Full text of Interpreting Early Warnings of Inflation : A Study of Statistical Indicators

View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

INTERPRETING
EARLY WARNINGS
OF INFLATION:
A STUDY OF
STATISTICAL INDICATORS

A CBO Technical Analysis Paper
September 1977

CONGRESSIONAL BUDGET OFFICE
U.S. CONGRESS
WASHINGTON, D.C.

INTERPRETING EARLY WARNINGS OF INFLATION:
A Study of Statistical Indicators

The Congress of the United States
Congressional Budget Office

For sale by the Superintendent of Documents, U.S. Government Printing Office
Washington, D.C. 20402
Stock No. 052-070-04222-2

PREFACE

Identifying inflationary pressures before they are reflected
in prices paid by consumers provides valuable information for
monitoring the economy and making future economic policy decisions.
Interpreting Early Warnings of Inflation presents some
relationships between consumer price changes and early indicators
of price pressure in markets for raw materials, labor, and finished
goods. These relationships should provide a useful advance warning
of probably changes in the rate of inflation.
This paper is one of several Congressional Budget Office
studies concerning inflation in the economy and possible policies
for controlling it. It was prepared by Mary Kay Plantes and Frank
de Leeuw at the request of the Senate Committee on the Budget.
Antoinette Gibbons capably performed the data adjustments and
statistical estimation.
Joel Popkin of the National Bureau of
Economic Research provided helpful comments.
The manuscript was
edited by Patricia H. Johnston, and the various drafts were typed
by Dorothy J. Kornegay.
In keeping with the Congressional Budget
Office's mandate to provide nonpartisan analysis of policy options,
the report contains no recommendations.

Alice M.
Director

111

Rivlin

TABLE OF CONTENTS

Page
Preface

iii

Chapter I.

Introduction

Chapter II.

A Theoretical Framework

Chapter III.

Main Empirical Results

Disaggregating the Consumer Price Index
Indicators of the "Abbreviated CPI"
Indicators of Food Price Changes

7
11
••••

Chapter IV.

Comparison With Some Alternatives

Chapter V.

Conclusion:

Using the Early Indicators

TABLES

Page

Consumer Price Index:
Items, December 1975.

Relative Importance of Selected

Decomposition of Fitted Change, Abbreviated CPI,
1976

FIGURES

Comparison of Six-Month Changes in Abbreviated CPI and
Total CPI

Comparison of Fitted to Actual Values of Six-Month
Change, Compounded Annually, in the Abbreviated CPI

vii

CHAPTER I.

INTRODUCTION

Ultimately, the rate of inflation in an economy depends on
factors causing changes in money demands (such as increases in
the quantity of money), factors causing changes in market structure (such as the formation of cartels), and factors causing
changes in potential supplies (such as growth in productivity).
There is, however, an uncertain and often long transmission
process from these ultimate determinants through demand and
supply conditions in thousands of interrelated markets to the
overall inflation rate faced by consumers.
For predicting the
course of inflation six months to a year ahead, it is more useful
to focus on the early and intermediate stages of the transmission
process than it is to focus on the ultimate determinants. If
prices paid by consumers are going to accelerate or slow down in
the next six months to a year, then there are probably already
early signals of the coming change in markets for crude materials, labor, or even finished goods themselves.
The approach of this study is to relate the rate of inflation in consumer prices over six-month intervals since 1949 to
early indicators of tightening in individual markets.
Indicators
tested include crude materials prices, commodity futures prices,
wage rates, unit labor costs, capacity utilization at various
stages of production, unemployment and other measures of labor
market disequilibrium, inventory/sales ratios, and unfilled
orders.
The second chapter of this paper explains this approach
in terms of a commonly used theoretical framework for understanding wage and price movements.
The third chapter demonstrates that over the last 30 years
in the United States, some indicators have been much more closely
related than others to consumer price changes.
For explaining
changes in an "abbreviated Consumer Price Index11 that excludes
certain highly volatile and unpredictable items (food, energy,
mortgage interest rates, and used cars), the most successful
set of indicators, as measured by the goodness of fit of a regression equation, consists of:

(1)

changes in an index of crude materials prices six
months earlier,

(2)

an index of help-wanted advertising 12 months earlier,
and

(3)

the ratio of inventories
months earlier.

to sales both six and 12

The user of this early indicator approach would do well, however,
not to confine attention only to these three variables but to
look at a range of other indicators that are also significantly
related to inflation. The third chapter of this paper presents
regression results for a number of alternative sets of indicators.
The early indicator approach may be compared with other
single-equation models relating inflation to indirect measures of
price expectations, such as interest rates, or to past rates of
inflation. The fourth chapter of the paper presents some comparisons with other single-equation approaches. Direct comparison of
the early indicator approach with full-scale macroeconomic models
is too complex for this paper.
The final chapter discusses the contribution of different
indicators to inflation both for the entire 1949-1976 period and
for the last year and a half.

