Full text of Review (Federal Reserve Bank of St. Louis) : May 1976

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FE D E R A L RESER VE B A N K
OF ST. LOUIS
m ay 1976

Food and Population: A Long V ie w ..........

2

Preferred Habitat vs. Efficient
Market: A Test of Alternative
Hypotheses ................................... 11

Vol. 58, No. 5




Food and Population: A Long View
CLIFTON B. LUTTRELL

w

TT ITH the sharp increase in food prices in 1973
and 1974, the world food-population ratio began to
receive increasing attention. Writers in both profes­
sional journals and more widely read magazines have
pointed to the prospect of rising world food costs and
starvation in the years ahead.1
The recent predictions, that per capita food
production will decline, are consistent with the basic
classical argument of the early 1800’s that the growth
rate of the world population tends to exceed that of
food production. These views are founded on pre­
sumptions of major constraints to increasing crop
y ie ld s and a con tin u in g high rate of w o rld p o p u la tio n
growth.2 The alleged constraints to food production
growth, however, give little recognition to the diver­
sity of the food-population problems among different
1Writings which represent these views include: Paul R.
Ehrlich, The Population Bomb (New York: Ballantine Books,
1968); Lawrence A. Mayer, “We Can’t Take Food for
Granted Anymore,” Fortune (February 1974), pp. 85-89
and 132-36; Gene Karetz, “The Global Food Shortage,”
Business Week, June 8, 1974, p. 63; “The Fat Years and
the Lean,” The Economist, ^ (November 2, 1974), p. 19;
“Formula for World Famine?”, U.S. News and World Report,
January 28, 1974, pp. 50-52; Wayne Bartholomew and George
A. Wing, “Profiles of the Future, Arab Petroleum = American
Food,” Business Horizons (Indiana University Graduate
School of Business, Vol. XVII, Number 6, December 1974),
pp. 5-14; “In the End, Even U.S. May Not Be Able to Feed
the World,” U.S. News and World Report, May 27, 1974, pp.
57-58; Lester R. Brown and Erik P. Eckholm, ‘Food and
Hunger: The Balance Sheet,” Challenge ( September-October
1974), pp. 12-24; Willard W. Cochrane, “Food, Agriculture,
and Rural Welfare: Domestic Policies in an Uncertain
World,” American Journal of Agricultural Economics, Vol­
ume 56, Number 5 (December 1974), pp. 989-997; and
“ U.S. Food Power: Ultimate Weapon in World Politics,”
Business Week, December 15, 1975, pp. 54-60.
2Ehrlich, Population Bomb, pp. 44 and 46-47; Brown and
Eckholm, ‘ Food and Hunger,” pp. 12-24; and Cochrane,
“Food Agriculture and Rural Welfare,” pp. 989-91.


Page 2


economies of the world, let alone take account of the
economic factors which affect the incentive to reduce
food production costs.
This article postulates that the United States and
the other more developed nations (M D Cs) will not
experience rising real food costs over the longer run
despite some increase in the early 1970s and the
numerous reports which point to world famine. It
hypothesizes that the food-population ratio in the
various nations of the world is largely a function of
the size and composition of per capita wealth, and
that per capita wealth remains near the subsistence
level for most of the less developed nations (L D C s).
Consequently, they are still subject to periodic fam­
ines. However, famines in the LD Cs will not spill
over into the MDCs which have gradually increased
per capita wealth and been free from famines for
more than a century.

Early Food - Population Views
Predictions of rising food scarcity and limits to
productivity growth are not of recent origin. Such
allegations can be traced back several centuries. They
became widely accepted following the writings of the
classical economists in the late 1700s and early 1800s.
Giovanni Botero in 1589 postulated that population
tends to increase to the limits imposed by the means
of subsistence.3 Adam Smith contended that the
means of subsistence limits the multiplication of
humans and all other species of animals.4 He and
3Joseph A. Schumpeter, History of Economic Analysis (New
York: Oxford University Press, 1954), pp. 254-55.
4Adam Smith, The Wealth of Nations (New York: The Modem
Library, 1937), pp. 79, 81.

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

other classical economists viewed the food producing
qualities of land as being highly inelastic with re­
spect to other inputs. They believed that any gains in
yields resulting from new technology would be quickly
offset by population growth.®
David Ricardo, a leading proponent of the classical
view on returns to land, reasoned that (1) rent arises
because of differences in soil fertility; (2) the value
of production on the unit of least fertile land in use
will only be sufficient to cover costs of nonland
inputs thus yielding no rent; (3) labor values are
determined by returns to labor on the less fertile
acres; and (4) marginal productivity of labor will
decline over time as the population increases and ad­
ditional marginal acres are brought under cultivation.
The proponents of this view held that the total
volume of real wages is relatively fixed, being limited
to a worker’s output on the least fertile land times
the total number of workers. Consequently, as popu­
lation increases, per capita real wages were expected
to decline, and starvation among the marginal non­
landed classes was expected to become widespread.
On the other hand, returns to the landed classes
would tend to rise since the difference in yield be­
tween the more fertile and the marginal acres would
be greater and rents higher.6
Thomas Malthus, the leading proponent of the
classical starvation view, contended that there is no
limit to the prolific reproduction of people except
when imbalances resulting from their crowding in­
terfere with each other’s means of subsistence. He
postulated that under favorable conditions the means
of subsistence might increase in an arithmetic ratio,
whereas population tends to increase in a geometric
ratio, doubling each twenty-five years.7
James Mill and other early 19th century writers
further developed the subsistence argument into a
wages-fund theory. Mill substituted all forms of capi­
tal for land in the Malthusian model and argued
that a decrease in the ratio of capital to population
over time will cause (real) wages to decline, imply­
ing a reduction in per capita output of all goods and
services including food. Like Malthus he believed that
population tended to increase at a faster rate than
5Smith, The Wealth of Nations, pp. 94-95; David Ricardo,
The Principles of Political Economy and Taxation (London:
J. M. Dent and Sons, Ltd., 1948), p. 279-80, and Thomas
Robert Malthus, On Population, ed. Gertrude Himmelfarb
(New York: Random House, 1960), pp. 151-57.
SRicardo, Principles, pp. 273-92.
7Malthus, On Population, pp. 154, 156.



MAY

1976

Table I

M A J O R FA M IN E S IN W ESTERN EUROPE
Date

Place

Estimated Deaths

3 1 0 A.D.

England
Rome

4 0 .0 0 0

436
1005

England

N.A.

101 6

Europe

N.A.

1 06 9

England

N.A.

1235

E ngland
Central and
W estern Europe

2 0 ,0 0 0 (in London)
1 0 % of population over
wide area

Italy

N.A.

1 3 1 5 -1 7
1 3 4 7 -4 8

N.A.

1693

France

176 9

France

1 8 1 6 -1 7

Ireland

7 3 7 .0 0 0

1 8 4 6 -4 7

Ireland

1,000,000

N.A.
5%

of population

N .A . — not available.
Source: Encyclopedia Britannica, 1970 ed., s.v. "Fam in e” .
Encyclopedia Am ericana, 1970 ed., s.v. “ Fam ine” .

capital, and was held in check by the limits on real
wages, i.e. the means of subsistence.8

Early Views Consistent with Evidence
The classical food supply views appear to explain
population growth throughout most of recorded his­
tory. Prior to the industrial revolution in the 1800s,
per capita wealth and production was relatively low
throughout the world and famines occurred frequently
even in the more developed areas. Some periods of
major famine reported in Western Europe are listed
in Table I. The great Irish famine of 1846-47 follow­
ing the failure of the Irish potato crop was the last
major famine to occur during peacetime in either
Western Europe or the United States. The population
of Ireland declined more than two million, or about
25 percent as a result of the famine, related deaths,
and migrations.

Threat of Famine Continues for Most People
World food production per capita has trended up
in recent decades, but the overall improvement has
been relatively modest. Food production per capita
rose one percent per year during the decade 1954-64
and about 0.8 of a percent per year during the decade
1964-74 (Table II). Total food production rose at
rates of 3.0 and 2.7 percent, respectively, in the two
decades. However, population growth was maintained
at a 1.9 percent rate throughout both decades, off­
setting much of the increase in food production.
8]ames Mill, Elements of Political Economy, Reprints of Eco­
nomic Classics (New York: August M. Kelley, Bookseller,

1963), pp. 40-50.

Page 3

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

1976

Table II

G R O W T H OF W O R LD PO PU LA TIO N A N D F O O D P R O D U C T IO N
(A ve rage A nnu al Rate of C hange)
1 9 5 4 -6 4

1 9 6 4 -7 4
Food Production

Food Production
Per
Capita

Population

Total

M o re Developed Countries*

+ 1 .3 %

+ 3 .0 %

+ 1 .7 %

Less Developed C o u n trie s**

+ 2.4

+ 3 .1

W orld

+ 1.9

+ 3 .0

+0.6
+ 1.0

Population* * *

Total

Per
Capita

+1.0%
+2.6

+ 2 .7 %

+ 1. 8 %

+ 1.9

+ 2.7

+ 0.8

+ 2.6

0

♦Western Europe, N orth America, Oceania, Eastern Europe, and the U.S.S.R.
♦♦A frica, F ar East, Latin America, N ear East, and the Asian Centrally Planned Countries.
♦♦♦1964-73.
Source: U .S.D.A., The World Food Situation and Prospects to 1985, Foreign Agricultural Economic Report N o. 98, December 1974.

