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Working Paper Series
Some Not So Unpleasant Monetarist
Arithmetic
WP 95-02
This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/
Michael Dotsey
Federal Reserve Bank of Richmond
WORKINGPAPER
95-2
SOME NOT SO UNPLEASANT
MONETARIST
ARITHMETIC
Michael Dotsey*
Research Department
Federal Reserve Bank of Richmond
June 1994
(Revised March 1995)
ABSTRACT
This paper analyzes the quantitative significance of Sargent and
Wallace's (1981) “Some Unpleasant Monetarist Arithmetic" in a model that is
parameterized to correspond with U.S. data. The major result is that the
monetarist arithmetic is not overly unpleasant and that the nominal side of
the economy is not very sensitive to whether money growth does or does not
respond to government debt.
*I would like to thank Paul Gomme, Peter Ireland, and Alan Stockman for a
number of useful suggestions and Sam Tutterow for research assistance. The
views expressed in this paper are those of the author and do not necessarily
represent those of the-Federal Reserve Bank of Richmond or the Federal Reserve
System.
I.
INTRODUCTION
The motivation for this paper is the well known controversial work
of Sargent and Wallace (1981).
In their paper they show the potential
importance of the government's budget constraint for the behavior of nominal
variables. The government's lifetime budget constraint can place restrictions
on the behavior of future money and thus influence current economic magnitudes
through expectational channels. Some of their results are indeed striking and
indicate that current tight monetary policy can lead to the unpleasant result
of both higher expected future inflation and higher current inflation.
Theoretically they highlight important intertemporal considerations, but one
wonders if these considerations are quantitatively meaningful in a dynamic
stochastic environment that might reasonably approximate an actual economy.
In order to investigate the quantitative significance of
unpleasant monetarist arithmetic in a dynamic stochastic model in which the
government's budget constraint has nontrivial importance, the methodology of
Dotsey (1994a) and Dotsey and Mao (1994b) is used.
Here both money growth and
distortionary tax rates are stochastic, but one or both must endogenously
respond to debt if the government is to maintain budget balance. The primary
focus of the analysis is the behavior of nominal variables and a comparison of
their behavior when the monetary authority does and does not respond to the
government's budget constraint. A basic result is that for reasonable
parameterizations it is very difficult to satisfy the government's budget
constraint solely through monetary policy.
For debt to remain bounded, fiscal
policy must respond to government indebtedness. With a responsive fiscal
policy, the underlying nominal behavior of the economy does not significantly
depend upon whether or not the monetary authority reacts to government
2
financing considerations. In this sense the monetarist arithmetic is not
overly unpleasant.
The considerations addressed in this paper are similar to those in
Leeper (1991) who extended the Sargent and Wallace work to a linear rational
expectations environment. Leeper's model is, however, somewhat different in
that the monetary authority uses an interest rate instrument and reacts (in
some cases) to inflation. With this modeling of policy, unique solutions only
obtain when either--but not both--the monetary authority or the fiscal
authority respond to the government's budget. When money is the policy
instrument, as it is in this analysis, both authorities can respond to debt.'
This modeling is more directly related to Sargent and Wallace, and since it
potentially allows both the Treasury and the monetary authority to respond to
debt it is more likely to be consistent with actual practice.
For example,
Bohn (1991) shows that for the U.S. both spending and tax revenues are
important means of achieving budget balance.
The paper proceeds as follows.
In section II,
both the behavior
of the government and the underlying technology are described.
In section III
the behavior of an economy that is characterized by a low interest sensitivity
of money demand is investigated. In particular, the differences between an
economy in which the monetary authority does and does not react to government
debt are examined.
Only minor differences are found.
Section IV concludes.
'One could always make the money supply rule more realistic by including
elements of interest rate smoothing.
3
II.
TECHNOLOGY AND GOVERNMENT BUDGET BALANCE
This section depicts the technology and the fiscal and monetary
policy processes that characterize the economic environment under
consideration.
a.
Technoloqv
Firms produce output via a Romer (1986) technology in which a
production externality allows for endogenous growth.
