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Income risk and fertility decision

The optimal fertility level in the open economy with idiosyncratic income risk. Family policies welfare effect.

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Income risk and fertility decision

  1. 1. Income risk and fertility decision Oliwia Komada November 22, 2018 Doctoral Seminar FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 1
  2. 2. Motivation
  3. 3. Risky childless world... • Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011; Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016) FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2
  4. 4. Risky childless world... • Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011; Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016) • Uncertainty meters a lot... FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2
  5. 5. Risky childless world... • Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011; Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016) • Uncertainty meters a lot... • Differences in income growth volatility account for 61% of fertility variation between US states during the post WWII baby boom. (Chabe-Ferret & Gobbi 2018) FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2
  6. 6. Risky childless world... • Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011; Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016) • Uncertainty meters a lot... • Differences in income growth volatility account for 61% of fertility variation between US states during the post WWII baby boom. (Chabe-Ferret & Gobbi 2018) • Increase of husband occupation earnings risk by 1sd yields to decrease of completed fertility by 1.5 children. (Sommer JME 2016) FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2
  7. 7. Risky childless world... • Fertility is pro-cyclical (ex. Sobotka, Skirbekk & Philipo PopDevRev 2011; Chatterjee & Vogl AER 2017; Jones & Schoonbroodt RED 2016) • Uncertainty meters a lot... • Differences in income growth volatility account for 61% of fertility variation between US states during the post WWII baby boom. (Chabe-Ferret & Gobbi 2018) • Increase of husband occupation earnings risk by 1sd yields to decrease of completed fertility by 1.5 children. (Sommer JME 2016) • Idiosyncratic earnings risk increase explains nearly 50% of fertility drop. (Sommer JME 2016) FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 2
  8. 8. This study 1. Fertility is too low or just lower due to idiosyncratic income risk? → individual vs. social planer choice → open vs. closed economy FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3
  9. 9. This study 1. Fertility is too low or just lower due to idiosyncratic income risk? → individual vs. social planer choice → open vs. closed economy 2. If fertility is too low, is child benefit welfare improving? → PAYG pension system: social benefits and individual cost → immediate cost and future benefits FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3
  10. 10. This study 1. Fertility is too low or just lower due to idiosyncratic income risk? → individual vs. social planer choice → open vs. closed economy 2. If fertility is too low, is child benefit welfare improving? → PAYG pension system: social benefits and individual cost → immediate cost and future benefits 3. Does it matter how we finance child benefit? → taxes imply a redistribution FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3
  11. 11. This study 1. Fertility is too low or just lower due to idiosyncratic income risk? → individual vs. social planer choice → open vs. closed economy 2. If fertility is too low, is child benefit welfare improving? → PAYG pension system: social benefits and individual cost → immediate cost and future benefits 3. Does it matter how we finance child benefit? → taxes imply a redistribution FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3
  12. 12. This study 1. Fertility is too low or just lower due to idiosyncratic income risk? → individual vs. social planer choice → open vs. closed economy 2. If fertility is too low, is child benefit welfare improving? → PAYG pension system: social benefits and individual cost → immediate cost and future benefits 3. Does it matter how we finance child benefit? → taxes imply a redistribution → redistribution can amplify risk: lump-sum tax → ... or insure against labor income risk: capital tax FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 3
  13. 13. Methodology
  14. 14. What do we do? Our approach We develop an overlapping generations model (OLG) with endogenous fertility and idiosyncratic risk. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 4
  15. 15. What do we do? Our approach We develop an overlapping generations model (OLG) with endogenous fertility and idiosyncratic risk. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 4
  16. 16. What do we do? Our approach We develop an overlapping generations model (OLG) with endogenous fertility and idiosyncratic risk. Main novelty • Optimal fertility decision in the model with idiosyncratic risk. • The computational model with endogenous fertility, idiosyncratic risk and general equilibrium. • Pronatalist policy effect with idiosyncratic risk captured. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 4
  17. 17. Results in a nutshell • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5
  18. 18. Results in a nutshell • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5
  19. 19. Results in a nutshell • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5
  20. 20. Results in a nutshell • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5
  21. 21. Results in a nutshell • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5
