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Population Economics Fall 2012

Population Economics Fall 2012. Productivity Growth Can Trump Aging in a Pure Pay-As-You-Go System. How a Pure Pay-As-You-Go System Works. Every Year Tax Collections = Benefits Paid Taxes =Total Wages (W) * tax rate (t) Benefits = Average Benefit (b)* Retirees (R) W*t = b*R.

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Population Economics Fall 2012

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  1. Population EconomicsFall 2012 Productivity Growth Can Trump Aging in a Pure Pay-As-You-Go System

  2. How a Pure Pay-As-You-Go System Works Every Year Tax Collections = Benefits Paid Taxes =Total Wages (W) * tax rate (t) Benefits = Average Benefit (b)* Retirees (R) W*t = b*R

  3. Assuming (b) is Fixed, How High Must the Tax Rate (t) be? • W*t = b*R • Therefore: • t = (b*R)/Wages • The tax rate must be equal to the ratio of Benefits to Total Wages

  4. Total Wages Equals the Average Wage times the Number of Workers • W = w * N • Thus we can calculate the needed tax rate as: • t = (b*R) / (w *N)

  5. Now Rearrange Terms • t = (b*R) / (w*N) becomes • t = (b/w) * (R/N) • Where b/w is the Replacement Rate • And R/N is the Dependency Rate

  6. The Needed Tax Rate is the Replacement Rate * the Dependency Rate t = RR * DR RR is Determined by Economics DR is Determined by Demography

  7. Convert to Growth Rates • The needed growth in the tax rate is (gt) • gt = gRR + gDR

  8. If the Repacement Rate is Fixed • the Needed Tax Rate Will Grow with the Dependency Rate • GRR = 0 means that • Gt = GDR

  9. But RR is Not Fixed • RR is equal to b/w therefore • gRR = gb – gw • gw depends on the rate of growth of labor productivity • If gw is greater than gb, RR will fall

  10. The needed tax rate depends of the growth rate of wages (productivity) • gt = gRR + gDR • gt = (gb – gw) + gDR • gt = (gb +gDR) - gw

  11. The tax rate need not grow if: • gw = (gb +gDR) • Or productivity growth equals the growth in the average benefit plus the growth in the Dependency Ratio

  12. The End

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