CHAPTER II.

A THEORETICAL FRAMEWORK

Aggregate wage relationships and aggregate price equations
are the focus of much recent research about inflation. Combining
an aggregate wage relationship and an aggregate price relationship into a single relationship explaining price changes provides
a simple framework for the present study. Tobin, among others,
set out such a framework in his introduction to the Conference on
the Econometrics of Price Determination held at the Federal
Reserve Board in 1971. JV The paragraphs below draw on Tobin's
exposition.
According to this framework, aggregate wage changes are
explained by labor market pressures and by past and expected
price changes. Aggregate price changes depend on changes in the
prices of inputs (including wage rates), on changes in productivity, and on demand pressures in goods markets.
Eliminating
wage changes in the second relationship by substituting the
explanatory variables from the first relationship leads to the
following determinants of inflation:
(1)

labor market pressures,

(2)

past and expected price changes,

(3)

prices of inputs other than labor,

(4)

productivity changes, and

(5)

demand pressures in product markets.

Labor market pressures are usually represented by an unemployment rate. Unemployment is, however, only one of a set of

James Tobin, The Econometrics of Price Determination (Board of
Governors of the Federal Reserve System and Social Science
Research Council, June 1972), pp. 5-6.

labor market pressure variables that have been found useful in
business cycle analysis. Help-wanted advertising, initial claims
for unemployment insurance, and average weekly hours are some
other useful indicators.
In most recent empirical work, it is
not the aggregate unemployment rate that is used, but rather
an unemployment measure that adjusts for changes in the age-sex
composition of the labor force in recent years.
Furthermore,
unemployment measures are usually found to have a nonlinear effect
on wage changes, the impact of a one percentage point change in
unemployment being greater when unemployment is low than when
unemployment is high.
The strength of past and expected price increases in determining current rates of inflation has been a key theoretical issue
in price research. If past and expected inflation is an important
enough determinant, then tolerating a higher rate of inflation can
buy only a temporary rather than a permanent improvement in unemployment. Since direct measures of expected price changes are not
readily available, the issue is very difficult to settle empirically. For the purpose of the present study, it is worth stressing
that past rates of inflation are an important element in wage
determination not only because of expectations that employers and
workers may hold but also because of automatic cost-of-living
adjustments in many labor contracts and because of the catching-up
with past price increases that is a feature of many multiyear labor
negotiations.
If past price changes are highly important in the determination of wages, then there should be long lags in the reduced-form
price relationship sketched out above. An important role for past
price changes thus increases the value and plausibility of an
early-warning indicator approach to projecting inflation rates.
Lagged inflation rates are not the only determinants of
expected inflation. Advocates of the so-called "rational expectations" hypothesis about economic behavior have made much of the
implausible implications of supposing that past rates of price
changes are the only determinants of price expectations. _2/ The
indicator approach in this paper does not make use of any other

For discussions of the information of inflationary expectations, see D.E.W. Parkin and J.M. Laidler, "Inflation:
A
Survey," Economic Journal (December 1975), pp 741-809, and T.J.
Sargeant and N. Wallace, "Rational Expectations and the Dynamics of Hyperinflation," International Economic Review (1973).

