The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
EC O N O M IC R E V IE W
The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by the
Bank’s Research and Public Information Department under the supervision of Michael W. Reran,
Senior Vice President, The publication is edited by William Burke, with the assistance of Karen
Rusk (editorial) and William Rosenthal (graphics). Opinions expressed in the Economic Review
do not necessarily reflect the views of the management of the Federal Reserve Bank of San
Francisco, nor of the Board of Governors of the Federal Reserve System.
For free copies of this and other Federal Reserve publications, write or phone the Public
Information Section, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco,
California 94120. Phone (415) 544-2184.
^®s©y[f(g© A ltoeatta—
Industry and Housing
I.
Introduction and Summary
5
II. An Intersectoral Analysis of the
Secular Productivity Slowdown
7
Jack Beebe and Jane Haltmaier
. . . Reduced capital deepening—slower growth of the capital-labor ratios
within industrial sectors—was an important factor in the laborproductivity slowdown of recent decades.
III.
Inflation Expectations and the Housing Market
Randall J. Pozdena
. . . The true "crisis” may be that too much—rather than too little—
housing is produced and consumed in the U.S. economy.
Editorial committee for this issue:
Yvonne Levy, John Scadding, and John Judd
29
"
I
I
in labor productivity. "Between the 1948-65
and 1973-78 periods, intersectoral shifts contributed only 0.3 percentage points of the 2.0percentage-point deceleration in aggregate labor-productivity growth. Moreover, sectorspecific declines became evident in nine of
twelve industrial sectors, indicating the widespread nature of the productivity slowdown."
The authors show that reduced capital deepening-slower growth of the capital-labor ratios within sectors-was an important factor in
the labor-productivity slowdown, accounting
for one-third to one-half of the deceleration.
On an industry level, this factor was especially
important in agriculture, mining, and the large
"commercial and other" sector. They also
show that the slowdown was not limited to
labor productivity, but was evident also in total
factor productivity (involving both labor and
capital inputs).
Beebe and Haltmaier cite a number of factors that might have contributed to the slowdown in capital investment and hence in productivity. These factors included economic
uncertainties, inflation, reduced output growth,
tax laws, and government regulations. Consequently, they conclude that "an appropriate
policy response would call for a re-examination
of governmental policies and other factors that
affect capital formation."
With relatively fewer resources allocated recently to industrial capital investment, the
question arises regarding the possible overallocation of resources to other sectors. Randall
Pozdena suggests that the beneficiary, to some
extent, may have been the housing sector. He
explores a paradox: housing prices rose relative
to most other prices in the economy between
1970 and 1980, prompting officials to argue
that housing had become "unaffordable" and
that more resources should be directed into
Public and private policymakers must deal
in the 1980's with the problems created by the
nation's low investment in capital goods and
heavy investment in consumption goods-with
all that that means in terms of reduced economic growth. This issue of the Economic Review analyzes two aspects of this sectoral resource-allocation theme. The first article
discusses the slowdown in U.S. productivity
growth as representing a prolonged failure to
allocate sufficient resources to capital investment in industry. The second article focuses on
policies toward housing and their effect on the
behavior of the market under the spur of inflation.
Jack Beebe and Jane Haltmaier note the
long-term nature of the slowdown in productivity, with labor productivity rising only about
one-third as fast in the 1973-78 period as it did
in the 1948-65 period. They also note the serious impact of this slowdown on the nation's
living standards-evidenced by the fact that
real income per hour would double in 22 years'
time at the 1948-65 productivity growth rate,
while 58 years would be needed to double real
income at the more recent pace of productivity
increase.
Studies in the early 1970s attributed much
of the deceleration in productivity growth at
that time to shifts in employment and output
among sectors with different levels of labor
efficiency. Indeed, the early postwar shift of
workers out of the low-productivity farm sector
to higher productivity sectors initially boosted
aggregate U.S. productivity growth, but this
positive effect waned as the farm share of total
employment dropped steeply in recent decades.
Beebe's and Haltmaier's results show that
intersectoral labor and output shifts accounted
for only a small part of the recent slowdown
5
and other assets, and not simply within housing itself. "Thus, capital that otherwise would
have flowed into industrial uses frequently has
been attracted to housing instead. Thus the
true 'crisis' may be that too much-rather than
too little-housing is produced and consumed
in our economy."
Pozdena adds that further inflationary distortions occur because of the way that housing
is treated in the consumer-price index, which
confuses the costs of purchasing housing assets
with various costs involved in holding such assets over time. Had an alternative "rental
equivalence" measure of housing costs been
used in the consumer price index, the index
probably would have stood more than eight
percent below its reported value in 1979. Thus
he concludes, "Considering the myriad public
and private programs and contracts which use
the CPI as an inflation index, such an overstatement itself has introduced inflation-related distortions into the economy."
the industry, and yet the consumption of housing services continued to rise during this period. Not only did the number of housing units
rise faster than the population, but the quality
of housing services also rose in terms of floor
area and amenities.
In attempting to unravel the paradox, Pozdena argues, "Inflation has been at the root of
many of the industry's problems-but this does
not mean that inflation has caused a crisis in
the form of unaffordable housing or unavailability of rental housing." He argues that housing costs, when properly measured, have fallen
relative to other prices despite the rise in housing prices. The widely observed trend away
from rental housing, including the conversion
of rental housing to owner-occupancy status,
meanwhile represents a natural consequence
of households' attempts to cope with the combined impact of inflation and tax regulation.
Moreover, he argues that the combination
of inflation and special tax treatment tends to
alter relative rates of return between housing
6
I
Jack Beebe and Jane Haltmaier*
tion of 10.0 percent would translate roughly
into price inflation of 6.8 percent. With a 1.2percent productivity increase, however, the
same rate of wage inflation would translate into
price inflation of 8.8 percent. Labor-productivity growth therefore is clearly central to the
political issues that arise when the gap narrows
between wage and price inflation.
What factors underlie the secular deterioration in productivity growth? A decade ago,
many studies attributed the deceleration in
productivity growth to shifts in employment
and output among sectors with different levels
of labor efficiency. 1 In particular, the earlypostwar shift of workers out of the lOw-productivity farm sector to higher-productivity
sectors initially boosted aggregate U.S. productivity growth, but this positive effect waned
as the farm share of total employment declined
from 18 percent in 1948 to 5 percent in the
1970s.
The productivity slowdown would not be a
major public-policy issue if this were all that
was involved, because basic structural changes
in the economy cannot be manipulated easily
by government policy.2 Even if they could be,
generally it would not be in the public interest
to do so, for such structural changes tend to
reflect the public's basic preferences to spend
their incomes and seek employment in ways
that increase society's general welfare.
Some studies suggest that sectoral shifts are
still of overriding importance, 3 but the evidence presented in this paper points strongly
to the conclusion that such shifts have accounted for only a small portion of the slowdown in aggregate labor-productivity growth.
This conclusion suggests the existence of other
causal factors, such as a general slowdown in
capital deepening-resulting perhaps from the
Economists and policymakers have become
increasingly concerned in recent years about
the slowdown in U.S. productivity. Productivity has always exhibited a strong cyclical movement in line with changes in business conditions, but analysts today are less concerned
with these quarter-to-quarter gyrations than
with the secular (noncyclical) trend. For the
private economy, the annual rate of increase
in labor productivity (output per hour) averaged 3.2 percent for the 1948-65 period, but
slowed to 2.3 percent in the 1965-73 period
and then to only 1.2 percent in the 1973-78
period. The rate of increase in total factor productivity (output per weighted unit of capital
and labor input) exhibited a similar slowdown-from an annual rate of 1.3 percent in
the first period to 0.7 percent and 0.4 percent
in the last two periods, respectively. Since
1978, the figures have been much worse,
largely reflecting adverse cyclical factors in addition to this secular weakness.
Concern over the secular trend of productivity stems from its role as the key determinant
of the nation's material standard of living. For
example, at a 3.2-percent annual growth rate
(the 1948-65 average), real income per hour
would double in only 22 years, whereas at a
1.2-percent rate (the 1973-78 average), 58
years would be required. Moreover, the rate
of labor-productivity increase is the major determinant of the difference between wage and
price inflation. With a 3.2-percent rate of increase in labor productivity, annual wage infla'Beebe is Director of Market Studies, Federal Reserve
Bank of San Francisco, and Haltmaier, presently a Ph.D.
candidate at the University of California at Berkeley, was
a Research Associate at the Federal Reserve Bank of
San Francisco. Tom Klitgaard provided research assistance for this article.
7
combined effects of economic uncertamtIes,
reduced output growth, inflation, tax laws, and
regulations. In this case, then, an appropriate
policy response would call for a re-examination
of governmental policies and other factors that
affect capital formation.
Many recent studies have approached the
productivity problem in an aggregate context.
This paper, in contrast, presents a disaggregated analysis of productivity in the private
domestic U.S. economy, concentrating on the
questions of intersectoral shifts and capital
deepening. 4 We first present a twelve-sector
disaggregation of labor productivity, and then
a seven-sector analysis of capital deepening
and total factor productivity.
Our technique advances the state of the art
by providing close approximations for the relationship between aggregate and sectoral labor-productivity changes. We decompose aggregate labor-productivity increase into "rate"
and "level" effects: the rate effect refers to the
portion attributable to productivity growth
within sectors, and the level effect refers to the
portion attributable to shifts in employment
and output across sectors. We then estimate
the important role of capital deepening (i.e.,
increases in the capital-labor ratio) within
seven major sectors, and examine in detail the
bias inherent in using aggregate as opposed to
sectoral data. Although we link a deceleration
in capital deepening to the productivity slowdown, we do not investigate the underlying
causes of retarded capital deepening. 5
The results show that intersectorallabor and
output shifts accounted for only a small
amount of the slowdown in aggregate labor
productivity. Between the 1948-65 and 1973-78
periods, intersectoral shifts contributed only
0.3 percentage points of the 2.0-percentagepoint deceleration in aggregate labor-productivity growth. Moreover, sector-specific declines became evident in nine of twelve industrial sectors, indicating the widespread nature
of the productivity slowdown.
Slower growth of the capital-labor ratios
within sectors was found to be an important
factor in the labor-productivity slowdown, accounting for almost half of the deceleration.
On an industry level, this factor was particularly important in agriculture, mining, and the
large "commercial and other" sector. The results of this study underscore the importance
of disaggregation, since the aggregate approach tends to attribute too little of the laborproductivity slowdown to slower capital deepening.
Finally, we show that the productivity slowdown was not limited to labor productivity, but
was evident also in total factor productivity
(both labor and capital). The secular rate of
increase in that more inclusive category declined from 1.3 percent per annum over the
1948-65 period to 0.7 percent and 0.4 percent
over the 1965-73 and 1973-78 periods, respectively. The deceleration was broad-based, with
acceleration evident in only two sectors- communication and commercial and other.
In Section I, we analyze the rate and level
effects of labor productivity in a disaggregated
framework. In Section II, we analyze total factor productivity, the role of the capital-labor
ratio, and measures of aggregation bias. Finally, we present the conclusions and policy
implications of the paper.
I. Sectoral Decomposition of Labor Productivity Change
Published labor productivity data are calculated with the use of direct aggregation: outputs are added across sectors, labor inputs are
also summed, and total output is then divided
by total labor input to arrive at a calculated
aggregate level of labor productivity.6 In a multisector model that employs directly aggregated data, aggregate labor productivity is af-
fected over time by productivity change within
each sector and by the shift of output and
employment among sectors with different levels of productivity. The following formulation,
which is derived in the note on page 24, decomposes aggregate productivity change into
rate, level and interaction effects. 7
8
The rate effect is the part of aggregate productivity growth that comes about as a result
of changes in productivity within sectors. In
the context of labor productivity, it is the
amount of change that would have occurred
over time had each sector's share of total employment remained constant. In contrast, the
level effect is the part of aggregate productivity
change that results solely from shifts of labor
(and output) among sectors-i.e., the amount
that would have occurred had productivity levels remained constant within sectors, while labor (and output) shifted among sectors of dif-
where
P
AP
P
aggregate output per hour (labor
productivity)
output per hour in the i-th sector
real output share of the i-th sector
share of hours employed in the i-th
sector
percentage change in productivity
over the discrete time period.
Table 1
Labor and Real Product Shares
by Industry for Selected Years, 1948-78
(Percent)
Labor Shares'
1948
1965
1973
100.0
100.0
100.0
18.3
8.5
Mining
1.7
Construction
Real Product Shares'
1948
1965
1973
1978
100.0
100.0
100.0
100.0
100.0
5.8
5.4
7.0
4.4
3.6
3.4
1.1
0.9
1.2
3.0
2.2
1.9
1.8
5.6
6.3
6.8
6.9
6.6
7.7
5.9
5.3
Nondurable Goods Mfg.
12.6
12.4
11.6
10.8
12.4
12.2
12.4
12.2
Durable Goods Mfg.
14.8
17.3
17.0
16.4
18.0
19.4
18.9
18.1
Transportation
5.7
4.4
4.2
4.1
6.8
5.1
5.1
4.8
Communication
1.2
1.3
1.6
1.5
1.4
2.3
3.2
4.2
Utilities
0.9
1.0
1.0
1.0
1.5
2.6
3.0
2.9
Wholesale Trade
4.8
5.7
6.2
6.8
6.6
7.6
8.9
8.9
16.9
18.0
18.2
18.2
12.9
12.4
12.4
12.3
3.3
4.9
5.7
6.3
9.7
10.5
10.4
11.1
13.9
18.8
20.8
21.2
14.2
13.6
14.3
15.0
Private Domestic
Nonresidential Economy
Agriculture'
Retail Trade
Finance and Insurance
Services
'Labor data are based on actual hours worked by persons engaged in production, which encompasses full- and part-time
workers as well as active proprietors. The data come from the National Income and Product Accounts (NIPA), Table
6. ll-except for agriculture (including forestry and fisheries), where data are obtained from household surveys undertaken
by the Bureau of the Census for the Bureau of Labor Statistics. (Unpaid household workers engaged in production are
included in the agricultural data, but excluded from data of other sectors.)
20utput data are actual 1972-dollar gross product (NIPA, Table 6.2). Output in the finance and insurance industry excludes
imputed output from owner-occupied farm and nonfarm dwellings (NIPA, Table 8.3, lines 63 and 75).
'Includes forestry and fisheries.
Sources: U.S. Department of Commerce and Bureau of Labor Statistics.
9
within sectors-accounted for 1.68 percentage
points of the 2.00-percentage-point decline in
aggregate productivity advance. 13
It is important to consider both the respective sizes of the two effects within periods and
their changes from period to period. For example, the level effect-the shifting of labor
among sectors of differing productivity levels-added 0.43 percentage point to the aggregateproductivity growth rate during the 1948-65
period. But this positive boost receded to 0.23
and 0.15 percentage points per year in the two
later periods, respectively. Despite its contribution to the productivity slowdown, the level
effect nevertheless was still positive.
Table 4 shows the contributions of each sector to the total rate effect. 14 The 1948-65 period
was dominated by the large positive contribu-
struction, trade, finance and insurance, and
services. However, the first two sectors have
shown large decelerations in productivity
growth, whereas the other two have not (footnotes 11 and 12).
