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Economic Review
Federal Reserve Bank of Dallas
May 1987

1

Enforcing Sanctions against
Employers of Illegal Aliens
john K. Hill and james E. Pearce

The 1986 immigration reform law will reduce employment
of illegal aliens in some sectors of the economy but not in
others. Small budgets will force authorities to enforce
sanctions selectively. Worksites with numerous jobs that
can be filled by illegals will be attractive targets. But such
worksites account for only 30-50 percent of the jobs
performable by illegals. By far, the majority of the attractive
targets are in manufacturing, which on average employs
eight times as many illegals per establishment as non manufacturing. The effectiveness of sanctions will be further diluted by leakage. About half of the illegals initially displaced
by sanctions will move to employment in sectors where
enforcement is weak. Thus, sanctions will reduce nonagricultural employment of illegals by 15-25 percent. In the first
year, the percentage may be larger. Small employers are
likely to avoid hiring iIlegals until they become familiar with
the law and the enforcement pattern.
17

Estimating the Inflationary
Consequences of Discretionary
Central Bank Behavior
Kenneth j. Robinson

There is fairly widespread agreement that, especially over
the long run, the central bank possesses the ultimate responsibility for maintaining price stability. The model of
Federal Reserve behavior derived in this article assumes
both benefits and costs are associated with inflation. Empirical results from a policy reaction function presented here
indicate that benefits~in the form of seigniorage-and
costs~as represented by deviations of unemployment from
its natural rate-are significant factors in explaining observed inflation rates. Further, Federal Reserve behavior
appears to be influenced by fiscal policy considerations but
not by election-year constraints.

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 Dallas
May 1987
President
Robert H. Boykin
first Vice President
William H _ Wallace
Senior Vice President and Director of Research
Harvey Rosenblum
Assistant Vice President and Senior Economist
Leroy 0 Laney
Eugenie D . Short

Economists
National/International
W . Michael Cox
Gerald P_ O'Driscoll. Jr.
John K Hill
Robert T Clair
Cara S. Lown
Kenneth J. Robinson
Regional/Energy
Stephen P A Brown
William C Gruben
Ronald H . Schmidt
Hilary H Smith
William T Long III
Jeffery W Gunther
Keith R. Phillips

Editorial
Virginia M Rogers
Elizabeth R. Turpin
Graphics and Typesetting
Graphic Arts Department

The Economic Review is published by the Federal
Reserve Bank of Dallas and will be issued six times in
1987 (January. March, May, July, September. and
November) The views expressed are those of the
authors and do not necessarily reflect the positions of
the Federal Reserve Bank of Dallas or th e Federal
Reserve System
Subscriptions are available free of charge Please
send requests for single- and multiple-copy
subscriptions. back issues, and address changes to the
Public Affairs Department, Federa l Reserve Bank of
Dallas, Station K, Dallas, Texas 75222 (214/651-6289)
Articles may be reprinted on the condition that the
source is credited and that the Research Department
is provided with a copy of the publication containing
the reprinted material.

Enforcing Sanctions against
Employers of Illegal Aliens
John K. Hill

James E. Pearce

Senior Economist

Vice President and
Director of Research

Federal Reserve Bank of Dallas

Federal Home Loan Bank of Atlanta

The Immigration Reform and Control Act of 1986 introduced sanctions, or penalties, against employers convicted
of knowingly hiring illegal aliens. 1 The sanctions were included in the legislation in the belief that potential illegal
immigrants would be discouraged from crossing the border
if jobs became more difficult to find. This confidence may
be justified, but a prerequisite is that employers comply with
the law.
Compliance cannot be taken for granted. In Hong Kong,
Canada, and several European countries, many illegal aliens
hold jobs despite the presence of sanctions to deter their
employment. Immigration control staff in these countries
claim that sanctions do help reduce illegal immigration, but
only if resources are devoted to discovering and punishing
violators of the law. 2
The sanctions in the new u.s. law apply to all of the nation's more than four and one-half million business, household, and nonprofit employers. 3 According to news reports,
authorities plan to employ between 1,500 and 3,000 agents
to enforce sanctions. 4 The number of agents seems tiny
compared with the number of employers, but the comparison exaggerates the magnitude of the task.
Economic Review - May 1987

The research reported in this article finds that about
three-fourths of all illegals are employed in industries accounting for only one and one-half million establishments.
Within this group of industries, manufacturing firms employ
over one-half the illegals in less than one-tenth of the establishments. Thus, the enforcement effort can be made
manageable by concentrating on particular types of employers.
A small budget and the uneven distribution of illegals
combine to make selective enforcement almost inevitable.
Obviously, an important part of such a strategy lies in
choosing the targets for enforcement. Worksites with the
potential for employing large numbers of illegals would certainly be attractive candidates. A few agents could monitor
many jobs performable by illegals if they focused most of
their attention on large employers. Indeed, employer size is
likely to be incorporated into the strategy when enforcement of sanctions begins in June.
With most laws, however, selective enforcement is actually less effective than it appears to be. The reduction in
violations where enforcement is strong is at least partially
offset by a rise in violations where surveillance is less thorough. An example is the recent experience with efforts to

eliminate the cultivation of marijuana. Production has declined in West Coast states, where enforcement has been
concentrated, but it has risen in Southeastern states, where
authorities have been less vigilant. 5 In the case of employer
sanctions, some illegal aliens initially displaced are likely to
find new jobs in lightly enforced sectors of the economy.
The research reported in this article examines the effects
of sanctions when targets for enforcement are selected exclusively on the basis of the number of jobs performable by
illegals at each worksite. Under this criterion, manufacturing contains most of the leading candidates for enforcement. Manufacturing establishments tend to be large and
to rely heavily on low-skilled labor. Conspicuously absent
from the list of attractive targets are the restaurant and
construction industries. Although many illegals do work in
these industries, they are thinly dispersed over a large
number of establishments.
The net reduction in employment of illegal aliens will depend on the number of illegals working in the heavily enforced sectors and on "Ieakage"-the percentage of illegals
initially displaced who find new jobs in the United States.
With targets based on potential illegals per establishment,
heavy enforcement would be limited to employers initially
accounting for 30-50 percent of the jobs held by illegal
aliens. With this enforcement coverage, the analysis indicates that leakage would be about 50 percent. Consequently, sanctions would reduce the employment of illegal
aliens by 15-25 percent.

Determinants of the enforcement level
In the introduction, the expectation that enforcement will
be selective is based on a comparison of the likely number
of inspectors and the number of employers. On the other

Figure 1

EXPENDITURES

hand, one might claim that the insufficiency of inspectors is
a temporary condition. Over the longer term, the number
of inspectors might be increased enough to achieve nearly
complete enforcement. But that line of reasoning overlooks
the controversy surrounding immigration reform . With so
many people and interest groups opposing sanctions,
widespread support for a large enforcement budget will be
difficult to obtain, even if increases would result in a much
higher compliance. 6 This suggests that the budget for
enforcement is subject to a ceiling. It also shows that the
relationship between the amount elected officials are willing
to spend and the removal of illegals has the shape of the EE
curve in Figure 1.
If the budget is indeed effectively subject to a ceiling, the
long-run level of enforcement will depend on how many of
the jobs that can be performed by illegals can be monitored
with the resources available. Although that point cannot
be determined precisely, the present study provides a rough
idea about whether and where diminishing returns to additional enforcement become evident. This information
makes possible an educated guess about where costs are
likely to approach the appropriation ceiling.
The relationship between the enforcement budget and
the reduction in illegal employment made possible by that
budget is portrayed by the CC curve in Figure 1. The relationship is a cost function, and it is drawn to exhibit
properties that are basic and common to cost functions.
Eventually a point is reached where increases in output are
achievable only with very large increases in costs. The key
questions become whether enforcement costs have this
property and where the marginal costs begin to rise.
The subsequent sections of this article address these
questions . The evidence indicates that successive reductions in employment of illegals do require increasingly
higher expenditures. As the amount of enforcement is increased, the number of establishments to be monitored
soon begins to rise faster than removals of illegals. The
enforcement appropriation probably will be exhausted before half of the jobs performable by illegals can be monitored for compliance.

Enforcement strategy and the distribution of iIIegals

ILLEGAL ALIENS
REMOVED

2

The activity that consumes the most resources in enforcement is monitoring. In the case of immigration law,
worksites where jobs can be done by illegals must be inspected. The cost of monitoring increases with the
dispersion of these jobs. If all such jobs are concentrated in
large establishments in a limited number of cities, monitoring costs will be low and increase at a constant rate. But if
only so me illegals are con centrated in this way, costs will
Federal Reserve Bank of Dallas

Table 1
MAJOR EMPLOYERS OF ILLEGAL ALIENS
IN THE UNITED STATES

Industry

Percentage of
all illegal
alien
employees

Crop farming ..
6.46
Agricultural services .
0.87
Horticulture
0.93
Construction
. . . . .. "
6.46
Meat products ............ .. .
1.40
Canned fruits and
vegetables
1.79
Grain and bakery products .
2.03
Beverages and miscellaneous
food products
0.83
Textiles ..
1.66
Apparel ..
10.59
Paper and allied products
1.00
Chemical and allied products
1.26
Rubber and plastics ........ .
1.26
leather and footwear ......... . 1.66
lumber and wood products
100
Furniture and fixtures
1 86
Primary metals
1 .39
Fabricated metals
2.53
Electronic computing
equipment ..
0.73
Electrical machinery ..
3.06
Transportation equipment .
2.40
Miscellaneous manufacturing
2.26
Wholesale grocers . . . . .. ..
1 33
Department stores ....... .
0.80
Retail grocers
1.40
Eating and drinking places ..
7.39
Real estate and services
to dwellings ... .
1 20
Auto repair ....... .
1.00
Private households
1.80
Hotels and motels
193
Cleaners
0.93
Hospitals .
1.53
Educational institutions
2.26
Total

7851

Percentage of
total employees
with less than 12
years of schooling

48.90
39.14
38.54
34.74
39.42
51.71
33.14
27.80
50.32
48.22
29.36
2037
32.40
52.15
45 .08
41 .20
3052
34.61
12.08
23.39
25.84
37.22
31 .18
23 .84
34.46
44.26
22.66
41 .11
57.74
36.45
43 .57
1544
10.41
30.03

SOURCE OF PRIMARY DATA: Public·Use Sample from the 1980
Census of Population

Economic Review - May 1987

rise at an increasing rate. Thus, in a general way, the shape
of the cost function facing the authorities can be inferred
by examining the geographic and industrial distribution of
illegals. In addition, data on the sizes of establishments in
industries employing large numbers of illegals will be useful.
Determining the exact industrial distribution of illegals is,
of course, not possible. Data on illegal aliens are not of the
same quality as data on the rest of the U.S. population. The
1980 Census of Population has become a widely used
source, and it will be employed here. Analysts at the Census Bureau have combined the Census data with other
sources to produce estimates of the number and geographic
distribution of illegal aliens. They estimate the number of
illegal aliens to be between 3 million and 5.5 million. 7
Some information on the origins and residences of illegal
aliens is displayed in Charts 1 and 2. These charts are derived from the Census Bureau's calculations. They indicate
that most illegals are Hispanic and that they are heavily
concentrated in a few areas of the United States. About
three-quarters have migrated from Mexico or elsewhere in
latin America. Of the illegals, 60 percent live in California
or Texas, and another 16 percent live in New York City and
Chicago. los Angeles County has almost one-third of the
illegal aliens, so that the nation's three largest metropolitan
areas contain about half of the illegals.
To assess the distribution of illegals across industries, we
did our own analysis of the Public-Use Sample from the 1980
Census. Because the Census data do not identify any individual's legal status, one must approach the analysis of illegal populations indirectly. The Census questionnaire
contained questions on each individual's country of birth
and ability to speak English. Individuals born outside of the
United States who lack a working knowledge of English
constitute a good proxy group for illegal immigrants. Because members of the proxy group and actual illegals have
similar skills and handicaps, the industrial distribution of the
proxy group is probably representative of the distribution
for illegals. 8
The industries that employ most of this proxy group's
members are listed in Table 1. These workers are highly
concentrated. Four industries-agriculture, apparel
manufacturing, construction, and the restaurant
industry-employ 30 percent of them. The extent to which
these industries rely on low-skilled labor is indicated by the
percentages of their workers who have not completed high
school. For many of the industries, the percentage of lowskilled workers is high, but in a few cases, the percentage is
below the average for the rest of the economy (which is
about 20 percent).
3