Furthermore, the rate of increase in food produc­
tion per person varied widely among the world econ­
omies. During the decade ending in 1974 all the per
capita increase occurred in the MDCs. The rate of
increase in total food production in the LD Cs de­
clined from 3.1 to 2.6 percent per year from the
decade ending in 1964 to the decade ending in 1974,
about the same as that in the MDCs. However, the
population growth rate in the LDCs rose from 2.4
percent in the decade ending in 1964 to 2.6 percent
in the latter decade, whereas the population growth
rate in the MDCs declined from 1.3 to 1.0 percent
(Table II). The rise in population during the latter
decade in the LDCs exactly offset the increase in
total food output while food production per capita
continued up in the MDCs at about the same rate as
in the earlier decade. Furthermore, more than a third
of the LDCs experienced a decline in per capita
food production during the 20 years ending in 1972.
Many people in the LDCs, which include Latin
America, and most of Asia and Africa, probably
remain near the Malthusian level of subsistence.
These nations have relatively high rates of population
growth and low rates of capital accumulation and
productivity per capita both on their farms and in
other industries. They add about 61 million to the
world’s population each year and account for 86 per­
cent of the world’s annual population increase.9 More
recent comparisons indicate a leveling off in the popu­
lation growth rates of these regions; however, there
is still little tendency for their rates of population
growth to decline.
Reflecting the low productivity levels in the LDCs,
their diets generally remain near the subsistence level.
9United States Department of Agriculture, The World Food
Situation and Prospects to 1985, FAE Report No. 98, 1974,
pp. 12-14 and 75.

Page 4



In 1970 per capita calorie and protein consumption
in these nations averaged only 69 and 60 percent,
respectively, of such consumption in North America.
Furthermore, the proportion of food obtained from
animal products was only about one-fifth of that in
the U.S.10
If the LDCs produced a large quantity of non-food
products, they could, as Japan has done, achieve
higher dietary standards by exchanging such products
for food produced by the MDCs. But, total produc­
tion of all goods per person in the LDCs is relatively
low and consists largely of subsistence type products
used domestically. In 1972, for example, national in­
come totaled only $55 billion in India, $54 billion in
Brazil, $16 billion in Turkey, $7 billion in Colombia,
and $2 billion in Ethiopia. National income totaled
$1,041 billion in the United States.11 A few of the
LDCs produce sizable quantities of crops and other
commodities for export such as coffee and soybeans
in Brazil, sugar in the Philippines, palm oil in Ma­
laysia, feed grains in Argentina, and petroleum in
the Organization of Petroleum Exporting Countries
(O PEC ), but as a general rule their low rate of
production does not provide a sufficient quantity of
foreign exchange to trade for large quantities of ad­
ditional food.
Saving and investment in capital goods are appar­
ently increasing in the LD Cs at a higher rate than
population growth, indicating some gains in the per
capita stock of capital. The Commission on Interna­
tional Development found that savings and gross in­
vestment in these nations totaled 15 and 17.8 percent,
10Food and Agricultural Organization of the United Nations,
Monthly Bulletin of Agricultural Economics and Statistics
(September 1974), pp. 3-6; and USDA, World Agricultural
Situation (December 1973), p. 51.
n United Nations, Monthly Bulletin of Statistics (February
1976).

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

respectively, of Gross National Product (GNP) dur­
ing the period 1960-67. However, saving and invest­
ment relative to GNP is still very low in the LDCs,
averaging well below that of the MDCs.12
Foreign aid has been a source of new capital in
many of the LDCs. Such aid has been evident in
providing machinery and equipment for industry, for
building roads and railways, ports, fertilizer plants,
and irrigation facilities. Some of the LDCs, especially
the more advanced, have received sizable amounts of
private capital. However, few LDCs present a favor­
able climate for private investment, either from for­
eign or-local sources. As pointed out by the Commis­
sion on International Development, “too few of these
countries recognize the tremendous contribution which
private investment can make to economic develop­
ment and in an environment unsympathetic to all
private entrepreneurship it is hardly suiprising that
foreign investors sense danger.”13 As indicated by
D. Gale Johnson a strong case can be made that the
major barriers to growth in the LDCs are political in
nature. He contends that the barriers to rising per
capita food supplies are neither primarily economic
nor scientific. However, he suggests that conditions
for significant increases in food production include:
a major expansion of agricultural research in the de­
veloping countries themselves, an adequate supply of
modern inputs required to increase yields, the im­
provement and expansion of the irrigated area, in­
centives to farmers to make the required changes
(including the expansion of the cultivated area), and
improvements in transportation, marketing, and proc­
essing institutions and facilities. In addition, increased
investment in human capital and improved com­
munications is desirable, not only because of its con­
tribution to increased agricultural output but also
because of the need to assist farm people in the longrun adjustments they must make to economic growth.14
The relatively low level of capital formation in the
LDCs carries over into their investment in knowledge
related to food production. In 1965 expenditures on
agricultural research and extension sendees in the
LDCs relative to farm production was only about
one-half of that in the MDCs.15
12Commission on International Development, Partners in De­
velopment (New York: Praeger Publishers, 1969), p. 31.
13Ibid, p. 105.
14D. Gale Johnson, World Food Problems and Prospects
(Washington, D.C.: American Enterprise Institute for Public
Policy Research, June 1975), pp. 77 and 79.
15Robert E. Evenson and Yoav Kisler, "Investment in Agri­
cultural Research and Extension: A Survey of International



MAY

1976

The LDCs have achieved some growth in recent
years increasing their real GNP at an estimated aver­
age rate of 4.8 percent from 1950 to 1967, or con­
siderably faster than that of the MDCs during their
early stage of development.16 However, because of
the accelerating rate of population growth, per capita
income growth has been relatively modest, and many
of the LDCs have realized very little, if any, per
capita income gains.
Individual nations formerly in the LD C group have
managed to move into the MDC group over time.
Occasionally a less developed country begins to make
progress. Once a significant amount of progress is
made and the political climate for private investment
is improved, imported private funds along with en­
hanced private domestic savings become major
sources of development capital. Then the LD Cs tend
to move into the more developed category of na­
tions. Notable examples of such movements in recent
decades have been Japan, Israel, and Greece. Fur­
thermore, once substantial progress has been made
few nations have dropped back into the low-productivity class. As long as low production persists,
however, the food supply-population situation in most
of these nations will not have a major impact on
food prices in the MDCs.

Food Still Limits Population Growth in
Some Areas . . .
Classical theories that population is limited by the
means of subsistence are consistent with the experi­
ence in many of the LDCs. People still exist near
the subsistence level in many of these nations, and a
year or two of below-average crop yields can result
in famine, severe malnutrition, and a slower growth
or decline in population. India, for example, has ex­
perienced a number of major famines since 1800.
Eleven major famines were reported in some parts
of the nation since then, as shown in Table III. The
longest interval between the major famines listed in
these sources was from 1900 to 1943 and other
sources list a number of famines even during this
interval.17
The preponderance of evidence indicates that low
per capita production has reduced the rate of popuData,” Economic Development and Cultural Change (April
1975), p. 510.
16Commission on International Development, Partners in De­
velopment, p. 27.
17See, for example, Rajpat Rai, England’s Debt to India (New
York: B. W. Huebsch), 1917, p. 267; and Dr. M. Arokiaswami
and T. M. Royappa, The Modern Economic History of India
(Madras-2, India: Newman Book House, 1959), p. 335.

Page 5

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

Table III

FA M IN E S IN IN D IA SIN C E 1800
Date
1 8 0 3 -4
1 8 3 7 -3 8

Place

Estimated Deaths

Western India

Thousands

Northwest India

8 0 0 ,0 0 0

1861

India

N.A.

186 6

India, Bengal
and O rissa

1,500,00 0

India, Rajputana,
Northwest and
Central India,
Punjab and Bom bay

3 3 % of total
population
in
Rajputana

1 8 6 8 -7 0

1874

India

N.A.

1 8 7 6 -7 8

India

5 ,0 0 0 ,0 0 0

1 8 9 6 -9 7

India

5 ,0 0 0 ,0 0 0

1 8 9 9 -1 9 0 0

India

1,2 50 ,0 0 0

India, Bengal

1,500,00 0

India

N.A.

1 9 4 3 -4 4
196 4
N .A . —- not available.

Source: Encyclopedia Britannica. ed.. s.v. "Fam in e” .
Encyclopedia A m ericana, ed., s.v. "F a m in e” .

lation growth in India during the past century from
what it would have otherwise been. Ansley Coale
and Edgar Hoover, using census data, show a small
decline in the nations population from 1891 to 1901,
and growth of less than one-sixth of one percent per
year from 1891 to 1921. They found a fairly constant
birth rate, but fluctuating death rates in response to
major epidemics and famines.18 Rajpat Rai estimated
that if the famines had not occurred, the population
of India would have been about 40 million greater
that it was in 1901.19
The acceleration of India’s population growth rate
in recent decades is also consistent with the classical
population-subsistence thesis. For example, during
the forty years from 1891 to 1931, the population re­
mained relatively stable, rising only 0.2 of a percent
per year. Available production data for this period
indicate little change in per capita wealth and in­
come. Colin Clark calculated that output of all
goods and services per breadwinner remained un­
changed from 1909-13 to 1935-38. On the basis of
NBER estimates GNP per person in the United States
during this period grew at an average rate of .9 per­
cent per year.20 Coale and Hoover found that since
18Ansley J. Coale and Edgar M. Hoover, Population Growth
and Economic Development in Low-Income Countries
(Princeton: Princeton University Press, 1958), pp. 30-31.
18Rajpat Rai, England’s Debt, p. 266.
20Colin Clark, The Economics of 1960 (London: Macmillan
and Company, Ltd., 1944), chart under back cover, and
U.S. Department of Commerce, Long-Term Economic
Growth 1860-1965.
Digitized for Page
FRASER
6


1931
have
riod.
rate

1976

both population and food production in India
increased rapidly compared to the earlier pe­
Population has increased at a 1.8 percent annual
and food production at a 1.6 percent rate.21

