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dissertation entitled

AN ECONOMETRIC ANALYSIS OF THE STABILIZATION
EFFECTIVENESS OF THE UNEMPLOYMENT INSURANCE PROGRAM

presented by

James M. McGibany

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Economics

 

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AN ECONOMETRIC ANALYSIS OF THE STABILIZATION
EFFECTIVENESS OF THE UNEMPLOYMENT INSURANCE PROGRAM

James M. McGibany

A DISSERTATION

Suhmitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

1983

ABSTRACT
AN ECONOMETRIC ANALYSIS OF THE STABILIZATION
EFFECTIVENESS OF THE UNEMPLOYMENT INSURANCE PROGRAM

by

James M. McGibany

This dissertation measures the amount of stabilization that
the Unemployment Insurance program provides to the economy of the
United States. Past research has shown that the Unemployment
Insurance program has been very effective in preventing further
declines in aggregate demand in several post-war recessions. This
study extends the research in this area by first improving the method
by which the stabilization effectiveness of the program is measured
during recession and recovery periods, than by using a completely
specified model of aggregate demand to estimate the measured
effectiveness of the program over any time period. The empirical
work covers the period from l955wl981.

The reaction of the Unemployment Insurance program to income
changes is first considered. All previous research assumed the reaction
of the program was contemporaneous to income changes, and that the
feedback from the program to income also occurred contemporaneously.
These assumptions enabled previous researchers to measure the
stabilization effectiveness of the program contemporaneously with
changes in income. This study tests the validity of these assumptions.

The tests reveal that the assumptions are valid concerning the reaction

of benefit payments to income changes, but may not be valid concerning
the reaction of tax collections to income changes. The latter is due
to institutional factors such as the practice of experience rating
used to establish tax rates. However, for simplicity I take the above
assumptions as valid for the entire program.

The next part of the dissertation introduces the concept of
measured effectiveness and derives a modified version of the measure
of stabilization effectiveness of the Unemployment Insurance program
originally found in previous research. The measure is simply a ratio
of two aggregate demand multipliers, one from a model including the
program, the other from a model without the program. The measure shows
the amount of a further (percentage) change in income prevented by the
inclusion of the program in the model. The modification is obtained
by incorporating the trend growth of benefits, taxes, and income in the
measure. This modification smoothes the measured effectiveness of the
program over recession and recovery. This is in contrast to the
asymmetric estimates of the measure found in previous research that
showed high effectiveness in recession and almost no effectiveness in
recovery. Using the modified version of the measure, I calculate that
the average measured effectiveness of the Unemployment Insurance program
is half that estimated in previous research. Also, using this measure,
I find that every discretionary extended benefit program has detracted
from the stabilization effectiveness of the program. This result shows
the program to be more effective at meeting the goal of stabilization
when it is left to work as an automatic stabilizer.

The final part of the dissertation derives, specifies, and

estimates a series of aggregate demand models that enable more accurate

estimation of the measured effectivness of the Unemployment Insurance
program as an automatic stabilizer. All previous research including
that of the proceeding section of the dissertation measured the
effectiveness of the program using a misspecified model of aggregate
demand by not including a money sector. Allowing for monetary reactions
to changes in fiscal policy, such as the Unemployment Insurance program,
reduces the measured effectiveness of the program below that found in
the previous section of the dissertation. This method of estimating
measured effectiveness is conceptually equivalent to estimating the
specification error between a misspecified model and a correctly
specified model. Incorporating a government budget condition in the
model that requires any change in the deficit be financed by an increase
in government bonds outstanding and/or an increase in the monetary base,
changes the estimated measured effectiveness of the program only
slightly. However, the true measured effectiveness of the program is
that estimated without the deficit financing condition and the induced

wealth and liquidity effects associated with this condition.

ACKNOWLEDGMENTS

Over the course of the many months that I have spent working on
this project, I have accumulated a sizeable number of debts. It is
with great pleasure that I take this opportunity to acknowledge the
people and organizations who contributed in bringing this project to
a successful completion.

My very special thanks go to Professor Daniel Hamermesh, Chairman
of my dissertation committee, who not only made invaluable comments and
suggestions on the direction, substance and style of this thesis but
who has helped cultivate my interest in the study of economics. I would
like to extend my special thanks to Professor James Johannes for his
comments and guidance not only on the macroeconomic details of the
thesis but on my past, present and future work in the field of economics.
I would also like to thank Professor John Goddeeris for many hours spent
reading the various drafts of this dissertation and for his numerous
insightful suggestions. In addition, my thanks to go Professor Norman
Obst for the contribution of his time and effort as the fourth member
of the dissertation committee.

This dissertation was fully funded by U.S. Department of Labor
Grant Number 55-26-82-08, and I gratefully extend my thanks to the U.S.
Department of Labor and the members of the Social Science Research
Council for selecting my initial proposal for funding. Of course,
neither the Department of Labor or the Social Science Research Council

are responsible for any remaining errors, nor do they necessarily adhere

ii

to the views and policy recommendations expressed within.

I also gratefully acknowledge the assistance of Cindy Ambler of
the Unemployment Insurance Statistics Division of the U.S. Department
of Labor for her help in locating missing data, and the expert typing
of the manuscript by Terie Snyder.

Finally, I would like to thank four special people. To my
parents, Carl and Alyce McGibany, I owe an unpayable debt of gratitude
for their unending support and encouragement through the years, even
though they often did not understand my reasons for continuing my
education. To Professor William Spellman, I owe my thanks for his
guidance at a time in my life when I needed just that. And to a very
special person, Priscilla Odland, I owe my deepest thanks for her love,
and for the encouragement and inspiration I need not only to see my way
through projects such as this but through many other difficult times in

my life.

iii

TABLE OF CONTENTS

PAGE

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . vi

LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . viii

CHAPTER
ONE - INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . 1
TWO - THE RESPONSIVENESS OF THE UI PROGRAM TO INCOME CHANGES . . 7
2.1 Introduction . . . . . . . . . . . . . 7
2.2 A Test for the Dependence of the UI Program on
Income Changes . . . . . . . . . . . . . . 8
2. 3 A Test for the Timing of the Feedback. . . . . . . 17
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . 22

THREE - THE EFFECTIVENESS OF THE UI PROGRAM AS AN AUTOMATIC
STABILIZER IN RECESSION AND RECOVERY . . . . . . . . . 24

3.1 Introduction . . . . . . . . . . . . . . . . . . 24
3.2 The Concept of Measured Effectiveness. . . . . . . 25
3.3 Modifying the Measured Effectiveness Equation. . . 33
3.4 Estimates of the Measured Effectiveness of the

UI Program in Recession and Recovery . . . . . . . 36
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . 73

FOUR - THE STABILIZATION EFFECTIVENESS OF THE UI PROGRAM IN
THE CONTEXT OF AN AGGREGATE DEMAND MODEL . . . . . . . 79

4.1 Introduction . . . . . . . . . . . . . . . . . . . 79
4.2 A Review of Measured Effectiveness . . . . . . . . 80
4.3 The Theory and Derivation of the Model . . . . . . 81
4.4 Estimation and Results . . . . . . . . . . . . . . 90
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . 101

FIVE - THE STABILIZATION EFFECTIVENESS OF THE UI PROGRAM IN THE
CONTEXT OF AN AGGREGATE DEMAND MODEL II: ADDING A
GOVERNMENT BUDGET CONDITION . . . . . . . . . . . . . 105

5.1 Introduction . . . . . . . . . . . . . . . . . . 105
5.2 Theoretical Background . . . . . . . . . . . . . . 106

iv

PAGE
FIVE - THE STABILIZATION EFFECTIVENESS OF THE UI PROGRAM IN THE

CONTEXT OF AN AGGREGATE DEMAND MODEL II: ADDING A
GOVERNMENT BUDGET CONDITION (cont'd.)

5. 3 Empirical Results . . . . . . . . . . . . . . . 110
5. 4 Models with the Money Supply Endogenous. . . . . . 124
5. 5 Conclusion . . . . . . . . . . . . . . . . . . . . 136
SIX - CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . 142
APPENDICES
APPENDIX A - DATA SOURCES . . . . . 148
APPENDIX B - THE DERIVATION OF THE MEASURED EFFECTIVENESS
EQUATION . . . . . . . . . . . . . . . 151
APPENDIX C - THE DERIVATION OF IMPACT ELASTICITIES IN
MODELS CONTAINING A GOVERNMENT BUDGET
CONDITION I O O C O O O O O C O O I O O O O 155

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . 166

2-1

2-2

2-5

3-1

3-2

3—9

3-10

3—11

3-12

3-13

3-14

3-15

3-16

LIST OF TABLES

Box-Jenkins Filters for U1 Taxes, UI Benefits, and GNP.
Cross Correlation Functions . . . . . . . . . . . .

Haugh Test Results. . . . . . . . . . . . . . . . . . . .
Granger Test Results. . . . . . . . . . . . .

Estimated Coefficients for the Granger Direct Test. . . .
Regression Coefficients: Time Trend Estimation. . . . .
Long-Run Measured Effectiveness, 1955-1980. . . .
Measured Effectiveness, Recession l957:III—1958:II.
Measured Effectiveness, Recovery 1958:11-1959zll. . . .

Quarter-By-Quarter Measured Effectiveness, 1957:111—
1959:II. . . . . . . . . . . . . . . . .

Measured Effectiveness, Recession l960:II-1961:I. . . . .
Measured Effectiveness, Recovery l961:I-l962:1. . . . . .

Quarter-By-Quarter Measured Effectiveness, 1960:II~
1962:I O O O O I O O I O O C O O O O O O O O 0

Measured Effectiveness, Recession 1969:IV—1970;1V . . . .
Measured Effectiveness, Recovery 1971:1-1971:IV . . . .

Quarter-By-Quarter Measured Effectiveness, 1969:IV—
1971:IVO O O O O C I O O O O O O O O I O O 0

Measured Effectiveness, Recession 1973:1V-1975zl. . . .
Measured Effectiveness, Recovery l975:I-1976:I. . . . . .

Quarter-By-Quarter Measured Effectiveness, 1973:IV-
1976:I . . . . . . . . . . . . . .

Measured Effectiveness, Recession 1980:1-1980:III

Measured Effectiveness, Recovery 1980:11I—1981:II .

vi

PAGE
12

l4

16

20

21

37

4O

42

45

47

50

54

56

59

61

62

63

66

68

71

3-17

4—1

5-3

5-4

5-10

LIST OF TABLES (Cont'd.)

Quarter-By-Quarter Measured Effectiveness, 1980:1-
1981:II. . . . . . . . . . . . . . . . . . . . .

Variables in the Models . . . . . . . . . . . . .
Regression Results, Goods Only, No UI Model (GNUI). . . .
Regression Results, Goods Only, UI Model (GUI). . . . . .
Regression Results, Entire Model, No UI (WNUI). . . . . .
Regression Results, Entire Model, UI (WUI). . . . . .
Impact Elasticity Comparisions. . . . . . . . . . . . . .
Impact Elasticities, Goods-Only Models. . . . . . . . . .
Impact Elasticities, Entire Models. . . . . .

A Comparison of Impact Elasticities, Models with a
Government Budget Condition. . . . . . . . . . . .

A Comparison of the Estimated Measured Effectiveness of
the UI Program from Different Models . . .

A Comparision of Impact Elasticities from Different
Models . . . . . . . . . . . . . . . . . . . . . .

Regression Results, Money Supply Endogenous, No UI
Model. . . . . . . . . . . . . . . . . .

Regression Results, Money Supply Endogenous, UI Model

Impact Elasticities, Models with the Money Supply
Endogenous . . . . . . . . . . . . . . . . . . . .

A Comparision of Measured Effectiveness of the UI Program
from Different Models. . . . . . . . . . . . . . . . .

A Comparison of Impact Elasticities from Different
Models . . . . . . . . . . . . . . . . . . . . . .

vii

PAGE

72

83

92

93

94

95

97

111

112

114

115

121

125

126

132

133

135

LIST OF FIGURES

PAGE

IS-LM Representation of Measured Effectiveness. . . . . . 26

Quarter-By-Quarter Measured Effectiveness, 1957:III
-1959:II o o o o o o o o o o o o o o o o o o o o o o o 43

Quarter-By—Quarter Measured Effectiveness, 1960:II
-1962:I. . . . . . . . . . . . . . . . . . . . . . . . 51

Quarter-By—Quarter Measured Effectiveness, 1969:IV
—1971:IV . . . . . . . . . . . . . . . . . . . . . . . 57

Quarter-By-Quarter Measured Effectiveness, 1973:IV
—1976:I. . . . . . . . . . . . . . . . . . . . . . . . 64

Quarter—By-Quarter Measured Effectiveness, 1980:I
-1981:II o o o o o o o o o o o o o o o o o o o o o o 0 6g

IS-LM Representation of the Comparison of Measured
Effectiveness Between Goods-Only and Entire Models . . 99

viii

CHAPTER ONE

INTRODUCTION

Of the many policy instruments that are available to policy
makers to help them influence economic activity, only a handful are
referred to as automatic stabilizers. As income changes in response to
autonomous shocks, automatic stabilizers provide countercyclical forces
which help reduce the effects of these shocks on the economy. Among
this group of policy instruments is the Unemployment Insurance program,
which was originally adopted as part of the Social Security Act in
1935. Initially the Unemployment Insurance (hereafter U1) program met
the need of providing social insurance to individual workers against the
loss of wages as a result of the adverse economic conditions during the
Great Depression. Its secondary goal is to help stabilize the economy
by maintaining the purchasing power of unemployed workers in order to
prevent further prolonged recessions or depressions.

The UI program helps stabilize the economy by impeding changes in
income caused by autonomous shocks. Like other automatic stabilizers,
the UI program moves the government toward a deficit as income falls by
paying out benefits to laid off workers and collecting fewer taxes from
employers as their wage bill shrinks. Government spending increases and
revenues decrease, causing the deficit to increase, but this slows the

decline in income. Conversely, as income rises, tax collections

increase as increased employment raises employers' wage bills, and
benefits cease, causing the government to move toward a surplus which
retards the increase in income.

The purpose of this study is to measure the amount of
stabilization effectiveness the UI program gives to the economy. The
measure of stabilization effectiveness is taken to be the amount of a
further change in income (due to an autonomous shock) that is prevented
by the UI program. The policy implications of this study are
straightforward. If the UI program can substantially stabilize the
economy, policy makers may wish to structure the UI program in such a
way that it provides the greatest amount of stabilization effectiveness
while still meeting the program's foremost goal: acting as a form of
social insurance.

Before detailing the course of action that was undertaken for
this study, I first must explain why I chose to analyze the UI program
instead of some other fiscal policy. The obvious reason is the fact
that it is an automatic program and does not suffer from discretionary
policy timing problems, such as the so-called recognition and
implementation lags. In this sense, the stabilization effectiveness of
this simple program is a better measure of the impact of fiscal policy
than that of all fiscal policies together. Another reason the UI
program is chosen is that its impact per dollar may be greater than
other fiscal policies. Two factors may lead to this increased impact.
First, peOple receiving U1 income may be constrained from using their
savings to help them supplement their UI income to maintain their
lifelong consumption pattern. Secondly, UI recipients tend to be lower-

income individuals with higher marginal propensities to consume than

non-recipients. The combination of these two factors may increase the
impact of the UI program above that of other fiscal policies. Because
of this possible larger impact and the automatic nature of the program
making it a better measure of the impact of fiscal policy, I have chosen
the UI program as the fiscal policy to analyze for purposes of this
study.

I examine three stabilization issues in this study. First, I
examine whether or not the response of the UI program to changes in
income is automatic. If it is not, the stabilization effectiveness
cannot be measured contemporaneously with a change in income. Second, I
measure the stabilization effectiveness of the UI program in recession
and recovery. Lastly, I measure the stabilization effectiveness of the
UI program in the context of an aggregate demand model.

Chapter II examines the issues of how quickly the UI program
reacts to changes in income, and how soon the feedback from the U1
program is felt on income. If the UI program reacts with a lag to
income changes, this must be accounted for in the measured effectiveness
of the program. I find no conclusive evidence from the quarterly
analysis in this study to contradict the assumption that the UI program
reacts to changes in income contemporaneously. The tests run in this
chapter are designed to test for the presence of independence between
variables, not Ehgg_the independence occurs. It is because of this that
I cannot make a definitive statement about the response time of the UI
program to income changes.

I measure the stabilization effectiveness of the UI program in
the five post-war recession/recovery periods in Chapter III. This issue

has been taken up in the past by Clement (1960), Rejda (1966), Lewis

(1963), Eilbott (1966) and von Furstenberg (1976) in the U.S., and by
Thirlwall(1969)and Hansen and Burroughs (1969) in the U.K. I employ a
more accurate version of the measure of stabilization effectiveness
found in these studies (see especially Eilbott (1966)), merely by taking
into account the growth of income over time and the dependence of the UI
program on this detrended series (rather than levels) of income. Using
the same measure as Eilbott, except for this minor change, the measured
effectiveness of the UI program falls by nearly fifty percent from that
of other studies during recessions. In addition, whereas previous
studies found almost no effectiveness during recoveries, I find measures
of stabilization effectiveness of nearly the same magnitude for
recessions and recoveries due to this minor correction.

Chapter III also analyzes the effect discretionary temporary
extended benefits programs have on the measured effectiveness of the
overall UI program. These discretionary programs all have a negative
effect on measured effectiveness. The primary reason for this is that
every one of these discretionary programs began as recovery, measured by
real national income turning upward, was underway.

Economic theory suggests that transfer payments, such as UI
benefits, should decline as recovery is underway. The negative effect
on measured effectiveness indicdates that U1 benefits are increasing
when extended benefits are included in total benefits, rather than
decreasing as theory suggests. This result makes it clear that
temporary extended benefit programs must be judged on their social
insurance merits (from a policy viewpoint), rather than their
contribution to stabilization effectiveness.

Chapters IV and V form the most important contribution to the

issue of the effectiveness of the UI program. The analysis in Chapter
III and that of all previous studies was done without a single aggregate
demand model being estimated to find the aggregate demand elasticities
used in the measure of effectiveness. In addition, all previous studies
implicitly assumed goods-sector-only aggregate demand models in their
analysis. Four models are specified and estimated in Chapter IV for use
in calculating the measured effectiveness of the UI program. The
principal result from this chapter is that the addition of a money
sector in the models, to account for monetary reactions to goods sector
shocks, reduces the measured effectiveness of the UI program compared to
that of goods-sector-only models.

Chapter V extends the models of Chapter IV by introducing a
government budget condition to the analysis. Forcing the government to
pay for any deficits created by increased spending has an impact on the
measured effectiveness of the UI program. The measured effectiveness
increases marginally when deficit financing is considered compared to
models that ignore financing. This is due to the countercyclical nature
of the program, as deficits will not be as large when income rises in
response to increased government spending, since UI benefits fall and UI
taxes rise. With a smaller deficit to finance, wealth and liquidity
effects increase the measured effectiveness Of the UI program. However,
this increase in measured effectiveness is small.

Chapter V also examines the effect different monetary targets
have on the measured effectiveness of the UI program. A model in which
interest rates are pegged and the money supply changes to equilibrate
the money sector is associated with greater measured effectiveness than
a model in which the model supply is targeted (exogenous). This is not

surprising, as accommodating monetary policy prevents private spending

from being crowded out by higher interest rates that usually accompany
increased government spending and deficits. Although the measured
effectiveness of the UI program increases when monetary policy is
accommodating, the increase is due to more liquidity being available,
not from the fiscal effect of the UI program.

The major contributions of this dissertation lie both in its
research methods and its conclusions. Chapter III shows how a seemingly
minor correction in methodology can result in a substantial difference
in measured effectiveness in both recession and recovery. The results
in Chapter III are much more appealing than the rather high measures of
effectiveness found in previous studies. I find that only ten to twelve
percent of a further change in income has been prevented by this small
program, rather than the twenty-five to thirty percent figure found in
some of the previous studies. (See Clement (1960) and Rejda (1966).)
Chapter III also provides an easy way to dissaggregate total benefits
paid into regular program benefits paid and temporary extended benefits
paid to assess the latter's impact on the measured effectiveness of the
overall UI program. Not surprisingly, the results show a negative
impact on overall effectiveness from temporary extended benefits. Most
importantly, this study estimates aggregate demand models containing an
endogenous UI benefit variable, a money sector, and a government budget
condition to measure more accurately the effectiveness of the UI
program. This methodology enables decomposition of the measure into the
fiscal effect due to the UI program from the monetary and deficit
financing effects. This breakdown allows me to show both the measure of
stabilization effectiveness of the UI program and the factors

contributing to this measure.

CHAPTER TWO

THE RESPONSIVENESS OF THE UI PROGRAM TO INCOME CHANGES

2.1 Introduction

 

A major factor in choosing the U1 program as the fiscal policy to
be analyzed in this study concerning stabilization effectiveness is its
automatic nature. Unlike discretionary programs, which suffer from
timing problems such as the so-called recognition and implementation
lags, automatic stabilizers quickly react to changes in economic
activity to mitigate these changes. Not only is the reaction of the
automatic stabilizer to a change in economic activity assumed to take
place soon after the change, but the feedback to the economy is assumed
to follow shortly after the reaction. The purpose of this chapter is to
answer the following questions:

1. Is the UI program dependent on changes in income, and if it
is, how long does it take for the program to react to income
changes?

2. When does the feedback from the above reaction of the UI
program to a change in income occur, and for how long is the

impact felt?

 

2.2 A Test for the Dependence of the UI Program on Income Changes

The first requirement for a program to be an automatic stabilizer
is that it must react toeashock to the economy in order to minimize the
effect of the shock on the economy. The second requirement is that this
reaction occur shortly after the shock to minimize quickly the effect of
the shock on the economy. A policy that does not meet both of these
requirements is not considered to be an automatic stabilizer.l! This
section tests the hypothesis that the UI program meets both of these
requirements.

Previous studies ignore question one by implicitly assuming the
UI program reacts to changes in income contemporaneously.2! This may be
correct, and one may gain little by exploring the possibility of a non-
contemporaneous reaction, especially for U1 benefits. However, there
are some institutional arrangements that make the reaction of U1 taxes
more su5pect, for example, the practice of experience rating.

States administer the UI program, even though there are some
exclusively federal taxes and benefits as part of the program.
Experience rating is the method states have developed to encourage
stability in employment practices by firms. This practice makes the
firms which generate more unemployment fund the payment of benefits, and
enables those firms with little or no unemployment to avoid most of the
burden of paying for the benefits going to other firms' employees.

Under a program of experience rating, each firm has an account set up by
the state UI program. Firms contribute to these accounts via tax
payments and are debited for all benefits paid to their employees. The

balance of the account of a firm determines the experience of its

employment practices, which is used to set the firm's tax rate. Firms
with negative balances are assigned higher tax rates, firms with
positive balances pay the minimum tax rate.

One result that can be drawn is that tax rates set using this
practice of experience rating move countercyclically. This can be shown
in a recession, for, as more workers become eligible to receive
benefits, a firm's account moves negatively (less payroll means less
taxes collected) and tax rates rise. Conversely, tax rates fall during
expansions as the firm's account moves toward a surplus. This fact has
led some previous studies to conclude that UI taxes are destabilizing.2!