Chart 1

Origin of Undocumented Aliens
Counted in the 1980 Census
OTHER LATIN
AMERICA
(22 PERCENT)

MEXICO
(55 PERCENT)

ASIA
(10 PERCENT)

SOURCE OF PRIMARY DATA: Jeffrey S Passel and Karen A Woodrow,
"Geographic Distribution of Undocumented
Immigrants Estimates of Undocumented Aliens
Counted in the 1980 Census by State," International
Migration Review 18 (Fall 1984)' 642-71

Chart 2

Illegal Aliens Residing in the United States

CALIFORNIA
(49.8 PERCENT)
FLORIDA
(3.9 PERCENT)

N.J., VA., MD.,
ARIZ., WASH.
(7.3 PERCENT)
ALL OTHERS
(11.9 PERCENT)

SOURCE OF PRIMARY DATA: Jeffrey S Passel and Karen A Woodrow,
"Geographic Distribution of Undocumented
Immigrants: Estimates of Undocumented Aliens
Counted in the 1980 Census by State," International
Migration Review 18 (Fall 1984): 642-71

4

Federal Reserve Bank of Dallas

Table 2
SIZES OF NONAGRICULTURAL EMPLOYERS OF IllEGAL ALIENS

Industry

Manufacturing
Meat products .
Canned fruits
and vegetables
Grain and bakery
products .
Beverages and
miscellaneous food
products
Textiles .......... .
Apparel
Paper and allied
products
Chemical and allied
products
Rubber and plastics
Leather and footwear
Lumber and wood
products
Furniture and
fixtures
Primary metals .......... .
Fabricated metals
Electronic computing
equipment
Electrical machinery .
Transportation
equipment ........... .
Miscellaneous
manufacturing ........ .
Nonmanufacturing ........ .
Construction
Wholesale grocers
Department stores
Retail grocers .
Eating and drinking
places
Real estate and services
to dwelling
Auto repair
........ .
Private households
Hotels and motels .. . .... .
Cleaners
Hospitals
Educational
institutions .

Employees per
establishment

Illegal aliens
per hundred
employees'

Illegal
aliens per
establishment'

Percentage of
illegal aliens in
nonagricultural
industries

61.42
87.69

12 .80
19.43

7.86
17.04

42 .61
1 .54

104.92

35.95

37.72

1 .97

65.16

21 .23

13.84

2.23

53.24
108.21
48.75

6.91
10.20
39.16

3.68
11.04
19.09

0.92
1 .83
11.64

9491

7.25

6 .88

1 .10

73 .32
50.69
73.05

6.38
8.16
36.64

4.67
4.14
26.77

1.39
1.39
1 .83

17.48

7.62

1.33

1.10

43 .59
120.96
41 .05

18.81
7.18
7.63

8.20
8.69
3.13

2.05
1 .53
2.79

194.31
116.36

9.53
7.04

18.52
8.19

0 .81
3.37

169 .00

6 .61

11 .16

2.64

24.11
20.73
9.36
17.49
151.83
15.81

26.02
4.58
6.64
8.69
2.32
3.03

6.27
0 .95
0.62
1 52
3.52
0.48

2.49
30.82
7 .10
1.46
0 .88
1 .54

14.59

6.97

1.02

8.13

1693
4.12
1.52
30.72
8.07
514.21

9.76
12.05
52.19
7.89
11.56
1 .60

1 .65
0 .50
0.79
2.42
0 .93
8.22

1.32
1.10
1 .98
2.12
1 .02
1 68

183.18

1.41

2.58

2.49

1 Computed as the number of illegal alien workers divided by the total number of employees . The estimates
of illegal workers were obtained by multiplYing an estimate of the size of the illegal nonagricultural
labor force by the industry's share of all proxy·group members engaged in nonagricultural employment
2 Column 3 equals column 1 times column 2, divided by 100.
SOURCES OF PRIMARY DATA: 1982 Censuses of US Industries (for data on total employees and number
of business establishments) .
Public·Use Sample from the 1980 Census of Population (for industry
distribution of alien proxy·group members)

Economic Review - May 1987

5

Table 3
GEOGRAPHIC DIFFERENCES IN
ILLEGAL ALIENS PER ESTABLISHMENT
Illegal aliens per establishment'
Industry

Manufacturing
Nonmanufacturing

California

Texas, New York,
Illinois. Florida

Other 45 states

22 .20
2.90

12.45
1 64

305
036

1 The number of illegal aliens employed in a given industry and region is computed by multiplying an estimate of the size of the illegal nonagricultural
labor force by the fraction of all nonagricultural proxy-group workers
employed In that industry and region The industries Included are those listed
in Table 2
SOURCES OF PRIMARY DATA 1982 Censuses of U S Industries
Public-Use Sample from the 1980
Census of Population

The distribution of illegals across establishments of different sizes is shown in Table 2. 9 This distribution is determined
from the industrial distribution of the proxy group and separate data on workers and establishments in the indicated
industries. The entries in the third column have been scaled
by an estimate of the number of illegal workers in the United
10
States. With this scaling, the computations produce approximations to the numbers of iIIegals per establishment.
The wide range in the number of illegals per establishment
is apparent in the third column. Consider the three nonagricultural industries employing the most illegals. Apparel
employs almost 20 illegals per establishment, while construction and restaurants employ about 1. In general, manufacturing industries employ more illegals per establishment
than do services or construction. The difference, which is
very large, is attributable to a combination of larger establishments and more aliens per hundred workers in manufacturing.
The geographic variation in illegals per establishment is
shown in Table 3. California, which has one-half of the illegal population, has a much larger number of illegals per
worksite than do other parts of the country. When combined, the four states ranking immediately below California
have half as many illegals and twice as many worksites. 11legals are even more widely scattered in the remaining
states. Indeed, California's service sector has almost as large
a concentration of aliens as manufacturing does in the 45
lightly penetrated states.
The estimated distribution of illegal aliens implies that
monitoring and inspection efforts should cover hospitals
and most of the manufacturing industries listed in Table 2.
6

large hotels, schools, and department stores also might be
included. If budgets are low, enforcement will have to stop
there. With a somewhat larger budget, enforcement could
be expanded to the larger remaining service-sector employers, particularly in California. Outside of these cases,
the number of additional worksites that would have to be
inspected in order to monitor a given number of additional
jobs becomes very high. Consequently, a very large budget
would be necessary to cover fully the non manufacturing
sector listed in the tables.
One might think that enforcement could be confined to
the five states singled out in Table 3. But if enforcement is
too selective geographically, factories will migrate to states
where enforcement is weak. (This is what happened in the
marijuana case.) Thus, some geographic dispersion is necessary.
Removal of iIIegals with incomplete enforcement

Two issues must be addressed in order to estimate how
many of the illegals displaced by selectively enforced sanctions would actually leave the country. The first issue is the
response of employers in the unenforced sector, in which
employment of illegals is subject to penalties but in which
violations are rarely detected. The question is whether employers can be expected to obey the law even if it is not
enforced. The second issue is the response of the aliens
themselves. The introduction of sanctions will produce a
decline in the demand for their labor, and this decline will
reduce the advantage to i1legals of working in the United
States as opposed to their returning home. The issue is what
Federal Reserve Bank of Dallas

Illegal Alie n Worke rs in the Texas Econo m y
Illegal aliens are more Important to the Texas economy
tnan they are to the national economy. Texas accounts for
6.8 percent of total U.S. employment. But based on information from the 1980 Census, the state employs 10.5 percent of all Illegais working In the United States. That a
relatively high percentage of Texas Walkers are illegalll"l itself makes the Stale a prime target fOI close supervision by
the Immigration authorities. However, illegal wOlkers are
mOle widely dl5persed acros:> Individual business establishments In Texas than they are in other states. This will make
enforcement more e)(J)ensive to carry out Within the state.
Shown in the table ale the 2Q nonagricultural industries
tnat employ the largest numbers of l11egal aliens in Texas.
The industrie5 are ranked according to the average number
of iIIegals that work at an Individual establishment. Following the discussion In the text, mdustries with a large
number of illegals pel establishment are likely to be monitored especially closely. The nature of the ranking for industries in Texas is very similar to that nationwide. Apparel
and food processing are at the top of the list, as they are in
the national figu res. And more generally, manufacturing
industries agam make the best targets for inspection. Of
the 10 industries with at least 5 megals per establishment,
7 are in manufactunng.
One Important difference between Texas and the nation,
however, is that a smaller percentage Or the illegals Il'I Texas
are employed in manufacturing industries. Manufacturing
employs 48.0 percent of the illegal workforce nationwide,
but only 31.4 percent of the illegal workers in Texas. This
is largely a reflection of the more important role that construction plays as an employer of illegal aliens in Texas.
Manufacturing, however, is the industry group with the
highest concentration of illegal workers at the individual
worksite. Outside of manufacturing. illegals are widely
scattered ac ross establishments. This means that the
monitonng of potential employers of illegal aliens will be
relatively expensive in Texas. 1/ enforcement efforts are
correspondingly less effective in Texas, this Will soften the
impact that the new Immigration law will have on the
state's economy.

Economic Review- May 1987

INDUSTRY DISTRIBUTION OF
IllEGAL ALIEN WORKERS IN TEXAS
P~.u·nt~lIe 01
,ll ea~1 ~henS

Indun",
Canned fruits
and vegetables
Apparel
Meat products
Primary metals
Beverages and
miscellaneous food
Hospitals
Electrical machinery
Transport equipment
Educational
institutions
Hotels and motels
Services to dwellings
Wholesale grocers
lumber and wood
products
Fabricated metals
Construction
Private households
Eating and drinking
places
Auto repair
Retail grocers
Oil and gas
extraction

...lS
Pl" t"ldbl .. hml'nl
11I"~~ 1 ~h

In

non~ g ,,~u!tu.al

'nduSI"es
1 .51
8 .73

82.74
40.32
24.10
17.01

147
145

9.74
9.61
8.22
8.04

1 42
1 .31
1 .79
1 .22

.'0
5.16

2.92
2.57
2.41
2.34

4.57
450

1&0

1.17
1 .74
18.88
2.&&

1.59
0,81
0.58

7.87
1 .36
1 .57

0.27

1 41

3.80
2.91
2.17

SOURC ES OF PR IMARV DATA 1982 Censuses 01 U S IfI(!uSl'oel,.
Pubhc·U~ S.mple foam the 1!16O

