Does the St. Louis Equation Now Believe in Fiscal Policy?
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Does the St. Louis Equation Now
Believe in Fiscal Policy?
KEITH M. CARLSON
1THE “St. Louis equation” was developed in 1968 with a multiplier usually estimated at about 1.5 or
in an article in this Review by Leonall Andersen and greater.3
Jerry Jordan.1 The St. Louis equation is an estimated
In a recent article, Benjamin Friedman pamblished
relationship (using the Almon procedure) betsveen updated estimates of the St. Louis equation.4 Accord-
changes in total spending (GNP) and changes in the
ing to Friedman, the St. Louis equation now “be-
money supply and high-employment Federal expen-
lieves in” fiscal policy. He presented results showing
ditures. The focus of the Andersen-Jordan article was
that the St. Louis equation yields a significant gov-
on the relative impact of monetary and fiscal actions. ernment spending multiplier of about 1.5 when esti-
They rejected the propositions that the response of mated with data through second quarter 1976. This
economic activity to fiscal actions relative to mone- result conforms with neo-Keynesian thinking. At the
tary actions was (1) larger, (2) more predictable, and
same time, Friedman duly noted that with these up-
(3) faster. In fact, their results suggested that the
dated estimates the relatively strong impact of mone-
overall effect of fiscal actions was relatively small and
tary actions continues to hold.
not statistically significant. It was this result that gen-
erated considerable controversy among members of The Friedmaxm results are indeed interesting, and
the economics profession.2 The conventional wisdom deserve closer examination. Those who accept the
of the time was that fiscal actions (whether in the tm
See, for example, Frank de Leeuw and Edward M, Grainlich,
form of a maintained increase in expenditures or a “The Federal Reserve-MIT Economne4rie Model,” Federal Re-
tax cut) did have an impact on economic activity, serve Bulletin (January 1968), pp. 11-40; James S. Duesen-
berry, Gary Fromm, Lawrence R. Klein, and Edwin Kuh,
1 eds,, The Brookings Quarterly Econometric Model of the
Leonall C. Andersen and Jerry L. Jordan, “Monetamy and United States (Chicago: Rand McNally, 1965); Michael K.
Fiscal Actions: A Test of Their Relative Importance in Evans and Lawrence R. Klei,,, The Wharton Econometric
Economic Stabilization,” this Review (November 1968), Forecasting Model, 2nd Enlarged Edition (Philadelphia: Uni-
pp. 11-24. versity of Pennsylvania, 1968); Maurice Liebenberg, Albert
2No attempt is made here to give a complete bibliography on A. Hirsch, and Joel Popkin, “A Quarterly Economnetrie Model
the St. Louis equation. Among the earher articles, see Frank of the United States: A Progress Report,” Survey of Current
Business (May 1966), pp. 425-56; and Daniel M. Suits, The
de Leeuw and John Kalchbrenner, “Monetary and Fiscal Ac-
tions: A Test of Their Relative Importance in Economic Economic Outlook for 1969, Papers Presented to the Six-
Stabilization — Comment,” this Review (April 1969), pp. teenth Annual Conference on the Economic Outlook at the
6-11; Richard C. Davis, “How Much Does Money Matter? A University of Michigan (Ann Arbor: University of Michigan,
Look at Some Recent Evidence,” Federal Reserve Bank of 1969), pp. 1-26.
t
New York Monthly Review (June 1969), pp. 119-31; E. Ger- Benjamin M. Friedman, “Even the St. Louis Model Now
ald Corrigan, “The Measurement and Imnportance of Fiscal Believes in Fiscal Policy,” Journal of Money, Credit, and
Policy Changes,” Federal Reserve Bank of New York Monthly Banking, (May 1977), pp. 365-67. Also mee William C. Dc-
Review (June 1970), pp. 133-45; and Edward M. Granmlieh, wald amid Maurice N. Marchon, “A Modified Federal Reserve
“The Usefulness of Monetary and Fiscal Policy as Discretion- of St. Louis Spending Equation for Canada, France, Germany,
ary Stabilization Tools,” Journal of Money, Credit, and Bank- Italy, the United Kingdom, and the United States,” forth-
ing (May 1971), pp. 506-32. comning in Kredit mind Kapital.
