

countries concerned. Which procedure to choose depends on the intended

purpose, but in the present case the choice is complicated because of the

diverse international structure of the markets for primary commodities.

The problem may be illustrated as follows. If the national price

indexes are averaged directly, the aggregate price level is described by

(7) Pt il

where is the logarithm of the aggregate CPI, pj is the logarithm of the

CPI for country j (denominated in the currency of that country), and the

wj are the weights. Alternatively, if the aggregate CPI is to be

denominated in the currency of (say) the first country, then the formula

may be written as

7
—
(7')
wy1 + . wi(ejt +
where ej is the logarithm of the exchange rate for country j, expressed

as the cost of local currency in terms of the currency of country 1.

The difference between these two measures of the aggregate CPI

constitutes an exchange rate between the currency of country 1 and the

 - 14 -

weighted geometric average of the other countries as a group:

(8) p - Pt — —
1X2wiei, et

For the tests in this paper, the aggregate CPI is constructed according

to equation (7); for convenience, the implicit currency basket in which

the data are thereby denominated will be referred to as the "group

currency unit" or GCU. )/

The difficulty posed by this choice is that the relationship between

commodity and consumer prices is not invariant with respect to the

currency in which the data are denominated. In order to isolate the

effects of commodity price movements on inflation from those of exchange

rate changes, it is desirable not only that commodity and consumer prices

be denominated in the same currency or basket, but also that that denomi-

nation correspond as closely as possible to the currency or basket that

is most relevant for the various markets concerned. This last concept,

however, is quite vague and difficult to judge empirically. Most

commodity prices are quoted in U.s. dollars, but a number of them are

quoted in other currencies, including notably pounds sterling, deutsche

marks, and Japanese yen. Furthermore, the currency in which prices are

quoted does not necessarily indicate the currency that is most relevant

for that particular market; for a price quoted in U.S. dollars, for

example, it is possible that movements in the effective exchange rate for

31 This procedure is equivalent to the methodology used in Fund

publications such as the World Economic Outlook for constructing
aggregate inflation rates for groups of countries.
 - 15 -

the dollar could systematically induce corresponding changes in the

dollar price.

The consequences of choosing an inappropriate denomination may be

demonstrated by reference to a simple bivariate model. First, letting

denote an index of commodity prices, note that the dollar-denominated

index (c') may be converted into GCUs:

(9) c_c - et

corresponding to the relationship described for the aggregate CPI in

equation (8). Now suppose that the "true" relationship between commodity

and consumer prices, free of exchange rate effects, holds when the data

are denominated in GCUs, expressed as

(10) Pt — a+ bc + c.

Obviously, if one were to estimate, instead of equation (10), a

regression in which commodity prices were denominated in dollars (or

another currency), a spurious exchange rate effect would be introduced.

Perhaps less obviously, a spurious effect would be introduced even if

kQ.h indexes were denominated in dollars. Suppose one were to estimate

p, — a+ +

which is equivalent to

(10') Pt — a +
ct + (fil)e +
 - 16 -

Unless p — 1, the exchange rate now enters the implicit equation in GCUs,

in contrast to equation (10).

In the absence of detailed knowledge about the nature of the

individual markets, the best that one can do is to use a broad index of

major currencies and to be sure that all data are measured commensurately.

Since the aggregate CPI is constructed according to equation (7), it is

appropriate to measure commodity prices in GCUs, converting dollar prices

by the exchange rate described in equation (8).

The commodity price index to be used for these tests uses a total of

40 prices, weighted according to 1979-81 shares in world exports. ,./ It

is the same index that is used in the World Economic Outlook, as noted in

the Introduction. Preliminary tests suggested that similar results

(though generally not quite as favorable) would obtain using other

weighting methods such as imports or consumption rather than exports. A

major decision is whether to include oil prices, since in 1979-81 oil

accounted for roughly 50 percent of world exports of primary commodities.

The inclusion of oil did somewhat improve the statistical properties in

preliminary tests, and it was therefore included in the final index.

2. Lona-run relationshiDs
The first empirical question to be analyzed is whether there exists

a stable long-run relationship between the level of commodity prices and

the level of consumer prices. If so, then it may be possible to make

quantitative inferences about future CPI inflation from observations of

commodity prices. In the absence of a long-run levels relationship,

Jj For a description of prices, see IMF (1986), Appendix II. The

export weights are listed in Table 4, below.
 - 17 -

there may still be qualitative linkages between changes in inflation

rates in the two data series, but one would want to avoid arguing that

any given change in commodity prices would be expected to be followed

(eventually) by a specified change in consumer prices.

