Model - big picture • Ex-ante heterogenous married and single households hit by uninsurable productivity shocks; → Permanent differences in endowments (education). → Permanent and persistent shocks to labor endowments. • Labor supply decisions at intensive and extensive margins; • Skill depreciation for females associated to non-participation; • Equilibrium model with imperfect substitutability of skills in production;
Model - big picture • Ex-ante heterogenous married and single households hit by uninsurable productivity shocks; → Permanent differences in endowments (education). → Permanent and persistent shocks to labor endowments. • Labor supply decisions at intensive and extensive margins; • Skill depreciation for females associated to non-participation; • Equilibrium model with imperfect substitutability of skills in production; • Policy → tax credits, transfers and non-linear taxes conditional on income and number of children
Model - big picture • Ex-ante heterogenous married and single households hit by uninsurable productivity shocks; → Permanent differences in endowments (education). → Permanent and persistent shocks to labor endowments. • Labor supply decisions at intensive and extensive margins; • Skill depreciation for females associated to non-participation; • Equilibrium model with imperfect substitutability of skills in production; • Policy → tax credits, transfers and non-linear taxes conditional on income and number of children • Model extension of prior work; Guner, Kaygusuz, and Ventura (2012a, 2012b, 2018).
Model – Demographics and Heterogeneity • Life-cycle economy, j = 1, ...., J R , .... J . [25,26,.......,65,.....,80] • Males ( m ) and females ( f ) , who differ in their permanent types – skilled and unskilled ( i = s , u ). • Male types map into productivity profiles, ̟ m ( i , j ) . • Female types map into initial productivity levels. • Agents can be single or married. Marital status is exogenous, and does not change over the life-cycle.
Model – Female Skills • Female types map into initial productivity levels, h 1 = η ( i ) . • After age 1, labor market productivity of females evolves endogenously: h i j + 1 = exp [ ln h i α i δ i j + χ ( l ) − ( 1 − χ ( l ))] , e ���� ���� depreciation growth e : labor market experience.
Model – Idiosyncratic Productivity Shocks
Model – Idiosyncratic Productivity Shocks • For an age- j single male of type i = s , u , earnings are given by w i ∗ ̟ ( j , i ) ∗ exp ( η j + ν ) ∗ l m ���� ���� � �� � wage by skill labor supply labor endowment
Model – Idiosyncratic Productivity Shocks • For an age- j single male of type i = s , u , earnings are given by w i ∗ ̟ ( j , i ) ∗ exp ( η j + ν ) ∗ l m ���� ���� � �� � wage by skill labor supply labor endowment • Persistent shock is governed by an AR(1) process η s , m j + 1 = ρη s , m + ε s , m j + 1 , j with η s , m = 0, ε s , m j + 1 ∼ N ( 0, σ 2 ε s , m ) . 1
Model – Idiosyncratic Productivity Shocks • For an age- j single male of type i = s , u , earnings are given by w i ∗ ̟ ( j , i ) ∗ exp ( η j + ν ) ∗ l m ���� ���� � �� � wage by skill labor supply labor endowment • Persistent shock is governed by an AR(1) process η s , m j + 1 = ρη s , m + ε s , m j + 1 , j with η s , m = 0, ε s , m j + 1 ∼ N ( 0, σ 2 ε s , m ) . 1 • Permanent shock is a Gaussian draw: ν ∼ N ( 0, σ 2 ν s , m )
Model – Idiosyncratic Productivity Shocks
Model – Idiosyncratic Productivity Shocks • For a single female of age- j who has human capital h j , earnings are given by w i ∗ h j ∗ exp ( η j + ν ) ∗ l f ���� ���� � �� � wage by skill labor supply labor endowment