Page 13FEDERAL RESERVE BANK OF ST. LOUIS FEBRUARY 1978
original St. Louis evidence regarding the relative tflrc’tof tllc’( data rec i~i0IiS ill the dStiTImatCd eoeffi
strength of monetary and fiscal actions do not ques- c’ieiitsis ‘iiiriiiniri i-cl iii lalilt’ I..’’’ Ipilate Of time
tion the importance of fiscal actions; such actions do equation ilsinLj re’ cccl data through I 1176 k presented
have economic impact over a certain period. How- in able Ii its a prelude to all e\aTninalion of the
ever, the size of the steady-state multiplier is in lac toN contributiiv to the appearance of a signifi—
dispute. In particular, past estimates of the St. Louis (~iiI ~ inultiplici-.
equation showed that there was a short-run impact
for fiscal actions, but this impact washed out over The l’,stnnau’.s
time. If the fiscal action were accompanied by a
in able I. consider first a comparison of Iii’- St.
change in the rate of monetary expansion, there
1.01115 equation as pulbii¼hled in \pril 1970 w tb a
would be an effect, but this would be attributable to
recent \ union e~tiTnatrd o’ i-r the same oi-iginal saw
the monetary action.
ph imiriucl ..-klI eoiKtraints and the number of Ia~s
To deal with Friedman’s results, the St. Louis equa- ate iiaiutained ..\t issue ~ is whether all the ri—
tion is examined for the original sample period from ‘i5TOlI~ of the \ational IliCIlille \ecounts i~sl\ - and
1953 through 1969, and then compared with updated [lie TnOTIe~ supply have altered tile coiichisi ins re-
estimates through 1976. On the basis of this exami- garding the rehiti~p impact of nlolletar\ and Ikeal
nation, it is found that in light of developments since actions drawn f roni the original St. Louis equation.
1969, the form in which the original St. Louis equa-
tion was specified is no longer statistically appropri- Table I
ate. The St. Louis equation was originally estimated
in arithmetic first difference form (with a constant), EFFECT OF DATA REVISIONS ON
that is, all variables were defined as first differ- ST. LOUIS EQUATION
ences in dollar amounts. Examination of the statisti- Based on Data Available in
April 1970 and Feb 1978
cal properties of this specification indicates that at
(Sanple Perod I 1353—IV’1969
least one of the assumptions of least squares estima- 1
4 4
tion appears to be violated when the experience from IV, ronstart . ‘ rn .IM. ‘~ e SE.
1969 to 1976 is added to the data set. An alternative ID .0
specification estimated with data through 1976 is April 1970 Estqna~r Feb 1975 Estirnale’
offered which appears to satisfy the assumptions of rn 122 (2731 ‘37 (2961
least squares estimation, and in the process the orig- rn 180 7341 192 47621
inal conclusions about the impact of fiscal actions are n’. ‘62 l425l 158 3961
found to hold. rn. 87 365~ 63 12591
rn, 06 1 121 24 4 521
557 8061 526 (801i
UPDATING THE ORIGINAL
e 56 12571 48 (2321
ST. LOUIS EQUATION
e 45 (343j 52 1407)
The original St. Louis equation, as published in P 01 I 081 15 I Blj
November 1968, was estimated with data from 1/1952 43 1 318~ 40 I 30~I
through 11/1968. A later version, published in April e. 54 I 2471 67 . 322
1970, used 1/1953 through IV/1969 as the sample 05 17 0/ i 2’,
period.5 This second version served as the fundamen-
Co~staqt 261 (3461 232 2 82l
tal relation in the “St. Louis model,” This model was
an extension of the original St. Louis equation ex- — EU 66 69
tended to include determination of prices, output, SF 384 397
unemployment, and interest rates. DW ‘75 193
There are several possible explanations of Fried-
man’s results, including the effect of data revisions. A — I. : ‘
1..!
