Macroeconomic Effects from Government Purchases

and Taxes

Robert J. Barro and Charles J. RedlickHarvard University

Fiscal-Stimulus Packages a big issue.

Empirical evidence on response of real GDP and other economic aggregates to added government purchases and tax changes is thin. Key issue is identification.

Present study uses long-term U.S. macroeconomic data with focus on defense spending. Framework could work for Canada, Australia, New Zealand—am working on these.

• Ongoing research on effects of New Deal spending on income/output across U.S. states (with Fishback).

• Kraay on effects on GDP from disbursements of World Bank loans in many countries.

• Shoag on effects of varying returns on pension-fund assets of U.S. state governments—effects on government spending and state personal income.

• Other work on U.S. government earmarks and defense contracts across U.S. states—Nakamura & Steinsson.

Present study: spending multipliers identified primarily from variations in defense spending, especially changes associated with buildups and aftermaths of wars.

Ramey’s defense-news variable gauges 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. Corresponds to tax on labor—working on measure for capital income.

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

Favorable aspects of major wars, notably 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. (More info for Canada, etc.)

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, changes 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, 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. Ramey and Gordon Liao and I working on this (and Canada, etc.).

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

Use NBER’s TAXSIM program (Dan Feenberg) to update Barro-Sahasakul data. Focus on average weighted by concept of income close to labor income.

In overlap, 1966 to 1983, Barro-Sahasakul and NBER series highly correlated in levels and changes. Comfortable in using merged series 1912 to 2006.

New construct adds average marginal income-tax rates from state income taxes.

Working on analogous construct for capital income-tax rates (dividends, interest, corporate profits).

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).

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, 2010) use narrative approach to assess all significant federal tax legislation for 1945-2007. Gauge tax changes by size and timing of intended effect on federal tax revenue. In contrast to AMTR, focus 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.

Theoretical Framework

• 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. Then add durables.

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 shows 2SLS regressions with annual data in form of eq. (1). Samples end 2006. Starting year 1950 (include Korean War), 1939 (include WWII), 1930 (include Great Depression), 1917 (include WWI and 1921 contraction). Also consider 1954 and 1914.

Equations for GDP Growth Various Samples

(1) (2) (3) (4) (5) (6)

Starting date

1950 1939 1930 1930(w/o 1949)

1917 1954

Δg: defense 0.68*(0.27)

0.44**(0.06)

0.46**(0.08)

0.48**(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)

0.25**(0.08)

0.16(0.08)

-0.54(0.56)

Δg*: dfns news

0.026(0.016)

0.039**(0.011)

0.034*(0.015)

0.034*(0.014)

0.034*(0.017)

-0.120(0.112)

U(-1) 0.50**(0.17)

0.58**(0.14)

0.61**(0.10)

0.58**(0.10)

0.47**(0.10)

0.51**(0.18)

Δτ(-1) -0.54**(0.21)

-0.16(0.16)

-0.26(0.22)

-0.52*(0.23)

-0.19(0.25)

-0.48*(0.22)

Yield spread

-43.9*(20.7)

-37.8(22.0)

-101.5**(12.8)

-103.4**(12.4)

-73.6**(12.2)

-43.1*(21.8)

• 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?

• Interaction between g and level of nominal interest rates? (1934-46 and 2009-10 have levels close to zero for 3-month T Bills.)

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. Omit 1949: column 4.

• 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 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). Think forces strong enough so that defense multiplier upper bound for non-defense—but conjecture.

Non-Defense Government Purchases and TransfersStarting date 1950 1930 1950 1930 1950 1950

Δg: defense 0.89**(0.27)

0.46**(0.08)

0.34(0.32)

0.51**(0.10)

0.84**(0.24)

0.46(0.26)

Δg: defense (-1)

-0.13(0.27)

0.21*(0.09)

0.08(0.28)

0.18*(0.09)

-0.36(0.25)

0.02(0.26)

Δg*: defense news

0.040**(0.016)

0.036*(0.016)

0.028(0.016)

0.033*(0.015)

0.014(0.013)

0.016(0.014)

U(-1) 0.64**(0.17)

0.60**(0.11)

0.43*(0.18)

0.62**(0.10)

0.26*(0.16)

0.55**(0.16)

Δτ(-1) -0.45*(0.20)

-0.25(0.23)

-0.56**(0.21)

-0.25(0.22)

-0.26(0.19)

-0.38(0.20)

Yield spread squared

-31.2(20.0)

-100.9**(13.3)

-28.4(25.4)

-102.3**(13.0)

-38.9*(18.1)

-21.6(20.5)

Δg: non-defense

2.65**(0.93)

0.12(0.63)

-- -- -- --

Δ(transfers) -- -- -1.53(0.92)

0.64(0.68)

-- --

Δ(GM sales) -- -- -- -- 3.66**(0.86)

--

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

R2 0.54 0.75 0.51 0.75 0.63 0.57

σ 0.017 0.027 0.017 0.027 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.

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.

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. (Lots of progress on data for New Zealand.)

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

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150

0.200

0.250

0.300Change in Actual Defense Purchases, New Zealand

Change in defense purchases expressed as a ratio to previous year’s GDP

19121913

19141915

19161917

19181919

19201921

19221923

19241925

19261927

19281929

19301931

19321933

19341935

19361937

19381939

19401941

19421943

19441945

19461947

19481949

19501951

19521953

19541955

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

New Zealand Defense News Shock (Expected Change in Defense Purchase)

The present value of expected change in future nominal defense spending, expressed as a ratio to the prior year’s nominal GDP

Year

1907

1909

1911

1913

1915

1917

1919

1921

1923

1925

1927

1929

1931

1933

1935

1937

1939

1941

1943

1945

1947

1949

1951

1953

1955

1957

1959

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5 Average Marginal Tax Rates for New Zealand, 1907 - 2009