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FEDERAL RESERVE BANK OF DALLAS
First Quarter 1993

Mark A. Wynne and
Nathan S. Balke

A IfJok at l.ollg-'li!rlJl /Jerein/)ll/eIl!." ill Ibe

I jz:,'1rilm Iio II

q/In co III e

Joseph H Haslag and
Lon L Taylor

'l1)e Cosl,' and 8ell~j7I.'· ofFired /JollaI'
Ercballge Nal }Ii in hllill America
John H. Welch and
Darryl McLeod

This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org)

Economic Review
Federal Reserve Bank of Oaf/as
Robert D. McTeer, Jr.
PT.

",.d Ch , Exec"""" O'h"

Tony J. Salvaggio
F,rsl V,ce PTe"d, nl .lnd Ch'ef 0"." Img OIlIC(lI

Contents

Harvey Rosenblum
SOfllor Vlt'l' PrE.- Hlp'" dfId O,roctor of R

~:frch

W. Michael COX
V/l':'8 PrOSI

fIt

Id ECOflomit. Adlj/'iOf

Gerald P. O'Driscoll, Jr.
~ I Pr6

,t idE,

Il1Ol Ie

Itvl

Stephen P. A. Brown
A ,1",,1 Vrcs P,

Page 1

d ~"",or fc """""it

Economists
Zsolt Beesl
Robert T Clair
John V Duea
Kenneth M Emery
Robert W Gilmer
David M Gould
William C, Gruben
Joseph H. Haslag
Evan F. Koenig
D'Ann M. Petersen
Keith R Phillips
Fiona D. Sigalla
Lori L Taylor
John H. Welch
Mark A, Wynne
KeVin J Yeats
Mine K Yileel

Recessions and
Recoveries
Mark A, Wynne and
Nathan S. Balke

Research Associates

Professor Nathan S Balke
Southern Method,st University
Professor Thomas B Fomby
Southern Methodist UniverSity
Professor Scott Freeman
University of Texas
Professor Gregory W Huffman
Southern MetllOdist University
Professor Roy J. Ruffin
University of Houston
Professor Ping Wang
Pennsylvania State UniverSity
Editors
Rhonda Hams
Virginia M Rogers

The EconomiC ReVIew IS published by the Federal Reserve Bank of Dallas The views
explessed aro those of the authors and do not necessallly reflect the positions of the Federal
Reserve Bank of Dallas 01 the Federal Reserve System
SUbSC',ptlons are avallablp free of charge Please send requests tor smgle-copy and multiple
copy subscnp\IOns. back IS ues. and address changes to the PubliC AffairS Department, Fedelal
Reserve Bank of Dallas Station K Dallas, Texas 75222. (214) 922 5257
Artlctes may be repnnted on the condit on that the source IS credited and the Re arch
Dcpartm m IS prOVided With a copy of the publication containing the repllnted mateltal

On the cover: an architectural rendering of the new Federal Reserve Bank of Daltas
headquarters.

The .•. recession that began inJuly 1990 may have ended
in April or May 1991. The pa e f the subseq uent re ov'ry
has b 'n so sluggish as to b ' indistinguishable, in the eyes of
many, from ontinued recession. n > explanation for the
sluggish pace f the recovety is that the recession itself was
not pani ularly sev re, at leasl when compared with thers ,
In this ani Ie, Mark Wynn' and athan Balke use monthly
data on industrial production to examine th hypothesis that the
s 'verity of a re e ion determine. the pa e of the ubseq uent
I' covery. Th y show that , histori ally, the relation. hip between
growth in the fin twel e months of a rec very and th ' decline
in industrial activity from p ak to trough is statistically signifjant. However, th re is no r >laLionship between th > length of
a re ession and the 'trength f the I' 'covery.
nsistent with
their finding of a bour1C -back ef~ ct for indu 'trial producti n,
the recovery from the 19 0-91 recession is the weakest in the
period covered by the Federal Re erve Board 's indu uial produ tion index, ju ·t as the d -cline in industrial production over
the ours of that r es 'ion is the mildest on record ,

Pag 19

A Look at Long-Term
Developments in the
Distribution ofIncome
Joseph H. Haslag and
Lori L. Taylor

Developments in the distribution f income have rec 'iv d
mu h all ' ntion over the pa 't de ade, everal analysts have
argued that inc me gains hav ' gon' almost exc\usiv Iy to the
highest paid 20 percent of th population, leaving n gains to
the remaining 80 percent.
Jo eph I I. Ha lag and Lori L. Taylor e amin> developm ' nts in in om' inequality over th ' past f rty years and 'stimat whi h factors a count for the e chang>s over time. While
some reseal' hers have found that inc me distribution be ame
m r' equal during the 1950s and 1960s and then less equal
aft'r th ' mid-1970 , IIaslag and Taylor find evidence that an
upward trend in incom > inequality has b en occurring sinc' the
early 1950s, Th y also find that movements in the in orne inequality measure are mostly deterll1in 'd by persistence; that
is, inc me inequality adju ts gradually, Demographi f atures
a ount for nearly 25 per ent ofth >variati n in inc 111 > inequality,
willi > p licy actions explain less than 15 per ent.

Economic Review
Federal Reserve Bank of Oaf/as
Robert D. McTeer, Jr.
PT.

",.d Ch , Exec"""" O'h"

Tony J. Salvaggio
F,rsl V,ce PTe"d, nl .lnd Ch'ef 0"." Img OIlIC(lI

Contents

Harvey Rosenblum
SOfllor Vlt'l' PrE.- Hlp'" dfId O,roctor of R

~:frch

W. Michael COX
V/l':'8 PrOSI

fIt

Id ECOflomit. Adlj/'iOf

Gerald P. O'Driscoll, Jr.
~ I Pr6

,t idE,

Il1Ol Ie

Itvl

Stephen P. A. Brown
A ,1",,1 Vrcs P,

Page 1

d ~"",or fc """""it

Recessions and
Recoveries
Mark A, Wynne and
Nathan S. Balke

Research Associates

On the cover: an architectural rendering of the new Federal Reserve Bank of Daltas
headquarters.

Pag 19

A Look at Long-Term
Developments in the
Distribution ofIncome
Joseph H. Haslag and
Lori L. Taylor

Mark A. Wynne

Nathan S. Balke

Senior Economlsl
Federal Reserve Bank of Dallas

ASSistant Professor of Economics
Southern Methodist University and
Research Associate
Federal Reserve Bank of Dallas

Contents
Recessions and Recoveries
Pag' 31

The Co t. and Benefit. of
Fixed Dollar Exchange
Rate in Latin America
John H, Welch and
Darryl McLeod

hronk' inflation and the import.lnce o[ the c'Xch,lI1ge
rate as .1 nominal anchor for the dOll1L..... ti<: price I '\d haH.:' led
som 'Lltin fm!riCall COUnLri 'Ii to con.,ider returning to a
fL ed dollar l'xchang , rate, John '\ deh .Inti DafT) I 1cL 'od
examine th ' (oslli .Ind henefits of real 'xch,lnge rat' l11()vem 'nls and their I' 'I '\ .ll1el' for the (fctlihilit) of inllallon
policics in countries nO\\ tontempiating rrel' trad ' ,lgrceOlcnh
with th ' ( nitl'd ~t.ltcs.
The author., di<. 'uss the cxperien . 'S of Sl'\ er.t1 Lllin
AJ11cric.tn countries .tnd des rihc the prohl 'Ill tllL'lr po!Jcymak 'rs I.Kc \\ h 'n d 'cidtng (0 rollO\\ 'ither fi cd or flc ible
'xch.lngL' rat' rull's. Fixcd exchange ratcs that .trl' crl'dihle
can det I' 'as' inn.llion rates, but only at till' cost of policy
Ilexibilit) in the face of "dverse cllang 'S in the terms of tradc
or for'ign intl'rest rat's. Thc CUlT 'nt r ']ati\ ' slahility of inter
national markcts has Icd som 'Latin m 'riean ('()untn 'S to
complement tllL'ir stahilil..llion and r >form polilics \\ ith fixed
'xehang , ratl'S .

h 'U.S. 'conomy L'1ll 'I' 'd recession in .lui)
1990 an I hegan to rccov'r, many analysts
b'li \ ',in pril or May 1991. in • then, lhe
econol11 h.\.., gr wn .It a pa L' so sluggish .11i to IX'
indistinguishahle, in S0111 > ~ ays, from contil1lll'd
reces. ion Ilem L'\·er.•IS early as spling 1991. sevL'ral
obs '1'\ ers Wl'r ' e,prt:ssing thL' opinion th.1t tlK'
f'cmery rrom the 1990-91 recession would not
b' particularly robust bL'c£luse th' fL' e'>Sfon ihdf
.. as nol particularly s '\ ere. For e,ample, in H/lsiIle~~, \l c'ekin.lune 1991, Alan Blind'rar~u'd,
"Sha llow recessions ar' followecl by weak r 'covcries for a simpl ' r ':lson: n' anomy thaI has
not fall 'n f.lr has liul ' GlIehing up to do. nd
catch-up i.., the main reason e onomies zoom
upward in the early slages fre overy." nJe
£C01l0Illi, I ma~azin " in an '<.iitori.1I on .I.lIlll.11
IH. 1992, point 'd out that "ther' aI" good rL'asons
(() thmk that th ' coming L' pansion may bc \\' 'ak 'r
than most of its prL'de esse [Ii," lh· rnall1 ne h 'lIlg
"th' mi ldn 'Sli or lh ' r , . 'ssion that I r 'ceded it."
10s1 re 'ent ly. the Shadow P'11 1nrket ommittee, an independent prh.1l group that ritiquL's
the actions of the Federal R 'sef\L', argu '<.I that
one of th ' main reasons th ' economy remained
sluggish in 1992 \\.as lhat "modest retessions .Ire
lIsu.1lly followl'd b modeM rl'co\eriL's" 0992, ";).
The notion that the e on my e,p 'ri 'nees a
"h unce-ba k" or "rubb 'r-band" 'fTe t [ollc)\'. ing
declinL's in ec )I1oml acth ity 'ontains a cel1ain
amount of intuitive appeal but se'llls to have
been subj 'ct to f '\J el11[)irical tests. Th ' L'arli 'st
study and on' of thl' l110st comrrel1L'nsi\.e analy
ses of this issue that we have found is ~loore
(961), ~ ho lriL'd to test the viL' that "the str 'ngth
of a recO\'ery in its 'arly ..,tages t!L·p 'nds upon the
I 'vel from which it stal1s" (p. 6). II' '.'amin'd
E o n oml Revi

Fir.l Quart r 1993

lh behavior of groups of leading, coint id 'nt, and
lagging indiC:llorli in the first seven month ... of six
recoveri 'S (the l'arli 'st being that 1'0110\\ ing the
trough inJuly 19_1, th' Int st being th.1l following
the trough in ugu ..,t 19"i I, liince r '\ iSL'd to la}
19,t> and tentati\ 'Iy concluded that "feU)\ eri ....
in output, t.'mplo'\.ll1ent. ,Ind [)rofit ha\ • usually
been fastl'r af lL'r "C\ ere de[)r'sslons tha n aft 'r
mild contractions (p. HH). I lore (196') cont,lins
a resLall'menL of the finding that sevcre contractions
tend to b ' followcd by strong ex[)ansiol1s, ,Ind
Bly :lI1d Boschan (1971) pr 'lient further evid 'n . ,
on this [)roposition, focusing on growth in nonagri ultural 'mploym 'nt.
1100her or the f '\\ author'> addressing this
question is 1ilton Fri 'dman, who asked, "(:., th '
magniludl: or ,In l"pansion r 'IatedliYl>lematk ,111)
to th magnitud ' or the suceL'ding contraction?
o 'Ii a boom tend on th ' .Iwrage (0 be rollowl'd
b) a larg' ontrallion? mild expanliion, by .1
mi l I contraction?" ( I'riedman 1969, 2 1). n the
basis of an examination of simple rank COlT '!alinn
coem ients for three difrerent meaSllf 'S of ac.ri\'it},
Fri 'clman round no relationship betwl'l'n the 'iiZl'
of an eX[)L1nsion .lnd the .,il. ' of the suce 'eding con
tfacti n hut did find that "a large contra 'lion in output tends to he rollowed on the a 'rage hy a 1.lrg ,
business eX[)ilnsion; a mild contraction, by a mild
>

We Wish to thank Adflenne C. Slack and Shengyi Guo for
excellent research assistance on thiS prolect ThiS article
draws on work reported In an Economies LaHers ar/lcle
(Wynne and Batke 1992) and In an unpubltshed paper
(Balke and Wynne 1992)

Mark A. Wynne

Nathan S. Balke

Senior Economist
Federal Reserve Bank of Dallas

Assistant Professor of Economics
Southern Methodist University and
Research Associate
Federal Reserve Bank of Dallas

Recessions and Recoveries

he U.S. economy entered recession in July
1990 and began to recover, many analysts
believe, in April or May 1991. Since then, the
economy has grown at a pace so sluggish as to be
indistinguishable, in some ways, from continued
recession. However, as early as spring 1991, several
observers were expressing the opinion that the
recovery from the 1990–91 recession would not
be particularly robust because the recession itself
was not particularly severe. For example, in Business Week in June 1991, Alan Blinder argued,
“Shallow recessions are followed by weak recoveries for a simple reason: An economy that has
not fallen far has little catching up to do. And
catch-up is the main reason economies zoom
upward in the early stages of recovery.” The
Economist magazine, in an editorial on January
18, 1992, pointed out that “there are good reasons
to think that the coming expansion may be weaker
than most of its predecessors,” the main one being
“the mildness of the recession that preceded it.”
Most recently, the Shadow Open Market Committee, an independent private group that critiques
the actions of the Federal Reserve, argued that
one of the main reasons the economy remained
sluggish in 1992 was that “modest recessions are
usually followed by modest recoveries” (1992, 5).
The notion that the economy experiences a
“bounce-back” or “rubber-band” effect following
declines in economic activity contains a certain
amount of intuitive appeal but seems to have
been subject to few empirical tests. The earliest
study and one of the most comprehensive analyses
of this issue that we have found is Moore (1961),
who tried to test the view that “the strength of a
recovery in its early stages depends upon the
level from which it starts” (p. 86). He examined
Economic Review — First Quarter 1993

the behavior of groups of leading, coincident, and
lagging indicators in the first seven months of six
recoveries (the earliest being that following the
trough in July 1924, the latest being that following
the trough in August 1954, since revised to May
1954) and tentatively concluded that “recoveries
in output, employment, and profits have usually
been faster after severe depressions than after
mild contractions” (p. 88). Moore (1965) contains
a restatement of the finding that severe contractions
tend to be followed by strong expansions, and
Bry and Boschan (1971) present further evidence
on this proposition, focusing on growth in nonagricultural employment.
Another of the few authors addressing this
question is Milton Friedman, who asked, “Is the
magnitude of an expansion related systematically
to the magnitude of the succeeding contraction?
Does a boom tend on the average to be followed
by a large contraction? A mild expansion, by a
mild contraction?” (Friedman 1969, 271). On the
basis of an examination of simple rank correlation
coefficients for three different measures of activity,
Friedman found no relationship between the size
of an expansion and the size of the succeeding contraction but did find that “a large contraction in output tends to be followed on the average by a large
business expansion; a mild contraction, by a mild