Specifically, output,
yt, is given by
(1)
yt = Ako n:-‘K:
where k is the firms capital stock, n is the labor hours, and K is the
aggregate per capita capital stock. The firm maximizes profits pt[yt-rtk,w,n,], where p is the price level, r is the rental rate on capital, and w is
the real wage rate, subject to (1). Using the parameterization atx = 1 and
the equilibrium condition that k, = K,, in equilibrium one observes that
(2)
r, = OIA n,?=
and
(3)
wt = (l-a)
A Kp;“.
In the model that follows, money has no direct effect on real
economic activity. Thus the choice of endogenous or exogenous growth is not
crucial to the underlying results.
computational reasons.-
b.
Government Budaet Balance
Endogenous growth is chosen, soley, for
4
A novel feature of the exercises undertaken in this paper is the
modeling of endogenous fiscal and monetary policies that are:
(a) stochastic,
(b) do not violate the government's budget constraint, and (c) do not rely on
lump sum transfers. Monetary policy is defined over changes in base growth
rather than the setting of nominal interest rates.
This depiction of policy
is more directly analogous to previous literature relating deficit finance and
inflation.2 It also allows one to investigate the consequences of money
growth's dependence on debt while incorporating the empirically relevant
behavior of taxes responding to debt (Bohn 1991).
Interest rate smoothing
concerns could easily be incorporated by allowing the monetary authority to
respond to unexpected movements in the nominal interest without affecting the
existence or the uniqueness of the solutions (see Boyd and Dotsey (1993)).
Mow, M,,is
introduced through open market operations, and money
behaves according to
(4) M, = M,-,U+v,)
where qt is the stochastic rate of money growth.
Taxes are distortionary and are levied on both the returns from
capital and 1abor.3 Thus tax revenues, T,, are given by
(5) T, = T&K,
+ w,N,)
where K and N refer to aggregate quantities of the per capita capital stock
and labor hours.
(6)
The government's nominal debt Bt+,,therefore, follows
Q,B,+,= G t TR t B, - T, - n,M,-,
'For example see Sargent and Wallace (1981),
(1984)) and McCallum (1984).
Drazen (1985), Liviatan
3To greatly ease the computational burden imposed by monetary and fiscal
policy processes government bonds are untaxed.
5
where G is "useless" government spending, TR are fixed transfer payments, and
Q, is the price of a bond at time t that pays one dollar at ttl.
The real
value of the debt relative to output, B,+,/(P,+,y,+,)
= bt+,,can be written as
(7)
41
+%I) F
4+, = R, [9+~+4-~t-h1(1
wt
t
p ,yt,
t+ +
where R, is the gross nominal,interest rate.
A sufficient condition for the government to obey its lifetime
budget constraint is for tax and money growth processes to behave so that the
debt to gnp ratio is bounded.
For that to happen either one or both must
respond to b,. When these processes respond to debt they are modeled as twostate markov processes with endogenous transition probabilities. Thus the
processes are time varying.
In particular let the transition probabilities
for taxes be
(8a) prob (TV+,= ~~17~ = 7,J = min (max [(l-#b,)““,O],
(8b) prob (7,+,=
7,,17t
=
7,,)
1)
= max (min [4bt"V, 11, 0),
and these for money growth be
Pa)
vob
(rl,,, = vglvt = ‘la) = min Max W-9b,)““,
01, 1)
W
prob(rlt+,
= tl,,
1tit
= q,)= maxbin Mb,“d,
11,01
where the subscripts e and h refer to low and high.
As long as .thedebt rises when both tax rates and money growth
rates are low and falls when tax rates and money growth rates are high, the
debt to gnp ratio is bounded and only rarely lies outside the interval [0,
l/41’ As b, approaches l/4 both taxes and money growth will be high with
probability one.
Similarly as b, approaches 0 both taxes and money growth
6
will be lo~.~ The parameters Y and 3 control the persistence of the two
processes.
For any given debt to gnp ratio as v and $ increase the
probability of remaining in the current state increases. Thus, the above
specifications imply that current realizations of policy have implications for
the entire future path of policy realizations through their direct effect on
debt.
It is important to note that both the unconditional mean and the
persistence of money growth do not depend on the debt to gnp ratio.
