Home Production and Social Security Reform

Home Production and Social Security Reform Michael Dotsey Wenli Li Fang Yang Federal Reserve Bank of Philadelphia SUNY-Albany October 17, 2012 Dotsey, Li, Yang () Home Production October 17, 2012 1 / 29

Motivation The macroeconomic e ects of unfunded U.S. Social Security system has been widely studied Insurance (due to incomplete markets) versus distortion (due to payroll tax) This paper incorporates home production in OLG model with incomplete markets and heterogenous agents Home production helps match life cycle properties as evidenced by Aguiar and Hurst (2009) and Dotsey, Li, and Yang (2010) insurance against negative income shocks Important for policy analysis We wish to investigate the impact of the insurance aspects of home production Dotsey, Li, Yang () Home Production October 17, 2012 2 / 29

Summary of main results Di erent responses of consumption in elimination of Social Security in the long run: Housing increases by 17% home input (food at home, household operations, furnishings and equipment, fuels, and public services) increases by 0.5% market consumption increases by 3.4% Market hours (work, job search and commute) increases substantially due to reform (6%); home hours (house work, house work service, shopping, pet care, car care, child care, adult care, shop search, car service, child care service and professional service) increase marginally (0.4%); leisure declines ( 1.5%) Dotsey, Li, Yang () Home Production October 17, 2012 3 / 29

Summary of main results Di erent responses of consumption in elimination of Social Security in the long run: Housing increases by 17% home input (food at home, household operations, furnishings and equipment, fuels, and public services) increases by 0.5% market consumption increases by 3.4% Market hours (work, job search and commute) increases substantially due to reform (6%); home hours (house work, house work service, shopping, pet care, car care, child care, adult care, shop search, car service, child care service and professional service) increase marginally (0.4%); leisure declines ( 1.5%) The welfare gain is 19% as measured by changes in market consumption The welfare gain is 16% if time is not needed in home production The welfare gain is 10% in one-good economy Dotsey, Li, Yang () Home Production October 17, 2012 3 / 29

Literature Review Most Related Nishiyama and Smetters (2007) Privatizing social security can improve labor supply incentives, but can also reduce risk sharing(heterogeneous agents with elastic labor supply face idiosyncratic earnings shocks and longevity uncertainty) Chen (2010) Housing consumption and non-housing consumption behave di erently after Social Security reform Imrohoroglu and Kitao (2009, 2010) Endogenous labor supply on both margins, extensive and intensive SS reform aggregate welfare results invariant to labor supply elasticity but large distributive e ects Dotsey, Li, Yang () Home Production October 17, 2012 4 / 29

Model Similar to the existing literature OLG general equilibrium model with endogenous labor supply decisions, and endogenous retirement decisions Uninsurable labor income risk, no annuity market, borrowing constraints Pay-as-you-go system: Social Security tax, pension income linked to lifetime earnings and retirement age Home production Market good function c h = fω 2 [ω 1 d 1 1 ς1 + (1 ω 1 )s 1 1 +(1 ω 2 )n h 1 1 1 ς2 1 1 g ς2 ς1 ] 1 1 ς2 1 1 ς1 F m (K, N m ) = K α (N m ) 1 α Dotsey, Li, Yang () Home Production October 17, 2012 5 / 29

Period Utility and housing market Period utility U(c, l) = [ω 4c 1 1 ς4 + (1 ω 4 )l 1 1 1 γ c = [ω 3 c 1 1 ς3 m + (1 ω 3 )c 1 1 ς3 Consumption di erent from expenditure 1 γ ς4 1 1 ) ς4 1 h ] 1 1 1 ς3 Dotsey, Li, Yang () Home Production October 17, 2012 6 / 29

Period Utility and housing market Period utility U(c, l) = [ω 4c 1 1 ς4 + (1 ω 4 )l 1 1 1 γ c = [ω 3 c 1 1 ς3 m + (1 ω 3 )c 1 1 ς3 Consumption di erent from expenditure 1 γ ς4 1 1 ) ς4 1 h ] 1 1 1 ς3 Competitive housing rental market, buy rental units, collect rent η next period No arbitrage condition: η = r + δ h Dotsey, Li, Yang () Home Production October 17, 2012 6 / 29