We wish to thank Adrienne C. Slack and Shengyi Guo for
excellent research assistance on this project. This article
draws on work reported in an Economics Letters article
(Wynne and Balke 1992) and in an unpublished paper
(Balke and Wynne 1992).

expansion” (p. 273). Friedman went further, to sketch
out a theory of business cycles (the “plucking
model of fluctuations”) that he felt was consistent
with these patterns in activity, but to date his
model seems to have received scant attention.
Finally, we note that Neftci (1986), in the
course of addressing a slightly different question,
reports results that are relevant to the recession–
recovery relationship. Focusing on the behavior
of pig iron production since the latter half of the
nineteenth century, he finds a significant negative
correlation between the length of expansions and
the length of contractions: for every additional
twelve months of expansion, the economy experiences 1.8 fewer months of contraction. However,
the length of contractions does not affect the length
of subsequent expansions. Furthermore, he shows
that there is a significant relationship between the
peak-to-trough decline in output and the increase
over the course of the subsequent expansion but
none between the gains in output over the expansion and the losses over the subsequent contraction.
In this article, we will study the behavior of
output during and immediately after recessions to
see whether there is any validity to the notion of a
bounce-back effect.1 Our analysis differs from that
of Moore, Friedman, and Neftci in a number of
ways. First, we focus on the behavior of industrial
production rather than look at a variety of indicators. The reason is that we can obtain reasonably
consistent estimates of industrial production for
long periods, allowing us to look at recoveries
from a large number of recessions. Second, we
estimate a simple linear regression model rather

Sichel (1992) also talks about a bounce-back effect following recessions in reference to a high-growth recovery
phase at the beginning of an expansion but does not look
at the relationship between the rate of growth during the
recovery phase and output losses during the recession. He
does, however, examine the predictive power of an outputgap variable for GNP growth, where the output-gap variable
is defined as the deviation of GNP (gross national product)
from its preceding peak value.
Interested readers are referred to Moore and Zarnowitz
(1986) for a detailed discussion of how the NBER dates
business cycles. The discussion here is a very brief summary of their article.

than look at simple correlations, which enables us
to discriminate between the effects of different
measures of the severity of the preceding recession.
The two measures of severity we focus on here
are the depth of the recession, as measured by the
output loss from the peak date to the trough date,
and the length of the recession, as measured by
the number of months from the peak date to the
trough date. Third, we look at a larger number of
recessions and recoveries than does either Moore
or Friedman, including a number of pre–World
War I business cycles. Each recession will be
viewed as an independent event, and we will look
for regularities common to the 23 recessions and
recoveries that the United States has experienced
over the past hundred years. Fourth, we only look
at output growth in the early stages of an expansion (either the first six months or the first twelve
months) and see how growth over this horizon is
influenced by the severity of the preceding recession. This contrasts with Friedman’s and Neftci’s
examination of the relationship between growth
over the entire expansion and the severity of the
preceding recession.
The article begins with a brief discussion of
how the National Bureau of Economic Research
(NBER) determines the dates of the peaks and
troughs in economic activity that give the business
cycle its name. We then specify a simple empirical
model for testing hypotheses about the relationship between recessions and expansions. We document the existence of a significant bounce-back
effect in various measures of U.S. industrial production and show that this finding is robust to a
variety of potential criticisms. Having established
the existence of a bounce-back effect, we provide
some intuition about the economic forces behind
it. We then consider the behavior of the economy
during the recovery from the 1990–91 recession
and show that it is consistent with the bounceback effect.
The U.S. experience with recessions
The NBER is responsible for the dating of the
peaks and troughs in economic activity that mark
the onset of recessions and expansions.2 The dating
of business cycles by the NBER is based on a
definition of business cycles first formulated by
Wesley Clair Mitchell in 1927:
Federal Reserve Bank of Dallas

Business cycles are a type of fluctuation
found in the aggregate economic activity of
nations that organize their work mainly in
business enterprises: a cycle consists of
expansions occurring at about the same
time in many economic activities, followed
by similarly general recessions, contractions, and revivals which merge into the
expansion phase of the next cycle; the
sequence of changes is recurrent but not
periodic; in duration business cycles vary
from more than one year to ten or twelve
years; they are not divisible into shorter
cycles of similar character with amplitudes
approximating their own (Moore and
Zarnowitz 1986, 736).

Note that the definition refers to fluctuations in
“aggregate economic activity” rather than a more
precisely defined aggregate, such as gross national
product (GNP), industrial production, or total employment. This vagueness is intentional and recognizes that business cycles consist of movements in
many different series that are not readily reduced
to a single aggregate. Looking at a variety of series
also helps minimize the risk of drawing erroneous
conclusions based on mismeasurement. Finally,
under the NBER definition, a period of slow, or
“subpar,” growth does not qualify as a contraction. Rather, peaks in activity are followed by
periods of absolute decline in aggregate activity.3
A recession is defined as a peak-to-trough
movement in economic activity. According to the
NBER business-cycle chronology, the United
States has experienced 30 recessions since the
middle of the nineteenth century (see Burns and
Mitchell 1946, Table 16; Moore and Zarnowitz
1986, Tables A.3, A.5). The dates of the peaks and
troughs in U.S. economic activity chosen by the
NBER are given in Table 1, along with statistics on
the duration of expansions and contractions for
the entire period. The chronology ends with the
date of the most recent peak, July 1990.
At the time of our analysis (October 1992),
the date of the trough marking the end of the
most recent recession had not been announced
officially, but several observers (including Moore
1992) have placed it in April or May 1991.4
Addi-tional clues to the likely date of the most
recent trough can be obtained from examining
Economic Review — First Quarter 1993

the recent behavior of the U.S. Commerce
Department’s composite index of coincident
indicators. This index is explicitly designed to
approximate cyclical movements in economic
activity and to have turning points that match
the business cycle. The coincident index
peaked most recently in June 1990, just one
month before the official peak in July, and
seemed to hit a trough in January 1992. However, revisions to the index currently being
undertaken by the Commerce Department and
discussed in Green and Beckman (1992) move
the trough in the index back to March 1991.
From the table we can see that the United
States has experienced nine recessions since the
end of World War II. This is a rather small sample
for testing the idea that severe recessions tend to
be followed by strong recoveries, so it is important to include pre–World War II recessions in our
sample to be reasonably confident of our findings. 5 However, extending the statistical analysis
to the pre–World War II period leads to problems
of data availability and consistency. Furthermore,
because the NBER chronology dates businesscycle peaks and troughs by month, a monthly
indicator of economic activity is preferable for
examining the hypothesis that deep recessions
are followed by strong recoveries.
The requirement that the selected measure
of aggregate economic activity be available at a
monthly frequency and extend back to the prewar
period leads us to use industrial production, as
measured by the Federal Reserve Board’s index of
industrial production.6 This index has the advan-

This is not true, however, of “growth cycle” chronologies.

See Hall (1992) for a discussion of the problem of determining the date of troughs in economic activity.

Alternatively, we could look at the experience of other
countries in the postwar period. Thus, in Balke and Wynne
(1992), we look for a bounce-back effect in the Group of
Seven countries during the postwar period, using the NBER’s
“growth cycle” chronology for these countries.

Moore (1961, 88) notes that the relationship between the
severity of a recession and the strength of the subsequent
recovery is strongest for industrial production.

Table 1

NBER Business-Cycle Chronology for United States
Duration (Months)
Peak

Trough

Contraction

Expansion

June 1857
October 1860
April 1865
June 1869
October 1873
March 1882
March 1887
July 1890
January 1893
December 1895
June 1899
September 1902
May 1907
January 1910
January 1913

December 1858
June 1861
December 1867
December 1870
March 1879
May 1885
April 1888
May 1891
June 1894
June 1897
December 1900
August 1904
June 1908
January 1912
December 1914

18
8
32
18
65
38
13
10
17
18
18
23
13
24
23

22
46
18
34
36
22
27
20
18
24
21
33
19
12
44

August 1918
January 1920
May 1923
October 1926
August 1929
May 1937
February 1945

March 1919
July 1921
July 1924
November 1927
March 1933
June 1938
October 1945

7
18
14
13
43
13
8

10
22
27
21
50
80
37

November 1948
July 1953
August 1957
April 1960
December 1969
November 1973
January 1980
July 1981
July 1990

October 1949
May 1954
April 1958
February 1961
November 1970
March 1975
July 1980
November 1982
n.a.

11
10
8
10
11
16
6
16
n.a.

45
39
24
106
36
58
12
92
n.a.

Comparative statistics

Pre–World War II
Post–World War II

Average length
of contractions

Average length
of expansions

21.2
10.7

28.9
49.9

n.a.—Not available.
NOTE: Length of contraction is the number of months from peak to trough.
Length of expansion is the length of the expansion after the trough date.
SOURCE: Moore and Zarnowitz (1986), Tables A.3, A.5.

Federal Reserve Bank of Dallas

tage of extending back to 1919, thus adding to the
sample of recessions. The obvious drawback is
that industrial production is an incomplete indicator
of aggregate economic activity: industrial production currently accounts for only about one-fifth
of total output. Looking at a broader measure
of output, such as GNP, would probably be
better; however, GNP estimates are available
only on a quarterly basis and only as far back
as 1947. On the other hand, movements in GNP
and industrial production are highly correlated,
with correlations of 0.998 using annual data
and 0.964 using quarterly data.7 Also, industrial
production is a component of the index of
coincident indicators, which is explicitly
designed to have turning points that are the
same as those of the business cycle.

Figure 1

Peak-to-Trough Change in Output and Output
Growth, as Measured by Industrial Production
(NBER Business-Cycle Dates)
Output growth in first
12 months of recovery
(Percent)
60

Great Depression
40

Is there a bounce-back effect?
A useful first pass at answering the question
of whether severe recessions are followed by
strong recoveries is, simply, to plot the data.
Figure 1 presents a scatter plot of the percentage
change in output in each of the 14 recessions
since 1919 (except the 1990–91 recession) against
output growth in the first twelve months of the
subsequent expansion, using the NBER businesscycle dates. A 135-degree line is included for
reference. The scatter of points in Figure 1
certainly suggests the existence of some degree
of correlation between the decline in industrial
production over the course of a recession and
growth in the first twelve months of an expansion. Obviously, the Great Depression (August
1929–March 1933) is very influential in suggesting
the existence of a self-correcting mechanism, but
it is clear that more is going on.8
This simple ocular analysis of the data suggests that there is a correlation between the peakto-trough decline in output over the course of
recession and growth in the early stages of the
subsequent recovery. Let us now turn to testing
and quantifying the strength of this correlation.
Empirical analysis
Our strategy for testing for the existence of
a bounce-back effect was to estimate a simple
linear regression model of the form
Economic Review — First Quarter 1993

0
–60

–50

–40

–30

–20

–10

Peak-to-trough change in output (Percent)

SOURCES OF PRIMARY DATA:
Board of Governors, Federal Reserve System.
Moore and Zarnowitz (1986).

Correlations were calculated using annual data for 1929–90
and quarterly data for 1947–90.

The recovery from the Great Depression of 1929–33 has
recently been examined in some detail by Romer (1991).
The specific question she addresses is, What proportion of
the extraordinary rates of real GNP growth observed in the
mid-1930s and late 1930s can be attributed to the severity
of the downturn, and what proportion can be attributed to
monetary and fiscal stimuli to aggregate demand? She
finds that stimulative monetary policy in the form of
unsterilized gold inflows played a key role in the recovery,
and she concludes that her findings suggest that “any selfcorrective response of the U.S. economy to low output was
weak or non-existent in the 1930s” (p. 1). The role of activist
fiscal and monetary policy in generating vigorous recoveries is an issue we do not address directly in this article.

Table 2

Rate of Growth During First Twelve Months of Recovery

Constant
Industrial
production

Manufacturing

Durables
manufacturing

Length of
recession

⎯R 2

8.24**
(2.79)

–.63***
(.13)

—

.64

6.27
(3.25)

–.47**
(.19)

.34
(.30)

.65

9.13**
(3.35)

–.62***
(.14)

—

.58

5.19
(3.58)

–.35*
(.19)

.63*
(.31)

.66

–.69
(8.22)

–1.31***
(.24)

—

.68

–.83**
(.29)

1.61**
(.70)

.77

9.00***
(1.16)

–.42***
(.10)

—

.59

6.90***
(1.51)

–.24*
(.13)

.26*
(.13)

.66

–10.50
(8.24)
Nondurables
manufacturing

Change
from peak
to trough

* Significant at the 10-percent level.
** Significant at the 5-percent level.
*** Significant at the 1-percent level.
NOTE: All data were seasonally adjusted. The sample period is January 1919–December 1991, which includes 14 recessions,
not counting the 1990–91 recession. Peak and trough dates are from the official NBER business-cycle chronology.
The dependent variable is the rate of growth during the first twelve months of recovery (defined as trough to trough
plus twelve months).
Figures in parentheses are standard errors.

⎛Y
⎛Y − YP ⎞
−Y ⎞
(1) ⎜ T +12 T ⎟ = α 0 + α1 ⎜ T
⎟ + α 2 (T − P )i + ei ,
⎝ YT
⎠i
⎝ YP ⎠ i

In Balke and Wynne (1992), we estimate a slightly different
model that allows us to distinguish between three measures
of the severity of a recession—length, depth, and steepness. Moore (1961, 86) notes that recessions have at least
three dimensions—”depth, duration, and diffusion.” We do
not consider diffusion as a measure of severity in this article,
primarily because of the degrees-of-freedom problem.