measure of expectations, since no direct measure is available over
a long time-span.
It does, however, make significant use of
recent errors in predicting inflation as a factor in projecting
inflation into the future. Changing expectations is probably one
of the more important "missing" variables represented by this use
of recent errors.
Input prices (other than labor costs) are represented in
the present study by crude materials prices.
Prices of capital
goods, the major input other than labor and materials, are not
thought to have sufficient influence on the inflation rate over a
six-month to one-year horizon to warrant inclusion in this study.
Like inflation expectations, their influence may be represented in
part by recent errors in inflation prediction.
The use of a crude materials price variable raises the question of why labor market pressures are represented by a quantity
measure (for example, unemployment rates, help-wanted advertising,
etc.) while pressures in materials markets are represented by a
price variable. When activity in a market begins to approach a
supply ceiling or constraint, should the earliest warning come in
the form of a quantity indicator or price indicator?
It seems likely that in markets where prices are contracted
for long periods and after extensive bargaining, a quantity such
as utilization, unemployment, or excess capacity would respond
to demand pressures earlier than would a price indicator.
In
contrast, in a market in which prices fluctuate continually to
balance supply and demand or where speculators pay a lot of
attention to anticipating future price pressures, the first sign
of an impending tight market situation might well appear in a
price measure rather than in a utilization measure. As the next
section of this paper will document, there is some indication that
labor markets follow the first pattern and markets for crude
materials often follow the second in their foreshadowing of
movements in consumer prices.
Productivity, like the cost of capital goods, probably does
not have an easily measurable impact on price changes over a
six-month to one-year horizon. Most macroeconomic models make use
of a long-term average of productivity changes in explaining price
movements. The empirical work underlying this study did not
uncover any role for current or recent productivity movements in
explaining consumer price inflation.

Demand pressures in product markets are the final category
of influence in the reduced-form relationship derived earlier.
Possible measures include capacity utilization in finished goods
industries, the level of unfilled orders, or the ratio of inventories to sales• Past empirical studies have shown mixed results
for variables of this kind. As the next section of this paper will
document, the present study does find a significant role for
inventory/sales ratios.
The framework just described doe.s not take account of any
direct government measures that affect prices, such as taxes,
payroll taxes, and wage and price guideposts or controls (in
contrast to indirect measures such as general monetary and fiscal
policy)# In the present study, measures of changes in excise taxes
or payroll taxes did not improve the explanation of past inflation.
A simple "dummy variable" representing periods of guideposts
or controls, however, does play a significant role in the results
presented in the next section*

CHAPTER III.

MAIN EMPIRICAL RESULTS

DISAGGREGATING THE CONSUMER PRICE INDEX
The framework described in the previous chapter does not
apply equally well to all consumer prices. It does not apply to
markets in which special developments, such as the formation of an
international cartel, can suddenly swamp all other price influences. Nor does it apply to markets in which trading in existing
assets, whether financial or real, has a more decisive impact on
prices than changes in current costs of production.
For these reasons, the first step in the empirical part of
the present study was to exclude from the Consumer Price Index
certain components which did not seem to fit into the underlying
framework. These components were:
(1)

energy items,

(2)

mortgage interest costs, and

(3)

used cars.

By and large, there is only a very weak relationship between
current developments in the overall economy and movements in these
price indexes. It is probably better to attempt to forecast these
components separately, using whatever special information is
available, than to attempt to bring them into the main framework
of this study.
Food prices were also excluded from the initial analysis.
While the framework used in this study essentially applies to
consumer food prices, lags between price indicators and final
product prices are much shorter for food than for most other
goods and services.
Among the reasons for this difference are

the perishability of food and the importance of prices as a
short-run market clearing device in food markets. 1/ This section
contains some results for consumer food prices which imply that
the use of the early indicator approach provides much less advance
warning of food price inflation than of inflation in other sectors.
The remainder of the Consumer Price Index can be divided into
the following seven categories:
(1)

durable commodities (except used cars),

(2)

nondurable commodities (except food and energy),

(3)

household services
utilities),

(4)

rent,

(5)

transportation services,

(6)

medical services, and

(7)

other services.

(except

mortgage

interest

and

This analysis has dealt with an aggregate of these seven categories rather than each one separately. The relative importance of
these seven categories and of the four special ones are shown in
Table 1.

In Okun's or Hicks' terminology, food materials prices are
determined in "auction11 markets whereas prices of most other
goods are determined in "sticky-price" markets in which
prices are slower to react to changes in factor market and
product market pressures.

TABLE 1.

CONSUMER PRICE INDEX:
ITEMS, DECEMBER 1975

Item

Special Items:
Food
Energy
Interest
Used cars
Subtotal
Abbreviated CPI:
Durable commodities
Nondurable commodities
Rent
Household services
Transportation services
Medical services

RELATIVE IMPORTANCE OF SELECTED

Relative
Importance

24.7
7.3
4.4
2.0
38.4

13.8

Other services
Subtotal
TOTAL

The "abbreviated CPI,11 or the Consumer Price Index excluding
food, energy, mortgage interest, and used cars, has had four
periods of accelerating inflation since 1948.
Figure 1 depicts
changes in the abbreviated CPI and the total CPI in the form
of nonoverlapping six-month changes, compounded at annual rates.
The two largest accelerations were in 1973-1974 and at the beginning of the Korean War. The gradual acceleration of inflation in
the late 1960s was smaller while the rise in 1956-1957 was only a
bit larger than minor variations throughout the period.