The somewhat faster rate of population growth rel­
ative to food production in India in recent decades
can be attributable to a larger volume of food im­
ports, improved internal transportation which facili­
tated food movements among the various provinces,
and improved health practices which limit the deaths
caused by diseases associated with malnutrition. Since
the late 1940s imports of food have averaged about
5 percent of total usage, whereas previously the na­
tion was largely self-sufficient. A large percentage of
the food imports have been financed by the MDCs
under various government aid programs. Farm com­
modity imports from the U.S., financed largely through
Government aid programs, averaged almost $300 mil­
lion per year during the last two decades.22 Sub­
sidized food shipments by the United States to India
began in 1935-36, but were relatively small until the
1950s. Then food shipments began to increase sharply
under the authority granted in Public Law 480 which
provided for the exchange of food for nonconvertible
Indian currency.
India has been able to increase yields and produc­
tion of cereal grains but the gains were not sufficient
to offset expanding consumption. From 1960-62 to
1969-71 average yields in India rose at an annual rate
of 2 percent and population rose at a rate of 2.6 per­
cent. Production of grains rose at a 3 percent rate, as
the acreage planted to grains was increased, but
grain consumption rose at a 3.4 percent rate.23
While food export subsidy programs of the U.S.
and other MDCs have prevented major famines in
recent years, the basic causes of malnutrition in India
and some other LD Cs have not been eliminated.
Professor Theodore W. Schultz, who has studied the
effects of aid, concluded that such shipments of food
products cannot solve the basic malnutrition prob­
lem.24 In a similar view Harry Walters reported
increasing food deficits and a growing dependence
on food imports in the traditional agricultural econo21Coale and Hoover, Population Growth, p. 30; UN Statistical
Yearbook; and World Almanac, 1974 ed., S.V. “India” .
-'-USDA Foreign Agricultural Trade of the United States,
(May 1974), p. 24.
23U.S.D.A., The World Food Situation and Prospects to 1985,
p. 18.
24Theodore W. Schultz, Economic Crises in World Agriculture
(Ann Arbor: The University of Michigan Press, 1965), p.
3, 19.

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

percent more food per capita than the LDCs. While
accounting for only one-fourth of the increase in
world population since the mid-1950s they accounted
for three-fourths of the increase in world food
output.27

Table IV

A V E R A G E YIELDS PER ACRE
U.S.
(Bushels)

W heat

1 8 6 6 -6 9

1928-31

1 9 7 1 -7

12.6

14.7

31.4
25.5

Rye

11.3

1 1.4

Corn

24.3

24.2

86.9

O ats

28.0

30.5

50.3

Barley

23.0

22.1

4 1 .7

Source: U.S.D.A., A gricu ltu ra l Statistics, annual issues; B a rley :
Acreage, Yield, Production, P rice , Value by States 1866195S, Statistical Bulletin No. 421 ; C o rn : Acreage, Yield,
and Production o f — , June 1954 ; F a rm Production, Farm
Disposition, and Value o f Oats 1909-191*1, July 1944 ;
Flaxseed and R y e : Acreage, Yield, Production, Price, Value
by States 1866-1953, Statistical Bulletin N o. 254; Wheat:
A creage, Yield, and Production, Statistical Bulletin N o. 158,
February 1955 ; C rop Production, various issues.

mies such as India.2r’ Thus, the age-old problem of
starvation and famine has not disappeared for many
people.
Technical assistance programs designed to enhance
food output in the LDCs likewise have not signifi­
cantly altered their food-population relationships.
Schultz concluded that in Latin America little real
per capita gain has resulted from our contribution of
$44 million to such programs from 1943 to 1955. Nine
Latin American countries lost ground on a per capita
basis, two of which had 110 programs; and eleven
countries gained, one of which received no assistance.
On average Latin America’s agricultural production
increased no faster than the rate of population growth.
Hence, very little association existed between such
programs and the well-being of the people.26

. . . But Many Nations Are No Longer
Subject to Famines
In contrast to the continued threat of famine in
many nations, for more than a century no famines
have occurred in most of the MDCs. These nations,
including the United States, Canada, Western Europe,
the U.S.S.R., Australia, and New Zealand, have had
relatively low rates of population growth and high
rates of capital formation and production. Their pop­
ulations grew at an average rate of 1.3 percent per
year from 1952 to 1962 and at a 1.0 percent rate from
1962 to 1972 (Table II). They produced three-fourths
of the world’s food output in 1973 and consumed 50
25Harry Walters, The World Food Situation (Report to the
Committee on Agriculture and Forestry for the 1975 U.S.
Agricultural Outlook, December 23, 1974), pp. 20-29.
26Schultz, Economic Crises, p. 55.



1976

Those MDCs such as Japan which are not self
sufficient in food production produce large quanti­
ties of other goods in which they have greater rela­
tive efficiency, and exchange such goods with other
nations that can produce food more cheaply. Hence,
even though they possess few food producing re­
sources, they do not have a serious food-population
problem.

Return to Famines Unlikely in the U.S.
Despite the sharp increase in world food costs in
recent years there is little evidence that the MDCs
are returning to the economic status of the LDCs.28
Real food costs over the long run reflect basic farm
product supply and demand conditions, and evidence
does not support the view that these conditions have
changed toward a reduction in the real food supply
in the United States and other MDCs. The long-run
food supply factors after adjustment for inflation have
moved sharply counter to the classical predictions
of universal famines for more than half a century. In
contrast to the classical view that crop yields are
relatively fixed, and that real returns to land will rise
with population growth, the evidence in recent dec­
ades supports the opposite view. The importance of
the original properties of the soils has declined rela­
tive to that of other investments in determining crop
yields.
Crop yields in the U.S. were relatively stable from
the 1860s, when yield data were first recorded, until
the early 1930s, tending to confirm the classical
views. Com yields averaged 24.3 bushels per acre in
the four years 1866-1869, inclusive, and 24.2 bushels
per acre in 1928-31 (Table IV). Rye yields were like­
wise relatively stable during this period. Wheat and
oat yields rose somewhat but barley declined. In
contrast to the stability of yields prior to the early
1930s, however, yields since then have increased
sharply. Com yields have more than tripled, wheat
and rye have more than doubled, and oats and barley
have almost doubled.
27U.S.D.A., The World Food Situation and Prospects to 1985,
pp. 14-16.
28For an opposite view, see Ehrlich, Population Bomb, pp. 44
and 46-47; Brown and Eckholm, “Food and Hunger, ’ pp.
12-24; and Cochrane, “Food Agriculture and Rural Welfare,”
pp. 989-91.

Page 7

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

Rising yields since the 1930s largely reflect the
increasing application to land of capital investments
in man-made productive factors. The quantity of such
yield increasing investments is determined by relative
prices and the incentive for invention and discovery.
Inventions and discoveries have contributed to more
viable seed, heartier and more productive plants,
shorter growing season requirements, lower-cost fer­
tilizers, a more balanced supply of plant nutrients,
improved weed, disease, and insect controls, crop
rotations, soil management, and improved planting,
cultivating and harvesting procedures. More efficient
machinery and equipment, has led to efficiencies in
planting, tillage, harvesting, irrigation, and drainage.
Real wages in the U.S. have also failed to follow
the predictions of Mill and other proponents of the
classical thesis who contended that population would
rise faster than capital formation and reduce wages
to the subsistence level. Instead of remaining near
the subsistence level real wages in manufacturing
have increased in each 20-year period during the last
60 years (Table V ). Real wages rose at an average
rate of two percent per year during the 60-year
period. Hence, in contrast to the food-population sub­
sistence theories espoused by the classical economists,
major gains in per capita wealth, production, and
income, have occurred in the United States. The
classical theories of relatively fixed soil productivity,
rising rents, and slow rate of capital formation did
not envision the extent of man’s ability to increase
production in the MDCs. Their population theories
overestimated man’s incentive to multiply and under­
estimated his wealth accumulations and productive
capacity in these nations. As a consequence, the sup­
ply of food and other real goods has expanded at a
faster rate than population growth.
Table V

E A R N IN G S —

P R O D U C T IO N W O R K E R S IN

M A N U F A C T U R IN G , UNITED STATES
A nn u al Rate
of Change
from
Previous Date
(real w ages)

Nom ina! W e e kly
W a g e Rate

W a g e s Adjusted
for C hanges in
Consumer Prices

1 91 4

$ 10.92

$ 36.28

193 4

18.20

45.39

+ 1 .1 %

195 4

70.4 9

87.57

+ 3.3

1974

176 .00

119 .16

Date

1 9 1 4 -7 4

+ 1.6
+ 2.0

Source: U.S. Departm ent o f Labor, Em ploym ent and E arnings
Statistics f o r the United States 1909-1972, pp. 35 ; E m ploy­
m ent and Earnings, September 1975, p. 73 ; and Bureau o f
Labor Statistics releases fo r price index data.