Looking at growth beyond twelve months is complicated by
the fact that for three of the recessions in our sample, the
subsequent expansion lasted twelve months or less.

where Y is some measure of output, T denotes
the month of a business-cycle trough as determined
by some business-cycle chronology, P denotes the
month of a business-cycle peak, i indexes recessions, and ⑀ is an error term.9 The dependent
variable is the percentage increase in output in
the twelve months after the trough month.10 The
explanatory variables, apart from the constant, are
the peak-to-trough change in output in percentage
terms and the length of the recession in months.
Federal Reserve Bank of Dallas

Table 3

Rate of Growth During First Twelve Months of Recovery,
Excluding the Great Depression

Constant
Industrial
production

Manufacturing

Change
from peak
to trough

Length of
recession

⎯R 2

9.72**
(3.22)

–.51**
(.19)

—

.35

6.26
(6.73)

–.47**
(.20)

.34
(.57)

.31

11.51**
(3.64)

–.43**
(.19)

—

.25

2.99
(7.39)

–.36*
(.19)

.81
(.62)

.30

5.52
(8.62)

–.97***
(.31)

—

.43

–.84**
(.31)

2.09
(1.42)

.48

9.61***
(1.12)

–.28**
(.12)

—

.29

7.69
(3.09)

–.24
(.14)

.19
(.28)

.25

Durables
manufacturing

–16.19
(16.88)
Nondurables
manufacturing

If deep recessions are followed by strong recoveries, the estimate of ␣1 should be negative. If long
recessions are followed by strong recoveries, the
estimate of ␣2 should be positive.
Table 2 reports estimates of this model using
the Federal Reserve’s industrial production index
and its three principal components—total manufacturing, durables manufacturing, and nondurables
manufacturing. Results are reported both with and
without the length-of-recession variable on the
right-hand side. The sample includes 14 recessions,
starting with the January 1920–July 1921 recession
and ending with the July 1981–November 1982
Economic Review — First Quarter 1993

recession, as determined by the NBER businesscycle chronology. For each production category,
there is a statistically significant relationship
between the size of the peak-to-trough decline
and growth in the twelve months after the trough.
The size of the bounce-back effect is strongest for
durables manufacturing. Recession length makes
no difference to the strength of the recovery in
total industrial production but does seem to be
important for manufacturing. Within manufacturing,
recovery in the durable goods sector seems to be
more affected by the length of the recession than
is the recovery in the nondurables sector. For all
7

sectors, including the length of the recession as an
additional variable on the right-hand side lessens
the bounce-back effect but does not eliminate it.
Because the sample period includes the
Great Depression, one of the most severe contractions ever in U.S. economic activity, the results in
Table 2 may be overly influenced by this extraordinary event. Table 3 reports results from estimation of equation 1 when the Great Depression is
excluded from the sample. As might be expected,
there is some loss of statistical significance, but
the results are broadly similar to those in Table 2.
The length of the recession is no longer significant in explaining growth during the first twelve
months of recovery. This is not too surprising,
because the Great Depression, with forty-three
months from peak to trough, is by far the longest
recession in the period covered by our analysis.11
How robust are the results?
How robust are our findings of a bounceback effect? We have already examined the sensitivity of the findings to the inclusion of the Great
Depression in the sample and have seen that the
results are not sensitive to its exclusion. In this
section, we will consider the robustness of our
results to a variety of other potential criticisms.
First, we will consider growth over horizons other
than the twelve months after the trough date.
Specifically, we will consider whether growth in
the first six months of an expansion is also significantly related to the severity of the preceding
recession. Second, we will increase the number of
recessions we look at by examining the behavior
of an alternative industrial production index constructed by Miron and Romer (1990) that covers
the period 1884–1940. We also consider the
behavior of this index when it is spliced to the
Federal Reserve production index in 1919. Finally,
we consider the sensitivity of our results to use

The Great Depression is not, however, the longest recession in the NBER chronology. The longest U.S. recession on
record was from October 1873 to March 1879, lasting sixtyfive months. This recession is not included in our analysis
because reliable measures of aggregate production at the
required frequency are not available that far back.

of the official NBER chronology by looking at the
dates suggested by Romer (1992) and the dates
obtained using the algorithm developed by Bry
and Boschan (1971).
The bounce-back effect at the six-month
horizon. To examine whether the bounce-back
effect can be found at the six-month horizon as
well, we estimated an obvious variant on equation
1, redefining the dependent variable to be growth
in the first six months after the trough. The results
are reported in Table 4. We only report the results
obtained when length of recession is not included
in the model, as the significance of this variable
seems to hinge completely on including the Great
Depression in the sample. Growth in the first six
months of the recovery is significantly correlated
with the peak-to-trough change in activity, but
excluding the Great Depression from the sample
seems to reduce the strength of the correlation a
lot more than we find for growth over the twelvemonth horizon.
The bounce-back effect in the Miron–Romer
industrial production series. It is possible to
extend the sample period further to include the
period before World War I by using the industrial
production index recently constructed by Miron
and Romer (1990). Their index covers the period
1884–1940, overlapping with the Federal Reserve
index for twenty-one years, from 1919 to 1940.
This period of overlap includes five recessions.
The Miron–Romer index was designed to improve
upon the older Babson and Persons indexes, which
made heavy use of indirect proxies for industrial
activity (such as imports and exports in the case
of the Babson index and bank clearings in the
case of the Persons index). Miron and Romer note
that their series has turning points (that is, peaks
and troughs) that are “grossly similar to but subtly
different from existing series” (p. 321).
The Miron–Romer index is less comprehensive than the Federal Reserve index and, according
to the NBER chronology, produces two anomalous
observations. Specifically, the Miron–Romer index
shows industrial production increasing in two
of the pre–World War I recessions, the recessions
of December 1895–June 1897 and September
1902–August 1904. This finding can be interpreted
as a drawback of the series or as suggesting a
need to reconsider the dating of pre–World War I
business cycles by using the improved index.
Federal Reserve Bank of Dallas

Table 4

Rate of Growth During First Six Months of Recovery

Constant

Change
from peak
to trough

⎯R 2

Including the Great Depression
Industrial
production

.39
(3.11)

–.63***
(.14)

.62

Manufacturing

.71
(3.51)

–.65***
(.15)

.61

Durables
manufacturing

–7.90
(8.45)

–1.08***
(.25)

.61

Nondurables
manufacturing

2.68**
(1.15)

–.68***
(.10)

.81

Excluding the Great Depression
Industrial
production

4.12
(2.94)

–.32*
(.17)

.25

Manufacturing

4.82
(3.17)

–.32*
(.17)

.25

Durables
manufacturing

3.91
(5.78)

–.44*
(.21)

.29

–.49***
(.11)

.67

Nondurables
manufacturing

3.48***
(.99)

* Significant at the 10-percent level.
** Significant at the 5-percent level.
*** Significant at the 1-percent level.
NOTE: All data were seasonally adjusted. The sample period is January 1919–December 1991,
which includes 14 recessions, not counting the 1990–91 recession. Peak and trough dates
are from the official NBER business-cycle chronology. The dependent variable is the rate
of growth during the first six months of recovery (defined as trough to trough plus six months).
Figures in parentheses are standard errors.

The results from estimating the model by using
the Miron–Romer index are reported in Table 5.
The first four rows of this table report the results
obtained using the raw (not seasonally adjusted)
series. Again, we find evidence of a significant
bounce-back effect in industrial production. The
inclusion of recession length as an additional explanatory variable makes no difference to this finding, nor does excluding the Great Depression.
Economic Review — First Quarter 1993

Table 5 also reports the results of combining the
Federal Reserve and Miron–Romer indexes (seasonally adjusted). We followed Romer (1992) in splicing
the two series in 1919 to obtain a single series on
industrial production for the period 1884–1990. This
gives us a sample of 24 recessions for examining
the bounce-back effect. The principal difference
between these results and those in Tables 3 and 4
is that length of recession is no longer significant in
9

Table 5

Rate of Growth During First Twelve Months of Recovery:
Results Using the Miron–Romer Index

Constant

Change
from peak
to trough

Length of
recession

⎯R 2

Number of
recessions

Miron–Romer Index
Including the
Great Depression

Excluding the
Great Depression

12.48**
(4.80)

–.79***
(.20)

—

.50

9.39
(9.86)

–.76***
(.23)

.20
(.55)

.47

12.42**
(5.00)

–.82***
(.24)

—

.45

–.82***
(.24)

.77
(.89)

.44

.16
(15.03)

Combined Federal Reserve/Miron–Romer Index
Including the
Great Depression

Excluding the
Great Depression

9.62***
(2.17)

–.65***
(.12)

—

.54

6.10
(3.71)

–.60***
(.13)

.27
(.23)

.55

9.94***
(2.30)

–.60**
(.16)

—

.38

3.99
(5.73)

–.64***
(.16)

.40
(.35)

.39

* Significant at the 10-percent level.
** Significant at the 5-percent level.
*** Significant at the 1-percent level.
NOTE: Peak and trough dates are from the official NBER business-cycle chronology. The dependent variable is the rate of growth
during the first twelve months of recovery (defined as trough to trough plus twelve months).
Estimates in the first four rows were obtained using the non-seasonally-adjusted Miron–Romer index. The sample period is
January 1884–December 1940, which includes 15 recessions. Estimates in the second four rows were obtained using the
combined Federal Reserve/Miron–Romer series, which is seasonally adjusted, not counting the 1990–91 recession. The
sample period is January 1884–December 1991, which includes 24 recessions.
Figures in parentheses are standard errors.

explaining the strength of the recovery, even when
the Great Depression is included in the sample.
The bounce-back effect in alternative businesscycle chronologies. Romer (1992) has questioned
whether the dates for the prewar cycles in the
official NBER chronology are strictly comparable
to those for the postwar period. Romer documents
evidence that the prewar dates are based on
10

detrended data while the postwar dates reflect
cycles in unadjusted data. Consequently, the prewar
NBER chronology tends to overstate the length of
contractions and understate the length of expansions. Romer corrects the NBER chronology by
formalizing the rule that the NBER used in dating
the postwar cycles and applying it to industrial
production for the prewar period to come up
Federal Reserve Bank of Dallas

Table 6

Alternative Prewar Business-Cycle Chronologies
NBER dates

Romer dates

Bry–Boschan dates

Peak

Trough

Peak

Trough

Peak

Trough

March 1887

April 1888

February 1887

July 1887

—

July 1890

May 1891

—

January 1893

June 1894

January 1893

April 1894

—

December 1895

June 1897

December 1895

January 1897

October 1895

August 1896

—

April 1897

June 1898

June 1899

December 1900

April 1900

December 1900

April 1900

October 1900

—

August 1901

June 1902

September 1902

August 1904

July 1903

March 1904

—

May 1907

June 1908

July 1907

June 1908

—

January 1910

January 1912

January 1910

May 1911

February 1910

December 1910

January 1913

December 1914

June 1914

November 1914

December 1912

January 1914

—

May 1916

January 1917

—

August 1918

March 1919

July 1918

March 1919

May 1918

March 1919

January 1920

July 1921

January 1920

July 1921

January 1920

March 1921

May 1923

July 1924

May 1923

July 1924

May 1923

June 1924

October 1926

November 1927

March 1927

December 1927

March 1927

December 1927

August 1929

March 1933

September 1929

July 1932

May 1929

July 1932

May 1937

June 1938

August 1937

June 1938

May 1937

June 1938

—

December 1939

March 1940

—

November 1891 September 1893

SOURCES: Moore and Zarnowitz (1986), Tables A.3, A.5.
Romer (1992), Table 3.
Authors’ calculations.

with an alternative set of dates.12 These dates are
shown in Table 6. One key difference with the
official NBER dates (reproduced in Table 6 for ease
of comparison) is that the average length of pre–
World War II contractions is shorter (11.4 months,
as opposed to 17.8 months in the NBER chronology), and the average length of pre–World War II
expansions is longer (30.3 months, as opposed to
24.9 months in the NBER chronology).13 The two
chronologies are in agreement for only two recesEconomic Review — First Quarter 1993

This rule is explained in the Appendix.

Note that these statistics compare the average length of
contractions and expansions during the period for which
the two chronologies overlap. The statistics on the average
length of prewar contractions and expansions reported in
Table 1 are the averages over all contractions and expansions in the NBER chronology for the prewar period.

sions, those of 1920–21 and 1923–24. They are
also in agreement on either the peak or the trough
dates for a number of other recessions. Finally,
note that Romer’s chronology excludes one recession that is included in the NBER chronology, the
1890–91 recession, while including two others that
are omitted from the NBER chronology, those in
1916–17 and 1939–40. One other noteworthy
feature of Romer’s chronology is that she dates
the trough of the Great Depression in July 1932,
which shortens the length of that downturn from
forty-three months to thirty-four months.
Table 6 also contains business-cycle dates
obtained from application of the algorithm devised
by Bry and Boschan (1971) to industrial production
for the entire period.14 The Bry–Boschan algorithm
is somewhat more complex than the rule devised
by Romer and picks slightly different cycles from
those picked by Romer and those in the official
NBER chronology. The Bry–Boschan algorithm
picks two cycles (1897–98 and 1901–2) that are not
included in the NBER chronology and misses four
(1887, 1893–94, 1903–4, and 1907–8) that are. The
Bry–Boschan algorithm also misses the 1916–17
and 1939–40 cycles, two cycles picked by the Romer
algorithm but not included in the NBER chronology.
The algorithm does capture some of the same peak
and trough dates as the Romer algorithm and the
NBER chronology. Interestingly, the Bry–Boschan
algorithm places the trough of the Great Depression in July 1932 (the same as Romer) but dates
its onset in May 1929, four months earlier than
Romer and three months earlier than the NBER.
Table 7 reports the results of estimating equation 1 with the Romer and Bry–Boschan businesscycle dates. For consistency, we used the dates
picked by these algorithms for the postwar period
as well, rather than the NBER dates. The differences
between the three chronologies for the postwar
period are minor, as both the Romer and Bry–
Boschan algorithms are designed to match as
closely as possible the NBER dating for this period.
Both chronologies suggest a statistically significant
bounce-back effect. In every case, the coefficient

The Bry–Boschan algorithm is described briefly in the
Appendix.

estimate on the change in output from peak to
trough is significant at the 1-percent level. The
length of the recession is not significant in either
chronology, even when the Great Depression is
included. Excluding the Great Depression does
significantly lower the explanatory power of the
basic model, as indicated by the drop in the R僓2,
and the size of the bounce-back effect, as indicated by the drop in the absolute value of the
coefficient estimate, but does not eliminate it.
To summarize, our finding of a bounce-back
effect in industrial production is common to a variety
of measures of industrial production, is found at
the six-month as well as the twelve-month horizon,
and is robust to potential shortcomings in the NBER
chronology for the prewar period. Some other
robustness tests (such as controlling for secular
trend) are reported in Balke and Wynne (1992)
and reinforce those reported here. The robustness
of the bounce-back effect merits taking it seriously
as a stylized fact about the business cycle.
The economics of the bounce-back effect
Having established the existence of a bounceback effect, we should provide an economic interpretation of what is going on. We argue that the
bounce-back effect tells us more about the dynamic
response of the economy to shocks than about
the nature or source of shocks themselves. Three
simple observations about the behavior of firms
and households help in understanding macroeconomic dynamics. First, households and firms
not only look at current economic conditions when
deciding how much to work, save, consume, and
invest but also take into consideration the likely
course of economic activity in the future. Second,
households prefer continuity in their consumption
patterns from year to year, rather than wild movements. And third, saving and investment decisions
made today have implications for what can be
done tomorrow through their effect on capital
accumulation, just as decisions made yesterday
have implications for what can be done today. The
bounce-back effect is a manifestation of the dynamic
response of the economy, as a result of these three
factors, to a shock that brings about a recession.
One interpretation of what happens when
the economy goes into recession is that the maximum level of output that can be attained with
Federal Reserve Bank of Dallas

Table 7

Results Using Alternative Business-Cycle Chronologies

Constant

Change
from peak
to trough

Length of
recession

⎯R 2

Number of
recessions

Romer Dating
Including the
Great Depression

Excluding the
Great Depression

7.01*
(3.60)

–.90***
(.18)

–.03
(.33)

.59

6.81**
(2.53)

–.89***
(.14)

—

.61

12.55**
(4.60)

–.73***
(.20)

–.40
(.38)

.35

8.67***
(2.78)

–.70***
(.19)

—

.34

Bry–Boschan Dating
Including the
Great Depression

–1.09
(3.60)

–.71***
(.18)