A very simple heuristic approach to this question is to examine the

stationarity of the relative price of commodities. As may be seen from

Chart 3, there has been a general downward trend in this relative price;

the extent of the drift, however, has not been uniform, and it was

starkly interrupted by a sudden and large rise in 1972-73. The

hypothesis that the relative commodity price is unbounded in the long run

would seem to be a reasonable oneto entertain.

One test of this hypothesis is to run augmented Dickey-Fuller

regressions for commodity and consumer prices:

(11) — Pk-i + EjyiXj

where the null hypothesis (no stationarity) is that fi — 0. Since the

data are monthly, without seasonal adjustment, these tests have been run

using 12 lags on As shown in Table 1, the tests have been

conducted over three sample periods, all ending in 1987. In addition to

the full-sample estimates, regressions have been run for samples

beginning in 1972, when commodity prices first began to show substantial

fluctuations; and beginning in 1974, after the apparently unique jump in

commodity prices that occurred in 1972-73.

In the case of commodity prices, the null hypothesis is rejected,

regardless of the sample period. For consumer prices, however, the

hypothesis that fi — 0 cannot be rejected, although the second differences

 CHART 3
COMMODITY PRICES: NOMINAL AND REAL, 196O_871
On GCUs; 1980=100)

125 125

100 100

75 75

50 50

Nominal
25 25

0 76 78 86 0
The real price is obtained by deflating by the eeven—country consumer price index.
 - 18 -

Table 1. Stationarity Tests for Commodity and Consumer Prices j/

Commodity Consumer
Prices Prices

I. Tests for First-Order Stationarity

1960-87 4.54** -0.86

1972-87 -0.73
1974-87 4.49** -1.37

II. Tests for Second-Order Stationarity 21

1960-87 -5.82**
1972-87 394**
1974-87 4.O7**

)j The numbers in this table are t-statistics from estimates of

equation (11) over the indicated sample periods using monthly data. The
distribution of these statistics is not standard; the 95 percent
confidence level for the rejection of nonstationarity (*) is approximately
3.17, and the 99 percent level (**) is approximately 3.77. See Engle and
Granger (1987).

21 These tests are relevant only where the hypothesis of first-order

nonstationarity has not been rejected. -
 - 19 -

appear to be stationary. The implication of these tests is that

conunodity prices are integrated of order 1, whereas consumer prices are

integrated of order 2; that is, the first differences in commodity prices

are stationary, whereas only the second differences of consumer prices

are stationary. In these circumstances, the two data sets cannot be

cointegrated, and the standard cointegration tests are not applicable

(see, for example, Granger (1986)). It is thus possible to turn to tests

of shorter-run relationships, ignoring the long-run constraints that might

otherwise have been imposed by the data. jJ

3. Short-run relationships

The next step is to evaluate the relationship between shorter-run

movements in commodity and consumer prices. For this purpose, it is

helpful to render the data stationary, which may be accomplished simply

by taking second differences of the data. As noted above, commodity

prices are reasonably stationary in first differences, but second

differencing is required to make the full data set stationary. In

addition, in order to reduce the importance of seasonal fluctuations,

inflation rates have been calculated as 12-month changes. Thus, the-

following tests relate to monthly changes in 12-month inflation rates:

z — (x x1)
- -
(xi2 xi3)
-

where x is the logarithm of the relevant index and z is the whitened form

of the data.

/ The absence of cointegration in these data was also documented in

Durand and Blöndal (1988).
 - 20 -

Causality tests

Table 2 summarizes the results of tests of whether commodity prices

"cause," in Granger's sense, consumer prices for the large industrial

countries as a group. The null hypothesis is that the lagged values

ofcommodity prices contribute nothing to predictions of aggregate CPI

inflation, given the predictions from lagged values of the CPI. In

addition, tests of reverse causation are also included. In view of the

ambiguities associated with the currency denomination of the data,

discussed above, the tests have been conducted both with the data

expressed in U.S. dollars and with the data denominated in GCUs.

Finally, given the rather different behavior of both consumer and

commodity prices before and after the early l970s, the tests have been run

over three overlapping samples. The full sample runs from 1960 through

1987; the second sample drops all data before 1972, when commodity prices

first displayed a rise in variability; the third begins after the major

commodity price inflation of 1972-73.