Table 3 shows the growth rate of aggregate
productivity decomposed into rate, level, and
interaction effects. From this evidence, the
productivity slowdown can be attributed
largely to a slowdown in the rates of productivity growth within sectors rather than to shifts
in employment across sectors. The rate of aggregate productivity growth declined 0.98 percentage points between the 1948-65 and 196573 periods (from 3.24 percent to 2.26 percent).
Of this decline, 0.77 percentage point was accounted for by the change in the rate effect,
and only 0.20 percentage point by the change
in the level effect.
Between the 1965-73 and 1973-78 periods
the story was similar, with the change in the
rate effect accounting for 0.91 percentage
point of the 1.02-percentage-point decline in
the rate of aggregate productivity growth. In
short, over the three subperiods, the rate effect-i.e., slowdown in productivity advance
Table 4
Decomposition of Rate Effect by Industry
(Percentage Contributions to Annual
Rates of Change)
1948-65 1965-73 1973-78
Private Domestic
Nonresidential Economy
Table 3
Decomposition of Labor Productivity
Change Into Rate, Level, and Interaction
Effects
(Annual Rates of Increase)
1948-65 1965-73 1973-78
Private Domestic
Nonresidential Economy
3.24
Percentage Point
Change
Rate Effect
2.82
Percentage Point
Change
Level Effect
0.43
Percentage Point
Change
Interaction
-0.01
2.26
1.24
2.82
2.05
1.14
Agriculture
.31
.21
.06
Mining
.11
0.4
-.09
Construction
.25
-.14
-.06
Nondurable Goods
Manufacturing
.40
.41
.28
Durable Goods
Manufacturing
.50
.40
.18
-0.98
1.02
Transportation
.17
.14
.04
2.05
1.14
Communication
.10
.13
.26
Utilities
.13
.10
.02
-0.77
-0.91
Wholesale Trade
.22
.27
-.04
0.23
0.15
Retail Trade
.34
.26
.13
-0.20
-0.08
Finance and Insurance
.14
.01
.09
-0.02
-0.05
Services
.16
.23
.28
Sources: Table 3 and the individual rate effects in equation
(1), iterated annually.
Sources: See Table 1. Calculated using equation (1), iterated annually.
Ll
The rate contribution accelerated in the
1973-78 span only in communication, services,
and finance and insurance-and in the latter
sector, it still fell below its 1948-65 annual contribution. The rate of labor-productivity increase accelerated sharply in communication
(largely the telephone industry) while the sector's share of real product also rose.
To summarize, the slowdown in aggregate
labor-productivity growth was almost wholly
attributable to productivity slowdowns within
the twelve industrial sectors. The level effect,
in contrast, accounted for only 0.3 percentage
point of the 2.0-percentage-point deceleration
in aggregate labor-productivity growth between the 1948-65 and 1973-78 periods. The
slowdown was spread widely across nine of the
twelve sectors, as demonstrated first by the
slowdown within sectors (Table 2), and also by
the individual contributions to the rate effect
(Table 4), which take into account both the
intrasectoral slowdowns and their relative
weights in the aggregate index.
tions of agriculture, construction, manufacturing, and trade. The sizable contribution of the
agricultural sector came mostly from its rapid
5.1-percent annual productivity increase (Table 2), as its real output share in 1948 was only
7.0 percent (Table 1). But agriculture's contribution to the rate effect was almost nil in the
most recent period, with a decline in its productivity growth rate to 1.6 percent and a decline in its real output share to only half of its
1948 level. In mining and construction, the rate
effects declined sharply, turning negative with
declines in the levels of labor productivity. In
the two manufacturing and two trade sectors,
the rate effects were large in the early period,
but declined significantly by the most recent
period (turning negative for wholesale trade).
The diminution in these rate effects can be
attributed almost entirely to slower rates of
labor productivity {ldvance within sectors (Table 2), because of the rough constancy of real
output shares (Table 1).
II. Capital Deepening and Total Factor Productivity
In this section, we measure total factor productivity-the rate of change of output per unit
of combined input of labor and capital.
Through the specification and estimation of
aggregate and disaggregated production functions, we estimate the slowdown in total factor
productivity for the aggregate economy and
for seven major sectors, and compare the
resultant trends to those of labor productivity.
We also estimate the role played by capital
deepening (rise in the capital-labor ratio) in
labor productivity growth, through a comparison of aggregate and disaggregated methods
of analysis.
Capital deepening affects labor productivity
differently from total factor productivity. It can
affect labor-productivity growth in at least two
ways. First, given a positive marginal product
of each factor of production, an increase in the
amount of capital used by the same number of
workers will result in a larger amount of output
produced per worker. Second, given the embodiment of technological improvements in
new plant and equipment, capital growth
should provide a further boost to labor productivity. If both effects are important, capital
formation will have a magnified impact on labor-productivity growth over time.
Table 5 shows a slowdown in growth in the
aggregate and sectoral capital-labor ratios 15
over time, with the exceptions of manufacturing and utilities. More importantly, slower
growth in the capital-labor ratios was not simply the result of slower growth in the capital
stock. Aggregate capital and labor growth both
accelerated in the second period, and labor
growth remained relatively high even in the
third period. On an aggregate basis, therefore,
the slower growth of the capital-labor ratio
largely reflected faster labor growth, particularly in the 1965-73 period when capital growth
also accelerated. The results for the 1973-78
period were mixed, however, as capital growth
decelerated from its 1965-73 rate in all but one
sector.
These patterns suggest no evidence of de12
used here (as in most aggregate productivity
studies) are net of intermediate inputs to production, so the production function should
properly include only the primary inputs-labor, land (including natural resources), and
capital. 17 Actually, we include only labor and
capital, because of the weakness of data for
land by industry. For simplicity, we use a standard Cobb-Douglas production function with
constant returns to scale. However, this type
of function requires strict separability18 and
constrains the elasticity of substitution between labor and capital to be constant and
equal to one. The function also includes a time
trend as a proxy for whatever technical change
that is not included in new capital investment:
clining investment (except in mining) until the
most recent period. However, the rate of new
investment failed to keep pace with accelerated labor growth in the 1965-73 period, and
has since dropped off precipitously. Norsworthy, Harper, and Kunze suggest that the behavior of capital-labor growth is consistent
with an observed acceleration in the price of
labor relative to capital between the 1948-65
and 1965-73 periods and a subsequent deceleration between the 1965-73 and 1973-78 periods. 16 Others have attributed this development to the rapid growth of inexperienced
workers over time. As the growth rate of inexperienced workers tapers off in the 1980s,
capital-labor growth may accelerate once
again, although the recent decline in capital
formation suggests that such optimism may be
unwarranted.
Q
=
AertK"U
(2)
where Q = output,
A = constant term,
r = rate change of disembodied technology or total factor productivity, 19
t = time trend,
Production Functions
To measure growth of total factor productivity, we must specify a production function linking labor, capital, and output. The output data
Table 5
Rates of Growth of Capital and Labor by Sector, 1948-78
(Percent)
1965-73
1948-65
1973-78
KlL
K
L
K/L
K
2.8
3.3
0.4
2.5
4.0
1.4
1.8
3.1
1.2
Agriculture!
7.3
2.8
4.2
7.3
3.0
-4.0
3.1
2.3
-0.8
Mining
5.4
2.9
-2.3
1.3
1.4
0.0
4.3
2.2
6.8
Manufacturing
1.9
2.8
0.9
2.3
3.3
1.0
2.4
2.6
0.2
Transportation
1.3
0.2
-1.0
0.4
1.2
0.7
-0.5
0.3
0.8
Communication
6.4
7.6
1.1
5.1
8.8
3.5
5.0
6.0
1.0
Utilities
5.1
6.0
0.9
4.3
6.4
2.0
5.0
5.9
0.9
Commercial and Other'
3.2
4.8
1.6
1.9
4.2
2.3
0.4
2.2
1.8
Private Domestic
Nonresidential Economy
L
KlL
K
L
'Data for agriculture differ slightly from those in Section I, because forestry and fisheries are excluded from agriculture
in this table (and in Section II) to conform to the capital-stock data.
'Construction, wholesale and retail trade, finance and insurance, and services.
Sources: Gross capital-stock data are from U.S. Department of Commerce for agriculture (excluding forestry and fisheries)
and manufacturing, and from Data Resources, Inc., for other sectors. (These data are calculated by DRI using
Department of Commerce service-life assumptions.) See Table 1 for sources of labor data.
13
K
L
= capital,
= labor,
(5). Similarly, equation (5) also can be estimated for each of the seven industries and the
contribution of the sectoral capital-labor ratio
to(s~~~)oral productivity growth is calculated as
a = elasticity of output with respect to
capital,
[3 = elasticity of output with respect to
labor.
The constant-returns constraint requires
a + [3 = 1. Using this constraint and dividing
both sides by L, we obtain an expression that
relates labor productivity (Q/L) to the capitallabor ratio:
P = Ak"e rt
k = KlL, P = Q/L
a
=
rdt+a(dk/k)
Before equation (5) can be estimated, terms
must be added to account for the effect of the
business cycle on labor productivity, and to
allow for secular shifts in the growth rate of
total factor productivity. To remove businesscycle-related movements, annual changes in
the manufacturing capacity-utilization rate
were used as a surrogate for business-cycle
conditions affecting the aggregate and sectors. 21
We allowed the value of r to vary over the
subperiods of the 1948-78 period, to reflect the
probability of a growth slowdown for total factor productivity as well as for labor productivity. Thus we added dummy variables to account for shifts in r among the 1948-65, 196573, and 1973-78 periods. 22
Adding the cyclical and dummy variables to
equation (5) produces the following equation
for estimating the aggregate and the seven sectors:
(3)
(4)
%ap
which can be approximated by
%aP = r+a(%ak)
.
I
In this formulation, a represents the elasticity
of labor productivity with respect to the capital-labor ratio (i. e., the percentage change in
labor productivity with respect to a one-percent change in the capital-labor ratio). If the
rate of growth of total factor productivity is
zero (i.e., there is no disembodied technical
change and r = 0), the rate of growth of labor
productivity is simply a times the rate of
growth of k, the rate of increase in the capital
intensity of production. This can be seen by
totally differentiating (3) logarithmically with
respect to time.
PdP
k
l
=
r + 0ld l + 02d2 +
a%ak+')'%aUCAP+J.L
(6)
where time SUbscripts have been suppressed
for simplicity. The estimated coefficients have
the following interpretations:
(5)
where r represents the percentage change in
total factor productivity (disembodied technical change).
To assess the role of capital formation in the
slowdown, it is necessary to determine a. Although this can be done in more than one
way,zo our approach estimates the aggregate
and sectoral production functions econometrically, using historical data. The contribution of
the capital-labor ratio to labor-productivity
growth, with the aggregate method, then is
r
average annual rate of increase in total
factor productivity (disembodied technical change), 1948-65;
01
shift in the average rate of change of
total factor productivity between the
1948-65 and 1965-73 periods;
O2
shift in the average rate of change of
total factor productivity between the
1948-65 and 1973-78 periods;
a = elasticity of labor productivity with respect to the capital-labor ratio (and of
output with respect to capital);
a(:k), where a is estimated from equation
14
=
'Y
elasticity of labor productivity with respect to the capacity-utilization rate in
manufacturing.
tors. However, there were a few exceptions,
especially the "commercial and other" sector,
which showed a deceleration in labor-productivity growth but an acceleration in total factor
productivity. Apart from data errors, we can
interpret the divergence in trends to mean that
improvements in efficiency helped improve the
productivity of costly capital inputs in this sector. This seems logical, because inexperienced
and inexpensive labor inputs tended to increase the fastest in areas such as retail trade
and services.
Because aggregate labor-productivity growth
is a function of within-sector productivity
growth, as well as of input and output shifts
among sectors, we can derive an alternative
estimate of the effect of capital-intensity
growth on aggregate labor-productivity change
by combining estimates for individual indus-
Table 6 shows the estimation results for
equation (6) with ordinary least squares, with
Cochrane-Orcutt data transformations. Given
that the equations are expressed in percentagechange form, the R-squared values are remarkably high, although the standard errors of
the regressions reveal considerable variation in
the estimated rates of labor-productivity
change within sectors. 23
The coefficients r, r + OJ, and r + O2 give the
estimated annual rates of increase of total factor productivity over the three subperiods. As
shown in Table 7, they indicate a similar movement in total factor productivity as in labor
productivity, in the aggregate and in most sec-
Table 6
Regressions of Production Functions for the Private
Domestic Nonresidential Economy and Major Sectors, 1948-78
!
Private Domestic
Nonresidential Economy!
~
~
R'
S.E.E.
D.W.
~
.37*
(5.48)
.61
1.1
2.05
-.25
( -1.39)
- .32*
3.87)
.71
2.6
1.92
-.53*
(- 3.36)
!!
!
1.3*
(2.52)
-0.6*
-0.9*
( -1.55) ( -1.77)
.67**
(4.21)
1.2
(1.25)
-0.6
(- .81)
1.2
( -1.14)
.64**
(5.60)
Mining
2.8*
(2.91)
-1.2
(- .94)
-6.0*
(-3.16)
.34**
(2.45)
.16
(1.68)
.68
2.4
1.44
.10
(.56)
Manufacturing
1.6*
(2.19)
-0.1
(- .12)
-0.6
(- .64)
.53**
(1.99)
.61*
(2.79)
.23
2.1
1.98
-.25
( -1.38)
Transportation
2.8*
(5.35)
0.0
(.04)
-1.7
( -1.64)
.19
(.85)
.36*
(3.00)
.41
2.2
1.87
-.24
( -1.34)
Communication
1.6*
(2.75)
0.0
(- .05)
2.6*
(4.46)
.59**
(7.43)
.14*
(2.66)
.62
1.5
2.25
- .42*
( -2.47)
Utilities
2.6*
(1.82)
-2.4*
-4.8*
( -2.78) (-4.94)
.68**
(2.54)
.09
(1.12)
.44
2.6
1.92
- .43*
( -2.54)
Commercial and Other
0.4
(.53)
.55**
(2.84)
.21'
(3.81)
.36
1.4
2.04
-.03
(- .15)
Agriculture'
0.1
(.08)
0.5
(.59)
(
Entries in parentheses are t-statistics. * Indicates that the coefficient is significantly different from zero with 9O-percent
confidence, with the use of a two-tailed test. ** Indicates the same with the use of a one-tailed test.
!Capital data were calculated as the sums of component sectors. With the use of the BEA aggregate for gross capital
stock in the private domestic nonresidential economy, the estimates were comparable: r=0.9; ()!= -0.7, ()2= -0.7,
0.=.73, '{=.37.
'Excludes forestry and fisheries.
Source: see text.
15
tries. To derive the proper weights, we begin
by dividing aggregate productivity change into
rate and level effects, as shown by the continuous version of equation (1),
(Rate) (Level)
2: . dP j + 2: . dlj
q, P,
q, I,
dP
P
obtain an estimate of the importance of growth
in the disaggregated capital-labor ratios to the
slowdown in aggregate productivity growth.
Table 8 compares this result with that obtained
Table 8
Contribution of Growth in the CapitalLabor Ratio to Labor Productivity Growth,
1948-78
(Average Annual Rates of Increase)
(7)
Substituting equation (4) for the individual
sectors, we obtain
1948-651965-731973-78
dP
P
h
were
= 2:qj
Aggregate Productivity
[ rjdt+uj k
dk j + T
dl j ]
dkj
Change from Prior Period
.