Labor productivity Competitive labor market; wage per e ciency unit w Exogenous deterministic age-e ciency pro le: e t Stochastic shocks to productivity level ln ε i t = ρ ε ln ε i t 1 + υ i t, υ i t s N(0, σ 2 ε ). (1) Total productivity: e t ε i t Dotsey, Li, Yang () Home Production October 17, 2012 7 / 29

Social Security system The government taxes labor earnings below the Social Security cap y max, at a constant rate, τ. f : the decision to claim SS. t r : age claiming SS; t 0 r = t + 1 if f 0 = 1; t 0 r = 0 if f 0 = 0 Agents with average life time earnings ey, and claims SS at age t r, receives SS payment pen(t r, ey) Dotsey, Li, Yang () Home Production October 17, 2012 8 / 29

Value function State variable (age, nancial asset, labor prod shock, average life time earnings, and retirement age) n V (t, a, ε, ey, t r ) = max U(c, 1 n m n h ) + fc m,s,d,a 0,n m,n h,f 0 g o βλ t EV (t + 1, a 0, ε 0, ey 0, tr 0 ) (2) budget constraint c m + ηs + d + a 0 b + (1 + r)a + e t εwn m (3) evolution of average earnings τ min(ey max, e t εwn m ) + pen(t r, ey), ey 0 = (t 1)ey + min (e t εwn m, ey max ) /t, if t r = 0 (4) ey 0 = ey if t r > 0 (5) borrowing constraint a 0 e t+1 εw Dotsey, Li, Yang () Home Production October 17, 2012 9 / 29

Calibration Parameters Value Source Technology α capital share in National Income 0.24 authors calculation δ k annual depreciation rate of capital 9% authors calculation δ h annual depreciation rate of housing 1% authors calculation ς 1 sub. between durable and housing 1.369 Dotsey, Li, and Yang (2010) Demographics g population growth rate 1% T maximum life span 90 λ t survival probability SSA Endowment e t age-e ciency pro le French (2005) ρ ε AR(1) coef. of income process 0.977 French (2005) σ 2 ε innovation of income process 0.014 French (2005) Preference γ risk aversion coef. 1.5 Attanasio, et.al (1999) Gourinchas et.al (2002) Dotsey, Li, Yang () Home Production October 17, 2012 10 / 29

Annual death probability (in %) efficiency unit 15 10 5 0 30 40 50 60 70 80 30 20 10 0 30 40 50 60 70 80 age Exogenous pro les Dotsey, Li, Yang () Home Production October 17, 2012 11 / 29

Calibration (continued) Parameters Value Pension e max 2.47 8 >< pen(ey) >: Tr 1 early ret. age 62 Tr 2 normal ret. age 66 pen(t r ) 0.9ey ey 0.2 0.18 + 0.32(ey 0.2) 0.2 ey < 1.24 0.5128 + 0.15(ey 1.24) 1.24 ey 0.6973 ey > e max 62 64 66 68 70 0.75 0.867 1 1.16 1.32 9 >= >; Dotsey, Li, Yang () Home Production October 17, 2012 12 / 29

Calibration (Consumption) Consumer Expenditure Survey 2003-2006 Housing service: actual rents for renters, the reported value of owned residence for home owners Home input good: food at home, household operations, household furnishing and equipment, utilities, fuels, public services, and transportation expenses prorated by travel time for home production Market good: food away from home, alcohol, tobacco, apparel, other lodging, fees and admissions for entertainment, and related equipment such as televisions, radios, sound systems, pets, toys, and playground equipment, reading, and personal care, education expenses and out-of-pocket medical expenses Dotsey, Li, Yang () Home Production October 17, 2012 13 / 29

Calibration (Hours) American Time Use Survey 2005-2007 Market hours: working, job searching, and commuting Home hours: house work,shopping, house work service, pet care, car care, child care, adult care, shop search, child care service, professional service Leisure: the rest Dotsey, Li, Yang () Home Production October 17, 2012 14 / 29