For the full sample (1960-87), the direction of estimated causation

depends entirely on the currency denomination. In terms of U.S. dollars,

it appears that consumer prices lead commodity prices; in terms of GCUs,

the reverse is true. For the shorter samples, there is no evidence of

causation in either direction for non-oil commodity prices. When oil

prices are included in the index, and the data are denominated in GCUs,

there appears to be causation running from commodity to consumer prices.

Given the lack of robustness of the results, it is difficult to draw any

firm conclusions from this exercise. Nonetheless, it does seem warranted

to conclude that if commodity prices are to serve as a leading indicator

 - 21 -

Table 2 Commodity Prices and Industrial-Country Inflation:

Granger Causality Tests LI

Non-oil Commodities All Commodities

Commodity CPI Commodity CPI
prices causes prices causes
cause commodity cause commodity
CPI prices CPI prices

With data in U.S. Dollars:

1960-87 -- ** -- **
1972-87 -- -- -- --
1974-87 -- -- -- *
With data in GCU5:

1960-87 ** -- ** --
1972-87 -- -- ** --
1974-87 *

j,J For the test of whether commodity prices Granger-cause the CPI, the
CPI has been regressed on 18 lagged monthly values of the commodity price
index plus 18 lagged values of itself. For the test of reverse causation,
the two series are switched. Industrial-country inflation is measured by
the average change in consumer prices for the seven largest countries; the
construction of the data is described in the text. All data have been
made stationary by taking monthly changes in 12-month inflation rates. A
single asterisk indicates that the null hypothesis- -that the aggregate
effect of the lagged values of the independent variable is zero- - is
rejected with 95 percent confidence. A double asterisk indicates
rejection of the null with 99 percent confidence.
 - 22 -

of industr-ial-couritry inflation, it is preferable to denominate the data

in terms of a broad currency basket rather than in terms of U.S. dollars.

Full-sample relationships

As a fairly simple test of whether commodity prices contribute to

predictions of inflation, the changes in the aggregate CPI inflation rate

have been regressed on lagged changes in itself plus lagged changes in

commodity-price inflation, using polynomial distributed lags (PDLs). jJ

The null hypothesis for this test is that the contribution of the PDL on

commodity prices does not add to the in-sample explanatory power of the

regression.

The baseline regression, omitting commodity prices, is estimated

(1962-87, monthly data) as

36 292
(12) Pt — .479 DW — 1.60
(3.39) i—l SEE — .224

and the expanded regression result is

36 36 2_
(13) Pt — .315 E + .108 E vjci DW — 1.59
(1.74) i—i (2.95) i—l SEE — .207

The F statistic for the additional contribution of the commodity price

index (c) is 13.8, which implies rejection of the null hypothesis with

more than 99 percent confidence.

/ The specific functional form is a 36-month, 4th-order PDL,

constrained to zero at the far end of the distribution.
 - 23 -

An interesting comparison may be made against predictions using an

aggregate measure of monetary growth in the large industrial

countries. ),J The data series for money stocks has been extended back

only to January 1964; using three-year lags on 12-month inflation rates

and taking moving averages, the regressions for this comparison therefore

start in February 1968. For this sample, a regression using only past

inflation (as in equation 12) has 2 — .345; the addition of a PDL on

current and lagged money growth has 2 — .361. The F statistic for the

significance of this improvement is 2.5 (significant with 95 percent

confidence), compared with 13.8 for commodity prices. It is, of course,

possible that other models- -allowing for other influences or developing

different lag structures--might alter these comparisons. Nonetheless,

there is a prima facie case for the value of commodity prices as an

inflation predictor.

Post-samtle tests

Table 3 presents information on the out-of-sample predictive ability

of commodity prices, with broad-money equations also included for

comparison. For this exercise, regressions such as those in equations

(12) and (13) were run over a series of six sample periods, starting with

1968-77 and then extending by two years up to 1968-85. In each case, the

estimated equations were used to generate dynamic predictions for the

aggregate CPI inflation rate over the 24 months following the end of the

sample. During the prediction period, commodity price inflation and

/ Money stocks in each country are broadly defined (money plus quasi-
money, as defined in International Financial Statistics). These stocks
are aggregated using the same procedure as the CPIs; thus the data are
implicitly denominated in CCTJs.
 - 24 -

Table 3. InfLation Predictions, 1976—87 1/

(In percent)