If
instead the monetary authority had no control over unconditional means or
persistence it would be a trivial exercise to show that the nominal behavior
of the economy crucially depended on fiscal policy.
Instead the more
difficult question of whether conditional dependence of monetary policy on
debt affects nominal magnitudes is explored.
Alternatively, cases where one of the processes are invariant to
the debt to gnp ratio can be investigated. We will see that it is difficult
to bound the debt to gnp ratio by relying solely on monetary policy, and that
fiscal policy, therefore, must respond to debt.
A monetary policy that is
independent of debt is feasible and such a policy will be compared to that
given by (9a) and (96).
4The debt to gnp ratio can temporarily move outside [0, l/4] because next
periods taxes and money growth depend on todays debt. If, for example b, =
l/$ - E and 7, = 7 and qt = Q then b,,,could be larger than l/4.
Furthermore, withjow probabifity TV+,= 7a and qt+, = r) implying b,,, > bt+,.
At this point, however, the debt to gnp ratio must dec4 ine since 7,+2 and 7)t+2
must equal 7,, and q,,,respectively.
III.
A MODEL WITH A LOW INTEREST ELASTICITY
OF MONEY DEMAND
This section compares economic outcomes when monetary policy
responds to debt and when monetary policy is independent. Since the primary
goal is to quantify the nominal consequences arising from a lack of central
bank independence, a low interest elasticity of money demand is modeled.
To
lighten the computational burden, a cash-in-advance model in which the
interest elasticity of zero is used. The results of the exercise would not be
substantially different if the interest elasticity was small, as it
empirically appears to be,5 but would change for unrealistically high values.
For interest elasticities in excess of one (see Drazen (1985)), it
is possible to obtain the spectacular case of Sargent and Wallace where both
current and expected inflation increase when the current money growth rate
declines.6 Since the interest elasticity of money demand appears to be quite
a bit less than one, this case is not an economically meaningful one.
It is,
therefore, not pursued.
Money is also neutral in this model and the inflation tax,
therefore, has no direct effect on real magnitudes. This purposeful omission
of real-nominal interactions is done to avoid confounding real effects with
the nominal effects generated by the path of expected future money.
This
allows one to highlight the implications that government budget balance has
5See Dotsey (1988) for evidence that currency is not very interest
sensitive.
6Furthermore, to achieve to the spectacular case with a model of monetary
policy given by (9a) and (9b) would require a high interest elasticity at high
debt levels in which expected future money growth is high no matter what the
current state. High expected future money growth implies high nominal
interest rates and the interest elasticity of money demand would need to be
insensitive to the level of interest rates.
8
for nominal magnitudes and concentrate on the main point raised by Sargent and
Wallace.
a.
Individuals Ootimization
The individuals optimization problem is to
5 pt [log c, + ~(1 -nJ]
M
maximize
NJ 9W,), {n,> 9WJ9 {B,)
subject to
M, + ~tkt+,+
Q&4+,5
~Jl-7,Hr$,
+ p,k,(l-6)
+ w,n,)
+ B, + M,_,
-
h-q,c,_,
+ TR,
and
O,c, 5 M,.
The parameter 8 determines the portion of consumption that is subject to the
cash-in-advance constraint. Because agents can use current wages to finance
current consumption, there is no direct inflation tax.7
b.
Eauilibrium
The relevant first-order conditions for this problem are
WA1
WW
Y
=
-tJ
8c
t
(lob)
l/c,
= BE,
rt+,(l
-tt+,)+ (l-6)
Or+1
71n the specification employed above agents are allowed to spend each
dollar once per period (i.e. there is a unitary velocity constraint). This
specification, although somewhat nonstandard makes computation easier, and
serves to eliminate the inflation tax, thus divorcing nominal and real sides
of the model. This dichotomy makes interpretation easier without affecting
the main results of the paper.
9
(1Oc)
Qt = pE,
prct
ct+1
Pt+1
P, = M,/W,)
(104
As these equations stand, the system is nonstationary since the model admits
Defining the following variables m=M/P, r = c/y, and fi=
endogenous growth.