β, τ, ζ i (i = 2, 3, 4), ω i (i = 1, 2, 3, 4) Moments (9) Model Data capital output ratio (K/Y) 1.714 1.714 Social Security budget balance 0.000 0.000 home input/housing 0.110 0.110 The Young (between ages 24 and 49) average expenditure on home input goods/income 0.236 0.245 average share of home hours 0.142 0.145 average share of market hours 0.212 0.199 The Old (between ages 50 and 80) average expenditure on home input goods/income 0.256 0.265 average share of home hours 0.155 0.157 average share of market hours 0.102 0.113 Dotsey, Li, Yang () Home Production October 17, 2012 15 / 29

Calibration Table 2. Calibration to Match Data Moments Parameters (9) Value Moments β discount factor 0.952 K/Y τ Social Security tax rate 0.101 SS balance ω 1 weight on durable 0.734 d/s ζ 2 sub. betw. d and s composite and n h 0.792 home hours ω 2 weight on d and s composition 0.826 (young, old) ζ 3 sub. betw. market and home goods 1.709 home input ω 3 weight on market goods 0.164 (young, old) ζ 4 sub. betw. consumption and leisure 1.421 market hours ω 4 weight on consumption 0.230 (young, old) home input, housing and home hours: complements market good and home good: substitutes nal good and leisure: substitutes Dotsey, Li, Yang () Home Production October 17, 2012 16 / 29

Lifecycle Pro les Related to Aguiar and Hurst (2009) Controlling for age, time e ects and some demographics H k it = β k 0 + βk age AGE it + β k y Y it + β k f F it + β k yc YC it + β k m M it + ε k it, β k age Hit k : log of consumption, or levels of hours in category k AGE it : a vector of 55 one-year age dummies Y it : a vector of one-year interview dummies F it : a vector of family structure dummies that include 9 family size dummies YC it : a dummy indicating whether the family has any children under the age of 6 M it : is a dummy for marital status : impact of life cycle conditional on other e ects. Dotsey, Li, Yang () Home Production October 17, 2012 17 / 29

housing market consumption home hours market hours Life-cycle pro les 0.4 0.3 home hours (model) home hours (data) 0.4 0.3 market hours (model) market hours (data) 0.2 0.2 0.1 0.1 0 30 40 50 60 70 80 0 30 40 50 60 70 80 0.8 0.6 housing (model) housing (data) 0.8 0.6 market c (model) market c (data) 0.4 0.4 0.2 0.2 0 0 0.2 0.2 0.4 30 40 50 60 70 80 0.4 30 40 50 60 70 80 Hump in market hours: labor productivity, SS; Hump in consumption: liquidity constraint, mortality, home production Di erence in hump, shape of home hour: home production Dotsey, Li, Yang () Home Production October 17, 2012 18 / 29

percent already claimed Life-cycle pro les 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 claimant by age (model) claimant by age (data) 0.5 62 63 64 65 66 67 68 69 70 71 72 Dotsey, Li, Yang () Home Production October 17, 2012 19 / 29

Social Security reform Set social security pension bene t and social security tax to zero Compare two steady states Aggregate and disaggregated statistics Compare a model with home production to (after recalibration) a model without home production (3 consumption goods) a model with one good Dotsey, Li, Yang () Home Production October 17, 2012 20 / 29

Table 4. Aggregate E ects of Eliminating Social Security Bene ts Variable SS Bene ts without SS Bene ts (relative to the init. s. s.) interest rate (r) 0.050 0.044 ( 12.640%) wage (w) 0.724 0.735 (1.470%) capital output ratio (K /Y ) 1.714 1.795 (4.729%) total housing/income 1.980 2.319 (17.114%) home input 0.218 0.219 (0.560%) market consumption/income 0.571 0.591 (3.442%) market hours 0.153 0.163 (6.174%) home hours 0.150 0.151 (0.433%) Welfare changes 19.064% low interest rates drives up housing consumption much more than other consumption goods, which puts upward pressure on home hours, no tax leads to higher market hours Dotsey, Li, Yang () Home Production October 17, 2012 21 / 29

home input market consumption market hour home hours 0.25 0.2 0.15 0.1 0.05 0 30 40 50 60 70 80 0.17 0.16 0.15 0.14 0.13 0.12 30 40 50 60 70 80 0.4 0.2 0 0.2 0.4 0.6 0.8 30 40 50 60 70 80 0.4 0.2 0 0.2 0.4 0.6 0.8 30 40 50 60 70 80 -*: benchmark with Social Security Bene t; B: benchmark without Social Security Bene t consumption pro les atter after reform (borrowing constraints less binding) higher housing consumption for young leads to more home hours; old works more in the market without SS Dotsey, Li, Yang () Home Production October 17, 2012 22 / 29