1976-77 1978-79 1980-81 1982—83 1984-85 1986-87

Actui. Inflation 7.5 9.5 10.3 4.9 3.7 2.1

Baseline Prediction 8.1 7.7 11.0 6.6 4.9 2.8
Baseline Prediction Error 0.6 -1.8 0.7 1.7 1.2 0.7

Predictions Using
Coinoditv Price5:
Predicted Inflation 6.6 5.5 12.0 7.5 4.9 2.7

Reduction in:
In—Sample Error 16.8 14.6 12.2 10.5 9.5 9.5

Prediction Error 2/ -- -- -- -- -- 0.1

RtE -- -- -- -- 2.3 60.9

Prediction Using
Broad Money Balances:
Predicted Inflation 7.5 7.5 10.2 7.5 5.3 2.7

Reduction in:
In—Sample Error 2.9 2.2 1.5 1.3 1.0 0.6
0.6 —-
Prediction Error 2/ 0.6 0.1

R0E —- 12.0 96.2 —- -- 41.0

J Post-sample 24-month dynamic predictions of the aggregate CPI from equations as

described in the text. The estimation sample is from February 1968 (plus prior lagged
data to December of the year preceding the listed forecast period.
I In percentage points.
 - 25 -

broad-money growth were projected on the basis of their own prior

history. As shown in the table, three comparisons were made. First,

didthe inclusion of commodity prices reduce the standard error of the

estimate within the sample period? Second, did the equations that include

commodity prices reduce the forecast error for the average inflation rate

over the two-year horizon? Third, did they reduce the root mean squared

error (RMSE) for the 24 monthly inflation forecasts?

Perhaps the most striking feature of Table 3 is that the RMSE is

reduced by the inclusion of commodity prices in only two of the six

forecast periods: 1984-85 and 1986-87. Throughout these four years, the

prior weakness in commodity prices provided useful information about how

rapidly consumer prices would decelerate. In the earlier periods, the

predictions are worsened somewhat in comparison with those made only on

the basis of the own history of the CPI. The equations using broad money

do somewhat better in the earlier periods, but less well in the last two.

Overall, the inclusion of neither commodity prices nor broad money

could be said to have improved the post-sample inflation forecasts. In

contrast, within each sample period, there is a substantial improvement in

the fit when commodity prices are included, and only a small improvement

when money balances are included. It thus appears that the quantitative

linkages between commodity and consumer prices are significant, but are

not stable enough to permit one to draw quantitative inferences about the

extent to which consumer prices might respond to a given change in

commodity prices.
 - 26 -

IV. Eiii,irical estimates of weiahts

The tests in Section III took as given the weights assigned to each

commodity in the price indexes. The purpose of this section is to examine

the feasibility of estimating optimum weights (optimum in the sense of

generating the best predictions of the aggregate CPI) for a commodity

price index through regression analysis.

a. Estimation of indexes

Two basic approaches have been used to estimate commodity price

indexes on the basis of their relationship with the aggregate CPI. One is

to allow the data to determine the weights freely, with all commodity

prices as contenders for inclusion in the index. The other involves

constraining the data, by eliminating negative weights and, in the final

set of estimates, by initially aggregating commodities that have small

weights in industrial-country trade or consumption into somewhat broader

categories. The second approach was intended to check whether the

efficiency of the estimates might be improved by the constraints.

Estimation using all available commodity Drice data

The objective of the first approach is to allow the maximum freedom

for the data to "speak" in determining the "best" weights for commodities

for the purpose of predicting CPI inflation. This approach uses the

prices that are incorporated into the available It'll commodity price

indexes, plus the prices of gold and petroleum, in an unconstrained

regression framework. There are some 30 years of monthly observations on

the 40 commodity price series, extending from January 1958 through Sep-

tember 1987. With a forecast horizon chosen to run from 1 to 36 months,

the problem is to devise a procedure that narrows quickly to the most

 - 27 -

important explanatory variables over different forecast horizons with a

minimum of loss in efficiency in utilizing the information in the data.

The procedure that was employed to estimate "optimum" indexes was as

follows. First, the aggregate CPI and all 40 series, expressed as

logarithms of GCU-denominated indexes, were transformed by taking the

first differences of their 12-month differences (i.e., changes in

inflation rates). Second, the forty principal components were extracted

from the data matrix of the transformed commodity price data, to produce

orthogonal regressors. Third, a multiple regression was estimated over

the period February 1962 to December 1982 with the transformed CPI as the

dependent variable and the forty principal components as independent

variables (with the constant suppressed) separately at each lag length

from 1 to 36 months. The termination of the sample at the end of 1982 was

chosen so as to leave a reasonably long post-sample period for testing the

stability of the results.