Cens .... of Pop ... laI,on

,

determines how many will remain working in the United
States.
Compliance without enforcement? The response of employers can, to some degree, be predicted by examining
how employers' costs depend on enforcement. In economic models of illegal activity, individuals weigh the expected gain from taking an illegal action against the
expected cost. The expected cost includes the expected
penalty imposed upon detection and the probability of detection. This model of behavior has a mixed record for explaining illegal activity, but it does provide a useful
framework for exploring the factors to be weighed by potential employers of illegals. 11
The penalty structure established in the new law is likely
to encourage compliance among employers who suspect
they are being monitored. 12 It is somewhat lenient on firsttime offenders, though. The fines vary with the number of
illegals employed and the number of previous offenses. First
offenses carry a fine ranging from $250 to $2,000 per alien
(except during the first year of enforcement, when first-time
violators will receive a warning). Fines for second offenses
are higher, and third offenses carry fines ranging from $3,000
to $10,000 per alien. Employers convicted of pattern or
practice violations are subject to criminal penalties.
This penalty structure will tend to reinforce the effect that
different monitoring intensities will have on the expected
cost of employing illegals. Employers with prior convictions
will be closely monitored and will face large fines for any
future detected violations. Employers who are not closely
monitored are unlikely to have had prior convictions and
will, therefore, be subject to small fines if their violations are
discovered. In such an environment, sanctions provide a
strong deterrent to hiring illegals for some employers and a
weak deterrent for many others.
Because fines are set on a per-alien basis, sanctions are
analogous to a tax on the employment of illegals. This
analogy is particularly useful if the employers know the
enforcement pattern and have no ethical or moral reservations about disobeying the law. Where the probability of
detection is high (near 1), the tax rate is the likely amount
of the fine to be imposed upon detection. Here, the advantage of employing illegals, which is assumed to be a
lower wage, would be be offset by the penalties of being
caught. Sectors with somewhat higher costs of monitoring
compliance would have somewhat lower probabilities of
detection. In these sectors, the tax rate would then be the
expected amount of the fine times the probability of detection. Sanctions would be a less powerful deterrent here.
In sectors in which high monitoring costs make probabilities
of detection very low, the tax rate would be negligible, and
8

sanctions would provide little deterrence to the employment of illegals.
The economic model implies that employers in sectors
where monitoring costs are high will continue to employ illegals. This conclusion rests on two assumptions-that employers know the enforcement pattern and that they not be
overly averse to risk. Behavior with respect to other laws,
such as income tax codes and speed limits, is consistent
with the assumption that people are aware of patterns of
enforcement and that they are willing to take some risks
where the odds appear to be in their favor. But the issue of
risk raises a question about what enforcement strategy the
authorities will adopt.
An emerging line of research indicates that uncertainty
about the probability of detection, even if low, serves as a
deterrent. 13 Consequently, one strategy the authorities
could adopt would be unpredictability. Experience, as well
as the plans of the Immigration and Naturalization Service
as reported in testimony before Congress, suggests that the
INS will not behave unpredictably.14 Law enforcement
agencies, from the Internal Revenue Service to the local
police, display a strong tendency toward predictable emphasis on specific targets. 15
This research on how unpredictable enforcement patterns
affect compliance has an important implication for compliance with the immigration law, however. Because knowledge about the enforcement strategy is likely to be scant
when the new law first goes into effect, compliance is likely
to be high initially. Recent media coverage, revealing that
employers were dismissing illegals soon after the law was
passed, supports this conclusion. 16 Once information about
detection probabilities becomes widely available, however,
compliance is likely to fall into a pattern. The research reported here thus applies better to an equilibrium achieved
after the law has been in effect for a year or two.
labor market adjustment. The effect of selectively enforced sanctions on employment of illegals can be explored
through a standard supply-demand analysis of the market
for illegal labor. How the policy is likely to affect the wages
of illegal workers and the location of their employment is
shown in Figure 2. The domestic economy has two sectors.
Sector A consists of industries subject to inspection by the
authorities and for which sanctions effectively operate as a
tax on illegal labor. Sector B comprises all other industries,
with enforcement in these industries considered negligible.
The supply of illegal workers and the demand for these
workers from industries in Sector B are shown in the left
panel in Figure 2. These relationships are used to derive the
excess supply schedule shown in the right panel. The market for illegal immigrant labor is in equilibrium when the
Federal Reserve Bank of Dallas

Figure 2

Effect of Employer Sanctions on the Market
for Illegal Immigrant Labor
WAGE

WAGE

S· Ds
S

w

w

w'

w'

0A
'

Ds j
IB

I'
B

I'

QUANTITY

excess supply from Sector B equals the demand from industries in Sector A.
Sanctions reduce the demand for illegal labor in Sector
A. This drives down the net immigrant wage from w to w'.
Given the expected penalty, the cost of illegal labor is still
higher for industries in Sector A. As a result, fA - 1/ workers
are displaced, and I - I' of these withdraw from the national
market. The remaining Is' - Is find employment in Sector B.
The single-market model outlined above can be used to
uncover the economic parameters that bear crUCially on the
way the displaced workers are allocated between countries.
A simple equation expresses the number of illegal workers
leaving the national labor market as a fraction of the total
number of workers displaced from the enforced sector:

The value of dl/dlA is seen to depend upon three parameters:
the elasticity of supply of illegal labor (1/), the share of illegal
workers employed in the unenforced sector (As), and the
elasticity of demand for illegal labor (8).
The direction of influence each parameter has on the solution is straightforward: The more responsive the supply
of immigrant labor to a decline in wages, the greater the
share of the displaced workers who withdraw from the U.S.
labor market. On the other hand, if a large fraction of illegal
workers are employed in the unenforced sector and the capacity of that sector to absorb additional workers is high (as
measured by a large elasticity of demand), then more of the
workers who leave the enforced sector will find jobs in the
unenforced sector.
Economic Review - May 1987

I'A

IA

QUANTITY

Quantifying the effects of sanctions

Simulation runs performed with a small model of the U.S
economy are discussed in this section. In having the simulations portray the effects of sanctions under varying levels
of enforcement, three alternative enforcement schemes are
analyzed. Industries are ranked according to the number
of illegal aliens per establishment. Enforcement is assumed
to start with the industry having the highest value and, in
stages, to displace all illegals from industries having eight or
more illegals per establishment (low enforcement coverage),
then from two or more (medium coverage), and finally from
all the industries listed in Table 2 (high coverage). The first
enforcement level covers hospitals and nearly all manufacturing-industries that employ about one-third of the
nonagricultural illegals. The second level extends coverage
to about half of these illegals. The third level covers almost
three-fourths of the illegals.
Assumptions. Several simplifying assumptions were necessary to make the computations feasible. 1 ? The economy
is divided into two sectors-one in which compliance with
sanctions is complete and another with sanctions ignored.18
Production in each sector is a function of four factors: illegal
immigrants, legal low-skilled labor, high-skilled labor (all
presumed to be legaD, and capital. All markets are competitive, and production is governed by constant returns to
scale. Assumptions about the various elasticities of substitution, demand, and supply are taken from the available
empirical literature. For two key parameters, the simulations have been conducted over a range of values.
9

Table 4
EFFECT OF SANCTIONS ON
EMPLOYMENT OF ILLEGAL ALIENS
Enforcem e nt level

Measure

Number of establishments
in enforced sector
(in thousands) ...
Percentage of illegal aliens
initially employed in enforced
sector
Fraction of initially displaced
illegal aliens leaving the
United States
Using favorable elasticities
(11=1.0. €=1.0)
Using intermediate elasticities
(11=1 .0. €=1 .5)
Using unfavorable elasticities
(11= .5. €=1 .5)
Percentage reduction in
employment of
illegal aliens
Using favorable elasticities
(11=1 .0. F1 .0)
Using intermediate elasticities
(11=1.0, €=1.5)
Using unfavorable elasticities
(11= .5, €=1 .5)

One of these parameters is the elastiCity of immigrant
supply (1'/ in the equation). Recall from Figure 2 that downward pressure on the wage of illegals is what motivates illegals to return to their native country. The supply elasticity
reflects the magnitude of this response. The simulation runs
used elasticities of 0.5 and 1.0. With these values, each
1.0-percent reduction in the illegal wage reduces the illegal
workforce by 0.5 and 1.0 percent.
The choice of this range is based on the results reported
in the empirical literature, which indicate that the elasticity
falls between 0.5 and 2.0.19 The values adopted are in the
lower portion of the range for two reasons. First, the simulations here attempt to capture the effect of large changes
in wages, whereas the estimates reported in the literature
are point estimates of responses to small changes. They will
therefore tend to overstate the response to large wage reductions. Secondly, the simulations do not directly incorporate the effect that immigration reform might have on the
labor market in Mexico. Using low values indirectly cap10

Low

Medium

Hi gh

99

275

1.516

33

49

73

61

65

.79

.48

.55

.71

.33

.39

.56

20

32

58

16

27

52

11

19

41

tures the possibility that wages of illegals will decline in their
home country as well as in the United States.
Another parameter of importance is the sensitivity of the
demand for illegals to their wage ( t: in the equation). This
elasticity measures the unenforced sector's ability to absorb
displaced illegals. The simulations assume values of 1.5 and
1.0. The literature suggests that the demand elasticity for
low-wage labor in general is about 1/° a value that should
be considered a lower bound for illegals. Normally, demand
is more elastic for an individual member of a family of goods
than for the entire family. For example, demand for a specific brand of soft drink is more sensitive to a change in its
price (when prices of other brands are held constant) than
is demand for all soft drinks as a group. Thus, estimating the
effect with a higher elasticity of 1.5 is useful.
Results. The simulation results are shown in Table 4. The
figures in the first two rows reflect how coverage varies
across the three enforcement regimes. The top row contains the number of establishments in the industries inFederal Reserve Bank of Dallas

c1uded in the enforced sector. The entries in the second
row are the percentages of illegal aliens that are employed
in the enforced industries before sanctions are applied.
Under the assumptions of the simulation model, these are
also the percentages of illegals initially displaced by the introduction of sanctions. The third through the fifth rows
show the extent to which iIIegals initially displaced actually
leave the country. Leakage-the fraction of those displaced
who become employed in the unenforced sector-can be
computed by subtracting these values from 1. Each row
shows the values under different supply and demand
elasticities. The bottom three rows show the reduction in
the employment of illegals after allowing for leakage.
Results with different elasticities are shown to illustrate the
range of likely effects. The elasticities used for the third and
sixth rows, labeled "favorable," show the maximum likely
effectiveness of sanctions for each level of coverage. The
fifth and eighth rows, computed under "unfavorable"
elasticities, reflect the minimal likely effectiveness.
What the simulations reveal about differences in the
enforcement level can be seen by looking across the rows.
Higher enforcement levels naturally lead to larger reductions in employment of illegals. With intermediate supply and demand elasticities, employment of iIIegals will fall
by 16 percent when enforcement is low and 52 percent
when enforcement is high. The obvious contributor to this
relationship is the larger number of illegals initially displaced
when enforcement coverage expands; initial displacement
in the simulations rises from 33 percent to 73 percent. Also
contributing, however, is an increase in the fraction of those
displaced who actually leave the country. With intermediate elasticities, the fraction rises from about one-half to
about seven-tenths. This pattern reflects the smaller unenforced sector and the greater downward pressure on wages
of illegals when enforcement coverage is higher.
The importance of the supply and demand elasticities can
be seen by comparing the appropriate rows. With medium
coverage, the reduction in employment of illegals will be 32
percent if the elasticities are favorable and 19 percent if they
are unfavorable. This difference is entirely attributable to
greater leakage when demand for immigrant labor is more
elastic and immigrant supply is less elastic. With medium
enforcement and favorable elasticities, only 35 percent (100
x [1 - 0.65]) of the initially displaced illegals find jobs in the
unenforced sector. This leakage is over 60 percent (100 x [1
- 0.39]) when the elasticities are unfavorable.
The simulations allow the effects of sanctions to vary over
a wide range. This range can be narrowed somewhat by
examining the costs of enforcement. Throughout the range
of enforcement considered in Table 4, marginal costs rise
Economic Review - May 1987

with reductions in employment of illegals. Expanding from
low to medium coverage increases the number of illegals
removed by 60-75 percent, but the number of establishments monitored rises by 175 percent. Expanding to high
coverage about doubles the removal of illegals, but it increases the number of establishments to be monitored by
450 percent. Reaching the high level thus requires that
Congress be willing to add a large amount to the enforcement budget for a relatively small gain in compliance. Consequently, enforcement at the high level is unlikely.
If one is willing to accept that enforcement will be somewhere in the low to medium range, then sanctions can be
expected to reduce the employment of illegals by one-tenth
to one-third. The range of possible effects can be further
narrowed by adopting the intermediate assumptions about
supply and demand elasticities. Then the simulations predict that employment of illegals would drop by one-sixth to
one-fourth.