Rejda has shown that, although tax rates may move in a
countercyclical pattern, tax collections move procyclically.fi/ The
following example verifies this claim. During a recession, unemployment
increases causing a firm's payroll to decrease and taxes collected to
fall. The Opposite occurs in an expansion. Employment increases
resulting in more taxes being collected. The main point of Rejda's
argument is that tax collections, not tax rates, are important in
determining stability. But, tax rate changes may offset the change in
tax collections and produce a destabilizing effect. Because there are
two Opposing forces working on U1 taxes, it is impossible to tell, 3;
priori, if UI taxes are stabilizing or not. This matter must be dealt
with empirically, as is done later in this chapter. However, because of
these two forces, the measured effectiveness of U1 taxes should move
toward zero (neutral). If that is the case, running a test for
dependence on income may show UI taxes to be independent of changes in

income.

Another significant result may be the timing of the effectiveness

10

of U1 taxes due to eXperience rating. Tax rates change with a lag, as
the employment "experience" is averaged over a period longer than a year
(usually), and reviewed only annually. Thus, tax rates do not change
immediately, only at regular intervals. Two results can be obtained
from this fact. First, the destabilizing aspects of UI taxes may not be
evident immediately, but will depend on the timing of the recession or
recovery vis a' vis the annual review. From the discussion above, UI
taxes should be no worse than neutral and may possibly even be
stabilizing in the short run as tax collections fall. However, over the
course of the business cycle, measured effectiveness should move toward
zero after tax rate changes have been made. Second, because of lags in
the setting of the tax rates, UI taxes may show destabilizing tendencies
only after several quarters.§y
With this in mind, there still seems to be little gained by not
assuming automatic means contemporaneous. One factor that can be tested
is the dependence of U1 taxes and UI benefits on income. To test this,
the Haugh test will be run.é/
To carry out this test, two covariance-stationary time series are
needed. If the series are not covariance-stationary, they must be made
so by prewhitening them by an ARIMA representation. The white-noise
residuals obtained upon estimation of the ARIMA representations are used
in the testal/ The use of ARIMA filters is justified on the grounds
that these filters eliminate the nonstationarity in the original series.
The data used for these tests are:
UI taxes, state collections plus federal taxes (FUTA);

UI benefits, regular state program benefits, plus unemployment

compensation for federal employees, plus unemployment compensation

11

for ex-servicemen plus automatic extended benefits (EB);

UI taxes and UI benefits are converted from monthly to quarterly
series to match the income series; and
Income, seasonally-unadjusted GNP.

Appendix A contains a detailed listing of all data sources.
Seasonally-unadjusted GNP is used as the income series to match it with
the seasonally-unadjusted UI taxes and UI benefits series. A
seasonally-adjusted income series would cause distortions in the tests.

These quarterly series are not covariance—stationary. Box-
Jenkins methodology is used to diagnose the ARIMA model, estimate the
parameters of the model, and obtain the residuals needed for the Haugh
test.§! Table 2.1 summarizes the results of the process.

The chi-square tests of the autocorrelation functions of all
three models show that the hypotheses that the residuals (et) generated
by the models are white-noise and cannot be rejected at the .05 level of
significance. The white-noise residuals are then used in the Haugh test
to check for independence of the series UI taxes and seasonally-
unadjusted GNP, and UI benefits and seasonally-unadjusted GNP,
respectively.

The hypothesis to be tested is for the independence of the two
series, i.e., zero cross-correlation values at all positive and negative

*
lags. For each lag, an S statistic is calculated, where

(2.1) 3* = N2(

|| MW

(N-le)-1 r; Y(j) .
_k 9

with N the number of observations, k the number of lags to be analyzed,

and r§ Y the cross-correlation value at lag j. For purposes of this
D

12

TABLE 2.1

BOX-JENKINS FILTERS FOR UI TAXES, UI BENEFITS, AND GNP

 

 

 

Series Diagnostic Check
UI Taxes (1-B)(1-B“)UIT - -.003+(1-.63B -.49B“)et1 x2 - 20.17 df = 21
(.0016) (.O42)(.O70)
UI Benefits (1-B)(1-E“)UIB - (1+.3AB)(1-.65534)ec2 x2 = 32.99 df = 22
(.080) (.072)
GNP (1-B)(1-B‘)NSAGNP - (1-.71B4)et3 x2 - 33.61 df = 23
(.064)
NOTES: (1) The B1 represents the back shift operator to the ith power.
(2) etx is the white noise residual for equation X.
(3) UIT, UIB, NSACNP are the natural logarithms of U1 taxes, UI
benefits and not seasonally adjusted GNP, respectively.
(4) The numbers in parentheses under the coefficients are standard

errors.

13

test, "X" will be UI taxes, then UI benefits; and "Y" will be seasonally
unadjusted GNP. Lagged and lead values of seasonally-unadjusted GNP are
combined with current values of U1 taxes and UI benefits (separately) to
obtain estimates of the cross-correlation values for each period.
Becuase the number of periods is relatively small (15 leads and lags), I
use the small sample statistic (8*) for this test. 8* is distributed as
a chi-square with 2k+1 degrees of freedom. The 8* value for k lags is
compared to a critical value of a chi-square with 2k+1 degrees of
freedom. If 8* is greater than the critical value, the hypothesis of
independence is rejected.

.A Simpler test to determine independence, which the Haugh test
improves upon, is to compare the cross-correlations to N.1 or (N-|k|)-1,
which are the asymptotic and small sample variances of the correlation
functions. To reject the hypothesis of independence of the two series,
one need find only one correlation value greater in absolute value than
two standard deviations from the (assumed zero) mean (2/N-1filor
2/(N-lk4)'IU2). The cross-correlations for 15 leads and lags for U1
taxes and seasonally-unadjusted GNP, and UI benefits and seasonally-
unadjusted GNP, and their respective two standard deviation measures
(known as the two sigma limit) are given in Table 2-2. For UI taxes and
NSAGNP, lags 1 and 2 are greater than the two sigma limit, implying the
two series areIuM:independent. Notice, the contemporaneous correlation is
not considered significant while the two significant periods, lags 1 and
2, exceed the two sigma limit only slightly. This may be due to the
experience rating factor discussed above. However, this conclusion
cannot be drawn from this test.

One can see there are several instances where the correlations

14

TABLE 2-2

CROSS CORRELATION FUNCTIONS

 

 

UIT-GNP UIB-GNP TWO
LAG CORRELATION VALUE CORRELATION VALUE SIGMA LIMIT
~15 -.0916 .0271 .1890
-14 -.1116 .0891 .1881
-13 -.0335 .0369 .1873
-12 .1480 .1164 .1865
-11 -.0378 -.0244 .1857
-10 -.0820 .0020 .1849
-9 -.1394 -.0941 .1841
-8 -.0137 .0889 .1833
-7 -.0672 -.0320 .1826
-6 -.1238 .1353 .1818
-5 -.0194 .2521 .1811
-4 -.0099 .1658 .1803
-3 .1481 .1575 .1796
-2 .1865 -.1033 .1789
-l .2646 -.2204 .1782
O -.0068 -.6311 .1775
1 -.0163 -.1861 .1782
2 .0416 -.l843 .1789
3 .0799 .0357 .1796
4 -.0699 -.0528 .1803
5 -.O720 .2697 .1811
6 -.0586 .0560 .1818
7 .0480 .1840 .1826
8 .1011 -.O425 .1833
9 -.0325 .1488 .1841
10 -.O759 -.0422 .1849
11 .0016 -.1491 .1857
12 .0406 .0352 .1865
13 -.0526 .1187 .1873
14 -.OO4O .0396 .1881
15 .0504 -.0703 .1890

 

NOTE:

The two sigma limit is twice the square root of the small sample
variance, 2(N-|K[)-]/2.

15

between UI benefits and NSAGNP exceed the two sigma limit, including the
contemporaneous correlation, as expected. This implies the two series
are not independent.

The results of the Haugh test are reported in Table 2-3. The 8*
statistics for various lead-lags are given for both the UIT-NSAGNP and
UIB-NSAGNP correlation functions. The 8* statistics indicate the
hypothesis that U13 and NSAGNP are independent can be rejected at the
.005 significance level for all leads or lags k. The hypothesis that
UIT and NSAGNP are independent can be rejected for small values of k,
but it cannot be rejected for large k. The possibility of U1 taxes
becoming independent of income changes due to the practice of experience
rating was postulated above, and the results of this test do not
disprove that hypothesis. However, all that can be shown from the Haugh
test is that UI taxes and NSAGNP, and UI benefits and NSAGNP are not
independent for at least some leads and lags. One cannot infer any
pattern or magnitude of correlation from this test, as it is only a test
for independence.

The answer to the question whether the UI program is dependent on
a change in income is found to be yes for both UI benefits and UI
taxes. The answer to the question of how long does it take for the
program to react to this change in income remains to be answered
explicitly. As in previous studies, I make the assumption that the UI
program reacts contemporaneously to a change in income. This assumption
may not be correct at all times, especially for U1 taxes, but one loses

little by assuming the reaction is contemporaneous in a quarterly study.

16

TABLE 2-3

HAUGH TEST RESULTS

 

 

CORRELATION
FUNCTION |K| = 1 [K] = 6 |K| = 12 [K] = 20
UIT-GNP 9.00** 21.28*** 31.64 41.23
UIB-GNP 61.23* 95.23* 110.96* 135.14*

 

NOTES: * Significant at the .005 level
** Significant at the .05 level.

*** Significant at the .10 level.

17

2.3 A Test for the Timing of the Feedback

 

Answering question one does not provide a quantifiable answer to
how effective the UI program is as an automatic stabilizer; it only
discusses the issue of when effectiveness begins. Question one is only
one side of the "when" issue, though. Question two is the other side of
this issue. The answer to this question is usually implied by the model
and/or by the theory backing the model. But investigating when an
automatic stabilizer reacts and then causes a change in a target
variable is an empirical question. It is unfortunate there is no test
specifically designed to help answer this question.

Other studies have passed over this issue, again assuming the
feedback effect is felt contemporaneously and continues throughout the
period in question. The closest test to determine when a variable
causes another to change is the Granger direct test.¥9/ However, this
test does not specifically determine when a variable affects another,
only if a variable affects another. If one determines from the test
there is a relationship, one can only infer the pattern of the
relationship from the coefficients on the apprOpriate lagged
variables. Because of the econometric problems discussed below, this
inference is by no means a sound test to determine the timing of the
relationship that is being tested.

Care should be taken when employing the Granger direct test to
determine when a variable causes another, while not testing whether
there is a relationship. First, the test is a two-sided test, but from
the assumption made at the end of Section 2.2, a change in GNP causes

both UI taxes and UI benefits to change. Since I am assuming causation

18

to run from GNP to UI taxes and UI benefits, the test of that side of
the relationship was not run. Second, if UI taxes and UI benefits are
automatic stabilizers, they must cause GNP to change. If this is
assumed, the Granger direct test is unnecessary, as the direction of
causation runs from GNP to UI benefits and UI taxes and back. Since I
have not made the assumption that the latter direction of causation
holds, I will test the hypothesis that UI taxes and UI benefits cause,
in the sense of Granger, NSAGNP to change.

Two econometric problems arise in using this test as planned.
First, the Granger direct test was designed to test whether the addition
of a variable helps in the prediction of another. If it does, the first
variable causes, in the sense of Granger, the other variable. Using
only two variables and their past values was not the intent of the test
and may bias the results. Second, since past values of the dependent
and independent variables are in the same equation, multicollinearity
will be present and any results obtained cannot be tested with a high
degree of precision, since the variances of the estimates will be
large. Because of these problems, the results of the tests should be
viewed with caution and skepticism. However, as a preliminary means of
answering the question, the use of the test is better than assuming the
problem away as previous studies have done.

As in the Haugh test, series for U1 taxes, UI benefits and
seasonally-unadjusted GNP are used. (See pages 11 and 12 for a list of
these series.) Again, the series must be covariance-stationary, but the
use of arbitrary filters (and seasonally-adjusted data) distorts the
results.ll! The first difference of the natural logs of the values will

be used as the stationary series. Two tests (sets of regression

l9

equations) were run, NSAGNP on past NSAGNP and past UI taxes, and NSAGNP
on past NSAGNP and past UI benefits. Four specifications are used for
each test. They are: six lagged values for both variables; six lagged
independent variables and four lagged dependent variables; four lagged
independent variables and six lagged dependent variables; and four
lagged values of both variables. Table 2-4 summarizes the results of
the test.

UI Taxes and NSAGNP

 

No causal relationship was found for any of the specifications of
this test. This is not surprising in light of the multicollinearity
problem discussed above, and the eXperience rating discussed in Section
2.2. This result is supported by (and supports) previous studies which
have shown UI taxes to be a weak stabilizing factor. Therefore, any
effect on NSAGNP should be negligible.

UI Benefits and NSAGNP

 

All specifications of this test were found to be significant. As
shown in Table 2-5, the largest coefficient is found on the T_1 lag of
UIB, with the expected negative sign. The other coefficients of lagged
UI benefits oscillate in sign and move toward zero in absolute value.
One may conclude that the largest effect on NSAGNP from UIB occurs
within two Quarters. Multicollinearity in the equations makes such a

conclusion imprecise, although the results are promising.

20

TABLE 2-4

RESULTS OF THE

GRANGER DIRECT TEST

 

 

A) UIT - GNP

 

 

Specification Number of Quarters Lagged F Value
1 GNP 6 UIT 6 .704
2 GNP 4 UIT 6 1.06
3 GNP 6 UIT 4 .834
4 GNP 4 UIT 4 1.21

B) UIB - GNP

 

 

Specification Number of Quarters Lagged F Value
1 GNP 6 UIB 6 4.46
2 GNP 4 UIB 6 5.84
3 GNP 6 UIB 4 5.84
4 GNP 4 UIB 4 7.18

 

Critical value of F at .05 level of significance:

F 2.47

4,90

F 2.21

6,90

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22

2.4 Conclusion

 

The results found in this chapter do not contradict those found
by others. However, I have examined the issues of whether changes in UI
benefits and UI taxes depend on changes in GNP, and the timing and
length of the feedback impact of the UI program, by using tests designed
to check for the independence and for a causal relationship of two
variables. The use of these tests is superior to the practice of
ignoring these issues by assuming them away, as was the case in previous
studies.

The Haugh test for independence of two series was used in Section
2.2 to show that both UI benefits and UI taxes are dependent on
seasonally-unadjusted GNP. The Granger direct test was used in Section
2.3 to determine if the direction of causation also runs from UI
benefits and UI taxes back to seasonally-unadjusted GNP. The results
from this section show the direction of causation to run only from GNP
to UI taxes, while there is some evidence of a feedback effect on GNP
from U1 benefits.

On the basis of these tests, I conclude that the assumptions made
in previous studies concerning the contemporaneous reaction of the UI
program to income changes, and the contemporaneous feedback from the UI
program to income, are essentially correct. The Haugh test shows UI
taxes may not react contemporaneously to income changes, while the
Granger direct test shows the feedback from UI taxes to GNP is
negligible. The practice of experience rating may be the reason that
these results contradict the assumptions made above. However, for
simplicity, these results are overlooked, and the above assumptions are

made throughout the remainder of this study.

CHAPTER TWO
NOTES

l/As a result of these requirements, automatic stabilizers automatically

 

increase the size of the government's deficit during recessions. A
larger deficit leads to more aggregate spending above what it would be
in a world without automatic stabilizers. This extra aggregate spending
is not a requirement but rather a side effect, or the result of
automatic stabilizers.

ZjThe major studies that this study evolves from and which this study
corrects, refines and expands are: Hart (1954); Clement (1960); Lewis
(1962); Eilbott (1966); Rejda (1966); Thirlwall (1969); Hansen and
Burroughs (1969); and von Furstenburg (1976).

éjFor example, see Hart (1954).
i/Rejda (1966), pp. 202-208.

.éijo other reasons may add to the destabilizing tendency of U1 taxes.
First, taxes are collected and reported with a lag so the reaction of
collections to income changes may occur with a lag. Second, taxes are
collected on only part of a firm's payroll, much like the Social
Security (F.I.C.A.) tax. Tax collections may fall at year's end because
of this and not any income change.

éjThis test is discussed in Haugh (1976).
Z/Haugh, pp. 377—378.
E/See Box and Jenkins (1970).

g/Haugh, has an example of this on pp. 383-384.
i2/This test was first discussed in Granger (1969).
1.1../Fiege and Pearce (1979) pp. 527-530, give examples why seasonally

adjusted data and arbitrary filtering process distort the results of
causality test.

23

CHAPTER THREE

THE EFFECTIVENESS OF THE UI PROGRAM AS AN AUTOMATIC STABILIZER IN

RECESSION AND RECOVERY

3.1 Introduction

 

The measured effectiveness of the UI program in five post-war
recessions is calculated in this chapter. Section 3.2 discusses the
meaning of measured effectiveness and what is meant by the phrase
stabilization effectiveness in this research, and presents a modest
survey of previous literature on the stabilization effectiveness of the
UI program in recession and recovery. In Section 3.3, I incorporate a
minor modification into this measure of effectiveness that produces a
significantly smaller result than previous studies. The impact of
several discretionary temporary extended benefits programs on measured
effectiveness is estimated in Section 3.4. Also in this section, I
present and analyze the measures of effectiveness of the U1 program
calculated in this chapter for five post-war recession/recovery periods.

The minor correction incorporated in Section 3.3 reduces measured
effectiveness in recession nearly fifty percent. It also makes measured
effectiveness nearly symmetric across recession and recovery which is
not the case in other studies. Not surprisingly, the impact of every

discretionary temporary extended benefits program is found to detract

24

25

from measured effectiveness. Comparing the five measures of
effectiveness reveals that the UI program has maintained a consistent

pattern of effectiveness throughout the period.

3.2 The Concgpt of Measured Effectiveness

 

One of the many goals of the UI program is to help reduce the
volatility of the U.S. economyel/ During periods of declining aggregate
demand more individuals begin receiving UI benefits, while UI taxes
collected from employers fall as workers are laid off and firms'
payrolls decline. Both these actions help slow the decline in
income. The first helps the unemployed maintain their purchasing
power, which prevents a drastic cutback in consumption. The second
action reduces firm's expensesgf, which increases profits (reduces
losses), and thus theoretically reduces their cutback in investment.
Since consumption and investment fall less than they would in the
absence of the U1 program, stability of aggregate demand is achieved.
Conversely, in an expansion, fewer workers receive UI benefits, causing
total benefits to fall, while UI taxes increase as employment rises.
These actions slow the growth of aggregate demand during expansions,
which keeps the economy from entering a period of excess aggregate
demand and higher inflation.

The impact of the UI program can be shown both algebraically and
graphically, as in Figure 3.1. Consider the simple aggregate demand

model represented by equations 3.1 through 3.6:

26

IS*

13*
new

 

 

 

IS
FC-fl I ISnew
i |I>Bv|
r-AH
2 1 O

y y

FIGURE 3.1

IS-LM REPRESENTATION OF MEASURED EFFECTIVENESS

27

(3-1) y

(3.2) c

c + i + g

a + b(y-t)
(3.3) i = d - er + fy
(3-4) s = 8*
(3.5) t = t*
(3.6) r = r*
where y is national income;
c is personal consumption expenditures;
1 is net investment;
g is government purchases;
t is personal taxes;
r is a nominal interest rate;
a,b,d,e,f are positive coefficients; and
all variables are in constant dollars.
For simplicity I have taken the money sector as given, represented by a
fixed interest rate (3.6). The equation of the IS curve in Figure 3.1

is found by simple algebra to be:

(3-7) r* = (a + d + g* - bt*)/e - ((1-b-f)/e)y.

The slope of the IS curve is -(l-b-f)/e, which is negative.
In a world with the UI program, I replace equation (3.2) with

(3.2*), and add equation (3.8) to the model,

(3.2*) c a + b(y-t+ui)

(3.8) ui u - zy

28

where
ui is UI benefits paid; and
u and z are positive coefficients.

The equation of the 18* curve is given by (3.7*),

(3.7*) r* = (a+d+bu+g*-bt*)/e - ((1-b-f+bz)/e)y.

The slope of the 18* curve is ((l-t3-f+bz)/e). Comparing the lepes of
the two curves, one can see the slope of I8* is larger in absolute
value, meaning it has a steeper SIOpe than 18. (See Figure 3.1.)
Automatic stabilizers increase the absolute value of the lepe of the IS
curve relative to an 18 curve without automatic stabilizers.

Suppose we decrease government purchases from g* to g**. This
reduces the r-intercept term in both equations (3.7) and (3.7*), which
causes both the IS and 18* curves to shift downward by an equal

amount. The new curves are ISne and 18*new in Figure 3.1.

w
Measured effectiveness is the amount of a potential change in
income that is prevented by the UI program. This can be seen
graphically in Figure 3.1. Without the UI program, income falls to y2,
or the distance A. This distance is given by the impact multiplier of
the IS curve, (l-f-b)-1, times the change in g. With the UI program in

the model, income falls only to y1

, or the distance B. This distance is
given by the impact multiplier of the 18* curve, (l-f-b+bz)-1, times the
change in g. The UI program decreases the impact multiplier of an IS
curve relative to an 18 curve without the program. The difference y1-
y2, or the distance C, is the amount of a potential change in income

that is prevented by the UI program. The custom has been to represent

29

measured effectiveness as the percent of a further change in income
prevented by the UI program. This is given by C/A (=A-B)/A). Noting
that A and B represent impact multipliers times the change in government
purchases, measured effectiveness is nothing more than one minus the
ratio of the impact multiplier of the 18* curve to the impact multiplier
of the IS curve.

In this research, the measure of stabilization effectiveness is
taken to be the amount of a potential change in income that is prevented
by the UI program. The larger the decrease in volatility of the
economy, the larger will be the measured effectiveness of the program.

I assume the UI program meets the goal of stabilizing by smooothing
changes in income. This is how other studies measured the
effectiveness of the program. Income is but one of many economic
variables that can he used to measure the stabilization effectiveness of
the program. One likely candidate is total employment (or unemployment).
Increasing U1 benefits when employment falls will help the unemployed
maintain their spending. This will keep inventories from building up,
and employers will call back laid-off workers, increasing employment.

As employment increases, UI benefits will fall. The UI program will
help prevent further changes in unemployment. Another likely candidate
is the gap between actual and potential GNP. As the gap widens, UI
benefits increase. This helps maintain spending (income) and prevents a
further widening of the gap. Notice in both cases, it is the
maintenance and/or change in spending that helps maintain or changes
income. The increase in income is evident in the increase in

employment and the decrease in the gap, although simultaneous increases

in all these variables are not evident. It is because of this

30

relationship between the maintenance and/or change in income and the
associated change in the UI program that I measure the effectiveness of
the program with respect to income.