.
2.26
1.24
-0.98
-1.02
1.66
1.23
-0.22
-0.43
1.34
0.76
-0.36
-0.58
Contribution of K/L
U(lZ represents the loth sector's contnI
Aggregate Method'
bution of growth in capital intensity to its own
sector's productivity growth. Therefore, the
weights for calculating the sectoral contributions of capital-intensity growth
3.24
(8)
( dk)
uciZ
1.88
Change from Prior Period
Disaggregated Method 2
to
1.70
Change from Prior Period
aggregate labor-productivity growth are the
output shares, qj.
We aggregated the industry contributions of
capital-intensity growth, using output shares to
'adklk.
2Lqiaidk/ki, where the q:s are the average shares within
the subperiods.
Sources: Tables 1, 3, 5, 6, and text.
Table 7
Labor Productivity and Total Factor Productivity, 1948-78
(Annual Growth Rates, in Percent)
Total Factor Productivity
Labor Productivity
1973-78
!948-65
1965-73
1.2
1.3
0.7*
5.1
1.9
1.1
0.5
-0.1
4.3
1.9
-4.8
2.8
1.6
-3.2*
Manufacturing
3.0
2.6
1.6
1.6
1.5
1.0
Transportation
3.1
2.9
0.8
2.9
2.9
1.2
Communication
5.4
4.6
7.1
1.6
1.6
4.2*
Utilities
6.3
3.5
0.7
2.6
0.2*
-2.2"
Commercial and Other
2.3
1.4
0.9
0.4
0.5
0.9
1948-65
1965-73
3.2
2.3
Agriculture'
5.3
Mining
Private Domestic
Nonresidential Economy
1973-78
0.4*
*Indicates a statistically significant shift in total factor productivity at the 90-percent confidence level, as compared with
the rate in the 1948-65 period (see Table 6).
lExcludes forestry and fisheries.
Sources: Tables 5 and 6.
16
from the aggregate estimated equation. Both
methods indicate a large role for capital deepening in the growth of labor productivity. However, the aggregate method attributes greater
importance to the capital-labor ratio in explaining labor-productivity growth (especially
in 1973-78), and less importance in explaining
its slowdown. Specifically, the aggregate
method attributes 0.65 percentage point (one
third) of the 2.00-percentage-point slowdown
in labor-productivity growth to slower growth
of the capital-labor ratio, while the disaggregated method attributes 0.94 percentage point
(almost half) to slower growth of the capitallabor ratio.
An explanation of this discrepancy involves
an analysis of the estimated a's from equation
(6). If the Cobb-Douglas specification of the
production function is appropriate, the estimated aggregate a should be roughly .2 to .4,
depending on whether one compares it to the
profit share or to the nonlabor share of gross
private domestic product. 24 However, as Table
6 shows, the estimated a from the aggregate
equation is .67. Clark (1978) obtained a similar
result of .70 for his aggregate equation using
gross capital stock (.48 using net capital
stock).25
Clark (1978 and 1979) attributed the discrepancy between his estimate of a and capital's income share to the embodiment of technical progress in new capital goods. (Under
this condition, new capital investment would
produce output greater than that predicted by
the percentage change in capital times its income share.) The estimated a from a simple
production function such as (5) might well be
greater than capital's share if technical progress
is introduced largely through its embodiment
in new capital goods. However, it would affect
the a's of both the aggregate and sectoral equations, and thus would not explain why the aggregate a is above the sectoral estimates.
but one of the a/s from the individual equations are lower than the aggregate, ranging
from .19 to .68, with an unweighted average
of .50.
Another way to compare the industry ai's
with the estimated a from the aggregate equation is to calculate a weighted average, with
the weights based on the following identity:26
(9)
The aggregate a in any time period depends
on the percentage increases in the capital stock
in each sector relative to the total, as well as
on the ai's and qi'S. Although the aggregate a
represents the percentage change in output
that occurs as a result of a one-percent increase
in aggregate capital stock, the size of this output increase will depend in part on the sources
of growth in capital stock. 27
Table 9
Output-Capital Elasticities vs. Nonlabor
Income Shares, 1948-78
Standard
Error
Industry
Private Domestic
Nonresidential Economy .67
Nonlabor
Income
Share
.16
.43
Agriculture
.64'
.11
.85"
Mining
.34'
.14
.63
Manufacturing
.53
.27
.31
Transportation
.19
.22
.31
Communication
.59
.08
.50
Utilities
.68
.27
.65
Commercial and Other
.55
.19
.45
'Significantly different from the nonlabor income share
at the 90-percent confidence level, with the use of a
two-tailed test.
"Because of the high proportion of self-employment in
farming, this share includes a significant amount of
income that should probably be classified as return to
labor.
Aggregation Bias
Comparison of the aggregate a with those
of the individual sectors (Table 9) indicates
that aggregation bias might be partly responsible for the high value of the aggregate a. All
Sources: Table 6, and National Income and Product
Accounts, Table 6.1.
17
Equation (9) provided values of u of .65,
.59, and .45 for 1948-65, 1965-73 and 1973-78,
respectively. The deceleration primarily reflected a slowing trend in the relative increases
in the capital stock of the large "commercial
and other" sector over the three periods.
These calculations for the aggregate u were all
lower than the value of .67 that was estimated
using the aggregate equation. Therefore, the
aggregate u is biased in its level, since one
would expect its estimated value to lie within
the bounds of the three calculated values.
it is biased in its insensitivity to compositional shifts in output and capital over time,
since the sectoral u/s imply an aggregate u that
declines in each subperiod.
As noted earlier, the contribution of capitalintensity growth to productivity growth with
the aggregate method is u(dk/k). In addition
to the biases in aggregate u, there is also a
(potentially offsetting)l bias in dklk. This bias
occurs because the aggregate method does not
distinguish between two different effectschanges in the aggregate capital-labor ratio, k,
that are due to growth of capital intensity
within sectors, and changes that are due to
shifts in employment shares among sectors
with different levels of capital intensity. These
compositional shifts are important because of
the persistent tendency for sectors with relalow capital-labor ratios (except agriculto expand their shares of employment
over time. Therefore, the rate of growth of the
aggregate capital-labor ratio understates the
combined within-sector rates of growth and the
combined effects of their decelerations over
the three subperiods.
The empirical importance of this effect can
be seen from Table 10, which decomposes the
aggregate growth of the capital-labor ratio into
rate and level effects using equation (B-2) in
A]:lpendix B. The rate effect accounts for the
Table 10
Breakdown of Aggregate Capital-Labor
Growth Into Rate and Level Effects
1948-65 1965-73 1973-78
Total
2.80
Change from Prior Period
Rate Effect
3.26
Change from Prior Period
Level plus Interaction Effect -0.46
2.47
1.83
-0.33
-0.64
2.86
2.17
0.40
-0.69
-0.39
-0.34
Source: Equation B-2 in Appendix B, using subperiod
averages for share variables.
within-sector growth of capital intensity, while
the level effect measures the net contribution
of shifts among sectors with different capitallabor ratios. The level effect is negative in all
three periods, and declines in absolute value
over time. Hence the growth rate of the aggregate capital-labor ratio (the total effect in Table 10) understates the amount of growth of
within-sector capital intensity (the rate effect)
during the three time periods, and also understates the extent of its decline.
The biases in aggregate u and in dk/k are in
part offsetting, but because of their combined
effect, the aggregate method underestimates
the importance of capital-intensity growth in
the slowdown of aggregate labor-productivity
growth. With the disaggregated method,
slower capital-intensity growth accounts for
0.94 percentage point (almost one-half) of the
2.00-percentage-point decline in labor-productivity growth between the 1948-65 and 1973-78
periods, as opposed to 0.65 percentage point
(one-third) of the decline with the aggregate
method. A detailed analysis of the aggregation
bias from a theoretical point of view is presented in Appendix B.
18
III. Summary and Conclusions
slowdown on a disaggregated basis, but only
one-third of the slowdown on an aggregate
basis. The aggregate method understates the
importance of the slowdown in capita.ldeepening, because of aggregation bias. OUf theoretical and empirical results strongly support
the use of disaggregated data-which is important because most other productivity studies have relied on aggregated· data. Shifts in
employment shares among sectors can cause
difficulty, both in the estimation of the.. production function and in its application toquestions such as those examined here. While it
would be impossible to avoid these difficulties
altogether, it is still worthwhile to disaggregate
the data as far as possible.
The effect of the slowdown in capital-intensity growth on labor productivity growth was
paralleled by a coincident decline in total factor productivity growth. The two trends signify
not only a decelerating substitution of capital
for labor, but also a deterioration in the rate
of increase in the combined efficiency of the
two inputs. That trend, in fact, has pervaded
most sectors of the economy. The aggregate
observations were confirmed-if not strengthened-by the disaggregated analysis.
The underlying causes and possible remedies
of these worrisome trends have become the
subject of much controversy. A number of contributing factors have been cited for the productivity slowdown, such as rapid increases in
the number of inexperienced workers, business-cycle uncertainties, higher energy prices,
inflation, governmental regulations, environmental priorities, and tax laws. Although all
factors seem to have had some impact, no single one stands out as the prime cause of the
slowdown in capital deepening or productivity
growth. But our analysis suggests that, whatever the underlying causes, the effects of the
slowdown have been pervasive throughout the
economy.
The growth rate of aggregate labor productivity slowed from 3.2 percent per year in the
1948-65 period, to 2.3 percent and 1.2 percent
in the 1965-73 and 1973-78 periods, respectively. In this study we have analyzed the linkages among the sectors and the aggregate. The
results indicate that the sharp productivity
slowdown was widely dispersed across most
sectors of the economy. Moreover, almost half
of the slowdown was related to capital investment's failure to keep up with the rapid growth
of the labor force.
Similar results were evident from our analysis of the broader measure, total factor productivity. This measure showed a deceleration
from a 1.3-percent annual growth rate in the
1948-65 period to rates of 0.7 percent over
1965-73 and 0.4 percent over 1973-78. This
deceleration also occurred widely across most
sectors.
Intersectoral shifts in employment and output-the "level" effect-explained only a minor part of the aggregate productivity slowdown. The effect of shifts across sectors with
differing productivity levels was relatively
small in the early period (0.43 percent per year
over 1948-65), and was even smaller in recent
years (0.15 percent per year over 1973-78).
The diminution of the level effect thus accounted for only 0.3 percentage point of the
2.0-percentage-point deceleration in aggregate
labor-productivity growth.
The small level effect evident in the U.S.
private economy over the past generation contrasts starkly with the large sectoral-shift effects normally evident in rapidly industrializing
countries, where workers move rapidly from
low-productivity agricultural employment to
high-productivity industrial jobs. The productivity boost from sectoral shifts of this type,
once important in U.S. economic history, apparently is no longer so.
Reduced growth of capital deepening explains almost half of the labor-productivity
19
Appendix A
The Rate Effect and Divisia Aggregation
One can interpret the rate effect under direct
aggregation as a close counterpart to laborproductivity change as measured by Divisia
aggregation. Economists believe Divisia aggregation to be particularly appropriate for measuring productivity change,28 because this approach is consistent with generalized production
functions such as the translog function, and
because the aggregate index is based on a
weighted average of within-sector rates of
change, thereby effectively netting out level
effects. For the multisector Divisia index of
aggregate productivity, outputs and inputs are
not summed directly across sectors as they are
under direct aggregation. Instead, growth rates
of real outputs (inputs) are calculated for each
of the sectors, and the aggregate index of real
output (input) growth is then computed as a
weighted average of the growth rates of real
outputs (inputs) in each of the sectors, where
the weights are nominal output (nominal input) shares. The Divisia productivity index is
thus the difference between the instantaneous
rates of growth of output and inputs.
In algebraic form, the multisector Divisia
productivity index may be stated29
where Yi
Oi
=
=
(A-2)
P I '+.::.w·" LlLi
I
Li
where the annual subscripts have been suppressed for simplicity.
There are two conceptual differences between the direct and Divisia productivity indices. First, the Divisia index essentially measures only the rate effect, and hence is free of
the "bias" imparted by a level effect. In the
aggregate Divisia index, within-sector growth
rates are weighted by shares that sum to one,
so that the growth rate of the aggregate index
reflects only the weighted average of the
growth rates within the individual sectors. Second, the Divisia index weights the growth rates
of sectoral components by their nominal output and factor shares. These nominal shares
are the products of real shares and relative
prices, the latter of which proxy for the marg.inal values (outputs) and marginal products
(mputs). Thus, the Divisia index is effectively
a value-weighted "rate" index.
The similarity between the Divisia index and
the direct-aggregation-rate effect can be demonstrated easily. From equation (1) in the text,
the continuous form of the rate effect in direct
aggregation is
= nominal output share of the i-th
Wi =
Li
1+
1 +~Yi LlO i
_LlP = _ _---:O:.:..i
sector
real output of the i-th sector
nominal wage share of the i-th
sector
labor hours employed in the ith sector
which can be rewritten as
(A-3)
The Divisia index is a continuous index, although it is normally approximated with a discrete counterpart because of the unavailability
of continuous output and input data. 30 With
annual data, the above formula can be approximated for annual growth rates:
By comparison, the Divisia index in equation
(A-I) can be rewritten as
(A-4)
20
where Pi
=
Vi
=
tween the two rests largely on whether or not
one prefers to weight data by prices as proxies
for marginal products.
the relative price of output in
the i-th sector
the relative wage of labor in the
i-th sector.
Table (A-1)
l\Yo Measures of Labor
Productivity Growth
(Annual rate, in percent)
Equations (A-3) and (A-4) demonstrate that
the rate effect under direct aggregation and the
Divisia productivity index are identical, except
that the rate effect uses real output shares as
weights (even for inputs), whereas the Divisia
index uses nominal output and input shares as
weights for outputs and inputs, respectively.
Table A-I demonstrates that the rate effect
and the Divisia index result in strikingly similar
measures of aggregate-productivity change.
Thus, both the rate effect and the Divisia index
provide a good measure of productivity change
net of "aggregation bias," and the choice be-
1948-651965-731973-78
Rate Effect
2.82
Percentage Point Change
2.80
Divisia Index
Percentage Point Change
2.05
1.14
-0.77
-0.91
2.07
1.18
-0.73
-0.89
Sources: Table 3 in the text for the rate effect. Equation
(A-2) is iterated annually for the Divisia index.
Appendix B
Aggregation Bias
Aggregation bias may occur when sectors
with varying characteristics are treated as if
they were homogeneous. If there were no aggregation bias-that is, if all components of
the aggregate were alike-the two methods
used in this paper to calculate the contribution
of the capital-labor ratio to productivity growth
would produce the same results. However, the
empirical results indicate that this is not the
case. To examine the theoretical difference between the two methods, we first need to separate changes in the capital-labor ratio into
rate and level effects, deriving results analogous to equation (3) for labor-productivity
change. Since
From equation (4), the contribution of the
capital-labor ratio to labor-productivity change
. dk
as measured by the aggregate method IS <XT'
or:
(B-3)
The contribution as measured by the disaggregated method, as previously described in
.....
dkiCIearly, the two cal. ()
equation
8, IS
..:.qi<XiT'
l
culations would produce identical results if
k
dl
k '
~ ~
(B-1)
then
<xK
K
<X
<Xi
Q./Q
K/K'
= 0 and - ' = <X.q. or _ = -''"
These conditions would be fulfilled if the sectors were homogeneous, since then k; = k for
all i, and thus the term
~~ dli is zero by defi-
nitioh. Also, since the output-capital ratios
would be the same across sectors, Q/Ki =
Q/K. The aggregate a could then be derived
from equation (9), setting <Xi = <Xi for all i and
j.