Page 8


1976

Recent Food Price Disturbances Do Not
Reflect a Change in Trend
While real food costs in the United States rose
sharply in 1973 and 1974, evidence points to shortrun explanations for much of the increase. A number
of short-run factors have had a stimulative effect on
food prices. Government food subsidies to lower in­
come groups have increased sharply, tending to en­
hance total food demand since 1969. The total value
of Federal distributions under the Food Stamps, Food
Distribution, and Child Nutrition programs of the U.S.
Department of Agriculture rose from $1.2 billion in
1969 to $5.5 billion in 1974, and to $6.8 billion in 1975.
While these programs may be permanent, the mo­
mentum of their upward pressure on food prices
should decline if fewer families are hereafter added
to the food aid lists.
Demand for food for export was enhanced by
relatively unfavorable weather over part of the world.
The much publicized Russian wheat sales and the
larger grain sales to Western Europe in 1972 reflected
poor crop growing conditions and a sharp increase
in production of livestock products in these areas. A
sharp cutback in Peruvian fish meal production in late
1972 and 1973, a source of protein for animal feed,
also contributed to higher demand for U.S. livestock
feed.
A number of factors on the supply side of the
domestic market also contributed to the food price
increases. Wage-price controls, environmental regula­
tions, relatively poor domestic weather conditions, a
sharp increase in fuel costs as a result of the OPEC
petroleum monopoly, and changes in the international
terms of trade all tended to reduce domestic food
supplies from what they would otherwise be.
Domestic wage and price controls in effect during
the early 1970s were especially harmful to the food
industry. They held the prices of some inputs, such as
fertilizer, below long-run equilibrium levels, which
reduced the incentive to expand output. Conse­
quently, fertilizer “shortages” developed and, once
the controls were lifted, fertilizer prices rose above
long-run equilibrium levels. Both the “shortages” and
the higher input prices, which followed the lifting
of the controls, tended to increase food costs. The
freeze on meat prices in the summer of 1973 was also
harmful. It reduced the incentive for farmers to pro­
duce, thus delaying increases in livestock production.
Environmental and safety programs imposed on a
wide scale have tended to reduce the supply of all
goods and services including food. Controls on chemi­

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

1972=100
750

---------

Price Changes for Food
and Selected Farm Products
ANNUA
DATA

1172=100

TERLY
TA

r

ANNUA
DATA

EGGS

None of the above factors appear to be the type
that will alter trend movements. Some, such as the
environmental protection measures and the oil cartel,
will cause only a once-and-for-all reduction in the
food supply (reduced quantity supplied at any given
price) unless further restrictive measures are taken.
On the other hand, per capita wealth is likely to
continue upward and the flow of cost-reducing tech­
nologies into the food industry is likely to be main­
tained causing the supply of food to continue to
increase.
The turnaround in food production and price pros­
pects for food this year relative to other prices is
evidence that food prices rose above longer-run equi­
librium levels following the short-run disturbances in
1972 and 1973. The disturbances largely affected the
prices of grain and other livestock feed. Average feed
prices increased sharply leading to reduced output
and higher prices for animal food products. But, fol­
lowing the large crop harvested last fall, grain prices
declined sharply and all food prices began to level
off. Consequently, the spread between food and all
consumer prices, that had developed since 1972, be­
gan to close ( see chart). During the period of sharply
increasing food prices, the percent of U.S. disposable
personal income spent on food at home rose, increas­
ing from 12.5 percent in 1972 to 13.1 percent in 1975.
With the turnaround in food prices relative to other
consumer goods, the percent of personal income spent
on food may resume its downward trend in 1976.

Summary and Conclusion
Fear of famines is not of recent origin. The tendency
for population growth to exceed that of food produc­
tion has been recognized as critical to the well-being



w

/
f

FOO

_

____

D NSUM

100

250

O U A fi TERLY
DA T A

A\

.

E D G R > IN S

The depreciation of the dollar relative to other na­
tion’s currencies in 1971 was likewise a short-run cost
increasing factor. It changed the relative prices of
internationally traded goods. Prices of domestic goods
to foreign purchasers were reduced and prices of
foreign goods to U.S. purchasers were increased.
Consequently exports of U.S. agricultural products
rose and imports of goods declined resulting in fewer
goods for domestic use including food.

1976

r

cals for crops and on growth additives for livestock
feed have both tended to increase farm production
costs and reduce food supplies. The OPEC oil cartel
which quadrupled the export price of oil has been an
important cost-increasing factor since late 1973. En­
ergy costs quickly permeate throughout the economy
and affect costs of producing all goods and services.

MAY

J'

\
\

'

V
- '"
BR O IL E R s r J

--

^

150

M IL K

x

R PRICE IN D E X

STEERJ A N D F EIFE R ^S

Jn
50

1972

1973

1974

1975

1976

1972

1973

1974

1975

1976

So u rc e : U .S.D .A . A g ric u lt u ra l P rice s, D a ir y S itu a tio n , P o u ltry a n d E g g S itu a tio n , Liv e sto c k
a n d M e a t Situ a tio n , a n d U.S. D e p a rtm e n t o f L abo r.
L atest d a ta p lotted: 1st q u arte r 1 9 7 6 b a s e d on e stim ates o f la te st d a ta a v a ila b le

of man throughout history. From time to time some
analysts propose that the solution to this imbalance
should receive top priority. Others, however, view it
as a continuous age-old problem associated w:.th
wealth accumulation and economic growth. To the
latter group the food shortages and starvation in the
LDCs is another episode in the classical model of
economic development and a problem not subject to
solution by “crash” programs.
The threat of famine is not worldwide. Essentially
two worlds exist in terms of per capita food sup­
plies— one, the LDCs, in which growth of popula­
tion tends to approach that of capital accumulation
and productivity, and to be limited by the means of
subsistence, and another, the MDCs, in which capital
and real per capita income growth is at relatively
high rates and population growth is at a relatively
low rate.
Famines in the LDCs during the past two decades
have been inhibited by food aid programs of the more
developed nations. This aid, however, has not im­
proved their per capita productivity. In contrast it
may have worsened their food-population relationship.
The success of technical assistance programs for
the LDCs has likewise been questioned. Some have
suggested that a large portion of future aid be chan­
neled toward a major expansion of research in the
LD Cs themselves. It is also apparent that progress
toward increasing total output could be quickened
by providing a more favorable political climate for
saving and capital investment in the LDCs. With a
more favorable climate for capital investment, tech­
nicians which accompany such investment serve to
hasten the technical training of the local work force,
Page 9

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

an important factor in achieving rapid gains in
production.
While starvation will likely remain a major prob­
lem in the LD Cs until a sizable increase is achieved
in per capita wealth and production, a downtrend in
the food supply is not likely to occur elsewhere. Sup­
ply and demand conditions in most of the LDCs do
not have a major impact on food supplies and prices
in the more affluent economies. Although they re­
ceive gifts from the MDCs, and some export sizable
quantities of goods, most of the LDCs have a rela­
tively small impact on world food prices.
Consequently there is little danger that starva­
tion and famines in the LDCs will spill over into the
more developed nations. The MDCs have in recent
years experienced some short-run reversals in real
food cost but the basic trend in food costs continues
downward. The growth of capital, technology, and
knowledge in these nations has continued. These




MAY

1976

factors increase man’s ability to produce goods and
services. Moreover, there has been no tendency in
recent years for their populations to increase at a
faster rate than heretofore. Instead of accelerating,
their population growth rate has declined. Conse­
quently, instead of a change toward scarcity and
famine, once the short-run disturbances are past, the
downtrend in real food costs is likely to be resumed.
If the LD Cs increase their wealth and develop
the capacity to expand output of nonfood goods suf­
ficiently to trade for major quantities of food, such
trade would not be detrimental to the well-being of
the MDCs. By trading food freely with such nations
the MDCs would be able to get more goods and
services from their scarce resources than if they pro­
duced solely for their own consumption. Consequently,
the MDCs have nothing to fear from the possibility
of rising productivity and rising food demand in the
LDCs.

Preferred Habitat vs. Efficient Market:
A Test of Alternative Hypotheses
LLAD PHILLIPS AND JOHN PIPPENGER*
Llad Phillips and John Pippenger are both Associate Professors of Economics at the University
of California at Santa Barbara. The following paper is based, in part, on research done while
Professor Pippenger was a visiting scholar at the Federal Reserve Bank of St. Louis in 1974. The
views expressed herein are solely those of the authors and do not necessarily represent the views
of the Federal Reserve Bank of St. Louis or the Federal Reserve System.

T
I HE standard Keynesian view is that actions taken
by monetary authorities affect aggregate demand by
altering interest rates. Since investment and consump­
tion presumably depend primarily on intermediate
and long-term rates and central banks operate pri­
marily in short-term markets, a transmission mechan­
ism is needed to explain how monetary policy affects
aggregate demand. Expressing long-term rates as a
distributed lag of short-term rates provides one such
link.
The Preferred Habitat hypothesis of interest rate
determination, as developed by Modigliani and Sutch,
has received rather wide acceptance in econometric
model building. The hypothesis of Modigliani and
Sutch implies that long-term interest rates depend on
a 16 quarter distributed lag of short-term interest
rates.1 The particular form of dependence implied
by the Modigliani-Sutch hypothesis is widely recog­
nized as the dominant lag structure and this lag
structure has been incorporated into several large
econometric models.2
There is, however, an impressive body of empirical
evidence indicating that interest rates follow a random
walk; that is, movement in a given period is inde­
pendent of movements in previous periods.3 This
°W e would like to thank Robert Rasche and Michael Ham­
burger for their helpful comments and suggestions.
1Franco Modigliani and Richard Sutch, “Innovations in Interest
Rate Policy,” American Economic Review (May 1966), and
“Debt Management and the Term Structure of Interest Rates:
An Empirical Analysis of Recent Experience,” Journal of
Political Economy, Supplement (August 1967).
-See, for example, the Federal Reserve-MIT-Penn model and
RDX2 developed by the Bank of Canada.
3See for example, G.O. Bierwag and M.A. Grove, “A Model of
the Structure of Prices of Marketable U.S. Treasury Securi


