Macroeconomic Effects from
Government Purchases
and Taxes
Robert J. Barro and Charles J. Redlick
Harvard University
Fiscal-Stimulus Packages are a big issue.
Empirical evidence on response of real GDP and
other economic aggregates to added
government purchases and tax changes is thin.
Present study uses long-term U.S.
macroeconomic data.
Spending multipliers identified primarily
from variations in defense spending,
especially changes associated with
buildups and aftermaths of wars.
Ramey’s defense-news variable allows us
to assess changes in expected future
defense outlays; thereby distinguishing
temporary from permanent spending.
Tax effects estimated mainly from changes in
newly constructed time series on average
marginal income-tax rates (AMTR) from
federal and state income taxes and socialsecurity payroll tax.
Attempt to differentiate substitution effects
due to changes in tax rates from income
effects due to changes in tax revenue.
Figure 1
Defense and Non-Defense Purchases
.3
.2
.1
.0
-.1
-.2
-.3
1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
change in defense purchases
change in non-defense purchases
Figure 1 shows dominance of war-related
variations in defense-spending variable.
For World War II, value is 10.6% of GDP
in 1941, 25.8% in 1942, 17.2% in 1943,
3.6% in 1944, followed by two negative
values of large magnitude, -7.1% in 1945,
-25.8% in 1946.
Favorable aspects of WWII for gauging spending multiplier:
• Principal changes in defense spending plausibly exogenous
with respect to GDP.
• Changes large, include positive and negative.
• Unlike many countries that experienced sharp decreases in
GDP during WWII, U.S. did not have massive destruction of
physical capital and suffered only moderate loss of life.
Demand effects should be dominant.
• Because unemployment rate in 1940 was still high, 9.4%,
some information on how size of defense-spending multiplier
depends on amount of slack.
U.S. time series contains two other warrelated cases of major, short-term changes in
defense spending. In WWI, defense-spending
variable was 3.5% in 1917 and 14.9% in 1918,
-7.9% in 1919 and -8.2% in 1920. In Korean
War, 5.6% in 1951, 3.3% in 1952, and 0.5% in
1953, -2.1% in 1954.
Post-1954 features much more modest
variations in defense spending. Largest
values—1.2% in 1966 and 1.1% in 1967—
during early part of Vietnam War. After end of
Vietnam, largest are 0.4-0.5% from 1982 to
1985 during “Reagan defense buildup” and
0.3-0.4% in 2002-2004 during post-2001
conflicts.
Red graph in Figure 1 shows non-defense
G. Note 2.4% in 1934 and 2.5% in 1936,
associated with New Deal. Otherwise,
only clear pattern is tendency for nondefense G to decline during major wars
and rise in aftermaths.
Hard to be optimistic about using macro
time series to isolate multipliers for
non-defense G. One problem is that
variations are small. More importantly,
many changes likely endogenous with
respect to GDP.
As Ramey (2008) observes, outlays by state and
local governments dominant part of non-defense
G (since at least 1929). These expenditures-particularly education, public order,
transportation--likely respond to fluctuations in
state and local revenue caused by changes in
aggregate economic conditions. Whereas war
and peace is plausibly exogenous driver of
defense spending, we lack similarly convincing
exogenous changes in non-defense G.
Figure 2 Defense-News Variable
1.6
1.2
0.8
0.4
0.0
-0.4
1920 1930 1940 1950 1960 1970 1980 1990 2000
Figure 2 on defense news: WWII stands out,
including run-up of 0.40 in 1940, 1.46 in 1941,
0.75 in 1942; wind-down of -0.07 in 1944, -0.19
in 1945.
Peak at start of Korean War (1.16 in 1950)
impressive, signaling concern about potential
WWIII.
Peak for WWI comparatively mild, 0.20 for
1917-18, but lots of assumptions here.
Average Marginal Income-Tax Rates
Barro and Sahasakul (1983, 1986) used IRS
Statistics of Income, Individual Income Taxes
from various years to construct average
marginal income-tax rates from U.S. federal
individual income tax 1916 to 1983. Series
weights by AGI and takes account of nonfilers. Subsequently added social-security
payroll tax (FICA).
Use NBER’s TAXSIM program (Dan Feenberg)
to update data. Focus on average weighted
by concept of income close to labor income.