.46
(.33)

.71

2.05
(2.89)

–.90***
(.13)

—

.69

8.69*
(4.90)

–.60***
(.17)

–.17
(.37)

.38

6.93**
(2.87)

–.57***
(.15)

—

.41

Excluding the
Great Depression

* Significant at the 10-percent level.
** Significant at the 5-percent level.
*** Significant at the 1-percent level.
NOTE: All data were seasonally adjusted. The sample period is January 1884–December 1991, which includes 25 recessions in
the Romer chronology and 21 recessions in the Bry–Boschan chronology. The dependent variable is the rate of growth
during the first twelve months of recovery (defined as trough to trough plus twelve months).
Figures in parentheses are standard errors.

existing resources of capital and labor temporarily
falls. Such a change might come about, for example,
as a result of a temporary increase in oil prices.
This is the type of shock typically emphasized in
New Classical real business cycle models. Or
alternatively, a coordination failure results in productive resources becoming idle and output falling
below potential. This story is more characteristic
of New Keynesian analyses of the causes of recessions. During the period of lower output, households try to maintain their consumption levels by
saving less. Part of this behavior translates into
Economic Review — First Quarter 1993

less investment by businesses and reduced purchases of consumer durables by households. The
result of these spending decisions of households
and firms is that when the economy hits the trough,
stocks of business capital and household capital
are below their “normal,” or desired long-run, levels.
This discrepancy between actual and normal levels
of capital is then associated with an investment
boom and an increase in purchases of consumer
durables when the economy turns the corner. In
some cases, the discrepancy in and of itself can
be enough to bring a recession to an end and set
13

the expansion in motion. The larger the discrepancy between actual and normal capital stocks at
the trough, the faster the economy will grow in
the months after the trough because of the greater
amount of ground that has to be regained.
This explanation merely touches on some
of the key elements of the more fully articulated
theories essential for a complete understanding of
the business cycle. In Balke and Wynne (1992), we
carry out a detailed analysis of a prototypical real
business cycle model and find that it performs
reasonably well in generating the bounce-back
phenomenon but does not capture other features
of the business cycle.
Examination of the 1991–92 recovery
The most recent business-cycle peak was in
July 1990. If we date the trough of this cycle as May
1991, as many analysts are doing (although the
official trough date has yet to be announced by the
NBER), the peak-to-trough decline in industrial production amounts to 3.6 percent. Industrial production bottomed out in March 1991, after declining
5.0 percent since July 1990. This compares favorably with either the average decline of 17.1 percent
for all the recessions covered by the Federal Reserve’s
index of industrial production or the average decline
of 8.8 percent for the post–World War II recessions.
Based on our estimates in Table 2, we would expect
industrial production to have grown 10.5 percent—
8.24 – (0.63)(–3.6)—from the tentative trough date
in May 1991 through May 1992. In fact, industrial
production grew only 2.3 percent over this period,
substantially less than the rate predicted by our
simple model. If we take the actual peaks and
troughs in industrial production, the decline from
September 1990 to March 1991 is 5.2 percent, and
predicted cumulative growth in industrial production from March 1991 to March 1992 is 11.5 percent—8.24 – (0.63)(–5.2)—as opposed to a realized
rate of 2.5 percent. Thus, our bounce-back equation dramatically overpredicts the strength of the
recovery, suggesting that the present recovery is
abnormally slow, even after taking into account
the shallowness of the recession.
However, because of the historical variability
of the growth rate of industrial production during
recoveries, the current recovery is still well within
the 95-percent confidence interval implied by the
14

bounce-back model. For the forecast growth rate
over the twelve months since May 1991, the standard
error associated with the forecast is 6.9 percentage
points. This means that based on the coefficient
estimates in Table 2, the 95-percent confidence
interval associated with the forecast value of the
growth rate of industrial production from May 1991
to May 1992 is 10.5 ± (1.96)(6.9)—that is, from –3.0
percent to 24.0 percent. Thus, the current recovery,
while substantially weaker than predicted, is nonetheless consistent with the bounce-back model.
An alternative perspective on how this recovery
compares with others is given in Figure 2. This
figure is a scatter plot of the peak-to-trough decline
in industrial production over the course of recession against growth in the first twelve months of
the recovery, with the recessions and recoveries
now ranked in order of severity and strength. Thus,

Figure 2

Rank Ordering of Recessions and Recoveries,
as Measured by Industrial Production
(NBER Business-Cycle Dates)
Recoveries, ordered by strength
16

Great Depression
15
14

1948–49
13
12
11
10
9
8
7
6
5
4

1973–75

3
2
1

1990–91 Recession and Recovery

0
0

Recessions, ordered by depth

SOURCES OF PRIMARY DATA:
Board of Governors, Federal Reserve System.
Moore and Zarnowitz (1986).

Federal Reserve Bank of Dallas

the horizontal axis ranks recessions in order of
severity, with 1 being the least severe and 15 being
the most severe. The vertical axis ranks recoveries
in terms of their strength, with 1 being the least
strong and 15 being the most strong. That the
points are clustered around the 45-degree line is
simply another way of demonstrating the bounceback effect: typically, severe recessions are followed
by strong recoveries. As we saw in Figure 1, the
most severe recession in the sample covered by
the Federal Reserve’s industrial production index,
the Great Depression, was also followed by the
most robust recovery in that sample. What we see
from Figure 2 is that the 1990–91 recession was
the least severe since 1919 in terms of the decline
in industrial production and, also, the recovery in
the twelve months since the tentative trough date
of May 1991 is the weakest since 1919. In other
words, the behavior of the industrial sector in the
most recent recession and recovery episode is
very much in line with historical experience.
It cannot be emphasized strongly enough
that this article focuses on the behavior of the
industrial sector in recessions and recoveries. In
terms of broader measures of aggregate activity,
such as total nonagricultural employment or GNP,
the picture is somewhat different. While the most
recent recession may have been one of the least
severe in U.S. history in terms of the decline in
industrial production, it is close to the postwar
average in terms of the decline in GNP. As for the
recovery, GNP growth over the year since the tentative trough date of May 1991 is the weakest in the
postwar period. Moreover, while the decline in
manufacturing employment between July 1990 and
May 1991 was the smallest in the postwar period,
the twelve-month period after May 1991 is the only
postwar “recovery” in which manufacturing employment declined. Outside the manufacturing sector,
service-sector employment posted its weakest
increase of any postwar recession except the
1957–58 recession—the only postwar recession in
which service-sector employment declined. In the
twelve months since May 1991, service-sector
employment has grown less than in any other
postwar recovery.
The 1990–91 recession and recovery episode
generated many puzzles for policymakers that are
not yet fully understood. With the passage of time,
our understanding of what happened will grow.
Economic Review — First Quarter 1993

The sluggish pace of the overall recovery remains
a puzzle, but the relatively modest growth in
industrial output is consistent with the bounceback effect that we have shown to be characteristic of previous recessions.
Conclusions
In this article, we have examined how rapidly
industrial production recovers in the twelve months
after a business-cycle trough. We considered two
variables as candidates to explain differences in
growth rates between recoveries—the depth and
the length of the preceding recession. We found a
statistically significant relationship between the rate
of growth of output in the twelve months after a
business-cycle trough and the size of the decline
in output from peak to trough. Furthermore, the
bounce-back effect appears to be stronger in
durables manufacturing than in nondurables manufacturing. The existence of this bounce-back effect
does not depend on including the Great Depression in our sample. However, the length of the
recession makes a difference for the strength of the
subsequent recovery only if the recovery following
the Great Depression is included in the sample.
In Balke and Wynne (1992), we have
examined the bounce-back effect in greater detail
and have shown that a similar phenomenon seems
to characterize the behavior of the Group of Seven
countries in the postwar period. In that paper, we
also look at the “shape” of cyclical movements
in various aggregates and document significant
asymmetries between expansions and contractions. In addition, we explore the implications of
these findings for some common (linear) statistical
and economic models of industrial output.
Given the relative robustness of our finding
of a bounce-back effect for the industrial sector, it
is important to ask whether the effect characterizes
the 1990–91 recession and recovery. If we take
May 1991 as the trough date marking the end of
the most recent recession, the decline in industrial
output from peak to trough was 3.6 percent, making
it one of the mildest recessions in terms of lost
industrial production. And consistent with the
bounce-back effect, the growth in industrial production since May 1991 has been the weakest
recovery in the period covered by the Federal
Reserve index of industrial production.
15

Appendix
Rules for Dating Business Cycles
Romer’s rules for dating cycles by using
industrial production
1. A fluctuation counts as a cycle if the
cumulative loss in the log of output
between the peak and the return to
peak exceeds 0.44—that is, 44 percentage-point months of output.
2. The second or later of multiple extremes is chosen as the turning point
if the cumulative loss or gain in output
is less than 0.11.
3. The first month after a peak or trough
counts as a horizontal stretch if the
cumulative loss or gain in output is
less than 0.008.
The Bry–Boschan algorithm for picking
turning points in a time series
1. Eliminate extreme values of raw series (greater than ± 3.5 standard deviations) and replace by values from a
Spencer curve. A Spencer curve is a
symmetric filter with declining weights.
2. Calculate a twelve-month moving average with the adjusted series. Find
the local maximums and minimums.
Use dates as tentative peak and trough
dates, being sure that peaks and
troughs alternate.

3. Calculate a Spencer curve with the
adjusted series. Find the highest (lowest) values of Spencer curves within
five months of the peaks (troughs)
identified from the twelve-month moving average. Be sure that the new
peak and trough dates alternate and
that cycle duration is at least fifteen
months.
4. Calculate a four-month moving average with the adjusted series. Identify
the highest (lowest) values within five
months of the peaks (troughs) identified from the Spencer curve. Be sure
that the peak and trough dates alternate and that cycle duration is at least
fifteen months.
5. Using the raw series, adjusted for
extremes, find the highest (lowest)
values within four months of the peaks
(troughs) identified from the fourmonth moving average. Be sure that
no peak or trough is within six months
of the beginning or end of the sample,
that peaks and troughs alternate, that
cycle duration is at least fifteen months,
and that expansion and contraction
phases are at least five months long.
The resulting peak and trough dates
represent the final turning points.

Federal Reserve Bank of Dallas

References
Balke, Nathan S., and Mark A. Wynne (1992),
“The Dynamics of Recoveries” (Federal Reserve
Bank of Dallas, August, Photocopy).
Blinder, Alan S. (1991), “What’s So Bad About a Nice
Little Recovery?” Business Week, June 24, 22.
Board of Governors of the Federal Reserve System
(1990), Industrial Production and Capacity
Utilization: G.17(419) Historical Data and
Source and Description Information (Washington, D.C.: Board of Governors of the Federal
Reserve System, May).

Klein (Homewood, Ill.: Richard D. Irwin for
American Economic Association), 488–513.
——— (1961), “Leading and Confirming Indicators
of General Business Changes,” in Business
Cycle Indicators, ed. Geoffrey H. Moore, vol. 1,
Contributions to the Analysis of Current Business Conditions (Princeton: Princeton University Press for National Bureau of Economic
Research), 45–109.

Bry, Gerhard, and Charlotte Boschan (1971),
Cyclical Analysis of Time Series: Selected Procedures and Computer Programs (New York:
National Bureau of Economic Research).

———, and Victor Zarnowitz (1986), “The Development and Role of the National Bureau of
Economic Research’s Business Cycle Chronologies,” app. A in The American Business
Cycle: Continuity and Change, ed. Robert J.
Gordon (Chicago: University of Chicago
Press), 735–79.

Burns, Arthur F., and Wesley C. Mitchell (1946),
Measuring Business Cycles (New York:
National Bureau of Economic Research).

Neftci, Salih N. (1986), “Is There a Cyclical Time
Unit?” Carnegie–Rochester Conference Series
on Public Policy 24: 11–48.

The Economist (1992), “Sam, Sam, The Paranoid
Man,” January 18, 13–14.

Romer, Christina D. (1992), “Remeasuring Business
Cycles: A Critique of the Prewar NBER Reference Dates” (University of California, Berkeley,
January, Photocopy).

Friedman, Milton (1969), “The Monetary Studies of
the National Bureau,” in The Optimum Quantity of Money and Other Essays (Hawthorne,
N.Y.: Aldine Publishing Company), 261–84.
Green, George R., and Barry A. Beckman (1992),
“The Composite Index of Coincident Indicators
and Alternative Coincident Indexes,” Survey of
Current Business 72 ( June): 42–45.
Hall, Robert E. (1992), “The Business Cycle Dating
Process,” NBER Reporter, Winter 1991/2, 1–3.
Miron, Jeffrey A., and Christina D. Romer (1990),
“A New Monthly Index of Industrial Production, 1884–1940,” Journal of Economic History
50 ( June): 321–37.
Moore, Geoffrey H. (1992), “This Man Says the
Slump Is Over,” Fortune, January 27, 24.
——— (1965), “Tested Knowledge of Business
Cycles,” in A.E.A. Readings in Business Cycles,
comp. Robert Aaron Gordon and Lawrence R.
Economic Review — First Quarter 1993

——— (1991), “What Ended the Great Depression?”
NBER Working Paper Series, no. 3829 (Cambridge, Mass.: National Bureau of Economic
Research, September).
Shadow Open Market Committee (1992), “Policy
Statement and Position Papers,” Public Policy
Studies Working Paper Series, no. PPS 92-02,
University of Rochester (Rochester, N.Y.: University of Rochester, Bradley Policy Research
Center, September 13–14).
Sichel, Daniel E. (1992), “Inventories and the Three
Phases of the Business Cycle” (Board of
Governors of the Federal Reserve System,
August, Photocopy).
Wynne, Mark A., and Nathan S. Balke (1992),
“Are Deep Recessions Followed by Strong
Recoveries?” Economics Letters 39 ( June):
183–89.

Federal Reserve Bank of Dallas

Joseph H. Haslag

Lori L. Taylor

Senior Economist
Federal Reserve Bank of Dallas

A Look at Long-Term Developments
in the Distribution of Income

trong economic growth in the United States
during the last half of the 1980s did not translate into economic gains for all income groups.
Poverty rates, for example, remained higher than
those observed in the 1970s.1 To paraphrase the
most common findings, the rich got substantially
richer during the 1980s, while the poor may have
gotten poorer.
A trend toward greater income inequality
can be cause for concern. Most Americans would
not consider it desirable if, over time, all our
society’s resources became concentrated in the
hands of a small group of individuals. On the other
hand, few Americans would desire a perfectly equal
distribution of income because income equality
implies, among other things, that people who are
college educated earn exactly the same income as
people who are high school dropouts. If everyone
earned the same income, there would be little
incentive for people to work harder, become better
educated, or find better, more efficient methods
of production. Thus, the reasons underlying a
trend toward greater income inequality are at least
as important for policy analysis as the level of
income inequality.
We set out to investigate how and why the
distribution of income has changed over time.
We find that the distribution of income has been
becoming more unequal since the early 1950s,
making what occurred in the 1980s a continuation
of a longer-running trend. We also find that the
distribution of income gains over the past dozen
years is close to its historical average. Finally, we
examine how rising income inequality relates to
changes in the economy’s demographic, businesscycle, and policy characteristics. We find that factors
outside of direct policy control, such as the age
Economic Review — First Quarter 1993

and education profiles of the population, the
gender composition of the labor force, and (mostly)
inertia in income inequality, explain the lion’s
share of the forecast error variance. Policy variables, such as transfer payments and tax rates,
account for only 15 percent of the variation in
prediction errors.
What has happened to
the distribution of income?
Our description of changes in the distribution
of income proceeds in two parts. In the first part,
we divide the population into five equal-sized
subgroups, or quintiles, and examine each subgroup’s gains from income growth.2 In the second

We wish to thank Zsolt Besci, Stephen P.A. Brown, Christopher Carroll, and Keith R. Phillips for their helpful comments
and suggestions, and Anne E. King and Adrienne C. Slack
for their research assistance.
1

A change in how poverty rates were calculated means that
poverty rates before 1975 are not comparable to those
since 1975. Poverty rates stayed below 10 percent during
the period 1975–80. During the 1980s, poverty rates climbed
and then fell, staying above the 10-percent threshold. While
economic growth appears to have roughly coincided with
the declines in poverty rates, growth failed to lift enough
people out of poverty to reduce the poverty rates below 10
percent.