The technique to determine how much of a potential change in
income that is prevented by automatic stabilizers was introduced by
Musgrave and Milleregf Clementéj used this approach to measure the
impact of all automatic stabilizers in the recession/recovery periods of
1949, 1954 and 1957. He found UI benefits to be a strong
countercyclical force in recessions, preventing up to thirty-five
percent of a further change in national income. However, UI taxes in
both recession and recovery, and UI benfits in recovery were found to be
very weak countercyclical forces. Rejda2/, using the same methodology,
but extending the analysis to the 1960-1961 recession/recovery, also
found UI benefits to be an excellent stabilizing force in recessions.
Like Clement, he found UI taxes, in general, and UI benefits in
recoveries to help little to stabilize the economy.

There is a question as to what is meant by stabilization
effectiveness in recovery. Automatic stabilizers should help prevent
further changes in income. Therefore, during recovery or other periods
of increasing income, automatic stabilizers should be retarding the
increase in income. In a sense, they are keeping the economy from
reaching a level of full employment income as quickly as would be the
case in a world without them. The path from trough to full employment
cannot be determined in the static model used in this research. I
assume the UI program meets the goal of stability during recovery by
retarding the growth of income. Small measures of effectiveness in

recoveries suggest that the UI program is not helping to retard the

31

increase in income. This may be a desired result if the economy is far
from full employment. However, this may lead to excess demand if the
economy is near full employment. As above, this cannot be determined in
a static model. In recession as well as recovery, the measure of
stabilization effectiveness is measured by the amount of a change in
income is prevented, i.e., by smoothing the changes in income.

Eilbottél modified the Musgrave and Miller technique slightly.
He allowed for a specific transfer payment variable in the consumption
function (equation 3.2*), and separated the corporate and household
sectors for tax and spending considerations. His measured effectiveness
(ME) is given by equation (3.9) which is modified for U1 program only,

instead of all automatic stabilizers.

-C(EBB)+i(ETT)

_ _ _ 3
1 CK iZ CEBB+iETT

(3.9) ME =

 

where
c is the marginal propensity to consume out of disposable income;
EB is the income elasticity of U1 benefits;
B is the ratio of U1 benefits to national income at the beginning
of the period of analysis;
1 is the marginal propensity to invest out of corporate profits
after tax;
ET is the income elasticity of U1 taxes;
T is the ratio of U1 taxes to national income;
X is the share of a change in national income to the household
sector;

2 is the share of a change in national income to the corporate

32

sector, X + Z = 1; and

MB is the measured effectiveness of the UI program.
2 is derived by relating the change in pretax undistributed profits to
the change in national income during each period analyzed.

Equation (3.9) is shown in Appendix B to be one minus the ratio
of two different 18 impact multipliers, one without the UI program, the
other with the UI program in the model. The implied model behind the
equation is also discussed in Appendix B. Using this equation, I
recalculate measured effectiveness to be only in the neighborhood of
twelve to eighteen percent in recessions, and less than five percent in
recoveries, depending on assumed values of C and 1.1! It is interesting
to note that the stabilization effectiveness of U1 taxes is actually
negative (or destabilizing) for some recessions in Eilbott's study, as
in Clement's study. The recalculated stabilization effectiveness of U1
benefits ranges from thirteen to twenty percent in recessions, and less
than five percent in recoveries, again depending on C and i.

There are two troublesome aspects about the measures of
effectiveness found in these studies. First, each study found a very
small or destabilizing impact of U1 taxes on the economy. The
discussion in Chapter II on experience rating shows that although a
destabilizing impact is theoretically possible, it should be the case
that the measured effectiveness of U1 taxes be no worse than neutral.
Second, each study shows the UI program, specifically UI benefits, to be
a strong countercyclical force in recession, but not in recovery.
Theoretically (and intuitively) the UI program should have a more
symmetrical countercyclical effect to be a useful automatic stabilizer

to reduce the volatility in the economy. In Section 3.3, I incorporate

33

some minor modifications to equation (3.9) to help solve these problems.

3.3 Modifying the Measured Effectiveness Equation

 

The first modification incorporated into equation (3.9) accounts
for the fact that an extra dollar of U1 benefits and an extra dollar of
other income are not consumed at the same rate. Hamermesh (l982)§!
tries to explain this behavior by showing some UI benefit recipients are
constrained from borrowing and spend all their income (including UI
benefits) in an effort to maintain consumption. Aggregating over all UI
recipients results in a larger marginal prOpensity to consume out of UI
income than non-UI income. He finds about one half of the UI recipients
behave as if they are constrained and spend all their disposable
income.2/

The first modification is to include two marginal propensity to
consume parameters in equation (3.9), one for U1 benefits, the other for
the household's share of income changes. Let Cl represent the marginal
propensity to consume out of non-UI income, and C2 be the marginal
prOpensity to consume out of U1 income. I will assume the fraction of
the UI recipients constrained is one half, thus C2 equals .5C1 + .5-
This assumes half the UI recipients spend all their UI-income, and the
other half treat UI income just like non-U1 income. Measured

effectiveness is now given by

-c E B+iE T
(3'9*) ME = l-c Xiig-c ETB+iE T '
1 23 T

 

The second modification takes into account the trend or growth

34

over time of income, UI profits and UI taxes in calculating the
elasticities in (3.9*). The approach is similar to that used by
Thirlwallin studying unemployment compensation in England. Instead of
measuring the stabilization effectiveness of the UI program as the
percent of a potential change in the level of income, this approach
measures the stabilization effectiveness of the program as the percent
of a potential change from the growth trend of income. This assumes the
UI program responds to deviations from the growth of income rather than
absolute changes. If this is the case, calculating the elasticities
needed in (3.9*) will bias the measure of effectiveness. The amount and
direction of the bias depends on the deviation of income from its trend.
Assume that the UI program is such that it is consistent with a
growth of five percent in income per period and the associated growth of
all other economic variables at five percent income growth, such as the
rate of growth of employment and the rate of change of the gap between
actual and potential GNP. A growth of income of three percent this
period will cause changes in the UI program, with 01 benefits increasing
and UI taxes falling. Theory would suggest an increase in UI benefits
and a decrease in UI taxes if income falls. Using absolute changes in
the variables would cause a destabilizing result, as income is
increasing while benefits increase and taxes decrease. If income falls
absolutely, deviating from its trend by more than the assumed average
growth of five percent, the method for calculating the elasticities
needed for (3.9*) using absolute changes correctly shows stabilization
effectiveness. However, the estimated measure of stabilization
effectiveness is biased upward. A small absolute change in income is

associated with larger changes in the 01 program. Since it is assumed

35

the UI program is set for an economy growing at five percent per period,
a decrease in income causes the program to react vigorously. The
calculated elasticities are large, yielding a large estimate of the
measured effectiveness of the program.

The large changes in the UI program should be paired with a large
change in income. It has fallen by more than five percent from its
assumed average growth. Using a method to calculate the elasticities
needed in (3.9*) that uses deviations-from-trends instead of absolute
changes results in a smaller estimate of the measured effectiveness of
the program in recession. In recovery, as income increases faster than
its average growth trend, this deviation method results in larger
estimates of the measured effectiveness of the program than the absolute
method. The UI program is assumed to react only to the increase in
income over its average growth. Then deviation method yields smaller
calculated elasticities than those obtained with the absolute method.
Notice the deviation method smoothes the estimates of the measured
effectiveness of the program over recession and recovery compared to the
asymmetric estimates obtained using the absoute method.

All previous U.S. studies used the absolute method to calculate
the elasticities needed in their versions of (3.9*). This is the reason
they found very high measures of effectiveness in recession and very low
measures of effectiveness in recovery. The deviation method provides a
more accurate estimate of the UI program over recession and recovery.
'Fhe measures of effectiveness shown in the next section are estimated
using the correct deviation method. The simple time trends of U1
benefits, UI taxes and national income are obtained by regressing each

(of those variables on time over a period (in most cases, forty quarters)

36

prior to the peak quarter of each recession/recovery period.hl/ Using

these estimates, calculations can be made to show what these variables
would have been if they had grown at their trend value from the peak
quarter rather than deviated. The estimated coefficients for each
variable are shown in Table 3-1. The estimated value of TIME in each
equation is added to the peak quarter value of the dependent variable
for each quarter the recession (or recovery) lasts. These trend values
are then compared with the actual values of the variable over the

period.

3.4 Empirical Estimates of the Measured Effectiveness of the UI Program

in Recession and Recovery

 

The recession/recovery periods selected to be analyzed are
defined by turning points (peak, trough) as established by the National
Bureau of Economic Research.h£/ In all cases recessions are analyzed
first, then periods of similar length directly after the trough quarter
are analyzed as the recovery periods. It should be noted that these
recovery periods are of arbitrary length and do not conform to the
expansion periods established by the NBER. Reasons for selecting these
periods as recoveries will be explained as part of the discussion of the
results from those periods as well as in the conclusion of this chapter.

The data sources used in estimating the measured effectiveness of
the UI program can be found in Appendix A. UI taxes are the same series
\ased in Chapter II. UI benefits include any relevant discretionary

temporary extended benefits programs. To be comparable to other studies

and to begin the notion of calculating measured effectiveness in

I37

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38

relation to aggregate demand, national income is selected as the income
variable. The rest of the variables used in the estimation of measured
effectiveness are: Consumption-personal consumption expenditures;
Investment-~net private non-residential domestic fixed investment;
Corporate profits after tax; Corporate profits before tax, including
inventory valuation adjustment and capital consumption allowance;
Undistributed corporate profits; Disposable personal income; and the
Three-month Treasury bill rate as a proxy for consumer credit
conditions. All the dollar-valued variables are converted to constant
1972 dollars using the national income deflator.

Instead of selecting C1, C2, and i from a range of values as
Eilbottléj, I estimate these parameters. The values are dynamic
prOpensitieshi/ which can be used for quarter-by-quarter as well as
overall period analysis. As is the case for the trend estimates of U1
taxes, UI benefits, and national income, a forty quarter period up to
the peak quarter is used (when possible) as the period over which the
marginal propensities are estimated. These figures are then assumed to

be the same throughout the recession and corresponding recovery.

The equations used are:

(3.10) Ct = Co + C1 DPY + C2 [(TBRt+TBRt_1+TBRt_2)/3]

+ C3 Ct-l

(3-11) NIt = 10 + iICPATX + i2[(TBRt+TBRt-1+TBRt_2)/3]

+ 13 NIt-l

where

39

Ct is consumption;

DPYt is disposable personal income minus UI benefits;

TBRt is this period's three-month Treasury bill rate;

Ct-l is lagged consumption;

NIt is net investment;

CPATXt is corporate profits after tax; and,

NIt_1 is lagged net investment.
To estimate these equations, a two-stage process, similar to that
suggested by Johnstonlél is performed since ordinary least squares (OLS)
is inefficient and may have simultaneous equations bias. This procedure
is used to correct for autocorrelation caused by the lagged dependent
variables in the equations. The error terms of the equations are
assumed to be of the form Vt = pvt_1 + et, with p less than one in
absolute value, and et assumed to be NID(O, 0 e2). This method amounts
to doing 0L8 twice, once to get an estimate for p , then again on an
equation involving p -transformed variables in each equation. This
process continues iteratively until p converges within some specified
value. This procedure is a maximum likelihood technique used to
estimate equations with errors of the form assumed above.¥é/

Before analyzing Specific recession/recovery periods, I estimate
the long-run or average measured effectiveness of the UI program from
1955 to 1980. For this measure, I can estimate the average
elasticities needed for the measure of effectiveness. This cannot be
done in Specific recession/recovery periods due to a lack of
«observations. The equations relating UI taxes and UI benefits to income

are log-linear, not only to estimate these elasticities, but also to

:rvoid the problem of growth over time. Table 3.2 summarizes the

4C)

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41

estimates of the elasticity equations as well as the other results of
the process to estimate measured effectiveness. The estimates of C1 and
i are the dynamic (long-run) values of these parameters. They are
obtained by multiplying the estimated values by the inverse of one minus
the estimated coefficient of the lagged variable.hl/

The results conform to previous studies, in that most of the
effectiveness is due to UI benefits. The average effectiveness of the
UI program is about that found by Eilbott and Lewis for averages of
specific recessions.h§/ However, a better test for the accuracy of the
measured effectiveness equation is to look at specific recessions and
recoveries to see how it holds up to other studies in a direct

comparision.

The Recession of 1957-1958

 

Table 3-3 and Figure 3.2 summarize the estimates of measured
effectiveness in this recession. The deviation method elasticities are
calculated using the estimated time trend values for this period shown
in Table 3-1. Deviations from the estimated trend values rather than
absolute changes in the apprOpriate values are used in the calculation
of these elasticities. For illustrative reasons, the absolute and
deviation-from-trend methods of estimating measured effectiveness are
compared in Table 3-3 for this recession only. Two important points
arise from the results. The first is the considerable difference
between the absolute and deviation methods. The results from the
absolute method are nearly twice as large for the overall and U1 benefit
effectiveness, and have the wrong sign (destabilizing) for U1 tax
effectiveness compared to the more accurate deviation method. These

results illustrate the bias inherent in the absolute method. The

42

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MEASURED EFFECTIVENESS

43

 

 

157.1

107.?

57..0

.7. ,_.._...,- ..... «A 41“,.“ M ,. .1
t+l t+2 t+3 t+4 t+5 t+6 t+7

 

T IME I N QUARTERS

 

__ Overall Program, Without TUC
-—--—- Overall Program, With TUC

----- UI Benefits Only, With TUC
UI Benefits Only, With TUC

, ..... .. U1 Taxes Only
FIGURE 3.2

QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, 1957:III-1959:11

44

effectiveness measures calculated by the absolute method for all
subsequent recessions have the same bias problem as for this

recession. Consequently, the results of the absolute method will not be
given for the remaining recessions.

The second important point is the estimates of measured
effectiveness obtained using the deviation method. About 11.5 percent
of a potential change in income is prevented. Almost all of the
effectiveness is credited to UI benefits, which confirms the hypothesis
that the effectiveness of U1 taxes is very small. Putting this measure
in dollar terms, with a $20 billion actual change in real income, the
measure indicates that the UI program prevented an additional decline in
real income of about $2.3 billion.

The recovery period, 1958:11-1959:II, is analyzed next to see how
the measure stands up in a recovery. Beginning in 1958:II and lasting
over the duration of the recovery, the first discretionary temporary
extended benefits program was in effect. This program, enacted under
the Temporary Unemployment Compensation (TUC) Act of 1958, provided for
additional benefits for up to half (13 weeks) of the regular benefit
duration to individuals who had exhausted their regular benefits. The
program was voluntary and only 22 states adapted this or their own
extended benefits program.12/ The discretionary nature of this program
brought about bad timing from a countercyclical point of view, since the
program did not begin until the recovery had started. When these
extended benefits are added to the regular benefits, the 01 program
becomes less effective at stabilizing the economy. See Table 3-4 and
Figure 3-2.

Previous studies showed that during recoveries measured

45

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46

effectiveness of the UI program was smaller compared to that during
recessions.22/ This may be due to their use of absolute changes in
estimating measured effectiveness. Another possible explanation is that
employment lags the business cycle; thus in the early stages of a
recovery unemployment may be high, keeping UI benefits up and UI taxes
down. Since these studies only calculated an average total measured
effectiveness for the period in question, the early tendency toward
destabilization may have reduced the equivalent of ME.

Two effective measures are calculated, one excluding extended
benefits paid under TUC, the other including these benefits. The
marginal propensity figures are assumed to be the same as in the
recession, but the elasticity and ratio figures are recalculated. The
estimates of the time trends necessary to recalculate the elasticities
are shown in Table 3-1. Two points can be made about the results.
First, because of the limited acceptance of TUC, there is little
difference in the measures. Second, the measures are larger than the
measures for the recession, counter to the results obtained in previous
studies. This is directly attributable to the use of the correct
deviation method to estimate measured effectiveness.

The quarter-by-quarter results (Table 3-5) show how measured
effectiveness changes each quarter. For example, the t+1 period shows
measured effectiveness after one quarter of the recession, computed with
the prOper dynamic propensities, ratios, and elasticities. The t+3
period represents measured effectiveness after the first quarter of the
recovery. Finally, the t+7 period represents measured effectiveness

over the entire recovery. These are the results found in Table 3-4.

The estimates values of C1, C2 and i shown in Table 3-5 are the

47

TABLE 3-5

QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, 1957:III - 1959:11

———-—

 

 

 

Parameters Period

t+1 t+2 t+3 t+4 t+5 t+6 t+7
C1 .396 .537 .649 .396 .537 .649 .739
C2 .698 .767 .825 .698 .767 .825 .87
i .21 .26 .29 .21 .26 .29 .31
X .62 .56 .56 .71 .72 .66 .58
Z .38 .44 .44 .29 .28 .34 .42
T .005 .005 .005 .0036 .0036 .0036 .0036
ET 1.2 1.1 .80 -1.15 .45 —.03 4.8
B .004 .004 .004 .0092 .0092 .0092 .0092
B (with TUC) .01 .01 .Ol .01
EB -8.9 -25.1 -19.6 -15.9 —12.9 -4.3 -lO.3
Program Measured Effectiveness

t+1 t+2 t+3 t+4 t+5 t+6 t+7
Overall Program
Without TUC 3.73% 12.0% 11.45% 13.332 14.48% 6.13% 15.85%
With TUC .191 5.32% 2.212 15.60%
UI Benefits Only
Without TUC 3.552 11.82 11.27% 13.432 14.432 6.14% 15.13%
With TUC .322 5.25% 2.22% 14.82%
U1 Taxes Only .191 .241 .232 -.l3Z .082 -.012 1.17%

Recession Recovery

 

NOTES: (1) C1 and i are dynamic multipliers estimated from the regression
equations found in Table 3—3. C2 is calculated using the formula,

C2 ' .5 + .5(C1).
(2) See note 3, Table 3—4.

(3) A.minus sign on measured effectiveness indicates destabilization.

48

cumulative effects of the dynamic propensities estimated using equations
(3.10) and (3.11). The cumulative effect (CE) for C1 is given by
x

X
.2 (c1><c3> .
1=O

(3.12) CE

where C1 and C3 are given in equation (3.10). The cumulative figures
attempt to represent the dynamic response to a change in the program
over the period. I assume the estimates remain constant over the entire
recession/recovery but analyze each recession and recovery separately.
This is why the cumulative effects for the first quarters of each period
are equal. The ratios and elasticities are calculated each quarter by
the processes described in Section 3.3, and from the estimates in Table
3-1. Measured effectiveness is calculated each quarter with the proper
values of the propensities, ratios and elasticities given in the upper
half of Table 3-5.

The quarter-by-quarter results indicate measured effectiveness is
not consistent throughout the period, reflecting the fact that the
movements in income were not consistent over the business cycle. This
can be seen graphically in Figure 3.2. Note that the measured effective—
ness of UT taxes is close to zero until the last quarter of the recovery.
This is not surprising, considering the practice of experience rating
discussed in the previous chapter. 01 taxes added to measured
effectiveness only well after the recovery was underway, when
unemployment began to fall from its (higher) recessionary level.

The results also show that measured effectiveness of the UI
program including TUC is very small until the last quarter of the

recovery period. By this quarter the program had all but run its

49

course. Benefits also fell significantly as unemployment drOpped. The
result was a marked rise in measured effectiveness in the quarter. The
impact of this program on measured effectiveness is overlooked if one
only considers the results for the entire period.

The Recession of 1960-1961

This recession was not so severe as the previous one, and both
are considered mild compared to more recent recessions. More employees
were covered by the UI program and benefit duration had been increased
in some states, both of which led to a larger amount of benefits paid in
this period relative to the first. Table 3-6 and Figure 3.3 summarize
the estimates of measured effectiveness in this recession. The
calculated elasticities are obtained using the estimated time trend
values for this period shown in Table 3-1, and the deviation method
described earlier. Over twenty-five percent of a potential change in
income was prevented by the UI program in this recession, but since the
actual change in income was around five billion dollars, the dollar
effectiveness was less than the 1957-1958 recession.

Another discretionary temporary-extended benefits program began
as the recovery started. This program was enacted in the Temporary
Extended Unemployment Compensation (TEUC) Act of 1961. The program was
essentially the same as TUC of 1958, except that it was mandatory that
all states adopt it. Table 3-7 and Figure 3.3 summarize the estimates
of measured effectiveness in this recovery.

Two effectiveness measures are again calculated, one excluding
extended benefits paid under TEUC, the other including these benefits.
The measures are almost identical since the program was not large, and

by March 1962, few people were still eligible for the benefits, either

50

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N.NH- u as Neco. u N ON. n x NNN. n ANqu. + N. H No
NNNNN2<N<N ems<ssos<o
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no Nun . u.
eN NNN. NNN. N Hz No.1.N\A ”:2. w v SN...xs<eo NN. + em.N u Hz AAANe.vaNN.V W "V eNN. u A
N . N
Nos.NV NNN.NV IAANN.N-V ASN.NVANN.NV IA
H-e N z.6 0-. on. N
eN NNN. sNN. o 36.1. \A NNN w V em...Neo NN. + ON.NN u u Aere.VANN.V w "V NAN. u u
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2 Ne e Nzoosasos zoNNNNeomm Nemsmz<mee ame<zNNNm

 

II. ll..|l.l 1*

Huaooa I HHuoomH ZOHmmmUmm .mwmzm>HHummmm Dmmam<mz

cum m4m<e

MEASURED EFFECTIVENESS

252 4

U"
N

51

 

 

t+1 t+2 t+3 t+4 t+5 t+6

TIME IN QUARTERS

 

t+7

 

-—— Overall Program, Without TEUC
’--’ Overall Program, With TEUC

----- U1 Benefits Only, Without TEUC

......... U1 Benefits Only, With TEUC

6.-....“ UI Taxes Only
FIGURE 3.3

QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, 1960:II-1962:I

52

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Rim m4m<H

53

because their benefits had been exhausted or they had returned to
work. As with TUC, the UI program (especially UI benefits) was less
effective with TEUC during the recovery.