Model – Idiosyncratic Productivity Shocks • For a single female of age- j who has human capital h j , earnings are given by w i ∗ h j ∗ exp ( η j + ν ) ∗ l f ���� ���� � �� � wage by skill labor supply labor endowment • Persistent shock : η s , f j + 1 = ρη s , f + ε s , f j + 1 j with η s , m = 0 and ε s , f j + 1 ∼ N ( 0, σ 2 ε s , f ) . 1
Model – Idiosyncratic Productivity Shocks • For a single female of age- j who has human capital h j , earnings are given by w i ∗ h j ∗ exp ( η j + ν ) ∗ l f ���� ���� � �� � wage by skill labor supply labor endowment • Persistent shock : η s , f j + 1 = ρη s , f + ε s , f j + 1 j with η s , m = 0 and ε s , f j + 1 ∼ N ( 0, σ 2 ε s , f ) . 1 • Permanent shock: ν ∼ N ( 0, σ 2 ν s , f )
Model – Idiosyncratic Productivity Shocks
Model – Idiosyncratic Productivity Shocks • For married couples, earnings are given by + ν m , f ) w i f h i j exp ( η m , f l f + w i m ̟ ( i m , j ) exp ( η m , m + ν m , m ) ∗ l m j j � �� � � �� � labor endowment labor endowment
Model – Idiosyncratic Productivity Shocks • For married couples, earnings are given by + ν m , f ) w i f h i j exp ( η m , f l f + w i m ̟ ( i m , j ) exp ( η m , m + ν m , m ) ∗ l m j j � �� � � �� � labor endowment labor endowment • For j > 1, the bivariate AR(1) process is η m , m j + 1 = ρη m , m + ε m , m η m , f j + 1 = ρη m , f + ε m , f , j j + 1 j j + 1 with η m , m = η m , f = 0 and 1 1 � 0 � 0 , σ 2 σ ε f ε m ( ε m , m j + 1 , ε m , f ε m , m j + 1 ) ∼ N , σ 2 σ ε f ε m ε f , f
Model – Idiosyncratic Productivity Shocks • For married couples, earnings are given by + ν m , f ) w i f h i j exp ( η m , f l f + w i m ̟ ( i m , j ) exp ( η m , m + ν m , m ) ∗ l m j j � �� � � �� � labor endowment labor endowment • For j > 1, the bivariate AR(1) process is η m , m j + 1 = ρη m , m + ε m , m η m , f j + 1 = ρη m , f + ε m , f , j j + 1 j j + 1 with η m , m = η m , f = 0 and 1 1 � 0 � 0 , σ 2 σ ε f ε m ( ε m , m j + 1 , ε m , f ε m , m j + 1 ) ∼ N , σ 2 σ ε f ε m ε f , f • Permanent shocks: � � 0 , σ 2 σ ν m ν f 0 ( ν m , m , ν m , f ) ∼ N ν m , m 1 σ 2 σ ν m ν f ν f , f
Model – Idiosyncratic Productivity Shocks Comments:
Model – Idiosyncratic Productivity Shocks Comments: • Many parameters.
Model – Idiosyncratic Productivity Shocks Comments: • Many parameters. • Note that we assume common persistence of shocks. But variances and covariances depend on gender and marital status.
Model – Idiosyncratic Productivity Shocks Comments: • Many parameters. • Note that we assume common persistence of shocks. But variances and covariances depend on gender and marital status. • We infer these variances and covariances from data – inequality in wages and correlations in wages between spouses at different stages in life cycle.
Model – Idiosyncratic Productivity Shocks Comments: • Many parameters. • Note that we assume common persistence of shocks. But variances and covariances depend on gender and marital status. • We infer these variances and covariances from data – inequality in wages and correlations in wages between spouses at different stages in life cycle. • Specification of shocks is a mixture of RIP and HIP.
Model – Demographics and Heterogeneity • Married households and single females differ in terms of the number of children attached to them. • Three possibilities: without , early , late ( b = 0, 1, 2 ) • If a female with children works, married or single, then the household has to pay for child care costs, that vary with the age of children • Children do not provide any utility. • Joint market work for married couples also implies a utility cost, q • Residual heterogeneity in labor force participation.