Using (2) and (3) the first-order conditons can be rewritten as
m/c.
(1
Wa)
4
-a1
=
-ft+,)
yc
t
WW l/t, = I=, (l/C,,) :I;;
nt+1
(llc)
[I-ti+ccA&=(1-t,,)]
t+1
pLt= 8
A solution to this problem involves finding the policy function
Kt+1
=
fi(b,,
7,’
rl,,
K,), where fi satisfies
'-= + (l-6)] Ki
(12)%+I=YbptpQI[Ant
This is particularly convenient since it implies that the capital stock can be
eliminated as a state variable. The problem is reduced to so'lvingthe
functional equations for r (b,
7,
q), h(b,
7,
q), and p(b,
7,
7))along with
the transtion equation for government debt.
Once the function {, cc,and h are found, the various pricing
relationship can also be derived.
(13) R,
(14)
E?
= (l/B)[:l/E,(1/(1+1),+,))1,
= c/l,'-=
Et 1
1 +‘I t+1
&“[A$”
and
These are
1,
+ (1-S)]
10
(15)
pt = IfiB&
nt
l-a
ct+f n~;“(An~-”
t
(I-8))
11
where pt is the gross rate of interest paid on a bond promising to deliver one
unit of consumption next period.
C.
Parameterization
For the most part parameter values are consistent with those used
in other studies in dynamic stochastic macroeconomics. The stochastic process
for taxes is calibrated to roughly conform with the Barro and Sahasakul (1986)
series.
Thus the mean of
7
is .27. Government spendings mean is .17 and is
taken from Christian0 and Eichenbaum (1992) while transfers are set equal to
.lO.
Given these values for fiscal policy choosing A=2.0, 8=.98, 78=4.0,
6=.10 and a=.30 yields steady state real output growth of 1.02, a real aftertax interest rate of 1.04, a fraction of time worked equal to .20, and
consumption's share of gnp equal to .64. The parameter B is set so that the
ratio of consumption on nondurables and services to the monetary base is .lO
(which is approximately equal to its actual 1991 value of .09). This implies
e=. 10.
With no interest elasticity of money demand, the tax base for
inflation is independent of the inflation rate and there is not a problem in
using monetary policy to bound the debt from above.
However, if tax rates are
allowed to take on values somewhat,greater than the sum of government spending
plus transfers, it is impossible to counteract the resulting declines in the
debt to gnp ratio through the open market sale of securities. Debt will be
unbounded below.
In this model the revenue from open market operations is
11
h,/U+v-,))(M,/y,)
= (v,/Uw,))&,.
Because qt must be greater than -.02 to
assure positive nominal interest rates, the debt to gnp ratio can only be
increased by .0013 (when e=.lO) through open market operations. Hence a
realistic fiscal policy process requires the responsiveness of tax rates to
debt.
d.
Results
The experiments below will contrast two different monetary
policies one exogenous and the other responding endogenously to debt.
Both
the tax process and money growth rates will be highly persistent with v=16 and
either #=2 or the transition probability of money growth remaining in the same
state equal to .85. With these parameters the autocorrelation coefficient for
taxes is .83, which is very close to the value of .78 displayed by the Barro
and Sahasakul (1986) series, while the autocorrelation coefficient for money
growth is approximately is .63 when money is endogenous and .67 when money is
exogenous. These values are also fairly close to the actual autocorrelation
coefficient of .67 for base growth from 1960-1993.
Tax rates take on the
values .23 and .31 while money growth rates take on the values .02 and .08.
This leads to a standard deviation for taxes of .04, which is almost exactly
the value of .039 exhibited by the Barro-Sahasakul series. The mean of taxes
is ,273 again replicating the .278 mean of the actual data.
Money growth has
a mean of .063 in the exogenous case and .067 in the endogenous case while the
standard deviations are .024 and .025, respectively. This compares with
actual data on base growth from 1959-1993 which has a mean of .065 and a
standard deviation of .023.
12
The policy functions for the case of exogenous monetary policy are
displayed in figures (la)-(lf), while those for endogenous money are shown in
figures (2a)-(2f). One immediately notices that there is little to
distinguish the basic shapes of the various policy and equilibrium pricing
functions.