evidence is consistent with the hypothesis that capital
markets are efficient in the sense that prices fully
reflect all available information.4 If capital markets
are efficient and both long-term and short-term in­
terest rates essentially perform a random walk, then
long-term rates are not determined by a long dis­
tributed lag of short-term rates. If long-term interest
rates do not depend on a distributed lag of short-term
rates, then some important econometric models con­
tain a potentially serious misspecification.
This conclusion would be particularly relevant for
the FRB-MIT-Penn model. In this model, the trans­
mission mechanism is essentially from monetary ac­
tions to short-term interest rates, to long-term interest
rates, to aggregate expenditures, output and employ­
ment.5 Since the effect of short-term rates on long­
term rates is distributed over 16 quarters, the effects
ties,” Journal of Money, Credit and Banking (August 1971);
C.W.J. Granger and H.J.B. Rees, “Spectral Analysis of the
Term Structure of Interest Rates,” Review of Economic
Studies (January 1968); John Pippenger, “A Time Series
Analysis of Post-Accord Interest Rates: Comment,” Journal
of Finance (September 1974); and Richard Roll, The Be­
havior of Interest Rates (New York: Basic Books, 1970).
For some conflicting evidence, see Stanley Diller, The Sea­
sonal Variation of Interest Rates, NBER Occasional Paper
No. 80, 1969.
4For an excellent survey of the evidence bearing on and sup­
porting the Efficient Market hypothesis, see Eugene Fama,
“Efficient Capital Markets: A Review of Theory and Empiri­
cal Work,” Journal of Finance (May 1970).
5“ . . . the structure of our model implies that the money supply
can affect consumption, as well as every other component of
demand, only through its effect on the short-term rate . . .”
Franco Modigliani, “Monetary Policy and Consumption:
Linkages via Interest Rate and Wealth Effects in the FMP
Model,” Consumer Spending and Monetary Policy: The Link­
ages, F. Modigliani et al. (Federal Reserve Bank of Boston,
1971, pp. 61-62).

Page 11

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

1976

of monetary actions tend to be spread over a very
long period of time.6

market expectations about future short-term rates con­
tain both regressive and extrapolative elements.8

The long distributed lag from short-term to long­
term interest rates in the FRB-MIT-Penn model may
at least partially explain why that model yields sub­
stantially different estimates from that indicated from
St. Louis Federal Reserve Bank research concerning
how rapidly nominal income responds to monetary
policy. For example, the original Andersen-Jordan re­
sults suggest that the response of nominal income to
a change in the monetary base is completed within
about only four quarters. On the other hand, Modig­
liani describes the response of nominal income in the
FRB-MIT-Penn model to a change in unborrowed
reserves as follows: “The response is clearly rather
slow, as the money supply responds but gradually to
the increase in reserves and in turn GNP responds
gradually to the change in M. Still, by the end of the
third year, the GNP multiplier seems to be close to its
limiting value.”7

According to Modigliani and Sutch, the long-term
rate L ( t ) depends on current and past short-term
rates S(t) and a risk premium F (t ) that reflects the
difference between the premium on long-term and
short-term bonds generated by the Preferred Habitat.

The results of our tests lead us to reject the
Modigliani-Sutch Preferred Habitat hypothesis in
favor of the Efficient Market hypothesis. This con­
clusion indicates that the FRB-MIT-Penn model em­
bodies a misspeeification of the transmission mechan­
ism for monetary policy. In particular, our results
suggest that the FRB-MIT-Penn model and other
econometric models using a similar distributed lag
relationship between long-term and short-term inter­
est rates are likely to overstate the length of the lag
from monetary policy to employment, income, and
prices.

ALTERNATIVE HYPOTHESES
Modigliani-Sutch Preferred
Habitat Hypothesis
As developed by Modigliani and Sutch, the Prefered Habitat model (hereafter referred to simply as
M&S and PH, respectively) is a combination of three
logically independent hypotheses. One is that market
participants have a preferred habitat, that is, they
tend to match the term structure of their assets and
liabilities. The second is that long-term rates depend
on expected future short-term rates. The third is that
6In models which incorporate monetary channels of influence
other than, or in addition to, the cost of capital channel, the
shortening of the lags between the changes in money and
the long-term interest rate would not necessarily shorten the
lags between changes in money and output, prices, and
employment.
7Franco Modigliani, “Monetary Policy and Consumption,” p. 54.

12
Digitized forPage
FRASER


(1) L(t) = a + 0oS(t) +

16
v j8iS(t - i) + F(t) + n(t)
i= 1

The |3i’s first rise and then fall as a result of extra­
polative and regressive expectations.9
Since various proxies for F (t) have yielded at best
only weak results, this term has been omitted in prac­
tice. The operational version of the Preferred Habitat
hypothesis therefore is
(2) L(t) = a' + A ,S(t) +

16
S ftS (t - i) + n'(t)
i= l

where F(t) is now absorbed into the constant a ' and
error term r|'(t).

Efficient Market Hypothesis
The essence of the Efficient Market hypothesis is
that current interest rates fully reflect all available
information. This hypothesis is in conflict with the
Modigliani-Sutch postulate that market expectations
contain both regressive and extrapolative elements.
If capital markets are efficient and interest rates es­
sentially perform a random walk, then market ex­
pectations contain neither regressive nor extrapolative
elements.10
8Although the second and third hypotheses are logically sepa­
rate, they are not independent empirically. As long as we
do not have any direct measure of expected future short­
term rates, the hypothesis that current long-term rates depend
on expected future short-term rates is empirically empty
without a theory of how those expectations are formed.
9Modigliani and Sutch, “Innovations in Interest Rate Policy,”
p. 188.
10In a later paper, Franco Modigliani and Robert J. Shiller
attempt to demonstrate that a similar model is consistent
with the concept of Rational Expectations developed by
J. F. Muth. Although the concepts of Rational Expectations
and Efficient Markets seem to have much in common, the
two approaches have developed almost entirely independ­
ently, and the relationship between them is not at all clear.
See Franco Modigliani and Robert J. Shiller, “Inflation,
Rational Expectations and the Term Structure of Interest
Rates,” Economica (February 1973). For some apparently
conflicting results, see Thomas J. Sargent, “Rational Ex­
pectations and the Term Structure of Interest Rates,”
Journal of Money, Credit and Banking (February 1972),
as well as Michael J. Hamburger and Elliott Platt, “The
Expectations Hypothesis and the Efficiency of the Treasury
Bill Market,” Review of Economics and Statistics ( May
1975).

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

A large amount of empirical evidence indicates
that there is essentially no exploitable regularity in
the movement of interest rates. If that is correct, and
capital markets are efficient, then current interest
rates fully reflect all available information, and there
should be no systematic relation between current
long-term rates and lagged short-term rates. In other
words, if past short-term rates contain information
about future long-term rates that is not fully reflected
in current long-term rates, as is the case in the PH
model, then current long-term rates do not fully re­
flect all available information, and in this sense long­
term capital markets are not efficient.
In order to provide an explicit hypothesis against
which we can test the PH hypothesis of M&S, we
develop a simplified Efficient Market hypothesis (here­
after referred to as SE M ).11 For simplicity, the im­
pact of new information on capital markets is ar­
bitrarily divided into three components: the impact
of new information that is relevant primarily to the
determination of short-term rates x(t), the impact of
new information that is relevant primarily to long­
term rates y(t), and the impact of new information
that is relevant to both rates z(t).
Under these assumptions, current long-term and
short-term interest rates can be described as follows:
(3) L(t) = L(t - 1) + M t) + y(t)
(4) S(t) = S(t - 1) + z(t) + x(t)

where x(t), y(t) and z(t) are independent of each
other and each is distributed independently over time.
This approach is based on the idea that both long­
term and short-term rates essentially perform a ran­
dom walk and that they are related to each other to
the extent that both respond to the same information
z(t). This suggests we can express the relation be­
tween long-term and short-term rates as follows:
(5) L(t) = L(t - 1) + AAS(t) + u(t)

where u(t) is a nonserially correlated random varia­
ble. However, since AS(t) is only a proxy for z(t), and
u(t) [which equals y(t) — Xx(t)] is not independent
of AS(t), OLS estimates of A are biased.
The interpretation of equation (5) is that capital
markets are efficient and that both long-term and
short-term rates are influenced by a common body of
information. It would be more realistic to permit x(t),
y(t), and z(t) to have some structure or to postulate
a whole spectrum of information and to develop a
11This and other discussions of the Efficient Market hypothesis
in this paper ignore the important role of transaction costs.



MAY

1976

model explaining the response of both long-term and
short-term interest rates to each segment in that spec­
trum. But simplicity is a virtue, and we believe that,
given the present state of knowledge, equation (5)
represents a useful model for our purpose, which is
to test the Preferred Habitat hypothesis of ModiglianiSutch against the Efficient Market hypothesis.12

Levels Versus Differences
Over the years the results of several studies, which
have used a variety of techniques, have cast doubt
on the reliability of the lag structure estimated by
M&S.13 One of the most important of these is the
study by Michael Hamburger and Cynthia Latta, who
used a model originally suggested by John Wood.14
According to Wood, as a reasonable approximation,
we can express the relation between long-term and
short-term rates as follows:
(6) L(t) = a + bS(t) + v(t)

First-differencing this equation, which is the form in
which Wood tested it, yields an equation that is ap­
parently similar to equation (5), but differs in that
the error term v(t) in the Wood model is implicitly
assumed to be independent of the short-term interest
rate.
M. Hamburger and C. Latta compared the PH and
Wood models in differences. Their paper, which an­
ticipates much of the empirical work presented here,
yields results that lead them to reject the PH model.
12It should be clear, however, that such a model is not the
best possible alternative. A model that explicitly identified
the events reflected in x (t), y (t), and z (t) and related
them to long-term and short-term rates would yield a more
useful explanation. The model developed by M. Feldstein
and G. Chamberlain in “Multimarket Expectations and the
Rate of Interest,” Journal of Money, Credit, and Banking
(November 1973), is one example of such an attempt.
13See, for example, R. Dobell and T. Sargent, “The Tenn
Structure of Interest Rates in Canada,” Canadian Journal
of Economics (February 1969); T. Cargill and R. Meyer,
“A Spectral Approach to Estimating the Distributed Lag
Relationship between Long and Short Term Interest Rates,
International Economic Review (June 1972), and “Estimat­
ing Term Structure Phenomena from Data Aggregated over
Time,” Journal of Money, Credit and Banking (November
1974); V. Chetty, “Estimation of Solow’s Distributed Lag
Models,” Econometrica (January 1971); G. Pierson, “Effect
of Economic Policy on the Term Structure of Interest Rates,”
Review of Economics and Statistics (February 1970); and
especially M. Hamburger and C. Latta, “The Term Structure
of Interest Rates,” Journal of Money, Credit and Banking
(February 1969). For a reply to Hamburger and Latta,
see Franco Modigliani ancf Richard Sutch, “The Term
Structure of Interest Rates: A Re-examination of the Evi­
dence,” Journal of Money, Credit and Banking (February
1969).
14Hamburger and Latta, “The Term Structure of Interest
Rates.” John H. Wood, “The Expectations Hypothesis, the
Yield Curve, and Monetary Policy,” Quarterly Journal of
Economics (August 1964).