Conclusions
The analysis presented here produces some straightforward
conclusions:
•

That enforcement of sanctions will be selective and
that worksites with numerous jobs that can be filled by
illegals are the most attractive targets;

•

That effective enforcement will be limited to 30-50
percent of the jobs performable by illegals and that the
vast majority of these jobs will be in manufacturing,
particularly in California; and

•

That about 50 percent of the illegals displaced by
enforcement of sanctions will find employment in industries where enforcement is negligible.

Thus, a forecast that sanctions will reduce the employment
of illegals by 15-25 percent is consistent with this analysis.
This prediction applies to the environment expected to develop after sanctions have been enforced for a year or so.
In the initial period of enforcement, sanctions may be more
effective because ignorance about the pattern of enforcement will make employers more cautious about hiring illegals.
Whether an effect of this magnitude is deemed to be satisfactory will depend on the beholder. Up to now, the debate has been confined largely to whether sanctions are
"good" or "bad." Enforcement has tended to be discussed
as an all-or-nothing question. In this light, a 20-percent reduction in the employment of illegals might not seem very
impressive. But such a reduction could represent one
11

million people, a number that is difficult to dismiss as inconsequential.

1. See The House Committee on the Judiciary, The "Immigration Reform
and Control Act of 1986" (P.L. 99-603): A Summary and Explanation, 99th
Con g., 2d sess., December 1986 (Washington, D.C.: Government Printing Office, 1986). For background coverage of the various issues related
to the present topic, see the list of references at the end of this article.
2. See U.S. General Accounting Office, Illegal Aliens: Information on Selected Countries' Employment Prohibition Laws, Briefing Report to the
Chairman of the Subcommittee on Immigration, Refugees, and Internationallaw, House Committee on the Judiciary (Washington, D.C.:
Government Printing Office, October 1985). This document reports the
results of a survey of Hong Kong and nine countries (Austria, Canada,
Denmark, Federal Republic of Germany, France, Italy, Spain, Sweden,
and Switzerland). Although most countries reported that sanctions reduced the number of illegal aliens, none provided any evidence supporting that claim. Thus, the extent to which sanctions are effective has
not been rigorously analyzed .
3.

This figure is based on 1982 data. It probably understates the number
of employers in existence in 1987. See the footnotes to Table 2 for
sources.

4. Enforcement responsibilities are divided between the Department of
labor and the Immigration and Naturalization Service. The number of
enforcement agents has not been determined because funding has yet
to be authorized. Newspapers have reported that the INS will assign
1,632 investigators (see Gilbert Bailon, "Funds to enforce alien law debated: Critics say more needed to avert 'nightmare,'" The Dallas Morning News, 11 February 1987, lA, 14A) and that the agencies combined
will employ 2,700 agents (see Dudley Althaus, "Reform act may hinder
u.s. growth," The Dallas Times Herald, 23 March 1987, A-l, A-ll).
5.

See Kenneth R. Weiss, "Shift From West: Marijuana Growers Taking
Root In Southeast," Sarasota (Fla.) Herald-Tribune, 15 March 1987

6. Opposition arises from a variety of sources. For presentations of views
from several perspectives, see Senate Committee on the Judiciary, Immigration Reform and Control Act of 1985: Hearings, On S. 1200, A Bill to
Amend the Immigration and Nationality Act to Eflectively Control Unauthorized Immigration to the United States and for Other Purposes, 17, 18,
24 June 1985, Before the Subcommittee on Immigration and Refugee
Policy, 99th Cong., 1st sess, S. Hrg. 99-273, Serial J-99-35 (Washington,
D c.: Government Printing Office, 1985) Also, see William F. Shughart,
Robert T. Tollison, and Mwangi S. Kimenyi, "The Political Economy of
Immigration Restrictions," Yale Journal of Regulation 4 (Fall 1986): 79-97,
for an analYSis of how the opposing positions of business and organized
labor have been reconciled to produce small budgets for border
enforcement that have varied over time.
7

12

See Jeffrey S. Passel, "Estimating the Number of Undocumented Aliens,"
Monthly Labor Review 109 (September 1986): 33. In his article "How
Many Illegal Aliens?" (in The Journal of the Institute of Socioeconomic
Studies 10 [Winter 1986J: 13-20), Courtenay Slater provides a good,
nontechnical summary of research on the number of illegals. The article
contains a history of the methods used to obtain the estimates, as well
as many references .

8. Evidence supporting the use of this group as a proxy for illegal immigrants is presented in James E. Pearce and Jeffery W. Gunther, "Immigration from Mexico: Effects on the Texas Economy," Economic
Review, Federal Reserve Bank of Dallas, September 1985, 1-14 . Kevin F.
McCarthy and R. BurCiaga Valdez, in Current and Future Eflects of
Mexican Immigration in California (Santa Monica, Calif.: The Rand Corporation, May 1986), also use this approach to approximate the distribution of illegals.
9. Crop farming is excluded from the list because the reform legislation
contains two special provisions for meeting the fruit and vegetable
growers' seasonal demand for labor with immigrant workers. The first
provides for employment of guest workers allowed in the country temporarily to harvest perishable crops. The second provides for
legalization of illegals who worked in seasonal agriculture in the year
ending May 1986. These workers are required to work in agriculture for
90 days for three years after their legal status has been adjusted . The
law also provides for additional workers to be legalized in a similar
fashion if the supply of initially legalized agricultural workers is exhausted .
10. The value used is 4 million . It was derived by assuming a population of
6 million illegals, from which allowances are made for those not working, those working in agriculture, and those eligible for amnesty. The
resulting estimate is probably too high, but because the error affects all
industries equally, the ranking is preserved.
11 . The seminal articles in this endeavor are Gary S. Becker, "Crime and
Punishment: An Economic Approach," Journal of Political Economy 76
(March/April 1968): 169-217; and Isaac Ehrlich, "Participation in illegitimate Activities: A Theoretical and Empirical Investigation," Journal of
Political Economy 81 (May-June 1973): 521-65, The model has been applied extensively to compliance with tax laws. For surveys and assessments of this literature, see Ann D, Witte and Diane F, Woodbury,
"What We Know About the Factors Affecting Compliance with the Tax
laws," in Income Tax Compliance, A Report of the ABA Section of Taxation, Invitational Conference on Income Tax Compliance (American
Bar Association, 1983), 133-48; and Michael W . Spicer, "Civilization at a
Discount: The Problem of Tax Evasion," National Tax Journal 39 (March
1986): 13-20. For a more general survey, see chap. 9 of Peter Schmidt
and Ann D. Witte, An Economic Analysis of Crime and Justice: Theory,
Methods, and ApplicatiOns (Orlando, Fla: Academic Press, Inc., 1984).
12 See The "Immigration Relorm and Control Act of 1986" (P.L. 99-603) .
13 See lawrence W. Sherman, "Uncertain Risks, Uneasy Criminals," Wall
Street Journal, 11 September 1986, Southwest ed ., 34 Spicer also mentions that uncertainty about the probability of detection can serve as a
deterrent This idea also relates to strategies for monitoring employees .
Guillermo A. Calvo and Stanislaw Wellisz, in "Supervision, loss of Control, and the Optimum Size of the Firm," Journal 01 Political Economy 86
(October 1978): 943-52, discuss the efficiency of discontinuous, but unpredictable, monitoring to discourage employees from shirking.
14 INS Commissioner Nelson testified that plans for enforcing employer
sanctions involve targeting specific employers for intensive monitoring
See Alan C. Nelson, "Statement by Alan C. Nelson, CommiSSioner, Immigration and Naturalization Service," in Hearings, On H.R 1510, Immigration Relorm and Control Act 011983,1,2,9,10,14, and 16 March
1983, Before the Subcommittee on Immigration, Refugees, and Internationallaw, House Committee on the Judiciary, 98th Cong, 1st sess"
Serial 2 (Washington, D,C: Government Printing Office, 1983)

Federal Reserve Bank of Dallas

15. See Sherman's article in the Wall Street Journal.
16. See recent coverage by Maria E. Recio, Julie Flynn, Aaron Bernstein, and
Staff, "Reform Breeds Its Own Crisis: The New Immigration law Causes
Headaches All Over: Business Week, 30 March 1987, 26-27.
17. See John K. Hill and James E. Pearce, "The Incidence of Sanctions against
Employers of Illegal Aliens: Working Paper, Federal Reserve Bank of
Dallas, April 1987, for a complete discussion of the model. In addition
to quantifying the removal of iIIegals, the model produces estimates of
the changes in wages of legal workers and changes in output in both
sectors.

Economic Review - May 1987

18. The model assumes that employment of all nonagricultural illegal aliens
not eligible for amnesty is sanctionable. The law, however, exempts illegals who were hired before 6 November 1986. But this assumption
will not result in misleading data if turnover among iIIegals is high, a
condition likely to be met.
19. See P. Krugman and]. N. Bhagwati, "The Decision to Migrate: A Survey:
in The Brain Drain and Taxation : Theory and Empirical Analysis, edited
by]. N. Bhagwati (Amsterdam: North Holland, 1976).
20. See A. Zucker, "Minimum Wages and the long Run Elasticity of Demand
for low Wage labor: Quarterly Journal of Economics 87 (May 1973):
267-77; and P. Cotterill, "The Elasticity of Demand for low Wage labor:
Southern Economic Journal 41 Oanuary 1975): 520-25.

13

References
Althaus, Dudley. "Reform act may hinder u.s. growth." Dallas
Times Herald, 23 March 1987, A-l, A-ll.
Ashenfelter, Orley, and Robert S. Smith. "Compliance with the
Minimum Wage Law." Journal of Political Economy 87 (April
1979): 333-50.
Bailon, Gilbert. "Funds to enforce alien law debated: Critics say
more needed to avert 'nightmare."' The Dallas Morning
News, 11 February 1987, lA, 14A.
Becker, Gary S. "Crime and Punishment: An Economic Approach." Journal of Political Economy 76 (March/April 1968):
169-217.
Calvo, Guillermo A., and Stanislaw Wellisz. "Supervision, Loss of
Control, and the Optimum Size of the Firm." Journal of Political Economy 86 (October 1978): 943-52.
Clotfelter, Charles T. "Tax Evasion and Tax Rates: An Analysis of
Individual Returns." The Review of Economics and Statistics 65
(August 1983): 363-73.
Cotterill, P. "The Elasticity of Demand for Low Wage Labor."
Southern Economic Journal 41 (January 1975): 520-25.
Ehrlich, Isaac. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation." Journal of Political Economy
81 (May-June 1973): 521-65.
Graetz, Michael J., and Louis L. Wilde. "The Economics of Tax
Compliance: Fact and Fantasy." Paper from National Tax
Association-Tax Institute of American Symposium. Emerging
Issues in Tax Policy. Washington, D.C., 20, 21 May 1985. National Tax Journal 38 (September 1985): 355-63.
Hill, John K., and James E. Pearce. "The Incidence of Sanctions
against Employers of Illegal Aliens." Working Paper. Federal
Reserve Bank of Dallas, April 1987.
Krugman, P., and J. N. Bhagwati. "The Decision to Migrate: A
Survey." In The Brain Drain and Taxation: Theory and Empirical
Analysis, edited by j. N. Bhagwati. Amsterdam:
North
Holland,1976.
McCarthy, Kevin F., and R. Burciaga Valdez. Current and Future
Effects of Mexican Immigration in California. Santa Monica,
Calif.: The Rand Corporation, May 1986.
Nelson, Alan C. "Statement by Alan C. Nelson, Commissioner,
Immigration and Naturalization Service." Hearings. On H.R.
1510, Immigration Reform and Control Act of 1983. Before the
14