Figure 1

COMPARISON OF SIX-MONTH CHANGES IN ABBREVIATED CPI
AND TOTAL CPI
Percent

I
I
1948 '50

I I
'52

I I
'54

I I
'56

I I
'58

I I
'60

I I
'62

I I
'64

I I
'66

I I
'68

I I
70

I I
72

I I
74

I I I
76
78

Calendar Years

The use of nonoverlapping six-month periods is designed to
minimize estimation difficulties due to the choice of time intervals.
Use of intervals shorter than six months is likely to
include so much random noise in the dependent variable that it
would be difficult to detect underlying influences.
Use of
periods much longer than six months is likely to smooth over some
of the actual accelerations and decelerations in price movements.
Finally, use of overlapping six- or 12-month changes avoids both of
the first two dangers but produces a time-series with such a high
degree of autocorrelation that statistical analysis is extremely
difficult.

INDICATORS OF THE "ABBREVIATED CPI"
In the labor market, movements in quantity indicators such
as unemployment or help-wanted advertising provide a better advance
indication of inflation than wage measures such as hourly compensation. Numerous empirical wage models in which the lagged unemployment rate is an important determinant of wage changes reflect this
market characteristic.
Chapter II suggested why quantity indicators might be more sensitive to demand pressures in labor markets.
In materials markets, in contrast, an index of wholesale
prices of crude materials (excluding food) leads the Korean and
1973 accelerations in the Consumer Price Index by wider margins
than a utilization measure such as the Federal Reserve capacity
utilization index for materials. Furthermore, the Federal Reserve
utilization index has reached high levels in a number of other
periods when crude materials prices did not begin to rise substantially and when there was no subsequent acceleration in consumer
prices. One reason for the superiority of the prices indicator is
that it includes goods whose prices are set in world markets, while
utilization series reflect the situation in domestic markets
alone.
The most useful equation explaining six-month changes in the
abbreviated Consumer Price Index appears to be the following:
(1)

ACPI = 6.30 + 4.78 HELPWANTED (t-2)
(3.77) (1.22)
+ 0.12 AWPIH (t-1) + 0.03 AWPIL (t^i)
(0.03)
(0.03)
- 11.79 INV/SALES (t-1) + 7.02 INV/SALES (t-2)
(4.21)
(2.97)
+

0.99 CONTROLS (t) + 0.47 ERROR (t-1)
(0.41)
Time span:

R2
DW
SE

=
=
=

1949, 2nd half to
1975, 2nd half

0. 72
1. 79
1. 32

Standard errors are in parentheses.

where
ACPI

percentage change of abbreviated
CPI (at anntial rates) over s i x month spans.
Mean value * 3.17.

HELFWANTED

index of help-wanted advertising
divided by the c i v i l i a n labor
force, lagged one year*
Mean
value * 0.74.

AWPI H ,AWPI L

percentage change of Wholesale
P r i c e Index ( W PI) for crude
materials excluding food (at
annual r a t e s ) over six-month
spans, lagged s i x months.
To
allow for a nonlinear relation,
the variable is divided into high
and low s e r i e s *
AWPIJJ i s the
percentage change minus 10 when
this difference i s positive and
zero otherwise.
AWPIL i s the
percentage change minus 10 when
this difference i s negative and
zero otherwise.
Mean values =
2.75 for
AWPIH and - 8 . 5 0 for
AWPIL.

INV/SALES

r a t i o of book v a l u e i n v e n t o r i e s
to s a l e s , covering manufacturing
and t r a d e . INV/SALES ( t - 1 ) i s
lagged s i x months and INV/SALES
( t - 2 ) i s lagged one y e a r .
Mean
v a l u e s of INV/SALES ( t - 1 ) 1.538.

CONTROLS

dummy v a r i a b l e f o r Korean War,
guide-posts, and Phase I-IV price
controls. Equals - 1 . 0 during these
periods, zero otherwise.

