Government size and macroeconomic stability in life-cycle economies
Alexandre Janiak1, Paulo Santos Monteiro2 and Varinia Tromben3 1
University of Chile and IZA 2 University of Warwick 3 University of Chile
A. Volatility of gross domestic product and taxes
V ola tility of G ross Dom e stic Prod uc t
0.03
R 2 = 0.3481 0.02
0.01
0.00 15
20
25
30
35
40
45
50
Ta x ra te (% o f G DP)
B. Volatility of employment and taxes
V o la tility o f Em p lo y m e nt
0.04
R 2 = 0.2145 0.03
0.02
0.01
0.00 15
20
25
30
35
40
45
50
Ta x ra te (% o f G DP)
C. Volatility of unemployment rate and taxes V o la tility o f une m p lo y m e nt ra te
0.30
0.25
0.20
R 2 = 0.0006
0.15
0.10
0.05
0.00 15
20
25
30
35
Ta x ra te (% o f G DP)
40
45
50
A. Volatility of gross domestic product and taxes
V ola tility of G ross Dom e stic Prod uc t
0.03
R 2 = 0.3481 0.02
0.01
0.00 15
20
25
30
35
40
45
50
Ta x ra te (% o f G DP)
B. Volatility of employment and taxes
V o la tility o f Em p lo y m e nt
0.04
R 2 = 0.2145 0.03
0.02
0.01
0.00 15
20
25
30
35
40
45
50
Ta x ra te (% o f G DP)
C. Volatility of unemployment rate and taxes V o la tility o f une m p lo y m e nt ra te
0.30
0.25
0.20
R 2 = 0.0006
0.15
0.10
0.05
0.00 15
20
25
30
35
Ta x ra te (% o f G DP)
40
45
50
Research question • Can the stochastic growth model replicate the negative correlation between government size and output volatility? • Question raised by Galí (1994) o As you move down the labor supply curve, labor-supply elasticity increases and so employment/output volatility o Positive correlation between government size and volatility • Alternatives: rule-of-thumb consumers o Galí, López-Salido and Vallés (2007) o Andrés, Domenech and Fatás (2008)
Labor supply
w
Aggregate shock bands: low tax Aggregate shock bands: high tax L
Our contribution • We augment the stochastic growth model with a life-cycle structure along the lines of Gomme, Rupert, Rogerson and Wright (2004) • When the tax rate increases, there is a standard income effect o with leisure and consumption as normal goods o young agents work less because their debt is reduced o old agents work more because they are less wealthy • But young workers display larger labor supply elasticity • Obtain negative correlation between gov size and macro volatility • Calibration exercise and some empirics
Motivation: some correlations • Here we mainly draw on Jaimovich and Siu (2008) • Employment volatility at business-cycle frequencies for several countries and age groups • Random-effect regressions for GDP volatility over age-group size and government size • Random-effect regression of share of volatile labor force over government size
Business Cycle Volatility of Employment by Age Group, OECD 16 Austria France 14
Belgium Netherlands Luxembourg
12
New Zealand Czech Republic Slovak Republic
10
Turkey Finland Hungary
8
Italy Greece Denmark
6
Sweden United Kingdom Poland
4
Switzerland Australia Iceland
2
Portugal Norway Germany
0 15‐19
20‐24
25‐29
30‐39
40‐49
50‐59
60‐64
Figure 1: Standard deviation of cyclical employment/hours worked by age group, OECD/US states Employment, OECD:
Employment, US states:
Hours workerd, US states:
Notes: the data is annual and the source is the OECD Labour Force Statistics. All variables are reported in logs as deviations from an HP trend with smoothing parameter 7. Volatility expressed relative to the 40-49 year old group. For Japan, the 60-64 age group is replaced by 65+. Countries in the legend are sorted in descendant order according their volatility of the 60-64 year old group.
