Macroeconomic Effects from Government Purchases

and Taxes

Robert J. Barro and Charles J. RedlickHarvard 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 social-security payroll tax.

Attempt to differentiate substitution effects due to changes in tax rates from income effects due to changes in tax revenue.

Figure 1Defense and Non-Defense Purchases

-.3

-.2

-.1

.0

.1

.2

.3

1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

change in defense purchaseschange 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 war-related 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 non-defense 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

-0.4

0.0

0.4

0.8

1.2

1.6

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 non-filers. 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 income-tax 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 3Average Marginal Income-Tax Rates

.0

.1

.2

.3

.4

.5

20 30 40 50 60 70 80 90 00

TotalFederal Income TaxSocial-Security Tax (FICA)State Income Taxes

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 (g∙ t – gt-1)/yt-1 + β2 (g∙ t*– gt-1*)/yt-1 + β3 (τ∙ t – 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 non-defense 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 PurchasesStart date 1950 1939 1930 1917 1950 1950

Δg: defense 0.89**(0.27)

0.44**(0.06)

0.46**(0.08)

0.46**(0.08)

0.84**(0.24)

0.46(0.26)

Δg: defense (-1)

-0.13(0.27)

0.21**(0.06)

0.21*(0.09)

0.19*(0.09)

-0.36(0.25)

0.02(0.26)

Δg*: def news

0.040**(0.016)

0.041**(0.013)

0.036*(0.016)

0.040*(0.018)

0.014(0.013)

0.016(0.014)

U(-1) 0.64**(0.17)

0.58**(0.15)

0.60**(0.11)

0.45**(0.11)

0.26*(0.16)

0.55**(0.16)

Δτ(-1) -0.45*(0.20)

-0.13(0.18)

-0.25(0.23)

-0.15(0.25)

-0.26(0.19)

-0.38(0.20)

Yield spread

-31.2(20.0)

-35.6(22.3)

-100.9**(13.3)

-71.2**(12.2)

-38.9*(18.1)

-21.6(20.5)

Δg: non-defense

2.65**(0.93)

0.25(0.72)

0.12(0.63)

0.51(0.51)

-- --

Δ(GM sales)

-- -- -- -- 3.66**(0.86)

--

Δ(GE sales) -- -- -- -- -- 17.6**(4.7)

R2 0.54 0.82 0.75 0.67 0.63 0.57σ 0.017 0.019 0.027 0.030 0.015 0.016

• Results for non-defense G in various samples. Different results with WWII and Great Depression because cyclical pattern of non-defense 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: GDP Consumption Investment Non-defensegovernmentpurchases

Net exports

g: defense + - - - -g*: defense news

+ - + - +

Table 5 Effects on Components of GDPSample: 1950-2006

Dependent variable:

Δ(c: non-dur.) Δ(c: dur.) Δ(invest) Δ(g: non-def.) Δ(x-m)

Δg: defense 0.005(0.093)

-0.171*(0.073)

-0.083(0.185)

-0.081(0.041)

0.004(0.079)

Δg: defense (-1) 0.179(0.095)

0.147*(0.075)

-0.142(0.189)

0.055(0.042)

-0.231**(0.080)

Δg*: defense news

-0.0035(0.0053)

0.0106**(0.0041)

0.0377**(0.0105)

-0.0055*(0.0023)

-0.0135**(0.0044)

U(-1) 0.112(0.058)

0.145**(0.045)

0.382**(0.115)

-0.053*(0.026)

-0.095(0.049)

Δτ(-1) -0.184**(0.071)

-0.145**(0.056)

-0.300*(0.142)

-0.033(0.032)

0.122*(0.060)

Yield spread squared

-5.4(7.0)

-3.5(5.5)

-22.7(13.9)

-4.8(3.1)

-6.7(5.0)

Sample: 1939-2006Δg: defense -0.011

(0.022)-0.115**(0.016)

-0.356**(0.045)

-0.009(0.011)

-0.071**(0.021)

Δg: defense (-1) 0.107**(0.022)

0.038*(0.016)

0.096*(0.046)

-0.011(0.011)

-0.027(0.022)

Δg*: defense news

0.0044(0.0040)

0.0116**(0.0030)

0.0341**(0.0084)

-0.0082**(0.0021)

-0.0023(0.0039)

U(-1) 0.101(0.052)

0.094*(0.038)

0.401**(0.109)

-0.030(0.027)

-0.002(0.051)

Δτ(-1) -0.008(0.059)

-0.103*(0.043)

-0.067(0.124)

-0.105**(0.030)

0.114*(0.058)

Yield spread squared

1.1(8.0)

-3.1(5.9)

-20.3(16.8)

-6.5(4.1)

-8.0(7.8)

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)

-- -- --

RomerΔtax

-- -- -- -- -0.03(0.55)

-- -- --

Δ(fed rev)(-1)

-- -- -- -- -- -0.46(0.27)

-0.17(0.30)

--

Δ(fed rev) -- -- -- -- -- -- -- 0.46(0.53)

Yield spread

-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)

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 Romer-

Romer 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 DefensePurchases (relative to GDP)

-.25

-.20

-.15

-.10

-.05

.00

.05

.10

.15

1920 1930 1940 1950 1960 1970 1980 1990 2000

Australia: Change in DefensePurchases (relative to GDP)

-.15

-.10

-.05

.00

.05

.10

.15

1920 1930 1940 1950 1960 1970 1980 1990 2000