In overlap, 1966 to 1983, Barro-Sahasakul and
NBER TAXSIM series highly correlated in levels
and changes. Therefore, comfortable in using
merged series for 1912 to 2006.
New construct adds average marginal incometax rates from state income taxes.
Figure 3 shows time series 1912 to 2006 for
overall AMTR and 3 components: federal
individual income tax, social-security payroll
tax, state income taxes. 2006: overall AMTR
35.3%, breaking down into 21.7% for federal
individual income tax, 9.3% for social-security
levy, 4.3% for state income taxes.
Figure 3
Average Marginal Income-Tax Rates
.5
.4
.3
.2
.1
.0
20
30
40
50
60
70
80
Total
Federal Income Tax
Social-Security Tax (FICA)
State Income Taxes
90
00
Many increases in federal AMTR on individual
income involve wartime: WWII (rise from
3.8% in 1939 to 25.7% in 1945), WWI (0.6% in
1914 to 5.4% in 1918), Korean War (17.5% in
1949 to 25.1% in 1952), Vietnam War (21.5%
in 1967 to 25.0% in 1969). Rate tended to fall
during war aftermaths: 25.7% in 1945 to
17.5% in 1949, 5.4% in 1918 to 2.8% in 1926,
25.1% in 1952 to 22.2% in 1954. No
reductions after Vietnam War.
Rising federal AMTR for 1971-78, from 22.7%
to 28.4%. Increase reflected shifting toward
higher rate brackets due to high inflation in
un-indexed system. Small tax-rate hikes
include Clinton, 21.7% in 1992 to 23.0% in
1994 (24.7% in 2000), George H.W. Bush,
21.7% in 1990 to 21.9% in 1991. Given hype
about Bush’s “read my lips, no new taxes,”
surprising that AMTR rose by only two-tenths
of percentage point in 1991.
Major cuts in AMTR under Reagan
(25.9% in 1986 to 21.8% in 1988, 29.4%
in 1981 to 25.6% in 1983), George W.
Bush (24.7% in 2000 to 21.1% in 2003),
Kennedy-Johnson (24.7% in 1963 to
21.2% in 1965), and Nixon (25.0% in 1969
to 22.7% in 1971).
Behavior in Great Depression: federal AMTR
fell from 4.1% in 1928 to 1.7% in 1931, mainly
because falling incomes pushed people into
lower rate brackets. Then, particularly
because of attempts to balance federal budget
by raising taxes under Hoover and Roosevelt,
AMTR rose to 5.2% in 1936.
Although social-security AMTR (employees,
employers, and self-employed, taking account
of income ceilings) have less high-frequency
variation, they increase sharply in some
periods. AMTR did not change greatly from
original 0.9% in 1937 until mid 1950s, then
rose to 2.2% in 1966. Most noteworthy period
of rising AMTR is from 1971—still 2.2%—until
1991, when it reached 10.8%.
One identifying assumption is that changes in
AMTR lagged one or more years can be
satisfactorily treated as pre-determined with
respect to GDP. One way to evaluate this
assumption is from tax-smoothing approach.
Romer-Romer Tax-Change Series
Romer and Romer (2008) use narrative approach
to assess all significant federal tax legislation from
1945 to 2007. Gauge tax changes by size and
timing of intended effect on federal tax revenue.
In contrast to AMTR, focus is on income effects
related to tax collections. High positive
correlation between Romer-Romer and change in
AMTR. (Reagan 1986 as counter-example.)
Romer-Romer avoid obvious simultaneity
between actual tax revenue and GDP. Main
endogeneity issue is politics; changes in tax law
related to current or anticipated economic
conditions. They use 4-bin approach; 2 regarded
as exogenous. One of the endogenous is about
G; really an omitted variable. Other categories
not so clear. We use Romer-Romer as instrument
for contemporaneous change in AMTR or total
federal revenue.
Framework for Empirical Analysis
• Barro and King (1984). Central features:
• Representative agent, time-separable preferences over
consumption and leisure.
• Consumption and leisure both normal goods.
• “Market clearing.”
• Baseline model has closed economy, absence of
durable goods, lump-sum taxes.