‘ . I
‘‘Ni’
Since the original presentation of the St. Louis equa- ‘I m 51’
tion, many data revisions have occurred. The net II ‘“ho’ h~’ I
. ~,i
5 v.
Leonall C. Andersen and Keith M. Carlson, “A Monetarist ii’. “
Mode) for Eeonomnic Stabilization,” this Review (April 1970),
pp. 7-25.
Page 14FEDERAL RESERVE BANK OF ST. LOUIS FEBRUARY 1978
Table I indicates that the effect of all data revisions interesting feature of these updated estimates is that
since April 1970 has been slight. The sum effect of even though the sum effect of monetary actions did
monetary actions (rm,) is slightly smaller, but the not appear to change much, the pattern of the lag
pattern of time distribution among these coefficients distribution changed substantially. Originally the ef-
continues to hold. Similarly, for fiscal actions, the fect peaked for the change in money lagged one
effect of data revisions is very small. The sum effects quarter (AM, ~), but for the sample period extended
on total spending of the independent variables con- through 1976, the peak came on AM, and only AM,
tinue to be dominated by the money variable. The and AM,.., are significant.
summary statistics indicate a slightly larger R~,an
improved Durhin-Watson statistic, but a larger stan- Examination of the coefficients for the change in
dard error of the regression. In general, there is high-employment Federal expenditures (AE) indi-
nothing to indicate that data revisions have changed cates a much greater change for the updated version
the fundamental conclusions drawn from the original of the equation. The sum effect of fiscal actions
St. Louis equation. climbed from .07 with data through 1969 to 1.64 with
data through 1976. Furthermore, the t statistic for
The equation was then estimated through 1976, the sum effect of fiscal actions is statistically signifi-
with 1953 maintained as the beginning of the sample cant in the 1953-76 regression. It is this result that
period.6 These estimates are shown in Table II. The Friedman emphasized.
total effect of monetary actions continues to be im-
portant when the equation is estimated through 1976.
A Critique of These Updated Estimates
The sum effect of monetary actions is somewhat
smaller —4.48 for the period through 1976, compared To better understand what underlies these
with 5.26 for the earlier period. Probably the most changed results, the error pattern of the St. Louis
equation is examined in greater detail. This error
Table Ft pattern is shown in Chart I for the equation as esti-
EFFECT OF UPDATING ST LOUIS EQUATION mated for the original sample period through
IV/1969, and for the updated version through
4 4
Si constant mm.SM ~ e XE IV/1976.
1 0 iO
Sampte Period Sample Period The IV/1969 version shows extreme errors only for
1/1953 IV/1969 (/1953 IV/1976 those periods associated with major strikes. Such is
137 (296) 224 (404) not the case, however, for the updated version. There
1 92 (7.62) 1 55 (4 39) are three periods that stand out 1/1975, 111/1975,
—
rn2 1 58 (3.96) 43 ( 88) and 1/1976. The equation performs poorly in these
m 63 (259) 07 ( 21) periods, yet these quarters were not associated with
.24 ( 52) 40 ( 70) major sfrikes.
526 (8.01) 448 (598)
A crucial assumption in linear regression is that the
.48 (2 32) 34 (1 83) variance of the error term is constant. Examination
e 52 (407) 25 (I 80) of the errors for the period 1/1975 through 1/1976
15 ( 81) 21 (I 34) suggests that this assumption might be violated. If
40 (—307) 36 (2.65) this is so, in the absence of collateral information
e —.67 ( 322) 48 (247) about the relationship between the nonconstant error
07 (21) 164 (450) variances, the power of the standard t and F tests
Constant 232 (2.82) .45 ( ‘as) becomes indeterminate.7 If, for example, these errors
are positively correlated with the size of the devia-
.69 .70
tion of the independent variables about their means.