Unlike the last recession/recovery period measured effectiveness
of the overall UI program is almost identical in the recovery as it was
in the recession. The composition of effectiveness changes, as
expected, with UI tax measured effectiveness higher, and UI benefit
measured effectiveness lower in recovery than recession, as is the case

in all other studies. However, UI tax measured effectiveness is

surprisingly large (7.3%), which is higher than in any previous

2
study.-2/

The quarter-by-quarter results for the entire recession/recovery
period are listed in Table 3-8 and shown in Figure 3.3. There are three
points to be made about the results. First, except for the first
quarter of the recovery, the measured effectiveness of the UI program is
only slightly lower when considering TEUC compared to that of regular
benefits only. Unlike the previous recovery, the temporary extended
benefits program in this recovery did not have much of an impact on
measured effectiveness. Second, benefits actually declined during the
first quarter of the recession indicating the mildness of this recession
and the difficulty in establishing turning points. Third, UI tax-
measured effectiveness may be influenced by a seasonal effect. The last
quarters in the recession and recovery were also the first quarters of
calendar years 1961 and 1962, respectively. UI tax collections are
larger in the first quarter of a year, as taxes are collected as a
percentage of the firm's payroll up to a maximum amount of wages per

employee. Since few, if any, employees covered by the UI program reach

QUARTER-BY-QUARTER MEASURED EFFECTIVENESS,

54

TABLE 3-8

1960:II - 1962:I

 

 

 

Parameters Period

t+l t+2 t+3 t+4 n+5 t+6 t+7
C1 .528 .647 .718 .528 .647 .718 .761
C2 .764 .823 .859 .764 .823 .859 .88
i .518 .64 .716 .518 .64 .716 .763
X .334 .597 .50 .599 .692 .745 .641
Z .667 .403 .50 .401 .308 .255 .359
T .008 .008 .008 .008 .008 .008 .008
ET 5.2 2.6 .5 8.2 2.1 .84 3.3
B .0065 .0065 .0065 .0093 .0093 .0093 .0093
B (with TEUC) .011 .011 .01] .011
EB 8.3 -1.9 ~18.1 -22.1 —28.7 ~14.4 ~8.l
EB (with TEUC) ~10.3 22.5 -11.9 -5.6
Program Measured Effectiveness -~“H” -- 7
Overall Program
Without TEUC -4.29% 6.15% 26.0% 28.61% 38.6% 29.09% 26 05%
With TEUC 20.19% 37.0% 28.57% 23.23%
UI Benefits Only
Without TEUC -9.43% 2.75% 25.6% 24.78% 37.5% 28.25% 21 22%
With TEUC 15.37% 35.8% 27.97% 18.01%
UI Taxes Only 4.31% 3.59% .99% 6.65% 2.86% 1.63% 7.30%

Recession Recovery

 

NOTES: (1)
(2)

(3)

See note 1, Table 3—5.
See note 3, Table 3—7.
A minus sign on measured effectiveness indicates destabilization.

55

their maximum limit in the first quarter, the entire covered payroll is
taxed. As the year goes on and workers reach their maximum taxable
limit, tax collections fall short of the first quarter's tax
collections. Therefore, tax collections are higher in the first quarter
than any other quarter, and far exceed the tax collections in the third
and fourth quarters. In the recession, as income fell in 1961:I, UI
taxes showed an upward movement due to this institutional seasonal
effect. This lowered UI taxes effectiveness in the last quarter of the
recession. Conversely, in 1962:I, not only did an increase in
employment cause UI taxes to increase, but this seasonal effect caused
UI taxes to rise further, enhancing the measured effectiveness of U1
taxes in the quarter.

The Recession of 1969-1970

 

This recession was more prolonged than the previous two
recessions, although it was not as deep as the 1957-1958 recession in
terms of the actual or percentage decline in income. All but one of the
previous studies were done prior to 1969, so no direct comparisons of
the results in this study can be made. However, one can compare the
measures between periods to see if the UI program has achieved its
stability goal as well as in previous recessions. This recession marked
for the first time a decline in national income with (considered then)
serious inflationary problems, which might affect the measure if constant
dollar values were not used. Table 3-9 and Figure 3.4 summarize the
results for this period. The calculated elasticities are obtained using
the estimated time trend values for this period shown in Table 3-1, and
the deviation method described earlier. For both the measured

effectiveness of U1 benefits and UI taxes, typical results are obtained

56

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MEASURED EFFECTIVENESS

57

 

 

20%

15%

10%”

57;. 3 .

/ \\
\ /"/\ '
OZ - ' A r/ ‘xx ‘ I ‘
‘\. ,,- , I
v . ‘ \o.
-5%» t+l t+2 t+3 t+4 t+5 t+6 t+7
TIME IN QUARTERS

 

 

-—-—- Overall Program, Without EB
-—- Overall Program, With BB

.H...- 01 Benefits Only, Without EB
.."”.H. UI Benefits Only, With EB

........ UI Taxes Only
FIGURE 3-4

QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, 1969:IV-1971:1V

58

compared to previous recessions, as most of the effectiveness is due to
UI benefits.

The recovery period is again marked by an extended benefits
program enacted as the recovery had just started. However, this program
became permanent and automatic, unlike the previous extended benefits
programs. The program was part of the Extended Unemployment
Compensation Act of 1970, and began as earlyau30ctober 1970.22! This
bill called for permanent extended benefits (EB) program, with the
benefits to be triggered "on" automatically whenever the insured
employment rate (IUR, the unemployment rate of those workers covered by
the U1 program) for the nation was 4.5% or above for three consecutive
months (later changed).2£/ Table 3-10 and Figure 3.4 summarize the
results for the recovery. Since the EB program is permanent and
automatic, it becomes part of regular benefits, but measured
effectiveness can be found with and without EB as part of U1 benefits to
isolate the impact of the program.

Once again, since this program was essentially started during the
recovery, measured effectiveness with EB included is lower. But the
difference is minor, since less than half of the states complied during
the period. The magnitude of the measured effectiveness of U1 taxes is
as large as 7.6%, and the measured effectiveness of U1 taxes for the
overall recovery is 2.5 times that of the recession. One reason for
this may be the U1 tax part of the EB program. The funding for the EB
program included a 0.1% increase in the FUTA tax and also included a
clause to raise the taxable wage base from the first $3,000 an
individual earns to the first $4,200 the individual earns by January 1,

1972.22! However, some states increased the taxable wage base during

59

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2111.!

 

 

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CHIM mqm<k

60

1971. These changes may be the reason the measured effectiveness of U1
taxes is higher than some previous recessions.

The quarter-by-quarter results for the entire recession/recovery
period are listed in Table 3-11 and shown in Figure 3.4. The recession
results follow the same pattern as previous recessions, with the overall
program measured effectiveness being primarily due to UI benefit
measured effectiveness. The quarter 1970:IV is omitted due to the
changing institutional arrangements. The recovery results show the
effect of the tax increase clearly, and show a remarkably consistent
level of measured effectiveness for U1 benefits (with and without EB)
throughout the period.

The Recession of 1973-1975

 

This recession was by far the worst of the period, in terms of
length and severity. However, the nwasured effectiveness of the
overall U1 program remains about the same as other recessions and
slightly above the average measured effectiveness estimated earlier.
Table 3-12 and Figure 3.5 summarize the results of this recession's
estimated effectiveness measures. The calculated elasticities are
obtained using the estimated time trend values for this period shown in
Table 3-1, and the deviation method described earlier. Note that EB
increased the measured effectiveness of the U1 program by about ten
percent, and Federal Supplemental Benefits (FSB, discussed below), which
began in the trough quarter, increased measured effectiveness another
five percent.

The results for the recovery are listed in Table 3-13 and shown
in Figure 3.5. As in previous periods, another extended benefits

program was enacted during the recession, but not implemented until the

6].

TABLE 3-11

QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, 1969:IV — 1971:1V

 

 

 

 

Parameters Period

t+1 t+2 t+3 t+4 t+5 t+6 t+7
Cl .467 .602 .696 .762 .467 .602 .696
C2 .733 .801 .848 .881 .733 .801 .848
i .496 .642 .746 .82 .496 .642 .746
X .45 .333 .452 .468 .572 .60 .674
Z .55 .667 .548 .532 .428 40 .326
T .005 .005 .005 .005 .0043 .0043 0043
ET 1.7 —2.0 .12 1.0 -6.0 11.5 7.5
B (with BB) .006 .006 .006
EB -40.0 -25.8 —24.0 -l7.l —26.3 -l6.3 -13.8
EB (with EB) -20.8 -15.2 —12.7
Program Measured Effectiveness

t+l t+2 t+3 {1+4 t+5 t+6 t+7
Overall Program
Without EB 15.1% 12.96% 18.0% 15.8% 15.9% 21.88% 18.8%
With EB 13.0% 21.45% 18.1%
U1 Benefits Only
Without EB 14.5% 14.25% 17.9% 14.66% 17.6% 16.48% 16.12%
With EB 14.9% 15.99% 15.35%
U1 Taxes Only .81% -l.75% .16% 1.8% -2.5% 7.6% 4.49%

Recession Recovery

 

NOTES: (1)
(2)

(3)

See note 1, Table 3—5.
See note 3, Table 3-7.
A minus sign on measured effectiveness indicates destabilization.

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63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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MEASURED EFFECTIVENESS

20%

0%

-10%

-15%

-20%

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64

 

 

t+l t+2 t+3 n+4 t+5 t+6 t+7

TIME IN QUARTERS

n+8

 

t+9

 

°—'—" Overall Program, With EB
--- Overall Program, With EB, FSB

-""" U1 Benefits Only, With EB
”““' U1 Benefits Only, With EB, FSB

”— “” U1 Taxes Only
FIGURE 3.5

QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, l973:1V-l976:1

65

very end of the recession and the beginning of the recovery. Actually,
two programs were implemented because of the severity and, more so, the
length of the recession, as many individuals exhausted both their
regular and (permanent) extended benefits. The first program was the
Emergency Unemployment Compensation Act of 1974, referred to as FSB, for
Federal Supplemental Benefits. This program supplemented existing
regular and extended benefit programs by providing additional weeks of
benefits (up to thirteen) to those who had exhausted their benefits
under existing programs because of the high rate of and lengthy
unemployment.z§/

The other extended benefits program was enacted in 1975. It
added to and changed the provisions of the FSB Act of 1974. This act,
The Emergency Compensation and Special Unemployment Assistance Extension
Act of 1975, known as SUA, increased FSB's to twenty-six weeks from
thirteen weeks, and extended coverage to previously uncovered workers.
This program began in the second quarter of 1975.21!

These programs took effect as recovery was beginning, but because
recovery was not rapid, unemployment remained high and these programs
performed their social insurance function. As seen in Table 3-12, the
addition of FSB during the recession increased measured effectiveness
about five percent. Because of the high insured unemployment rate
during the recovery, measured effectiveness was small. The inclusion of
FSB and SUA in U1 benefits (shown as only FSB in Tables 3-13 and 3-14,
and Figure 3.5) caused the measure to indicate that the program had
become very destabilizing. The best results were obtained when the

regular (no EB) benefits were only considered as U1 benefits paid, and

this measure was still below the average measured effectiveness. U1

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66

 

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67

taxes showed a destabilizing effect, because, as unemployment remained
high, tax (mallections did not match the increase in national income.
The quarter-by-quarter results for the entire recession/recovery
period are listed in Table 3-14 and shown in Figure 3.5. The pattern of
measured effectiveness for the recession indicates the recession was
inconsistent. Indeed, in the middle quarters of 1973, real national
income rose slightly then leveled off, somewhat below its pre-recession
peak. As a result of this, measured effectiveness declines in these
quarters. The recovery results show the destabilizing impact of the
temporary benefits programs on measured effectiveness. For the first
time in any period analyzed, the measured effectiveness of U1 taxes was
lower throughout the recovery than the recession. Finally, even though
the percentage of potential change prevented by the U1 program was only
about average for this recession/recovery period, the actual dollar
change prevented was the highest due to the severity of the recession.

The Recession of 1980

 

The most recent recession analyzed in this chapter was is the
shortest of any studied, but, in terms of actual changes in income, it
was more severe than the two earliest recessions studied in this
chapter. The length of the recession may have influenced measured
effectiveness, as it is smaller than that of any recession studied.
Table 3-15 and Figure 3.6 summarize the results of measured
effectiveness in this recession. The calculated elasticities are
obtained using the estimated time trend values for this period shown in
Table 3-1, and the deviation method described earlier. Interestingly,
excluding the automatic extended benefits from the calculations show

that regular benefits declined over much of the period, producing a

68

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as NNN scN. u cNN..+ > V::. w V NNm ..NeaoN + NN N- n u NNNeNN VNmN V W "V Nme u o
N . N
z m n mzoNN<aom zonmNNoNN mememz<m<m NNN<2NNmN

 

 

1 1 1.11.]- 1.1.1.. .11-. I‘.‘
. I ..II :11 1‘1111111111

 

HHHuowoa 1 Huowofi ZOHmmmumm

malm mam<E

I... . -III1 11

 

.mmmzm>HHummhm amm2m<mz

MEASURED EFFECTIVENESS

69

10% ‘

 

 

-5%

 

t+l t+2 t+3 t+4 t+5

TIME IN QUARTERS

 

— Overall Program, Without EB
-——— Overall Program, With EB

-—.—-u- UI Benefits Only, Without EB
......... U1 Benefits Only, With EB

00...... UI Taxes only
FIGURE 3.6

A QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, 1980:I-1981:11

70

destabilizing effect. Including EB produces a small stabilizing effect,
but still the smallest of any recession. The majority of the U1
program's effectiveness stems, surprisingly, from U1 taxes.

The results of the subsequent recovery are more in line with
those of past periods. Higher measured effectiveness is shown during
the recovery than was evident in the recession. The exception to the
pattern is that UI taxes are destabilizing in the recovery, meaning tax
collections fell as income rose. The reason is the insured unemployment
rate did not fall enough in the recovery to lead tax collections to
rise. The results for the recovery are listed in Table 3-16 and shown
in Figure 3.6.

The quarter-by-quarter results for the entire recession/recovery
period are listed in Table 3-17 and shown in Figure 3.6. The first
quarter after the peak saw a sharp decline in national income, but
unlike in past recessions, the U1 program failed to be effective in this
quarter, and, in fact, was destabilizing. This is surprising, since the
decline in income was the largest absolute and percentage decline in any
"first" recession quarter studied. In the next quarter, as income
remained essentially constant, both U1 benefits and U1 taxes responded
dramatically, yielding an overall program stabilizing effect. This is
eSpecially true of U1 taxes, as only with EB did UI benefits exhibit the
expected effect.

The pattern of measured effectiveness in the recovery is
different from past periods. Most notably, U1 taxes are
destabilizing. Seasonal factors may be the cause for the slip in the
measured effectiveness of the overall UI program and U1 benefits in

1981:I as benefits increased even though income increased in the

71

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72

 

 

 

 

TABLE 3-17
QUARTER-BY-QUARTER MEASURED EFFECTIVENESS, 1980:I - 1981:11
Parameters Period

t+l t+2 t+3 t+4 t+5
Cl .50 .653 .50 .653 .761
C2 .75 825 .75 825 .88
i .673 774 673 774 .82
X .386 485 .88 87 .85
Z .614 515 .12 13 .15
T .0082 .0082 .0074 .0074 .0074
ET -.24 4 1 3.0 -2 8 —1.8
B .0074 .0074 .0074 .0074 .0074
B (with EB) .0076 .0076 .0084 .0084 .0084
EB 2.6 2 6 —ll.0 - 40 -8.9
EB (with EB) 1.1 - 86 -5.6 20 -9.0

Program Measured Effectiveness

t+l t+2 t+3 t+4 t+5
Overall Program
Without EB -4.l4% 3.2% 11.54% -3.9% 11.5%
With EB -l.95% 9.0% 9.00% -4.99% 12.8%
U1 Benefits Only
Without EB —3.78% -5.44% 10.74% .63% 14.05%
With EB -l.6l% 1.70% 6.55% —.36% 15.25%
U1 Taxes Only - 33% 7.70% 3.0% -4.59% -3.45%

Recession Recovery

 

NOTES: (1) See note 1, Table 3-5.
(2) A minus sign on measured effectiveness indicates destabilization.

73

quarter. Finally, the measured effectiveness of U1 benefits with EB is
actually higher in 1981:11 than that without EB. This result is counter
to the results of all previous recoveries. The fact that this
recession/recovery period was immediately followed by a severe recession

may have caused the uncharacteristic results found in this period.

3.5 Conclusion

 

This chapter shows how effective the U1 program has been as an
automatic stabilizer. Although this issue has been studied in the past,
this paper presents effectiveness measures for recession-recovery
periods not covered by previous studies, including the three recession-
recovery periods since 1969. In each period studied, 1 have
disaggregated data on UI benefits into a permanent and temporary
program. As in past studies, the permanent component has a significant
positive effect on stabilization. However, due to the discretionary
nature of temporary benefit programs, they prove to be destabilizing in
every period analyzed.

This paper presents effectiveness measures for five recession-
recovery periods from 1957 through 1981. Other studies reported the UI
program prevented up to an average of twenty-six percent of a further
change in income for recessions during the late forties through the
early sixties.2§! The effectiveness measures estimated in this chapter
are more accurate than those of previous studies for two reasons.

First, a deviation-from-trend method that takes account of growth in
variables is used to calculate the elasticities needed in the estimation

of the effectiveness measures. Second, the other coefficients needed in

74

the estimation process are themselves estimated instead of chosen at
random from a range of possible values. The average potential change
prevented by the U1 program from 1955-1980 found in this chapter is
fourteen percent, which is about the mean of the other studies. For the
two recession/recovery periods that are analyzed in this chapter as well
as most other studies, I find an average effectiveness measure of about
nineteen percent in recessions and eighteen percent in recoveries. The
recession average is below that of other studies, while the recovery
average is greatly above that of other studies.

Using a slightly modified version of the effectiveness measure
develOped by Eilbottzgl, and using a procedure used by Thirwallqgl, I
measure the stabilization effectiveness of the U1 program over selected
recession/recovery periods. For specific recessions and recoveries, the
measure varies from a maximum of 26.05 percent, to a minimum of 3.2
percent. The results show the bulk of measured effectiveness is
generally due to UI benefits, as the seasonality of collections and
other institutional arrangements (as experience rating) associated with
UI taxes reduce its measured effectiveness and at times cause UI taxes
to become destabilizing.

Unlike previous studies which showed the UI program to work
effectively in recessions, but have virtually no effect in recoveries,
this study shows the effect is nearly equal across recession and
recovery. There are two explanations for this. The first is that the
recovery periods used here do not correspond to the expansion periods
used in earlier studies. Recoveries in this paper refer to an arbitrary
length of time (four to five quarters) immediately after the trough

quarter of the recession, while previous studies used the entire period

75

from trough to peak for their expansion periods. The length of time may
have tempered their results. I would argue my approach is the correct
one, for previous studies base their estimates on periods of steady
growth, not recoveries. Second, the use of absolute changes by previous
researchers biased their results downward. The combination of the two
may explain the majority of the disparity.

Finally, the results show the effect of the various extended
benefits programs throughout the period. These programs were
implemented to aid individuals who experienced lengthy unemployment.
They were not designed to achieve stabilization as their primary goal.
Since (un)employment lags the business cycle, these programs, begun as
recoveries started, reduce effectiveness measures that include them
below those that do not. One program, the permanent Extended Benefits
(EB) program, did increase effectiveness in later recessions since this
program works automatically.

From a policy viewpoint, the most important result found from
measuring the effectiveness of the U1 program is the destabilizing
effect of every (temporary) discretionary extended benefits program.
This result is caused by two factors. The first is the fact they are
discretionary. Their discretionary nature causes them to be implemented
with a lag, after the recession has ended and the recovery has begun.
This causes an increase of U1 benefits as income rising. Since
automatic stabilizers should retard the growth in income in recoveries,
the extended benefits programs are detracting from the stabilization
effectiveness of the program. The second factor is the concept of
stabilization effectiveness used in this research. Stabilization

effectiveness is measured with respect to income. Since employment lags

76

beind the movements in income, extended benefits programs meet the goal
of social insurance.31/ If stabilization effectiveness was measured
with respect to employment, these programs may be found to meet the goal
of stabilization as well. However, since stabilization effectiveness is
taken to be the amount of a further change in income prevented by the
program, and these programs reduce the amount of a change in income
prevented by the program, they detract from the measured effectiveness
of the program. All in all, the UI program helps in stabilizing the
economy, although its contribution is in the neighborhood of preventing
ten percent of a farther change in income.

The measures of effectiveness estimated in this chapter should be
viewed as the upper limit of effectiveness. One cannot credit the
entire change in income to changes in fiscal policy, whether
discretionary or automatic. As Appendix B shows, the measured
effectiveness of the UI program (ME) estimated in this chapter is based
on an implied aggregate demand model that contains only a goods

sector. This implied model assumes monetary phenomena have no impact on

measured effectiveness.

CHAPTER THREE
NOTES

l!2e11 (1977), p. 5.

EjThe decrease in U1 taxes collected will only reduce firms' expenses
relative to a world in which the same taxes are collected but in a
manner uncorrelated to the number of employees.

E/Musgrave and Miller (1948).
EJClement (1960).

E/Rejda (1966).

.E/Eilbott (1966), p. 451—455.

.Z/This result was obtained using the parameters given in Eilbott's
paper, except for the UI data which conflicted with the data used in
this study. Using the U1 data from this study (given in Appendix A) and
his parameters, I find a range of 12-18% for measured effectiveness in
recession and less than 5% in recovery for the U1 program. Hamermesh
(1977), p. 63, has an excellent summary of the estimates of measured
effectiveness of previous studies.

E/Hamermesh (1982).

EjHamermesh (1982), p. 110. Especially take note of his footnote 21 on
this result.

EQ/Ihirlwall (1969).

Ll/In addition to time as a regressor in the UI tax and UI benefit

equations, seasonal dummies are included to try to rid these series of
their seasonal variation.

Lg/The turning points established by the National Bureau of Economic
Research are: 1957:III-1958:11; l960:II-1961:I; 1969:IV-1970:1V;
1973:1V-1975:I; and, 1980:I-1980:III.

LE/Eilbott choose the values .8, .85, and .9 for c and .3, .4, and .5
for i in his study.

lfi/Okun, in Heller (1968), uses a similar technique to find the effect
of the 1964 tax cut.

lélJohnston (1973), p. 316-318.

77

78

LEjActually, the estimation of these equations is an iterative search
version of the procedure outlined in Johnston, iterating over rho values
that give the equation the smallest standard error of the regression.

kZ/The term 1/1-C3)-1 is the appropriate value of the geometric series
(1 + c3 + c3 + C33 + ...). Multiplying this series (or the above term)
by the MPC (Cl) is equivalent to the formula to estimate a dynamic
multiplier,

° 1
: c1c3 .

1‘0
k—/See Hamermesh (1980), p. 63.

xg/This information along with a more complete description of the TUC

program can be found in "Unemployment Compensation: Final Report,"
1980, p. 58.

QQ/Rejda shows the largest measured effectiveness of 5% in the eXpansion
of 1958-60 compared to his average measured effectiveness in recessions
of 24.0%. Clement's largest measured effectiveness is 3% during the

expansion of 1949-1953 compared to his average measured effectiveness of
25.2%.

zl/See Unemployment Compensation: Final Report," p. 58.

 

23/See footnote 20.

zl/See Unemployment Compensation: Final Report," p. 58-59.

 

2i/Unemployment Compensation: Final Report, pp. 60.

 

zé/Unemployment Compensation: Final Rgport, pp. 13, 58, 80.

 

2E/Unemployment Compensation: Final Report, pp. 60-61.

 

ZZ/Unemployment Compensation: Final Report, pp. 61-62.

 

2E/See Hamermesh (1980), p. 63.

32/311botc (1966).

39/Thirlwall (1969).

Ql/Although ill-timed to achieve stability, these programs are timed
well for social insurance purposes. Unemployment lags the business
cycle, and is highest at the beginning of recoveries, just as these
programs are implemented. In all the periods covered in this study,
unemployment rates as high or higher in the first quarter of the
recovery as compared to all other quarters in the period.