Model – Preferences • Single males and single females: m ( c , l ) = log ( c ) − l 1 + 1 f ( c , l ) = log ( c ) − l 1 + 1 γ , γ . U S U S
Model – Preferences • Single males and single females: m ( c , l ) = log ( c ) − l 1 + 1 f ( c , l ) = log ( c ) − l 1 + 1 γ , γ . U S U S • Married couples 1 + 1 1 + 1 U M ( c , l f , l m , θ , q ) = 2 log ( c ) − l γ γ − θ l − χ { l f } q . m f
Model – Preferences • Single males and single females: m ( c , l ) = log ( c ) − l 1 + 1 f ( c , l ) = log ( c ) − l 1 + 1 γ , γ . U S U S • Married couples 1 + 1 1 + 1 U M ( c , l f , l m , θ , q ) = 2 log ( c ) − l γ γ − θ l − χ { l f } q . m f θ takes two values at start of life cycle with equal probability; θ ∈ { θ L , θ H }
Model – Government I • Income tax functions : T M ( I , b ) and T S ( I , b ) • We estimate these functions from Internal Revenue Service (IRS) micro data – Guner, Kaygusuz and Ventura (2014) • There is a social security system financed by a flat payroll tax, τ p , plus additional flat capital income tax τ k .
Model – Government II
Model – Government II • Child-related transfers: Child Tax Credit (CTC), Childcare Credit (CDCTC) and CCDF (childcare subsidies).
Model – Government II • Child-related transfers: Child Tax Credit (CTC), Childcare Credit (CDCTC) and CCDF (childcare subsidies). • Earned Income Tax Credit (EITC)
Model – Government II • Child-related transfers: Child Tax Credit (CTC), Childcare Credit (CDCTC) and CCDF (childcare subsidies). • Earned Income Tax Credit (EITC) • Welfare Programs: we use the Survey of Income and Program Participation (SIPP), 1995-2013. • Effective transfer functions from Rauh, Guner and Ventura (2019) • Include AFDC/TANF, SSI, Food Stamps/SNAP, WIC and Housing Assistance.
Model – Government II • Child-related transfers: Child Tax Credit (CTC), Childcare Credit (CDCTC) and CCDF (childcare subsidies). • Earned Income Tax Credit (EITC) • Welfare Programs: we use the Survey of Income and Program Participation (SIPP), 1995-2013. • Effective transfer functions from Rauh, Guner and Ventura (2019) • Include AFDC/TANF, SSI, Food Stamps/SNAP, WIC and Housing Assistance. • Total transfer functions: TR M ( I , b , j ) and TR S ( I , b , j )
Decisions – Big Picture
Decisions – Big Picture • Households decide how much to consume, save and work of their members.
Decisions – Big Picture • Households decide how much to consume, save and work of their members. • Given their state, married households decide whether the female member should work. • Costs of work: child care expenses, additional taxes. • Benefits: higher household income, future human capital.
Decisions – Big Picture • Households decide how much to consume, save and work of their members. • Given their state, married households decide whether the female member should work. • Costs of work: child care expenses, additional taxes. • Benefits: higher household income, future human capital. • Taxation plus presence and generosity of transfers affect the cost and benefits of work.
Model and Data Statistic Data Model Capital Output Ratio 2.93 2.93 LFP of Married Females (%), 25-54 Unskilled 68.2 67.7 Skilled 77.4 77.3 Total 71.8 71.5 Skill Premium 1.8 1.8 Variance log-wages (Married Females, age 40) 0.33 0.35 Variance log-wages (Married Males, age 40) 0.37 0.37 Variance log-hours (Married Females, age 40) 0.13 0.14 Correlation Between Wages of Spouses (age 25) 0.27 0.27 Correlation Between Wages of Spouses (age 40) 0.31 0.31 Variance log-consumption (Age 50-54 vs 25-29) 0.08 0.07
The Structure of Shocks
The Structure of Shocks • Permanent Shocks . Variance single males: σ 2 ν s , m = 0.255 Variance single females: σ 2 ν s , f = 0.226 Variance married males: σ 2 ν m , m = 0.220 Variance married females: σ 2 ν m , f = 0.216 Correlation (married males, married females): 0.047
The Structure of Shocks • Permanent Shocks . Variance single males: σ 2 ν s , m = 0.255 Variance single females: σ 2 ν s , f = 0.226 Variance married males: σ 2 ν m , m = 0.220 Variance married females: σ 2 ν m , f = 0.216 Correlation (married males, married females): 0.047 • Persistent Shocks .
