[Joseph_E._Stiglitz,_Carl_E._Walsh]_Economics(Bookos.org) (1)

Thinking Like an Economist
INCENTIVES AND THE REAL AFTER-TAX
RATE OF INTEREST
In other chapters we have emphasized that real values determine
incentives. Thus, decisions to save and invest respond
to real interest rates. So far, deriving the real interest rate
from the nominal interest rate has been straightforward:
subtract the rate of inflation from the nominal interest rate.
But for the sake of simplicity we have ignored another important
factor, the effect of taxation. In the absence of taxes on
interest income, a nominal interest rate of 2 percent and 0
percent inflation yields the same real return as a nominal interest
rate of 6 percent and 4 percent inflation. If nominal interest
income is taxed, then the relationship between the nominal
interest rate, inflation, and the real interest rate becomes more
complicated.
Suppose nominal interest income is taxed at a 25 percent
rate. If inflation is 0 percent and the nominal interest rate is
2 percent, the after-tax nominal return would be the 2 percent
return minus the taxes (.25 × 2 percent = 0.5 percent), leaving
an after-tax nominal return of 1.5 percent. With 0 percent
inflation, this is also the real return.
Now consider the situation when inflation rises to 4 percent.
If the nominal interest rate were to rise to 6 percent, the
after-tax return would be 6 percent minus taxes (.25 × 6 percent
= 1.5 percent), leaving a nominal after-tax return of 4.5 percent.
Since inflation was 4 percent, the real after-tax return is
only 0.5 percent! Even though the nominal interest rate rose
by the same amount as inflation, the real after-tax return fell.
To maintain the same 1.5 percent real after-tax return that
was obtained with 0 percent inflation, the nominal interest
rate would need to rise to 7.33 percent when inflation increases
to 4 percent. With a nominal return of 7.33 percent, the nominal
after-tax return would be 5.5 percent, and the real aftertax
return would be 1.5 percent. The nominal interest rate
must more than match increases in inflation in order to maintain
the same real return. In this example, if inflation increases
4 percent, the nominal interest rate must rise 5.33 percent.
The relationship would be different if countries designed
their tax systems to tax real returns rather than nominal
returns. In the case of 4 percent inflation, a nominal interest
rate of 6 percent would yield a real before-tax return of 2 percent
and an after-tax return of 1.5 percent, the same after-tax
return as was earned with 0 percent inflation and a 2 percent
nominal interest rate.
expenditures will be explained in Chapter 34; here we can note that it serves to reinforce
the negative effect on aggregate expenditures of a rise in the real rate. Thus the
basic effects of interest rates on the AE schedule in a closed economy will also be
observed when we are studying the determination of GDP in an open economy.
Wrap-Up
THE REAL INTEREST RATE AND
EQUILIBRIUM OUTPUT
A fall in the real rate of interest increases investment spending and household
purchases of durables and new homes. These increases shift the aggregate
expenditures schedule up, raising equilibrium output.
684 ∂ CHAPTER 30 AGGREGATE EXPENDITURES AND INCOME