Framework for Empirical Analysis
(1)
(yt – yt-1)/yt-1 = β0 + β1∙(gt – gt-1)/yt-1
+ β2∙(gt*– gt-1*)/yt-1 + β3∙(τt – τt-1)
+ other variables.
yt : per capita real GDP, gt : per capita real government
purchases, gt*: expected future g (Ramey), τt : marginal
income-tax rate.
Other variables: lagged U (business-cycle dynamics) and
default spread for interest rates (money/credit).
• Given gt*, gt reflects temporary changes. Coefficient β1 is
multiplier for temporary change in g. Is it positive,
greater than 1, higher with more slack, gauged by Ut-1?
• Model predicts β2 > 0, β3 < 0. As approximation (given
Ramey construction), multiplier for permanent change in
g is β1 + 4*β2 .
• Timing for effects on yt from g and τ? Include lag of g
and focus on lag of τ.
In first regressions, instrument list has
contemporaneous change in defense spending.
Results similar when instrument list has change in
defense spending interacted with “war years.”
Instrument list also has lagged change in AMTR and
lagged U.
Use Romer-Romer (exogenous part) as instrument
when assessing contemporaneous effect of change in
τ or total federal revenue. Also consider as
instrument change in τ computed from prior year’s
incomes.
Include lagged default spread on instrument list.
Empirical Results
Table 2 shows 2SLS regressions with annual
data in form of eq. (1). Samples end in 2006.
Starting year is 1950 (include Korean War),
1939 (include WWII), 1930 (include Great
Depression), or 1917 (include WWI and 1921
contraction). Also consider 1954 and 1914.
Table 2 Equations for GDP Growth
(1)
(2)
(3)
(4)
(5)
Starting
1950
1939
1930
1917
1954
Δg: defense
0.68*
(0.27)
0.44**
(0.06)
0.46**
(0.08)
0.47**
(0.08)
0.98
(0.65)
Δg: defense
(-1)
0.01
(0.28)
0.20**
(0.06)
0.21*
(0.09)
0.16
(0.08)
-0.54
(0.56)
Δg*: def
news
0.026
(0.016)
0.039**
(0.011)
0.034*
(0.015)
0.034*
(0.017)
-0.120
(0.112)
U(-1)
0.50**
(0.17)
0.58**
(0.14)
0.61**
(0.10)
0.47**
(0.10)
0.51**
(0.18)
Δτ(-1)
-0.54**
(0.21)
-0.16
(0.16)
-0.26
(0.22)
-0.19
(0.25)
-0.48*
(0.22)
Yield
spread
-43.9*
(20.7)
-37.8
(22.0)
-101.5**
(12.8)
-73.6**
(12.2)
-43.1*
(21.8)
p-value:
defense
0.030
0.000
0.000
0.000
0.47
R2
0.48
0.82
0.75
0.66
0.45
σ
0.017
0.019
0.027
0.030
0.018
• Samples with WWII, multiplier for temporary defense
spending 0.4-0.5 contemporaneously, 0.6-0.7 over 2 years.
• If change in defense spending “permanent” (gauged by
Ramey’s defense-news variable), multipliers higher by 0.1-0.2.
• Multipliers all significantly less than 1 and apply for given
average marginal income-tax rates.
• Positive versus negative values for change in g?
• Interaction term between g and U(-1) has coefficient close to
zero. Comparison with results when g* omitted?
Post-1950 sample: coefficient of -0.54
(s.e.=0.21) on Δτ(-1). Accords with micro
estimates of labor-supply elasticities. Result
corresponds to “tax multiplier” around -1.1.
Samples that start earlier than 1950 show less
impact from Δτ(-1) on GDP. Effects from
command and control during wars? Mismatch
of 1948 tax cut with 1949 recession.
• Effects of default spread negative in all
samples. Larger in magnitude for
samples that include Great Depression.
• Results on fiscal variables similar if
default-spread variable omitted.
Results in Table 2 seem to provide reliable estimates of
multipliers for defense spending: around 0.4-0.6 for
temporary, 0.15 higher for permanent.
To evaluate typical fiscal-stimulus packages, more
interested in multipliers for non-defense G. Hard to
estimate because observed movements likely
endogenous with respect to GDP.
Hence, important to know whether defense-spending
multiplier provides upper or lower bound for nondefense G.