ERROU

regression residual
six-month period.

Figure 2 compares actual movements in the abbreviated CPI
witti f i t t e d values according to this equation.

Figure 2

COMPARISON OF FITTED TO ACTUAL VALUES OF THE SIX-MONTH
CHANGE, COMPOUNDED ANNUALLY, IN THE ABBREVIATED CPI
Percent
12
• Fitted Values From Equation (1)

-2

• Actual Values

1949

'51

'53

'55

I ! i

'57

'59

'61

'63

'65

'67

'69

Calendar Years

Crude Materials Prices
The separation of the change in crude materials prices into
two variables, one measuring the excess (if any) over a 10 percent
rate of crude materials inflation and the other measuring the
reduction (if any) below 10 percent, is a simple way of representing what evidence suggests is a highly nonlinear relationship. If
materials prices are accelerating at a 10 percent rate, an additional 10 percentage point rise in materials prices will cause the
abbreviated CPI inflation rate to rise by approximately one percentage point after six months. However, accelerations in materials prices when the initial rate is under 10 percent have practically no effect on the abbreviated CPI, according to equation (!)•

If crude materials prices are simply a component of costs,
it is hard to see why they should have a nonlinear relationship to
consumer prices. If rapid increases in the crude materials index
also represent the development of inflationary expectations,
however, then a nonlinear effect is easier to understand.

Help-Wanted Advertising
The index of help-wanted advertising is divided by the labor
force, which has the effect of eliminating at least some of the
trend in the index over time. It is the most successful of a
number of indicators of labor market tightness, and enters the
equation with a one-year lag. The coefficient implies that at the
present size of the labor force a 0.1 rise in the level of this
ratio causes about a 0.5 percentage point increase in the abbreviated CPI. An alternative equation using the unemployment rate for
males in the 25 to 54 age group gave these results:
(2)

ACPI - 11.52 - 1.08 UNEML (t-2)
(4.39) (0.43)
+ 0.13 AWPI H (t-1) + 0.04 AWPIL (t-1)
(0.04)
(0.04)
- 8.82 INV/SALES (t-1) + 3 . 5 INV/SALES (t-2)
(4.45)
(3.13)
+ 0.79 CONTROLS (t) + 0.48 ERROR (t-1)
(0.44)
Time span:

R2
DW
SE
RHO

=
=
=
=

1949, 2nd half of
1975, 2nd half

0.70
1.67
1.44
0.48

where

a six-month average unemployment rate for males,
aged 25 to 54, less 4 percent, when this difference is negative; zero otherwise.
Lagged one
year.

Dividing the prime-age male unemployment series into a high and
low series, one measuring the excess (if any) over a 4 percent rate
and the other the reduction (if any) below 4 percent, suggests a
nonlinear relationship between price inflation and this measure of
labor market tightness. The coefficient on the high unemployment
series was not significant, and was excluded from the final estimation. A 1 percent fall in prime-age male unemployment starting
from a 4 percent rate or below is associated with a 1.08 percent
rise in the abbreviated Consumer Price Index after one year.
Too much should not be made of the higher R in equation
(1) using the help-wanted index than in equation (2) using unemployment. Even after dividing by the labor force, the help-wanted
advertising index has an upward trend that may be spuriously
correlated with the upward trend in abbreviated CPI inflation.
Inventory/Sales Ratio
The ratio of inventories to sales in manufacturing and trade
enters for both the immediately preceding six-month period and
for the six-month period before that. The opposite signs for the
two coefficients in the equation are best interpreted as saying
that both a high level of this ratio and an increase in the ratio
cause—after a l a g — a reduction in the rate of inflation. The size
of the coefficients in equation (1) implies that a ratio which is
0.1 higher produces an inflation rate 1.2 percentage points lower
after six months, of which 0.5 percentage points remains in effect
after a year.
Regression equations for subperiods of the entire post-World
War II period indicate that the inventory/sales ratio is a more
significant predictor of inflation earlier in the postwar period
than it has been in recent years.
The principal contribution of
this variable is in explaining why inflation did not continue at a
high rate after the initial burst at the start of the Korean
War.
Labor markets were as tight then, by any quantity measure,
as they have been at any time since World War II and yet the
inflation rate was close to zero in 1952-1953. _2/ Equation (1)

The effectiveness of controls, furthermore, declined during
1952, and controls were removed in early 1953 with little
upsurge in inflation.
Thus the low inflation rate is not
explained, or not entirely explained, by controls.

implies that the recession in consumer goods in 1952 and its
accompanying high inventory/sales ratio is an important part of the
explanation.
Other measures of product market tightness, such as
unfilled orders or capacity utilization, did not indicate low
inflation rates in this period and in general added less to the fit
of equation (1) than inventory/sales ratios.