CHAPTER FOUR

THE STABILIZATION EFFECTIVENESS OF THE U1 PROGRAM IN THE

CONTEXT OF AN AGGREGATE DEMAND MODEL

4.1 Introduction

 

Previous studies on the effectiveness of the UI program
calculated a measure of effectiveness that compared two aggregate demand
multipliers, one with the U1 program explicitly included in the
multiplier, the other without.l/ This measure of effectiveness
implicitly assumes an aggregate demand model to obtain the necessary
multipliers. However, no explicit models were estimted or tested to
derive multipliers in any of these studies. The purpose of this chapter
is to present an aggregate demand model of the economy, and estimate and
test the model under different assumptions and conditions to obtain
different sets of elasticities. Using these estimates, I obtain a more
accurate measure of the stabilization effectiveness of the UI program
than those found in previous studies.

All previous work done on the subject dealt only with the goods
sector of aggregate demand. The money sector was simply ignored or
assumed to equilibrate whenever the goods sector was in equilibrium.
This was apparently done for simplicity by assuming money did not affect

the stabilization effectiveness of fiscal policy. These assumptions are

79

80

at the center of the debate over fiscal and monetary policy of the past
twenty years. Much of the debate has focused on the findings of the
many studies that have tested these assumptions empirically. Although
no conclusive evidence has been found to support fully either the
monetarist or fiscalist position, it has been accepted that the issues
are best dealt with empirically rather than by assuming them away. This
is precisely what I will show in this chapter. Specifically, I show
that the inclusion of a monetary sector in an aggregate demand model
significantly reduces the measured effectiveness of the UI program as an
automatic stabilizer.

This chapter is divided into three sections. Section 4.2 is a
brief review of the concept of measured effectiveness and its relation
to this chapter. The theory and derivation of the model is covered in
Section 4.3. Finally, Section 4.4 covers the estimation and testing of
the model, and the results and conclusions drawn from the estimated

coefficients.

4.2 A Review of Measured Effectiveness

The measure of effectiveness used by others and adopted for this
analysis is a ratio of two aggregate demand multipliers.£!
Effectiveness is measured as the amount of a further change in some
indicator of economic activity that is prevented by the automatic
Stéibilizer, the UI program. It is calculated by comparing two aggregate
(knnand multipliers, the first in a world with the U1 program, the second

ihl a world without the program in the model. One minus the ratio of the

Imxltiplier with the U1 program to the multiplier without the program is

81

taken to be the measure of effectiveness. In Section 4.4, all the
models are log-linear, giving estimated elasticities rather than
multipliers. Using elasticities rather than multipliers does not alter
the results of Appendix B, except that measured effectiveness is now the
amount of a further percentage change in income that is prevented by the
U1 program. The use of a log-linear model alleviates the problems
encountered by past studies in their measurement of the stabilization
effectiveness of the UI program. Instead of the variables in Appendix B
being constant proportions of national income, these relationships
become exponential. This helps take account of growth over time, which
was shown in Section 3.3 to yield more accurate estimates of measured
effectiveness.

This method necessitates estimating a consumption function (and
thus the entire model) twice. One estimate of the model includes the U1
program eXplicitly in consumption and aggregate demand, the other
estimate excludes the program from the model. This is true for each
condition to be imposed on the model, such as exogeneity of the money
supply versus interest rates, and models including goods only versus
models with both goods and money. Measured effectiveness is the
percentage difference between the estimated impact elasticities obtained

from the two models.

4.3 The Theory and Derivation of the Model

 

The structure of the model used in this chapter is to be
consistent with conventional macroeconomic theory, except for those

additions and changes necessary for the analysis of the effectiveness of

82

the U1 program. It contains several basic macroeconomic variables such
as consumption, investment, national income, interest rates,
unemployment, and wages, as well as policy variables such as a money
supply measure and government spending. The model is intended to be
sufficient to capture the movements of aggregate demand correctly, yet
be as manageable and general as possible. Examples of the models drawn
upon for the formulation of this model are: Pindyck and Rubinfeld
(1981);]; Kmenta and Smith (1973)é!; the Wharton model (l974)2/; and the
FRB-MIT-MPS MODEL (1968).§/

The model consists of a minimum of five equations, of which four
are behavioral. As different assumptions and conditions are imposed,
the model reaches nine equations, eight of which are behavioral.
Throughout the model, all endogenous and exogenous variables are
expressed in terms of the natural logarithms of their observed values.

The endogenous and exogenous variables of the model are listed in
Table 4-1. It is important to note that some variables are endogenous
or exogenous (of course not at the same time) depending on the
conditions imposed on the model. Also, some variables only appear in
versions of the model that contain the U1 program explicitly. The
models in order of their estimation are: (l) goods only, no UI program
(GNUI); (2) goods only, U1 program included (GUI); (3) entire model, no
UI’ program (WNUI); and (4) entire model, U1 program included (WUI). The

Valriables are listed with model reference in Table 4-1.

I have limited the number of models in this chapter to four. The
real.supply of money is assumed exogenous, while interest rates are
assumed endogenous in the models that contain a money sector. The

anallysis of the assumptions of an endogenous money supply and exogenous

83

TABLE 4-1

VARIABLES IN THE MODELS

 

VARIABLES MODELS*

ENDOGENOUS:
C Personal consumption expenditures All
INR Nonresidential investment All
IR Residential investment All
Y National income All
TAX Total tax receipts All
UIB Unemployment Insurance payments GUI, WUI
U Insured unemployment rate GUI, WUI
YD Disposable Income minus UIB All
TBR Three-month Treasury bill rate WNUI, WUI
RB Moody's AAA corporate bond rate WNUI, WUI

EXOGENOUS:

G Government spending minus UIB All
V0 Fixed Taxes All
WEALTH Net household wealth All
TBR Three-month Treasury bill rate GNUI, GUI
RB Moody's AAA corporate bond rate GNUI, GUI
PD Average potential duration GUI, WUI
COV Extent of U1 coverage GUI, WUI
WAGEX Real wage rate GUI, WUI
YP Potential national income GUI, WUI
Dzl
D3. Seasonal dummy variables GUI, WUI
D4}
P Implicit price deflator, national income WNUI, WUI
Ml % change of money supply (Ml definition) WNUI, WUI

 

* The four models are: GNUI, goods only, no U1 program; GUI, goods only,
UI program; WNUI, entire model, no U1 program;
and, WUI, entire model, U1 program.

(1) See Appendix A for the data sources for the variables listed here.

84

(pegged) interest rates in models containing money is postponed until
the next chapter, dealing with the addition of a government budget
condition to the models.

National income, Y, and its components, consumption, C, net
investment, I, and government pruchases excluding U1 benefit payments,
G, are all in constant 1972 dollars, as are all other dollar-valued
variables. The model assumes a closed economy, so there are no imports
or exports included in the identity. Net investment is disaggregated,
and separate equations estimated to explain nonresidential (fixed)
investment, INR, and residential investment, IR. The national income

identity is written as

(4.1) Y = C + INR + IR + G.

Disposable income is estimated indirectly through estimation of a

simple tax function. Total tax receipts are given by a simple equation

relating receipts to taxable income. This equation is

Total taxes are given by fixed taxes, V0 and a constant marginal tax

rate, V1, times national income. Disposable income is given by the

following identity:

(4.2A) YD = - vO + (l-V1)Y.

The remainder of this section focuses on the specification of the

85

equations of the four models mentioned above. First, I discuss the
structure of the goods only models, then I incorporate the equations
making up the money sector into these models to generate what I call the

entire model.

Goods Sector Equations

 

The goods-only model has three basic equations; a consumption
equation and two investment equations. Nonresidential investment is
taken to depend on income.1/ Since there is usually some period of time
between an investment decision and the outlay for investment, income
should enter the equation with a lag. Nonresidential investment also
should depend on the long-term interest rate and a measure of the
capital stock. Since there is no reliable published source of the
capital stock, I use a sum of the past periods measure of nonresidential
investment as a proxy (CAP) to represent the existing stock of
capital. The equation for nonresidential investment is in the form

n

(4.3) INR = INR(Y, Z RBt_i)/n+1 , CAP) + e

i O 3

Residential investment is difficult to explain in a small
macroeconomic model, but one investment equation did not capture the
movements in total investment sufficiently. Residential investment
depends on mortgage rates, mortgage availability, and housing
construction costs, none of which is included in the model. Therefore,
I use proxies for these variables in an effort to capture the movements
in residential investment for purposes of this model. I use income, the

short-term interest rate, and the difference between the long-term and

86

short-term rates (AVAIL) to explain residential investment. The short-
term rate is used as a proxy for the mortgage rate. (It fared better
than the long-term rate based on several summary statistics for the
equation.) The difference between the long and short rates is used as a
proxy measure of mortgage availability. This is done because credit
(mortgages) has (have) become harder to obtain as the short rate nears
the long rate. Finally, a second-order autoregressive scheme is
included in the equation to help explain the cyclical nature of this
market. This imposes a distributed lag on income and the interest rate
and credit proxy variables. The second-order relationship out-performed
a first-order relationship based on summary statistics for the

equation. The equation is of the form

(4.4) IR = IR(Y,TBR AVAIL, IRt_1, IRt_2) + e4

t-l'

The consumption function has two formulations, one explicitly
including the UI program to help explain consumption, the other without
the program as an argument in the function. First, I look at the model
without the UI program. Consumption depends heavily on disposable
income, but also on consumer credit and household wealth. The series
used for constant-dollar (real) household wealth is derived in a unique
way in this section. The amount of real net household wealth in the
present period is defined as the sum of last period's real net household
wealth (from the U.S. Commerce Department's net household wealth series)
plus the change in the real value of money held as currency by the
public and financial institutions, and money held as deposits by

financial institutions at the Federal Reserve (outside money which is

87

assumed equal to the monetary base), plus the changes in the real value
of government bonds outstanding. The reason for this derivation will be
made clear in the chapter dealing with the addition of a government
budget condition. The consumption function has the form of a geometric
lag distribution, with lagged consumption entering the equation. The

non-UI consumption function is of the form:

(4.5) c = C(YD, WEALTH, TBR, ( IE1 Ct_1)/n) + e5 . .81
i=1

The consumption function changes when the UI program is
introduced into the model explicitly. (The form of the consumption
function is that found in Hamermesh (l982)2/ and adapted for use into
this model.) Two features of the function differ from the above
equation. First, consumption now depends not only on disposable income,
but on disposable income disaggregated into UI income, UIB, and other
disposable income, YD. By doing this I can show (and test) that there
is a difference between the marginal prOpensities to consume out of the
two sources of income. The reason there should be a difference is that
some (not all) individuals who receive UI payments are surprised by the
sudden fall in income, and have not saved enough to maintain their
lifetime consumption pattern with their lower (UI) income. These peeple
would spend more of an additional dollar of U1 income (to try to
maintain their lifetime consumption) than other peOple spend out of an
additional dollar of non-U1 income. Other UI recipients expect
temporary spells of unemployment and save more during employment to be
able to maintain their lifetime consumption pattern while receiving UI

income. It is assumed there are only two groups of U1 recipients, those

88

who save enough during their employment stretches to maintain their
consumption pattern, and who thus spend like the individuals who receive
no benefits, and those who spend the entire amount of their UI payments
(MPC=1) in an effort to maintain their consumption pattern.

The other feature that is different between the two consumption
functions is that the UI consumption function depends on the insured
unemployment rate, U. The fraction a times U represents the percent of
U1 recipients who are constrained by too little savings and spend all
their benefits. The fraction (1- a) times U represents those U1
recipients who behave like non-UI individuals and consume at the same
rate out of U1 payments as out of other disposable income. The
consumption equation in a model with the UI progam included is

(4.5*) C = a0(a-aU) + alYD + (al-ala+a)UIB + aZWEALTH

2
+ a3[( 2 TBRt_1)/3] + a4( i Ct-i/Z) + e5* .
i=0 i=1
In this model, the amount of U1 benefits and the insured
unemployment rate are endogenous, both negatively related to the level
of income. However, instead of using only the level of income to
eXplain these variables, the gap between observed income and potential
income is used since it performs better (statistically) in the equations
than the level of income. Potential income is derived from the
potential GNP series of John Tatom (1982).12/
The level of real wages is used as a scale variable to explain
the amount of U1 benefits. A policy variable, the average potential
duration of benefit payments in weeks, PD, tries to eXplain the

generosity of the UI program and thus the amount of benefits paid.

Finally, a policy variable which tries to capture the extent of and

89

change in coverage of the UI program, COV, the ratio of covered
employment to the total labor force, is also included in the UIB
function. The real level of U1 benefits (measured as the replacement
ratio of benefits to wages) remained fairly constant over the period and

was not included in the UIB function. The UI equation is of the form

(4.6) UIB = UIB(PD,WAGEX, cov, Y-YP) + e6.

In addition to the gap between observed and potential income, the
insured unemployment rate is explained by average potential duration,
the first-order change in income, and the lagged insured unemployment
rate. The function also includes dummy variables to remove the effect
of seasonality from the data. The first quarter of the calendar year
(winter) finds seasonal workers increasing the insured unemployment rate
significantly over the other three quarters of the year. The dummy
variables capture this effect in the data. The form of the insured

unemployment rate equation is

(4.7) U = U(PD,Y-YP, Y-Yt_1, D2, D3, D4, Ut_1) + e7.

Money Sector Equations

 

The main purpose of this chapter is to show that the conclusions
about the measured effectiveness of the UI program in a model estimated
without a money sector in the model are incorrect. To show this, I add
a simple money sector to the model to show that the elasticities of the
exogenous variables are lower compared to a model of the goods sector

only. In this chapter, I have chosen to take changes in the money

9O

supply as exogenous and let interest rates be determined in the model.
There are two interest rates, a short-term rate represented by
the three-month Treasury bill rate, and a long-term rate represented by
Moody's AAA corporate bond rate. The short-term rate, TBR, is a
function of income, changes in lagged income, changes in the money
supply and a moving average of current and past inflation rates
represented by percentage changes in the implicit price deflator for
national income (INF). The last term captures the effects of higher
inflation and inflationary expectations on interest rates without adding
to the complexity of the model, i.e. introducing expectation generating

equations. The form of the equation is
(4.8) TBR = TBR(Y, Yt-l - Yt-Z’ Ml, INF) + e8

The long-term rate, RB, responds to the level of the short-term
rate and to changes in the short-term rate, all with a geometric lag to
account for the slow adjustment to these changes. This formulation
assumes that changes in the money supply and the price level affect the
long-term rate only indirectly through the short-term rate. The

equation is of the form:
(4.9) RB = RB(TBR, TBR-TBRt_1, RBt_1) + e9.
4.4 Estimation and Results

All the sets of models were estimated using quarterly data over

the period 1955-l to 1981-3. All the behavioral equations were

91

estimated using three-stage least squares. The national income identity
equations, which yield the impact elasticities necessary for the
analysis of the effectiveness of the UI program, are then obtained by
the derived reduced-form estimation method, using the structural
estimates of the models.ll! The standard errors included with the
estimates of the derived reduced-form equations were estimated following
the procedure develOped by Goldberger, Nagar, and Odeh (l961).¥£! This
procedure estimates the asymptotic variances and standard errors of the
reduced-form equations using the estimated variances and covariances
obtained from the apprOpriate structural equations. Tables 4-2 through
4-5 contain the results of the estimation of the four models.

The first model considered (Table 4-2) contains a goods sector
only and no UI program (GNUI). As indicated in the table, a three-
period moving average of the short-term rate is the best proxy for
consumer credit conditions in the consumption function. Also, a two-
period moving average of past consumption gave the best results for the
lagged dependent variable. For the nonresidential investment equation,
a four-period moving average of past long-term rates provided the best
results for the rate of return on investment. A three-period moving
average of the level of nonresidential investment was used as the proxy
for the capital stock. All the apprOpriate signs are found in all the
equations.

Adding the UI program explicitly to the model changes the form of
the consumption function (Table 4-3). As expected, the coefficient on
UI benefits paid exceeds that on other diSposable income. The remainder
of the model yields coefficients with the eXpected signs. With the

addition of the UI program, one expects to find that the coefficient on

92

 

 

 

 

 

 

 

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93

TABLE 4-3

REGRESSION RESULTS, GOODS ONLY, 01 MODEL (GUI)

 

 

 

 

DEPENDENT MEAN OF
VARIABLE REGRESSION EQUATION N DLR VAR.SEE
2 3
C - .374 (1-.06U) + .09YD + .144UIB + .054wEALTH-.02 ( E TBRt_i)64294(E Ct B/, 102 6.44 .008
1-0 i=1 ' ‘
(.108) (.021) (.031) (.023) (.004)
INR = .02 + .077Y -.47 ( f RB .)/ -.066CAP 102 5.33 .069
t-l i=0 t—1 4
(.236)(.036) (.033) (.029)
IR - .319 + .201Y - .096TBRt_1 + .078AYAIL + 1.031Rt_1 - .ZOIRE2 102 3.76 .004
(.213) (.061) (.029) (.055) (.104) (.102)
TAX - 4.09 + .56Y or YD - —4.09 + .44Y 102 5.06 .12
(4.47)(10.00) ***
UIB = .26 + .ZlPD + .22WAGEX + .OllSCOV - .l46(Y-YP) 102 .184 .074
(.388)(.O4l) (.147) (.008) (.041)
U - 1.06 - .18 (Y—YP) - .063 (Y—Yt-l) + .59PD - .4402 - .46D3 - .3504 + '18Ut-1 102 -3.74 .139
(.78) (.028) (.034) (.134) (.072) (.038) (.037) (.071)
REDUCED—FORM EQUATION
2 2 3
- u + o - o f 1 + a . ". V
Y 434 07mm 02:: (f TERI-1V3 1 21(E CPR/2+ o9axrt_1 607 (f Abbi)“
1-0 1-1 180
(.255) (.009) (.003) (.111) (.032) (.057)
- .085CAP - .124TBRt_1 + .lOAVAIL + 1.33IR!_1 - .2581Rt_2 + .0196PD + .O4HACEX
(.025) (.016) (.043) (.113) (.046) ( 011) (.013)
+ .0021COV + .021YP + .014D2 + .014D3 + .011D4 - '006Ut-l + 1.291 C
(.009) (.019) (.022) (.011) (.012) (.004) (.116)
NOTES: (1) The structure of the model is log-linear.
(2) Standard errors are the numbers in parentheses under the estimated coefficients.

yg—u-r—fi

94

TABLE 4-4

RECRESSION RESULTS, ENTIRE MODEL. NO 01 (WNUI)

bEAN 0F

— ...-fl ‘—‘ “-4.

 

 

 

 

DEPENDENT
VARIABLE RECRESSION EQUATION N 019. VAR. SEE
2 2
c - .395 + .11210 + .056WEALTH —.02 ( E TBRt_i)3+.876( E Cc-1)/2 102 6.44 .0077
i=0 1-1 ‘
(.061) (.047) (.012) (.003) (.059)
INR - .06 + .118Yt_l-.448 8:0 RBt.Q/a-’.O62CAP 102 5.33 .07
( 213)( 037) (.034) ( 029)
IR - .278 + .309 - .137rnapl + .OZbAVAIL + 1.0718“1 - .26IRt_2 102 3.76 .041
(.206) (.057) (.03) (.028) (.111) (.105)
TAX - 3.97 + .555Y or YD . -3.97 + .4451 102 5.06 .116
(.703)(.O48) ****
TBR - .49 + .868Y + .059(Yt_l—Yt_2) - .437Ml + .3061NF 102 1.54 .268
(.26) (.314) (.033) (.206) (.103)
RB - .17 + .059TBR + .20 (TBR-TBRt_1) + .93RBt_1 102 1.83 .026
( 099)(.o13) (.043) (.077)
REDUCED—FORM EQUATION
% 2
- . 0 + . 728WE TH -. 2 . ' . . lY —. 2 5
Y 1 0 AL 0 6 (1:1 TBRt_1)/2+L14(iEICt_1)/2+ 143 Y“, 0 P 58 (i R (4)/3
(.124)( 026) (.009) (.41) (.068) (.008) (.21)
_ - - - . '2
.OBlCAP .OélTBRt_l + .033AVAIL + 1.39IR[_1 .3381Rt_2 54 RB[_1
(.042) (.029) (.019) (.503) (.179) (.195)
+ .O77Hl — .OSSINF + 1.300
(.041) (.032) (.467)
NOTES: (1) The structure of the model is log-linear.

(2)

Standard errors are the numbers in parentheses under the estimated coefficients.

95

TABLE 4-5

REGRESSION RESULTS, ENTIRE MODEL, UI (WEI)

 

 

 

 

 

DEPENDENT MEAN OF
VARIABLE RECRESSION EQUATION N DEF. VAR- SEE
2 2
C - .332 (1—.O910) + .165YD + .235018 + .OZSREALTHo .038 ( E TBRt_ly3+.72 (Z Ct_gé 102 6.44 .013
i=0 i=1
(.038) (.045) (.081) (.009) (.021) (.087)
’ - . + . ' _ I -.O 7CAP 10“ 5.33 .075
INR 06 201?1 ”11(1EORBt'iy“ 5 2
(.177)(.042) (.037) (.033)
IR - .206 + .293Y - .156TBRE_1 + .OOZAVAIL + 1.161Rt_l - .331Rt.2 102 3.76 .041
(.233) (.072) (.037) (.005) (.099) (.095)
TAX = 4.00 + .546Y or YD - -4.00 + .454Y 102 5.06 .285
(.97) (.051)
TBR - .024 + 1.15Y + .14 (Yr-1 Yt-Z) - .39M1 + .O771NF 102 1.54 232
(.016) (.285) (.12) (.189) (.069)
RB - .63 + .OSTBR + .21S(TBR-TBRL_1) + .94RBt_1 102 1.82 .026
(.097)(.Ol4) (.037) (.078)
UIB - .19 + .11PD + .17wACEX + .0055COV - .205(Y—YP) 102 .184 .053
(.213)(.035) (.066) (.004) (.061)
U - .94 - .42(Y-YP) - '16(Y-Yt-l) + .425PD - .7402 - .5503 + .3604 + .700“1 102 .374 .116
(.417)(.165) (.038) (.101) (.066) (.042) (.043) (.091)
REDUCED-FORM EQUATION
Y . . .. 1 . E . .2
037 03WEALT1 046 (1.1 TBRt_1»&+ 866:21 Ct-ifl2+ 209 Yt-l + 0 4 Yt-Z
(.0247)(.0145) (.0215) (.103) (.0843) (.0138)
3
- .494 v. ‘ — . . ’ . - .
(121n:-1)/3 068CA1> 082TBRt_1+ 0024A\AIL+139IR[_1 40111t~2
(.0964) (.0579) (.0332) (.0027) (.25) (.111)
+ .069M1 - .013INF + .0156PD + .048WAGEX + .OOlSCOV + .O42YP - .545RBE_1
(.0302) (.0095) (.0081) (.0326) (.00083) (.0259) (.0781)
+ .02602 + .0203 + .01304 - .0250t_1 + 1.2060
(.0221) (.0212) (.0178) (.0114) (.374)
NOTES: (1) The structure of the model is log-linear.
(2) Standard errors are the numbers in parentheses under the estimated coefficients.
(3) See note 3. Table 4-3.