17
Table 1: Random-effect regressions for GDP cyclical volatility (OECD), where government size is the share of government current receipts (excluding gross interest receipts) in GDP Share of workers in the labor force aged between 15 and 29 aged between 30 and 39 aged between 40 and 49 aged between 50 and 59 aged between 60 and 64 Government size 20 Constant Time dummies Gov. size averaged over 11 years Variation in the fiscal coefficient Observations # countries R-squared:within between overall
0.099** (10.47) 0.046** (4.10) 0.054** (4.06) ref — 0.078** (2.88) — — -0.043** (5.08) No — — 499 25 0.3231 0.0157 0.0933
— 0.098** — 0.089** 0.045** — 0.048** — — (10.51) — (8.66) (3.20) — (3.38) — — 0.056** — 0.050** 0.02 — 0.026 — — (4.87) — (4.15) (1.52) — (1.92) — — 0.060** — 0.055** 0.041* — 0.043** — — (4.47) — (3.85) (2.53) — (2.67) — — ref — ref ref — ref — — — — — — — — — — 0.081** — 0.084** 0.045 — 0.047 — — (3.03) — (2.98) (1.61) — (1.66) — -0.033** -0.019** -0.039** -0.021** — -0.012* -0.012* -0.013* (5.90) (3.19) (6.17) (2.95) — (2.02) (2.03) (1.96) -0.027** -0.040** 0.030** -0.033** — — — — (11.57) (4.70) (11.23) (3.69) — — — — No No No No Yes Yes Yes Yes No No Yes Yes — No No Yes — -44% — -49% — — +7% — 499 499 444 444 499 499 499 444 25 25 25 25 25 25 25 25 0.0685 0.3368 0.0911 0.2933 0.3767 0.3636 0.3791 0.3256 0.1183 0.0654 0.1154 0.0636 0.0001 0.0053 0.0357 0.0178 0.0753 0.1253 0.0760 0.0969 0.1324 0.1553 0.1692 0.1365
Notes: the data is annual and the sources are the OECD Labour Force Statistics and the OECD economic Outlook. The countries included in the regression are Australia, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, South Korea, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Spain, Sweden, Switzerland, UK and USA over the period 1970-2004. Because of data limitation Austria, Luxembourg, Hungary, Mexico and Turkey are not considered. * means significant at the 5% level and ** at the 1% level.
0.035* (2.41) 0.02 (1.42) 0.031 (1.80) ref — 0.046 (1.67) -0.014* (2.15) — — Yes Yes +6% 444 25 0.3361 0.0418 0.1403
Table 2: Random-effect regressions for GDP cyclical volatility (OECD), where government size is the share of government current disbursements (excluding gross interest payments) in GDP Share of workers in the labor force aged between 15 and 29 aged between 30 and 39 aged between 40 and 49 aged between 50 and 59 aged between 60 and 64 Gov. Size 21 Constant Time dummies Gov. size averaged over 11 years Variation in the fiscal coefficient Observations # countries R-squared:within between overall
0.099** (10.55) 0.046** (4.13) 0.054** (4.07) ref — 0.083** (3.14) — — -0.043** (5.14) No — — 504 25 0.3277 0.0181 0.0973
— — — — — — — — — — -0.011* (1.97) -0.018** (8.48) No No — 504 25 0.002 0.1599 0.0621
0.099** — 0.093** 0.045** — 0.045** — 0.047** (10.54) — (9.20) (3.26) — (3.23) — (3.30) 0.047** — 0.048** 0.02 — 0.021 — 0.023 (4.16) — (4.03) (1.61) — (1.59) — (1.67) 0.055** — 0.052** 0.042** — 0.041* — 0.041* (4.10) — (3.70) (2.60) — (2.57) — (2.44) ref — ref ref — ref — ref — — — — — — — — 0.084** — 0.088** 0.050 — 0.049 — 0.057* (3.18) — (3.21) (1.83) — (1.80) — (2.09) -0.003 -0.018** -0.007 — -0.000 -0.000 -0.006 -0.006 (0.53) (2.86) (1.14) — (0.09) (0.00) (1.04) (1.10) -0.043** 0.021** -0.039** — — — — — (5.06) (8.40) (4.36) — — — — — No No No Yes Yes Yes Yes Yes No Yes Yes — No No Yes Yes -75% — -62% — — -99% — +5% 504 459 459 504 504 504 459 459 25 25 25 25 25 25 25 25 0.3274 0.0093 0.2909 0.3828 0.3700 0.3829 0.3167 0.3348 0.0266 0.1515 0.0344 0.0002 0.0239 0.0002 0.0007 0.0206 0.1043 0.0688 0.0836 0.1351 0.1091 0.1348 0.1132 0.1254
Notes: the data is annual and the sources are the OECD Labour Force Statistics and the OECD economic Outlook. The countries included in the regression are Australia, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, South Korea, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Spain, Sweden, Switzerland, UK and USA over the period 1970-2004. Because of data limitation Austria, Luxembourg, Hungary, Mexico and Turkey are not considered. * means significant at the 5% level and ** at the 1% level.