21
L~k dl;, in the growth equation for the capital-
(B-4)
labor ratio (B-2) is correlated with the level
effect in equation (7), which (from footnote 8)
can be written equivalently as
and since LdK; = dK, ex = a;.
In this situation, therefore, there is no ambiguity involved in the definition of the aggregate ex, which is independent of the data. Since
there is no aggregation bias, use of a disaggregated method provides no further information.
Given the Cobb-Douglas production function and a perfectly competitive economy, the
two methods would also produce the same results so long as there were no employment
shifts among sectors. The Cobb-Douglas funcQ; for a11 1,. an d pe rfect
. Imp
. l'les -SQ; = 0.;bon
SKi
Ki
oQ
SQ
competition implies - ' = _ J Therefore,
oK;
SKj'
Q.
Q
exi..--2 = exi-l, and from equation (B-4) ,
K;
dP
P
=
(Rate) (Level)
dP;
P;
Lqi T , +L pdli.
(B-6)
Hence the independent variable in the aggre·
gate-productivity equation (4), dk/k, is correlated with the error term. This can be seen by
first adding an error term to equation (4) for
the aggregate and sectors, assuming for simplicity that r = 0 (no disembodied technical
change):
dP
P
dk
k
- = ex-+u
(B-7)
dP i
dk i
= ex·-+u
'
Pi
'ki
(B-8)
and
Kj
-
_ L Qi K dK; _ SQ; K LdKi
ex - a;Ki Q dK - oKi Q dK
SQi K
=-SKiQ
Hence, the condition exQ
K
=
(B-S)
Then, substituting (B-8) into (B-6), and (B2) into (B-7), we have:
dP
i
aLt
Pi
1
a?Ki would hold
=
under constant employment shares even if the
sectors were not perfectly homogeneous. However, the existence of sectoral shifts in employment shares will result in a difference between
the aggregate and disaggregated methods, so
long as sectors are not homogeneous. Specifically, the difference will be
dk;
-P = Lq·ex·+ Lq"u + :S-dl
, 'k,.
P
(B-9)
Kdk
k
exL.....! - ' + exL.2dl + u.
K ki
k'
Rearranging terms, (B-9) becomes
dl i, or the
p + L ( --!
P
level effect in capital·labor ratio growth multiplied by ex.
The existence of this level effect also introduces bias into the ordinary·least-squares estimation of the aggregate ex. Since sectors with
higher capital·labor ratios typically have higher
labor·productivity levels, the shift effect,
k)
(B-l0)
k dl,.
0..2
As before, if the sectors are homogeneous,
exiqi = aK;lK, Pi = P, and ki = k. Then, the
second two terms in (B-l0) reduce to zero, and
the error term, u, is composed only of the
weighted random components Ui' If the sectors
22
~~ dl.
~Ki dli
"::'k "or"::' K I.
are not homogeneous, however,theerror term
will consist solely of random components only
if there is no aggregation bias. As before, this
condition will be met if the Cobb-Douglas and
perfect-competition assumptions hold, so that
aQ/K = (XiQ/Kj, and if there are no changes
in employment shares. If the Cobb-Douglas
and perfect-competition assumptions hold, but
there are shifts in employment shares, (B-lO)
reduces to:
1
Ki ai
Substituting K = a qi, this term becomes
dl
+ ~qi(l- ai)j .
(B-12)
The estimate of a will be biased if the non-
~q/l
ai) ~li is
1
correlated with
~k.
h
Since the nonrandom part of u is
(1 - ai)
dl
j, the degree to which a is biased
1
1
random part of the error term,
a
depends on how close (1 ai) is to ai' We know
that the ai must lie between 0 and 1; the closer
they are to 0.5, the closer will be the correspondence between the independent variable
and the error term in equation (4).
As we have seen, the industry output-capital
elasticities in fact cover a fairly wide range, .2
to .7 (Table 9). However, the unweighted average is .50, while the average weighted by
output shares is .45. Therefore, there is some
indication that the independent variable, dk/k,
in the aggregate equation (4) (or equation (6»
is positively correlated with the error term.
This correlation should produce an upward
bias in the estimation of a in the aggregate
equation. This seems to be the case, because
of the discrepancy between the estimates of a
and ai in Table 6.
Recalling that P = Q/L, k = KlL, and making
use of the relation aiqi = aK/K, we can write
equation (B-ll) as
= ~qiUi
dl i
~qi
(B-ll)
u
1
-~aiqi-'
The level or bias effect in
dk
-;-, i.e., the second term in equation (B-2), is
K
23
RATE AND LEVEL EFFECTS
Several studies have decomposed aggregate productivity change into rate and level effects, but
the formulae used were complicated and difficult to interpret. Nordhaus (1972) derived a multisector framework that somewhat resembled the one in this paper. Independently, Grossman and
Fuchs derived a two-sector model that was simplified and extended by Beebe. Subsequently, Clark
and Blakemore formulated and solved the multisector problem much more concisely, and their
analysis was used by Haltmaier. The derivation below extends that of Clark and Blakemore, and
results in a decomposition that is easily interpreted and applied.
Using the following definitions,
Qi
real output in the i-th sector (i = 1, ... , N)
Q
~Qi = aggregate real output
qi
Q/Q = i-th sector's share of real output
Li
labor hours employed in the i-th sector
L
~Li = aggregate hours employed
Ii
L/L = i-th sector's share of hours employed
Pi
Q/Li = real output per hour in the i-th sector
P
Q/L = aggregate output per hour
and beginning with the identity,
~Q
~PL
P == Q/L = - ' = _'_I =
L
L
~PJ.
II
,
then for a discrete time period,
.lP = ~li.lPi + ~Pi.lli + ~.lPi.lli ,
where the three terms represent the rate, level, and interaction (second order) terms, respectively.
For a percentage change over the finite interval,
.lP
1
1
1
P = p~li.lPi + p~Pi.lli + paPiali .
Using the following identities,
and
Pi _ Q/I.., or'! = Q/Q 1. ,
Q/L'
P
L/L ~
and substituting into the above equation,
.lP
L;
Q/I..;
Q/Q 1
P = ~Q.lPi+~ Q/L .lli+~ L;!L ~.lPi.lli
P=
=
~Li ~.lP + ~Qi .!al + ~.lPi Qi .ll;
Q Pi
'
Q I;
P; Q Ii
1
_ ~ .lP; ~ .lli ~ aPi .lli
- q; p. + qi I + qi p. I.'
I
1
1
l
which are the rate, level, and interaction effects used in the text.
24
FOOTNOTES
1. Denison (1973) and Nordhaus (1972). Because these
studies were done prior to the 1973 business-cycle peak
and the economy had not recovered fully from the effects
of the 1970 recession, it was difficult to measure the
secular productivity slowdown.
and
9. The private domestic nonresidential economy excludes
output of government and government enterprise. "rest of
the world," and the imputed rental value of farm and nonfarm dwellings. Residential construction is included in the
total.
3. For example, see Thurow, pp. 86-87.
4. For other recent papers that employ various degrees of
disaggregation, see Norsworthy, Harper, and Kunze, Haltmaier, Gollop and Jorgenson, Gollop, Kendrick and Grossman, and Bennett.
10. Labor productivity exhibits a strong cyclical component, because the stock of capital is largely fixed in the
short run and labor may be combined with capital at differing intensities. Moreover, because there may be significant costs associated with labor turnover, fluctuations in
labor productivity tend to lag the business cycle (see Gordon and Sims). For the data in this section, the cycle in
productivity is removed by calculating trends between selected "peak" years for productivity: 1948, 1965, 1973,
and 1978. (see Norsworthy, Harper, and Kunze, pp.
389-90.) For the regressions in Section II, a cyclical variable is entered directly into the equations to account for
the cyclical component of productivity. Moreover, the entire
analysis was performed on cyclically adjusted output and
labor data that were constructed using an econometric
scheme derived from work by Clark (1978) and Nordhaus
(1972). The results based on cyclically adjusted data were
very close to the ones reported here. The two methods
gave similar growth rates because the end points of the
periods are peak productivity years.
5. For an extensive analysis, see Norsworthy, Harper, and
Kunze. For comprehensive summaries see Kendrick,
Denison, and Tatom. Other recent papers of importance
are by Berndt, Crandall, Nordhaus (1980), and Kopcke.
6. Direct aggregation is not the only method of aggregation; nor is it necessarily the best, particularly in the case
of productivity. However, it is used officially and is commonly understood-all official pUblished productivity data
are based on direct aggregation. For these reasons, the
formulae derived in this paper are based on direct aggregation, although we compare our results to those obtained
using Divisia aggregation.
7. Equation (1) can be calculated over a full period or
calculated iteratively within the period. For example, in
analyzing the rate, level, and interaction effects over, say,
a 10-year period, one could perform a single calculation
for the entire period using the q at the beginning of the
10-year span and the full 10-year percentage changes in
each of the other variables to arrive at the calculated
components. The rate, level, and interaction components
would sum to the total, with each component and the total
expressed as a 10-year percentage change. In converting
to annualized compound rates of change, however, the
components no longer would sum to the total because of
nonlinearities involved in compounding. (See Levine for
a generalization of this problem.)
11. The relatively steady behavior of the productivity series for finance and insurance and for services may result
from unreliable output data. See Footnote 12.
12. The decline in the construction industry is sometimes
attributed to erroneous real-output data, although it is difficult to explain why data problems would cause a sudden
shift in the behavior of the series. In the construction,
finance and insurance. and service industries, output is
measured in terms of inputs in several constituent industries where there is no standardized product. There also
is inadequate correction for quality change in the price
indices within these industries. These problems suggest
that the output and productivity data for these sectors may
be of insufficient quality for productivity analysis, although
they do not suggest that the shifts in trends are necessarily
linked to data problems. See Norsworthy, Harper, and
Kunze, p. 393, and Rees.
An alternative is to iterate equation (1) annually (or over
any other short period), calculating a rate of change for
the total and each component for each year in the 10-year
period and allowing the qj to change for each year. This
method, which is used throughout the paper, has three
advantages: the annualized growth rates of components
always sum to that of the total; the q are representative
of the average values of each subperiod rather than simply
the initial values; and the methOd of calculation is comparable to that of the annual Divisia index against which
the rate effect is compared in Appendix A.
13. Pre-1972 data were utilized in some studies that attributed the deceleration in the late-1960's and early1970's to the level effect. Because of the difficulty in removing the cyclical· effect of the 1970 recession from the
data, the years beyond 1968 could be relied on only tenuously. At that time, the diminished level effect due to the
declining shift out of agriculture appeared to explain a
large part of the small deceleration then apparent in aggregate productivity growth. The recent contention of Thurow, pp. 86-88, reiterating the present importance of the
level effect, simply is not supportable using disaggregation
at the level used in this (or his) study.
8. An individual sector's contributions to the overall rate,
lavel, ar.d interaction effects are respectively,
~P;
I
~
d
I. ,an q
,
~P;
P
I
In this form, the level effect is the change in the sectors'
labor shares weighted by their relative productivity levels.
2. Such shifts may be tied in part to the relative supplies
of inexperienced and experienced workers. See Perry and
Wachter and Perloff.
q T ' qj
~~I
P
~
I
Since q/lj may be expressed alternatively as PIP (the
sector's relative level of productivity) the level effect may
also be written as
25
18. Strict separability requires that exclusion of some inputs, such as goods in intermediate stages of production,
not affect the optimal mix of the included inputs, labor and
capital.
14. To get the rate effect, one does not simply mUltiply
the real product share in Table 1 times the annual rate
of increase in Table 2, although these figures are appropriate for analyzing that effect. For its calculation, see
Footnote 7.
19. Disembodied technical change and changes in total
factor productivity are used interchangably to mean a shift
in the production function. See Jorgenson and Griliches,
p. 250, and Norsworthy, Harper, and Kunze, p. 395.
Sectoral level effects are not shown in Table 4 because
the individual level effect is negative if al; is negative, i.e.,
if the sector's labor share declined over the period. So
long as a sector's labor share increased, the level effect
is positive even if the sector displays relatively low productivity. Thus, the level effects measure only a portion of
the full effect on aggregate productivity when labor shifts
from one sector to another. To see this, consider what
would happen if a worker were to shift from the agricultural
to the manufacturing sector. Both output and employment
would fall in agriculture, but would rise in manufacturing.
The full effect of such a shift depends on the productivity
levels in both sectors, and thus cannot be picked up by
a level effect associated with a single sector. Generalizing
from this example suggests that one should focus on the
aggregate level effect (Table 3) rather than on the individual level effects of the sectors.
20. Under the assumptions that production conforms to
the Cobb-Douglas formulation and that the economy is
perfectly competitive, the elasticity of output with respect
to each factor will be equal to that factor's share of total
income. Thus, a can be estimated as capital's historical
income share. This is the approach used by Denison.
21. Because capacity utilization in manUfacturing is probably not a good surrogate for business conditions in many
sectors, we experimented with other ways of removing the
cycle in labor productivity. Data for normal hours and output were constructed using a technique based on work by
Clark (1978) and by Nordhaus (1972). Although this
method produced similar results, it is much more complex
and has led to much controversy. We also used the
method described in the paper, with percentage changes
in 1972-dollar GNP (less the mean percentage change)
in place of the capacity-utilization rate. Although real GNP
is preferable because of its broader-based coverage, it
imparts a bias because its percentage changes are endogenous to the secular trend in productivity. Therefore,
we found it preferable to use the manufacturing capacityutilization rate as a proxy for the economy-wide business
cycle.
Separate analysis by the authors shows that the most
important labor shifts impinging on the level effect have
been the declining share of labor in agriculture (a sector
with a low relative level of productivity); an increasing
labor share in services (low relative productivity level) and
finance and insurance (high relative productivity level);
and a shift in mining (high relative productivity level) from
a declining to a rising labor share. Although the labor
shares of the manufacturing sectors have declined on
balance, the productivity levels of these sectors are very
close to the aggregate average.
22. The dummies are zero except for the following years:
d, = 1 for the annual changes 1965-66 through 1972-73,
and d2 = 1 for 1973-74 through 1977-78.
15. As noted in Table 5, capital data are for gross capital
stocks. The sources are the Department of Commerce for
agriculture and manufacturing, and Data ResoUices, Inc.,
for the other sectors. (Data for the total are sums of the
sectoral data.) The analysis was performed also using
sectoral data by Kendrick and Grossman. The results
were comparable except for a few sectors, most notably
mining, where the estimated a'S made little sense. Jane
Haltmaier is exploring other data sources, but we are not
yet prepared to make strong statements about the quality
of our data. We have also run our equations using Commerce data for aggregate gross and net capital stocks,
and we report these results in the paper.
23. The means of the dependent variables are the average
rates of labor-productivity change over the 1948-78 period, which can be approximated from Table 7.