Page 13

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

1976

However, as pointed out by M&S, when the PH and
Wood models are compared in levels, the PH model
has greater explanatory power.15
The superiority of the PH model over the levels
version of Wood’s model, however, cannot be used
to discriminate between the SEM and PH models.
If the SEM model is essentially correct, then we
would expect a distributed lag model such as the PH
model to yield better results than the levels version
of Wood’s model. This point is demonstrated in the
Appendix.

Replication of Modigliani-Sutch Evidence
Before proceeding further, we replicate the Modig­
liani-Sutch evidence supporting their version of the
Preferred Habitat hypothesis. They estimate their
equation for two overlapping periods running from
the first quarter of 1952 (1/1952) to the fourth quar­
ter of 1961 (IV/1961) and from 1/1952 to 1/1966. In
both periods, they use quarterly data, estimate the
current short-term rate separately, and use a fourth
degree Almon lag, with the 17th lag constrained to
zero, to estimate the lag structure. Although they use
the yield on taxable long-term government bonds to
measure long-term rates in both periods, they use the
yield on three-month Treasury bills calculated on a
discount basis as a measure of short-term rates in the
shorter period and the same rate calculated on a bond
yield basis in the longer period. In the results pre­
sented here we use their measure of long-term rates
and their bond yield measure of short-term rates.16
When we reestimate their model using equation (2)
for the period running from 1/1952 to 1/1966, we get
the same results. When we reestimate their model for
the period 1/1952 to IV/1961 using the bond yield
measure of the short-term rate rather than the yield
on a discount basis, we obtain essentially the same
results. Table I shows our estimates (labeled P&P)
for both periods as well as the estimates reported by
M&S for the period 1/1952 to IV/1961. Our estimates
of the coefficients for lagged short-term rates with a
band of plus or minus one standard error are shown
in Figure I.
15Modigliani and Sutch, “The Term Structure of Interest
Rates: A Re-examination of the Evidence.”
16Except for the long-term rate from 1/1952 to 1/1953, the
data are taken from Sutch’s dissertation, pp. 216-17. For
the period 1/1952 to 1/1953, we use quarterly averages of
the long-term Treasury bond yield reported in the Treasury
Bulletin on a monthly basis. Sutch apparently dropped
these five quarters from his later work because the maturity
of the long-term bonds used to calculate the yield changed
twice during this period.
Digitized for Page
FRASER
14


HYPOTHESES
The widespread acceptance and use of the Modig­
liani-Sutch version of the Preferred Habitat hypothesis
in econometric model building is based essentially on
the results shown in Table I and Figure I. As com­
pared only to the alternative hypothesis that there is
no relation between long-term rates and current as
well as lagged short-term rates, this evidence would
lead one to accept their hypothesis.
But the null hypothesis of no relation is a straw
man. In order to determine whether or not their
hypothesis is the best available explanation of the
determination of long-term interest rates, it should
be tested against a strong alternative hypothesis.
Given the very impressive amount of evidence sup­
porting the hypothesis that organized capital mar­
kets are efficient and that both long-term and short­
term interest rates essentially perform a random walk,
the SEM model developed above provides a strong
alternative hypothesis.
The fundamental difference between the two hypo­
theses is the way capital markets respond to new
information. In the SEM model formalized in equa­
tion (5), long-term and short-term rates respond fully
and simultaneously to a common body of new in­
formation. As a result, all relevant information con­
tained in past short-term rates is fully reflected in the
lagged long-term rate, and the current change in the
short-term rate can be viewed as a proxy for the new
information that affects both rates.

MAY

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

In the PH model, new information in­
fluences long-term rates slowly and in­
directly. There the implicit hypothesis is
that new information alters current short­
term rates and the change in the current
short-term rates then continues to alter
long-term rates over several quarters as
expected future short-term rates respond
over time to the new information.
Suppose, for example, that there is an
unanticipated open market sale of short­
term government securities. The SEM hy­
pothesis says that both long-term and
short-term rates respond fully and simul­
taneously to this event when it happens.
The PH hypothesis however implies that
the open market operation first affects
essentially only current short-term rates.
Then, in response to extrapolative and re­
gressive expectations about future short­
term rates, the long-term rate responds
over time to the open market operation
and the initial rise in short-term rates.
These two ways of viewing the relation
between long-term and short-term interest
rates are fundamentally different, and the
essence of the difference concerns the na­
ture of the information contained in lagged
short-term interest rates.

Table I

PREFERRED HABITAT PARAMETER ESTIMATES
O btained from Equation

£«

t value

P&P

t value

Bi

t value
(7.15)

0
1

0.3 1 6

(1 0 .5 3 )

0 .3 0 7 6

(1 0 .3 7 )

0 .2 6 0 7

0 .0 2 2 9

(1 0 6 )

0 .0 2 2 3

(1.0 6 )

0 .0 1 4 2

(0.53)

2

0.0 2 9 3

(3.2 1 )

0 .0 2 8 6

(3.2 2 )

0 .0 2 2 5

(1.92)

3

0 .0 3 7 3

(6.90)

0 .0 3 6 6

(6.9 8 )

0 .0 3 0 5

(4.66)

4

0 .0 4 5 8

(7 .6 3 )

0 .0 4 4 9

(7.7 3 )

0 .0 3 8 0

(5.46)

5

0 .0 5 3 6

(9.24)

0.0 5 2 5

(9.3 7 )

0 .0 4 4 4

(6.49)

6

0 .0 5 9 9

(1 2 .4 7 )

0 .0 5 8 6

(1 2 .4 2 )

0 .0 4 9 4

(8.50)

7

0.0641

(1 4 .5 6 )

0 .0 6 2 6

(1 4 .5 6 )

0 .0 5 2 9

(1 0 .4 4 )

8

0 .0 6 5 6

(1 3 .3 8 )

0 .0 6 4 0

(1 3 .4 4 )

0 .0 5 4 7

(10.81 )

9

0 .0 6 4 4

(1 1 .7 0 )

0 .0 6 2 6

(1 1.68)

0 .0 5 4 6

(9.18)

10

0 .0 6 0 3

(1 0 .7 6 )

0 .0 5 8 6

(1 0 .6 6 )

0 .0 5 2 6

(8.71)

11

0 .0 5 3 7

(1 0 .1 3 )

0 .0 5 2 0

(1 0 .0 5 )

0.0 4 8 8

(8.67)

12

0 .0 4 4 9

(8 .8 0 )

0 .0 4 3 4

(8.6 4 )

0 .0 4 3 3

(8.25)

13

0 .0 3 4 7

(5.98)

0 .0 3 3 4

(5.8 4 )

0 .0 3 6 3

(6.30)

14

0 .0 2 3 9

(3.41)

0 .0 2 2 8

(3.3 2 )

0.0281

(4.04)

15

0 .0 1 3 6

(1.83)

0 .0 1 2 8

(1.7 7 )

0 .0 1 9 0

(2 .5 4 )

(0 .9 1 )

0 .0 0 4 7

(0.86)

0.0 0 9 5

16

0.0051

Constant

1.239

(4 4 .2 5 )

1.251

(2 1 .5 5 )

1.474

R2

0.975

D -W

1.42

1.39

0.5 7 9

Standard
Error

0.093

0.093

0.1 2 7

16
S ftS (t - i) + n'(t)
i= l

(6) L(t) = a + bS(t) + v(t)

to see whether the 16 lagged short-term rates have
any significant explanatory power.
Such a test does get at the heart of the issue. But,
as we point out above and demonstrate in the Ap­
pendix, if the SEM model is essentially correct, then
this test is likely to be prejudiced in favor of the PH
model.
Another alternative is to compare equation (2) and
the SEM model as described by equation (5).




1/1952 to
1/1966
P&P

M&S

One possibility, and the one M&S insisted upon in
their exchange with Hamburger and Latta, is to com­
pare equations (2) and (6)

(5) L(t) = L(t - 1) + MS(t) + u(t)

(2)

1/1952 to IV /1961

The next logical step is to formulate a test that
will permit us to discriminate between these two
models. In order to be effective, such a test must not
be prejudiced and should cast light on the essential
difference between the two approaches.