Another issue arises because we use tax returns as our data
source. People do not have to file tax returns if their income
levels are too low. Consequently, the sample we use is
truncated in the sense that the lowest paid people are
omitted.

part, we look at developments in an aggregate
measure of income inequality known as the Theil
entropy index. The Theil index measures the
degree of income inequality across the entire
population in one number.
The distribution of income gains. Much of the
recent attention to the issue of income inequality
has focused not on the distribution of income but
on how the gains from income growth were distributed across different income strata. According
to work by Paul R. Krugman related in a memorandum from the Congressional Budget Office
(1992), the top-paid 20 percent of the population
received 94 percent of the gains in after-tax income
between 1977 and 1989. In contrast, a 1992 U.S.
Treasury report shows that people who were
among the richest 1 percent of American taxpayers
in 1979 received only 11.3 percent of the total
gains in income during the 1980s (Sylvia Nasar
1992). In the New York Times, Nasar quotes Isabel
V. Sawhill’s finding that people who were in the
top-paid 20 percent of the population in 1977 saw
their incomes decline 11 percent over the next
decade, while people who had climbed into the
top category by 1986 had experienced, on average, a 65-percent increase in income.
To contribute to these discussions, we calculate summary statistics for the proportion of gains
from income growth received by each population
subgroup over the recent twelve-year period and
compare those results with what occurred over
the entire 1952–89 sample.3 We find that nearly
60 percent of the gains in adjusted gross income
during the period 1977–89 accrued to the top
income quintile.
Analysts can reach such strikingly dissimilar
conclusions because analyses of the distribution

Annual adjusted-gross-income data for this study are obtained from various issues of Statistics of Income, published by the United States Internal Revenue Service (IRS).
For our analysis, we divide the population into quintiles, as
follows: the IRS organizes tax returns by adjusted gross
income, ranking by groups from lowest paid to highest paid.
By dividing the total number of returns by five, we obtain the
number of returns for each quintile. Thus, between any two
periods the change in adjusted gross income earned by
each quintile necessarily equals the aggregate change in
adjusted gross income.

of income are very sensitive to the definitions of
income, time horizon, and population with which
the analyst works. For example, there are many
possible definitions of income. One can examine
the distribution of total income before taxes and
transfers, total income after taxes but before transfers (such as Aid to Families with Dependent
Children), total income after taxes and transfers,
wage income, and still other variations. It is not
too surprising that one finds different results when
comparing, say, the income distribution of individuals with the income distribution of households,
or the income distribution of taxpayers with the
income distribution of all persons.
We focus on adjusted gross incomes rather
than after-tax incomes because reliable data on
both taxes and transfers are not available. We
consider misleading any estimates of the income
distribution after taxes but before transfers because
they illustrate only part of the government’s redistributive activities. In our opinion, one should
either analyze the distribution of total factor incomes
before taxes and transfers, which indicates the
distribution of market-based claims on society’s
resources, or the distribution of income after both
taxes and transfers, which indicates the distribution of purchasing power. Analyses of after-tax
incomes that do not include information on transfers are neither fish nor fowl and are very problematic to interpret.
Analysts can also reach different conclusions
from one another when they use different measurement techniques. In Krugman’s analysis, the share
of income gains accruing to population group i is
represented as
(1)

Pi = ∆µi / n∆µ,

where µ i is the change in average income for
income group i, µ is the change in average income for the total population, and n is the number
of equal-sized income groups. One can interpret
equation 1 as the ratio of the weighted-average
gain of a specified group to the average gain of
the population as a whole. The equation highlights changes over time in the average income
of a quintile.
The Council of Economic Advisers (CEA)
analyzes growth in income by quintile for the
1992 Economic Report of the President. We comFederal Reserve Bank of Dallas

bine the CEA and Krugman approaches to represent the share of income gains earned by the i th
group of the population as
(2)

Pˆi = ∆Yi / ∆Y ,

where Y i is the change in income received by
the i th group, and Y is the change in income for
society as a whole. Equation 2, therefore, is the
ratio of income gains received by the i th group to
the income gains received by the population as a
whole. Note that the Krugman and CEA-based
measures yield identical results only when the
population size is constant.
The following example illustrates how the
interaction of population and income growth can
affect the distribution of income gains as measured
by the Krugman approach and the CEA-based
approach. Suppose the economy has two workers
with annual incomes of $30,000 and $20,000,
respectively. The next year, these same workers
earn $40,000 and $30,000, respectively, and two
new workers obtain jobs and earn $20,000 each.
Total income increased by $60,000. Average
income among wage earners increased by $2,500
(from $25,000 to $27,500), while average income
for the top half of the distribution increased by
$5,000 (from $30,000 to $35,000). According to
Krugman’s original calculation, the top half of the
distribution accounted for 100 percent of the gains
from economic growth—$5,000/(2 × $2,500).
Average income for the bottom half of the distribution did not change, indicating that the bottom
half accounted for zero percent of the gains from
economic growth using equation 1. Therefore,
although each of the four participants in this
hypothetical society earned more in the second
year than they did in the first, the Krugman
measure would indicate that all of the income
gains accrued to the top half of the distribution.4
Using the CEA-based technique, the interpretation is somewhat different. The top half of
the distribution received $40,000 more ($70,000 –
$30,000), while the bottom half of the distribution received $20,000 more ($40,000 – $20,000).
Thus, the top half accounted for 66.6 percent of
the gains from economic growth using equation
2, while the bottom half received 33.3 percent of
the gains.
The intuition behind the difference between
Economic Review — First Quarter 1993

Krugman’s approach and the CEA-based approach
is fairly straightforward. In Krugman’s approach,
income received by a particular subgroup of the
population must grow at a rate faster than population growth. Otherwise, average (per capita) income
for that subgroup would not rise, and Krugman’s
measure would indicate that they failed to share in
the income gains. Thus, if the original workers in
the example above earned $35,000 and $25,000,
respectively, in the second year, and all other aspects
of the example remained unchanged, then the
average income of the top half of the distribution
would remain at $30,000 [($35,000 + $25,000)/2],
and the average income of the bottom half of the
distribution would remain at $20,000. Krugman’s
measure would indicate that neither group has
experienced any income gains.
By the CEA-based measure (equation 2), the
condition for subgroups to share in income gains
is that the sum of population growth and income
growth for that particular subgroup exceeds zero.
Given sufficient population growth, it is possible
for the CEA-based measure to indicate that each
quintile experienced income gains even when
average income was falling for all quintiles. Thus,
relative to Krugman’s measure, the CEA method
requires that a weaker condition is satisfied for
any one subgroup to have a positive share in the
distribution of income gains.
Both Krugman’s and the CEA-based measures do not use longitudinal data. Neither of the
statistics follows a particular group of people
through time to trace how much of the aggregate
gains are distributed to that group. Therefore,
when there is substantial income mobility, these
measures of the aggregate economy say little
about the incomes received by specific individuals.
However, they say much about the distribution of
possible incomes and, therefore, about individual
opportunities. (For a discussion of income mobility
in the United States, see the box titled “Trends in
Income Mobility.”)
Table 1 reports the distribution of changes in
income for several periods. Specifically, the table

Michael Boskin (1992) lays out this example in describing
Krugman’s distribution of income gains.

Trends in Income Mobility
From year to year, people can and do
move from one income class to another. For
periods as long as a decade, the changes in
people’s income, especially for people in the
lowest income group, are remarkable. Table
B1 shows movements in the income distribution from 1979 to 1988.1 The data indicate
substantial income mobility, particularly among
the lower income groups. Only 65 percent of
the people who were in the top-paid 20 percent of the population in 1979 were still in the
top-paid 20 percent in 1988. Two-thirds of the
people in the middle income quintile changed
classification over that ten-year period, while
more than 85 percent of the people in the
lowest income quintile changed income classifications. More than 17 percent of the people
in the lowest income category in 1979 had
climbed into the highest income category by
1988. Except for people in the highest income
category (who, by definition, could not improve), those who changed income quintiles
were more likely to move up than down.
One caveat to interpreting this evidence
is that the study follows individuals who filed

IRS returns in each of the ten years from 1979
through 1988. Accordingly, those who earned
such low amounts that they did not have to file
returns in any of the ten years were omitted
from the sample. These people may well be
permanently poor, making the upward mobility evidence less strong. Further, mobility out
of the lowest income categories may be overstated because the low income groups in
1979 undoubtedly include students and parttime workers who became better compensated as they accumulated education and
experience.

See Joel Slemrod (1992) for evidence on the upward bias
imparted to income inequality when looking at year-to-year
income changes. Slemrod calculates the average income
for each taxpayer over the seven-year period from 1979 to
1985. Slemrod refers to this approach as a time exposure.
Compared with the snapshots of the income inequality over
the same time period, the time-exposure Gini coefficient is
roughly 7 percent lower, suggesting that income inequality
declines somewhat as the time horizon lengthens. The
findings are consistent with changes in income from period
to period that are smoothed over when one uses income
measured over several years, instead of capturing jumps in
income that occur in any given year.

Table B1

Changes in Income Quintiles, 1979 and 1988
Status in 1988

Top-paid
20%

Next
highest paid
20%

Middle
20%

Next
lowest paid
20%

Lowest paid
20%

Top 20%

64.7

20.3

9.4

4.4

1.1

Next highest paid 20%

35.4

37.5

14.8

9.3

3.1

Middle 20%

15.0

32.3

33.0

14.0

5.7

Next lowest paid 20%

11.1

19.5

29.6

29.0

10.9

Lowest paid 20%

17.7

25.3

25.0

20.7

14.2

Status in 1979

Federal Reserve Bank of Dallas

Table 1

Percentage of Income Gains Distributed Among
the Five Population Quintiles
Using the CEA-based method:
Period

1977–89

2.7

6.4

12.1

21.8

57.1

1980–85

3.3

9.8

11.0

23.6

52.4

1985–89

1.0

2.3

11.4

17.3

68.0

Using Krugman’s method:
Period

1977–89

2.8

5.8

11.1

20.8

59.5

1980–85

3.3

10.0

10.5

23.3

53.0

1985–89

1.8

0.0

10.7

14.7

74.5

reports the changes in adjusted gross income
received by each quintile for the periods 1977–89,
1980–85, and 1985–89.5 The top half reports the
distribution of gains in nominal, pre-tax, and transfer income using the CEA-based method (equation 2). The bottom half of the table reports the
distribution of income gains from the same data
using the Krugman method (equation 1).
Somewhat surprisingly, the results using the
Krugman method are quite similar to those using
the CEA-based method. The Krugman method
indicates that a slightly higher percentage of
income gains is going to the top quintile than indicated by the CEA-based method, but this difference does not change the implication that the top
quintile reaped the majority of the income gains.
Table 1 shows that over the period 1977–89, about
60 percent of the gains in factor income (income
before taxes and transfers) went to the top-paid
quintile.
Another question is how income gains are
distributed across different subperiods. For example,
were the 1980–85 or 1985–89 periods substantially
different in terms of how income gains were disEconomic Review — First Quarter 1993

tributed? The evidence presented in Table 1 suggests
that the 1985–89 period saw gains going more to
the highest paid quintiles and less to the lowerpaid quintiles. For example, during the 1980–85
period the two lowest paid quintiles accounted for
slightly more than 13 percent of the income gains,
while during the 1985–89 period the same two
quintiles accounted for less than 4 percent of the
income gains. The share of income growth received by the middle-paid quintile was virtually unchanged from the 1980–85 period to the 1985–89
period, while the share of income growth received
by the second highest paid quintile declined more
than 25 percent. The declines in the first, second,
and fourth quintiles were matched by the increases
of the highest paid quintile. Using the CEA-based
method, the top-paid quintile accounted for about

These statistics also represent the distribution of real income gains, assuming that each quintile has the same
deflator.

52 percent of the income gains in the first half of
the 1980s, rising to about 68 percent of the gains
in the second half.
By reporting the historical averages received
by each quintile, one can see how these recent
time periods compare with the entire sample. Using
the CEA-based method, we calculate the share of
income gains received by each quintile annually
for the period 1952–89. As the evidence in Table 2
illustrates, on average the two lowest paid quintiles
received about 4.5 percent of the real income
gains over the 1952–89 sample. The highest paid
quintile averaged about 58 percent of the income
gains, while the middle-paid and second highest
paid quintiles averaged almost 11 percent and 27
percent of the gains, respectively. The evidence,
therefore, suggests that what happened during the
1977–89 period is not that different from what
happened during the postwar period.
Note that the standard deviations are substantially different across the five quintiles. As Table 2
shows, the standard deviation is 5.2 percentage
points for the lowest paid quintile. There is much
greater variability in the highest paid (44.7), the
second highest paid (25.0), and the second lowest
paid (31.8) quintiles. Thus, the standard deviation
for the lowest paid quintile is only about one-third
the size of the standard deviation for the other
quintiles. This evidence suggests that the lowest
paid quintile receives a fairly steady proportion of
the income gains across time, especially when
compared with the proportions received by the
other four quintiles.
In short, the IRS data suggest that the toppaid quintile did account for most of the gains in
factor income during the period 1977–89. However, a substantially smaller proportion went to the
top-paid quintile than was reported in Krugman’s
study of after-tax (but before transfer) incomes.
The proportion of income gains accruing to the
top-paid group increased during the latter half of

See Anthony Shorrocks (1980), John Bishop, John Formby,
and Paul Thistle (1989), and Daniel J. Slottje (1989) for the
set of properties that an income inequality measure possesses. This version of the Theil index differs from the
population-weighted version used by Keith R. Phillips (1992).