24. Since only two factors of production (labor and capital)
have been included in the estimated equations, it is difficult to say which figure should be used. The figures correspond to the shares of income (output) classified as (1)
profit-type return only, and (2) profit-type return plus net
interest, indirect business taxes, and capital consumption
allowances. The latter share has been quite stable over
the 3D-year period, ranging from .39 to .47. The income
(output) measure is gross domestic product, less government. Data are from Table 6.1 of the National Income and
Product Accounts.
16. Norsworthy, Harper and Kunze found that the capitallabor ratio accelerated in the 1965-73 period for the private nonfarm business sector. According to their analysis
(pp. 419-20), the investment tax credit appears to have
reduced the rise in the cost of capital during the 1965-73
period, while the sudden rise in energy prices in 1973-74
(and the apparent complementarity of energy and capital
in production) may have retarded capital formation in the
1973-78 period.
25. Net capital stock is not available on a disaggregated
basis. In estimating our aggregate equation using the BEA
series for net capital stock, we obtained an estimate of
.55. Thus our empirical results are quite close to those of
Clark.
26.Equation (9) is derived as follows:
17. Much debate has centered around the inclusion of
energy input or its price in a value-added production function. Most energy use should be excluded, although the
price of energy might provide a reasonable surrogate for
other factors, such as changes in the optimal capital-labor
ratio. See Kopcke.
_ dO JS. _ 2: dO; ~ JS. = 2: dO; -'S-- dK;
a - dK 0 dK; dK O '
dK; 0; dK q;
=
26
dK;
2:a;q ( ~
IKdK)
K
K
pp. 250-254 and 260-261, gives perhaps the clearest
and most precise derivation of the multisector Divisia productivity index.
27. Since the aggregate a depends on the sectoral mix of
capital-stock growth, the concept of an aggregate ex as a
simple elasticity becomes ambiguous once one pursues
the microeconomic approach. This problem, which is not
new in economics, lies at the heart of the aggregate vs.
sectoral relationships addressed in this paper.
29. Jorgenson and Griliches, p. 252. There is also an
equivalent dual counterpart expressed in terms of prices,
since Divisia aggregation presumes that prices equal marginal values.
28. Siegel, Jorgenson and Griliches, Solow, Norsworthy,
Harper and Kunze, Gollop and Jorgenson, Gollop, Star
and Hall, and Richter. The Jorgenson and Griliches paper,
30. See Jorgenson and Griliches, p. 260-261, and Star
and Hall.
REFERENCES
Haltmaier, J. "The Importance of Capital Formation in the
Recent Productivity Slowdown," Working Paper No.
104, Federal Reserve Bank of San Francisco, March
1980.
Beebe, J. "A Note on Intersectoral Shifts and Aggregate
Productivity Change," Annals of Economic and Social Measurement, Vol. 4, No.3, 1975.
Bennett, P. "American ProductiVity Growth: Perspectives
on the Slowdown," Federal Reserve Bank of New
York Quarterly Review, Autumn 1979.
Jorgenson, D. and Griliches, Z. "The Explanation of Productivity Change;' Review of Economic Studies,
July 1967.
Berndt, E. "Energy Price Increases and the Productivity
Slowdown in United States Manufacturing," in The
Decline in Productivity Growth, Conference Series No. 22, Federal Reserve Bank of Boston, June
1980.
Kendrick, J. "Survey of the Factors Contributing to the
Decline in U.S. Productivity Growth;' in The Decline
In Productivity Growth, Conference Series No. 22,
Federal Reserve Bank of Boston, June 1980.
Kendrick J. and Grossman, E. Productivity in the United
States: Trends and Cycles, Johns Hopkins University Press, 1980.
Clark, P. "Capital Formation and the Recent ProductiVity
Slowdown," Journal of Finance, June 1978.
Clark, P. "Issues in the Analysis of Capital Formation and
Productivity Growth," Brookings Papers on Economic Activity, 2:1979.
Kopcke, R. "Capital Accumulation and Potential Growth;'
in The Decline in Productivity Growth, Conference
Series No. 22, Federal Reserve Bank of Boston,
June 1980.
Clark, P. and Blakemore, A. "Productivity by Sector,"
Council on Wage and Price Stability, memorandum,
July 31,1978.
Levine, H. "A Small Problem in the Analysis of Growth;'
Review of Economics and Statistics, Vol. 42
(1960), pp. 225-228.
Crandall, R. "Regulation and Productivity Growth," in The
Decline in Productivity Growth, Conference Series
No. 22, Federal Reserve Bank of Boston, June 1980.
Nadiri, M. "Sectoral Productivity Slowdown," American
Economic Review, May 1980.
Denison, E. "The Shift to Services and the Rate of Productivity Change," Survey of Current Business,
October 1973.
Nordhaus, W. "The Recent Productivity Slowdown,"
Brookings Papers on Economic Activity, 3:1972.
Denison, E. "Explanations of Declining Productivity
Growth," Survey of Current Business, Part II, August 1979.
Nordhaus, W. "Policy Responses to the ProductiVity Slowdown," in The Decline In Productivity Growth,
Conference Series, No. 22, Federal Reserve Bank of
Boston, June 1980.
Gollop, F. "Accounting for Intermediate Input: The Link
Between Sectoral and Economy-Wide Measures of
Productivity Growth," Working Paper No. 7819, Social System Research Institute, University of Wisconsin (Madison), August 1978.
Norsworthy, J.; Harper, M.; and Kunze, K. "The Slowdown
in Productivity Growth: Analysis of Some Contributing Factors;' Brookings Papers on Economic Activity, 2:1979.
Gollop, F. and Jorgenson, D. "U.S. Productivity Growth by
Industry," Working paper No. 7712, Social Systems
Research Institute, University of Wisconsin (Madison), September 1977.
Perry, G. "Labor Force Structure, Potential Output, and
Productivity;' Brookings Papers on Economic Actlvlty,3:1971.
Rees, A. "Improving Productivity Measurement;' American Economic Review, May 1980.
Gordon, R. J. "The 'End-of-Expansion' Phenomenon in
Short-Run Productivity Behavior," Brookings Papers on Economic Activity, 2:1979.
Richter, M. "Invariance Axioms and Economic Indexes;'
Econometrica, October 1966.
Grossman, M. and Fuchs, V. "Intersectoral Shifts and Aggregate Productivity Change;' Annals of Economic
and Social Measurement, Vol. 2, No.3, 1973.
Siegel, I. "Concepts and Measurement of Production and
Productivity," Working paper of the Bureau of Labor
Statistics, U.S. Department of Labor, 1952.
Haltmaier, J. "Preliminary Report on Productivity," Council
on Wage and Price Stability, Mimeo, September
1978.
Sims, C. "Output and Labor Input in Manufacturing,"
Brookings Papers on Economic Activity, 3:1974.
27
Tatom, J. ''The Productivity Problem," Federal Reserve
Bank of St. Louis, Review, September 1979.
Solow, R. "Technical Change and the Aggregate Production Function," Review of Economics and Statistics, August 1957.
Thurow, L. The Zero-Sum Society, New York: Basic
Books, 1980.
Star, S. and Hall, R. "An Approximate Divisia Index of
Total Factor Productivity," Econometrica, March
1976.
Wachter, M. and Perloff, J. "Productivity Slowdown: A
Labor Problem?" in The Decline In Productivity
Growth, Federal Reserve Bank of Boston, June
1980.
Conference Proceedings Available
Copies are now available of the Proceedings of the 1979 West
Coast AcademiclFederal Reserve Research Seminar. The Proceedings contain five papers (with discussion) on the effects of money
on employment, output, prices and interest rates. The Proceedings are aimed primarily at an audience of financial analysts and
academic economists... Free copies of the Proceedings of the 1979
conference-as well as the Proceedings of earlier (1978 and 1976)
conferences-can be obtained by calling or writing the Public Information Section, Federal Reserve Bank of San Francisco, P.O. Box
7702, San Francisco 94120. Phone (415) 544-2184.
28
Randall J. Pozdena*
There is a growing consensus that inflation
is not an entirely "neutral" process. Institutional features of the economy, such as tax and
credit-market policies, can interact with inflation to affect relative prices, leading to disturbances in the levels of real activity in various sectors of the economy.! Nowhere is this
phenomenon more evident than in the housing
market. Significant changes in the relative
price of housing have accompanied the general
inflation of the last decade and a half. These
events have also prompted changes in the level
of housing consumption and patterns of housing tenure.
This article presents a simple model of the
housing market and examines the behavior of
the market during a period of rising inflation
expectations. The demand for housing is
viewed as the demand for an asset stock in a
household or landlord's portfolio. This approach distinguishes between the "price" and
user "cost" of housing, and emphasizes the
role of expectations in determining housing
demand. We describe how inflation expectations and other economic variables can produce observed changes in housing prices,
rents, and tenure patterns.
The results of the analysis have a number of
implications for housing policy and for the reg-
I. Recent
ulation of home-mortgage credit. In particular,
we find little evidence that, in the aggregate,
a "crisis" exists in the price or supply of housing, or that "affordability" has been a serious
constraint. Moreover, we argue that the oftenlamented decline in the rental market-with
the related rise in conversions of apartments
to condominiums--ean be seen simply as a
symptom of the market's adjustment to inflation pressures. Finally, the discussion puts into
focus the current debate about the appropriate
methodology for incorporating housing costs
in the most commonly used index of prices,
the Consumer Price Index (CPI).
The first section of this paper describes the
trends in the housing market that have developed during the recent inflation. The second
section presents a highly simplified view of the
housing market, and explores the processes
that determine housing prices, rents, and the
balance between rental and owner-occupant
modes of housing tenure. A third section provides some elaborations of the simple model,
including its consistency with rational expectations and the effects of imperfections in the
credit market. The fourth section presents empirical support for the thesis developed in this
paper, and the final section discusses the policy
implications of the paper's conclusions.
Tre~ds
The housing market has changed dramatically during the last decade, as seen most notably in the rapid increase in housing prices
relative to most other prices in the economy.
in Housing
Between 1970 and 1980, the price of a singlefamily home 2 of a given quality increased at
about a 9.3-percent annual rate, compared
with a 6.8-percent annual rise in overall consumer prices (measured by the personal-consumption expenditures deflator). This increase
in real housing prices (Chart 1), coupled with
'Economist, Federal Reserve Bank of San Francisco.
Lloyd Dixon and Kathleen Hagarty provided research assistance for this article.
29
depended upon rental housing for their housing needs, but by 1980 the figure may have
dropped to as low as 33 percent. Such a decline
in the rental share would be four times greater
than the percentage decline registered in the
previous decade. 4
As one of the manifestations of this trend,
many young households, traditionally renters,
have become owner-occupants. In 1970, only
about 39 percent of household heads under the
age of 30 were owner-occupants; by 1975 that
proportion had increased to over 46 percent. 5
Although homeownership has broadened to
include some relatively low-income young families, the very poorest families remain in rental
housing. Renters on average earned 64 percent
of the national median income in 1970, but
only 55 percent in 1977.
nsmg mortgage rates, has prompted officials
to argue that housing had become "unaffordable." Yet, the consumption of housing services, by any measure, has apparently continued to rise. The simple number of housing
units has grown faster than the population
(Chart 2), while the quality of housing services
has risen as well. The average new home in
1979 had a greater floor area, more bathrooms
and bedrooms, and more amenities (such as
garage space and central air conditioning) than
a new home in 1970. 3
Another major recent phenomenon has
been the decline of the rental housing market.
The earlier steep decline in the rental share of
the housing market had slowed in the 1960s,
but then accelerated again in the last decade.
In 1970, 37 percent of all American families
Chart 1
Index of Real Housing Prices
r
1972= 100
1.
30
1. 25
r
1.20
1.15
1.10
1.05
1.00
I
1967
I
1969
I
1971
30
I
I
1973
1975
I
1977
I
I
1979
In contrast to the trends in housing prices,
housing rents have generally fallen relative to
general consumer prices. Between 1970 and
1980, real rents declined approximately 10 percent (Chart 3). Combined, the trends in prices
and rents have reduced the attractiveness of
rental-property investment for many investors,
despite the prospect of capital gains. The
often-heard lament is that investment in rental
housing does not "pencil OUt."6
In terms of the housing stock itself, the shift
away from rental housing has taken two forms.
First, the rate of construction of rental property has dropped significantly despite large
Federal subsidies. In 1979, a generally average
year for housing, total rental-unit construction
(subsidized and unsubsidized) declined almost
20 percent from a year earlier, The 210,000
unsubsidized units started in 1979 was the lowest number in 20 years, and less than half the
historic peak, and the number started in 1980
may have dropped as low as 120,000 units. 7
Second, many existing multi-unit properties
have been converted to condominiums. In
1979, 195,000 rental units were converted-up
70 percent in a single year. A more subtle form
of conversion, however, has also occurred with
a decline in the proportion of rented singlefamily homes. In 1970, 19.3 percent of singlefamily homes were occupied by renters; by
1976, this figure had fallen to 16.6 percent. 8
Some policymakers see these trends as creating a dual "crisis" in housing. On the one
hand, they fear that rising housing prices and
mortgage rates are rapidly making owner-occupied housing "unaffordable."9 On the other
hand, they fear that the shrinking rate of new
rental housing construction and the conversion
of existing rental properties to condominiums
are choking off the rental alternative. Policymakers have developed many responses to this
perceived crisis, including expansion of governmental responsibility in the housing area.
Indeed, in 1979, an estimated 75 percent of
multifamily starts were Federally subsidized or
insured, and governmental mortgage-assistance programs have proliferated, particularly
at the local level. It is important, therefore, to
understand clearly the genesis of the trends
which have stimulated this policy response.
Chart 2
Occupied Housing Units Per Capita
.36
.34
.32
.30
.28
.26
.24
.22
.20
........&.
.....&...
1900
1910
1920
1930
1940
31
1950
1.........
1960
..........1
1970
1980
Chart 3
Index of Real Rental Costs
1972= 100
1.08
1.06
1.04
1.02
1.00
.98
.96
.94
.92
.90
01-
1964
1966
-'-
1968
1970
1972
1974
1976
1.000ooO
.......
1978
1980
II. Modelling the Housing Market
In this section we employ a demand-andsupply model of the housing market to demonstrate how the economic environment of recent years has produced the changes noted
above in housing prices, rents, and tenure patterns. The model first analyzes owner-occupied housing and then expands to incorporate
the rental market as well. The discussion focuses on the market for the housing stock, but
it also has implications for the market for housing services, because housing services flow in
rough proportion to the stock.
To simplify matters, we assume that the
housing stock can be meaningfully measured
in quality-adjusted units. Thus an increase in
the stock can be interpreted as either an increase in the number of structures, an increase
in their quality (that is, their ability to produce
housing services), or both.
purchase price and the consumer's income are
the relevant arguments of demand. 10 However,
the housing stock is not a consumption good
per se, but rather an asset that can be employed
by owner-occupants to produce for themselves
a flow of consumption services (shelter, privacy, access to community services, etc.) many
periods into the future.
