The Fisher Equation
i = r + (beta)p^e
i = nominal interest rate
r = real interest rate
beta = adjustment coefficient
p^e = expected inflation rate

solve for r & let beta = 1:
r = i – p^e
 
 

Ex post v. Ex ante
Ex post
“from afterward”
realized or actual inflation
only observable after the fact

Ex ante
“from before”
expected inflation
observed in advance
 

Ex post v. Ex ante
Expected inflation is not always the same as realized inflation
Ex post and ex ante real interest rates also differ
Ex ante real interest rates determine agents’ behavior
Behavior responds to expected inflation

Inflation Surveys
Michigan Survey – surveys households

Livingston Survey – surveys “experts”
aka Philadelphia Fed Survey
Both available in FRED

Real interest rates & taxes
r = i – p^e
r_at = i(1 - t) – p^e
“after-tax ex ante real interest rate”

Historical behavior
r, i both procyclical
r often negative in times of high, accelerating inflation
Suggests expected inflation rises faster than actual, once inflation becomes high enough.

Supply shocks and r
Increase in energy prices
Lowered the marginal productivity of capital, therefore lowering the desired capital stock.
Firms substitute other, less energy-intensive factors for capital
Return on capital investment declines, lowering r.

Taxes and r
Higher taxes and/or stricter regulations -
Lower return on capital investment
Lower r.
Lower taxes and/or deregulation –
Higher return on capital investment
Higher r.

The Deficit and r
As deficit increased rapidly, with no end in sight (1980s)…
r rose also.
As deficit came under control (1990s)…
r fell.

Financial deregulation
Regulation Q
Repeal allowed for higher, more competitive interest rates on deposits
Also led to higher yields on securities
Raised r.

Fed conduct
Tight monetary policy raises nominal interest rates
Lowers inflationary expectations
Lowers r.

Money illusion
People don’t consider the impact of inflation
Workers will be happy with an annual raise even if it’s less than the inflation rate

Tax illusion
People don’t consider the impact of taxes and inflation
Raises that match the cost of living push workers into higher tax brackets
Lowering their standard of living and real disposable income.