For example, consider the policy functions for labor hours
depicted in (la) and (2a).
taxes are low.
In both economies individuals work harder when
As debt rises the chances of staying in the low tax state
decrease and individuals take greater advantage of lower taxes by more
aggressively substituting labor for leisure. Similarly when taxes are high,
rising debt makes it more likely that taxes will remain high and there is less
intertemporal substitution out of labor and into leisure.
High money growth
reduces debt levels increasing the probability that tax rates will either fall
in the future or remain low.
Thus in both the high and low tax states high
money growth reduces effort, but the response is so small that it is barely
noticeable in the figures.8
Consumption behaves just like leisure with individuals consuming
more goods when they consume more leisure. With effort greater when taxes are
low and less consumption, real interest rates must be lower in order to induce
a market clearing level of investment. One notes from the policy functions
for investment and the real interest rate that increasing debt crowds in
investment and lowers the real rate, a decidedly non-Keynesian result.
While money growth rates have only small effects on the policy
functions for real variables, they do, alter, somewhat, the equilibrium policy
functions for expected inflation and the nominal rate of interest. Under both
8For a larger dispersion of tax rates the differences between high and
low money growth states becomes more significant.
13
types of monetary policy, higher money growth rates imply higher nominal rates
and higher expected inflation. When money is exogenous debt levels have no
effect on either the nominal rate or expected inflation where as both the
nominal rate and expected inflation are increasing in debt when money is
endogenous. The intuition for these results follows directly from (13) and
(14). When money is endogenous, higher debt implies a greater probability of
high money growth and thus higher nominal rates and expected inflation.
Whether money is exogenous or endogenous does not significantly
affect the behavior of the nominal side of the economy, as shown in figures 4
and 5.
When money is exogenous money growth oscillates somewhat less than
when monetary policy reacts endogenously (compare figures 3b and 4b).
The
oscillatory behavior in (4b) can be dampened somewhat by constructing a hybrid
example in which money only responds to debt at the upper and lower bounds of
the debt to gnp ratio.
The oscillatory behavior of endogenous money imparts similar
oscillations in the other nominal variables. Although the means of the series
are almost identical under the two types of policy, the standard deviations of
the series are somewhat higher when money is endogenous (see Table 1).
In
comparing the model's generated data with actual data on after-tax nominal
interest rates and inflation (measured using the gdp deflator) the data
generated using exogenous money seems to conform better.
deviation for after-tax nominal rates (1970-1993)
The standard
is .014 and inflation has a
standard deviation of .024 over the period 1960-1993.
The correlation coefficients also show some differences between
the two economies.
While the correlations between nominal variables is quite
similar across monetary regimes, the correlations between real variables and
14
the nominal interest rate is quite different (see Table 2).
The reason for
this is the behavior of money and its correlation with tax rates.
When money
growth is endogenous it follows a stochastic process similar to tax rates (see
figures 5a and 5b).
This correlation drives the significant correlation
between money and real variables which was not present under a regime of
exogenous money growth.
The correlations of money with real variables in turn
drives the significant correlations between other nominal variables and the
real side of the economy.
One then sees that apart from a slight increase in the standard
deviations of nominal variables that a regime of endogenous money growth
induces only minor differences in the behavior of nominal magnitudes.
Thus
from the standpoint of unpleasant arithmetic there is really nothing very
unpleasant. The major differences across regimes occurs in the correlations
between real variables and the nominal interest rate.
These correlations do
not occur because of any major causality running from monetary policy to real
magnitudes, but occur because money growth is correlated with tax policy.
We have just seen that nominal behavior does not depend critically
on whether the monetary authority responds to debt.
However, for the two
cases considered an econometrician could easily uncover whether or not the
monetary authority responds to debt by running a regression of money growth on
lagged money growth and lagged debt.9 The results of such an exercise when
money is endogenous is
%
= aT, t
-33 q-1 t ,066 b,..,
(.016)
LW
9Regression coefficients are an average of 250 simulated regressions.
15
However, if the monetary authority were only required to respond to debt at
its upper bound a simple regression would not be sufficient for uncovering the
link between money growth rates and debt.