(2) L (t) = a + ft>S(t) +

1976

(Ad|.) 0.971

(1 .6 6 )
(2 3 .4 5 )

(Adj.) 0.955

But there are two reasons for not doing this. First, the
SEM model contains a lagged long-term interest rate
and this could prejudice the result in favor of the
SEM model. Second, such an approach does not pro­
vide a direct test of the essential difference between
the two models. That is whether or not there is in­
formation in lagged short-term rates that is not fully
captured by L ( t -1).
A third alternative, and the one we choose, is, in
effect, to difference the PH model as expressed by
equation (2) and to rewrite the differenced version
as follows:
16
(7) L (t) = L (t - 1) + ft, AS(t) +

S ft AS(t - i) + An(t)
i= l

This puts the SEM and PH models on exactiy the
same footing and permits us to get at the essence of
the difference between the two models. In addition,
this approach does not appear to involve any preju­
dice against the PH model. For the shorter period,
equation (2) yields a slightly higher adjusted R2 than
equation (7) (0.975 versus 0.962), but for the
Page 15

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

1976

longer period the results are reversed (0.955 versus
0.974).17
We believe equations (5) and (7) provide the
basis for a fair and direct test of what is the essence
of the difference between the PH and SEM models.
If the market for long-term government securities
is essentially efficient, the error term obtained from
estimating equation (5) should be free of autocor­
relation and adding lagged changes in the short-term
rate should not reduce significantly the mean-squarederror. If the market is not efficient and expectations
contain both regressive and extrapolative elements,
then we would expect equation (7) to yield a better
explanation of the long-term rate, in terms of a statis­
tically significant smaller mean-squared-error, than
equation (5).
The results from estimating equation (5) for the
two overlapping periods chosen by Modigliani and
Sutch are as follows:
1/1952 to IV/1961
L(t) = 0.0453 + 0.9949L(t - 1) + 0.2218 AS(t)
(0.447) (32.506)
(6.146)
R2 = 0.964

SE = 0.1047

1/1952 to 1/1966
L(t) = 0.0696 + 0.9861L(t - 1) + 0.2246 AS(t)
(0.922) (46.415)
(7.1346)
R 2 = 0.975

SE = 0.0949

where t values are shown in parentheses.
Since the regressions contain a lagged dependent
variable, the Durbin-Watson statistic is biased toward
2.0 and a more appropriate measure for serial cor­
relation in the residuals is the h-statistic which has a
standard normal distribution.18 The h-statistic is
- 0.199 for the shorter period and - 0.002 for the longer
period. As implied by the SEM model, there is no
indication of any first order serial correlation in the
residuals.
The estimated parameters of equation (7) are shown
in Table II and the estimates of the coefficients for
lagged changes in short-term interest rates are shown
in Figure II with a band of plus or minus one standard
error. Following Modigliani and Sutch we estimated
17Since A S (t) and u (t) are correlated in equation (5 ), the
estimate of X is biased downward. This errors in variables
problem can be corrected using an instrumental variables
technique to estimate equations (5) and (7). Estimating
equations (5) and (7) using an instrumental variables
technique suggested by Durbin does not alter the conclusions
drawn from the OLS estimates presented below that there
is no information in the lagged A S (t)’s. J. Johnston, Eco­
nometric Methods (New York: McGraw-Hill, 1972), p. 284.
18See Johnston, Econometric Methods, pp. 312-13.

Page 16


the lag structure using a fourth degree Almon lag
with the 17th lag constrained to zero.
In both periods, with the exception of the first
coefficient, the lag structure retains the inverted U
shape, but now none of the lagged coefficients are
statistically significant at the five percent level. An F
test indicates that lagged short-term interest rates
contain no information that is not already captured
by the lagged long-term interest rate. For the shorter
16

period, adding Z (31 AS(t-i) to equation (5) does
i= l
not increase significantly the explained variance (an
F-statistic of 0.506). For the longer period the same
comparison yields the same result (an F-statistic of
0.77) .19 This evidence does not support the claim that
expectations contain regressive and extrapolative ele­
ments and that, therefore, lagged short-term interest
rates contain additional information not captured by
the lagged long-term interest rate.
Although there is no evidence that lagged short­
term interest rates contain any significant information,
the tendency for the inverted U shape to persist sug­
gests that there might be at least some information in
19In order to be significant at the 5 percent level, the F
statistic would have to exceed 2.66 for the shorter period
and 2.56 for the longer period. There is the possibility that
estimating the PH model as equation (7 ) introduces spurious
autocorrelation into the residuals, thus possibly tending to
bias the F tests against the PH model. The insignificant
h-statistic for the estimates of both the SEM and PH models,
however, suggests this is not a serious problem.

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

MAY

models is based primarily on three factors.
They are as follows. First is the ability of
the model to explain the behavior of long­
term interest rates over the sample period
in the sense of a high R2. Second is the
significance of the lag structure. Many of the
t-statistics are over 5. Third, the estimated
lag coefficients take the form of a smooth
inverted U, which Modigliani and Sutch in­
terpret as being consistent with extrapola­
tive and regressive expectations.

Table II

PREFERRED HABITAT PARAMETER ESTIMATES
O btained from Equation (7 )
1/1952 to 1/1966

1/1952 to IV / 1 9 6 1
t

i

t

0

0 .2 3 3 8

(5 .3 4 8 )

0 .2 3 8 5

(6 .6 0 4 )

1

0 .0 2 0 9

(0 .6 6 3 )

0 .0 1 5 0

2

0 .0 1 7 0

(0 .6 8 9 )

0 .0 1 3 6

(0 .5 7 6 )
(0 .6 9 2 )

3

0 .0 1 8 3

(0 .6 8 1 )

0 .0 1 6 0

(0 .7 7 5 )

4

0.0 2 2 8

(0 .7 6 9 )

0 .0 2 0 4

(0.9 2 3 )

5

0 .0 2 8 9

(0 .9 1 9 )

0 .0 2 5 6

(1 .1 2 2 )

6

0 .0 3 5 4

(1 .0 7 7 )

0 .0 3 0 4

(1 .3 2 0 )

7
8

0 .0 4 1 0

(1 .2 0 6 )

(1 .4 6 3 )

0 .0 4 4 9

(1 .2 9 0 )

0 .0 3 3 8
0 .0 3 5 4

9

0 .0 4 6 6

(1 .3 2 6 )

0 .0 3 4 9

(1 .4 9 9 )

10

0.0 4 5 8
0 .0 4 2 4

(1 .3 1 1 )
(1 .2 3 8 )

0.0321

11
12

0.0272

(1 .3 9 8 )
(1 .2 2 1 )

0 .0 3 6 7

(1 .0 9 9 )

0.0 2 0 8

(0 .9 6 6 )

13
14

0.0 2 9 2

(0 .9 0 2 )

(0 .6 5 6 )

0 .0 2 0 6

(0 .6 7 8 )

0 .0 1 3 5
0 .0 0 6 4

(0 .0 4 5 )

0.0 1 1 9

(0 .4 6 1 )

0 .0 0 0 7

0 .0 0 4 6

(0 .2 7 3 )

-0 .0 0 1 9

(0 .1 8 4 )

L(t — 1)
Constant

0.9 8 7 3

(3 0 .4 9 4 )

0 .9 8 1 9

(4 4 .2 2 9 )

(0 .4 7 3 )

0 .0 7 0 5

0 .0 4 9 7
0.962

h
Standard
Error
DF

-

0.666

0 .1 0 7 6
33

the distributed lag. Alternatively, the smooth
inverted U may be the result of using a low
degree Almon polynomial rather than the
result of extrapolative and regressive
expectations.
In order to obtain some evidence on this
point, we estimate the lag structure in equa­
tion (7) using ordinary least squares. Since
changes in Treasury bill rates essentially are
uncorrelated, multicollinearity is not a prob­
lem and, under the assumptions of the PH
model, OLS regression provides an unbiased
estimate of the parameters. Regression re­
sults using ordinary least squares are shown
in Table III. Figure III shows the estimates
of the coefficients for lagged changes in
short-term rates with a band of plus or minus
one standard error. In neither period is there
a smooth inverted U. This result suggests
that the smooth inverted U is the result of
using the Almon lag.

CONCLUSION
The acceptance of the Preferred Habitat
model and its widespread use in econometric



As for the significance of the lagged short­
term rates that M&S found in their PH
formulation given by equation (2), the SEM
model proposed here suggests that such
statistical significance need not be inter­
preted as evidence of extrapolative and re­
gressive expectations. The SEM model, as
presented in the text and amplified in the
Appendix, explains how adding lagged short­
term rates can improve the fit obtained from

(0 .3 3 3 )

15

R2

With respect to the smooth inverted U,
our results suggest that this is due to the
Almon technique, which forces the estimates
to fit a smooth curve, rather than the result
of extrapolative and regressive expectations.