Table 2

Summary Statistics of the
Proportion of Real Income Gains
for each Quintile, 1952–89
(CEA-based method)
Quintile

Mean

Standard Deviation

2.9

5.2

1.5

31.8

10.9

13.8

26.7

25.0

58.0

44.7

the 1980s. However, the tendency toward increasing income inequality began in the 1950s, and the
1977–89 period appears to be well within the
variability observed historically.
The Theil index. At a more aggregate level, one
can measure income inequality with the Theil
entropy index:
n

( 3)

T ( y ,n ) = (1 / n )∑ ( y j / µ ) ln( y j / µ ),
j =1

where n is the number of equal-sized population
groups, y denotes income for population group j,
and µ is average income (that is, µ =

∑y

/ n ).6

j =1

The Theil index is defined so that it takes on values
greater than or equal to zero and increases as income inequality increases. To illustrate this point,
consider the limiting case in which income is evenly
divided among all people in the economy. With
yj /µ = 1 for j = 1, 2, ..., n, then ln(yj /µ) = 0 in
equation 3 and the Theil index equals zero. Another
attractive feature of the Theil index is that a transfer
of income from a high income person to a low
income person will cause the Theil index to fall.
Figure 1 plots estimates of the Theil entropy
measure over the period 1952–89. The plot indicates an upward trend in the Theil index since 1952.
Federal Reserve Bank of Dallas

Figure 1

Theil Index for Adjusted Gross Income, 1952–89
Percent
17
16.5
16
15.5
15
14.5
14
13.5
13
12.5
12
’52

’56

’60

’64

’68

’72

’76

’80

’84

’88

SOURCE OF PRIMARY DATA:
U.S. Internal Revenue Service, Statistics of Income.

Regressing the Theil index against time, one finds
more concrete support for the notion that the
Theil index has been increasing. The regression
coefficient on time suggests that the Theil index
has, on average, increased 0.4 percentage points
each year. Figure 1 also shows a decline in
volatility in the Theil index. Beginning around
1980, the Theil index appears to follow a less
variable path compared with the swings observed
in the pre-1980 sample. Thus, the two apparent
inferences drawn from plotting the Theil index are
that income inequality has been increasing over
the past forty years and that volatility in the
income inequality measure has decreased somewhat during the past ten years.7
Our conclusions about the time path of income inequality differ somewhat from other work
in the field. For example, Barry Bluestone and
Bennett Harrison (1988) find that the percentage
of workers falling into the low-wage stratum
follows a U-turn: the statistic falls in the 1950s and
1960s, reaches its trough in 1970, fluctuates in a
narrow band around the trough value, and then
increases beginning in 1979. The results in Figure
1 suggest that the trend toward greater income
inequality may have started even earlier than Bluestone and Harrison identify. As such, our findings
Economic Review — First Quarter 1993

support those of Peter Henle and Paul Ryscavage
(1980), who find that inequality in wages has
been increasing since the late 1950s. A note of
caution in comparing the results: we are using
adjusted gross income from the IRS, while Bluestone and Harrison and Henle and Ryscavage are
using wage data from the Current Population
Survey. Hence, the results are not directly comparable; our analysis does not overturn Bluestone
and Harrison’s.
There is evidence on income inequality for
broader measures of income. Using the Current
Population Survey, Daniel J. Slottje (1989) calculates the Theil index over the period 1947–84. The
income measure used here is before taxes but
after transfers. According to Slottje, the Theil
index falls to its lowest value in the late 1960s,
rising thereafter for the remainder of the sample
period. The implication is that a U-turn is present
in comprehensive income measure employed in
the Current Population Survey data. Again, the
income concepts used in Slottje are not the same
as ours because they include transfers and the
data sets are different. Our finding, however,
raises a question about when (and if) the U-turn
occurred in a broader income measure, when one
looks at income before taxes and transfers. It also
suggests that the U-turn in the inequality of aftertransfer income may reflect changes in the distribution of transfer policy rather than factor incomes.
What determines the distribution of income?
In this section, we turn from describing what
happened to income inequality to examining why
the distribution of income changed. The factors
affecting income inequality that we consider fall into
three categories: demographics, economic conditions, and fiscal policy. Our demographic data are

The Theil index invariably measures changes in the income
distribution differently from other inequality measures because it weights transfers differently. To check the robustness of our inferences, we also calculated another aggregate measure of income inequality—the Gini coefficient.
The results are not materially different whether one uses the
Gini coefficient or the Theil entropy measure.

the age and educational composition of the potential labor force, and the female share of the labor
force.8 Following Alan S. Blinder and Howard Y.
Esaki (1978), we include some measure of businesscycle conditions and the inflation rate as variables
that might explain variation in income inequality.
Finally, we use the maximum marginal personal
income tax rate and real per capita transfer payments to individuals (defined as the sum of
federal, state, and local transfers) as the policy
variables. The Theil index is our measure of
income inequality.
To determine whether these characteristics
can be used to predict changes in the Theil index
over time, we estimate a VAR system of eight
equations—one for each of our eight variables—
using ordinary least squares regression. Each equation estimates contemporaneous values of the
variable as a function of two lagged values of itself
and two lagged values each of the other seven
variables. All the variables except the growth rates
for prices and gross domestic product are expressed
as first differences (the change in value between
period t and period t –1), and the variables that
are bounded by zero and one (such as the percentage of women in the labor force) are logistically transformed.9

The age composition of the labor force is defined as the ratio
of people between 16 and 25 to those between 16 and 65.
The education composition of the potential labor force is
measured by the percentage of the population over age 25
that has graduated from college.

David Hendry and Jean–Francois Richard (1982) argue
that a logistic transformation should be applied to any
dependent variable defined over the [0,1] interval. Formally, the transformation redefines the variable as follows:
ln (xt /1–x t ).

The issue with multicollinearity is that close correlation
between the explanatory variables will result in inflated
standard errors. The upshot of this is that test statistics are
downwardly biased when multicollinearity is present.

We apply a Choleski decomposition with the following
ordering for the recursive system: AGE, TAX, ED. ATTAINMENT, THEIL, FEM SHARE, GDP, INFL, and finally TRANS.
See Christopher Sims (1980) for a more complete discussion of the Choleski decomposition applied to VARs.

Table 3

Tests of Exclusions
Restrictions in Theil Index Equation
F statistic

p value

.15

.86

ED.
ATTAINMENT

1.61

.23

FEM SHARE

1.02

.38

TAX

1.67

.22

GDP

.87

.44

INFL

.78

.47

TRANS

.61

.55

Variable

AGE

Table 3 reports the results of exclusion restrictions for each variable in the equation in which
the Theil index is the dependent variable. The
tested hypothesis is that the coefficients on lagged
values of the variable also are jointly equal to
zero. The interpretation of the test results, then, is
whether changes in the variable help to predict
changes in the Theil index. The F statistics are
small in each case, which is consistent with the
notion that none of these variables, except past
values of the Theil index itself, helps to predict
changes in the Theil index. However, all of the
variables together explain almost 50 percent of
the variation in the Theil index. Correlations
among some of the variables may be introducing
multi-collinearity.10
Although a variable may have insignificant
explanatory power in the VAR regressions, its compound influence over time may still be considerable. Table 4 reports how much of the two-, five-,
and ten-step-ahead forecast error variances result
from innovations in the variables.11 The evidence
strongly suggests that innovations in the Theil index
account for most of the forecast error variance.
Indeed, 54 percent of the ten-step-ahead forecast
error variance results from innovations in the Theil.
The analysis suggests that the Theil index displays
Federal Reserve Bank of Dallas

Table 4

Proportion of Forecast Errors for the Theil Index*
Innovation to

Step-Ahead

AGE

FEM
SHARE

ED.
ATTAINMENT

Theil

TAX

GDP

INFL

TRANS

Two

5.6

1.1

5.7

72.0

10.3

0.7

1.6

3.0

Five

5.1

3.0

16.3

54.9

8.9

4.3

2.0

5.6

Ten

5.5

3.4

16.3

53.6

8.9

4.3

2.2

5.8

*Proportions may not sum to 100 due to rounding error.

lots of persistence, accounting for movements in
the Theil over time.12
The other factors explain the rest of the tenstep-ahead forecast error variance. Together, the
age composition and educational attainment of
the population, and the female share of the labor
force, account for slightly more than 25 percent.
Fiscal policy variables account for about 15
percent of the forecast error variance, while
inflation and output growth account for 2.2 and
4.3 percent, respectively. The evidence, therefore, suggests that 85 percent of the variation in
income inequality arises from factors outside
direct policy control.
Sheldon Danziger, Robert Haveman, and
Peter Gottschalk (1981) also examine the role that
the U.S. transfer payment system has on income
inequality. They use both welfare payments and
Social Security as their definition of the transfer
payment system. Comparing the distribution of
total factor income with the distribution of total
factor income plus transfer payments (but before
taxes), Danziger, Haveman, and Gottschalk conclude that income inequality (as measured by the
Gini coefficient) is 19 percent lower after transfers
than it is before them. The Danziger, Haveman,
and Gottschalk comparison excludes the complex
general equilibrium effects that transfer payments
have.
Using a narrower definition of transfer payments and assuming that a recursive model repreEconomic Review — First Quarter 1993

sents the structure, we find that transfer payments
have much less explanatory power. In our analysis,
transfer payments explain less than 6 percent of
the ten-step-ahead forecast error. In addition, the
impulse response functions suggest that increases
in transfer payments are associated with increases
in factor income inequality.
Summary and conclusions
In this article, we examine developments in
the income distribution over almost four decades
and the relative contributions of demographic,
policy, and economic conditions toward explaining
these movements. Our analysis indicates that recent
developments in income inequality and the distribution of gains from income growth are not much
different from historical norms. We find that the
top-earning 20 percent of the population reaped a
disproportionate share of the income gains during
the 1980s. However, we find that the top income

Steven N. Durlauf (1991) examines the evolution of income
inequality and finds that persistent income inequality can
develop even with identical starting conditions. Education
and neighborhood effects reinforce one another to stratify
the economy, imparting substantial persistence in income
inequality.

group has been receiving similarly large shares of
the income gains for the past forty years. Further,
using the Theil index to measure income inequality, we find that income inequality increased over
the period 1952–89.
In addition, we look at the relationship
between various factors associated with changes
in the distribution of income. In particular, we
ask which factors explain movements in income
inequality over time. We investigate demographic
factors, economic conditions, and policy variables.
The evidence reported in this article suggests that
there is a great deal of persistence in income inequality. Most of the forecast error variance in the

income inequality measure is explained by innovations in the inequality measure itself. Fiscal policy
actions—measured as the maximum marginal tax
rate and per capita transfers—account for only about
15 percent of the variation in the forecast errors.
Overall, the evidence presented in this article
focuses on developments in income inequality
over time. In doing so, the contribution is largely
in describing how income inequality has evolved,
excluding some factors that are widely believed to
affect income inequality. The aim of future research
is to formulate theories about what determines
income inequality.

Federal Reserve Bank of Dallas

Appendix
Data Definitions
Variable

Source

GDP

Board of Governors of the Federal Reserve System FAME
dataset

CPI

Bureau of Labor Statistics

AGE

U.S. Department of Commerce, Bureau of Census; population
between 15 and 25 divided by the population over 16, less those
over 65 (Citibase data)

FEM SHARE

U.S. Department of Commerce, Bureau of Census; total number
of employed women divided by the total labor force (Citibase
data)

TRANS

National income and product accounts, transfer payments to
individuals paid by federal, state, and local governments (Citibase
data). This variable is deflated with the fixed-weight GDP deflator.

TAX

Internal Revenue Service, Statistics of Income, various issues.

ED. ATTAINMENT

Current Population Survey, series P-60; percent of population
over 25 with four or more years of college.

Economic Review — First Quarter 1993

References
Bishop, John, John Formby, and Paul Thistle (1989),
“Statistical Inference, Income Distributions
and Social Welfare,” in Research on Income
Inequality, vol. 1, Daniel J. Slottje, ed. (Greenwich, Conn.: JAI Press, Inc.): 49–81.
Blinder, Alan S., and Howard Y. Esaki (1978),
“Macroeconomic Activity and Income Distribution in the Postwar United States,” Review
of Economics and Statistics 60 (April): 604–07.
Bluestone, Barry, and Bennett Harrison (1988),
“The Growth of Low-Wage Employment,
1963–86,” American Economic Review 78
(May): 124–28.
Boskin, Michael (1992), “Letters to the Editor,”
Wall Street Journal, July 3, Southwest edition.
Congressional Budget Office (1992), “Measuring
the Distribution of Income Gains,” CBO Staff
Memorandum (Washington, D.C.: Congressional Budget Office, March).
Council of Economic Advisers (1992), Economic
Report of the President (Washington, D.C.:
U.S. Government Printing Office, February).
Danziger, Sheldon, Robert Haveman, and Peter
Gottschalk (1981), “How Income Transfer
Programs Affect Work, Savings, and the
Income Distribution,” Journal of Economic
Literature 29 (September): 975–1028.
Durlauf, Steven N. (1991), “Persistent Income
Inequality I: Human Capital Formation, Neighborhood Effects and the Emergence of Poverty” (Unpublished manuscript).

Henle, Peter, and Paul Ryscavage (1980), “The
Distribution of Earned Income Among Men
and Women, 1958–1977,” Monthly Labor
Review 103 (April): 3–10.
Mankiw, N. Gregory (1992), Macroeconomics
(New York: Worth Publishers).
Nasar, Sylvia (1992), “The Rich Get Richer, but the
Question Is by How Much?” New York Times,
July 20, C1.
Phillips, Keith R. (1992), “Regional Wage Divergence and National Wage Inequality,” Federal
Reserve Bank of Dallas Economic Review,
fourth quarter, 31–44.
Shorrocks, Anthony (1980), “The Class of Additively Decomposable Inequality Measures,”
Econometrica 48 (April): 613–26.
Sims, Christopher (1980), “Macroeconomics and
Reality,” Econometrica 48 ( January): 1–48.
Slemrod, Joel (1992), “Taxation and Inequality: A
Time-Exposure Perspective,” NBER Working
Paper Series, no. 3999 (Cambridge, Mass.:
National Bureau of Economic Research).
Slottje, Daniel J. (1989), The Structure of Earnings
and the Measurement of Income Inequality in
the U.S. (Amsterdam: North Holland).
Stiglitz, J. E. (1969), “Distribution of Income and
Wealth Among Individuals,” Econometrica 37
( July): 382–97.

Hendry, David, and Jean–Francois Richard (1982),
“On the Formulation of Empirical Models in
Dynamic Econometrics,” Journal of Econometrics 20 (October): 3–33.

