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Can Productivity Growth Offset Aging in a Pay-As-You-Go System?

This analysis explores how a pure pay-as-you-go system relies on a calculated tax rate based on benefits and total wages. By examining the relationship between the average benefit, retirees, and the dependency ratio, we derive the necessary tax rate. The interplay of productivity growth and dependency rates is crucial; as productivity increases, the tax rate may not need to rise if it matches or exceeds the growth in benefits and dependency. Understanding this dynamics is essential to maintaining the sustainability of social benefits in an aging population.

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Can Productivity Growth Offset Aging in a Pay-As-You-Go System?

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  1. Population EconomicsFall 2010 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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