Subcommittee on Immigration, Refugees, and International
Law, House Committee on the Judiciary, 1, 2, 9, 10, 14, and
16 March 1983. 98th Cong., 1st sess. Serial 2. Washington,
D.C: Government Printing Office, 1983.
Passel, Jeffrey S. "Estimating the Number of Undocumented
Aliens." Monthly Labor Review 109 (September 1986): 33.
- - - , and Karen A. Woodrow. "Geographic Distribution of
Undocumented Immigrants: Estimates of Undocumented
Aliens Counted in the 1980 Census by State." International
Migration Review 18 (Fall 1984): 642-71.
Pearce, James E., and Jeffery W. Gunther. "Immigration from
Mexico: Effects on the Texas Economy." Economic Review,
Federal Reserve Bank of Dallas, September 1985, 1-14.
Schmidt, Peter, and Ann D. Witte. An Economic Analysis of Crime
and Justice: Theory, Methods, and Applications. Orlando, Fla.:
Academic Press, Inc., 1984.
Recio, Maria E.; Julie Flynn; Aaron Bernstein; and Staff. "Reform
Breeds Its Own Crisis: The New Immigration Law Causes
Headaches All Over." Business Week, 30 March 1987, 26-27.
Sherman, Lawrence W. "Uncertain Risks, Uneasy Criminals." Wall
Street Journal, 11 September 1986, Southwest ed., 34.
Shughart, William F.; Robert T. Tollison; and Mwangi S. Kimenyi.
"The Political Economy of Immigration Restrictions." Yale
Journal of Regulation 4 (Fall 1986): 79-97.
Slater, Courtenay. "How Many Illegal Aliens?" The Journal of the
Institute for Socioeconomic Studies 10 (Winter 1986): 23-32.
Spicer, Michael W . "Civilization at a Discount: The Problem of
Tax Evasion." National Tax Journal 39 (March 1986): 13-20.
Stigler, George j. "The Optimum Enforcement of Laws." Journal
of Political Economy 78 (May/June 1970): 526-36.
Tulacz, Gary, Esq. How to Comply With the Tough New Immigration Law. Personnel Management, Labor Relations, Bull. 1,
sec. 2, January 1987. Paramus, N.J.: Prentice-Hall Information
Services, 1987.
U.S. Congress. House. Committee on the Judiciary. Hearings.
On H.R. 1510, Immigration Reform and Control Act of 1983.
Before the Subcommittee on Immigration, Refugees, and International Law, 2, 9, 10, 14, and 16 March 1983. 98th Cong.,
1st sess. Serial 2. Washington, D.C.: Government Printing
Office, 1983.
Federal Reserve Bank of Dallas

References (Continued)

- - -. The "Immigration Reform and Control Act of 1986" (P.L.
99-603): A Summary and Explanation. 99th Cong., 2d sess.,

Report to the Chairman, Subcommittee on Immigration, Refugees, and International Law, House Committee on the Judiciary, October 1985, GAO/GGD-86-17BR. Washington, D.C.:
Government Printing Office, 1986.

December 1986. Washington, D.C.: Government Printing
Office, 1986.
- - - . Senate. Committee on the Judiciary. Immigration Reform and Control Act of 1985: Hearings. On S. 1200, A Bill to
Amend the Immigration and Nationality Act to Effectively Control Unauthorized Immigration to the United States and for
Other Purposes. Before the Subcommittee on Immigration

and Refugee Policy, 17, 18, 24 June 1985. 99th Cong., 1st sess.
S. Hrg. 99-273. Serial 9-99-35. Washington, D.c.: Government Printing Office, 1985.

u.s. Department

of Commerce, Bureau of the Census.

1980

Census of Population and Housing. Washington, D.C.: Gov-

ernment Printing Office, March 1982.
- - -. Five-Year Censuses of u.s. Industries. Washington, D.C.,
1982. (Censuses used include those for Manufactures, Construction Industries, Service Industries, Wholesale Trade, Retail Trade, and Mineral Industries.)

u.s. General

Accounting Office. Illegal Aliens: Information on
Selected Countries' Employment Prohibition Laws. Briefing

Economic Review - May 1987

-

- - . Illegal Aliens: Umited Research Suggests Illegal Aliens May
Displace Native Workers . Briefing Report to Congressional

Requesters, April 1986, GAO/PEMD-86-9BR.
D.C.: General Accounting Office, 1986.

Washington,

Weiss, Kenneth R. "Shift From West: Marijuana Growers Taking
Root In Southeast." Sarasota (Fla.) Herald-Tribune, 15 March
1987.
Witte, Ann D., and Diane F. Woodbury. "What We Know About
the Factors Affecting Compliance with the Tax Laws." In Income Tax Compliance . A Report of the ABA Section of Taxation, Invitational Conference on Income Tax Compliance,
American Bar Association, Reston, Va., 16-19 March 1983.
American Bar Association, 1983.
Zucker, A. "Minimum Wages and the Long Run Elasticity of Demand for Low Wage Labor." Quarterly Journal of Economics
87 (May 1973): 267-77.

15

Estimating the Inflationary
Consequences of Discretionary
Central Bank Behavior
Kenneth

J.

Robinson

Economist

Federal Reserve Bank of Dallas

Traditional examinations of central bank behavior assume
the Federal Reserve conducts monetary policy in an attempt
to achieve various macroeconomic goals, such as full employment and price stability. It has been hypothesized,
however, that the central bank's objectives include not only
macroeconomic goals and constraints but political goals
and constraints as welL 1 Viewed in this manner, policy
outcomes are the result of a series of trade-offs emanating
from an attempt to balance the perceived benefits and costs
(both economic and political) accruing to the Fed.
Unlike previously estimated models of central bank behavior, the following analysis utilizes this benefits-costs approach. A Federal Reserve reaction function is derived in
an attempt to explain why a central bank might allow or
even pursue an inflationary monetary policy. That is, a certain mode of behavior on the part of the central bank is
hypothesized to exist. The Fed is assumed to conduct policy
based on the goals implied by the model of central bank
behavior developed and the constraints under which the
policymaker is assumed to operate. The model is built on
the assumption that the central bank values implicit revenue from both money creation and the reduction in real
federal debt outstanding. In addition, the policymaker faces
certain constraints, particularly deviations of unemployEconomic Review - May 1987

ment from its "natural" rate and the costs associated with
following an inflationary monetary policy.
The empirical results indicate that seigniorage is a significant factor in explaining observed inflation rates. Moreover, the effect of this source of revenue on inflation varies
with fiscal policy considerations. These findings lead to a
certain amount of skepticism regarding central bank autonomy. Unemployment deviations are also significant factors
behind central bank behavior but are not affected by
election-year considerations. Thus, the evidence regarding
central bank independence appears mixed.

Considerations of the policymaker
In its conduct of monetary policy, the central bank considers certain goals or objectives. The objectives assumed in
this model are achieved through manipulation of inflation
rates over time. That is, revenue from both money creation
and depreciating federal debt outstanding is available
through variations in the inflation rate. The macroeconomic
constraints under which the Fed operates-namely, unemployment deviations and the costs of an inflationary
policy-are also related to the central bank's policy outcome of inflation.
17

Revenue. A central bank that can create money has at its
disposal a relatively easy means of obtaining revenue. For
every dollar the central bank prints, it creates that many
extra dollars for use by government to finance its spending.
Given that the inflation rate is positively related to growth
in the money supply, inflation amounts to a tax (implicit) on
holdings of money. Revenue, in real terms, from the inflation tax is composed of two parts: the base of the tax,
which is the level of real cash balances held by the public,
and the rate of the tax, which is the rate of depreciation in
the real value of money. If growth in the money supply is
constant, the rate of inflation that yields maximum revenue
occurs when the elasticity of demand for real cash balances
equals - 1. When allowing for economic growth, there are
two sources of revenue available to government: the proceeds of the tax on existing cash balances and further revenue from providing additional cash balances demanded
by the public as income rises.
Inflation, especially when unanticipated, favors some
groups over others as it reduces the repayment burden of
debtors and may encourage various types of investments.
Since government is a large debtor, it stands to gain from
the redistribution that favors debtors at the expense of
creditors. The process by which this redistribution is accomplished stems from the fact that government commits
itself to repay a fixed number of dollars when redeeming its
securities and paying interest on them. "Unanticipated inflation reduces the amount of real resources embodied in
this commitment. Hence, inflation captures, from those
who purchased bonds, resources which otherwise either
would not be available for Governmental use or distribution
or would have to be financed with other taxes.,,2
Macroeconomic goals. The assumption that the Fed
conducts monetary policy only with the consideration of
extracting revenue imputes a rather narrow, bureaucratic
mode of behavior to the central bank. Ample evidence exists, however, that the Federal Reserve, in its conduct of
policy, is guided by macroeconomic goal variables. Federal
Reserve reaction functions are estimated in an attempt to
capture the effect on monetary policy of departures of certain macroeconomic targets from their "desired" levels. Reaction functions differ in what is assumed to be the policy
variable (or dependent variable). These functions also differ
in the definition of the actual targets and of the levels
deemed optimal by the central bank. 3
Regardless of the policy instrument considered, though,
evidence is presented indicating a strong, consistent response by the monetary authorities to departures of unemployment from the target rate. Departures of other goal
variables from their targets-such as inflation, balance of
18

payments surplus, and real gross national product (GNP)exhibited a less systematic response by the Fed in the models estimated. Therefore, unemployment deviations are assumed to be the macroeconomic goal representing the
Federal Reserve's concern about economic performance.
Consequences of inflation. Evidence from more traditional views of central bank policymaking also indicates a
concern on the part of the Fed about the ramifications of
sustained inflation. An inflationary monetary policy imposes costs upon the economy that the Fed considers in its
conduct of policy. For instance, unanticipated inflation
hinders effective economic planning. Inflation, even when
antiCipated, also inflicts welfare costs on the economy resulting from reductions in the amount of real money balances demanded. This decline in the use of money leads to
costs in the form of loss of convenience, increasingly awkward barter arrangements, and so on.
Fischer and Modigliani provide a descriptive analysis of
the costs of anticipated and unanticipated inflation. 4 In addition, Fischer derives estimates of the effects of inflation on
returns to capital and savings that amount to as much as 2
to 3 percent of GNP. Fischer concludes, "While the evidence and numbers cited ... are far from definitive, they
support the notion that the welfare costs of high inflation,
even if the inflation is expected, are large in the current
United States economy."s
Given the assumed objectives, it is possible to formulate
a model of Federal Reserve policymaking. Such a formulation facilitates empirical testing of whether these considerations provide any inSights into explaining observed
inflation rates.