  22. 22. Results in a nutshell • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: → lump sum tax welfare deteriorating FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5
  23. 23. Results in a nutshell • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: → lump sum tax welfare deteriorating → capital income tax brings welfare gains. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 5
  24. 24. Part I - analytic framework
  25. 25. Model I
  26. 26. Consumers Vt = ln(cy t ) + φ ln(nt+1) + β ln(co t+1(ζt+1))dΦ subject to: cy t + at+1 + (p − ϕ)nt+1 = wt(1 − τ) − θt co t+1 = at+1Rt+1 + κζt+1wt+1 + ηt+1 where ζt+1 ∈ {1 − δζ, 1 + δζ} and probability of each stage is equal to 1 2 FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 6
  27. 27. Government • covers child benefit adjusting lump sum tax: θt = ϕnt • balances pension system ηt+1 = wt+1τnt+1 Producers Standard perfectly competitive representative firm with Cobb-Douglas production function FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 7
  28. 28. Results I
  29. 29. Fertility is just lower due to risk in open economy • individual consumer fertility choice n = φ p − ϕ c∗ y (δζ) FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8
  30. 30. Fertility is just lower due to risk in open economy • individual consumer fertility choice n = φ p − ϕ c∗ y (δζ) • steady state social planer fertility choice n = φ + β p + k − d c∗ y (δζ) where c∗ y (δζ) is decreasing function FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8
  31. 31. Fertility is just lower due to risk in open economy • individual consumer fertility choice n = φ p − ϕ c∗ y (δζ) • steady state social planer fertility choice n = φ + β p + k − d c∗ y (δζ) where c∗ y (δζ) is decreasing function FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8
  32. 32. Fertility is just lower due to risk in open economy • individual consumer fertility choice n = φ p − ϕ c∗ y (δζ) • steady state social planer fertility choice n = φ + β p + k − d c∗ y (δζ) where c∗ y (δζ) is decreasing function Individual consumer ignore pension benefits and fertility link → fertility too low FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8
  33. 33. Fertility is just lower due to risk in open economy • individual consumer fertility choice n = φ p − ϕ c∗ y (δζ) • steady state social planer fertility choice n = φ + β p + k − d c∗ y (δζ) where c∗ y (δζ) is decreasing function Individual consumer ignore pension benefits and fertility link → fertility too low Individual consumer ignore the cost of capital for future generation → fertility too high FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8
  34. 34. Fertility is just lower due to risk in open economy • individual consumer fertility choice n = φ p − ϕ c∗ y (δζ) • steady state social planer fertility choice n = φ + β p + k − d c∗ y (δζ) where c∗ y (δζ) is decreasing function Individual consumer ignore pension benefits and fertility link → fertility too low Individual consumer ignore the cost of capital for future generation → fertility too high Idiosyncratic income risk has the same impact on the individual consumer and social planer → higher the risk lower the optimal fertility FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 8
  35. 35. Fertility may be too low due to risk in closed economy Intuition: • idiosyncratic income risk → precautionary savings FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9
  36. 36. Fertility may be too low due to risk in closed economy Intuition: • idiosyncratic income risk → precautionary savings • additional savings lower the interest rate and increase wages FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9
  37. 37. Fertility may be too low due to risk in closed economy Intuition: • idiosyncratic income risk → precautionary savings • additional savings lower the interest rate and increase wages • ”risky” part of income increase FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9
  38. 38. Fertility may be too low due to risk in closed economy Intuition: • idiosyncratic income risk → precautionary savings • additional savings lower the interest rate and increase wages • ”risky” part of income increase • individual savings rate higher than social planer savings rate → (Ludwig Krueger 2018) FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9
  39. 39. Fertility may be too low due to risk in closed economy Intuition: • idiosyncratic income risk → precautionary savings • additional savings lower the interest rate and increase wages • ”risky” part of income increase • individual savings rate higher than social planer savings rate → (Ludwig Krueger 2018) • individual consumption lower than social planer choice FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9
  40. 40. Fertility may be too low due to risk in closed economy Intuition: • idiosyncratic income risk → precautionary savings • additional savings lower the interest rate and increase wages • ”risky” part of income increase • individual savings rate higher than social planer savings rate → (Ludwig Krueger 2018) • individual consumption lower than social planer choice • individual fertility lower than social planer choice FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 9
  41. 41. Part II - computational model
  42. 42. Consumers • uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods, • survival rate πj,t < 1 FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10
  43. 43. Consumers • uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods, • survival rate πj,t < 1 • enter labor market at j = 5 • uninsurable earnings: endogenous labor with idiosyncratic productivity process that follows AR(1) approximated by Markov chain FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10