(1 .5 2 3 )

16

1976

(0 .9 1 1 )
0.9 7 4
— 0.558
0 .0 9 5 7
50

Table III

PREFERRED HABITAT PARAMETER ESTIMATES
O btained from Equation (7 ) Using O LS
1/1952 to IV / 1 9 6 1
i

ft

1/1952 to 1/1966
t

ft

t

0

0 .2 7 5 0

(4 .7 0 6 )

0 .2 9 4 0

(6 .3 0 1 )

1
2

0 .0 1 1 9
0.0 4 3 5

(0 .1 7 7 )
(0 .5 8 9 )
(0 .9 2 8 )

— 0 .0 2 6 0
0.0511

(0.4 6 8 )
(0 .8 3 1 )
(0.6 6 8 )

3
4
5
6
7
8

0 .0 7 1 9

(0 .4 2 2 )

0.0 3 1 6
0 .0 0 3 0

0 .0 4 1 3
0 .0 1 1 9

(0 .1 8 8 )

(0 .0 3 5 )

-0 .0 2 9 1

(0 .4 1 9 )

0 .1 4 7 7
0 .1 8 8 6

(1 .6 8 5 )

0.0931

(1 .3 3 1 )

(2 .1 7 2 )

0.1431

(2 .0 0 8 )

-0 .0 9 6 0

(1 .0 2 8 )

— 0 .1 1 9 7

(1 .6 5 5 )

9

0.2 3 4 8

(2 .6 6 6 )

0 .2 0 3 5

(2 .8 2 1 )

10

(0 .1 5 7 )
(0 .9 4 4 )

-0 .0 4 7 0
0 .0 3 5 5

(0 .6 7 1 )

11

— 0 .0148
0.0 8 8 2

12

0 .1 1 9 3

(1 .4 2 0 )

0 .0 6 8 7

(1 .0 7 5 )

13

0 .0 5 2 5

(0 .5 9 6 )

0 .0 1 4 4

(0 .2 2 6 )
(0 .3 6 5 )

(0 .5 0 3 )

14

0 .0 2 5 7

(0 .3 0 4 )

0 .0 2 3 2

15

-0 .0 4 2 4

(0 .5 0 3 )

— 0 .0 3 2 0

(0 .5 6 2 )

16

0 .2 4 9 8

(1 .7 4 1 )

0 .0 5 8 5

(1 .1 9 7 )

L(t — 1)

0 .9 6 7 9

(2 8 .4 2 4 )

0 .9 8 5 6

(4 8 .0 4 6 )

Constant

0 .0 7 7 8

(0 .7 5 5 )

0 .0 4 8 2

(0 .6 7 4 )

R2

0.9 6 9

0.978

h

0.5 7 4

-0 .4 4 4

Standard
Error
DF

0 .0 9 6 9
21

0 .0 8 8 2
38

Page 17

MAY

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

regressing the current long-term rate on the current
short-term rate even though long-term rates do not
depend on lagged short-term rates.

F ig u re III

Distributed Lag Coefficients

I952-I to 1961-IV

W eight

1976

Weight

With respect to the high R2 obtained by M&S, we
find that in order to explain the current long-term
interest rate, it is sufficient to use the long-term rate
lagged one quarter and the current change in the
short-term rate. The addition of lagged changes in
short-term rates does not add significantly to the ex­
planation of the current long-term rate. This finding
is consistent with the SEM model, but inconsistent
with the PH model as specified by M&S. This result,
which is part of a large and growing body of evi­
dence that conflicts with the term structure model
suggested by Modigliani and Sutch, leads us to reject
the Preferred Habitat model in favor of the Simplified
Efficient Market hypothesis.
Although a comparison of the two models leads us
to reject the PH model, we recognize that the SEM
model is a naive hypothesis that can and should be
improved upon. We are trying to extend the SEM
model and we hope that in the process we will be
able to contribute to a better understanding of the
relation between short-term and long-term interest
rates.

L a g (q u a r t e r s )

APPENDIX
We can demonstrate as follows why we would expect
the PH model to yield better results than the levels ver­
sion of the W ood’s model. Equations (3 ) and (4 ) can be
solved as follows to express L ( t ) and S ( t ) in levels.
00

oo

(I) L(t) = K ! z(t-i) + S y(t-i)
i= 0
i= 0
00

(II) S(t) =

oo

S z(t-i) + £ x(t-i)
i= 0
i= 0

Using equations (I) and (II) to express the relation
between the long-term and short-term rate in levels
yields the following.
OO

(III) L(t) = \S(t) +



£ [y(t-i) - Ax(t-i)]
i=0

Com paring equations (III) and (6 ) we see that if the
SEM model is correct, the error term v ( t ) in the Wood
model is a random walk, i.e., a sum over time of uncor­
related random variables and, therefore, highly auto­
correlated. As a result, we would expect that the estimation
of the Wood model, i.e., equation ( 6 ), using ordinary
least squares would not do as well as alternative specifi­
cations which use proxies to explain some of the struc­
ture in the error term v ( t ) . One proxy, of course, is
lagged S ( t ) , which like v ( t ) , has strong positive auto­
correlation.
In addition we note from equation (4 ) that S ( t ) de­
pends on x ( t ) . Since v ( t ) is com posed partly of lagged
x ( t ) ’s, the addition to equation ( 6 ) 'o f a distributed lag
on S (t) should do better than the Wood model described
by equation ( 6 ) . That is,

FE DE RA L . R E S E R V E B A N K O F ST. L O U I S

n
(IV) L(t) = a + bS(t) + £ bjS(t-i) + v' (t)
i= l
should “explain” some of the residual variance in the
Wood model.

MAY

Table IV

PARAMETER ESTIMATES
From Equation (V I)
1/1952 to IV /1961

Under these conditions, however, such an improve­
ment does not imply that current changes in L ( t ) de­
pend in any way on the past behavior of S ( t ) . In other
words, the SEM model explains why a distributed lag
on S ( t ) could contribute to the explanation of L ( t )
even though changes in long-term and short-term rates
are only contempraneously correlated.
If the SEM model is essentially correct, then the rela­
tion between S ( t ) and L ( t ) is symmetric. We can derive
equation (V ) from equations (I) and (II)
(V) S(t) = a' + b'L(t) + w(t)
where
w(t) = 1 [x(t-i) - -J- y(t-i)]
i= 0
K
and w ( t ) , therefore, has the sam e properties as v ( t) in
equation ( 6 ). That is, w (t) should be roughly a random
walk and w (t) should not be independent of L ( t ) . If our
argument about the effect of adding lagged short-term
rates to equation (6 ) is correct, then we should obtain
similar results by adding lagged long-term rates to equa­
tion (V ). T hat is,
n
(VI) S(t) = a' + b'L(t) + 2 bi'L(t-i) + w'(t)
i=l
should “explain” some of the residual variance in equ a­
tion (V ).
When we estimate equation (V ) for the two periods
used by M&S, we get the following results:
1952-1 to 1961-IV
S(t) = -1.5934 + 1.1798L(t)
(2.92)
(7.24)
R2 = 0.579 DW = 0.4300 SE = 0.5654
1952-1 to 1966-1
S(t) = - 2.1021 + 1.3451L(t)
(5.07)
(11.66)
Ri = 0.7121 DW = 0.3572 SE = 0.5195
where t values are shown in parentheses.
If we follow M&S and use a fourth degree polynomial
with a tail constraint to estimate equation (V I) where
n equals 17, we obtain the results shown in T able IV. As
expected, the lagged long-term rates appear to add sig­
nificantly to the explanation of the current short-term
rate.
It should be pointed out that we did not search to
obtain an optimum fit. We simply reversed the roles of
long-term and short-term rates and then followed exactly
the procedure used by M&S. T he results shown in Table
IV strongly support our claim that the significant lag
structure obtained by M&S is not the result of extrapola­
tive and regressive expectations.



1976

ft

i

1/1952 to 1/1966

t
—

2.2 5 4 4

t
“
8.85

1.41

0 .1 7 5 5

0.91

0.20

— 0.0051

0.05

— 0 .1 5 6 5

2.68

0

2.0275

1

0 .2 8 1 4

2

0.0 1 7 8

3

-0 .1 8 1 3

3.04

f t
— 4

7.68

4

— 0 .3 1 7 2

4.89

-0 .2 7 1 4

4 .47

5

— 0 .3 9 2 9

6.45

— 0 .3 4 5 2

6.04

6

-0 .4 1 2 8

8.13

-0 .3 7 6 2

7.85

7

— 0 .3 8 3 3

8.38

— 0 .3 6 4 9

8.66

8

— 0 .3 1 2 6

6.30

-0 .3 1 4 9

7.14
4.82

9

— 0 .2 1 0 3

3.83

— 0 .2 3 2 3

10

— 0 .0 8 8 0

1.59

— 0 .1 2 5 7

2.63

11

0 .0 4 1 0

0.79

-0 .0 0 6 5

0.15

12

0 .1 6 1 9

3.2 7

0.1111

3.40

13

0 .2 5 7 9

4.51

0 .2 1 0 6

6 .54

14

0 .3 1 0 7

4.46

0 .2 7 2 5

6 .47

15

0 .3 0 0 2

4.05

0 .2 7 5 0

5.60

0 .2 0 4 5

3.64

0 .1 9 3 2

4.90

— 1.8271

4.95

— 1.8918

7.54

16
Constant
R2

0 .8 8 9

0.9 0 3

DW

1.2 3 4 4

0 .8 0 9 4

Standard Error

0.2901

0 .3 0 9 5

But equation (IV ) is not the only possible modification
of the Wood model which would account for some of the
variance in the error term v ( t ) . Equation (4 ) of the
SEM model implies that A S ( t) and x (t) are correlated.
Thus a distributed lag on A S ( t) should explain some of the
variance in the error term v ( t ) in equation ( 6 ). That is,
n
(VII) L(t) = a + bS(t) + 2 bjAS(t-i) + v"(t)
i= l
also should do better than the W ood model.
The SEM model, however, implies that the best way
to capture the error variance in W ood’s model is not
00

to restrict the proxies for

Z x ( t - i ) and the structure
i= 0
in v ( t ) to S ( t ) or A S ( t ) , but to use L ( t -1) and S ( t - 1).
From equation (III) we see that the error v ( t ) in the
W ood model can be expressed as follows:
OO

00

(VIII) v(t) = S y(t-i) - A 2 x(t-i) = L(t) - AS(t)
i= 0
i= 0
But equation (VIII) im plies that
OO

OO

(IX) L(t-l) - AS(t-l) = S y(t-i) - \ 2 x(t-i)
i= l
i= l
As a result, w e can use ( L ( t - l ) - A S ( t - l) )
all of v ( t ) except for the two terms y (t)
When we do this by combining equations
(I X ) , we return full circle to equation (5 )
error term is orthogonal.

to capture
and X x (t).
(III) and
where the

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