The Structure of Shocks • Permanent Shocks . Variance single males: σ 2 ν s , m = 0.255 Variance single females: σ 2 ν s , f = 0.226 Variance married males: σ 2 ν m , m = 0.220 Variance married females: σ 2 ν m , f = 0.216 Correlation (married males, married females): 0.047 • Persistent Shocks . Common persistence: ρ = 0.958 – Kaplan (2012) Variance single males: σ 2 ǫ s , m = 0.005 Variance single females: σ 2 ǫ s , f ∼ 0 Variance married males: σ 2 ǫ m , m = 0.008 Variance married females: σ 2 ǫ m , f = 0.0006 Correlation (married males, married females): ∼ 0
Var-Log Male Earnings - Married 0.600 0.500 0.400 0.300 0.200 0.100 0.000 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Age Model Data
Var-Log Married Female Earnings 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Age Model Data
Var-Log Married Female Hours 0.3 0.25 0.2 0.15 0.1 0.05 0 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Age Data Model
Married Female Labor Force Participation 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Age Model Data
Rethinking the Welfare State
Rethinking the Welfare State • What are the effects of abolishing the welfare state? Do households value the current scheme?
Rethinking the Welfare State • What are the effects of abolishing the welfare state? Do households value the current scheme? → Eliminate all transfers. Taxes reduced for all.
Rethinking the Welfare State • What are the effects of abolishing the welfare state? Do households value the current scheme? → Eliminate all transfers. Taxes reduced for all. • Replace all taxes and transfers with a Negative Income Tax (NIT) • Each household receives a transfer per member (including children) in all dates and states. • All households face same proportional income tax.
Rethinking the Welfare State • What are the effects of abolishing the welfare state? Do households value the current scheme? → Eliminate all transfers. Taxes reduced for all. • Replace all taxes and transfers with a Negative Income Tax (NIT) • Each household receives a transfer per member (including children) in all dates and states. • All households face same proportional income tax. • Open Economy
Eliminating Welfare State No Transfer System Output (%) 1.7 Married Females LFP (%) 3.4 Married Females LFP (unskilled, %) 4.8 Married Females LFP (skilled, %) 1.7 Aggregate Hours (MF, %) 3.8 Aggregate Hours (%) 2.8 Variance Log-Earnings (benchmark value: 0.524) 0.486 Welfare (CV, %) -2.9 Winning Households (%) 62.0
Eliminating Welfare State No Transfer System Output (%) 1.7 Married Females LFP (%) 3.4 Married Females LFP (unskilled, %) 4.8 Married Females LFP (skilled, %) 1.7 Aggregate Hours (MF, %) 3.8 Aggregate Hours (%) 2.8 Variance Log-Earnings (benchmark value: 0.524) 0.486 Welfare (CV, %) -2.9 Winning Households (%) 62.0 • Asymmetric welfare effects. Large welfare losses – but majority support for eliminating current scheme.
Eliminating Welfare State No Transfer System Output (%) 1.7 Married Females LFP (%) 3.4 Married Females LFP (unskilled, %) 4.8 Married Females LFP (skilled, %) 1.7 Aggregate Hours (MF, %) 3.8 Aggregate Hours (%) 2.8 Variance Log-Earnings (benchmark value: 0.524) 0.486 Welfare (CV, %) -2.9 Winning Households (%) 62.0 • Asymmetric welfare effects. Large welfare losses – but majority support for eliminating current scheme. • Elimination of welfare transfers (AFDC, etc) leads to largest losses.
