Population EconomicsFall 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

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

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)

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

The Needed Tax Rate is the Replacement Rate * the Dependency Rate

t = RR * DR

RR is Determined by Economics

DR is Determined by Demography

Convert to Growth Rates

• The needed growth in the tax rate is (gt)

• gt = gRR + gDR

If the Repacement Rate is Fixed

• the Needed Tax Rate Will Grow with the Dependency Rate

• GRR = 0 means that

• Gt = GDR

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

The needed tax rate depends of the growth rate of wages (productivity)

• gt = gRR + gDR

• gt = (gb – gw) + gDR

• gt = (gb +gDR) - gw

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

The End