SE. 3.97 755
there is increased probability of incorrectly rejecting
OW. 1.93 177
the null hypothesis of no significai~ce.~That is, a
n mlmol nd’hbrv moim dim ‘ TfmIeI particular coefficient would be incorrectly judged to
be significant.
kmFriedman also gave estimates for the sample period beginning 7
For further diseimssion, see Jan Kmenta, Elements of Econo-
in 1/1960. This was also done as a part of this study. How- metrics (New York: Macmillan, 1971), pp. 219-69.
ever, none of the conclusions reached here was affected by
this change in sample period. ~Ihid., p. 256.
Page 15FEDERAL RESERVE BANK OF ST. LOUIS FEBRUARY 1978
Chart I
Error Pattern of St. Louis Equation
First Difference (bY) Specification
Error Error
(Billions of Dollars) (Billions of Dollars)
Sample Period: 1/1953 - IV/1969
20
10 - Ic ic.i - .
20
10
0
~ E1IIIzI:E~E~E~IIIII:
IIITE~I~IIEIH 0
~-1O
-20 ii I
-10
-20
30 30
20 20
10 10
0 0
-10 -10
-20 -20
-30 -30
1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975
Nate, Error equals actual quarter.to.quarter first difference in GNIP) minus fitted value see equations in Table Ill for sample period
indicated, Dashed horizontal lines indicate plus-minus the standard error of the regression ~ far l/1953.lY/1969 and 7,55
far l/i953.lV/1976(.
To determine if the assumption of constant vari- tive specification which satisfies this assumption of
ance in the error term is being violated, a statistical least squares.1°
test was conducted for the sample period ending in
IV/1969 and the one ending in IV/1976. These re- AN ALTERNATIVE SPECIFICATION
sults are shown in Table III using the Goldfeld-
Updating the original St. Louis equation suggests
Quandt test for homoscedastieityY The assumption of
the emergence of statistical problems problems —
homoscedasticity (constancy of error variances across
which were not present when the equation svas first
all observations) is not rejected with this specification
estimated in 1968 and 1969. Rather than cling to that
of the equation for the sample period ending
specification, an alternative is examined in an effort
IV/1969, but is rejected for the period ending
IV/1976. In general, the St. Louis equation, as esti- SOTo determine the direction of the bias in the estimates of the
mated in its original first difference form, but up- standard error of the regression coefficients, the ressslts from
the 1976 regression were ranked according to the size of
dated through 1976, does not now appear to satisfy the independent variables and then grouped to compute
the requirement of least squares estimation that the error variances. Correlation of these error variances with the
squared deviations of the group means from the overall
variance of the error term be constant. Given the mean yielded the following:
evidence of nonconstancy of the error variances and Correlation Coefficient
the absence of reliable information about the relation- 8 Groups of 12 Groups of
ship among the error variances, confidence in the 12 Observations 8 Observations
Each Each
significance of the estimated coefficients is reduced,
One way around this problem is to seek an alterna- .90 .55
.83 .67
These results, although not conclusive, suggest that the esti-
9 mates of the standard errors are biased downward, that is,
S. M. Goldfeld and1 B, E. Quandt, “Some Tests for Homo-
seedasticity,” Jonrise of the American Statistical Association the associated t statistics are biased upward. See Ksnenta,
(June 1965), pp. 539-547. p. 256.