Rethinking the Welfare State Proportional NIT NIT Tax (2%) (4%) Output (%) 2.9 1.6 0.1 Married Females LFP (unskilled, %) 7.3 2.7 -2.3 Married Females LFP (skilled, %) 3.2 1.4 -0.8 Aggregate Hours (MF, %) 6.9 3.0 -1.3 Aggregate Hours (%) 4.4 2.3 0.0 Variance Log-Earnings (benchmark value: 0.524) 0.49 0.50 0.52 Tax Rate (%) 7.0 11.7 17.2 Welfare (CV, %) -4.0 -1.2 0.1 Winning Households (%) 50.4 63.4 73.8
Rethinking the Welfare State Proportional NIT NIT Tax (2%) (4%) Output (%) 2.9 1.6 0.1 Married Females LFP (unskilled, %) 7.3 2.7 -2.3 Married Females LFP (skilled, %) 3.2 1.4 -0.8 Aggregate Hours (MF, %) 6.9 3.0 -1.3 Aggregate Hours (%) 4.4 2.3 0.0 Variance Log-Earnings (benchmark value: 0.524) 0.49 0.50 0.52 Tax Rate (%) 7.0 11.7 17.2 Welfare (CV, %) -4.0 -1.2 0.1 Winning Households (%) 50.4 63.4 73.8 • Substantial effects on output and labor supply from a proportional income tax, but large welfare losses.
Rethinking the Welfare State Proportional NIT NIT Tax (2%) (4%) Output (%) 2.9 1.6 0.1 Married Females LFP (unskilled, %) 7.3 2.7 -2.3 Married Females LFP (skilled, %) 3.2 1.4 -0.8 Aggregate Hours (MF, %) 6.9 3.0 -1.3 Aggregate Hours (%) 4.4 2.3 0.0 Variance Log-Earnings (benchmark value: 0.524) 0.49 0.50 0.52 Tax Rate (%) 7.0 11.7 17.2 Welfare (CV, %) -4.0 -1.2 0.1 Winning Households (%) 50.4 63.4 73.8 • Substantial effects on output and labor supply from a proportional income tax, but large welfare losses. • NIT leads to welfare gains but smaller effects on output.
NIT, Welfare (right) and Winners (left) 80 0.5 0 70 ‐ 0.5 60 ‐ 1 50 ‐ 1.5 Winners (%) Welfare (%) 40 ‐ 2 ‐ 2.5 30 ‐ 3 20 ‐ 3.5 10 ‐ 4 0 ‐ 4.5 0 0.5 1 1.5 2 3 4 5 6 Percentage of Mean Household Income Winners Welfare
NIT, Welfare (right) and Output (left) 4 0.5 0 3 ‐ 0.5 ‐ 1 2 ‐ 1.5 Welfare (%) Output (%) 1 ‐ 2 ‐ 2.5 0 ‐ 3 0 0.5 1 1.5 2 3 4 5 6 ‐ 3.5 ‐ 1 ‐ 4 ‐ 2 ‐ 4.5 Percentage of Mean Household Income Output Welfare
NIT, Output (right) and Var ‐ Log Earnings (left) 0.54 4 0.53 3 0.52 2 Var ‐ Log Earnings 0.51 Output (%) 0.5 1 0.49 0 0.48 ‐ 1 0.47 0.46 ‐ 2 0 0.5 1 1.5 2 3 4 5 6 Percentage of Mean Household Income Var ‐ Log Earnings Output
Conclusions
Conclusions • Life cycle model goes a long way towards reproducing empirical patterns of inequality over the life cycle.
Conclusions • Life cycle model goes a long way towards reproducing empirical patterns of inequality over the life cycle. • Revenue-neutral elimination of all transfers leads to large welfare losses BUT is supported by a majority of households.
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