A model of central bank behavior
In developing the model, it is hypothesized that the Fed
considers both the benefits it derives and the costs incurred
when conducting monetary policy. The central bank controls its instruments to achieve its policy target (ostensibly,
money growth) in an attempt to attain the goal of maximizing its objective function. The objective function contains
as arguments: seigniorage, redistribution effects (here, those
associated with redUCing the value of government debt),
deviations of unemployment from a preferred rate or goal,
and regard for the costs associated with inflation .
The Fed values, or derives certain benefits from,
seigniorage, as it reduces the need for government to resort
to more conventional, overt methods of taxation in the financing of public expenditures. Further, the Fed values
certain redistribution effects associated with inflation, particularly with regard to debtors versus creditors. As the
Federal Government is a large issuer of debt, the reasoning
Federal Reserve Bank of Dallas

is analogous to that of the first assumption. Underlying
these two assumptions is an element of doubt regarding the
complete independence of the central bank. That is, the
Fed may be motivated at times to use inflation to extract
revenue if it perceives such action to be of value to either
the executive or the legislative branch of government. 6
It is also argued that Federal Reserve policymakers consider the costs associated with their actions. With this in
mind, it is hypothesized that the Fed is constrained by a
performance trade-off, especially in the case of unemployment. In addition, costs associated with an inflationary
monetary policy represent a further constraint on Federal
Reserve behavior. Thus, the central bank is allowed to possess different interests (or some independence) from elected
officials, particularly with regard to the consequences of its
policymaking.
Given these assumptions, a formal model of central bank
behavior is developed fully in Appendix A to determine the
extent to which observed inflation rates are the result of an
attempt to balance the hypothesized benefits and costs that
monetary policymakers face. The significance of these factors in explaining inflation provides insights into the degree
of autonomy enjoyed by the central bank. That is, a truly
autonomous central bank, attempting to achieve traditional
macroeconomic goals, such as full employment and price
stability, would resist any pressures placed on it to provide
government with revenue. The reaction function is then
modified to allow for detection of possible outside influences affecting monetary policy-namely, fiscal policy effects and election-year considerations. Such a specification
provides further evidence regarding the degree of central
bank independence.
Benefits. Seigniorage is defined formally as the extra dollars created by the central bank in any time period. In real
terms, then, seigniorage is the change in the money supply
divided by the current price level. The public's demand for
real money balances plays an important role in the amount
of revenue that can be collected. The more inflation people
expect, the less money they are willing to hold. In effect, the
public's holdings of money are inversely related to expected
inflation. If the Fed prints too much money, people come
to expect more inflation. Consequently, revenue could actually decline if the public rapidly reduces its demand for
real money balances.
Under a fractional-reserve banking system, the central
bank receives as seigniorage only a portion of the actual
money supply. The Fed supplies the monetary base, and the
actual money supply is some multiple of the base. Therefore, the amount of seigniorage the central bank collects is
related to the money supply multiplier. If the multiplier exEconomic Review - May 1987

ceeds unity, the Fed shares a portion of the revenue with
the banking system. If the multiplier is reduced, the portion
of inflationary finance accruing to the central bank is increased. 7
The national accounts in the federal budget treat the
Federal Reserve System as though it were a private corporation. Therefore, the transfer of revenue from the Fed to
the U.S. Treasury is classified as a tax on corporate profits. s
The percentage of total federal taxes on corporate profits
that these Federal Reserve payments account for is shown
in Chart 1. Over the 1951-85 period, these transfers have
made up an increasing proportion of the collected tax on
corporate profits. As Chart 2 demonstrates, however, Federal Reserve payments to the Treasury have remained a relatively small part of total Federal Government receipts.
Redistribution effects associated with reducing the value
of nominal federal debt outstanding also generate revenue
for government. This revenue is obtained by depreciating
the repayment burden borne by government and is accomplished by increases in the current price level. 9 In a
manner analogous to that associated with seigniorage, this
redistribution depends on the public's holdings of federal
debt. It is reasonable to assume that the demand for government debt depends on its expected real return, defined
as the nominal return less the expected inflation rate.
Therefore, if people expect more inflation, either the nominal return on government debt must increase or the demand for this debt will decrease. In either occurrence,
revenue collected depends ultimately on the amount of
debt the public is willing to hold.
According to Bach and Stephenson, households have
consistently been substantial net creditors, while government has been the main offsetting debtor. "Thus, since
World War II inflation has apparently caused a massive
transfer of wealth from households, as the major net creditors, to the federal government, as the major net debtor."'o
The Fed may be motivated to provide seigniorage and to
depreciate federal debt because of the gains accruing to
government. If the Fed is a quasi-independent agency, it
may derive certain benefits from following such a policy.
The benefits are assumed to rise one for one with these two
sources of government revenue.
Costs. The Federal Reserve is hypothesized to be concerned about the consequences of its actions. This concern
stems from inflation's effect on unemployment and, also,
any other costs inflation imposes on the economy.
Unanticipated changes in the inflation rate are assumed
to result in movements in the unemployment rate in the
opposite direction." The Fed is assumed to view deviations,
in either direction, of unemployment from the natural rate
19

Chart 1

Federal Reserve Payments to Treasury as a Share
of Corporate Profits Tax Accruals
PERCENT

35r-----------------------------------------,
30
25
20

15
10

5

'51

'54

'57

'60

'63

'66

'69

'72

'75

'78

'81

'84

SOURCES OF PRIMARY DATA: Board of Governors of the Federal Reserve System,
72nd Annual Report, 1985
Economic Report of the PresIdent, January 1987

Chart 2

Federal Reserve Payments to Treasury as a Share
of Total Federal Government Receipts
PERCENT
2.5~------------------------------------------_.

2.0

1.5
1.0

.5

o~~~~~~~~~~~~~~~~~~~~~~~

'51

'54

'57

'60

'63

'66

'69

'72

'75

'78

'81

'84

SOURCES OF PRIMARY DATA: Board of Governors of the Federal Reserve System,
72nd Annual Report, 1985_
Economic Report of the President, January 1987

20

Federal Reserve Bank of Dallas

as generating costs. Unemployment rates below the natural
rate are possible only by continuous, unanticipated increases in inflation. This occurrence is considered costly to
the extent that it results in expectations of accelerating inflation. Monetary policymakers desire to avoid such adverse effects on expectations because it then becomes more
difficult both to extract revenue and to exploit an inflationunemployment trade-off in the future. Increases in unemployment above the natural rate are also assumed to
generate costs in the form of obvious factors, such as forgone output and human suffering. In effect, a simple quadratic loss function is used, which implies that these costs
increase at an increasing rate with departures of unemployment from its preferred level.
Departures of inflation from zero are also assumed to
generate costs of the type implied in the section on consequences of inflation. Further, these costs are assumed to
increase at an increasing rate with departures of inflation
from zero.
Federal Reserve objective function

If the Federal Reserve attempts to maximize net benefits associated with monetary policy, then, from the results in
Appendix A, this leads to the following objective function:

(1)

Nt = P1tRmt

+ P2tRgt -

n
(P3tf2)(Ut - Ut )2

- (P4tf2)(TI t)2 .
The Fed chooses its policy target, the money growth rate,
to achieve its ultimate goal of maximizing the expected
value of equation 1. Since the Federal Reserve System has
never bound itself to any monetary rule, it is assumed that
the Fed is a discretionary policymaker. Discretion implies
no possibilities for prior constraints or commitments that
would restrict subsequent choices of money growth rates.
Further, a discretionary policymaker takes expectations as
given. 12 This is due to the fact that, under discretion, the
central bank's choice of money growth this period in no
way constrains its choice of money growth next period.
That is, current money growth supplies no additional
information about the objectives or technology of the
policymaker.
It is reasonable to assume that expectations of future inflation are a function of expectations of future money
growth rates. Thus, expectations of inflation are assumed
given to the Fed only if the choice of current money growth
has no implications for expectations of future money
growth rates (and therefore no implications for expectations
of future inflation), which is the essence of discretionary
policymaking. In particular, this concentration on the presEconomic Review - May 1987

ent does not derive from myopia on the part of the
policymaker. With given expectations, the policymaker has
no way at date t to influence future values of the objective
function.
Therefore, a discretionary policymaker chooses the
money growth rate to maximize the current expected value
of equation 1, given expectations. After substituting for the
expressions found in Appendix A for Rmt, Rgt, and Uu to solve
for the inflation rate, the assumption is made that
E(Ut - Uf) equals (Ut - Uf). This implies that the Fed's forecast of the gap between unemployment and its natural rate
equals the actual gap. Such an assumption suggests perfect
foresight on the part of the policymaker,13 leading to the
following reaction function:

(2)

TIt = (P1tfP4t)[(1/m t)(Mt- 1/Pt)]

+ (P2tfP4t)(G t- 1 /Pt)
+ Z[(P3t/P4t)(Ut - ut)] .
Interpreting equation 2 as a reaction function employs the
pivotal assumption that the Fed is capable of controlling the
inflation rate. The signs attached to the coefficients of the
reaction function reflect the assumed preferences of the
policymaker exhibited in equation 1 and, also, the assumption that in the central bank's view, increases in the inflation
rate raise revenue and reduce deviations of unemployment
above its target. If unemployment is below its desired level,
decreases in the inflation rate occur.
Equation 2 represents the (equilibrium) rate of inflation
that results when the policy maker maximizes the expected
value of his objective function, taking as given the formation of expectations. Further, equation 2 represents a rational expectations equilibrium in the sense that the
inflation rate is sufficiently high, such that the marginal
benefits of a hypothetical unit of surprise inflation just balance the marginal costs involved. In effect, systematic surprises do not occur in equilibrium. The presence of the
unemployment variable may seem surprising, given that
equation 2 implies that no systematic surprises in the inflation rate may occur in equilibrium. Barro and Gordon
provide an explanation:
Some people have argued that policymakers do not face
a "cruel choice" between inflation and unemployment in
a natural rate environment. This argument is misleading
in a context where monetary institutions do not allow for
policy choice to be committed .... [Plolicymakers do
optimize in each period subject to the appropriate givens,
which include the formation of expectations. Given these
expectations, the choice of TIt does influence the unemployment rate "right now"-that is, for date t. The social
21

trade-off between unemployment and inflation ... is
central to the policymaker's decision. 14

Empirical results
To assess the importance of the variables of the reaction
function as determinants of observed inflation rates, it is
necessary to estimate equation 2. In an effort to determine
whether the hypothesized benefits and costs are significant
determinants of Federal Reserve behavior, the following
modification of the reaction function is undertaken to facilitate empirical estimation and testing:

(3)

ANNUAL

= 0: 0 + 0:1*SEIGN + 0:2*RLDEBT

+ 0:3*(UNEMP -

NA TUN)

+ et,

where
ANNUAL = annual rate of inflation per quarter
SEIGN = (1/m t)*(Mt- 1/Pt)
RLDEBT = (GH/Pt)
UNEMP =z*Ut
NATUN = z*Ur
0: 0 = intercept
0: 1 = /31tl/34t
0: 2 = /32tl/34t
0: 3 = /33J /34t
et = random disturbance.
Since inflation influences as well as is influenced by SEIGN,
RLDEBT, and deviations of the unemployment rate that are
deemed acceptable by the Fed, the technique of instrumental variables- or two-stage least squares-is employed
to resolve the Simultaneity present in equation 3. For SEIGN
and RLDEBT the reverse causation flows through the current
price level, Pt. A change in Pt alters ANNUAL and will, by
definition, alter SEIGN and RLDEBT. The Simultaneity associated with unemployment operates through a usual Phillips
curve mechanism. Increases in the inflation rate may decrease unemployment, and vice versa.
The instruments generated attempt to capture the variables that explain SEIGN, RLDEBT, and (UNEMP - NATUN)
and are also exogenous with respect to the current inflation
rate. Since SEIGN is a function of the amount of the medium of exchange demanded, lags of personal income appear to represent a scale variable common in money
demand functions. Lags of interest rates are included to
capture the opportunity cost of money holdings. Finally,
lags of the regressor itself are used. Similar considerations
were employed in the construction of the other instrumental variables. 15 Using these instruments, consistent estimates of the parameters of equation 3 are then derived.
22

Table 1
INITIAL RESULTS OF FEDERAL RESERVE
REACTION FUNCTION CORRECTED
FOR SERIAL CORRHA TlON
CoeffiCient

Standard
error

-16.7900*

4.6890

SEIGN

30.8576*

4.7602

RLDEBT
(UNEMP - NA TUN)

-1.4351 **
.1203*

Variable

Intercept

.7085
0452

* Signiiicant at the l·percent level
.. Significant at the 5·percent level
NOn- R' = 7202

Estimates of the extent of the response of unemployment
to inflation surprises, z, are obtained from results found in
Barro and Rush. 16 Their study examines the effect of unanticipated money growth on the unemployment rate based
on both annual and quarterly data. It is estimated that a
1-percentage-point increase in unanticipated money
growth reduces the unemployment rate by a proportion of
3.5 to 5.8 percent. Assuming that unanticipated money
growth results in unanticipated inflation, these estimates
may be employed for the z parameter in equation 3. Finally,
values for the money supply multiplier are derived by dividing real money balances by the monetary base.
Results are reported in Table 1 for z equals 4.5, approximately the midpoint of the Barro-Rush range, using quarterly data for the 1951-83 period. The estimates are
obtained after correcting for the presence of serial correlation indicated by the Breusch-Godfrey test. 17 In order to
purge the data of autocorrelation, the Cochrane-Orcutt
process is used to estimate the first-order autocorrelation
coefficient, along with the Prais-Winsten modification to
account for the first observation. The estimated value of
rho, the autocorrelation coefficient, is 0.383. Using this
value, the data are transformed to obtain weighted least
squares estimates.
The results indicate that seigniorage collected by the Fed
and deviations of unemployment from the Fed's target possess the hypothesized sign and are significant at the
1-percent level. RLDEBT, however, possesses the wrong sign
and is significant at the 5-percent level. The reaction function estimated assumes that Fed behavior is stable. It is
possible, though, that Federal Reserve policy shifts from one
goal to another, erratically or otherwise. If so, then emFederal Reserve Bank of Dallas

ploying a random coefficients specification results in mote
efficient parameter estimates. When the parameters are
allowed to enter as random variables, the coefficient on
RLOEBT is still negative but not significant at the 5-percent
level. The other coefficients retain their hypothesized, significant signs.