  44. 44. Consumers • uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods, • survival rate πj,t < 1 • enter labor market at j = 5 • uninsurable earnings: endogenous labor with idiosyncratic productivity process that follows AR(1) approximated by Markov chain • endogenous fertility: discrete choice made at j = 8 , n ∈ {0, 1, 2, 3} FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10
  45. 45. Consumers • uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods, • survival rate πj,t < 1 • enter labor market at j = 5 • uninsurable earnings: endogenous labor with idiosyncratic productivity process that follows AR(1) approximated by Markov chain • endogenous fertility: discrete choice made at j = 8 , n ∈ {0, 1, 2, 3} • work till retirement age j = 14, later receive pension benefits FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10
  46. 46. Consumers • uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods, • survival rate πj,t < 1 • enter labor market at j = 5 • uninsurable earnings: endogenous labor with idiosyncratic productivity process that follows AR(1) approximated by Markov chain • endogenous fertility: discrete choice made at j = 8 , n ∈ {0, 1, 2, 3} • work till retirement age j = 14, later receive pension benefits • pay Soc Sec contributions, labor, capital, consumption taxes FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10
  47. 47. Consumers • uncertain lifetimes: live for j = 1, 2, ..., 20 five-year periods, • survival rate πj,t < 1 • enter labor market at j = 5 • uninsurable earnings: endogenous labor with idiosyncratic productivity process that follows AR(1) approximated by Markov chain • endogenous fertility: discrete choice made at j = 8 , n ∈ {0, 1, 2, 3} • work till retirement age j = 14, later receive pension benefits • pay Soc Sec contributions, labor, capital, consumption taxes FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 10
  48. 48. Government • Collects taxes from labor income, capital income, consumption and lump sum tax. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 11
  49. 49. Government • Collects taxes from labor income, capital income, consumption and lump sum tax. • Finances government spending. • Balances pension system. • Services debt. Producers Standard perfectly competitive representative firm with Cobb-Douglas production function FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 11
  50. 50. Calibration Preferences • Preference for leisure γ matches average hours 33% • Preference for children φ matches fertility rate 1.9 • Discounting rate δ matches interest rate 4% Idiosyncratic productivity shock based on Kruger and Ludwig (2013): • Persistence η = 0.95 • Variance ση = 0.0375 FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 12
  51. 51. Calibration Pension system • Replacement rate ρ matches benefits as % of GDP 5.2% • Contribution rate balances pension system in the initial steady state Child cost {pt = 0.15(1 − τ)(1 − τl )wt} matches average child cost in terms of average wages Taxes {τc, τl , τk} match revenue as % of GDP {9.2%, 3.8%, 3.6%} Depreciation rate d matches investment rate of 25% FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 13
  52. 52. Results
  53. 53. Fertility rate decreases when income variance is higher FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 14
  54. 54. Fertility rate decreases when income variance is higher FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 15
  55. 55. Variance change explains 50 % of fertility drop FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 16
  56. 56. Child benefit raises fertility FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 17
  57. 57. Effects are similar for different fiscal tools FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 18
  58. 58. Fertility is higher. Does it make the World better place? Measuring welfare effects • Compare utility under the veil of ignorance → In which World would I rather be born? • P − efficiency → care only about utility level, ignore cohort size • express as a percent of consumption from pre-reform scenario FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 19
  59. 59. Welfare is lower when we use lump sum tax FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 20
  60. 60. Welfare increase when we use capital tax FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 21
  61. 61. Summary
  62. 62. Insights from this study • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22
  63. 63. Insights from this study • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22
  64. 64. Insights from this study • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22
  65. 65. Insights from this study • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22
  66. 66. Insights from this study • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22
  67. 67. Insights from this study • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: → lump sum tax welfare deteriorating FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22
  68. 68. Insights from this study • In standard OLG model fertility and idiosyncratic labor income risk are negatively correlated. • It reflects well pattern observed in the data. • Child benefit increase fertility however welfare effects are ambiguous. • It matters how we finance child benefit: → lump sum tax welfare deteriorating → capital income tax brings welfare gains. FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 22
  69. 69. Thank you for your attention! w: grape.org.pl t: grape org f: grape.org e: o.komada@grape.org.pl FAME|GRAPE, Group for Research in Applied Economics, Warsaw School of Economics 23

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