Viewed from this perspective, a consumer's
decision on housing-stock ownership thus has
features of both a consumption decision and
an investment/production decision. This has
several implications for the proper specification of the demand relationship. First, since a
household uses housing over a period of time,
the "price" variable relevant to today's housing
demand is the expected cost of this use, relative
to other prices, for each period over the planning horizon-not simply the purchase price of
the asset itself. Obvious cost flows associated
with homeownership include the foregone interest earnings on the equity in the house, the
interest cost of borrowed funds, depreciation,
maintenance, insurance, property taxes and
real-estate transaction costs. In addition, however, the "investment" aspects of homeown-
Housing demand
The first step in devising our model is the
specification of the demand for the housing
stock. Many housing studies have treated the
demand for the housing stock analogously to
the demand for consumption goods, where the
32
ership offer the prospect of capital gains or
losses over the holding period; thus user costs
are reduced by any expected increase in the
value of the house.
Second, a household's consumption of goods
and services-including housing services-apparently changes proportionally with the
household's wealth or permanent income.
Since housing services flow in proportion to
the stock, stock demand thus should depend
upon the household's real wealth-primarily,
of course, the present value of expected future
real income-as perceived by the household at
the time it does its planning.
We can thus write the demand for housing
assets more precisely as
terest rate should be expressed in after-tax
terms. Second, U.S. tax laws potentially affect
the capital-gains term in the user-cost formula.
However, the exemptions from capital gains
taxes are so liberal that, for practical purposes,
the homeowner can anticipate receiving the
gross capital gain.
Another important implication is the influence of inflation expectations on the nominal
interest rate. In particular, if lenders expect
prices to rise over an extended period into the
future, they will require higher long-term interest charges in order to compensate for the
expected loss in purchasing power. Empirical
studies indicate that the relationship is a simple
one: the nominal interest rate is the sum of the
real interest rate and the expected rate of inflation.
Taking these tax features into account, and
incorporating the assumption that the nominal
interest rate is the sum of the real interest rate,
r, and the expected rate of general price inflation, z, we may restate the nominal user cost
as
where Un is the nominal user cost of housing
capital (assumed for simplicity to be the same
for each period in the planning horizon), Pc is
the price of consumption goods each period,
and W is a measure of real wealth. 11 The desired stock, D~, is positively related to the scale
variable, W, and negatively related to relative
"prices," UnlP c, as in traditional consumer theory.
On the assumption that there are no income
taxes and that depreciation, maintenance and
property taxes can be ignored, the nominal
user cost can be approximated by
Un
Pn«r+z)(l-t) -(Pc/Pn))
Pn«r+z)(l-t)-h)
where h is the expected rate of inflation in
housing prices and t is the household's marginal tax rate. Finally, dividing by Pc, the price
of consumption goods, we obtain
U
= P«r+z)(l-t)-h)
where U = UnlP c is the real user cost relevant
to the housing-demand relationship and
P = PnlPc is the real price of housing.
The conceptualization of housing demand as
the demand for a durable good offers a number
of insights which are often overlooked in analyses of the housing market. First, the factor
which acts like a "price" variable in the demand relationship is not simply the current
price of housing, but the expected cost to the
owner of the housing asset per period. Unlike
the typical consumption-good price, therefore,
the analogous housing variable is inherently
more difficult to observe because of its prospective nature.
where i is the nominal interest rate on longterm investmel).ts, Po is the nominal price of
housing, and Pc is the expected nominal increase in home values. The first term in this
equation is the interest cost of housing (that is,
the sum of foregone interest on equity and
borrowing cost) and the second term is the
expected capital gain.
Income-tax law potentially affects this simple measure of an owner-occupant's user capital cost in a number of ways. First, interest
income is taxable and interest payments are
deductible from taxable income. Thus the in33
Second, inflation expectations and taxes play
an important role in determining user costs
and, hence, housing demand. For example, if
households expect housing prices to increase
at the same rate as other prices in general (that
is, z = h), then an increase in those expectations should cause real user costs to fall and,
hence, housing demand to rise. The potency of
the effect, however, is dependent upon the tax
rate. If the tax rate is zero, real user costs will
be insensitive to inflation expectations. (Of
course, if housing inflation expectations differ
from general inflation expectations, user costs
would be sensitive to expectations regardless
of the tax rate-as will be discussed later in
the paper.)
The demand relationship can be illustrated
graphically. The demand curve, D, for the
stock of housing is downward sloping with respect to the real price (Figure 1), because lower
housing prices imply lower user costs, everything else being equal. Changes in inflation
expectations, the tax rate, the real interest rate
or wealth will cause shifts in this curve. An
increase in inflation expectations, for example,
will shift the demand curve outward to D1.
short run is above the price implied by longrun supply conditions. The long-run supply
curve may not be perfectly elastic with respect
to price, however, because one of the factors
used in housing production-land-is in fixed
supply.
Figure 1 can be used to illustrate the response of housing prices and the housing stock
to increased inflation expectations. The curve
Sl represents perfectly inelastic supply, and the
curve S2 represents more elastic supply conditions, as might prevail in the long run. The
market is initially in long-run equilibrium at
Po. An increase in inflation expectations would
cause the demand curve to shift from D to D1.
In the short run, the real price would rise to
Pi> inducing additional supply, until the longrun equilibrium price, P 2 , is reached.
This simple model shows that first, the market is always in equilibrium, in the sense that
housing-asset prices adjust to equate the desired and actual supply. Unless the long-run
supply of housing is perfectly elastic, an increase in inflation expectations will thus cause
a long-run increase in real housing prices. Second, this increase in real housing prices is a
one-shot affair. For real housing prices to rise
continuously relative to general prices, inflation expectations must continually be revised
upward.
Third, the model helps distinguish between
movements in the price of housing and movements in the user cost of housing. The rise in
the real price of housing that accompanies an
increase in inflation expectations does not necessarily imply that the real user cost has risen.
On the contrary, in the case of fixed supply
and unchanged wealth, an increase in inflation
expectations leaves the real user cost unchanged. Otherwise the desired stock (which
depends upon the user cost) would differ from
the fixed supply. The real price has simply risen
to offset the initial reduction in U caused by
the increase in inflation expectations, and
makes households willing once again to hold
the available stock of housing.
Similarly, the real user cost of housing must
fall in response to an increase in inflation ex-
Housing supply and market equilibrium
The equilibrium real price of housing assets
is the price that equates the desired stock demand with the actual stock supply. In the short
run, the latter is fixed, but in the long run,
additions to the stock can be made as long as
the real price that clears the market in the
Figure 1
Real
Housing
Price
81
82
P,
o
34
shifts back from Dl to D and the price falls
from P z to Po.) With unchanged wealth, however, the decline in the housing stock can be
made consistent with demand only if real user
costs are higher in equilibrium.
These examples make it clear that housing
prices do not always move in the same direction as the perceived cost of housing to the
consumer. Indeed, in the examples above, only
changes in wealth affected user costs and
prices in the same way. Since it is housing costs
that are relevant to housing demand-and the
consumer's welfare-the use of housing prices
in the consumer-price index is thus theoretically unsatisfactory and may lead to biased
measures of inflation. Indeed, under circumstances of rising inflation expectations, the use
of housing price data creates the impression
that costs are rising when precisely the opposite may be true. We will return to this issue
later in this paper.
pectations when supply is elastic. Otherwise,
households would be unwilling to hold the increased stock supply that is stimulated by the
rise in the real price of housing.
Other variables can also affect the relative
movement of housing prices and costs. Consider, for example, the effect of a change in
wealth. Unless supply is perfectly elastic, an
increase in demand caused by an increase in
wealth will cause real prices to rise. Since there
is no change in inflation expectations to offset
this effect, the user cost must also rise. This is
necessary to clear the market for the available
stock at the higher level of real wealth.
Finally, consider the effect of an increase in
the interest rate (nominal or real). This causes
the demand for the housing stock to decrease,
everything else being equal. If the housing supply is imperfectly elastic, this will, in turn,
cause real housing prices to fall and the housing stock to decline. (In Figure 1, demand
III. The Rental Market
The model of the housing market described
above involved owner-occupants only. This approach permitted a simplified presentation
while still offering useful insights into the
workings of the housing market. Moreover,
since owner-occupancy is the dominant mode
of housing tenure in the United States, such a
simplification is useful in the aggregate. However, this begs an interesting question: why is
homeownership so dominant?
Frequently it is said that Americans prefer
certain features of owner-occupied housing,
which differs qualitatively from rental housing.
This view suggests that rents and owner-occupant user costs can move with considerable
independence; indeed the relative level of
these variables would determine the tenure
balance. This "segmented markets" approach
has been followed in several recent studies of
the home-ownership decision. 12 Such an approach, however, seems somewhat ad hoc. It
is difficult to conceive of important housing
services that can not be obtained in the rental
market; essentially all types of housing are
available on a rental basis. There are other
distinctions, of course, that arise as a result of
the nature of the transactions involved-homeownership may impede mobility, for examplebut such transaction costs tend to affect the
level of owner-occupant housing costs, and not
necessarily their relationship to the market
rent for similar housing.
We take an alternative approach, assuming
that there is no important distinction between
the services of rental and owner-occupied
housing, and argue that other factors determine the equilibrium tenure share. In particular, we extend the model to incorporate the
different tax treatment of landlords and owneroccupants. We illustrate how taxes alone can
make the tenure balance determinate even
when market rents, and owner-occupant user
costs, are equal on the margin.
Tax policy and the rental market
Both landlords and owner-occupants perceive a user cost of capital associated with
ownership of housing. Indeed, if a rented unit
35
were indistinguishable from an owner-occupied unit-and if there were no difference in
tax treatment-the user cost perceived by the
landlord would be the same as that perceived
by an owner-occupant. A landlord would be
unable to charge a rent in excess of this user
cost because households, by assumption, can
obtain equivalent services through ownership.
In such a case, the tenure balance would be
indeterminate without additional assumptions
about quality differences, tastes, transactions
costs, or other factors.
In fact, of course, the tax system alters this
simple description in several ways. First, tax
law treats property owned by landlords and
property owned by occupants quite differently.
Unlike owner-occupants, landlords are taxed
on the income that flows from their housing
stock because that income is "realized" in the
form of rental income. Landlords are also
more likely to pay taxes on the nominal capital
gains they enjoy. Both factors tend to make
the breakeven rent that a landlord must charge
greater than the user cost perceived by an
owner-occupant facing a similar tax rate and
level of inflation expectations. For example,
assume that the landlord also faces the rate, c,
on capital gains. Then the breakeven situation
for the landlord is to charge a rent, R, per
period, which, after tax, is equal to after-tax
user costs. That is
R(1-t)
=
an increase in inflation expectations reduces R
by less than it reduces U, everything else being
equal. 13 This differential sensitivity to inflation
expectations, as we shall see, may contribute
importantly to changes in tenure patterns.
A second important aspect of income-tax
policy is the differential impact of different tax
rates. Because of the treatment of nominal interest, individuals in higher income-tax brackets perceive lower user costs of housing capital
than do individuals in lower income-tax brackets. This applies to both landlords and owneroccupants. Market rents have to be quite high
to encourage individuals in low income-tax
brackets to own housing, either as landlords or
occupants. This makes both the number of
rental housing units and the number of owneroccupied units increasing functions of the market rent.
Rental-market equilibrium
These implications of the tax treatment of
housing suggest a way to determine the equilibrium rent and tenure balance. First, given
the assumption of qualitative equivalence of
rented and owned housing, the market rent
must equal the user cost of owner-occupancy
on the margin. Otherwise some tenants would
be motivated to become owner-occupants, or
vice versa. Second, the total demand for housing at that rent (or user cost) must be exactly
equal to the supply. Otherwise the price of
housing would change (thereby affecting rents
and user costs) to equilibrate demand and supply. Finally, given the assumption that there
are no market imperfections to cause vacant
or unused housing, the entire stock must be
"supplied" by either landlords or owner-occupants.
The consequences of these conditions, given
a fixed supply of housing, can be illustrated
graphically (Figure 2). The curve labelled R
represents the relationship between the market
rent and the ownership or "supply" of rental
units. The curve labelled U graphs the same
relationship for owner-occupied housing. Both
are increasing functions of the market rent (for
the reasons given earlier), but are drawn backto-back to incorporate the assumption of a
P«r+z)(1+t)-(1-c)z)
or
1
R = (1-t) P«r+z)(1-t)-(1-c)z).
This market rent is clearly greater than the
implicit rent or user cost
U = P«r+z)(1-t)
z)
perceived by a similarly situated owner-occupant. Moreover, it can be shown that rents and
owner-occupant user costs respond differently
to changes in inflation expectations. In general,
for capital-gains tax rates of a reasonable size,
36
will cause aggregate housing demand to exceed
the fixed supply. Of course the variable which
will move to ration the housing supply is the
price of housing. Since supply is fixed, only
one rental, R *, clears the market, and housing
prices must rise enough to return user costs to
this previous level. The increase in prices affects both landlords and owner-occupants, so
the R curve shifts to RI and the V curve shifts
to V2 until the opportunity costs are the same
as they were before the change in expectations.
Although opportunity costs are unchanged,
owner-occupancy has been increased, or to put
it somewhat differently, some rental housing
has been converted to owner-occupied housing. 14 If aggregate supply were somewhat elastic (rather than fixed), real housing prices again
would rise and the tenure balance would
change in the direction of owner-occupancy,
but real user costs and real rents would remain
depressed relative to their initial levels. 15
Figure 2
Real
Market
Rent
Real
User
Cost
R*
..
Rental Units
..
Owner-occupied Units
Housing Units
fixed total stock of housing. Both curves are
drawn for a given price of housing and a given
level of inflation expectations.
At the intersection of the supply curves V
and R, two of the necessary equilibrium conditions are satisfied: the owner-occupant user
cost equals the market rent, R *, and the total
stock of housing is allocated between landlords
and owner-occupants. As drawn (with a higher
landlord-cost relationship) the tenure balance
is skewed toward owner-occupancy. If R * also
happens to be that rent which makes desired
total demand equal to the fixed supply, then
the figure fully describes the market equilibrium.
The diagram can be used to study the effect
of changes in inflation expectations on rentals
and tenure choice, since any factor which affects the user costs of landlords or owner-occupants can be graphed as shifts in the curves
R and V, respectively. For example, if increased inflation expectations significantly reduce the user costs of owner-occupants (but
not of landlords), then the curve V will shift
downward to VI. The intersection of VI with
R describes a lower market rent (and owneroccupant user cost) as well as a further skewing
of the tenure choice toward owner-occupancy.
This is not the final equilibrium, however,
because the lower cost for both types of tenure
Relevance of model
The model presented above suggests that
rising inflation expectations have significantly
affected recent changes in housing prices,
rents, and tenure patterns. Widely observed
increases in real housing prices and in the equilibrium quantity of housing can be explained
in this fashion. Of course, increases in demand
caused by growing numbers of households or
expanded wealth might also be responsible for
these trends, given a somewhat inelastic supply. However, as the model suggests, such factors would cause real user costs (and, hence,
real rents) to rise as well, and no such phenomenon has been observed. On the contrary,
real rents have fallen quite consistently for
over a decade. In toto, the relative behavior of
housing prices and rents can best be explained
by rising inflation expectations. 16
Recent increases in owner-occupancy may
also have been stimulated in part by the consequences of increased inflation expectations.
Analysis of tax law suggests that such expectations may be more beneficial to owner-occupants than to landlords. As a consequence,
rising inflation expectations will cause the ten-
37
ure balance to shift toward increased owneroccupancy to restore the equivalence, on the
margin, of the user costs faced by the two types
of owners. It should be noted that this tenure
shift occurs without movement in the relative
equilibrium values of rents and user costs. Indeed, market rents are a useful measure of
user costs.