In this case the estimated
regression would be
‘It = aI, +
.58 t,+-, + -020 bt-,r
(.015)
W)
and the coefficient on lagged debt would be insignificantly different from
zero.
Thus, if the monetary authority is independent in all but fiscal policy
crises, establishing a link between fiscal and monetary policy could be a
fairly subtle exercise.
v.
CONCLUSION
This paper has analyzed the quantitative significance that
lifetime government budget balance has for monetary policy and economic
variables. While explicit consideration of the government's budget constraint
has interesting implications for the effects of fiscal policy--for example,
crowding in of investment and somewhat lower real interest rates--these
consideration have only marginal and not very significant effects on nominal
variables."
As long as the monetary authority can control the essential
features of monetary policy, money growth rates and their dispersion, whether
policy responds to debt or not is of little consequence. Since the
responsiveness of fiscal policy to debt appears/to be critical for the
existence of a well defined equilibrium, and that money policy is at best of
limited practical use in bounding debt, it may be that societies with well
developed taxing technologies place little importance on using a central bank
"For a more detailed analysis of fiscal policy see Dotsey (1994a) and
Dotsey and Mao (1994b).
16
as an agent of fiscal policy. Thus empirical results such as those in King
and Plosser (1985) and Plosser (1982) that indicate that seignorage and other
nominal magnitudes are independent of debt are not very surprising.
17
Barro, Robert J., and Chaipat Schasakul. "Average Marginal Tax Rates from
Social Security and the Individual Income Tax," Journal of Business,
vol. 59 (October 1986), pp. 555-66.
Bohn, Henning. "Budget Balance Through Revenue or Spending Adjustments? Some
Historical Evidence for the United States," Journal of Monetarv
Economics, vol. 27 (June 1991), pp. 333-60.
Boyd, John H. III, and Michael Dotsey. "Interest Rate Rules and Nominal
Determinacy," Manuscript, February 1994.
Christiano, Lawrence J., 'and Martin Eichenbaum. "Current Real Business Cycle
Theories and Aggregate Labor Market Fluctuations," American Economic
Review, vol. 82 (June 1992), pp. 430-50.
Dotsey, Michael. "The Demand for Currency in the United States," Journal of
Monev, Credit and Banking, vol. 20 (February 1988), pp. 22-40.
"Some Unpleasant Supply Side Arithmetic," Journal of Monetarv
Economics, vol. 33 (June 1994), pp. 507-24.
Dotsey, Michael, and Ching Sheng Mao. "The Effects of Fiscal Policy in a
Neoclassical Growth Model," Working Paper 94-3. Richmond: Federal
Reserve Bank of Richmond, February 1994.
Drazen, Allan. "Tight Money and Inflation: Further Results," Journal of
Monetarv Economics, vol. 15 (January 1985), pp. 113-20.
King, Robert G., and Charles I. Plosser. "Money, Deficits, and Inflation,"
Carneaie-Rochester Conference Series on Public Policv, vol. 22 (Spring
1985), pp. 147-95.
Leeper, Eric M. "Equilibria Under 'Active' and 'Passive' Monetary and Fiscal
Policies," Journal of Monetarv Economics, vol. 27 (February 1991), pp.
129-47.
Liviatan, Nissan. "Tight Money and Inflation," Journal of Monetarv Economics,
vol. 13 (January 1994), pp. 5-16.
McCallum, Bennett T. "Are Bond-Financed Deficits Inflationary? A Ricardian
Analysis," Journal of Political Economv, vol. 92 (February 1984), pp.
123-35.
"Government Financing Decisions and Asset Returns,"
Plosser, Charles I.
Journal of Monetarv Economics, vol. 9 (May 1982), pp. 325-52.
Sargent, Thomas J., and Neil Wallace. "Some Unpleasant Monetarist
Arithmetic," Federal Reserve Bank of Minneapolis Ouarterlv Review,
(Fall 1981), pp. l-17.