Controls or Guidelines
The variable representing price a n H w a g e controls or guidelines is very simple.
During the internals 1951:first half to
1952:second half, 1962:first half to 1965:second half, and 1971:
second half to 1973:second half, it takes a value of minus 1. In
all other six-month periods, it takes on a value of zero. On
average, according to equation (1), controls or guidelines lowered
the inflation rate by almost 1 percent.
As Chapter II pointed out, the use of the lagged equation
error in helping to predict inflation is one way of representing
the persistence of inflation due to inflationary expectations.
Without the inclusion of the lagged residual, the estimated equation is as follows:
(3)

ACPI = 0.59 + 4.41 HELPWANTED + 0.17 AWPI H (t-1)
(5.87) (0.97)
(0.03)
+ 0.05 AWPI L (t-1) - 7.82 INV/SALES (t-1)
(0.03)
(4.49)
+ 6.78 INV/SALES (t-2) + 0.93 CONTROLS (t)
(3.39)
(0.47)
Time span:

—2
R

DW
SE

1949, 1st half to
1975, 2nd half

= 0.68
= 1.05
= 1.53

The fit of equation (3) is not as good as equation (1), but the
difference in standard error is probably smaller than might be
expected in view of the heavy emphasis in recent discussions on
expectations as a major factor in the persistence of inflation.

Other Variables
A number of other variables included in previous inflation
studies were tried but rejected. One of them, changes in the
ratio of federal excise taxes to GNP, was not significant in any of
the equations in which it was tried. Change in the effective
social security tax was a significant indicator but its coefficient
was so small it did not warrant inclusion in the final equation
Finally, changes in a long-run productivity series did not prove
significant; to the extent that the long-run growth in productivity
is constant over time, the constant term is picking up its effect
on price inflation.

INDICATORS OF FOOD PRICE CHANGES
For food, there are market indicators of price trends at
three distinct stages preceding the retail level. Earliest is an
index of commodity futures prices, related to retail food prices as
follows:
(4)

Apf - 3.75 + 0.101 AFut (t-2)
(0.83) (0.041)
Time span:

—2
R

DW
SE

=
=
=

1958, 1st half to
1975, 2nd half

0.12
1. 72
4.95

where
Apf

AFut

_3/

percentage change in consumer food prices (at annual
rates) over six-month spans.
Mean value = 4.31.

= percentage change over six-month spans (at annual
rates) in futures price index of Commodity Research
Bureau, lagged one year. _3/

The index was obtained from the Commodity Research Bureau.
The index at period t represents the average price of futures
contracts exercisable anytime within one year. Some nonfood
items are included in the index, but it is predominantly
composed of grain and livestock futures prices. The index is
available back to 1957:1.

A much closer relationship, but one with a much shorter
lag, exists between the crude foodstuffs component of the Wholesale
Price Index and retail food prices as follows:
(5)

Apf - 1.84 + 0.571 AWPIC
(0.54) (0.062)
Time span:

1958, 1st half to
1975, 2nd half

=
=

0. 70
2. 39

2.89

where
AWPIQ

percentage change over six-month spans (at annual
rates) in wholesale crude food prices, lagged two
months.

Curiously, the relationship of the finished food component of
the Wholesale Price Index to retail food prices is not as close as
the relationship of crude, and the lag is even shorter:
(6)

Apf = 3.07 + 0.229 AWPI f
(0.64) (0.038)
Time span:

R2
DW
SE

1958, 1st half to
1975, 2nd half

0.50
1.31
3. 75

where
AWPIf

percentage change over six-month spans (at annual
rates) in wholesale prices of finished foods,
lagged one month.