These regression results were used to select significant principal

components for the remaining analysis. Two selection criteria were used

to narrow the set of principal components. The first was to rank themby

average absolute t-ratio across lags. The second was to select principal

components with coefficients that were significant at the 1 percent level

at at least 4 different lags, of which at least one was longer than 12

months. The second criterion yielded eight principal components, of which

six coincided with those in the highest eight on the average absolute

t-ratio criterion. Thus the two criteria together yielded a list of ten

candidate principal components for the next stage.

 - 28 -

Next, a regression was estimated with the transformed CPI as the

dependent variable, and fourth-order PDLs with length 36 months

(constrained to zero at the far end only) on the candidate principal

components as independent variables along with a similar PDL on the lagged

transformed CPI. This regression (over the 1962-82 period) had an

adjusted R2 of .57, compared with .32 for a regression of the transformed

CPI only on its own lags. Each of the ten selected principal components

contributed significantly to this regression. Finally, the coefficient on

the weighted (and normalized) lag distribution on each principal component

was taken as an estimate of the contribution of that component to the

index being derived.

The lag distributions on the ten principal components in the final

regression differ in length and shape. Therefore, when the implied

weights on the commodity prices are retrieved, a weighting matrix is

obtained, which in principle would have a different set of weights for

each lag length. Thus the distributed lag coefficients on the final

principal components equation could be used to estimate a different set of

weights for the commodity prices at each forecast horizon, reflecting

differences in the information in the various commodity prices for

explaining aggregate CPI inflation at different forecast horizons. This

step was not taken at this stage. Instead, a single set of weights was

calculated, reflecting the average information in the commodity price

series across forecast horizons. These are the weights shown in the first

column of Table 4.

The most notable feature of the weights in the unconstrained index

is that about half of the commodities have negative weights. In

 - 29 -

Table 4. Econometrically Estimated Weights for

Commodity Price Indexes j/
(In percent)

Memorandum:
Eliminating Using World
Negative Prior Export
Commodity 2/ Unconstrained Weights Aggregation Weights 2/

Cereal 2L1 1Q
Wheat -4.8 -- 5.0 5.1
Maize 60.8 7.3 3.7 3.8
Rice -77.8 -- 1.6 1.6

Vegetables ..LJ
Soybeans 16.0 10.9 3.9 4.5
Other -20.6 1.2 1.0 1.2

Meat 3.9 3.3

Beef -38.7 -- 2.8
Lamb 32.4 3.9 0.5

Sugar 2.Li

Bananas

Beverages 1Q
Coffee -19.7 12.1 3.8
Cocoa 42.5 5.1 1.6
Tea 15.5 1.9 0.6

Agricultural
new materials 26.3 52.2 12.0
Timber 60.0 7.2 15.6 5.4
Cotton -88.7 -- -- 2.0
Wool -39.1 -- -- 1.2
Rubber 25.9 3.1 11.9 1.3
Tobacco 54.5 6.5 24.7 1.3
Other 46.4 9.4 -- 0.7

Metals -7.6 23.1 2.1 14.9

Copper 24.3 2.9 0.4 3.0
Aluminum -0.5 -- 0.3 2.3
Gold 5.0 0.6 0.5 3.7
Iron ore 62.6 7.6 0.3 2.1
Other -99.1 12.1 0.6 3.8

Petroleum 25.8 3.1 29.4 45.5

Total 100.0 100.0 100.0 100.0

J Detail may not add to totals, owing to rounding.

Several of the listed commodities are divided into two or more
2/
components in the full data set. Jhen negative weights were reset to
zero for the second index, the calculations were made at that
disaggregated level.
/ Based on 1979-81 data. Source: IMF, Commodities Division.
 - 30 -

particular, within most groups, some commodities have positive and some

negative weights. The reason for the negative weights is not that a rise

in the price of a particular commodity, by itself, would be expected to

lead to a fall in consumer prices; it is rather that the regression

essentially computes the weights for an optimal portfolio of commodity

prices that minimizes the residual error vis-a-vis the CPI. This

procedure assigns negative weights to some prices that have positive

covariance with the others. Small changes in specification could easily

reverse the signs on individual commodities. The individual weights

therefore should not be assigned much intrinsic value.

The time path of this index is shown in the far left panel of

Chart 4. It is apparent that this is a much more volatile index than

the others. In 1974 it even took on negative values, reflecting rapid

increases in prices- -especially certain metals- - that have negative

weights in the index. Nonetheless, a moving average of this index would

have a time profile reasonably similar to those of the other indexes

shown in the chart.