Table 3: Random-effect regressions for share of volatile workers in the labor force, OECD
20
Explicative variable → Total government receipts (%GDP) Total government disbursements (%GDP) Gov size coef -0.493*** -0.059* -0.639*** -0.054 -0.219*** -0.027 -0.322*** -0.059 (9.74) (1.68) (11.25) (1.22) (4.44) (0.85) (5.46) (1.49) Constant 0.529*** 0.427*** 0.588*** 0.424*** 0.417*** 0.395*** 0.458*** 0.386*** (24.59) (28.68) (24.61) (23.55) (20.73) (29.13) (19.24) (24.56) Time dummies No Yes No Yes No Yes No Yes Dependent variable averaged over 11 years No No Yes Yes No No Yes Yes Observations 499 499 444 444 499 499 454 454 # countries 25 25 25 25 25 25 25 25 R-squared: within 0.181 0.752 0.276 0.730 0.032 0.756 0.065 0.743 between 0.134 0.468 0.131 0.415 0.162 0.300 0.139 0.219 overall 0.159 0.542 0.186 0.501 0.116 0.459 0.120 0.385 Notes: the data is annual and the source is the OECD Labour Force Statistics. The countries included in the regression are Australia, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, South Korea, Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Spain, Sweden, Switzerland, UK, USA. Absolute value z-stats are in parenthesis. The share of volatile workers in the labor force corresponds to the share of workers aged between 15-29 and between 60-64.
Technology • Technology =
log = log + ~ 0,
• Small open economy: given • Capital depreciation rate
Technology • This yields a constant capital-output ratio: = +
• And the following dynamics for wages: log = Φ + log + 1 − with Φ = 1 − log 1 − !
% "#$
& '(&
)
Demographics • Mass *, of individuals born in each period (age + = 1)
• The mass of new-born grows at rate ,
• Agents aged + die at a rate 1 − -. : *.#,# = -.# *.,
• Endowments: 0. efficiency units and 1 unit of time each period • Retirement occurs after age 1, i.e. 0. = 0 if + > 1
• Derive flow utility from consumption 3., and leisure 41 − 5., 6 9
41 − 5., 6 743., , 1 − 5., 6 = log 3., + 8. 1−:
Government and market clearing • Government taxes income at a rate ;
• Expenditures adjust in each period so that deficit is always zero: ?
< = = ;4>., + 0. 5., 6 • Labor market clearing:
.@
=
?
,., 0. 5., =
.@
Annuities market • Since the length of life is uncertain, agents want to insure against this risk • We introduce actuarial fair annuities as in Blanchard (1985)
• Survivorship premium: 1⁄-.
• This implies the following law of motion for financial wealth >.#,#
1 + 1 − ; = >., + 1 − ; 0. 5., − 3., -.
Household program • The value function reads as B. 4 , >., 6 = max 743., , 5., 6 + J.# B.# 4# , >.#,# 6 FG,H ,IG,H
with >.#,#
J. = J′-.
1 + 1 − ; = >., + 1 − ; 0. 5., − 3., -. >?#, ≥ 0 >, = 0
Household program • Euler equation:
N1 + 1 − ;O 1 = J M P 3., 3.#,#
• First-order condition for leisure: 1 − 5.,
/9 8. 3., =Q R 0. 1 − ;
Numerical methodology • We approximate the distribution for aggregate productivity with a Markov chain with 5 states using Tauchen (1986) • We recursively solve the model with Carroll (2006) method of endogenous gridpoints and obtain policy functions >.#,# = >. 4>., , 6 • Calibration (see below) • Quantitative exercises
5., = 5. 4>., , 6
Calibration • Time period is a year • We set 1 = 50 and maximum age U = 72 so that individuals work from 15 to 64 and die at most at 86 • Demographic data from US vital statistics • Capital income share: = 1/3
• Solow resid from Gomme et al. (2004): = .8953, \ = .0153 • Depreciation rate (Gomme and Rupert, 2007): = .0956 • Investment-output ratio implies = .1503
• Government spending to GNP ratio implies ; = .2338
Calibration • IES from estimations by Rupert et al. (2000): 2/3 • Preference for consumption relative to leisure 8. : o CPS data on hours worked o match the prediction of a polynomial regression with time dummies and age dummies • Discount factor J = .8949: o average annual expenditures from the BLS, 1984-2006 o we interpolate age categories (<25, 25-34, 35-44, 45-54, 55-64) o match the prediction of a polynomial regression with time dummies and age dummies
250
200
κ
150
100
50
0 15
20
25
30
35
40 Age
45
50
55
60
65
5
5
Steady state financial wealth over the life cycle
x 10
0 −5
annual consumption ($)
−10 15
20
25
4
10
35
40
45
50
55
60
65
55
60
65
55
60
65
Steady state consumption over the life cycle
x 10
model data
5
0 15
30
20
25
30
35
40
45
50
Steady state labor supply over the life cycle weekly hours
60 model data
40 20 0 15
20
25
30
35
40
45
50
Table 6: Baseline model: statistics Data 0.0136 0.0119 0.8701
σY σL σL /σY
Model 0.0386 0.0130 0.3375
Demographic Groups 15-19
σLage σLage /σL σLage age σL /σL
20-24
25-29
30-39 Data 0.0436 0.0213 0.0147 0.0107 3.6639 1.7899 1.2353 0.8992 Model 0.0335 0.0286 0.0250 0.0178 2.5769 2.2000 1.9231 1.3692
40-49
50-59
60-65
0.0079 0.0082 0.0131 0.6639 0.6891 1.1008 0.0070 0.0079 0.0135 0.5385 0.6077 1.0385
Source: CPS and authors own calculation; data from the BEA; hours volatility by demographic group is from Jaimovich and Siu (2008).