There is not a terribly high degree of multicollinearity
among these three early indicators of food price changes. Nor are
any of them closely correlated with labor market conditions, which
appear to have a weak but possibly significant relationship to

retail food price trends. For forecasting, therefore, it is useful
to combine all of these indicators into a single predictive equation:
(7)

3.05 + 0.09
fut (t-2) + 0.08 AWPI C
(1.28) (0.01)
(0.04)

+ 0.42 AWPIf - 0.47 UN (t-2) - 0.53 ERROR (t-1)
(0.08)
(0.22)
Time span:

1958, 1st half to
1975, 2nd half

R2
DW
SE

0.86
2.19
2.01

where

unemployment rate for males aged 25 to 54, lagged one

Figure 2 compares actual movements in consumer food prices
with fixed values provided by this equation.
According to equation (7), a 10 percent rise in wholesale
food prices at both the crude and the finished level raises consumer food prices by about 5 percent. A 1 percent fall in primeage male unemployment will raise consumer food prices by 0.47
percent. Other indicators of market pressure were unsuccessful in
providing additional explanation of food price changes.
The usefulness of equation (7) in monitoring inflationary
pressures is less than the earlier equations for the abbreviated
CPI. Forecasts of food price changes more than two months in
advance are possible only with the use of predicted values of the
WPI indexes for crude and finished food, and these predictions are
subject to substantial error.

CHAPTER IV.

COMPARISON WITH SOME ALTERNATIVES

Forecasts of inflation often rely on elaborate macroeconomic
models, on judgment by experienced observers about collective
bargaining trends and price markups, or on some mix of these two.
It is not feasible to compare systematically the results of this
study with these approaches. If the results of this study prove
promising, they may well be incorporated into one or both of these
approaches in the future.
What is possible is a comparison of the present approach with
two other simple methods of predicting inflation. One is a relation between the current rate of inflation and its own past values.
The other is a relationship between inflation and interest rates.
As shown below, the indicator approach outperforms both of these
alternatives.
The first alternative, an autoregresslve relationship, is
represented by a regression of the current six-month change in the
abbreviated CPI on its own values one and two periods earlier. The
equation is:
(8)

p « 1.16 + 0.83 p (-1) - 0.18 p
(0.42) (0.14)
(0.14)
Time span:

R2
DW
SE

m
=

(-2)

1949, 2nd half to
1975, 2nd half

0.49
1.89
1.93

where
p

p
p

(-1) is lagged one period,
(-2) is lagged two periods.

percent change of abbreviated CPI
over six-month spans.

(at annual rates

The standard error of this equation is 46 percent higher than that
of equation (1) in the preceding chapter.
Furthermore, the autoregressive approach, as would be expected, regularly lags at
turning points.
The view that interest rates are a measure of expected
inflation—a view going back to Irving Fisher's writings early in
this c e n t u r y — h a s had a revival recently.
A nominal rate of
interest is viewed as the sum of a real rate of return and an
unbiased expectation of price inflation. To compare this approach
to forecasting inflation with the indicator approach, CBO has used
the six-month Treasury bill rate as the relevant nominal interest
rate and used the velocity of M^ as a proxy for the real rate of
interest. The regression results follow:

(9)

p - 5.57 + 1.35 R + 0.64 V
(2.0)
(0.21) (0.63)
Time span:
R2
DW
SE

=
-

1959, 2nd half to
1975, 2nd half

0. 83
1. 62
1. 12

where
p

the percentage change
abbreviated CPI.

the beginning and mid-year values of a six-month
moving average of the market yield on U.S. Government
six-month bills.
semiannual values of

over

six-month

spans

in the

velocity.

The coefficient of the nominal interest rate is significant
and of expected sign, but the coefficient of velocity is neither.
The standard error, 1.12, should be compared with the standard
error of an indicator-type equation to fit to the same time-span, a
shorter span than was used for equation (1) (due to the lack of
six-month bill rate data for earlier years). Over the identical
span, a regression using the same variables as equation (1) of the
previous chapter gives a standard error of 0.85, 31 percent lower

than that of equation (9). Furthermore, the indicator approach
gives some insight into the sources of inflationary pressures
while the nominal interest rate and autoregressive approaches do
not.
A third alternative, a regression of the six-month inflation
rate on current and lagged percent changes in the money supply
(demand deposits plus currency), also provides a significantly
worse fit than the indicator approach.
Other investigators,
however, using specifications somewhat different from the sixmonth, nonoverlapping changes of this study, seem to have been more
successful with a money supply equation.

CHAPTER V.