A regression of the transformed aggregate CPI on its own history plus

a 36-month PDL on this first index yielded an adjusted R2 of .32. The

reduction from .57 is a measure of the cost of time aggregation into a

single index; in fact, it may be seen that most of the improvement over

equation (12) has been lost through time aggregation. The out-of-sample

performance of this index is examined in the next subsection.

 ECONOMETRICALLY ESTIMATED INDEXES, THE EXPORT—WEIGHTED INDEX,
AND CONSUMER PRICES, 1960—87
(In GCUs; 1980=100)
240
Negative Weights Eliminated
(Second Index)
210

180

150

120

90

60

30

—30

—60
 - 31 -

Estimation subject to constraints

The second index was derived from the first by simply eliminating all

of the commodities whose prices had negative coefficients in the first

index. The weights for this index are shown in the second column of

Table 4. As may be seen by comparing these weights with the export

weights in the last column of the table, and by examining the movements

in the index as shown in Chart 4, this index looks more like a conven-

tional price index than does the unconstrained version.

A regression of the transformed aggregate CPI on itself lagged, plus

aPDL on the transformed version of this second index, yielded an adjusted

R2 of .33, which is slightly higher than that for the first index but

still well below the performance of the conventional export-weighted

index (equation 13, above).

The third index (third column of Table 4 and lower left panel of

Chart 4) was derived by a procedure that differed in two major respects

from that used for the first two indexes. First, most of the prices in

the original set of forty were aggregated into broader categories, in

order to reduce the amount of detailed information required for the

estimation process and to eliminate the possibility that a commodity with

relatively little importance in trade or consumption might have a large

weight in the estimated index. This aggregation procedure, using world

export weights, produced six aggregates (cereals, vegetable oils,

 - 32 -

beverages, meat, metals, and fibers) and five single commodities (sugar,
petroleum, rubber, tobacco, and timber). )/

When these 11 prices were converted into stationary series by taking

changes in 12-month rates of change, there was very little multicol-

linearity in the data matrix. Therefore, it was decided to compute the

regressions using these transformed prices rather than their principal

components. Thus the second stage of the procedure was to regress the

transformed aggregate CPI on PDLs of the 11 transformed price series,

plus the PDL on its own lagged values. 2/ That regression yielded an
adjusted R2 of .52, compared with .57 for the unconstrained estimation of

the first index. As before, the coefficients on the sums of the lag

distributions from this regression were normalized to sum to unity and

were used as the weights for the third index. The time profile for this

index (Chart 4) is quite similar to that of the export-weighted index,

although there are periods when they move independently. A regression

using a PDL on this index had an adjusted R2 of .43; this is the best in-

sample result for any of the four indexes.

j/ The prices of bananas, hides, jute, and sisal, which did not fit
neatly into the sub-aggregates and which had a small weight in both
consumption and trade, were elimated from this data set. The price of
sugar for this exercise is a weighted average of the three prices in the
full data set (a free market price and the U.S. and European Community
import prices).
2/ In order to further simplify the procedure, the lag lengths in this
regression were shortened to 12 months (except for petroleum, whose
effect ran out to 24 months), the polynomials were constrained to third
rather than fourth degree, and the end-point constraint was dropped. -
 - 33 -

b. Evaluation of the estimated indexes

The properties of a leading indicator are, of course, not well

defined by how well they fit within the sample period. This subsection

therefore examines the post-sample properties of the estimated indexes. -

These properties are summarized in Table 5, which may be compared with

the results presented above in Table 3.

As with the full-sample results, it may be seen that the third index

does much better than the other two estimated indexes, and a little

better than the export-weighted index, in terms of reducing the standard

error of the estimate for in-sample CPI predictions. Post-sample,

however, the unconstrained index does quite a bit better: the average

prediction error is reduced in three of the six periods, and the RMSE is

reduced in four of six cases.

The apparently poor overall quantitative performance of commodity

prices as additional inflation predictors is attributable in part to the

difficulty of forecasting commodity prices during the forecast period.

When actual commodity prices are used in the post-sample period, the

prediction errors drop sharply. The use of a 24-month dynamic forecast

period is a harsh standard, and the choice is to some extent arbitrary.

Given the strong in-sample performance- -especially for the third estimatec

index as well as for the export-weighted index- - it is likely that better

results would be obtained for shorter horizons.