Federal Reserve Bank of Dallas

John H. Welch

Darryl McLeod

Senior Economist
Federal Reserve Bank of Dallas

Associate Professor
Fordham University

The Costs and Benefits of Fixed Dollar
Exchange Rates in Latin America

he major Latin American countries have embarked on broad-based economic reform
programs to raise economic efficiency, promote
investment, and accelerate output growth.1 To
achieve these goals, these countries are attempting
to foster economic stability, and in some cases,
the tool they are using is an exchange rate fixed
to the U.S. dollar.
When establishing economic stability is an
important goal, the purposes fixed exchange rates
can serve go beyond what is immediately obvious.
Not only do fixed exchange rates stabilize the
domestic prices at which exporters can sell and
importers can import, a fixed exchange rate regime
also has important implications for domestic
monetary and price stability.
Implications for domestic monetary and price
stability involve international differences in inflation
rates. For a country’s exchange rate to remain fixed,
a country’s inflation rate and the inflation rates of
its trading partners must be the same. If the country’s
inflation rate persistently exceeds those of its trading
partners, the country’s citizens will buy foreign
products. After all, prices of domestic products in
a country with a fixed exchange rate will eventually
rise above prices of foreign imports. The same price
phenomenon will hurt the country’s exports. Money
growth is a primary cause of inflation; therefore,
a country that fixes the price of its currency relative to some other country’s currency implicitly
must follow that country’s monetary policy.
As a result, a fixed exchange rate can signal
to investors a government’s intent to follow a
stable monetary policy. If the government prints
money to cover budget deficits or to postpone
unpleasant adjustments to adverse external shocks,
investors will notice quickly. The policy will be
Economic Review — First Quarter 1993

obvious as the country’s inflation outstrips that of its
trading partners, the demand for foreign (domestic)
currencies rises (falls), and the country’s foreign
exchange reserves disappear.
Thus, a persistently fixed exchange rate lends
credibility to a government’s commitment to a stable
monetary policy. Such credibility is important. Even
if a government is firmly committed to a stable
monetary policy, private-sector behavior can nullify
the expected benefits of such a policy if the private
sector does not believe the policy will last.
But there is a problem with using a fixed
exchange rate to signal such credibility. A government’s commitment to fixing the exchange rate may,
itself, be incredible. Almost any government faces
temptations to renege on both exchange rate and
monetary policy targets. If the returns from unexpectedly devaluing are high, a fixed exchange rate
is not very credible. For a government to make a
fixed exchange rate credible, it must demonstrate
or create circumstances that make the cost of
devaluation high.
This article assays the policy and economic
characteristics that could make fixed exchange
rate regimes credible and, therefore, make credible
a government’s commitment to monetary stability.

We would like to thank without implicating Bill Gruben, Joe
Haslag, Evan Koenig, and Carlos Végh for their helpful
comments. Any errors and omissions, as well as any opinions, propositions, or conclusions, are exclusively our own.
1

Examples include Argentina, Bolivia, Chile, Colombia,
Mexico, Venezuela, and to a lesser extent, Brazil.

The factors that result in such credibility—or in a
lack of credibility—are complicated because the
benefits of reneging are not always what one
might expect. The obvious gain that would make
reneging likely—that a devaluation could result in
economic growth—is not the only benefit. Even
when a devaluation clearly will not result in rising
income and growing government revenues, some
countries still devalue, and we outline what governments get when they do. Some governments,
for example, are simply trying to accumulate
foreign exchange so that they can defend their
currencies in the future.
In the next section of this article, we use a
simple game to examine the dilemma Latin American governments face when choosing whether to
fix their exchange rate. We then consider the importance of the effects of devaluation on output growth
and discuss key economic relationships that determine the effects of changes in exchange rates.

This article tries to treat credibility as endogenous, that is,
the credibility of a fixed exchange rate is dependent on the
costs of devaluing to society. We ignore the political process. Credibility will also depend upon how effectively the
political process punishes policymakers and governments
for bad economic outcomes.

These include Kamin (1988), Giovannini (1990 and 1992),
Agénor (1991), Devarajan and Rodrik (1991), and Dornbusch and Fischer (1991).

See Diaz–Alejandro (1963) and Cooper (1971) for early
analyses of contractionary devaluation. More recent studies include Krugman and Taylor (1978), Lizondo and Montiel
(1986), Edwards (1989), Faini and de Melo (1990), and
Cooper (1992).

At best, devaluations tend to be neutral in Edwards’ analysis
(Edwards 1989, chapter 8). Output tends to fall before the
devaluation, usually as a result of a deterioration in the terms
of trade. When devaluation finally occurs, output tends to
improve but not necessarily to a level greater than or equal
to output before the terms of trade shock. Kamin (1988) also
comes to similar conclusions. McLeod and Welch (1992)
find a nonlinear relationship, where small (surprise) real
devaluations increase output growth and large devaluations decrease it in Argentina, Brazil, Colombia, and Venezuela, while any devaluation decreases output in Chile
and Mexico.

The credibility of exchange rate
and anti-inflation policy
Although we know that official promises to
follow a monetary or exchange rate rule are not
credible if reneging is not costly, identifying costliness is not always easy.2 Attempts to address
related issues in the area of domestic monetary
policy appear in the “rules versus discretion”
literature, which considers alternative economic
scenarios and the likelihood of various government reactions to them.
Although the issue of rules versus discretion
was developed without a focus on exchange rates
(Kydland and Prescott 1977 and Barro and Gordon
1983a and 1983b), numerous authors have recently
applied this framework to questions about appropriate exchange rate regimes.3 In many such applications, surprise devaluations are assumed to
increase inflation, a result countries generally do
not want, and to increase output, a result countries almost universally want. Overall, when these
are the likely outcomes of devaluation, a fixed
exchange rate is not very credible unless authorities despise inflation so much that they will avoid
devaluation at any cost.
The story became more complicated, however, when Edwards (1989) and Faini and de Melo
(1990) showed that developing countries often
suffer a fall in output growth from surprise devaluations, a scenario first outlined for Latin America by
Diaz–Alejandro (1963).4 Thus, while the earlier literature tells us something about when fixed exchange
rates may be incredible, Edwards (1989) and Faini
and de Melo (1990) offer information about when
fixed exchange rates may prove credible.
Contractionary devaluations result from a
variety of sources.5 One involves the economic
structure generated in Latin America by its postWorld War II protectionist policies. Protected
domestic industries relied heavily on imported
inputs, especially capital goods. In addition, protection of industry rendered investment in agriculture and other exporting sectors unprofitable.
Therefore, exporting sectors had a tendency to
stagnate. In these circumstances, devaluation can
have perverse effects on output. Devaluation
increases the price of investment goods, which
leads to a collapse of investment. Because Latin
American countries generally did not have capital
Federal Reserve Bank of Dallas

goods-producing sectors, and import substitution
policies left exporting sectors weak and inflexible,
the devaluation would not generate an expansion
of domestic capital goods production nor an offsetting increase in export revenue to buy imported
capital goods. Economic stagnation would result,
if only temporarily.
These peculiar circumstances mean that, unlike
some countries in other parts of the world, Latin
American nations have avoided using exchange rate
policies to improve output growth. If anything,
Latin American governments have resisted devaluation, even in the face of severe overvaluation.
(See the Appendix, “Inflation and Exchange Rates
in Latin America,” for a description of exchange
rate policies in Latin America). Indeed, in addition
to the economic costs of higher inflation and, in
some cases, lower output growth, Latin American
devaluations often entail political costs.6
Despite the negative economic and political
effects, Latin American countries have devalued.
Even in cases when fixed exchange rates have
been an explicit objective of policy, such credible
fixed exchange rates have not been part of Latin
America’s experience over the past thirty years.7
These difficulties not only raise questions
about the process of devaluation and exchange
rate manipulation, but also about the process of
credibility formation. Where devaluations are
known to weaken output growth and increase
inflation, special care must be taken in considering
the nature of policy trade-offs. Why, after all,
would governments want what many of their
citizens would regard as prejudicial?
One explanation that Kydland and Prescott
(1977), Barro and Gordon (1983a and 1983b), and
Dornbusch and Fischer (1991) suggest is that a
government might want to increase inflation tax
revenue through surprise inflation. In the case of
Latin America, this argument is not credible. Dornbusch and Fischer find that the pure public-finance
motive for inflation explains little in the context of
Latin American countries experiencing moderate
inflation, such as Brazil in the 1960s and Chile,
Colombia, and Mexico. Dornbusch, Sturzenegger,
and Wolf (1990) show that the public-finance
motive only marginally explains the acceleration
of inflation in the high-inflation Latin American
countries—Argentina, Bolivia and Brazil in the
1980s, and Peru.
Economic Review — First Quarter 1993

Another argument, however, is credible.
Latin American countries have had to use nominal
exchange rate surprises to generate substantial
balance of payments (trade) surpluses to service
their foreign debts.8 Other factors suggest that the
generation of foreign exchange reserves is an
important consideration when a policymaker
contemplates the consequences of devaluation in
the context of debt-servicing difficulties. Eaton and
Gersovitz (1980) point out that foreign exchange
reserves take on special importance in providing
liquidity services for export and import transactions, especially if the country faces credit limits in
international markets.9 Similarly, van Wijnbergen
(1990) emphasizes the insurance value of foreign
exchange reserves when trade-contingent debt
instruments do not exist in international capital
markets for these countries. For these reasons, we
introduce reserve growth as an objective of policy.
A model of the exchange rate credibility
problem in Latin America
We present a game to simulate the special
exchange rate credibility problems that a Latin
American policymaker might face. We then address
some of the issues the game raises for Latin America.

See Edwards (1989) and Edwards and Montiel (1989).

The most noteworthy cases are those of the Southern Cone
countries of Argentina, Chile, and Uruguay in the late 1970s
and early 1980s. These countries combined trade and
capital account liberalization with exchange rate pegging
to bring down inflation. All the programs had collapsed by
1982, due to severe terms of trade shocks, interest rate
shocks, and the fact that the fixed exchange rate did not
necessarily force the adoption of fiscal, monetary, and
financial policies consistent with fixed exchange rates.

See Faini and de Melo (1990) for a discussion of the central
role of real exchange rate depreciation in the stabilization
policies in the debt crisis of the 1980s.

To support this claim, Eaton and Gersovitz (1980) provide
evidence that debt and foreign reserves were asset substitutes for less-developed countries in the 1970s. As these
countries borrowed internationally, reserve holdings fell.
Once voluntary lending dried up in the early 1980s, the
demand for reserves increased accordingly.

Consistent with our discussion in the previous
section, the model introduces a balance of payments surplus target, the growth in foreign exchange
reserves, in the objective function so that the
trade-off in policy objectives is between inflation
and the growth in foreign reserves (a balance of
payments surplus).10
To present exchange rate credibility problems
as simply as possible, we assume that unanticipated depreciations of the currency improve the
balance of payments or, equivalently, increase
foreign exchange reserve growth. Equation 1
characterizes the forces that may affect growth or
the decline in reserves as11
R˙ = α [e − E (e )] + ω ,

(1)

where R is the level of foreign reserves held by
the central bank, a (⋅) signifies a rate of change
over time, e is the rate of depreciations of the
nominal exchange rate, E is the expectations
operator, and ␻ is an external shock that is equal,
on average, to zero. This shock could represent
unexpected changes in the terms of trade, defined
as the (foreign) price of exports over the (foreign)
price of imports, or changes in foreign interest
rates over some expected value. All variables are
expressed in natural logarithms. ␣ measures the
(temporary) increase in reserve growth due to a
surprise devaluation per unit of (infinitesimal)
time; exchange rate depreciation can only increase reserve growth if it is a surprise. The short-

Sachs (1985) analyzes the U.S. trade deficit in a similar way.
The relationship could also include the capital account. We
exclude the capital account for ease of exposition.

In a more complete model, the country produces nontraded
goods as well as traded goods, and the direct effects of
exchange rate changes are concentrated on the tradedgoods sector.

This timing could be generated by the overlapping contracts framework of Gray (1976) and Fischer (1977), or it
could be due to the government having an informational
advantage, as in Canzoneri (1985). It is unlikely, however,
that the government will observe terms of trade shocks
before the private sector. The inertia in prices due to contracting gives the government room to use surprise devaluation to increase reserve growth, as discussed below.

term nature of the analysis assumes that the quantum of exports and imports does not quickly
adjust to terms of trade or interest rate shocks and,
therefore, any such shock translates completely
into reserve changes. The expected external shock
is equal to zero.
All goods in this simple model are traded.
Inflation is determined purely by expectations of
inflation. We can assume that goods price arbitrage
(purchasing power parity) holds and that individuals
have rational expectations. The private sector,
however, sets its inflation expectations before the
government decides where to set changes in the
exchange rate and, thus, inflation.12 Individuals in
the private sector lose mainly through incorrect
predictions of the exchange rate, although, on
average, individuals correctly predict inflation.
Thus, we assume that individuals in the private
sector maximize the following utility function:

(2)

Up = −

[

]

2
1
π − E (π ) .
2

Accordingly, they try to forecast the inflation
rate as accurately as possible to minimize their
losses from miscalculation. Hence, individuals will
act so that

( 3)

π = E (π ) = E (e ) + E (π * ) = E (e ),

where is domestic inflation and * is the foreign
inflation rate, set equal to zero for simplicity. In
the long run, expected values of all variables will
equal their actual values. But we assume the
government can react to shocks to the system
more quickly than the public because prices
(and wages) are set before the shock is revealed.
Therefore, the government can temporarily cause
departures from purchasing power parity by
unexpectedly changing the nominal exchange
rate.
The government minimizes a quadratic loss
function, which penalizes any inflation rate
(positive or negative) not equal to zero and
deviations from a target growth rate of foreign
reserves, R˙,
(4 )

⎡π 2 β
⎤
max U = − ⎢ + (R˙ − R˙ * )2 ⎥ ,
2
2
⎣
⎦

where –␤ (R˙ – R˙*) measures the marginal utility of
a deviation of an increase in reserves. If reserve
Federal Reserve Bank of Dallas

Table 1
Payoff Matrix for the Government and Private Sectors Under Fixed and Flexible Exchange Rates*
Private sector expects
e > 0 (flexible)

e = 0 (fixed)
e=0
(fixed)
Government
chooses

e>0
(flexible)

−

[

]

0, −

β 2α 2 ˙ * 2
R
2

β ˙ *2
R + σ ω2 , 0
2

−

[

]

1 2 2
β 2α 2 ˙ * 2
[β α + β(1 + α 2 β )2 ]R˙ *2 + βσ ω2 , −
R
2
2
−

⎛ 1 + βα 4 ⎞ 2 ⎤
β⎡
2
*2
⎢(1 + βα )R˙ + ⎜
⎟ σ ω ⎥, 0,
2⎣
⎝ (1 + βα 2 )2 ⎠ ⎦

where e = rate of devaluation, E = expectations operator, ␴2␻ = E (␻2) is the variance of external shocks.
*The first value in the ordered pair represents the government’s payoff and the second the private sector’s payoff.

growth is below its target rate, the marginal utility
is positive, and if reserve growth is above its
target rate, the marginal utility is negative.
The game proceeds in two simple stages.
The private sector sets its devaluation and, thus,
inflation expectations, and enters into contracts
based on these price expectations. The government then sets its rate of devaluation. Table 1
presents the payoff matrix for the government and
private sectors, and Table 2 presents the analytical
solutions to the game under two conditions:
credible precommitment, in which the government irrevocably fixes the exchange rate, and
flexible exchange rates, which are equivalent to
a noncredible fixed exchange rate.13
If the government cannot be forced to
honor a commitment to a fixed exchange rate,
the dominant strategy for the government is a
flexible rate.14 Knowing this, the private sector
will always expect exchange rates to be flexible.
Accordingly, the equilibrium will correspond to
the lower right quadrant of Table 1. On the other
hand, suppose the government precommits to a
fixed exchange rate and, through legislation or
membership in a currency bloc, the commitment
is credible. Then one possible equilibrium of the
game could correspond to the upper left quadrant of Table 1. The other equilibrium is still the
flexible exchange rate equilibrium in the lower
right quadrant of the table.
Economic Review — First Quarter 1993

If “commitment technologies” exist that can
force the government to establish an irrevocably
fixed exchange rate, which regime will the
government pick? This game does not yield an
unambiguous choice.15 Both regimes have different implications for inflation and reserve growth.
We now investigate these different outcomes.