Table 7: Government size and aggregate volatility
σY σL
Tax rate (i.e.: government size) 0.00 0.15 0.30 0.45 0.60 0.0424 0.0412 0.0386 0.0370 0.0334 0.0163 0.0149 0.0126 0.0105 0.0079
Table 8: Government size and work-force composition
τ 0.00 0.15 0.30 0.45 0.60
15-19 0.0390 0.0312 0.0249 0.0195 0.0146
20-24 0.0781 0.0665 0.0566 0.0476 0.0388
Demographic Groups 25-29 30-39 40-49 0.0861 0.2369 0.3505 0.0769 0.2239 0.3560 0.0690 0.2123 0.3593 0.0617 0.2024 0.3617 0.0544 0.1942 0.3639
50-59 0.1813 0.2078 0.2286 0.2462 0.2628
60-65 0.0281 0.0378 0.0492 0.0609 0.0712
Note: Fraction of total hours which is supplied by each demographic group. Each row sums to one.
Table 9: Correlation between the share of taxes in output and macroeconomic volatility with and without cross-country variation in demographics
No cross-country variation in demographics With cross-country variation in demographics
25
hours 0.1568 -0.1602
output consumption 0.0625 -0.3189 -0.0526 -0.165
Life−cycle average hours 0.7 t =0.00 t =0.15 t =0.30 t =0.45 t =0.60
0.6
0.5
0.4
0.3
0.2
0.1
0 15
20
25
30
35
40
45
50
55
60
65
Table 6: Baseline model: statistics Data 0.0136 0.0119 0.8701
σY σL σL /σY
Model 0.0386 0.0130 0.3375
Demographic Groups 15-19
σLage σLage /σL σLage age σL /σL
20-24
25-29
30-39 Data 0.0436 0.0213 0.0147 0.0107 3.6639 1.7899 1.2353 0.8992 Model 0.0335 0.0286 0.0250 0.0178 2.5769 2.2000 1.9231 1.3692
40-49
50-59
60-65
0.0079 0.0082 0.0131 0.6639 0.6891 1.1008 0.0070 0.0079 0.0135 0.5385 0.6077 1.0385
Source: CPS and authors own calculation; data from the BEA; hours volatility by demographic group is from Jaimovich and Siu (2008).
Table 7: Government size and aggregate volatility
σY σL
Tax rate (i.e.: government size) 0.00 0.15 0.30 0.45 0.60 0.0424 0.0412 0.0386 0.0370 0.0334 0.0163 0.0149 0.0126 0.0105 0.0079
Table 8: Government size and work-force composition
τ 0.00 0.15 0.30 0.45 0.60
15-19 0.0390 0.0312 0.0249 0.0195 0.0146
20-24 0.0781 0.0665 0.0566 0.0476 0.0388
Demographic Groups 25-29 30-39 40-49 0.0861 0.2369 0.3505 0.0769 0.2239 0.3560 0.0690 0.2123 0.3593 0.0617 0.2024 0.3617 0.0544 0.1942 0.3639
50-59 0.1813 0.2078 0.2286 0.2462 0.2628
60-65 0.0281 0.0378 0.0492 0.0609 0.0712
Note: Fraction of total hours which is supplied by each demographic group. Each row sums to one.
Table 9: Correlation between the share of taxes in output and macroeconomic volatility with and without cross-country variation in demographics
No cross-country variation in demographics With cross-country variation in demographics
25
hours 0.1568 -0.1602
output consumption 0.0625 -0.3189 -0.0526 -0.165
Table 6: Baseline model: statistics Data 0.0136 0.0119 0.8701
σY σL σL /σY
Model 0.0386 0.0130 0.3375
Demographic Groups 15-19
σLage σLage /σL σLage age σL /σL
20-24
25-29
30-39 Data 0.0436 0.0213 0.0147 0.0107 3.6639 1.7899 1.2353 0.8992 Model 0.0335 0.0286 0.0250 0.0178 2.5769 2.2000 1.9231 1.3692
40-49
50-59
60-65
0.0079 0.0082 0.0131 0.6639 0.6891 1.1008 0.0070 0.0079 0.0135 0.5385 0.6077 1.0385
Source: CPS and authors own calculation; data from the BEA; hours volatility by demographic group is from Jaimovich and Siu (2008).