Page 16FEDERAL RESERVE BANK OF ST. LOUIS FEBRUARY 1978
able Ill
RESULTS OF THE GOLDFELD QUANDT TEST FOR HETEROSCEDASTICITY
(Si Version of Equation)
Sample Null Alternative Critical Calculated Test
Hypothesis Hypothesis F F Result
1/53 lV/76
A tll/67—1V176 H V( s)A V( ~ Ha V(e )A V(e ) F ~ ~ —224 F 357 H rejected
0 56
~ H V(et)A V(e )~ H V(er)A V(e ) F( 454 2.02 F 5.30 H rejected
10 05 0
l/53—IV/69
H V(c~)~
V(EJ~ H V(e 14 V( )~ F Oh 2 24i 266 F 89 H not rejected
0 0
B i/53—ll/61 H Vfrt)A V(ej~ H V( ) VK5)~ F , ~ 2.3 F .46 H not rejected
0 5 10 0
$ mboi
vi ~t ‘an ofre dot 5
A B obgroup wherrA o C dofhvnt I rre.odul , hn0
d or e at fond udnoof ohtqurds r,b ,.drndorn nhl u op nparnsh oc tf,go,fi a oddo’
‘don in non a a dde m n a
to avoid these specification problems.~~The alterna- The Estimates
tive chosen here is to express all variables in the
Estimates of the St. Louis equation in rate-of-
equation in rates-of-change formX’
change form for the two sample periods ~ue shown in
In their original article, Andersen and Jordan sug- Table IV. The pattern of estimated coefficients as the
gested that a rate-of-change specification might be Table IV
preferable.13 At that time both specifications gave
ALTERNATIVE SPECIFICATION OF
essentially the same results with regard to the rela-
tive impact of monetary and fiscal actions. They opted ST. LOUIS EQUATION
4 • 4
for the first difference form because it gave direct Y, constant mM~ ‘ e ~
estimates of multipliers which, at the time, were more to to
commonly used than elasticities in summarizing the Sample Period Sample Period
economic impact of changes in policy variables, /1953 I’I/1969 I 1953 IV/1976
rn 30 (206) 40 (2.96)
1
‘ There are various methods of avoiding the statistical prob- m 47 (590) 41 (526)
lems discussed here, so it cannot be said with certainty that 38 (3.01) 25 (214)
the altemative specification chose,s here is “the correct one.”
However, if an alternative is found to satisfy the assumption m 09 (119) 06 (71)
of homoscedastielty, along with the other assumptions of rn 16 (--1.10) 05 (— 37)
least squares, more confidence can be placed on the esti-
mated regression coefficients from that specification than in 108 (495) 106 (559)
the original one.
t2 e 07 (1 77) 08 (2 26)
Since the primary- problem with the arithmetic first difference
(including a constant) specification seems to be one of e 09 (363) 06 (252)
heteroscedasticity when the sample period is extended through e 03 ( .75) 00 ( 02)
1976, an attempt was made to identify the source of the
problem. To see whether a specification error may he the e -09 ( 368) 06 ( 220)
3
source of the problem, the Brown-Durbin-Evans test for con- —16 ( 407) 07 ( 183)
stancy of the regression coefficients over time was applied to
the first difference specification. The hypothesis of constancy 06 ( 88) 03 ( 40)
of the coefficients was not rejected for the original sample
period, but rejected for the extended period. However, for Constant 3 22 (4 04) 2 69 (3 23)
the rate-of-change specification, the hypothesis of constancy Ri 53 40
of the coefficients was accepted for both the original and
extended sample periods. See II. L. Brown, J. Durbin, and SE 325 375
J. 14. Evans, “Techniques for Testing the Constancy of Re- DW. 1.85 178
gression Relationships Over Time, with Comments,” Journal
of the Royal Statistical Society, Ser. B (1975), pp. 149-92.
t3
Andersen and Jordan, “Monetary and Fiscal Actions,” fn. 10, An ~nhoI ad bb,.’soon r,dflneci,n hi xp h d too
hi gutS mpoursded onutol rat of h is
p. 16.