We assume that the targeted growth rate of reserves R˙* and
shocks ␻ are independent. In Table 2, the subscript r
denotes rule, while the subscript d denotes discretion.

To see this, compare the total payoff to the government
when e = 0 and when e > 0. The payoff when e > 0 is
unambiguously larger than when e = 0.

If we subtract the expression for E(U)d from E(U)r in Table
2, we find
⎛ βα 2 [(2 + α 2 (β − 1)] ⎞ 2 ⎤
β⎡
E (U )r − E (U )d = ⎢βα 2R˙ * 2 − ⎜
⎟ σω⎥ .
2 ⎢⎣
(1 + βα 2 )2
⎝
⎠ ⎥⎦
The sign of this expression depends on the government’s
marginal rate of substitution between inflation and international reserves, ß (> 0), and the effects of devaluation on
reserve growth as well as the target level of reserve growth
and the variance of external shocks. The partial derivatives
of are

∂ [E (U )r − E (U )d ]
∂ [E (U )r − E (U )d ]
> 0,
< 0, and
∂σ ω2
∂R˙ *
∂ [E (U )r − E (U )d ] > ∂ [E (U )r − R − E (U )d ] >
< 0,
< 0.
∂β
∂α

Table 2
Equilibrium Inflation, Reserve Growth, and Expected Government Utility
Under Fixed and Flexible Exchange Rates
Credible precommitment
to a fixed exchange rate

Flexible exchange rate
(No credible commitment)

π r = R (er ) = er = 0

βα 2
ed = βαR˙ * −
ω
1 + βα 2
π d = E (e ) = βαR˙ *
1
R˙ d =
ω
1 + βα 2

Ṙr = ω

E (U )r = −

[

β ˙ *2
R + σ ω2
2

]

E (U )d = −

⎛ 1 + βα 4 ⎞ 2 ⎤
β⎡
2
*2
⎢(1 + βα )R˙ + ⎜
⎟ σω⎥ ,
2⎣
⎝ (1 + βα 2 )2 ⎠ ⎦

where ␲ = inflation rate, e = rate of devaluation, ␶ = terms of trade, E = expectations operator, U = government’s utility, ␴␻2 = E (␻2)
is the variance of external shocks.

A government that convinces the public it will keep exchange rates fixed can improve welfare by cheating in the
current period. For an explanation, note that expected
inflation in the current period will be zero. Maximizing
equation 3 with respect to e yields
e=

1 ⎡ ˙*
R − ω ⎤.
⎦⎥
α ⎣⎢

Expected and actual reserve accumulation under cheating
will be
R˙C = R˙ *.

Expected utility will be equal to zero, which is clearly an
improvement over credibly fixed exchange rates and, as we
shall see, flexible exchange rates since both generate
negative expected utility. Such a situation, however, is not
consistent. The public would recognize the government’s
large incentive to cheat, and the equilibrium outcome
reverts to the discretionary flexible exchange rate case
above. Also, once the public realizes that the government
has cheated, cheating can never be used again. Addressing sustainable equilibria over time and the relationship
between credibility and reputation are beyond the scope
of this article. For discussion and analysis, see Barro and
Gordon (1983a and 1983b), Rogoff (1985 and 1987),
Canzoneri (1985), Cukierman (1986), Agénor (1991),
Obstfeld (1991), and Fischer (1990).

Inflation and reserve growth with
a credibly fixed exchange rate
Suppose the government can credibly commit
to the exchange rate rule that sets e r=0. From
Table 2, the equilibrium exchange rate depreciation and inflation, r, will be zero, and expected
reserve growth will be zero, while actual reserve
fluctuations will completely accommodate unexpected terms of trade or foreign interest rate
fluctuations.
Notice that the larger the government’s
desired reserve accumulation, the more government welfare falls. A government that credibly
commits (forever) to a fixed exchange rate will be
continuously frustrated in increasing its stock of
reserves if this divergence persists. A higher
variance of the shock term also decreases welfare.
Such a policy, however, is not time consistent.
The government can improve on this outcome
temporarily by announcing a fixed exchange rate
and then devaluing.16 Rational individuals will
recognize the government’s incentive to renege on
its exchange rate stance and will set expectations
Federal Reserve Bank of Dallas

and prices so that the marginal cost of devaluing
will equal the marginal benefit to the government.
Inflation and reserve growth under
flexible exchange rates
Assuming that optimal reserve growth is positive, a government that can gain foreign exchange
reserves by devaluing will face the well-known
inflationary bias of policies that lack credibility.
The private sector, knowing that the government has an incentive to devalue to raise reserve
growth, expects a devaluation. The private sector
will set prices accordingly, generating positive
inflation regardless of the government’s policy
stance. Even if the government does not devalue
when the private sector expects a devaluation,
the economy will suffer from high inflation. The
positive rate of inflation, combined with the fixed
exchange rate, will cause a surge in imports and
a fall in exports, culminating in a loss in foreign
reserves. Following a no-devaluation policy without credibility is doubly costly to the government:
both inflation and a balance of payments crisis
will result. The government will devalue, one
way or another.
Formally, one can see this result by taking
expectations on the equilibrium solution for
devaluation and inflation under flexible exchange
rates and noting that the ex ante expected shock
is zero. Then from Table 2, expected inflation and
devaluation is

(5 )

E (ed ) = E (π d ) = βαR˙ *.

It should be noted that the adjustment
programs undertaken in Latin America included
devaluation for the explicit purpose of increasing
foreign exchange reserves. The analysis suggests
that this policy will be inherently inflationary. On
the other hand, governments may intend to fix
exchange rates forever but cannot resist the temptation to devalue to increase reserves. Economic
agents, recognizing this, act to protect themselves
from the devaluation by increasing the rate of
price increases.
Because the coefficient on the shock term
in the solution for reserves under flexible exchange
rates in Table 2 is less than the corresponding
coefficient under fixed exchange rates, the flexible
Economic Review — First Quarter 1993

rate regime can smooth fluctuations in foreign
exchange reserves due to unexpected changes in
the terms of trade or foreign interest rates. Again,
as in the credible fixed exchange rate case, the
government cannot affect the expected (average) rate of foreign reserve accumulation in the
long run.
To fix or not to fix? The importance
of output effects of real devaluation
A comparison of the game’s outcomes under
the two regimes suggests that a credible commitment to a fixed exchange rate regime eliminates
the inflationary bias of the flexible rate regime.
Unfortunately, however, this policy increases the
economy’s susceptibility to external shocks. The
choice of regime, therefore, depends on the relative
importance a particular government places on
each of these two objectives and on how sensitive
the balance of payments is to exchange rate surprises. Whether a country fixes its exchange rate
depends on how heavily the policymaker values
reserves relative to inflation (␤), how sensitive
reserve growth is to devaluation (␣), the variance
of external shocks ␴ ␻2 , and the target reserve
growth R˙*.
Before the early 1980s, Latin American
countries grew significantly. The terms of trade
and international interest rates remained fairly
steady. Most Latin American countries maintained
fixed exchange rates throughout this period,
despite the breakdown of the Bretton Woods
system of fixed exchange rates in the early 1970s.
The external trauma of the late 1970s and early
1980s brought increases in world interest rates
and a major decline in the terms of trade to most
of Latin America. The model predicts that an
increase in the variance of foreign shocks will
increase the desirability of a more flexible rate,
and, in fact, many Latin American countries
moved toward a more flexible rate.
In the early 1990s, adjustment to these
shocks is nearly complete for most Latin American
countries, and interest rates and terms of trade are
stable. The theory presented above suggests that
Latin American countries will tend toward fixed
exchange rates in the near future, barring any
major disruption of international trade and capital
flows.
37

Costs and benefits of fixed and flexible
exchange rate regimes
Most Latin American countries had to devalue
their exchange rates dramatically in the 1980s in
the face of the balance of payments problems
brought about by the debt crisis and adverse terms
of trade movements. The adjustment under more
flexible exchange rates imposed high economic
costs. Most Latin American countries suffered
large declines in gross domestic product (GDP)
per capita in the first half of the decade. From
1981 to 1985, the cumulative fall in per capita
GDP was 12.6 percent in Argentina, 14.9 percent
in Chile, 8.7 percent in Mexico, and 14.5 percent
in Venezuela.17 Brazil and Colombia managed to
increase GDP per capita by 4.1 percent and 1.9
percent, respectively, after suffering initial contractions between 1981 and 1984. Inflation, as
discussed in the Appendix, also accelerated in all
six of these countries in the first half of the 1980s.
The costs of balance of payments crises were
high, especially in those countries where output
fell as a consequence of real devaluation.
Latin American terms of trade movements
settled down in the 1980s, and international

interest rates have declined significantly in recent
years. Given these results, we are not surprised to
see countries such as Argentina and Mexico returning to fixed exchange rates after more than a
decade of adjustment to the debt crisis. Enhanced
credibility should greatly improve these countries’
macroeconomic performances, barring any new
balance of payments crisis. The costs of renewed
real devaluation emanating from large government
deficits and excessive money growth in the form
of high inflation and losses of foreign reserves
should temper any moves back to macroeconomic
mismanagement. Terms of trade shocks, however,
can still undo these fixed exchange rates and,
thus, keep the exchange rate regimes from being
completely credible. Consequently, some flexibility in the exchange rates in Latin America may be
desirable.
Ultimately, however, the credibility of
government policy will depend on its prolonged
effort to maintain monetary and fiscal discipline
for low inflation and, more generally, to keep the
reform process on track. Latin American countries
seem, at least for the moment, to be headed in
this direction.

Inter-American Development Bank (1991).

Federal Reserve Bank of Dallas

Appendix
Inflation and Exchange Rates in Latin America
Figure 1

Figure 2

Trends in Argentina

Trends in Brazil

Inflation rate and nominal exchange rate
(Percent)

400

Nominal Exchange Rate Change (RF)
Inflation Rate (CPI)

300

200

100

0
1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990

1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990

Standard deviation of changes in terms of trade
(Percent)

200

100

1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990

For most of the period since World War
II, Latin American countries have generally
maintained fixed exchange rates with the
U.S. dollar. These fixed exchange rate regimes usually collapsed, but Latin American
central banks most often returned to a fixed
exchange rate following devaluation.
Argentina, Brazil, Chile, Colombia,
Mexico, and Venezuela tried to maintain parities fixed to the dollar until the late 1960s.
Colombia, Mexico, and Venezuela were more
successful than Argentina, Brazil, and Chile,
even in the face of high inflation and overvaluation. The ultimate devaluations, however, were followed by a return, if only

temporarily, to pegged exchange rates.
Figures 1 through 6 show trends for
these six countries.1,2 The figures also show

Economic Review — First Quarter 1993

Descriptions of exchange rate policies in each of these countries can be found in Cavallo and Cottani (1991) for Argentina,
Coes (1991) for Brazil, Edwards and Edwards (1987) and de la
Cuadra and Hachette (1991) for Chile, Edwards (1986) and
Garcia Garcia (1991) for Colombia, Ortiz (1991), and McLeod
and Welch (1991) for Mexico.

Inflation (upper charts in Figures 1 through 6) is measured as
the logarithmic percentage change in the consumer price index
(CPI), with data from the International Monetary Fund (IMF).
Nominal exchange rates are taken from the IMF’s RF series.
The lower charts in Figures 1 through 6 show (three-year
moving average) standard deviations of logarithmic changes in
the terms of trade, with data from the World Bank (1991).

(Continued on the next page)

Inflation and Exchange Rates in Latin America—Continued
Figure 3

Figure 4

Trends in Chile

Trends in Colombia

Inflation rate and nominal exchange rate
(Percent)

250

Nominal Exchange Rate Change (RF)
Inflation Rate (CPI)

200
30

150
20

100
10

1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990

Standard deviation of changes in terms of trade
(Percent)

800

600

400

200

200
0

1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990

that inflation rates and changes in exchange
rates tend to be highest when the variability of
the terms of trade is high for most of these
countries.
The figures reflect Brazil’s and Colombia’s moves to crawling pegs in the late 1960s.
Argentina briefly used a crawling peg from
1964 to 1966 and during 1971. Argentina,
however, reverted to imposing fixed exchange
rate regimes throughout the postwar period.
Chile, on the other hand, seems to have
implicitly used a crawling peg arrangement
until fixing in 1971, although officially the
country had fixed rates.
Economic disturbances in the early
1970s, especially OPEC’s 1973 oil embargo,
caused a new set of devaluations in Argen-

tina, Chile, Mexico, and Venezuela, while
Brazil and Colombia had to accelerate their
exchange rates’ devaluation rate. After these
large devaluations, Argentina and Chile
followed crawling pegs until 1978. In 1979,
Argentina and Chile, along with Uruguay, tried
to use their exchange rates to lower inflation
by slowly decreasing the rate of crawl to zero.
Rising international interest rates in the
late 1970s and severe terms of trade shocks
in the early 1980s caused all six countries to
abandon fixed rate regimes and adopt more
flexible exchange rates. They continuously
devalued their currencies. Each of these countries had to increase its exports and decrease
(Continued on the next page)

Federal Reserve Bank of Dallas

Inflation and Exchange Rates in Latin America—Concluded
Figure 5

Figure 6

Trends in Mexico

Trends in Venezuela

Inflation rate and nominal exchange rate
(Percent)

Nominal Exchange Rate Change (RF)
Inflation Rate (CPI)

–10

1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990

Standard deviation of changes in terms of trade
(Percent)

600

8,000

500

6,000

400
300

4,000

200

2,000

100
0

1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990

its imports to service the large foreign debts it
had accumulated in the 1970s. During this
period of flexible exchange rates in the mid1980s, inflation accelerated to unprecedented
levels in all Latin America, with the exception
of Chile.
Flexible exchange rate regimes lasted
until the late 1980s, except for brief periods of
fixed exchange rates in Argentina (1985–87)
and Brazil (1986–87) during their failed socalled “heterodox” inflation stabilization plans,
which used wage and price controls. In 1988,
Mexico initiated a successful anti-inflation program designed to keep exchange rate depreciation slower than the inflation rate. (By late
1991, the Mexican peso’s exchange rate was
virtually fixed.) Argentina followed Mexico in

early 1991 by fixing the Argentine exchange
rate to the U.S. dollar and promising full convertibility of Argentine australs (now pesos)
into dollars.
These most recent fixed exchange rate
policies represent governments’ use of exchange rates to signal the governments’ intentions concerning future inflation and to
increase the credibility of anti-inflation programs. Such exchange rate pegs are never
fully credible because governments have an
incentive to devalue and inflate once the
public formulates inflation expectations. Some
countries, especially Chile and Argentina,
have enacted constraints to eliminate the
governments’ ability to renege on announced
policy rules.

Economic Review — First Quarter 1993

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