96

the exogenous policy variable, government spending, declines. For
example, a decline in government spending reduces national income, which
is then transmitted to declines in consumption and investment leading to
a further fall in national income through the multiplier process.
However, with the addition of the UI program, disposable income does not
fall as much, helping to maintain consumption and preventing income from
falling as much as in a world without the 01 program. Therefore, the
coefficient on government spending should be smaller in a world with the
UI program. As expected, the size of the coefficient on government
spending is reduced by the inclusion of the 01 program in the model.

The reduction in the coefficient between the models is 8.83 percent. In
reality, the models without an explicit UI program and with no money
sector are incorrectly specified. This specification error causes the
estimated coefficient on government spending to be biased upward. The
amount of specification error is equivalent to the measured
effectiveness of the UI program. Table 4-6 shows comparisons of
important impact elasticities obtained from the reduced-form equations
of the four models. This simple comparison of impact elasticities of
exogenous variables is almost what other studies used as their measure
of effectiveness of the 01 program.

The next two models to be compared are those adding a money
sector to the goods sector, with and without the UI program included
(Tables 4-4 and 4-5). This comparison can be seen graphically in Figure
4.1. Comparison of the derived reduced-form equation from the two
models reveals a 7.20 percent reduction of the impact elasticity on
exogenous spending due to the inclusion of the UI program in the

model. To simplify Figure 4.1, I assume only one interest rate in the

97

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98

model. 15 and 18* are the initial IS curves for models without and with
the UI program respectively. A decrease in government spending or some
other exogenous variable shifts both curves down by an equal amount.
ISNEW and IS*NEW are the IS curves after such a change corresponding to
IS and IS*. The addition of the money-sector equations in the model
causes the slope of the LM curve to become positive, rather than zero in
the goods-only models. The LM curve for a goods-only model is
represented by a horizontal line at a fixed interest rate, r*. Above,
measured effectiveness was estimated to be 8.83 percent. This is
represented in Figure 4-1 as (Y4-Y2)/(Y4-YO). The LM curve for a model
that includes a money sector (an endogenous interest rate) is
represented by the LM curve in Figure 4-1. Measured effectiveness of
the 01 program was estimated to be 7.20 percent for these models. This
is represented in Figure 4-1 as (Y3-Y1)/(Y3-YO). (Figure 4-1 is not
drawn to coincide with the estimates obtained in Tables 4-2 through 4-5,
merely as an aid to illustrate the comparisons found in Table 4-6).

The inclusion of the UI program in the model reduces the impact
elasticities of exogenous variables in both models. The percentage
reduction of the impact elasticity of exogenous spending is smaller in
the model including money. The inclusion of a money sector allows
interest movements that affect investment and consumption, and thus
income. (This is the crowding out effect.) This effect further reduces
the impact elasticity of exogenous spending below that of the goods
only, no UI model. Since the reduction in the impact elasticity of
exogenous spending due to the addition of the UI program is taken as a
measure of the stabilization effectiveness of the UI program, the

measured effectiveness of the program is reduced by 18.46 percent when a

18* 99

 

 

 

 

 

 

15*
NEW
1'
LN
17*
'1
l 1'-
I:
II
'I'
| ,, I.
II
I i I ISNEW
I
, [I
V
y1

y4 y3 y2 y0

FIGURE 4-1

IS-LM REPRESENTATION OF THE COMPARISON OF
MEASURED EFFECTIVENESS BETWEEN GOODS-ONLY AND
ENTIRE MODELS

100

money sector is introduced in the model. This figure is just the
percentage change in the estimated effectiveness measures of the two
models shown in Table 4-6 and Figure 4-1.

One other pair of models can be compared to determine the effect
the addition of a money sector has on the effectiveness of the UI
program as an automatic stabilizer. Looking at the two models that
incorporate the 01 program, one can determine the effect the addition of
a money sector has on the impact elasticities of average potential
duration, UI coverage, and government spending. The impact elasticity
of average potential duration is .0196 in the goods-sector-only model.
This means that a one percent increase in duration, measured in weeks,
will cause national income to rise by .0196 percent. The impact
elasticity of UI coverage shows that a one percent increase in the ratio
of covered employment to the total labor force will increase national
income by .0021 percent. The impact elasticities of average potential
duration and UI coverage are reduced to .0156 (a 20.4 percent decrease)
and .0015 (a 28.6 decrease) respectively, due to the addition of a money
sector to the model. The smaller reduction in the effect of average
potential duration shows it may be a better vehicle for maintaining
consumption and stabilize the economy than expanding coverage. Expanded
coverage would most likely be awarded to those not constrained by too
little savings or the inability to borrow at a reasonable interest rate
to help maintain their consumption. With a smaller percentage of U1
recipients spending all of their UI income, a smaller "bang for the
buck" would result, causing the measured effectiveness to decrease.

The government spending elasticity is reduced by 6.6 percent due

t0 the addition of a money sector. This is the crowding-out effect.

101

This is shown graphically in Figure 4-1. The reduction in the
government Spending elasticity is (Yz-Yl)/(Y2-Y0). This reduction is
smaller than the two UI policy variables, because a one percent change
in government Spending induces more of a change in consumption and
income than a one percent change in either avarage potential duration or
UI coverage. The larger effect on consumption is not as overwhelmed by
the interest-induced changes in consumption and investment caused by the
monetary reactions to changes in these policies. Therefore, the
percentage reduction in the elasticity of government spending is less
than that of the two UI program policy variables.

On the basis of the elasticity comparisons above, I conclude that
the estimates of measured effectiveness obtained in Chapter III and
other previous studies assuming only a goods sector in aggregate demand

are overstated by between ten and twenty percent.

4.5 Conclusion

Failing to include a money sector in estimating the measured
effectiveness of the UI program causes an overstatement of measured
effectiveness Inltentxatwenty percent. The lack of a money sector ignores
the possibility of monetary reactions to fiscal policy (such as crowding
out in the Hicksian sense). All previous studies implicitly credited
all the dampening of the movements in income during business cycles to
the UI program alone by failing to take account of a money sector. No
credit was given to changes in the monetary sector produced by fiscal
Policy nor to any monetary policies. I have shown that this omission is

a serious flaw in their analysis, and conclusions drawn from such

102

analyses must be viewed with this in mind.

Another way to explain the overstatement in the measured
effectiveness of the UI program when a money sector is not included in
aggregate demand is the concept of specification error (bias). Measured
effectiveness is equivalent to a measure of the bias in the coefficients
obtained by estimating a misspecified model rather than a correctly
specified model. Failing to include the UI program in goods-only model
produces an upward bias in the estimated impact elasticities of the
exogenous variables in the model. I estimate this bias to be 8.83
percent of the coefficients from the correctly specified model. Using
the definition of measured effectiveness, I claim that 8.83 percent of a
further change in income is prevented by the UI program. However, the
model is still misspecified because it does not include a money
sector. Therefore, the above estimate of the bias is itself biased
upward. Including a money sector reduces the estimate of the bias to
7.20 percent. Failing to include the UI program in aggregate demand
produces a 7.20 upward bias in the impact elasticities of the exogenous
variables. The estimated measured effectiveness of the UI program is
7.20 percent. This is below the estimates of the average measured
effectiveness of the program obtained in previous research.k§/

The conclusions found in Chapter III must be viewed carefully, as
the analysis proceeded implicitly under a goods-only model. What do the
findings of this chapter mean in terms of those results? The average
effectiveness of five postwar recessions was found to be 15.6 percent,
and the average effectiveness of the five subsequent recoveries was
found to be slightly lower, 15.2 percent. The findings here suggest these

figures should be reduced on the order to (say) fifteen percent. This

103

is the midpoint of the range of the specification error (bias) produced
by not including a money sector in models of aggregate demand. This
reduces the average effectiveness measures to 13.3 percent and 12.9
percent for recessions and recoveries, respectively.

The results also have an implication for the finding in Section
3.4 that all discretionary extended benefits programs detracted from the
effectiveness of the UI program. Since the addition of a money sector
reduces the stabilization effectiveness of the program, it should be
that the addition of a money sector reduces the destabilization induced
by extended benefits. This is indicated by the reduced impact
elasticity of the policy variable, average potential duration, when
comparing models with and without a money sector and containing the U1

program.

CHAPTER FOUR

NOTES

l/For example, see Clement (1960); Rejda (1966); and Eilbott (1966) for
the U.S., and Thirlwall(1969) for the U.K.

Z/In Appendix B, I derived the measured effectiveness equation used to
estimate the measured effectiveness of the UI program in recession and
recovery (Section 3.4). The model behind the equation was assumed
linear, so the estimated coefficients are simple derivations that yield
impact multipliers. In this chapter, I assume the model to be log—
linear. The estimated coefficients in this model are impact elasticities
rather than multipliers. This does not alter the results of Appendix B
except measured effectiveness is not the amount of a further percentage
change in income that is prevented by the UI program. The use of a
log-linear structure alleviates the problems encountered by past studies
in their measurement of stabilization effectiveness of the UI program.
Instead of disposable income, corporate profits after tax, UI taxes and
01 benefits being constant prOportions of national income as in Appendix
B, these relationships become exponential. This helps take account of
growth over time of these variables, which was shown in Section 3.3 to
yield more accurate estimates of measured effectiveness.

 

E/Musgrave and Miller (1948)-
i/Pindyck and Rubinfeld (1981), Chapter 13.

-§/Kmenta and Smith (1973).

éjDuggal, Klein, and McCarthy (1974).
-Z/Rasche and Shapiro (1968)-
8/

-Actually, GNP would be more appropriate, but to keep the model simple

and to keep the simple tax equation correct (the use of GNP would eliminate
the effect of business taxes), income is used instead of GNP throughout

the model.

E/Hamermesh (1980).

lQ/The potential GNP series is found in Tatom (1982), p. 16.

ll/Goldberger, Nagar, and Odeh (1961).

l-‘?'-/See the table listing estimates of measured effectiveness of the 01
program obtained by previous studies on p. 63, Hamermesh (1977).

104

CHAPTER FIVE

THE STABILIZATION EFFECTIVENESS OF THE UI PROGRAM IN THE CONTEXT OF AN

AGGREGATE DEMAND MODEL II: ADDING A GOVERNMENT BUDGET CONDITION

5.1 Introduction

The analysis of the stabilization effectiveness of the UI program
in the previous chapter focused on an aggregate demand model and on
the monetary reactions that accompany changes in exogenous, fiscal
policy variables. Impact elasticities for several policy variables were
estimated for each of four models, allowing the calculation of several
measures of effectiveness of the UI program. The major conclusion of
Chapter IV was that the addition of a money sector decreases the
measured effectiveness of the UI program. By not taking account of
monetary reactions to fiscal policy and of exogenous goods-sector
shocks, measured effectiveness is overestimated by ten to twenty
percent. This overestimate may lead to an unwarranted reliance on the
UI program as an automatic stabilizer by policy makers.

The analysis of the previous chapter dealt only with monetary
reactions to changes in the goods sector, whether the changes were
autonomous shocks or changes in fiscal policy. This chapter takes the
analysis one step further by introducing a government budget condition

to each of the models. This condition requires that the government

105

106

finance deficits that arise due to increased government spending or
higher UI benefit payments by selling bonds to the public or to the
Federal Reserve. Section 5.2 contains the theoretical background for
including a government budget condition to the model. Section 5.3
reports the estimated impact elasticities for the policy variables in
the models when the deficit financing constraint is considered. Also in
this section is a comparison of these impact elasticities to those
estimated in Chapter IV, as well as an analysis of how measured
effectiveness is changed due to the addition of the government budget
condition to the models. Two new models are estimated in Section 5.4.
These models assume that changes in the money supply are endogenous and
interest rates are pegged. Impact elasticities for these models are
estimated and compared to those of the four models in Section 5.3. This
chapter, especially section 5.2, draws heavily on Silber (1970) l],
Christ (1969) 2!, Blinder and Solow (1974)'2/and Infante and Stein

(1976). 1‘!

5.2 Theoretical Background

 

Assume the government finances any deficits that arise by
either: (1) issuing bonds to the public thereby increasing the amount
of government bonds outstanding; (2) selling bonds to the public, who
then sell these bonds to the Federal Reserve, effectively monetizing
the debt by increasing the money supply; or (3) some combination of (l)
and (2). Case (3) is the general case with (l) and (2) being the
extremes.

In a world without the UI program, the deficit can be described

107

by

(5.1) DEF = G - TAX + BIP;
where DEF is the deficit;

G is government spending;

TAX is total tax receipts; and

BIP is the amount of interest paid on outstanding government

bonds.
All values are in 1972 dollars. The deficit can be negative, i.e., a
surplus, meaning tax receipts more than cover the outlays for interest
payments and government spending. An increase in the deficit is
analytically equivalent to.a decrease in the surplus. This is an
important fact when dealing with the 01 program, as the UI Trust Fund
was in aggregate in surplus through 1981, but the surplus has declined
since the 1969-1970 recession.

Deficits can be financed either by a change in the money supply,
a change in government bonds outstanding, or both. The deficit equation
becomes

(5.2) DEF = G - TAX + BIP = BASE + B;
where B is the percentage change in the number of bonds outstanding; and
BASE is the percentage change in the monetary base. Government bonds
are assumed to be fixed price, variable coupon bonds. The price can be
assumed to be fixed at $1.00, so the dollar amount of bonds outstanding
equals the number of bonds outstanding. All variables are measured in
constant dollars.

These types of bonds introduce a complication into the
analysis. When the models involving a money sector with endogenous

interest rates are analyzed, the BIP term becomes endogenous. This

108

makes the method of financing endogenous, making everything, including
the money supply and/or the number of bonds outstanding, endogenous.
Theoretically, this complication can be handled, but problems arise when
trying to estimate the model. Specifically, the inclusion of interest
payments on government bonds outstanding causes the money supply to
become endogenous. This makes the entire money sector endogenous, and
causes the model to become underidentified as the number of
predetermined variables falls below the number of endogenous

variables. The model cannot be estimated when this condition holds. To

alleviate this rather difficult problem, I omit interest payments from

the deficit equation.2! The revised deficit equation is

(5.2*) DEF = G - TAX = BASE + B.

With the addition of the UI program, the deficit equation must
also include the amount of U1 payments. For simplicity, I assume there
are no UI taxes in this analysis. Alternatively, UI taxes could be
lumped with total taxes and enter the deficit equation in that manner.
The analysis is not substantively affected by either assumption. The

deficit equation becomes

(5.3) DEF = G - TAX + UIB = BASE + B.

Each of the four models from Chapter IV is estimated subject to
the apprOpriate government budget condition for that model. Each model
is solved algebraically for its reduced-form equation under two
assumptions: (1) The government budget condition is ignored; and (2)

The government budget condition is considered. The first assumption was

109

implicit in the estimates obtained in Chapter IV. After solving the
model algebraically, I substitute in the values of the estimated
coefficients obtained in Chapter IV, including the terms involved in the
government budget condition when it is considered. The algebraic
derivations of the impact elasticities of the models subject to a
government budget equation are found in Appendix C. For example, in the
goods-sector-only, no UI model (GNUI), the impact elasticity of
government spending with respect to income when the deficit financing

constraint is considered is

(5.4) dY/dcF = [(az/D)d(BASE+B)/dG] + (1/D);

where
dY/dCF is the impact elasticity of government spending with
respect to income when the deficit financing constraint is
considered;
(l/D) is the impact elasticity of government Spending with respect
to income when deficit financing is ignored, i.e., dY/dGNF;
d is the total differential Operator; and
32 is a positive coefficient.
dY/dGF is the sum of the impact elasticity on government spending when
deficit financing is ignored,§! plus a term involving changes in

wealth~Z/ From Appendix C, the wealth effect is

(5.5) d(BASE+B) = (az/D)(1-V1(dY/dCNF)).

Substituting this expression into (5.4), then substituting the

110

appropriate values of a2, V1, D, and dY/dGNF from Table 4-2 will produce
an estimate of dY/dGF.

Appendix C gives the condition under which the wealth effect is
greater than zero. When the wealth effect is positive, the impact
elasticity of government spending with respect to income when the
deficit financing constraint is considered is larger than that when
deficit financing is ignored. This particular result holds true for the
goods-sector-only models no matter whether an increase in bonds
outstanding or an increase in the money supply is used to finance the
deficit. This result is due to the assumptions of an automatically
equilibrating money sector and fixed interest rates in this class of
models. With no increase in interest rates, income increases by more
than the fiscal effect, through the wealth effect on consumption.

5.3 Empirical Results

 

Following the procedures outlined in Appendix C, I estimate
impact elasticities for all four models of Chapter IV. Tables 5-1 and
5-2 contain the result of these estimation procedures, and are analyzed

in this section.

Goods-Sector-Only Models

 

The impact elasticity from the goods-only, no UI model (GNUI)
ignoring deficit financing, was estimated in Chapter IV to be 1.416.
The parameters necessary for calculating the wealth effect are obtained
from Table 4-2. These parameters are: a2 = .078, V1 8 .533, D - .706,
and as indicated above, dY/dGNF a 1.416. The estimated wealth effect is

.024, giving the estimated impact elasticity of government spending when

111

TABLE 5-1

IMPACT ELASTICITIES, GOODS-ONLY MODELS

Estimated Wealth Fiscal

 

 

Model Elasticity Value Effect Effect

GNUI

No Financing Government Spending 1.416

Financing Government Spending 1.440 .024 1.416

GUI

No Financing Government Spending 1.291

Financing Government Spending 1.2972 .0062 1.291

No Financing Average Potential Duration .0196

Financing Average Potential Duration .0329 .0133 .0196

No Financing U1 Coverage .0021

Financing UI Coverage .0028 .0007 .0021

NOTES: (1) The models are: GNUI, goods only, no UI program; and,
GUI, goods only, U1 program.

(2) The No Financing elasticities are estimated in models
where the government budget condition is ignored. The
estimated values of these elasticities are taken from
Table 4-2 for GNUI, and Table 4~3 for GUI.

(3) The Financing elasticities are estimated in models that

are subject to the government budget condition. The
estimated values of these elasticities are obtained
following the procedure shown in Appendix C.

112

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113

the deficit financing constraint is considered of 1.44. (See Table 5-
1.)

The goods-sector-only, U1 model (GUI) is also shown in Table
5-1. As shown in Appendix C, the impact multipliers of the three policy
variables can be obtained by totally differentiating the reduced-form
equation for income, and assuming changes in all variables except the
policy variables are equal zero. When considering the elasticity of
government spending with respect to income, dPD = dCOV = O. The impact
elasticity of government spending with respect to income when the

deficit financing constraint is considered is written as

(5.6) dY/dGF = (aZ/D)(1-(V1+f4)(dY/dGNF) + dY/dGNF.

The fiscal effect was estimated as 1.291 in Chapter IV. Using
the appropriate estimated parameters obtained from Table 4-3, the wealth
effect is .006. Thus, the impact elasticity of government spending with
respect to income with the deficit financing considered in this model is
1.297. Table 5-3 shows comparisons of important impact elasticities
obtained in this section. The addition of the UI program has reduced
the impact elasticity of government spending with respect to income by
9.9 percent in the goods-sector-only models. Thus, 9.9 percent is the
measured effectiveness of the UI program in this model.

Comparisons of the changes of the measured effectiveness of the
UI program due to the addition of a money sector and the addition of a
government budget condition are listed in Table 5-4. The measured
effectiveness of the UI program in goods-sector-only models ignoring

deficit financing was estimated to be 8.83 percent in Chapter IV. This

114

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116

compares with 9.9 percent when the deficit financing constraint is
considered, an increase of 10.8 percent.

The above increase is due to the wealth effect. The addition of
the UI program not only reduces the fiscal effect (by 8.83 percent), but
it reduces the amount of the deficit that need be financed. As
government spending is increased, the increase is partly funded by an
induced increase in tax revenues. In a model with no UI program, the
difference between the increased spending and the smaller increased
revenue must be financed by selling bonds indirectly to the Federal
Reserve through the public (money financing) or directly to the public
(bond financing). The addition of the UI program reduces the difference
between increased spending and increased revenue via benefit reductions
as income (employment) increases in response to the fiscal policy.

(With a special UI tax argument in the government budget equation, the
difference would shrink further as more revenues would be added.) A
smaller deficit requires less financing, which means less of a wealth
effect. Because the addition of the UI program reduces both the fiscal
and wealth effects when the deficit financing constraint is considered
(instead of just the fiscal effect when deficit financing is ignored),
measured effectiveness of the UI program increases.

Entire Models

 

The analysis above is continued for the models containing a money
sector, with and without the UI program. However, unlike the goods-
sector-only models, the analysis depends on how the increased deficits
are financed, since a money sector is included in the models. The
wealth effect is still calculated the same way and does not depend on

the method of financing. However, if the government sells bonds

117

indirectly to the Federal Reserve through the public to finance the
deficit, effectively monetizing the deficit by increasing the money
supply, there is a further effect on income, the liquidity effect.§! An
increase in the money supply causes an excess supply of money beyond
what is demanded at the new equilibrium income level and interest
rates. Interest rates fall inducing an increase in investment and
consumption, and thus in income. The combination of falling interest
rates and rising income gives rise to a larger demand for money to
equilibrate the money sector. Financing the deficit by selling bonds to
the Federal Reserve serves to increase the impact elasticities of the
policy variables. The liquidity effect is not evident when bonds are
sold to the public since there is no increase in the money supply.
Consequently, impact elasticities are smaller under bond financing than
under money financing.

When a money sector is added, there is a further effect that
reduces impact elasticities in either a bond or money financing
regime. This effect is known as the portfolio effect.2! Assuming net
household wealth plays a role in the decisions about the demand for
money, an increase in wealth via an increase in bonds and/or money
increases the demand for money. For given levels of income and money
supply, pe0ple demand more money, causing a shortage when wealth
increases. Interest rates rise, and this induces a fall in income
through investment and consumption effects. This combination of
declining income and rising interest rates equilibrates the money sector
by inducing a decrease in money demanded.

If money financing is employed, the combination of wealth and

liquidity effects will overwhelm the portfolio effect.L9/ This will

118

make the impact elasticities of the policy variables with respect to
income subject to the deficit financing constraint larger than the
impact elasticities ignoring deficit financing. However, when there is
bond financing, the wealth effect may not be large enough to overwhelm
the portfolio effect. Therefore,the impact elasticities subject to the
deficit financing constraint may be smaller than the impact elasticities
when deficit financing is ignored. This is strictly an empirical matter
and a topic which has received much attention in the debate on fiscal
versus monetary policy.££/ Unfortunately, much of the controversy
depends on the role that bond interest payments play in the deficit
equation and on the stability of the model when these payments are
included.13/ Since I have disregarded bond interest payments in this
paper in order to estimate the model, I do not add to the controversy.
I only report on how much the impact elasticities fall due to the
portfolio effect.k§/

Impact elasticities for the entire model, no UI program (WNUI),
are listed in Table 5-2. From Appendix C, the impact elasticity of

government Spending with respect to income when the deficit financing

constraint is considered is written as

(5.7) dY/dGF = (a2/D)d(BASE+B)/dG + (1/D)dM1/dG+1/D

+ portfolio effect.1fi/

The term (l/D)dM1/dG enters the elasticity equation only if the money
supply is increased to finance the increased government spending. This
term is the liquidity effect. For simplicity, I assume BASE and M1 are

equal in this chapter and Appendix C. This would be the case if the M1

119

money multiplier is equal to one. Since it is greater than one, the
estimates obtained in this chapter are somewhat overstated. The wealth
and portfolio effects are part of the elasticity equation regardless of
the method of financing.