Page 17FEDERAL RESERVE BANK OF ST. LOUIS FEBRUARY 1978
Chart II
Error Pattern of St. Louis Equation
Rate of Change (1’) Specification
Error Error
(Percent) Sample Period: 1/1953 - IV/1969 (Percent)
I
10 10
5 5
II I- II I~I
0 — £4- -S~-S- — — — - -~• .,• a- 0
-5
._—-L..~ -i -5
-10 0
~-1
Sample Period: 1/1953 - IV/1976
15 15
10 10
5 5
0 0
-5 ~ -5
-10 -10
-15 -IS
1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975
Note: Error equals actual quarter.to.quarter annual rate of change in GNP) minus fitted value see equations in Table lVl for sample
period indicated. Dashed horizontal lines indicate plus-minus the standard error of the regression 13.25 for I/1953.IV/1969
and 3.75 for 5/1953.IV/197ol.
equation is updated differs substantially from thQse of the test periods, the null hypothesis of constancy
presented for the first difference form in Table II. in the error variances is not rejected. By reason of this
The sum effect of both monetary and fiscal actions argument, there is no reason to suspect bias in the
changes little, Although there is some bunching of estimated standard errors for this specification. The
the coefficients towards t = 0, the coefficient on M.., sum effect for the monetary variable is significant,
is still the peak quarter of effect. but for the fiscal variable it is not.
Examination of the estimates of the fiscal effect
indicates that the sum effect changes from negative SUMMARY AND CONCLUSION
to positive as this specification is updated. However, Benjamin Friedman has published results showing
the total of the fiscal effect is not significantly different that the St. Louis equation now “believes in” fiscal
from zero for either the original or extended sample policy. This conclusion was based on updated esti-
periods. The distribution of the lag coefficients is mates of the equation in its originally ptiblished first
little changed as the equation is updated through difference form. Friedman’s conclusion is shown to be
1976, in contrast to the first difference specifications suspect on statistical grounds. Estimation of that equa-
in Table II. tion in arithmetic first difference fonn no longer ap-
pears to be acceptable because there is evidence of
Analysis of the Error Pattern nonconstant error variance. Hence, it is difficult to
assess the statistical reliability of any conclusions
The results of updating the St. Louis equation in
about the impact of monetary and fiscal actions based
rate-of-change form differ substantially from those in on estimates with that form of the equation.
first difference form (Chart II). Using rates of change
instead of first differences appears to satisfy the as- To correct these statistical problems, the St. Louis
snmption of constant error variances. The results of the equation was reestimated in rate-of-change form. All
Goldfeld-Quandt test are shown in Table V. For each other properties of the specification were maintained,
Page 18FEDERAL RESERVE BANK OF ST LOUIS FEBRUARY 1978
Table V
RESULTS OF THE GOLDFELD QUANDT TEST FOR HETEROSCEDASTICITY
{Y Version of Equatton)
Sample Null Alternattve Cnttcal Calculated Test
~2g~sts F F Result
1/53 IV!76
11162 H V(e 14 V( t~a H Vied V( ;~ F 13535) 224 F 78 H not relected
4 0
H V( d4 V(e )~ H VIEJA V( )a F , 4 4) 2.02 F 97 H not rejected
0 5 10 0
1/53 IV/69
H V( ~A V( )~ H VfrJA V(e )~ F o’ 2424) 2.66 F 34 H not rejected
0 0
Il/Cl H V(e 14 Vfr~) H V(e~) V{ed~ ot at I) 235 F 21 H no rejected
9 4 0
$ymbols
Vt ~t ax, of r sodusi
A B bgroups cbs’ A t uspe ted of B g Is ‘udsial varsan than B
F S di F tat to faroodprsdn atwob tar do rbtedrsudosnvn Se 55th rp nparnh refra vel s sO-n nddgr a
r domtnnun a nddenns a r
that is the number of lags the constraints and degree preferred on statistical grounds the original empirical
of polynomial, and the definitions of the variables, conclusion regarding the steady-state effect of fiscal
This alternative specification satisfied the least actions was not altered. The evidencc does not sup
squares assumptions concerning constancy in the port the contention that the St. I ouis equation now
error variance. With this rate-of-change alternative believes in” fiscal policy.
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