Qualitative relationships may be as important as quantitative ones

if commodity prices are to serve as a leading indicator. That is, one

may be at least as interested in predicting turning points in CPI

 — 34 —

Table 5. Inflation Predictions Using Estimated Coiiinodity Price Indexes, 1976-87 /

(In percent)

1976—77 1978-79 1980—81 1982—83 1984-85 1986-8?

Actual Inflation 7.5 9.5 10.3 4.9 3.7 2.1

Baseline Prediction 8.1 7.7 11.0 6.6 4.9 2.8
Baseline Prediction Error 0.6 -1.8 0.7 1.7 1.2 0.7

Predictions Using First

(Unconstrained) Index:

Predicted Inflation 7.9 8.4 11.0 6.3 4.9 3.3

-
Reduction in:
In—Sample Error 4.8 5.0 5.3 4.3 4.7 4.3
Prediction Error 0.2 0.7 -- 0.3 -- --
RE 32.8 27.0 —— 21.1 19.0 -—

Prediction Using Second

(Positive-Weight) Index:
Predicted Inflation 8.3 6.0 11.2 7.3 6.4 4.3

Reduction in:
In—Sample Error 8.0 8.5 6.5 6.5 6.3 5.3

Prediction Error -- -- -- -- -- --
-- -- -- -- -- --

Prediction Using Third

(Prior—Aggregation) Index:
Predicted Inflation 3.8 6.2 11.8 7.5 3.8 3.2
Reduction in:
In-Sample Error 18.2 16.4 15.2 14.7 12.5 12.6

Prediction Error -- -- -- -- 1.1 --

RHSE -- -- -- -- 94.6 12.7

/ Poet-sample 24-month dynamic predictions of the aggregate CPI from equations as

described in the text. The estimation sample is from February 1962 (plus prior lagged
data to December of the year preceding the listed forecast period.
 - 35 -

inflation as in predicting the value of the future inflation rate. It

was already noted (see Chart 1) that there is an observed tendency for

inflation in the export-weighted commodity price index to display

cyclical patterns that are similar to those of the aggregate CPI

inflation (though with differing amplitudes) and that frequently lead CPI

turning points. This tendency is examined more closely in Table 6.

The first three columns of Table 6 list the turning points in the

aggregate CPI inflation (denominated in CCTJs) since the beginning of

1970. j,./ These turning points are defined by a shift in direction that i

sustained for at least three months. For a peak, it is also required tha

it exceed the previous trough by at least 75 basis points; troughs must b

at least 50 basis points below the previous peak. These requirements are

obviously rather arbitrary, but they do capture the major turns in CPI

inflation, taking account of the general upward drift in the data.

The remaining columns of Table 6 indicate the lead times that one

would have obtained from various commodity price indexes, or from

monetary growth. These lead times are shorter than the actual lead times

usually by three or four months, in order to take account of the need for

identifying a turning point. For example, when commodity price inflation

reaches a trough, one cannot immediately identify it as such; only after

it has risen for two or three months can one know that a trough has

occurred. These turning points are defined as for the CPI, except that

the required magnitudes are larger and are symmetric, reflecting the

L' The 1960s were eliminated from this test because the aggregate CP1
displayed very little cyclical behavior during that decade.
 - 36 -

Table 6. Prediction of Turning Points in Aggregate CPI Inflation

Turning Points in Lead Time for Predic tion J

Agarezate CPI Inflation (in months)
Peak or Inflation Export First Second Third Broad
Date Trough Rate Weights Index Index Index Money

Feb. 1970 P 6.0 -- 4 -- -- 1

June 1972 T 3.9 -- 6 6 4 --

Nov. 1974 P 13.7 7 -- Ox 7 --

July 1976 T 7.1 6 -- Sx 6 --

June 1977 P 8.2 lx 15 2 2 --

April 1978 T 6.4 -- -- -- -- 7

April1980 P 12.1 0 16 6 -- --
Dec. 1986 T 1.0 2x -- lix lx --
Nov. 1987 P 3.1 0 -- -- -- --

1/ A indicates that a false signal preceded the correct one.

- - indicates
that (a) the index was pointing in the wrong direction at the
time of the turning point in the CPI or (b) that the index called the turning
point more than 18 months in advance or before the preceding turning point.
 - 37 -

different patterns in the data. j/ A lead time of zero months is treated

as a successful prediction, because the commodity price data are available

a few weeks earlier than the CPI data.