18
TABLE 1
Sumnary Statistics for Model Generated Data*
money exogenous
means
s.d
rho
7
.273
.040
.827
tl
.063
.024
.682
b
.286
.173
.968
n
.198
.017
.801
c
.645
,020
.757
i
.185
.020
.757
r
1.040
.015
.799
R
1.085
.017
.682
Ile
1.044
.022
.719
A
1.043
.030
.657
money endogenous
means
s.d
rho
.273
.040
.825
.067
.025
.630
.282
.172
.967
n
.198
.017
.798
I
.644
.020
.753
i
.186
.020
.753
r
1.040
.015
.799
R
1.089
.018
.886
7re
1.047
.027
.873
R
1.047
.034
.700
7
*lOO simulations of 60 periods
19
TABLE 2
Correlation Coefficients
(a) money exogenous
7
7
1.0
rl
- .016
b
n
.221
-.992
rl
b
r
i
n
R
?re
II
1.0
-.120
1.0
-.003
-.118
1.0
-.070
-.974
.070
.974
.018
1.0
r
.938
i
-.938
-.018
r
- .915
- .022
- .312
.881
- .788
R
- .016
1.0
-.120
-.003
.018
-.595
- .608
'lie
.608
.721
.113
A
.592
,765
- .021
-1.0
1.0
.788
1.0
-.018
.022
.551
-.551
-.663
.721
,611
- .611
-.513
.765
1.0
1.0
.926
1.0
(b) money endogenous
7
7
rl
b
n
c
i
r
R
ne
A
1.0
rl
.307
b
.207
n
- .991
c
.936
i
-.936
r
-.912
1.0
.600
-.239
1.0
-.lOl
1.0
-.689
-.973
1.0
-.112
.089
.973
-1.0
-.361
-;304
.875
-.777
.112
1.0
.777
1.0
.027
-.343
R
.257
.864
.903
-.155
- .027
Ile
.687
.765
.759
-.600
.426
-.426
-.794
.842
'II
.771
,823
.488
-.727
.621
- .621
-.740
.696
1.0
1.0
.875
1.0
Figure
1: Policy
Figure
Functions
lo:
LABOR
for
Low
Interest
Elasticity
Figure
HOURS
-0.01
0.10
0.21
0.32
Debt /GNP
Figure
1 c:
0.54
0.65
-0.12
0.76
-0.01
high
tax,
Figure
RATIO
Id:
0.10
0.21
Debt /GNP
0.32
0.43
0.54
0.65
0.76
Ratio
REAL
INTEREST
RATE
money
tax,
high
money
high
-0.01
low money
0.21
tax,
0 t
-0.12
RATIO
money
low
high
0.10
tax.
Debt /GNP
Ratio
INVESTMENT-GNP
low tax,
high
0.43
Exogenous)
1 b: CONSUMPTION-GNP
high
-0.12
(Money
0.32
Ratio
0.43
0.54
0.65
0.76
c-l1
9
-
-0.12
-0.01
0.10
0.21
Debt /GNP
high
L
0.32
money
Ratio
1
1
0.43
0.54
0.65
0.76
Figure
le:
NOMINAL
low tax,
high
high
tax,
INTEREST
RATE
Figure
high
money
high
1 f:
money
EXPECTED
tax,
high
INFLATION
money
88-
low tax,
high
!-
low money
tax,
low
money
in
6
-
-0.12
-0.01
0.10
0.21
Debt /GNP
0.32
Ratio
0.43
0.54
0.65
0.76
8
-
low
-0.12
-0.01
0.10
tax, low money
0.21
Debt /GNP
0.32
Ratio
0.43
0.54
0.65
0.76
Figure
2:
Policy
Figure
Functions
2a:
LABOR
for
Low
Interest
Elasticity
Figure
HOURS
2b:
(Money
Endogenous)
CONSUMPTION-GNP
high
tax,
RATIO
high money
low money
F,
,
/
d
-0.120
-0.013
high
tax.
tax.