CONCLUSION:

USING THE EARLY INDICATORS

This concluding chapter expands on the results of the analysis
by measuring how much different indicators "contributed" to the
abbreviated CPI recently and during the whole range of experience
since 1949.
During the two six-month intervals following the end of the
period of fit, the early indicators of inflation provided reasonably accurate predictions for the rate of change in the abbreviated
CPI. The actual change in the first half of 1976 was 5.8 percent
while the predicted change using equation (1) was 6.1 percent. For
the second half of 1976 the actual and predicted rates were 5.4 and
4.9 percent, respectively.
The predicted values are decomposed
into contributions by each explanatory variable in Table 2.
A useful way to gauge the contribution of various indicators
to the overall rate of inflation is to look at high and low values
for the period since 1949.
On this basis, prices of crude materials have accounted for the greatest range of variation in the
inflation rate. The change in materials prices (at an annual rate)
was under 10 percent, where it contributes very little to explaining the abbreviated CPI, during virtually the entire period from
the middle of the Korean War until early 1972. At the start of
the Korean War, however, the rate was 30 percent for two half-year
periods. It decelerated 36 percent in the second half of 1957,
while in 1973-1974 it was over 50 percent for one half-year and 44
percent for another. The additional inflation due to a 50 percent
rate of rise in materials prices as compared to a 36 percent fall
is 4.8 percentage points.
Labor market pressures have had nearly as large a range
in their "contribution" to the rate of inflation. Help-wanted per
member of the labor force has ranged from lows of 0.55 in the
second half of 1949 and the first half of 1950 and to a high of
1.53 in early 1969. Differences of this range would, according to
equation (1), lead to differences of about 4.7 percentage points in
the rate of inflation.

TABLE 2.

DECOMPOSITION OF FITTED CHANGE, ABBREVIATED CPI, 1976

Crude Materials
Inflation Less
10%, 6-mo. Lag

Help-Wanted Per
Member of Labor
Force, 1-yr. Lag

Inventory/Sales Ratio
6-mo. Lag
1-yr. Lag

Constant

0.904

1.51

1.57

1.00

3.89

0.12

4.78

-11 .79

7.02

6.30

0.47

0.24

4.321

-17. 803

11.021

6.300

1.828

3.88

0.931

1 .50

1.51

1.00

1.554

0.12

4.78

-11 .79

7.02

6.30

0.47

0.466

4.450

-17.685

10.600

6.300

0.730

Highest Value since
1949 (Date)

43 .3%
(73: 2nd half)

1.534
(70:2nd half)

1.690
(75:1st half)

Lowest Value since
1949 (Date)

-33 .1\%
(49: 1st half)

0.554
(49:2nd half)

1.220
(50:2nd half)

Residual,
6-mo. Lag

Abbreviated CPI
Predicted Actual

Contribution to 1976:
First Half Prediction

(a) Value with appropriate lag

(b) Coefficient

3.53%

6.091

5.817

4.861

5.360

Contribution to 1976:
Second Half Prediction
(a)

Value with appropriate lag

(b) Coefficient
(c) Value x
coefficient

The alternative measure of labor market pressure used in
equation (2), the distance below 4 percent of the prime-age male
unemployment rate, has ranged from zero in every recession (and
a number of other periods as well) to -2.4 in the last half of
1968. According to equation (2), a range of this magnitude would
account for only 2.6 points in the abbreviated CPI, or somewhat
less than the contribution of labor market pressure as measured by
the help-wanted index.
The inventory/sales contribution has generally been the
smallest of the factors in equation (1). The ratio was below 1.25
at the start of the Korean War and it reached a one-time high value
of 1.69 in early 1975. The difference between these two extremes
of 0.27 would initially contribute 5.2 percent to the rate of
inflation if the entire difference developed in one half-year but
only 2.1 percent when spread out over two or more half-years,
because of the opposite signs of the coefficients of six- and
twelve-month lags in the ratio.
Preliminary estimates for the first half of 1977 indicate
that equation (1) continued to fit closely during this period. The
six-month change in the abbreviated CPI from December 1976 through
June 1977 (at annual rates) was 6.4 percent, somewhat higher than
during 1976.
The calculated value based on equation (1) was 6.3
percent. Latest values for the indicators in equation (1) and for
a range of other indicators suggest little prospect for a lessening
of inflation in the abbreviated CPI in the near future.

U. S. GOVERNMENT PRINTING OFFICE : 1977 O - 95-466

Full text of Interpreting Early Warnings of Inflation : A Study of Statistical Indicators

FRASER