Table 2
ESTIMATES OF FEDERAL RESERVE
REACTION FUNCTION FOR FISCAL POLICY
AND ELECTION-YEAR EFFECTS
Variable

Federal Reserve independence

The degree to which policy actions undertaken by the Federal Reserve System are independent of any political considerations has long been a source of debate. 18 Results from
Table 1 provide some evidence regarding the independent
status of the Federal Reserve. A truly autonomous central
bank would not respond to pressures that may exist to extract revenue from money holdings. An additional test for
central bank independence is available from certain implications that follow from the reaction function. If the Fed
perceives an increased need for revenue, then the rate of
inflation should rise. This need might be acute in periods
when alternative sources of revenue give rise to greater
welfare losses at the margin or when government expenditures increase sharply.
An attempt to capture these influences on Federal Reserve
behavior is made by modifying the estimation equation (3)
to include two additional variables:

Intercept .
SEIGN
RLDEBT . .... .

Coefficient

-16.9046*

3.6935

15.9615*

5.8409

-.5756

.4409

(UNEMP - NA TUN)
(TAX/PI)*SEIGN
(DEF/GNP)* RLDEBT
DUM*(UNEMP - NA TUN)

Standard
error

.2065*

.0447

94.9179*

18 .1066

-20.2121 *

4.5719

-.0670

.0687

• Significant at the 1-percent level
NOTE R' = .6690

tual inflation. Therefore, the response by the central bank
to the last term in the estimation equation is assumed to
depend on a dummy variable whose value is 1 if in a presidential election year and 0 otherwise.

(6)

(4)
and

(5)
First, the desire to collect seigniorage is assumed to depend
on (TAX/PJ), personal tax and nontax payments expressed
as a percentage of personal income. This variable attempts
to capture the extent of the increasing burden of conventional taxation. Increases in this variable are hypothesized
to result in an increase in seigniorage. In addition,
(OEF/GNP) is the federal budget deficit as a percentage of
GNP, accounting for periods when government spending
increases sharply. In such circumstances, the central bank
may be more motivated to depreciate outstanding federal
debt. 19 This modification gives insight into fiscal policy
pressures that might confront monetary policymakers. The
degree to which the Fed responds to these pressures provides a rough test of the extent of central bank independence. 2o
Further, if unemployment exceeds the natural rate, the
extent of the response of inflation depends on (1(3' the costs
of unemployment deviations relative to how costly the Fed
perceives inflation. The rate of inflation should increase if
the costs of the unemployment gap exceed the cost of acEconomic Review - May 1987

This variable attempts to capture the possibility that the Fed
may view increases in unemployment as more costly in a
presidential election year. If so, additional evidence is provided regarding the degree of central bank independence. 21
Substituting these specifications into the version of the
reaction function used for estimation purposes gives the
following:
(7)

ANNUAL

= (1(0 + a10*SEIGN + a20*RLDEBT

+ a30*(UNEMP -

NA TUN)

+ a11( TAX/PI)*SElGN
+ a22*(DEF/GNP)*RLDEBT

+ a33*OUM*(UNEMP -

NA TUN)

+ 8t .

Estimates of equation 7 are found in Table 2.
The results indicate that the effect of SEIGN on observed
inflation rates depends strongly on the variable (TAX/PI).
That is, the higher are personal tax payments as a percentage of income, the more the Fed attempts to extract implicit
revenue through seigniorage. The data indicate that the
Federal Reserve is not influenced by political considerations
in its reaction to unemployment deviations. Finally, the ef23

fect on observed rates of inflation from reducing the value
of nominal federal debt is insignificant, while the interaction
term associated with this variable indicates a negative effect
on inflation. It appears as though the Fed tends to "tighten"
in light of expansionary fiscal policy, possibly to prevent
unemployment from falling below its natural rate.

(April 1980): 199-211; George Macesich, The Politics of Monetarism: Its
Historical and Institutional Development (Totowa, N.J.: Rowan &
Allanheld, 1984); and John T. Woolley, Monetary Politics: The Federal
Reserve and the Politics 01 Monetary Policy (Cambridge: Cambridge

University Press, 1984).

2- Charlotte E. Ruebling, "Financing Government Through Monetary
Expansion and Inflation," Federal Reserve Bank of St. Louis Review, February 1975, 21

Conclusions
Recently, models of Federal Reserve policymaking have
been formulated to attempt to analyze hypothesized tradeoffs the central bank faces. The model of central bank
behavior developed in the analysis here utilizes this framework. It is argued that Fed policy is guided by trade-offs that
manifest themselves in revenue and unemployment. Under
this assumption, a reaction function is derived to explore
the degree to which seigniorage, revenue from reducing the
value of nominal federal debt outstanding, and deviations
of unemployment from the natural rate prove to be significant variables in explaining observed inflation rates.
Seigniorage is found to be an important determinant of inflation, leading one to question, to some extent, the degree
of independence possessed by the Federal Reserve System.
Further, the model exhibits a significant effect on inflation
of deviations of unemployment from the natural rate.
Next, the reaction function is modified to provide a further
test for central bank autonomy. The effect of seigniorage
on inflation depends on the proxy for the increasing burden
of conventional taxation. Deviations of unemployment,
however, are not significantly affected by the electoral cycle, making it more difficult to draw definitive conclusions
regarding the independent status (or lack thereof) of the
Federal Reserve.
This model of central bank behavior only examines the
stability of Fed policymaking with regard to fiscal policy effects and presidential elections. A useful extension of the
model would be to examine its stability as a function of the
tenure of various chairmen of the Board of Governors of the
Federal Reserve System. That is, are periods with different
chairmen meaningful subperiods in which to classify this
model of monetary policymaking? Also, the extent to which
the model developed is applicable to other countries can
be investigated. The role revenue considerations and unemployment play in explaining observed inflation rates provides insights into the independence of foreign central
banks.

See, for example, Robert J Gordon, "The Demand for and Supply of Inflation," Journal 01 Law and Economics 18 (December 1975): 807-36;
Edward J. Kane, "Politics and Fed Policymaking: The More Things Change
the More They Remain the Same," lournal 01 Monetary Economics 6

24

3.

For a summary of the literature on reaction functions, see James Barth,
Robin Sickles, and Philip Wiest, "Assessing the Impact of Varying Economic Conditions on Federal Reserve Behavior," Journal 01 Macroeconomics 4 (Winter 1982): 47-70.

4_

Stanley Fischer and Franco Modigliani, "Towards an Understanding of
the Real Effects and Costs of Inflation," Weltwirtschaltliches Archiv 114,
nO . 4 (1978): 810-33

5.

Stanley Fischer, "Towards an Understanding of the Costs of Inflation: II,"
in The Costs and Consequences 01 Inflation, Carnegie-Rochester Conference Series on Public Policy, ed. Karl Brunner and Allan H. Meltzer,
vol 15 (Amsterdam: North-Holland Publishing Company, 1981), 36, The
classic analysiS of the welfare cost is found in Martin J. Bailey, "The
Welfare Cost of Inflationary Finance," Journal of Political Economy 64
(April 1956): 93-110 .

6. For an explanation of why the Fed might respond to these government
branches, see Kane, "Politics and Fed Policymaking," and Edward J. Kane,
"External Pressure and the Operations of the Fed," in Political Economy
of International and Domestic Monetary Relations, ed _Raymond E.
Lombra and Willard E. Witte (Ames: Iowa State University Press, 1982),
211-32.
7_ Estimates of the importance of seigniorage are found in Robert J. Barro,
"Measuring the Fed's Revenue from Money Creation," Economics Letters
10 (1982): 327-32. In actuality, the U.s . Treasury does not simply regard
newly created monetary base as current revenue . However, when the
Fed permanently increases the base, it usually lends money indirectly to
the Treasury by increasing its holdings of US Government securities_
While the Treasury pays the Fed interest, the Fed transfers its profits
(composed mostly of these interest payments) back to the Treasury. See
J. Huston McCulloch, Money and Inflation: A Monetarist Approach, 2d
ed . (New York: Academic Press, 1982). Over the period from 1914 to
1983, Federal Reserve System payments to the Treasury totaled $128
billion, or almost 90 percent of the System's gross income (Verle B.
Johnston, "The Formative Years," Federal Reserve Bank of San Francisco
Weekly Letter, 9 November 1984).

8.

Robert J Barro, Macroeconomics (New York: John Wiley & Sons, 1984),
302 n_ 1.

9_ If government debt is viewed as permanent and, thus, part of nominal
net wealth, it has the same effect on inflation as increases in the money
supply Such an occurrence makes it impossible to attribute inflation
solely to the policy actions of the central bank. For evidence of this
proposition, see W Michael Cox, "Inflation and Permanent Government
Debt," Federal Reserve Bank of Dallas Economic Review, May 1985,
13-26, and the references cited therein. But according to Charles I
Plosser, "Government Financing Decisions and Asset Returns," Journal
01 Monetary Economics 9 (1982): 325-52; Barro, Macroeconomics, 380;
and Roger C. Kormendi and Philip Meguire, "Government Debt, Government Spending, and Private Sector Behavior: Reply," American EcoFederal Reserve Bank of Dallas