In Appendix C, I use the government budget equation to find the
values of [(dBASE+dB)/dG] to substitute into equation (5.7). The

substitution is:

(5.8) dBASE/dG or (dBASE+dB)/dG = 1-V1(dY/dGNF).
Using the estimated values of a2, V1, D and dY/dGNF from Table 4-4, the
estimated liquidity effect is .021 if the deficit is financed by selling
bonds to the Federal Reserve, and the estimated portfolio effect is
-.0028 using the procedure from footnote 13. The estimated impact
elasticity of government spending with respect to income under a bond
financing regime is 1.317. The estimate impact elasticity under a money
financing regime is 1.338. In the general case of mixed financing, that
is, some bond financed and some money financing, the impact elasticity
would take on values between 1.317 and 1.338. Notice that the
additional effects created by considering the deficit financing
condition make very little difference in the estimated impact elasticity
of government spending.

The next model introduces the UI program into the structural
equations and the deficit equation. The impact elasticity equation is
the same as equation (5.7). From Appendix C, the expression substituted

into (5.7) for the wealth and liquidity effect is:

120

(5.9) dMl/dG or (dBASE+dB)/dG = 1-(V1+f4)(dY/dGNF).

Using the estimates for V1, f4, a2, D and dY/dGNF from Table 4-5, the
estimated wealth effect is .0028. The estimated liquidity effect is
.0065 assuming all money financing, and the estimated portfolio effect
is -.OOO43 using the procedure described in footnote 13. The estimated
impact elasticity of government spending with respect to income under a
bond financing regime is 1.208; under a money-financing regime it is
1.215. Again, the additional effects created by considering the deficit
financing condition make very little difference in the estimated impact
elasticity of government spending.

As was the case for the goods-sector-only models, Table 5-4 shows
comparisons of the changes of the measured effectiveness of the U1
program due to the addition of a money sector, and due to the addition
of a government budget condition. The measured effectiveness of the UI
program for model containing a money sector but ignoring deficit
financing is 7.2 percent. When the deficit financing constraint is
considered, measured effectiveness increase to 8.27 percent (an increase
of 12.9 percent) for all bond financing, and to 9.19 percent (an
increase of 21.6 percent) for all money financing. The reason for the
increase was explained in the previous subsection. The addition of the
UI program reduces the fiscal, wealth and portfolio effects, increasing
measured effectiveness.

The estimated impact elasticities for average potential duration
and UI coverage with respect to income are listed in Table 5-5. The
reduction in these impact elasticities due to the addition of a money

sector in models ignoring deficit financing is 20.4 percent and 28.6

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122

percent for average potential duration and UI coverage, respectively.
The calculation of these impact elasticities when the models are

subjected to the deficit financing constraint is shown in Appendix C.

For example, for the goods-sector-only, UI model (GUI), the deficit-

financing constraint when UI coverage is assumed to change is

(5.10) d(BASE+B)/dCOV = -(V1+f4)(dY/dCOVNF) + f3.

This expression is substituted for the wealth effect term in the impact

elasticity equation for U1 coverage,

(5.11) dY/dcovF = (az/D)(-(V1+f4)(dY/dCOVNF) + £3)

+ (dY/dCOVNF)

After substituting the appropriate values of a2, V1, f4, f3, D, and
dY/dCOVNF, the estimated wealth effect is .0007, making the estimated
elasticity .0028. Again, this means a one percent increase in the ratio
of covered employment to the total labor force increases national income
by .0028 percent.

The wealth effect represents a twenty-five percent increase in
the elasticity due to considerations of deficit financing. The extra
benefit payments from extending coverage do not increase income enough
to raise tax revenues sufficiently to reduce the increased deficit
substantially. With a larger deficit, more money and/or bonds are
injected into the economy to finance the deficit. The ratio of deficit
financing to increased spending is higher for an increase in UI coverage

than for an increase in government spending. Therefore, the wealth

123

effect is larger relative to the fiscal effect for an increase in UI
coverage than for an increase in government spending.

Following a similar approach, the impact elasticity of average
potential duration in the goods-sector-only model is .0329. Again, this
meanszaone percent increase in average potential duration will lead to a
.0329 percent increase in national income. This impact elasticity
increases 40.4 percent (from .0196) due to the addition of a government
budget condition. The same reasoning found in the preceding paragraph
explains this relatively large increase in the estimated impact
elasticity.

Table 5-5 shows the estimated impact elasticities for average
potential duration and UI coverage in models containing a money sector
and subject to the deficit-financing constraint. There are three
important points note when comparing these elasticities. First, it is
clear that money financing make these fiscal measures more expansionary
than bond financing. Second, the increases in the elasticities due to
the addition of a government budget condition in models containing a
money sector are similar to those in goods sector only models, only_when
money financing is used. This is not a surprising result, as money
financing prevents interest rates from increasing and is nearly
equivalent to the fixed interest rate assumption held in goods sector
only models. The increases in the multipliers when all bond financing
is considered fall far short of the increases in the goods sector only
model. Finally, the estimated portfolio effects are smaller than the
estimated wealth effects for these variables. This occurs because a
substantial amount of deficit financing is needed when either of these

two variables change. The effect of this financing serves to increase

124

income more through the wealth effect on consumption than it does to
decrease income through consumption and investment falling in response

to higher interest rates brought on by a larger money demand.

5.4 Models with the Money Supply Endggeneous

 

Up to this point, I have analyzed mOdels with changes in the
money supply exogenous and interest rates endogenous. There is nothing
sacred about this assumption; however, it does lend itself to easy
exposition of the various effects (wealth, liquidity and portfolio) when
deficit financing is considered.k§/ For the remainder of this section,
I assume changes in the money supply are endogenous while interest rates
are exogenous (pegged). As mentioned earlier, I assume that changes in
M1 are equivalent to changes in the BASE in this chapter and in Appendix
C.

The goods sector of these models contain the same equations as
the four models already analyzed. (See Tables 4-2 through 4-5 for these
equations.) The interest rate equations are replaced by one money
market equation and an identity equating money supply with money
demand. The estimated structural equations are shown in Tables 5-6 and
5-7. The standard errors included with the estimates of the derived
reduced-form equations were estimated using; the procedure described in
Chapter IV developed by Goldberger, Nagar, and Odeh.1§/ The money
market equation is a standard equation with changes in money depending
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term interest rate, and change in income. The equation is

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127

(5.12) M1 = qo+q1M1t_l+q2WEALTH-q3(TBR-TBRt_l)-+q4(Y-Yt_1)+eM1

where

qi, i=l,2....are positive, and all variables are listed in Table

4-1 0

To find the exogenous impact elasticity, substitute the
disposable income and money supply equations into the consumption
equation. Then substitute consumption and both types of investment into

the income identity to get

(5.13) Y Constant + a1(l-V1)Y - A + a2(1+q2)(WEALTH-BASE)

a1 0

+ - - + — + 1
aqu Mlt-l a2q3(TBR TBRt_1) a2q4(Y Yt-l) a2q2M

’ 33 1:0 TBRt-i + 34 1:1 Cc—1+b1Yc-1 ’ b2 1:0 R3: 1 ’b3CAP

+ clY - CZTBRt-l + c3AVAIL + C4IRt-l - CSIRt-Z + G .

There will be continuous substituting for the BASE term that
appears in the wealth term of the money market equation. This
continuous substitution produces a geometric series (1+q2+q22+q23+-o-)
which is equivalent to (1/(1-q2)). This term becomes part of the
estimated coefficients of all the terms in the money market equation.

Performing this Operation gives the intermediate-step equation

128

(5.14) Y = Constant + a1(l-V1)Y - alA0 + a2(1/(l-q2))(WEALTH-BASE)

+azq1(1/(1-q2)>M1t_1 - a2q3(1/(1-q2))(TBR-TBRt‘I)
+ 82%“ 1"‘12))(Y"Yc«-1) " 33 (1:0 TBRt—i)/3+ 31. (1:1 Ct-i)/2

+bY - bzggORBEiVA-b CAP+cY -c

1 t-l 3 1 2TBRc—

1

+ c3AVAIL + C4IRt-l - IRt-Z + G .

The reduced-form equation for Y is

(5.15) Y = Constant*-(al/D)AO + (aZJ/D)(WEALTH-BASE)
' (a3/D) SiovrBfiai)/3+(aA/D)(1:1(had>/2+((b1'32q4J)/D)Yc-1
- (1.2/15) (120 RBt_i)/4-(b3/D)CAP - ((c2-a2q3J)/D)TBRt_1
- (a2q3J/D)TBR + (c3/D)AVAIL + (CA/D)IRt_1 - (cs/D)IRt_2
+ (a2q2J/D)M1t_1 + (l-D)G ,
where
J = (1/(1-q2)); and

D
II

(l-al(1-V1)-C1-a2q4J)-

D-1 is the implicit elasticity of government spending with respect to

129

income, dY/dG. This term can be broken down into two parts: the first
three terms, (1-a1(l-V1)-C1), and the last term, (-32q4J).

The first part is the simple impact elasticity of government
spending in a model with no UI program and no money sector, ignoring
deficit financing i.e., the fiscal effect. The second part needs to be
explained. With interest rates fixed the money supply responds to
changes in income. As (for example) government spending is increased,
income rises, raising the demand for money. The supply of money must
increase to equilibrate the money market. The assumption of fixed
interest rates and an endogenous money supply force the money supply to
increase when deficits are increased by fiscal policy. The final term
is an aggregation of the wealth, liquidity, and portfolio effects
described in the last section. The last term represents how much income
must rise to induce money demand to increase to equilibrate the money
market at the new higher money supply created by deficit financing.
Since interest rates are pegged, the portfolio effect cannot be removed
by rising interest rates. It must be dealt with by increasing the money
supply. There is a succession of portfolio effects: this shows up in
the geometric part of this term, J. Clearly, for stability, 0 < q2

< l, or the money supply and income would increase continually and not
approach an equilibrium. This condition holds empirically, as peOple
only demand a fraction of their increased wealth (the higher money
supply) as money. (See Tables 5-6 and 5-7 for the value of 92 in each
of the models.) The value of the impact elasticity can be estimated
using the prOper estimated coefficients from the structural equations of
the appropriate model. The estimated impact multiplier for government

spending in the model without UI is 1.465.

130

The reason models with changes in the money supply endogenous
were not analyzed until now should be apparent. Explicit in the impact
multipliers found in these models are deficit financing considerations,
as the money supply changes when income responds to fiscal policy (or
autonomous shocks). It is theoretically possible to have mixed finance
and to have an additional wealth effect due to the number of bonds
outstanding increasing, but it is not possible to have all bond
financing. The proportion of bond financing (or additional money
financing) can only be as high as (1 - TAXES - dBASE) percent of the
increase in spending.

In other words, bond financing is necessary only when the
increased tax revenues plus the increased money supply brought on by
increased income do not cover or exceed the increase in government
spending. The procedure to calculate to amount of bond financing needed
and the subsequent wealth effect is found in Appendix C. The amount of

bond financing needed is shown by the following equation:

(5.16) dB/dG = 1-(V1+dM/dY)(dY/dGNF);

where dM/dY is the estimate of q4 in equation (5.12).

Substituting the appropriate estimates of V1,k q4, and dY/dGNF from
Table 5-6, the estimated value of bond financing needed is .07. In
other words, bond financing need be used for only seven percent of any
increased government spending. By substituting for the apprOpriate
values of 32, J, dY/dGNF, and dB/dG following the procedure in Appendix
C, the estimated wealth effect is .006. The impact elasticity on

government spending including this wealth effect is 1.471.

131

Substituting the appropriate estimated coefficients for a2, D,
V1, f3, J, and dY/dGNF from Table 5-7, I find the estimated impact
elasticity on government spending for the model with the UI program to
be 1.30. Following the procedure in Appendix C, I find that additional
bond financing is not necessary. The combination of increased tax
revenues, decreased UI payments and an increase in money supply to meet
the increased money demand, all due to an increase in income brought on
by an increase in government Spending, more than covers the increased
deficit. Therefore, there is no additional wealth effect.

Impact elasticities for average potential duration and UI
coverage are also estimated for models with an endogenous money
supply. These estimates are shown in Table 5-8. The estimated values
of both these elasticities are larger in the model with an endogenous
money supply than in models with an exogenous money supply. There is
additional bond financing needed for changes in both the UI program
policy variables that increases the estimated values of their
elasticities with respect to income.

Comparisons of the measured effectiveness of the UI program
estimated from the different models are shown in Table 5-9. Measured
effectiveness is 11.26 percent for money supply endogenous models,
ignoring additional bond financing, and 11.6 percent when additional
bond financing is necessary. Notice that the measured effectiveness of
the UI program is greater in a world in which interest rates are pegged,
compared to a world in which the money supply is exogenous.

The explanation for this is the accommodating action of the
endogenous money supply as it reacts to changes in income. As income is

increased by expansionary fiscal policy or exogenous, good sector

132

TABLE 5-8

IMPACT ELASTICITIES, MODELS WITH THE MONEY SUPPLY ENDOGENOUS

 

Model Elasticity Estimated Value Estimated Value with
Necessary Financing

 

NO UI Government Spending 1.465 1.471
UI Government Spending 1.300 1.300
UI Average Potential Duration .0174 .0251
U1 U1 Coverage .0026 .00281

 

NOTE: The estimated value with necessary financing is obtained following
the procedure in Appendix C.

133

 

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134

shocks, the money supply rises, rather than interest rates. This
increase in liquidity maintains investment and consumption whereas an
increase in interest rates discourages these types of Spending. The
increase in liquidity encourages consumption to increase through the
wealth effect, and the portfolio effect is removed by continually
increasing the supply of moneylzj, which increases the impact elasticity
further. Therefore, although measured effectiveness of the UI program
is larger under an interest-rate-pegging regime, the larger effect is
due to monetizing part of the deficit caused by an increase in fiscal
policy.

Table 5.10 shows a comparison of impact elasticities for average
potential duration and UI coverage estimated from different models. The
impact elasticity of average potential duration ignoring financing in a
world with the money supply endogenous .0174. This means that a one
percent increase in average potential duration, measured in weeks, leads
to an increase in income of .0174 percent. This is compared to .0157
percent in a world in which the money supply is exogenous. When the
deficit financing constraint is considered, the estimated impact
elasticities are .0251 in a world with the money supply endogenous and
bond financing is necessary, .0249 in a world with the money supply
exogenous and a money financing regime, and .0181 in the same world
under a bond financing regime.

The impact elasticity of U1 coverage with rspect to income is
.0026 in a money-supply endogenous world ignoring deficit financing.
This indicates that a one percent increase in the ratio of covered
employment to the total labor force will increase income by .0026

percent. This is compared to .0015 percent in a world where the money

135

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136

supply is exogenous and deficit financing is ignored. When the deficit
financing constraint is considered, the estimated impact elasticities
are .00281 in a world with the money supply endogenous and bond
financing necessary, .00191 in a world with the money supply exogenous
and a money financing regime, and .00161 in the same world under a bond
financing regime.

There are two important points to be made about the results
obtained above. First, as with the impact elasticity of government
spending, the average potential duration and UI coverage elasticities
are larger in the model with the money supply endogenous than in the
model with the money supply exogenous. Second, the necessary bond
financing (and wealth effect) is relatively larger in estimating the
elasticities for these variables than the government spending
elasticity. This is because income does not increase significantly in
response to changes in these variables, therefore, tax revenues and the
money supply do not increase enough to cover as much of the deficit as

was the case to an increase in government spending.

5.5 Conclusion

 

The measured effectiveness of the UI program is influenced by
many economic factors. This and the previous chapter have shown that
the measured effectiveness of the UI program was not accurately
estimated in previous studies because of one serious flaw and two
important omissions. The serious flaw was not structuring, estimating
and testing any models from which the aggregate demand elasticities (or

multipliers) necessary to measure the stabilization effectiveness of the

137

UI program could be calculated. The previous chapter showed that
omission of a money sector resulted in an overestimate of the measured
effectiveness of the UI program of ten to twenty percent. This chapter
adds a government budget condition to the model and finds the
consequences of deficit financing for measured effectiveness of the UI
program. In most cases, measured effectiveness increases, as the
inclusion of the UI program in the three classes of models (goods-
sector-only, entire, and money-supply-endogenous) induced smaller
deficits and less financing compared to models without the UI program.
This leads to larger differences in impact elasticities between the
models, which increases measured effectiveness.

The measured effectiveness of the UI program rises from 7.2
percent in a model with both goods and money sectors but ignoring
deficit financing, to 8.277 percent in that same model but under a bond
financing regime, to 9.19 percent in the same model but under a money
financing regime. Similar increases are found when comparing the impact
elasticities of average potential duration and UI coverage across models
with and without the deficit financing constraint considered. These are
not the true estimates of the measured effectiveness of the UI
program. These estimates include the liquidity, portfolio and wealth
effects induced by deficit financing. The increasezhithe estimates of
the measured effectiveness of the UI program obtained in this chapter is
due to the additional wealth and liquidity in the economy brought on by
financing an increase in all types of government Spending. The true
estimates of the measured effectiveness of the UI program are found in
Chapter IV. Those estimates do not include the additional effects

caused by deficit financing.

138

Two new models were estimated in this chapter incorporating the
assumptions of an endogenous money supply and fixed interest rates.
These models resulted in larger impact elasticities than the
corresponding impact elasticities of the models with an exogenous money
supply. The reason for this is the accommodating effect of the money
supply, as it is forced to increase to maintain money market equilibrium
when eXpansionary fiscal policy raises income. Although the measured
effectiveness of the UI program is increased in this world, all of the
increase is not due to fiscal policy alone. Part of the effectiveness
of the UI program is due to accommmodating monetary policy. This
increase in stabilization effectiveness must be weighed against the loss
of the controllability of the money supply, which must change

continuously to equilibrate the money market as income changes.

CHAPTER FIVE
NOTES

l/Silber (1970).

.Z/Christ (1969).

éjBlinder and Solow (1973).

é/Infante and Stein (1976).

éjlf the deficit equation (no U1) is

(N.1) c - TAX + BIP = dMl + dB ,

and the deficit changed in a model with interest rates endogenous, the
equation would become

(N.2) dG - dTAX + dBIP = dMl + dB, or,
(N.3) dG - Vl dY + dBIP == dMl + dB .

The problem term is dBIP. Since BIP = B * TBR ,
(N.4) dBIP = dTBR * B + dB * TBR .

Consider the easy money financing case first.

(N.5) dG - V1 dY 'f dTBR * B = dM, since dB = O .
Changes in the money supply, assumed exogenous are now tied to changes
in the interest rate. Therefore, the increase in money supply is
actually endogenous. Following this to its logical conclusion,
everything in the model is endogenous, as the model is subject to
equation (N.5). If everything is endogenous, the model cannot be
estimated. The case of all bond financing is similar, except the
increase in the number of bonds outstanding is endogenous. Since all
money and all bond financing are just the extremes of a general mixed
financing case, in general the model would be underidentified and
inestimable with interest payments on the government debt in the deficit
equation.

.é/This term is referred to as the fiscal effect in Silber (1970).
.1/This term is referred to as the wealth effect in Silber (1970).

§/Si1ber (1970).

139

140

21511ber (1970).

kQ/This would be true even if all the increased wealth was held as
money. In that case, the liquidity effect would be offset by the
portfolio effect, but the wealth effect is still positive and would
cause the impact elasticity to increase.

{l/Blinder and Solow (1973), Infante and Stein (1976), Brunner and
Meltzer (1976), and Tobin and Buiter (1976) are four of the many
articles that try to analyze this controversy.

kg/See especially Blinder and Solow (1973) and Infante and Stein (1976).

LéjActually, the portfolio effect cannot be explicitly derived from
these models. The portfolio effect represents how much investment and
consumption fall due to a rise in interest rates that accompanies an
increased money demand. Symbolically, the portfolio effect is

(N.6) dY/dTBR = (dC/dTBR)(dTBR/dWEALTH) +
(dINR/dRB)(dRB/dTBR)(dTBR/dWEALTH) .

The problem lies in the fact that I have no estimate of
(dTBR/dWEALTH). Putting wealth into the interest rate equation was
judged faulty based on several summary statistics used to test for
multicollinearity and goodness of fit. The term (dTBR/dWEALTH) can be
written

(N.7) (dTBR/dWEALTH) = (dTBR/dMD)(dMD/dWEALTH) ,

where MD is money demand. I have an estimate for (dMD/dWEALTH) when I
consider models with the money supply endogenous. The estimated values
for that term are in the vicinity of .10. The term (dTBR/dMD) should
be bounded by -(dTBR/dMS), where MS is money supply, since it is
doubtful an increase in the money supply, thus wealth, is held as all
money. If it were, an increase in the supply of money would have no
effect on interest rates. Thus, for the term (dTBR/dWEALTH) I am using,

(N.8) (dTBR/dWEALTH) = -(dTBR/dMS)(dMD/dWEALTH) .

This approximation most certainly will be too large (in absolute
value). Equation (N.8) is substituted into equation (N.6), and these
terms as well as the other terms in this equation are taken from the
estimated models of Chapter IV, to produce the portfolio effects shown
in Chapter V.

55/Silber (1970), has a theoretical model with an endogenous money
market equation that he substitutes for his endogenous interest rate
equation and gets all the effects shown in Section 5.3. However, he
assumes an exogenous money supply and solves for the endogenous interest
rate to enable him to disaggregate the impact multiplier into wealth,
liquidity, and portfolio effects as I have done in Section 5-3.

141

1i/Poole (1970), shows that attempting to control interest rates when
there are exogenous goods sector shocks leads to the loss of control of
the money supply by the monetary authority.

CHAPTER SIX

CONCLUSION

This dissertation measures the stabilization effectiveness of the
Unemployment Insurance program in the context of an aggregate demand
model. In addition, the stabilization effectiveness of the UI program
in recession and recovery is measured, and the speed of response of the
UI program to changes in aggregate demand is examined.

The major results of this study are:

1. Monetary reactions to fiscal policy and financing deficits
caused by increased government spending are important factors in
measuring the stabilization effectiveness of the UI program. These
factors were completely ignored in all previous studies that attempted
to measure the effectiveness of the UI program as an automatic
stabilizer. Monetary reactions to fiscal policy, through interest rate
changes, reduce the measured effectiveness of the UI program below that
of aggregate demand models that incorporate only a goods sector.
Subjecting aggregate demand models to a deficit financing condition
increases marginally the measured effectiveness of the UI program by
reducing interest rate changes in the models and/or increasing income
through a wealth effect.