By implication, the decline in the share of
the housing market owned by landlords is accompanied by a change in the type of taxpayers
who find housing ownership attractive on the
margin. At reduced real rents, only very hightax rate individuals remain as landlords,
whereas owner-occupancy can be broadened
only if relatively low-tax rate households are
embraced. Both tendencies are consistent with
our analysis concerning the proliferation of
homeownership and the poor environment for
investment in rental housing.
The analysis also helps explain the condominium-conversion phenomenon. In effect,
the model suggests that rental property is converted because rising inflation expectations
make the cost of holding a unit of housing in
a household's portfolio lower for that household than for a landlord. 17 Tax policy makes
the housing more valuable to potential owneroccupants than to the landlord, and conversion
brings about the necessary redistribution. In
reality, of course, actual conversion decisions
depend upon changes in taste, landlords' fears
of rent controls, and other factors. However,
the model offers an economic rationale for this
phenomenon that does not depend upon such
ambiguous variables.
IV. Other Considerations
A highly simplified asset-stock demand
model thus appears to be useful in analyzing
present-day housing trends, at least in a casually empirical manner. A number of other
considerations deserve discussion, however,
because of their policy or empirical implications.
market trends. First, the qualification constraint may not be effectively binding in the
long run because of changes in lender behavior. An increase in inflation expectations does
not affect the ultimate "security" of a loan.
Neither the present value of a fixed-payment
loan, nor the present value of a borrower's
income, differ at different levels of inflation
expectations. Thus profit-oriented lenders
have an incentive, as inflation expectations
rise, to relieve the borrower of the constraint
imposed by the qualification standard. This relief may take the form of a broadened income
definition (which recognizes the spouse's income, for example), more liberal interpretation of qualification standards, or pressure on
regulators to develop mortgage instruments
(such as the graduated payment mortgage)
which help borrowers overcome the cash-flow
burden imposed early in the life of the typical
fixed-payment mortgage.
Second, individuals have some ability to
rearrange their asset portfolios so as to mitigate an undesired constraint on the amount of
mortgage liabilities they hold in their portfolios. In particular, individuals may dissave to
make larger contributions to home equity, and
thereby reduce their mortgage requirements.
Credit-market imperfections
One such consideration concerns the effect
of certain lending conventions on the behavior
of the housing market. Lenders regularly employ loan-qualification standards which limit
loan-income ratios, such as the ratio of
monthly loan payments and the borrower's
current monthly income. Critics argue that this
practice, combined with the convention of a
fixed payment mortgage, causes "affordability"
problems as rising inflation expectations (and,
hence, rising nominal interest rates) cause
monthly loan payments to rise relative to income. (An unstated corollary of this view is
that the rise in housing demand and prices can
then only be explained by increases in wealth
or by population-based demand pressures. )18
There is good reason to believe, however,
that the "affordability" problem thus may have
been only a minor element in recent housing38
of the movements in housing demand and
housing prices. This view, argues, in effect,
that households have formed their housing inflation expectations separately from "general"
inflation expectations (as incorporated in nominal interest rates), and that they have relied
heavily on past housing-price movements to
form these expectations. With such an adaptive model, it is easy to construct a scenario
with an explosive rise in real housing prices, in
the following manner. A real increase in housing price (however initiated) would cause individuals to expect additional increases. (In the
language of our model, h increases more than
z.) This, in turn, causes housing demand to
rise and stimulates further increases in real
housing prices. With further increases in expectations, the process of rising real prices continues until some other factor intervenes and
dampens or reverses expectations. With the
process reversing, the "bubble" can then burst
in a crescendo of falling real housing prices.
Such a scenario seems to be implicitin many
popular discussions of real-estate booms and
crashes. 20 The relevance of "price bubbles" in
asset markets has been questioned, howeveron an empirical if not a theoretical level-by
economists working within the framework of
"rational expectations" theory.21 Thus, we are
led to conclude that the explanation for recent
housing-market developments should be sought
in changes in general inflation expectations,
rather than separately formed housing expectations.
Finally, and most importantly, the notion of
an increasingly binding "affordability" constraint is inconsistent with observed housingmarket trends. A borrowing constraint, in effect, tends to raise the user cost of housing
capital and, therefore, tends to raise real rents
in equilibrium. 19 But if this constraint had
tightened in recent years, real rents should
have risen rather than fallen as they apparently
have done. Of course, the possibility remains
that loan-qualification practices and "cash
flow" constraints have had some effect, but
have been overwhelmed by other factors.
Speculation and the housing market
Our model suggests that inflation processes
can produce changes in real housing prices during the transition period while the housing
market adjusts to a new level of inflation expectations. With unchanged expectations about
the general rate of inflation-and with housingprice expectations linked to these general expectations~prices would rise only at the rate
of prices in general. Why, then, have we seen
a relatively sustained rise in real housing prices
over the last decade or so? One possibility that
is consistent with the model is a frequent upward revision in overall inflation expectations-understandably so, since households
were buffeted by an acceleration of actual inflation during this period.
Another possibility-one that is compatible
with the popular notion of a "speculative bubble"-is the potentially self-reinforcing nature
V. Empirical Analysis
Our analysis appears to offer a description
of housing-market behavior that is consistent,
in a very general way, with observed market
trends. However, there are a number of advantages to exploring the implied relationships
in a more rigorous way. First, since many other
factors may influence the housing market, it
would be useful to observe the significance of
the statistical relationship between housingmarket trends and inflation expectations. Second, empirical analysis might shed some light
upon several unresolved theoretical issues. For
example, does a representation of general inflation expectations satisfactorily explain housing prices and rent relationships, or is it necessary to add housing inflation expectations as
well? Also, is "affordability" a factor in the
behavior of the housing market?
Rental-price relationship
To explore these issues, we employ two relationships derived from the earlier discussion.
The first is the equilibrium condition that real
rents should equal owner-occupant housing
39
costs, or
R
=
ployed a separate variable, assuming that housing inflation expectations are formed adaptively. (See Appendix A for details on the
construction of these measures.) Each model
was estimated using both ordinary least
squares (OLS) and a Cochrane-Orcutt technique for treating serially correlated errors.
Outside estimates of the marginal tax rate,
t, suggest values in the .20 to .30 range and a
figure of 5 to 7 percent for the fraction of real
housing value represented by maintenance, depreciation, property taxes and other valuebased components of user costs (Table 1).22 On
this basis, the first model performs quite well.
The marginal tax rate (.27) and the maintenance factor (8.8) are quite precisely estimated
and near the anticipated values, if we assume
that the affordability constraint (measured by
"a") is not significant.
The second model performs less well, in a
statistical sense, and is sensitive to the estimation technique. In the Cochrane-Orcutt version, for example, the constraint term is indistinguishable from zero. More importantly,
however, a large affordability constraint (that
is, a large "a" coefficient) is necessary to yield
reasonable tax-rate estimates. Thus, in this
model at least, the finding of an affordability
constraint is linked with the assumption of separately formed housing inflation expectations.23
Since there is little empirical evidence to sup-
P((l-t)(r+z)-h+f)
which may be rewritten
RlP+h
= (l-t) i+f
where f represents the effects of depreciation,
maintenance, insurance and property taxesassumed to be a constant proportion of the
value of the stock. If overcoming a cash-flow
constraint imposes costs on a household in proportion to the nominal interest rate, then
R/P+h
=
(l-t+a)i+f
where "a" is the cash-flow proportion. With
the aid of regression analysis and information
on i, h, and R/P, we can obtain estimates of f
and the coefficient on i. We can then compare
these estimates with a priori notions to obtain
a crude indication of the consistence of the
model with the data.
We estimated this linear relationship using
quarterly data and two different classes of assumptions concerning the formation of housing-price inflation expectations. In the first
modei, we assumed that households expect
housing prices to rise at the same rate as prices
of goods overall. In the second model, we em-
Table 1
Regressions on the Rental/Price Relationship, 1965.1 to 1978.1V
Regression Coefficients
Implicit Point Estimates
Depreciation,
Nominal
Interest
Maintenance,
R2 D.W. Tax Rate
et. al. (0/0)
Constant
Rate
Housing Price Inflation
Expectations Assumption
Estimation
Technique
1a.
Same as consumption prices
in general
OLS
8.92
(15.42)
.722
(9.55)
.69
1.21
.28( + a)
8.9
lb.
Same as consumption prices
in general
CochraneOrcutt
8.83
(9.31)
.734
(5.93)
.70
1.94
.27( + a)
8.8
2a.
Housing expectations formed
separately
OLS
8.62
(3.60)
1.10
(3.53)
.41
1.06
.1O( +a)
8.6
2b.
Housing expectations formed
separately
CochraneOrcutt
5.07
(0.92)
1.44
(2.14)
.54
1.90 - .44( +a)
5.0
Model
NOTE: t-ratios are in parentheses. The dependent variable is RIP + h. The independent variable is a distributed lag on
the nominal interest rate, i. See Appendix A for additional computational details.
40
All of the signs of the estimated coefficients
are consistent with the thesis we have presented under the assumed circumstances of imperfectly elastic supply (Table 2).25 Increases
in wealth per household (proxied by real disposable permanent income) cause both prices
and rents to rise. Increases in the nominal interest rate decrease real housing prices but, as
expected, cause real rents to rise as the resultant low prices cause reductions in the housing
stock. The effect of capital-gains expectation
is captured by the sign of the coefficient on
inflation expectations. It indicates that increases in housing inflation expectations increase real housing prices, but reduce real
rents as suppliers respond to high prices by
adding more housing to the stock.
Finally, the significance of the coefficient on
the lagged housing stock suggests that stock
adjustment is, indeed, a sluggish process; the
existing stock is an important determinant of
current prices and rent levels. The coefficient
has a negative sign, as expected, because increases in the existing stock reduce both real
prices and rents, everything else being equal.
Since the coefficient on the housing-stock variable in the long-linear regression can be interpreted as an elasticity, the real housing price
apparently is quite responsive to changes in
the existing stock. A one-percent change in the
lagged stock supply results in over a two-percent change in the price. In a world in which
the housing supply is imperfectly elastic and
adjustment processes are sluggish, this is consistent with inelastic housing-stock demand.
port the existence of "speculatively" formed
expectations in asset markets, we are inclined
to reject the finding of an affordability constraint as well. In light of the combined evidence, therefore, there appears to be little support for the notion that housing inflation
expectations are formed separately (at least as
modelled), or that "affordability" is an important factor in the housing market.
Levels of prices and rents
The model also identified the factors that
should affect the levels of real housing prices
and real rents. In particular, under conditions
of imperfectly elastic supply, real housing
prices should be positively related to housing
inflation expectations and household wealth,
and negatively related to the interest rate,
everything else being equal. We have argued
that real rents, on the other hand, should behave in the same way as user costs. Thus, following our earlier arguments, rents should be
negatively related to housing inflation expectations and positively related to wealth and the
interest rate, everything else being equal.
These implications can be tested by regressing data on real housing prices and real rents,
respectively, on measures of inflation expectations, the interest rate, and household
wealth. However, a lagged measure of the
housing stock, because of its probable sluggish
adjustment, must also be included in the
regression. Everything else being equal, a
larger existing supply implies lower housing
prices and rents. 24
Table 2
Price and Rent Regressions, 1965.1 to 1978.1V
(all variableS in log form)
Constant
Nominal
Interest
Rate
Inflation
Expectations
Permanent
income/Household
Lagged Real Housing
Stock/Household
R2
D.W.
1. PRICE
-7.9
(2.6)
-.30
(6.5)
.58
(7.8)
1.7
(4.0)
-2.8
(4.7)
.98
2.3
2. RENT
1.0
(1.0)
.063
(1.6)
-.13
.55
(4.0)
-1.6
(8.0)
.99
1.6
(5.26)
NOTE: t-ratios presented in parentheses. See Appendix A for additional computational details.
41
VI. Policy Implications
Rising inflation expectations apparently
have been closely involved in the recently observed pattern of rising housing prices, falling
real rents, and-by implication-a shrinking
rental-housing sector. However, we have found
no evidence to suggest any similar separate
influence of housing-price inflation expectations, as in models of speculative price bubbles. Similarly, trends in real rents suggest that
"affordability" has had little if any impact on
recent housing trends. A number of policy implications flow from these results and from our
earlier discussion.
Nonetheless, the distortion by inflation on
housing patterns is arbitrary and thus unlikely
to be socially optimal. In addition, the distortion is not confined to choices within the housing market. The combination of inflation and
special tax treatment tends to alter relative
rates of return within housing, and also between housing and other assets in the economy.
(In terms of tax treatment, incidentally, a landlord's housing investment is analogous to investment in general.) Thus, capital that otherwise would have flowed into industrial uses
frequently has been attracted to housing instead. Trends in the composition of household
portfolios verify a dramatic shift by households
out of financial assets (including corporate
equities) into housing assets. 26 Thus the true
"crisis" may be that too much-rather than too
little-housing is produced and consumed in
our economy.
Housing crisis
Inflation has been at the root of many of the
industry's recent changes-but this does not
mean that inflation has caused a crisis in the
form of unaffordaBle housing or unavailability
of rental housing. In general, properly measured housing costs have fallen relative to other
prices despite the rise in housing prices. The
trend away from rental housing, including the
conversion of rental housing to owner-occupancy status, represents a natural consequence
of households' attempts to cope with the combined impact of inflation and tax regulation.
Some communities have tried to address the
"loss" of rental housing to condominiums by
blocking conversions, but that "solution" actually reduces households' aggregate welfare,
because it blocks their attempts to find the
lowest-cost housing alternative.
Disparate tax treatment of the two types of
property appears to be the basic cause of the
shift away from rental housing in an inflationary era. The trend could be reversed, perhaps,
if owner-occupants' implicit rental income
were included in their taxable income, and if
landlords' depreciation allowances reflected
market rather than historic value. Public-finance economists have frequently proposed
such changes on grounds of tax equity, but the
political realities argue against their acceptance, especially in view of the longstanding
policy commitment to encourage homeownership.
Inflation and the CPI
More indirectly, inflation's impact on housing aggravates a problem created by the incorrect treatment of housing in the consum~r
price index. The appropriate measure of housing costs-that is, the measure that is relevant
to demand and welfare analysis-is the opportunity cost or user cost of housing. Although
this measure depends importantly on price expectations and is inherently impossible to observe directly, theory suggests that it should
move with market rentals.
In contrast, CPI procedures developed in the
1950's to reflect homeownership costs confuse
costs of purchasing the asset with various costs
involved in holding the asset per period. 27 The
consumer-price index currently employs
weighted data on the price of new homes (part
of the CPI's "home purchase" component) and
mortgage interest costs (the component "contract mortgage interest costs"), in addition to
property taxes, insurance, and maintenance
and repair. The home-purchase and mortgageinterest components, with a weight of about
17 percent in the overall CPI, increase sharply
in magnitude as inflation expectations rise. But
42
as we have seen, this is exactly when real housing costs tend to fall. The current CPI procedures thus lead to severe overstatement of the
contribution of housing to inflation.
A conservative estimate of the overstatement can be derived from experimental "rental
equivalence" measures developed by the Bureau of Labor Statistics. 28 The CPI apparently
was at least 8 percent higher in 1979 than it
should have been, due to overstatement of
housing costs during the 1968-79 period (Chart
4). Considering the myriad public and private
programs and contracts which use the CPI as
an inflation index, such an overstatement itself
has introduced inflation-related distortions
into the economy.