Implications from Theory,
Defense versus Non-Defense G
• Temporary versus permanent changes in G.
• Command & control and rationing.
• Patriotic boost to labor supply (but threat to
future property rights?).
• Command & control and patriotism stressed by
Mulligan (1998). We think these forces strong
enough so that defense multiplier is upper bound
for non-defense multiplier—but just conjecture.
Table 3 More on Government Purchases
Start date
Δg: defense
Δg: defense
(-1)
Δg*: def
news
U(-1)
Δτ(-1)
Yield
spread
Δg: nondefense
Δ(GM
sales)
Δ(GE sales)
R2
σ
1950
1939
1930
1917
1950
1950
0.89**
(0.27)
-0.13
(0.27)
0.040**
(0.016)
0.44**
(0.06)
0.21**
(0.06)
0.041**
(0.013)
0.46**
(0.08)
0.21*
(0.09)
0.036*
(0.016)
0.46**
(0.08)
0.19*
(0.09)
0.040*
(0.018)
0.84**
(0.24)
-0.36
(0.25)
0.014
(0.013)
0.46
(0.26)
0.02
(0.26)
0.016
(0.014)
0.64**
(0.17)
-0.45*
(0.20)
-31.2
(20.0)
2.65**
(0.93)
--
0.58**
(0.15)
-0.13
(0.18)
-35.6
(22.3)
0.25
(0.72)
--
0.60**
(0.11)
-0.25
(0.23)
-100.9**
(13.3)
0.12
(0.63)
--
0.45**
(0.11)
-0.15
(0.25)
-71.2**
(12.2)
0.51
(0.51)
--
0.26*
(0.16)
-0.26
(0.19)
-38.9*
(18.1)
--
0.55**
(0.16)
-0.38
(0.20)
-21.6
(20.5)
---
--
--
--
--
3.66**
(0.86)
--
0.54
0.017
0.82
0.019
0.75
0.027
0.67
0.030
0.63
0.015
17.6**
(4.7)
0.57
0.016
• Results for non-defense G in various samples.
Different results with WWII and Great
Depression because cyclical pattern of nondefense G different from post-1950.
• Results for GM and GE “multipliers” illustrate
problems of endogeneity with respect to GDP.
Table 4
Predicted Effects from Defense Spending on
Components of GDP
Increase in:
g: defense
g*: defense
news
GDP
Consumption
Investment
Non-defense
government
purchases
Net exports
+
+
-
+
-
+
Table 5 Effects on Components of GDP
Sample: 1950-2006
Dependent
variable:
Δg: defense
Δg: defense (-1)
Δg*: defense
news
U(-1)
Δτ(-1)
Yield spread
squared
Δ(c: non-dur.)
Δ(c: dur.)
Δ(invest)
Δ(g: non-def.)
Δ(x-m)
0.005
(0.093)
0.179
(0.095)
-0.0035
(0.0053)
0.112
(0.058)
-0.184**
(0.071)
-5.4
(7.0)
-0.171*
(0.073)
0.147*
(0.075)
0.0106**
(0.0041)
0.145**
(0.045)
-0.145**
(0.056)
-3.5
(5.5)
-0.083
(0.185)
-0.142
(0.189)
0.0377**
(0.0105)
0.382**
(0.115)
-0.300*
(0.142)
-22.7
(13.9)
-0.081
(0.041)
0.055
(0.042)
-0.0055*
(0.0023)
-0.053*
(0.026)
-0.033
(0.032)
-4.8
(3.1)
0.004
(0.079)
-0.231**
(0.080)
-0.0135**
(0.0044)
-0.095
(0.049)
0.122*
(0.060)
-6.7
(5.0)
-0.009
(0.011)
-0.011
(0.011)
-0.0082**
(0.0021)
-0.030
(0.027)
-0.105**
(0.030)
-6.5
(4.1)
-0.071**
(0.021)
-0.027
(0.022)
-0.0023
(0.0039)
-0.002
(0.051)
0.114*
(0.058)
-8.0
(7.8)
Sample: 1939-2006
Δg: defense
Δg: defense (-1)
Δg*: defense
news
U(-1)
Δτ(-1)
Yield spread
squared
-0.011
(0.022)
0.107**
(0.022)
0.0044
(0.0040)
0.101
(0.052)
-0.008
(0.059)
1.1
(8.0)
-0.115**
(0.016)
0.038*
(0.016)
0.0116**
(0.0030)
0.094*
(0.038)
-0.103*
(0.043)
-3.1
(5.9)
-0.356**
(0.045)
0.096*
(0.046)
0.0341**
(0.0084)
0.401**
(0.109)
-0.067
(0.124)
-20.3
(16.8)
Effects on Components of GDP
1939 sample, estimates for effects on GDP in Table 2 were 0.44 for
g and 0.039 for g*. Corresponding effects on components of GDP in
Table 5 add to -0.56 for g (crowding out) and 0.039 for g*.