nomic Review 76 (December 1986): 1180-87, it is not evident that

government debt is part of nominal net wealth.
10. G. L. Bach and James B. Stephenson, "Inflation and the Redistribution of
Wealth," Review of Economics and Statistics 56 (February 1974): 4. Additional redistribution effects associated with inflation that the Fed may
consider in its policymaking are described in Basil J. Moore, "The
Endogenous Money Stock," Journal of Post Keynesian Economics 2 (Fall
1979): 49-70; Alan S Blinder, "The Anatomy of Double-Digit Inflation in
the 1970s," in Inflation: Causes and Effects, ed. Robert E. Hall (Chicago:
University of Chicago Press for National Bureau of Economic Research,
1982), 261-82; Michael J. Mumper and Eric M . Uslaner, "The Bucks Stop
Here: The Politics of Inflation in the United States," in The Politics of
Inflation: A Comparative Analysis, ed . Richard Medley (New York:
Pergamon Press, 1982), 104-26; and Kane, "External Pressure and the
Operations of the Fed." See Fischer and Modigliani, "Towards an
Understanding of the Real Effects and Costs of Inflation," for an explanation of the difficulties involved in considering these other effects.
11. See Robert J. Barro and David B. Gordon, "A Positive Theory of Monetary
Policy in a Natural Rate Model," Journal of Political Economy 91 (August
1983): 589-610. The assumption is that only unanticipated monetary
expansions lead to increases in real economic activity. Equivalently,
these nominal shocks lower the unemployment rate below its natural
rate. This hypothesis is consistent with rational expectations models
used in Robert E. Lucas, Jr., "Some International Evidence on OutputInflation Tradeoffs," American Economic Review 63 (June 1973): 326-34,
and in Robert J. Barro, "Rational Expectations and the Role of Monetary
Policy," Journal of Monetary Economics 2 (January 1976): 1-32.
12. This analysis of discretionary policy follows the general line of argument
presented in Robert J. Barro, "Inflationary Finance Under Discretion and
Rules," Canadian Journal of Economics 16 (February 1983): 1-16, and in
Robert J. Barro and David B. Gordon, "Rules, Discretion and Reputation
in a Model of Monetary Policy," Journal of Monetary Economics 12
(July 1983): 101-21. The assumption of discretion on the part of the
policymaker ignores the possibility that the central bank invests in its
reputation or credibility. In reputational models of central bank behavior, it is assumed that current actions of the policymaker influence
expectations regarding future actions. The link between current actions
and expectations is the Fed's reputation or credibility. For a summary
of the research to date on credibility, see Alex Cukierman, "Central Bank
Behavior and Credibility: Some Recent Theoretical Developments,"
Federal Reserve Bank of St. Louis Review, May 1986, 5·17.
13. See William G. Dewald and Harry G. Johnson, "An Objective Analysis
of the Objectives of American Monetary Policy, 1952·61," in Banking
and Monetary Studies, ed. Deane Carson (Homewood, III.: Richard D
Irwin, 1963), 171-89; Ann F Friedlaender, "Macro Policy Goals in the
Postwar Period: A Study in Revealed Preference," Quarterly Journal of
Economics 87 (February 1973): 25-43; and Thomas Havrilesky, "A Test of
Monetary Policy Action," Journal of Political Economy 75 (June 1967):
299-304. Richard K Abrams, Richard Froyen, and Roger N. Waud, in
"Monetary Policy Reaction Functions, Consistent Expectations, and the
Burns Era," journal of Money, Credit, and Banking 12 (February 1980):

instrumental-variable procedure to overcome the errors in variables.
Judging the relative merits of the instruments in this case, however, is
impossible. As these authors point out, "How efficient these estimates
[instrumentsl will be depends on how high the correlation is between
the actual forecasts and our measures of these forecasts ... . The
unobservability of the true policymaker forecasts makes the measurement of these correlations impossible" (Abrams, Froyen, and Waud,
p. 34 [emphasis added]).
14. Barro and Gordon, "A Positive Theory of Monetary Policy in a Natural
Rate Model," 601 .
15. "Any instruments that fulfill the requirement of being un correlated with
the stochastic term and correlated with the regressors will result in a
consistent estimate of the parameters" (George G. Judge, William E.
Griffiths, R. Carter Hill, and Tsoung-Chao Lee, The Theory and Practice
of Econometrics [New York: John Wiley & Sons, 1980l, 533). Because
lagged values are used to generate predicted values for the endogenous
variables, the instruments are not affected by (are exogenous with respect to) the current rate of inflation and, hence, are "uncorrelated with
the stochastic term ." This condition holds, however, only if the estimation equation is purged of any serial correlation. The first-stage regressions resulted in R2 values that exceeded 90 percent, thus fulfilling
the second requirement for instrumental variables. This use of instrumental variables is consistent with that employed by John H. Wood, "A
Model of Federal Reserve Behavior," in Monetary Process and Policy: A
Symposium, ed . George Horwich (Homewood, III.: Richard D. Irwin,
1967),135-66; Richard T. Froyen, "A Test of the Endogeneity of Monetary
Policy," journal of Econometrics 2 (July 1974): 175-88; and Abrams,
Froyen, and Waud, "Monetary Policy Reaction Functions, Consistent
Expectations, and the Burns Era." See Appendix B for a description of
the data and instrumental variables used .
16. Robert J. Barro and Mark Rush, "Unanticipated Money and Economic
Activity," in Rational Expectations and Economic Policy, ed. Stanley
Fischer (Chicago: University of Chicago Press for National Bureau of
Economic Research, 1980), 23-48.
17. As the Durbin·Watson statistic is inappropriate in the case of stochastic
regressors, the test employed is that developed by T. S. Breusch, "Testing
for Autocorrelation in Dynamic Linear Models," Australian Economic
Papers 17 (December 1978): 334-55, and l. G. Godfrey, "Testing for

Higher Order Serial Correlation in Regression Equations When the
Regressors Include Lagged Dependent Variables," Econometrica 46 (November 1978): 1303-10. This discussion assumes the absence of vector
autocorrelation of the type described in David K Guilkey," Alternative
Tests for a First·Order Vector Autoregressive Error Specification," journal of Econometrics 2 (May 1974): 95·104, That is, we assume the error
terms of the first-stage regressions are serially uncorrelated and are uncorrelated with each other
18. See Woolley, Monetary Politics .
19. The variables (TAX/PI) and (OEF/GNP) can be thought of as proxy variables To the extent that these variables measure with error the increasing burden of conventional taxation and government spending,

30-42, argue that this assumption Introduces two sources of bias. First,
simultaneous-equation bias is present if the dependent variable of the
reaction function affects the explanatory variables within the period
Second, an errors·in·variables problem exists because the policymaker's
forecast differs from the actual outcome Therefore, inconsistent pa·
rameter estimates are obtained We introduce instrumental variables

underestimation or overestimation of the parameters is possible when
two regressors are measured with error, making it difficult to correct for

to resolve the first problem Abrams, Froyen, and Waud suggest an

the inconsistency

Economic Review - May 1987

respectively, there is an errors·in-variables problem . As such, the parameter estimates are inconsistent. G. S. Maddala, Econometrics (New
York: McGraw-Hili Book Company, 1977), 158-62, argues that either

25

20. Such an approach is found in Richard C. K. Burdekin, ' Fiscal Pressure
and Central Bank Policy Objectives," Federal Reserve Bank of Dallas
Economic Review, May 1986, 1-9.

tives of the Federal Reserve System," Quarterly Journal of Economics 92

21 . Similar arguments are found in Froyen, 'A Test of the Endogeneity of
Monetary Policy'; Glenn T. Potts and Dudley G Luckett, 'Policy Objec-

(August 1982): 415-45.

26

(August 1978): 525-34; and Nathaniel Beck, "Presidential Influence on the
Federal Reserve in the 1970s," American Journal of Political Science 26

Federal Reserve Bank of Dallas

Appendix A
A Model of Central Bank Behavior
Given the following:
Mt = nominal money stock in period t
C t = nominal stock of net federal debt
Pt = the general price level
n t = log(Pt{Pt-1)
Ilt = log(Mt /Mt _ 1)
nr+1 = expected inflation from t to t + 1
Rmt = seigniorage in period t
Rgt = revenue obtainable from depreciating
federal debt outstanding
Yt = level of real income,
where Ilt is the Fed's target variable; Cv nrH and Yt are
exogenous variables; Mv Pt, and n t are endogenous variables; and Rmt and Rgt are arguments of the Fed's objective
function.
Seigniorage in period t is defined as

(Al)

Rmt = (Mt - Mt-1)JPt
= MtlPt - (Mt-1/Pt-1)(Pt-1/Pt) .

It is assumed that the demand for real money balances
depends inversely on expected inflation and positively on
real income:
(A2)

then

The benefits the Fed derives are assumed to increase
monotonically with these two sources of revenue:
(A7)

where P1t and P2t represent the Fed's benefit parameters.
Given the following Phillips curve relationship:

(A8)
where Ut is the current unemployment rate and Up is the
"natural" rate of unemployment, inflation surprises result in
reductions in the unemployment rate.
It is assumed the natural rate can shift over time because
of autonomous real shocks, 6, and that these shocks generate a persisting influence on the unemployment rate:
n
(A9)
Utn = lUr"_1 + (1 - l)U + 6 t ,
where 0::;; l ::;; 1 and
Therefore,

un

is the long-run mean of Up.1

Then, seigniorage collected by the Fed is equal to

(A3) Rmt = (l/m t ) [exp(aYt - bn~+1)

The costs that the Fed confronts in its conduct of policy
are assumed to include the following:

(All)
Revenue associated with reducing the value of outstanding federal debt is expressed as
(A4)

Rgt = (C t- 1/Pt- 1) - (C t- 1/Pt) .

Assuming that holdings of government debt depend on the
difference between the nominal rate of interest on such
debt, iv and also on expectations of inflation:
(AS)

Economic Review - May 1987

The reaction function given by equation 1 in the text is
differentiated using three conditions: (dnt/dll t ) Inr,nr+1)
= 1, which follows from equation A2; (dnr+1/dllt) = 0; and
E(6 t ) = O. Solving for the rate of inflation gives equation 2
in the text.

1.

See Robert J. Barro and David B. Gordon, "A Positive Theory of
Monetary Policy in a Natural Rate Model," Journal of Political
Economy 91 (August 1983): 589-610.

27

Appendix B

Description of Data Set
Quarterly data are available for all variables. The time period chosen for the analysis is 1951-83- the period following the U.S. Treasury-Federal Reserve accord of 1951-to
assume a maximum amount of independence of the Federal Reserve System. The criteria used here for "independence" are described by Woolley:
At a minimal level, a central bank can be considered to be independent if it can set policy instruments without approval from outside authorities,
and if, for some minimal period of time, the instrument settings clearly differ from those preferred by
the fiscal authority.l
Data between the post-World War II period and 1951
exhibit the effects of the Fed's "pegging" operations as directed by the Treasury. From 1914 until the middle 1930s,
the Comptroller of the Currency and the Secretary of the
Treasury were members of the Board of Governors of the
Federal Reserve System, rendering this time period questionable in meeting the definition of independence. Finally,
the remaining years are excluded because of the distortions
caused by the Great Depression and World War II.
M, is defined as the narrow money stock, or Ml. This
constitutes currency plus demand deposits plus other
checkable deposits (available after 1980). The data for the
series are not adjusted for seasonal variation as it is this
amount from which the Fed's revenue accrues. P, is defined
as the implicit price deflator for GNP (1972 = 100). U, is
defined as the total unemployment rate-all civilian workers as a percentage of the civilian labor force, adjusted for
seasonal variation. Data on M" P" and U, are found in U.S.
Department of Commerce, Bureau of Economic Analysis,
Business Statistics 1979 and Business Statistics: 1982 (supple-

28

ments to the Survey of Current Business) and also in various
issues of the Federal Reserve Bulletin.
The monetary base is defined as total reserves plus currency outside the U.S. Treasury, Federal Reserve Banks, and
vaults of nonmember banks, not seasonally adjusted. Data
for the base are found in Board of Governors of the Federal
Reserve System, Annual Statistical Digest, 1970-1979, and
Annual Statistical Digest, 1982, plus various issues of the
Federal Reserve Bulletin. G, is defined as total gross public
debt of the u.s. Government held by the public, excluding
that held by U.S. Government agencies and trust funds and
that held by Federal Reserve Banks. These data are available in various issues of the Federal Reserve Bulletin. Estimates of the natural rate of unemployment were obtained
from Gordon.2
The following data were used to construct instrumental
variables: personal income, seasonally adjusted totals at
annual rates; Federal Government outlays, calendar years;
the yield on three-month Treasury bills; the index of industrial production (1967 = 100), adjusted for seasonal variation; and estimated retail sales, adjusted for seasonal
variation and trading-day differences, at all types of retail
stores. Data for these variables are found in the 1979 and
1982 editions of Business Statistics and various issues of the
Survey of Current Business. Data for personal tax and nontax payments, the federal budget deficit, and gross national
product are found in Business Statistics: 1982 and subsequent issues of the Survey of Current Business.

1. John T. Woolley, "Central Banks and Inflation," in The Politics of
Inflation and Economic Stagnation: Theoretical Approaches and
International Case Studies, ed leon N. lindberg and Charles S.

Maier (Washington, D.c.: Brookings Institution, 1985), 320
2.

Robert J. Gordon, Macroeconomics, 3d ed . (Boston: little, Brown
and Company, 1984), Table B-2.

Federal Reserve Bank of Dallas