Table 7: Government size and aggregate volatility
σY σL
Tax rate (i.e.: government size) 0.00 0.15 0.30 0.45 0.60 0.0424 0.0412 0.0386 0.0370 0.0334 0.0163 0.0149 0.0126 0.0105 0.0079
Table 8: Government size and work-force composition
τ 0.00 0.15 0.30 0.45 0.60
15-19 0.0390 0.0312 0.0249 0.0195 0.0146
20-24 0.0781 0.0665 0.0566 0.0476 0.0388
Demographic Groups 25-29 30-39 40-49 0.0861 0.2369 0.3505 0.0769 0.2239 0.3560 0.0690 0.2123 0.3593 0.0617 0.2024 0.3617 0.0544 0.1942 0.3639
50-59 0.1813 0.2078 0.2286 0.2462 0.2628
60-65 0.0281 0.0378 0.0492 0.0609 0.0712
Note: Fraction of total hours which is supplied by each demographic group. Each row sums to one.
Table 9: Correlation between the share of taxes in output and macroeconomic volatility with and without cross-country variation in demographics
No cross-country variation in demographics With cross-country variation in demographics
25
hours 0.1568 -0.1602
output consumption 0.0625 -0.3189 -0.0526 -0.165
Reverse causality • The negative correlation could be driven by demographics too: o Suppose a country is hit by a baby-boom o The share of young increases as well as volatility o The share of taxes decreases because they pay lower taxes • We estimate survival probabilities with WHO data for the OECD a − 0 bc d _ ` = a − 1
• Can cross-country differences in demographics drive the negative correlation with a constant tax rate?
1
0.9
0.8
Survival probability
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50 age
60
70
80
90
100
Figure 6: Estimated survival functions, OECD (1950-1970) Source: World Health Organization and authors’ calculations.
27
Table 6: Baseline model: statistics Data 0.0136 0.0119 0.8701
σY σL σL /σY
Model 0.0283 0.0094 0.3336
Demographic Groups 15-19
σLage σLage /σL σLage σLage /σL
20-24
25-29
30-39 Data 0.0436 0.0213 0.0147 0.0107 3.6639 1.7899 1.2353 0.8992 Model 0.0281 0.0251 0.0228 0.0175 2.9894 2.6702 2.4255 1.8617
40-49
50-59
60-65
0.0079 0.0082 0.0131 0.6639 0.6891 1.1008 0.0086 0.0090 0.0162 0.9149 0.9574 1.7234
Source: CPS and authors own calculation; data from the BEA; hours volatility by demographic group is from Jaimovich and Siu (AER 2008).
Table 7: Government size and aggregate volatility
σY σL
Tax rate (i.e.: government size) 0.00 0.15 0.30 0.45 0.60 0.0311 0.0298 0.0277 0.0257 0.0225 0.0124 0.0104 0.0085 0.0065 0.0048
Table 8: Government size and work-force composition
τ 0.00 0.15 0.30 0.45 0.60
15-19 0.0348 0.0288 0.0233 0.0187 0.0146
20-24 0.0755 0.0649 0.0551 0.0460 0.0377
Demographic Groups 25-29 30-39 40-49 0.0820 0.2322 0.3490 0.0734 0.2211 0.3564 0.0649 0.2089 0.3614 0.0567 0.1957 0.3652 0.0487 0.1817 0.3680
50-59 0.1935 0.2156 0.2379 0.2590 0.2789
60-65 0.0328 0.0399 0.0485 0.0587 0.0703
Note: Fraction of total hours which is supplied by each demographic group. Each row sums to one.
Table 9: Correlation between the share of taxes in output and macroeconomic volatility with and without cross-country variation in demographics
No cross-country variation in demographics With cross-country variation in demographics
25
hours 0.1568 -0.1602
output consumption 0.0625 -0.3189 -0.0526 -0.165
Conclusion • We provide a micro-founded mechanism for the negative correlation between government size and output volatility • Issues and next steps: o Consumption volatility anomaly: should we extend the model with home production as in Baxter and Jerman (1999)? o Examine the closed economy o Or introduce capital adjustment costs