Mortgage policy
Finally, some brief observations may be
made concerning the relationship between
mortgage instruments and the housing market.
The general trends in the data and the simple
regression analysis presented here are not consistent with the notion of severely binding
cash-flow constraints on housing. However,
our tests are admittedly weak, and it is impossible to say whether the standard fixed-payment mortgage and mortgage lenders' qualifi-
Chart 4
Alternative Housing Cost Measures and Inflation
1967= 100
280
260
240
220
Homeownership (Present CPI)
200
"
180
All Items (Present CPI)
140
120
1969
1971
1973
43
1975
1977
1979
constraint has been at least somewhat binding.
With given supply conditions, this should lead
to an increase in the real price of housing,
though not by enough to fully offset the reduced implicit costs of housing assets.
cation standards are completely unimportant,
or are simply overwhelmed by other factors.
Policies to relieve the constraint-such as promoting graduated-payment mortgages or equity-sharing arrangements with lenders-should
help cause housing demand to increase if the
VII. Conclusion
In our analysis, rIsmg inflation expectations-interacting with the tax treatment of
housing-help account for several major recent trends in the housing market. Our emphasis on inflation expectations is not meant
to deny the influence of other factors. Indeed,
the maturing of the "baby boom" generation,
local restrictions on new housing investment,
and the proliferation of single-headed households all have contributed to rising real housing prices. However, the lack of evidence of
any rise in user costs (as proxied by real market
rents) suggests that such factors have not been
the dominant force in stimulating rising housing prices. Moreover, our analysis suggests that
the housing "crisis" is not one of widespread
unavailability of housing at reasonable costs.
On the contrary, inflation and the tax structure
may have encouraged too great a commitment
of resources to housing, and may have created
further distortions because of the mismeasurement of housing costs in the CPl.
Appendix A
Computational Details
stock per household was obtained from the
Bureau of Economic Analysis (US. Department of Commerce) estimates of the value of
fixed, residential capital in the US. The series
is reported in the Survey of Current Business.
This annual series was interpolated quarterly
using the quarterly measure of the number of
housing units.
Households. Annual data on the number of
households is reported in the Bureau of the
Census, Current Population Reports, Series p20. Quarterly values were interpolated.
Nominal Interest Rate. The AAA corporatebond rate is employed as a measure of the
nominal interest rate. The mortgage rate was
also tested, but a useful series could not be
obtained because of variations in the features
of the instrument over time. In addition, an
open-market rate such as the AAA bond rate
more accurately reflects the opportunity costs
of housing equity.
Permanent Income. An estimate of permanent income per household was obtained with
data on disposable personal income, and with
an estimation method described in Darby
(1974).
This study utilized quarterly US. data series
throughout. The following is a list of the
sources of the data, with manipulations performed as noted.
Price. A real housing-price index was constructed with the C-27 data of the US. Department of Commerce, which relate to the
price of new one-family houses, including the
value of the lots. This index is for a unit of
fixed characteristics, and was deflated by the
personal-consumption expenditures deflator.
Rent. A real rental index was constructed
with the rental survey component of the consumer-price-index, deflated by the personalconsumption expenditures deflator.
General Inflation Expectations. A number of
series were tested. The one employed in the
regressions is from Scadding (1979), based on
analysis of the inflation forecasting implicit in
consumption behavior.
Housing Inflation Expectations. A number of
series were tested. The one employed in Table
1 is an eight-quarter, third-degree polynomial
distributed lag on the change in nominal housing prices.
Housing Stock. The real value of the housing
44
Rental/Price Ratio. The benchmark ratio of
nominal rents and prices was obtained from
data from the 1975 National Housing Survey.
The rental-price index and the housing-price
index reported above were used to complete
the series.
Econometric Methods. All of the reported
regression estimates were obtained with the
use of ordinary least-square methods. An
eight-quarter, third degree, unconstrained
polynomial distributed-lag structure was em-
ployed on the components of the opportunitycost variable in the regressions reported. This
was done because the opportunity-cost variable should theoretically be entered separately
for each period into the future; we have assumed that a household's forecast of these future values is contained in current and recent
past estimates of the opportunity cost. (The
regressions were also run using contemporaneous values only; the results were qualitatively similar.)
FOOTNOTES
1. See, for example, Feldstein, Green and Sheshinski
(1978).
Hess (1977) tests and rejects the exclusion of wealth from
asset-stock demand relationships.
2. The best data are available for new housing only. However, theory would suggest that the prices of close substitutes (existing homes, for example) would move similarly. The available data suggest that this is, indeed, the
case.
Although, conceptually, opportunity costs for each period
in the future are separately relevant to asset-stock demand, we assume that inflation expectations are constant
over the entire planning horizon, and thus the entire time
path can be represented by a single period's opportunity
costs.
3. Increased quality accounts for approximately 15 percent
of the increase in average sales prices of homes sold in
the period 1970-79. The data on new housing prices and
characteristics are available in U.S. Bureau of the Census
Reports C-25 and C-27.
12. See, for example, Rosen and Rosen (1980).
13. Ignoring depreciation, a profit-maximizing landlord
adds to his housing stock until after-tax rental income
equals the (after-tax) cost of carrying the stock per period.
That is, until
4. Data on housing tenure are available from the Current
Population Survey of the Bureau of the Census. There is
some lack of comparability between this relatively recent
source of data and the decennial census that makes comparisons of tenure patterns over time difficult. Moreover,
we are primarily interested in the value-weighted tenure
share, to control for quality changes. One such attempt to
create this type of data (published periodically in U.S.
Department of Commerce, Survey of Current Business),
also shows an acceleration in owner share, however.
(1 -t)R = ((1-t)(r+z) - (1 -c)z)P
where t is the landlord's effective capital-gains tax rate.
(Note the assumption, for simplicity, that h=z.) Thus
R = ((r+z)
z(1-c)/(1-t))P
relates the market rental and expectations. By comparison, owner-occupant opportunity costs are
U = ((1 -t)r - tz)P
5. See the Annual Housing Survey, General Housing
Characteristics, Part A.
under similar conditions. Clearly, in the extreme case
where capital gains are treated like ordinary income, t = c
and 8R/8z = O. That is, landlord costs are unaffected by
inflation expectations. Even for lower capital-gains tax
rates, however, landlord costs will not decline as much as
owner-occupied housing costs as long as t 2 ';;;c. The tax
treatment of depreciation causes further offsets in. the
cost-reducing effect of rising inflation expectations, because the historic-cost basis of landlords' depreciation
allowances causes the depreciation deduction to fall in
real value as inflation rises. See, for example, de Leeuw
and Ozanne (1979) and Feldstein, Green and Sheshinski
(1978). In addition, a non-tax feature-the fear of rent
control-may cause landlords to feel that their future income or capital gains are compromised by rising inflation.
This may be an important factor in some markets and it
is one that deserves separate attention; for simplicity, however, we treat these effects as an element of a "tax" policy
toward rental housing since it, too, has the effect of making
the breakeven rent less favorably sensitive to inflation
expectations.
6. See, for example, S. Nicholson, "Rental Housing: Why
Don't the Numbers Work?" Building, December 1979.
7. "Apartment Trends," U.S. Housing Markets, March
1980, p. 10, and Rental Housing: A National Problem
that Needs Immediate Attention, Report to Congress by
the Comptroller General, General Accounting Office, November 8, 1979, p. 11.
8. "Condo Conversions: 79's Boom Won't Bust," Housing, March 1980, p. 35, and "Apartment Trends," U.S.
Housing Markets, September 1979, p. 10.
9. See, for example, N. Mayer (1977).
10. See, for example, A. Polinsky (1979).
11. See, for example, W. E. Diewert (1974). In the view
taken here, wealth is considered to be an exogenous
variable and therefore appears as an argument of the
demand relationship. If wealth is viewed as endogenous,
then the optimal stock of an asset depends only on opportunity costs if the asset's services are easily marketed.
45
figure for both is probably justifiable. (See Laidler in Harberger, 1969) Property taxes average 2.5 percent of market value. Insurance and expected uninsurable losses
likely add less than one percent. Finally, in the context of
our model, transactions costs and any costs due to the
"liquidity" of the housing asset must be added to these
other components.
14. This approach is in sharpest contrast to that of Rosen
and Rosen (1980), in which changes in tenure patterns
are related to differences between the equilibrium levels
of rents and opportunity costs. They do not detail the
model which underlies their analysis, and it is not clear
why rents and opportunity costs should not move together,
although their empirical work assumes that this is the
case.
23. Indeed, the fact that Kearl (1979) employs this assumption and finds an affordability constraint may be related.
15. A technical appendix describing a mathematical version of the model is available from the author.
16. A securely rising marginal tax rate and/or a falling real
interest rate could also contribute to this effect. Indeed,
these may represent additional avenues through which
inflation-induced distortions can affect the housing market.
Marginal tax rates can rise as the result of "bracket
creep"-the effect of a progressive tax-rate structure applied to nominal income. Feldstein and Summers have
also argued that inflation (coupled with tax policy) can
reduce aggregate loan demand and, hence, the (real)
interest rate. (See Feldstein and Summers, "Inflation, Tax
Rules and the Long Term Interest Rate," Brookings Papers on Economic Activity, Volume 1, 1978.) Although
these effects are not specifically addressed in this paper,
they are consistent with the general notion that inflationinduced distortion, rather than income or demographics,
is the primary factor behind relative price and rent movements in the housing market.
24. The model may be solved for the absolute level of real
housing prices and rents by making some assumptions
about supply conditions. That is, we have assumed that
prices move to equate the stock demanded with the available total stock, or to preserve
D(U,W)
=
D(R,W)
=
K,
where K is the available housing stock. However, K is not
fixed, but rather is itself a function of real housing prices.
Specifically, if one imagines the housing industry responding with a lag to changes in the real price,
K - K_ 1
=
d(K*(P)-K_ 1)
where K* is the long-run stock supply implied by the current real price and d is a constant or function denoting the
relationship between actual and long-run changes in the
stock. Thus in general the supply relationship may be
written
17. See, for example, the viewpoints cited in "Legislating
to Restrain Coops and Condos," Business Week, February 18, 1980, p. 90-91.
18. The most careful study of "affordability" is Kearl
(1979). However, Kearl attempts to measure the effects
of "affordability" constraints by including the initial mortgage payment in his regressions. It is not clear that a
useful proxy for this effect can be devised, since the true
shadow price of the constaint is unobservable. In addition,
the variable used by Kearl is highly correlated with the
nominal mortgage rate, which would have the sign he
finds in his analysis irrespective of affordability problems.
and P may, in principle, be derived from the solution of
stock demand and this supply condition or,
P
=
P(u, W, K_ 1)
=
P(i, z,W, K_ 1).
Similarly, R may be determined as
R
=
R(P, W, K_ 1)
=
R'(u, W, K_ 1)
=
R'(i, z, W, K_ 1).
25. If supply were perfectly inelastic (with respect to the
real price), increases in the interest rate would depress
real prices, but not affect market rentals; conversely, if
supply were perfectly elastic, an increase in the mortgage
rate would not affect the real price but would depress real
rentals. Our finding that both are affected is consistent
with the notion of imperfectly elastic supply.
19. See A. Hess, "Credit conditions and Automobile Demand," University of Washington (mimeo), August 1976
and March 1980, revised. See also van Order and Villani
(1979), who propose a less general form of constraint.
20. A recent popular version of this hypothesis is presented in Cardiff and English (1979).
26. See Kane (1980).
21. See, for example, R. Flood and P. Garber, "Market
Fundamentals versus Price-Level Bubbles: The First
Tests," Journal of Political Economy, September, 1980.
27. The method of constructing the housing component
is detailed in "Housing Costs in the CPI," Monthly Labor
Review, February 1956, pp. 184-196.
22. This is the range of tax rates implicit in the relative
rates of return of taxable and non-taxable securities of
similar quality, as well as the tax on interest income, estimated using Colin Wright's technique from IRS statistics.
(See Colin Wright in Harberger, 1969.) The real-estate
industry uses an estimate of one percent of market value
each for maintenance and depreciation, although a higher
28. Janet Norwood, "The Consumer Price Index Puzzle,"
Challenge, March-April, 1980, pp. 41-45, Tables 1 and
2. This is conservative because the weights employed in
the "rental equivalence" series are based on expenditures
and do not incorporate capital-gains effects on income.
46
REFERENCES
Aaron, H. J. Shelter and Subsidies: Who Benefits from
Housing Policies?, Washington, D.C.: Brookings Institution, 1972.
Cardiff, G. E., and English, J. W. Coming Real Estate
Crash, Arlington House, 1979.
Kearl, J. R. "Inflation, Mortgages and Housing," Journal
of Political Economy, (87) 1979, pp. 1115-1139.
de Leeuw, F. and Ozanne, L. "The Impact of the Federal
Income Tax on Investment in Housing," Survey of
Current Business, December, 1979, pp. 50--61.
Darby, M.· "The Permanent Income Theory of Consumption," Quarterly Journal of Economics, May 1974,
pp.228-250.
Diewert, W. E. "Intertemporal Consumer Theory and the
Demand for Durables," Econometrica, (42) 1974,
pp. 497-516.
Feldstein, M. "Inflation, Income Taxes, and the Rate of
Interest," American Economic Review, December
1976, pp. 809-820.
Feldstein, M.; Green, J.; and Sheshinski, E. "Inflation and
Taxes in a Growing Economy with Debt and Equity
Finance," Journal of Political Economy, (86) pp.
553-570.
Mayer, N. "Homeownership: The Changing Relationship
of Costs and Incomes and Possible Federal Roles,"
Washington, D.C.: Congressional Budget Office,
January 1977.
Melton, W. C. "Graduated Payment Mortgages," Federal
Reserve Bank of New York Quarterly Review, September 1980, pp. 21-28.
van Order, R. and Villani, K. "Alternative Measures of
Housing Costs," Washington, D.C.: Department of
Housing and Urban Development, December 1979.
Parks, R. W. "Demand and Supply of Durable Goods and
Durability," American Economic Review, March
1974, pp. 37-47.
Hess, A. C. "A Comparison of Automobile Demand Equations," Econometrica, April 1977, pp. 311-327.
Harberger, A. C. and Bailey, M. Taxation of Income from
Capital, Washington, D.C.: Brookings Institution,
1969.
Polinsky, A. M. "An Empirical Reconciliation of Micro and
Grouped Estimates of Housing Demand," Review of
Economics and Statistics, May 1979.
Rosen, H. S. and Rosen, K. "Federal Taxes and Homeownership: Evidence from Time Series," Journal of
Political Economy, (88) 1980, pp. 59-75.
Howenstine, E. J. "Housing Costs in the U.S. and Other
Industrial Countries," Washington, D.C.: Department
of Housing and Urban De~elopment, 1979.
Scadding, J. "Estimating the Underlying Inflation Rate,"
Economic Review, Federal Reserve Bank of San
Francisco, Spring 1979, pp. 7-18.
Kane, E. J. "Accelerating Inflation and the Distribution of
Household Savings Incentives," Working Paper
#470, National Bureau of Economic Research, April
1980.
47
@FedFRASER