Correspondence between empirical and theory for investment.
Coefficients for g negative: -0.12 (s.e.=0.02) for durable C
and -0.36 (0.04) for I; for g* positive: 0.012 (0.003), 0.034 (0.008).
Theory predicted negative effects on consumption, but estimates
for non-durable C insignificant. Non-defense G (consumption?),
effect from g insignificant but g* negative, -0.008 (0.002). Net
exports, effect from g negative, -0.07 (0.02), g* insignificant. During
major wars, changes in g and g* tend to go along with changes in
other countries.
Table 7 More Results on Taxes, 1950-2006
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Δg:
defense
0.67*
(0.28)
0.53
(0.27)
0.66*
(0.28)
0.61
(0.35)
0.53
(0.28)
0.71*
(0.30)
0.72*
(0.29)
0.49
(0.31)
Δg: def
(-1)
0.01
(0.28)
-0.23
(0.28)
-0.05
(0.29)
0.05
(0.32)
-0.23
(0.28)
-0.21
(0.28)
-0.03
(0.29)
0.10
(0.26)
Δg*: def
news
0.025
(0.015)
0.029
(0.016)
0.027
(0.016)
0.023
(0.018)
0.029
(0.016)
0.016
(0.017)
0.021
(0.017)
0.015
(0.018)
U(-1)
0.51**
(0.17)
0.51**
(0.18)
0.48**
(0.17)
0.50**
(0.17)
0.51**
(0.18)
0.49**
(0.18)
0.49**
(0.18)
0.43*
(0.17)
Δτ(-1)
-0.53**
(0.21)
--
-0.43
(0.24)
-0.58*
(0.28)
--
--
-0.45
(0.24)
-0.52**
(0.18)
Δτ
--
--
--
0.12
(0.47)
--
--
--
--
Romer
Δtax (-1)
--
-1.08
(0.57)
-0.56
(0.62)
--
-1.08
(0.58)
--
--
--
Romer
Δtax
--
--
--
--
-0.03
(0.55)
--
--
--
Δ(fed rev)
(-1)
--
--
--
--
--
-0.46
(0.27)
-0.17
(0.30)
--
Δ(fed rev)
--
--
--
--
--
--
--
0.46
(0.53)
-47.2*
(20.2)
-43.4*
( 21.7)
-41.8*
(21.2)
-44.4*
(21.9)
-42.9
(21.9)
-64.9**
(20.7)
-52.5*
(21.3)
-37.4
(21.0)
Yield
spread
Tax Rates and Tax Revenue
• Changes in AMTR, lags and contemporaneous
(Romer-Romer as instrument).
• Romer-Romer exogenous tax-change variable,
lags and contemporaneous.
• Lagged AMTR and Romer-Romer jointly.
• Change in total federal revenue with RomerRomer as instrument.
• Substitutions effects from tax rates matter;
income effects?
Extensions
• Instruments for non-defense G? Political
variables in context of cross-state New Deal
spending?
• Apply to other countries? For defense G, need
cases like U.S. with large wartime variations in
G but without massive destruction of capital
and life. Promising cases are Canada,
Australia, New Zealand, South Africa.
Canada: Change in Defense
Purchases (relative to GDP)
.15
.10
.05
.00
-.05
-.10
-.15
-.20
-.25
1920 1930 1940 1950 1960 1970 1980 1990 2000
Australia: Change in Defense
Purchases (relative to GDP)
.15
.10
.05
.00
-.05
-.10
-.15
1920 1930 1940 1950 1960 1970 1980 1990 2000