low
low money
money
high
tax,
high
0.203
0.095
Debt /GNP
Figure
2c:
0.310
0.418
low
0.525
0.740
-0.120
-0.013
Figure
RATIO
money
low
tax,
0.095
low money
N
NO
2d:
0.310
0.203
Dcht /GNP
INVESTMENT-GNP
tax,
0.633
b
u-l
d
Ratio
d
low
money
0.418
0.525
0.633
0.740
Ratio
REAL
INTEREST
low tax,
low money
low tax,
high
RATE
money
1
m
d
V
-t
d
high
tax,
low
high
tax,
high
money
1
money
0
d
I
-0.120
-0.013
0.095
0.203
Debt/GNP
0.310
Ratio
0.418
0.525
0.633
0.740
_. . __
high
tax,
low money
high
tax,
high
13 0.310
-.Debt /GNP
Ratio
money
0.416
i
I
0.525
0.633
0.74q
‘I
Figure
2e:
NOMINAL
INTEREST
I
2f:
EXPECTED
INFLATION
I
tow tax.
high
high
tax,
high
high
2
Figure
RATE
-0.120
-0.013
0.095
money
mone
tax,
0.203
Debt /GNP
low money
0.310
Ratio
0.525
0.416
0.633
0.740
II
d
%
low tax,
-0.120
-0.013
0.095
low money
0.203
Debt /GNP
0.310
Ratio
0.418
0.525
0.633
0.740
1
3: Simulations
Figure
Figure
3a:
AVERAGE
for
TAX
Money
Figure
3b:
Exogenous
AVERAGE
MONEY
GROWTH
22
22
20
3 6 9
13
18
23
28
33
38
43
48
53
5i
sl....,.........._...........u..........
60
3 6 9
13
18
23
Period
Figure
3c: AVERAGE
28
33
38
43
48
53
51
Period
DEBT-GNP
Figure
RATIO
3d:
AVERAGE
18
23
LABOR
HOURS
2%
d
s.
d
2.
ci
%.
d
2.
d
0
d.
d
do
3 6 9
13
18
23
28
33
38
43
48
53
,o
3 6 9
13
Period
Figure
3e: AVERAGE
CONSUMPTION-GNP
RATIO
Figure
3f:
AVERAGE
d----Period
28
33
38
43
48
53
56
Period
20
-
3 6 9
13
la
23
INVESTMENT-GNP
28
33
Period
38
43
RATIO
48
53
E
Figure
39:
AVERAGE
REAL INTEREST
RATE
U-I
Figure
3h:
AVERAGE
NOMINAL
INTEREST
RATE
@z
33
Period
Period
Figure
3i: AVERAGE
EXPECTED
Figure
INFLATION
3j: AVERAGE
38
ACTUAL
43
48
53
51
INFIATION
2
+I
Period
3 6 9
13
18
23
28
33
Period
38
43
48
53
5
Figure
Figure
4: Simulations
40:
AVERAGE
for
TAX
0
6
st.................,....................
20 3 6 9 13 18 23 28 33 38
Period
Figure
4c: AVERAGE
43
Money
Figure
48
DEBT-GNP
5f
53
4b:
Endogenous
AVERAGE
GROWTH
.
3 6 9
13
18 23
28
33
38
43
48
53
5
Period
Figure
RATIO
4d: AVERAGE
LABOR
HOURS
0
I-
sl
60 3 6 9 13 18 23
28
33
38
43
48
53
51
3
20
3 6 9
13
18
23
Figure
4e:
3 6 9
AVERAGE
13
18 23
CONSUMPTION-GNP
28
33
Period
28
33
38
43
48
53
51
Period
Period
20
MONEY
38
43
48
RATIO
53
Figure
4f: AVERAGE
INVESTMENT-GNP
58
Period
RATlO
Figure
49:
AVERAGE
REAL INTEREST
RATE
Figure
4h:
AVERAGE
NOMINAL
INTEREST
RATE
$3
;;
22
20
3 6 9
13
18
23
28
33
38
43
48
53
5E
2
,O
3 6 9
13
18 23
Period
Figure
4i: AVERAGE
3 6 9
13
EXPECTED
INFLATION
Figure
E.
20
18 23
28
33
Period
28
33
38
43
48
53
51
Period
38
43
48
53
5
4j: AVERAGE
?,..
70
3 6 9
ACTUAL
INFLATION
13
18
23
28
33
Period
38
43
48
53
58
@FedFRASER