No home production Compare a model with home production to a model without home production (ω 2 = 1) c h = [ω 1 d 1 1 ς1 + (1 ω 1 )s 1 1 c = [ω 3 c 1 1 ς3 m + (1 ω 3 )c 1 1 ς3 1 ς1 1 1 ] ς1 h ] 1 1 1 ς3 FOC ω 1 η d = [ (1 ω 1 ) ]ς 1s d s, (6) 1 1 1 c h = [ω 1 1 1 ς1 d + (1 ω 1 )] ς1 s ch s (7) 8 9ς < ηω = 3 3 c m = 1 : ς1 ; chs cms. (8) (1 ω 3 )(1 ω 1 ) ch Dotsey, Li, Yang () Home Production October 17, 2012 23 / 29

Calibration (no home production) Parameters the same as in the benchmark ς 1 substitutability between durable and housing 1.369 ς 3 substitutability between market and home goods 1.709 Parameters used to target some aggregate moments β discount factor 0.953 τ Social Security tax 0.102 ω 1 weight on durable 0.734 ω 3 weight on market goods 0.583 ζ 4 sub. betw. consumption and leisure 1.419 ω 4 weight on consumption 0.089 higher ω 3 as setting ω 2 to 1 raised the productivity of home input & housing, needs to bring it down to match consumption moments lump home hours in leisure thus needs to bring ω 4 down Dotsey, Li, Yang () Home Production October 17, 2012 24 / 29

Table 6. Aggregate E ects of Eliminating Social Security Bene ts relative changes after the reform Variable benchmark no home prod. interest rate (r) wage (w) capital output ratio (K /Y ) total housing home input market consumption market hours welfare -12.640% 1.470% 4.729% 17.114% 0.560% 3.442% 6.174% 19.064% -11.923% 1.384% 4.449% 20.544% 4.453% 3.133% 7.232% 16.060% stronger savings motive, market hours up more as needs to work to save for older ages; interest rate comes down less; However housing consumption up more, so is home input; the bene t of SS is smaller when there is home production Dotsey, Li, Yang () Home Production October 17, 2012 25 / 29

One-good Economy Consume only one good (a sum of the market good, the home input, and housing services). Housing capital is part of the aggregate capital stock capital output ratio is 3.302 average depreciation rate is 0.047. capital share in production α is now 0.321 in order to match r = 5%. Table 7. Calibration to Match Data Moments One-good Economy β discount factor 0.953 τ Social Security tax 0.102 ζ 4 sub. betw. consumption and leisure 1.421 ω 4 weight on consumption 0.075 Dotsey, Li, Yang () Home Production October 17, 2012 26 / 29

Table 6. Aggregate E ects of Eliminating Social Security Bene ts relative changes after the reform Variable benchmark no home prod. one-good interest rate (r) wage (w) capital output ratio (K /Y ) market consumption market hours leisure welfare -12.640% 1.470% 4.729% 3.442% 6.174% -1.451% 19.064% -11.923% 1.384% 4.449% 3.133% 7.232% -1.303% 16.060% -13.276% 3.400% 7.340% 5.891% 7.925% -1.437% 10.400% households saves even more than before with less margin to adjust consumption bundle (low r no longer bene ts s consumption) work a lot more in the market SS provisions have the most bene ts Dotsey, Li, Yang () Home Production October 17, 2012 27 / 29

Welfare gain by initial productivity (%) all 1st 2nd 3rd 4th 5th benchmark 19.064 34.07 26.64 18.63 12.5 4.38 no home prod. 16.060 23.59 19.84 15.60 12.06 5.12 one good 10.400 16.89 14.43 11.49 8.92 3.91 Dotsey, Li, Yang () Home Production October 17, 2012 28 / 29

Conclusions Home production, as an insurance mechanism, increases the welfare gain of Social Security reform Future extensions Delay retirement age Transition path Dotsey, Li, Yang () Home Production October 17, 2012 29 / 29