The main conclusion to be drawn from Table 6 is that the commodity

price indexes- -with the exception of the first (unconstrained) estimated

index--are reasonably successful predictors of turning points. The

conventional export-weighted index predicted six of the nine turning

points, as did the second estimated index. These indexes gave from one tc

three false signals over the 18-year period. The third estimated index

predicted five turns, while the first predicted four. 21 In contrast,

growth in the aggregate stock of money predicted only two of the nine

turning points in the aggregate CPI.

V. Conclusions

This paper has argued that commodity prices might serve as a useful

leading indicator of inflation, based on the relative importance of

flexible auction markets for the determination of these prices. They thw

may have a tendency to respond relatively quickly, especially in response

to monetary disturbances. This conclusion holds regardless of whether

primary commodities serve mainly as final goods or as industrial inputs.

j/ For the first estimated index, which is highly volatile, the

required swing is 50 percentage points. For the other commodity price
indexes, the required swing is 5 percentage points. For broad money, the
requirement is the same as that for the CPI.
21 The results for the estimated indexes are hypothetical and
illustrative, because the indexes were constructed using data through
1982 and so could not have been used to predict the earlier turning point
 - 38 -

Empirical evaluation of conventional trade-weighted commodity price

indexes leads to several conclusions. First, commodity and consumer

prices are not co-integrated; the hypothesis that the relative price of

primary commodities is bounded, or that there is a reliable long-run

relationship between the level of commodity prices and the level of

consumer prices, may be rejected. Second, there is a tendency for changes

in commodity prices to lead those in consumer prices, at least when the

data are denominated in a broad index of major-country currencies. When

the data are denominated in U.S. dollars, consumer prices appear to lead

commodity prices. This conclusion underscores the importance of making

appropriate allowances for exchange rate changes in analyzing these

relationships. Third, although the inclusion of commodity prices

significantly improves the in-sample fit of regressions of an aggregate

(multi-country) consumer price index, the results may not be sufficiently

stable to improve post-sample forecasts. The prediction record, however,

improves in the most recent period.

Estimation of alternative commodity-price indexes, in which the

weights are chosen so as to minimize the residual variance in aggregate

inflation regressions, was not fully successful. The derived indexes do

track the behavior of the aggregate CPI reasonably well in-sample. On the

other hand, the weights are not robust with respect to changes in the

methodology, and the indexes work only moderately well in post-sample

predictions. Overall, the estimated indexes do not appear to offer

significant advantages over the conventional export-weighted index.

 - 39 -

The bottom line is that commodity prices do have a useful role to

play in this context, but one must be careful to interpret the

relationships correctly. The ratio of consumer to commodity price

movements changes over time, and the relative price of commodities

undergoes long sustained swings; nonetheless, the qualitative linkages

are quite evident in the data. Perhaps most importantly, turning points

in commodity-price inflation frequently precede turning points in

consumer-price inflation for the large industrial countries as a group.

 - 40 -

References

Angell, Wayne D., "A Commodity Price Guide to Monetary Aggregate

Targeting," paper prepared for Lehrman Institute, December 10, 1987.

Bosworth, Barry P., and Robert Z. Lawrence, Commodity Prices and the New

Inflation, The Brookings Institution (Washington), 1982.

Dornbusch, Rudiger, "Expectations and Exchange Rate Dynamics," Journal of

Political Economy, Vol. 84 (1976), pp. 1161-76.

Durand, Martine and Sveinbjorn BlOndal, "Are Commodity Prices Leading

Indicators of OECD Prices?" OECD Department of Economics and

Statistics, Working Paper No. 49 (February 1988).

Engle, Robert F. and C.W.J. Granger, "Co-Integration and Error

Correction: Representation, Estimation, and Testing,"

Econometrica, Vol. 55 (March 1987), pp. 251-76.

Frankel, Jeffrey A. "Expectations and Commodity Price Dynamics: The

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Frenkel, Jacob A. and Carlos A. Rodriguez. "Exchange Rate Dynamics and the

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(Washington) Vol. 29, No. 1 (March 1982), pp. 1-30.

Granger, C.W.J., "Developments in the Study of Cointegrated Economic

Variables," Oxford Bulletin of economics and Statistics, Vol. 48

(August 1986), pp. 213-28.

Hall, Robert E. (1982), Inflation: Causes and Effects, (Chicago: The

University of Chicago Press), 1982.

 - 41 -

Hall, Robert E. (1987), "Choice of Indicators for Monetary Policy,"

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