2. Accommodating monetary policy increases marginally the

measured effectiveness of the UI program by keeping interest rates from

142

143

rising and thus crowding out private spending. However, the loss of
control of the money supply is sacrificed for this increase in
stabilization effectiveness.

3. By not taking account of the growth in aggregate demand over
time, all previous U.S. studies that attempted to measure the
effectiveness of the UI program overestimated the program's
effectiveness in recessions and underestimated its effectiveness in
recoveries. Taking account of the growth in aggregate demand smoothes
the measured effectiveness of the UI program across recession and
recovery.

4. Although the UI program aids in stabilizing the economy,
discretionary temporary extended benefits programs have decreased the
measured effectiveness of the overall UI program. The main causes for
this are the timing/lag problems inherent in discretionary policy and
the fact that stabilization effectiveness is measured with respect to
income, not unemployment rates.

5. Although there is no suitable test to determine how fast the
UI program responds to changes in income, one can safely assume the
response is within one quarter. Therefore, the Stabilization
effectiveness of the UI program can be measured contemporaneously with
income changes in quarterly (or longer) time series models.

In measuring the stabilization effectiveness of the UI program,
this study uses several novel approaches that distinguish it from
previous work. First, the empirical work in Chapter IV and V is based
on estimation of completely specified models from which impact
elasticities can be found that are needed in calculating the

effectiveness measure. Secondly, the UI program is incorporated into

144

the model endogenously rather than being an implied exogenous

variable. I can measure the stabilization effectiveness of this one
fiscal policy in this way, instead of measuring the impact of all fiscal
policies together. Most importantly, the models incorporate a money
sector and a government budget condition that provide avenues by which
there can be monetary reactions to goods sector disturbances, and they
also show the effect that deficit financing has on measured
effectiveness.

The use of these methods enables me to decompose the
effectiveness measure into the part due to fiscal policy, the part due
to monetary reactions to the fiscal policy (or goods Side disturbances),
and the part due to deficit financing and accommodating monetary
policy. This decomposition of the effectiveness measure gives a clearer
understanding of how effective the UI program is as an automatic
stabilizer.

The results of this study lead to several policy conclusions.
First, discretionary temporary benefit programs cannot be used to
enhance the stabilization effectiveness of the UI program. These
discretionary programs may meet the social insurance goal of the UI
program by providing needed income to eligible individuals during a
prolonged Spell of unemployment and/or severe recession. However, all
discretionary benefit programs to date have begun as recovery started,
decreasing the stabilization effectiveness of the UI program. A more
effective way to meet both the social insurance and stability goals is
the permanent extended benefits program that is currently part of the UI
program. Although this program still has the disadvantage of increasing

benefits even as recovery has started, it is an automatic program and is

145

not subject to timing problems as are discretionary programs.

Second, the way in which benefits are extended is a factor in the
measured effectiveness of the UI program. Extending benefits produces
larger impact elasticities than does eXpanding coverage. The results of
Chapter IV bear this out. Extending benefits to those experiencing
lengthy unemployment increases the elasticity of consumption with
respect to benefits. Alternatively, expanding coverage would cause this
elasticity to decline, as more of the newly covered individuals would
likely have enough savings and/or liquidity to tide them over their
unemployment spell without Spending as much of their benefits as
constrained individuals. Further, these individuals are likely to be
higher-income individuals, so the combination of higher income and not
spending as much of their benefits causes the elasticity of consumption
with respect to benefits to decline. This causes the measured
effectiveness to decrease.

Further evidence of this difference can be seen when comparing
the impact elasticities of coverage and duration in models with and
without a money sector. The impact elasticity of coverage falls
substantially more than the impact elasticity of duration when money is
included in the model. Movements in interest rates cause more of a
squeeze on the illiquid UI benefit recipients, causing even more of them
to Spend all their UI income. This keeps the impact elasticity on
duration from drOpping as much as the impact elasticity on coverage.
This discussion must be tempered by the recognition that duration is
usually extended as recovery has started, which was found to detract
from stabilization. In fact, expanding coverage in recoveries would

also detract from Stabilization as more benefits would be paid out when

146

income is rising. In recovery, expanding benefits would have less of a
negative impact than extending duration. One can see that the
discretionary policy dilemma that arises hinges on recognition of the
correct action needed, one of the timing problems encountered by
policymakers.

The final policy conclusion has been stated previously when we
discussed accommodating monetary policy in general. By trying to hold
interest rates fixed while increasing government Spending or UI
benefits, monetary authorities lose control of the money supply. By
causing income to rise (or fall less than if no action was taken), money
demand increases above the level that would have occurred in the absence
of fiscal policy. In order to equilibrate the money sector without a
rise in interest rates, there must be an increase in the money supply.
This increases wealth, which causes another increase in money demand and
supply, and so on. Monetizing the debt brought on by increased spending
also puts in motion the above money demand/money supply reaction
process, further reducing control of the money supply. The consolation
is that the measured effectiveness of the UI program increases
marginally under this regime. Policy makers must weigh the cost of the
loss of control of the money supply against the gain in stability in
determining what policy to follow.

Further research remains to be done in two major areas. First,
the study measures effectiveness by comparing the changes in impact
elasticities of various exogenous variables when the UI program is
included in the model. A more realistic approach would be to compare
dynamic elasticities and time paths of key variables in response to

changes in the UI program. Specifically, the conclusions found in

147

Chapters IV and V may be quite different when a dynamic model is
employed.

Second, future research should consider supply-side effects and
the effect inflation has on the measured effectiveness of the UI
program. This is related to the first area of considering a dynamic
model, rather than a static model. Again, such research could
substantially affect the results of Chapter V on the measured

effectiveness of the UI program when deficit financing is considered.

APPENDICES

 

VARIABLE

APPENDIX A

DATA SOURCES

SOURCE

 

Unemployment Insurance

Unemployment Insurance Taxes

Average Potential Duration

1947-1963

1964-1976

1977-1981

1947-1963

1964-1981

1955-1963

1964-1981

148

Monthly issues of the Labor
Market and Employment
Security Review, U.S.
Department of Labor

Monthly issues of
Unemployment Insurance
Statistics, U.S. Department

 

of Labor, Tables 3 and 4.

Monthly issues of the Social
Security Bulletin, U.S.
Department of Health and
Human Services, Tables M-36
and M-37.

Monthly issues of the Labor
Market and Employment
Security Review, U.S.
Department of Labor.

Monthly issues of the Social
Security Bulletin, U.S.
Department of Health and
Human Services, Table M-4.

Monthly issues of the Labor
Market and Employment
Security Review, U.S.
Department of Labor.

Monthly issues of
Unemployment Insurance
Statistics, U.S. Department
of Labor, Table 8.

Coverage

Insured Unemployment Rate

Seasonally-Unadjusted Gross
National Product

Net Household Wealth

National Income

Disposable Personal Income

Implicit Price Deflator,
National Income

Non-Residential Fixed
Investment

Residential Investment

State, Local and Federal
Tax Receipts

149

1955-1963

1964-1981

1955-1963

1964-1981

1955-1980

1956-1981

1947-1981

1947-1981

1947-1981

1947-1981

1947-1981

1947-1981

Derived from the ratio of
covered employment to total
labor force, both found in
monthly issues of the Labor
Market and Employment
Security Review, U.S.
Department of Labor.

Covered employment found in
monthly issues of the Social
Security Bulletin, U.S.
Department of Health and
Human Services, Table M-36.

Total labor force found in
monthly issues of the Survey
of Current Business, Bureau
of Economic Analysis, U.S.
Department of Commerce.

Montly issues of the Labor
Market and Employment
Security Review, U.S.
Department of Labor.

Monthly issues of the Social
Security Bulletin, U.S.

Department of Health and
Human Services.

Data provided by the Bureau
of Economic Analysis, U.S.
Department of Commerce.
Data provided by the Bureau
of Economic Analysis, U.S.
Department of Commerce.

Data found in Citibank
Economic Data Base.

Ibid.

Ibid.

Ibid.

Ibid.

Ibid.

State, Local, and Federal
Expenditures for Goods and
Services

M1

The Three-Month Treasury
Bill Rate

Moody's AAA Corporate Bond
Rate

Average Hourly Compensation
of All Non-Agriculture
Employees (Wage Rate)

Potential Income

150

1947-1981

1955-1981

1956-1981

1947-1981

1947-1981

1947-1981

Ibid.

Ibid.

Ibid.
Ibid.

Ibid.

Derived from the potential
GNP series of the St. Louis
Federal Reserve, Federal
Reserve of St. Louis Review,
January 1982, p. 16.

APPENDIX B

THE DERIVATION OF THE MEASURED EFFECTIVENESS EQUATION

In Chapter III, I presented a simple aggregate demand model to
algebraically and graphically derive the notion of measured
effectiveness. In Section 3.2, I gave an equation formulated by Eilbott
(1966), that is a more complex version of the measured effectiveness
equation that I derived. This appendix provides a derivation of the
measured effectiveness equation (3.9) that is used to get the estimates
presented in Section 3.4.

The implied model with the UI program is given in equations 3.1-

8.6:

(B.1) Y = C + I + G

(3.2) C = a + cDY

(8.3) I = b + iCPATX

(3.4) G = G

(3.5) CPATX a kY

(B.6) DY = mY,

151

152

where
Y is national income;
C is consumption;
I is net investment;
G is government purchases minus UI benefits;
DY is disposable income minus UI benefits;
CPATX is corporate after tax; and
a,b,c,i,k, and m are positive Coefficients.

Solving this system yields the following equation:

(3.9) y = (a + b + E) (1 - cm - 11.)"1 .

(l-cm-ik) is the multiplier in a world without the UI program. m is the
percentage of a change in national income to the household sector; it is
equivalent to X in equation 3.9. k is the percentage of a change in

national income to the corporate sector; it is equivalent to Z in

equation 3.9.

Adding the UI program to the model changes equations (B.2) and
(3.3) to:
(B.2*) C = a + c (DY+UIB)

(B.3*) I = b + 1 (CPATX-UIT) ,

where
UIB is UI benefits paid; and

UIT is UI tax collections .

153

In addition to these changes, equations (B.7) and (B.8) relate UIB and
UIT to Y:

(B.8) UIT = tY ,

where
u and t are positive coefficients.

Solving the system yields the following equation:
- . . -1
(3°10) Y = (a+b+G)(1-cm+cu—ik—1t) .

(1-cm+cu-ik+it) is the multiplier in a world with the UI program. (-U)
is the change in U1 benefits paid caused by a change in national income;.
it is equivalent to EBB in equation 3.9. t is the change in UI taxes
collected caused by a change in national income; it is equivalent to ETT
in equation 3.9.

Measured effectiveness is one minus the ratio of the multiplier
without the UI program to the multiplier with the UI program. This is

given by the following equation:
(3.11) ME - 1 - [(1-cm-ik)Kl-cm+cu-ik-it1]

Collecting terms and simplifying yields the following equation:

cu+it

(3°12) ME 3 1-cm-ik+cu+it

154

Equation 8.12 is almost equivalent to equation 3.9 except the term
(cu) has the wrong Sign associated with it both times it appears in the
equation. It was noted above that (-u) was the equivalent to EBB in
equation 3.9. This explains the discrepancy, as the equation is of the

form:

-c(-u)+it
1-cm-ik-c(-u)+it ’

 

(B.12*) ME =

and simplifying algebraically produces equation B.12 above. Therefore,
the model implied by equations B.1-B.8 can be shown to yield the

measured effectiveness equation 3.9 or (B.12*).

APPENDIX C

THE DERIVATION OF IMPACT ELASTICITIES IN MODELS CONTAINING

A GOVERNMENT BUDGET CONDITION

The derivation of the impact elasticities used to estimate the
measured effectiveness of the UI program is slightly more complicated
when the models are subject to a government budget condition. This
appendix algebraically derives the impact elasticities for each of the
models in Chapter V. The algebraic derivations are then used with the
estimated models of Chapter IV and Chapter V to produce estimates of the

impact elasticities shown in Chapter V.

Goods-Sector-Only-Models

The following system of equations defines the goods-sector-only, no

UI program model (GNUI):

(0.1) Y = c + INR + IR + G;

2 2
( 2) c a0 alYD aZWEALTH a3 (120 TBRt_1/3) a4 (121 ct_1/2) e

23

155

156

3
. = + - _. o
(c 3) INR b0 blYt_1 b2 (120 RBt_1/4) b3CAP + e3,
(C.4) IR = c0 + clY - CZTBRt-l + c3AVAIL + C4IRt-l - CSIRt-Z + e4;

. = + + o
(c 5) TAX v0 V1Y e5,

(C.5A) YD = - V0 + (l-Vl) Y;
where the variables are those listed in Table 4-1 and all coefficients

(31, bi’ Ci, Vi’ 1 = 1,2...) are positive.

The reduced-form equation for Y for this model is:

(C.4) Y = (a0+b0+cO)/D - aIVO/D + (aZ/D) WEALTH
2 2
— (a3/D) (iZO‘TBRt_1/3) + (aA/D) (121 ct_1/2) + (bl/D)Yt_1
3
- (bZ/D) (120 RBt_i/4) - (b3/D)CAP - (cZ/D)TBRt_1
+ (c3/D)AVAIL + (CA/D)IRt_1 - (cs/D)IRt_2 + (l/D) G ;

where D 8 (1-a1(1-V1)-c1)-

The inverse of D is the impact elasticity of government Spending (and
other exogenous expenditures) with respect to income, ignoring the
deficit financing constraint (dY/dGNF). When the deficit financing
constraint is considered, I subject the reduced-form equation to the

government budget condition;

(C.6) DEF ' G - TAX 8 d(BASE + B) ,

157

where
DEF is the deficit;

B is the percentage change in government bonds outstanding;
BASE is the percentage change in the monetary base;
d is the total differential Operator.

All variables are measured in constant dollars.

Next, totally differentiate the reduced-form equation

(C.lB) dY = d(a0+b0+c0)/D - (al/D)dvO + (aZ/D)dWEALTH
3 2

- (a3/D)d (129 TBRt_1/3) + (a4/D) d<1§1 0,-1/2) + (b1/D)ch-1

+ (-b2/D)d (120 RBt_i/4) - (b3/D)d CAP - (CZ/D)dTBRt_1

+ (c3/D)dAVAIL + (ca/D)dIRt_ - (cs/D)dIRt_ + (l/D)dG .

l 2

Assume government spending increases. From (C.6), an increase in
government spending must be financed by an increase in money and/or
government bonds outstanding. Also, assume all other exogenous
variables remained fixed at their initial levels. These assumptions can
be represented by assuming all the terms except dY, dWEALTH and dc in

equation (C.lB) are equal zero. The resulting equation is

(C.7) dY = (az/D)dWEALTH + (l/D)dG .

Using the fact (from Chapter IV) that net household wealth can be

written as WEALTH - WEALTHt_1 + BASE + B, and assuming dWEALTHt_1 equals

zero, equation (C.7) becomes

158

(C.7A) dY = (aZ/D)d (BASE+B) + (1/D)G .

To find the impact elasticity of government Spending with respect to

income when the deficit financing constraint is considered, (dY/dGF).

divide equation (C.7A) by dc. The resulting equation is

(C.8) dY/dGF = (az/D)d(BASE+B)/dG + 1/D .

The impact elasticity of government spending with respect to income
when the deficit financing constraint is considered is the sum of the
impact elasticity of government spending with respect to income when the

deficit financing constraint is ignored, ((l/D) - dY/dGNF), 1 plus a
term involving changes in wealth.2 The latter is the increase in
consumption (thus income) due to an increase in net household wealth
brought on by deficit financing.

Using equation (C.6), I can derive the wealth effect by

substituting for d(BASE+B)/dG.

(C.6) d(BASE+B) = G-TAX 3 G - VlY .

The change in the deficit brought on by a change in government spending
equals the change in government Spending, dG, minus the increased tax
revenues caused by an increase in income, V1 dY. The deficit financing

constraint is

(C.6A) d(BASE+B) = dG - VldY .

159

Dividing by dc produces the expression for the wealth effect

(C.6B) d(BASE+B)/dG = 1 - V1(dY/dGNF) .

Substituting (C.6B) into C.8 and recalling l/D - dY/dGNF
o = — + o
(C 8A) dY/dGF (aZ/D)(1 V1(dY/dGNF)) dY/dGNF

This equation can now be estimated by substituting the apprOpriate
values of a2, V1, D, and dY/dGNF from Table 4-2. As long as V1 is 1688
than D (since dY/dGNF = D-l, V1 must be less than (l/D)-1 = D), the
wealth effect of an increase in government spending is greater than
zero.

A Similar procedure to the one just described is used to estimate
the impact elasticities of the three policy variables in the good-
sector-only, UI program model (GUI). The only changes are that the
apprOpriate equations for UIB and U be included in the model, and the

government budget condition is now
(C.6*) DEF = G - TAX = UIB = d(BASE+B) .
This can be written as

(C.6**) DEF = G - le + f1PD + £2 WAGEX + f3 COV - f4(Y-YP)

=- d(BASE+B) ,

 

160

where the variables are listed in Table 4-1, and the coefficients are
all positive.
Since it is assumed all exogenous variables except government

spending remained fixed, the deficit financing constraint becomes

(C.6A*) d(BASE+B) 3 d6 - VldY - fadY .

Dividing by dG produces the eXpression for the wealth effect

(C.6B*) d(BASE+B)/dc = l - (V1+f4)(dY/dGNF).
This expression is substituted into equation (C.8). The resulting
equation can be estimated by substituting the apprOpriate values of a2,
V1, f4, D, and dY/dGNF from Table 4-3.

Impact elasticitities for the policy variables average potential
duration, PD, and UI coverage, COV, are found using the same procedure
as that of government Spending. Instead of a change in government
spending creating the need for deficit financing, one of these variables
changes while all other exogenous variables remain fixed. The procedure
is followed from equation (C.7) using dPD or dCOV (separately) in place
of dG. It is important to note the coefficient on dPD and dCOV is not
(l/D) as it is for dG. This is because (1/D) represents dY/dGNF- The
impact elasticities of PD and COV when the deficit financing constraint

is ignored are found in Table 4-3.

Entire Models

 

As was explained in Chapter V, the method of financing the deficits

 

161

(either bonds, money or both bonds and money) matters in the estimation
of the impact elasticities of the policy variables for models with a
money sector. A procedure similar to that used for the (GNUI) model is
followed to estimate the impact elasticities for the entire model, no UI
program (WNUI). Equations explaining the money sector are added to
equations (C.l)-(C.5A) to define the system. A reduced-form equation is
found and totally differentiated to produce an equation like (C.lB).
Equation (C.6) is the appropriate government budget condition to use for
this model.

Government Spending is again assumed to increase, while all other
exogenous variables except the number of government bonds and/or the

money supply remain constant. This produces the equation

(c.9*) dY = (aZ/D)d(BASE+B) + (l/D)dM1 + (1/D)dG + Portfolio Effect ,

where the portfolio effect is discussed in footnote 13 of Chapter V.

The term (l/D) dMl represents the liquidity effect discussed in Chapter
V. To find the impact elasticity of government spending with respect to
income when the deficit financing constraint is considered, divide (C.9)

by dc, (this equation is the same as equation (5.7)).

(C.9A) dY/dGF = (az/D)d(BASE+B) + (l/D)dM1/dG

+ (Portfolio Effect)/dG .

To estimate the wealth and liquidity effects, I follow the
procedure shown in equations (C.6)-(C.8) above. For Simplicity, I

assume that changes in M1 are equivalent to changes in the BASE in this

162

appendix as well as Chapter IV and Chapter V. Therefore, the estimated
value for Eggp_the wealth and liquidity effects is given by the
expression in (C.6B). This eXpression is substituted into equation
(C.9A) for the wealth effect term regardless of the method of deficit
financing, and for the liquidity term when the deficit is financed by
monetizing the debt.3 The estimate of dY/dGF is found by substituting

in the apprOpriate values of a2, V1, D, and dY/dGNF from Table 4-4, and

calculating the portfolio effect described in footnote 13 of Chapter V.
The procedure used to estimate the impact elasticities of the three
policy variables for the entire model, UI program (WUI), is a
combination of the above procedure and that used to estimate impact
elasticities for the (GUI) model. The estimated coefficients needed to

estimate the impact elasticities for this model are found in Table 4-5.
Money with the Money Supply Endpgenous

In Chapter V, I noted that additional bond financing is necessary
only when the increased tax revenues plus the increased money supply
brought on by the accommodating nature of monetary policy do not cover
or exceed the increase in government spending. To calculate if
additional bond financing is necessary for a model with no UI program,

use the government budget equation
(C.lO) DEF a G - TAX = G - VIY 8 d(BASE+B) .

The change in the deficit is equal to the change in government

Spending minus the change in tax revenues caused by a change in income.

 

163

(C.lOA) dDEF = dG - VldY = d(BASE+B)
Since M1 is endogenous, the deficit financing constraint is
(C.lOB) dB/dG = 1 - v1(dY/dGNF) - dBASE/dG .

The last term in (C.lOB) can be written as dBASE/dG = (dMl/dY)(dY/dGNF),
since I assume changes in M1 equal changes in the BASE. Substituting

this expression into (C.lOB) produces the equation
(C.lOC) dB/dG = 1 - V1(dY/dGNF) - (dMl/dY)(dY/dGNF) .

This equation can be estimated by substituting the apprOpriate
values of V1, dY/dGNF, and dMl/dY (=q4) from Table 5-6.

If the estimated value of dB/dG is less than or equal zero, no
additional financing is necessary. If the estimated value is positive,
some bond financing is necessary, in which case a wealth effect need be
estimated. The wealth effect is estimated following the procedure used
in estimating impact elasticities for the (GNUI) model. A reduced-form
equation is derived and totally differentiated. All terms of the
totally differentiated equation are equal zero except dY, dB, and dG,
assuming government spending is changed. To find the impact elasticity

of government spending with respect to income when additional bond

financing is necessary, divide by dG to get

(c.11) dY/dGF = (32(1/(1-q2))/D) dB/dG + dY/dcNF .

164

The estimated wealth effect is found by substituting the apprOpriate

values of 32,1/(1—q2), and D from Table 5-6, and the estimate of dB/dG

above.
A similar procedure is followed to determine if additional bond

financing is necessary for the model with the UI program. The

government budget equation for this model is

(C.12) DEF = G - TAX = UIB 3 d(BASE+B) .

 

The procedure follows the Steps shown in (C.10)-(C.10C). If additional,
bond financing is necessary, the calculation of the wealth effect is

similar to that of (C.ll) using the appropriate estimated values from

Table 5.7.

APPENDIX C

NOTES

1This term is referred to as the fiscal effect in Silber (1970).
2This term is referred to as the wealth effect in Silber (1970).

3When there is mixed financing, both terms are substituted into equation
(C.9A), each multiplied by the percentage of the deficit each term
finances. For example, if bond financing is 20 percent, the wealth
effect term is still 100 percent, the liquidity effect term is
multiplied by .80, and the portfolio effect term is also multiplied by
.80 in this paper due to its construction (See footnote 13, Chapter V).

165

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