• How to measure the cost of living.
• The Consumer Price Index
• What is your real income.
• What is inflation, and U.S. experience.
• The inflation game. Who wins? Loses?
• The real interest rate, what is it?
• Relation of inflation to interest rates.

• Depends on change in the "cost of living,"
• If it rose slower than your income,
  your standard of living improved.
• If it rose faster, your standard of living fell.
• US cost of living rose about 2% in ‘99.
• More in 2000, about 3%.

• Using the Consumer Price Index or CPI
• Announced monthly by
• Dept. of Labor’s Bureau of Labor Statistics

• An index is expressed as a percentage of the value in a base period.
• CPI measures cost of living
  relative to a base period.
• CPI is 100 in base period 1982-84.
• In early 2001 it is about 175, meaning...
• Cost of living is 175% of 1982-84 value.

• Cost of "market basket" of goods and services purchased by a "representative" urban household in base period.
• BLS re-prices the market basket monthly.
• CPI is the cost today
  divided by cost in 1982-84.

• Actual purchases vary with
• family size,
• income,
• region,
• age,
• But CPI indicates important changes.

• Three sources:
• Assumes market basket fixed, but in reality consumers will substitute for costly goods.
• Slow to recognize new products.
• Hard to measure quality improvements
• Effect of these is upward bias in CPI.
• Boskin Commission estimated 1.1%/ year.

• BLS went test shopping,
• priced items in the market basket, added up,
• divided by cost in base period 1982-84,
• got 1.683, or 168.3%.
• So CPI was 168.3 in Dec. 1999.

• CPI was 163.9 in Dec. 1998, 168.3 in 1999.
• An increase of 2.7%.
• If your salary rose 6%,
  you have a higher standard of living.
• But not 6% higher.

• Concept: real income.
• The purchasing power of your income
• How many market baskets it can buy?
• Divide your salary by the CPI
• result is your real income.
• Called "deflating"

• Deflate each to get real income in each year:
• ‘98 real salary: $100,000/1.639 = $61,013
• ‘99 real salary: $106,000/1.683 = $62,983
• What kind of $$$???
• Constant dollars of 1982-84.

• current dollar or nominal income
  
  and
  
• real income.

• Take the change in real salary:
• ($62,983 - $61,013) = $1,970
• Divide by your 1998 real salary:
• $1970/$61,013 = .032 = about 3.2%
• Your real income did grow,
• but by less than the nominal 6%.

• 3.2% change in real income is roughly
  
  6% change in nominal income
  
  minus 2.7% change in the CPI.
  
• This is no coincidence!

• %Change Real =
  
• %Change Nominal minus %Change CPI

• Nominal = Real • CPI. Why?
• Let Nominal increase by fraction n, CPI by c, and Real by r,
• Nominal•(1+n) = Real•(1+r) • CPI•(1+c)
• Dividing the second equation by the first ,
• 1+n = (1+r) • (1+c) = 1 + r + c + rc
• If r and c are small, rc is very small,
• so n = r + c
• and r = n - c

• The % increase in nominal income =
  % increase in real income
  plus the % change in the CPI
  
• The % increase in real income =
  % increase in nominal income
  minus the CPI % change.

• Market basket that cost $30 in 1961 cost
  $100 in 1983 and
  $157 by 1996!
• A salary of
  $15,700 in 1996 same as $10,000 in 1983 and $3,000 in 1961.

• A fact of life
  since the 1970s.
• Now inflation is low.
• Will it stay there?
• What keeps it low?
• What would make it rise again?

• Inflation under Jimmy Carter contributed to his defeat by Reagan in 1980.
• Anti-inflation policy by the Federal Reserve under chair Paul Volcker.
• Continued by Fed chair Alan Greenspan.
• By 1992 inflation subsided to levels not seen for three decades!
• So far, it has stayed low.

• As cost of living rises, purchasing power falls.
• Purchasing power of $1 in terms of pizzas is
  
  = 1/ price of a pizza.
  
• A broader measure:
  
  = 1/ CPI.

• By 1983 it took $3.35 to have the purchasing power $1 had in 1961.
• having a dollar to spend in 1996 was like having 64¢ in 1983.
• Over 35 years, purchasing power
  fell 81%!

• Not a happy story
• nominal wage was $2.30/ hour in 1961
• rose to $13 by 1996,
• more than five-fold.
• but real wage is about the same!

• Only by adjusting for inflation can we see changes in the standard of living,
• that is what really matters.
• Why have real wages stagnated?
• Reduced the demand for unskilled labor due to
• changes in technology,
• global competition
• Industrial unions much less powerful

• Who are the Winners?
  
• the Losers?

• Expecting inflation of 4%,
  so expect real wage will rise 2%.
  
• If inflation turns out to be 6%,
  real wage will not rise at all.
  
• Then, union members are losers,
  the employer is the winner.

• Who wins?
  
• Who loses?

• When inflation is higher than expected -
  lenders lose, borrowers win.
  
• When inflation is lower than expected - lenders gain, borrowers lose.

• Homeowners with mortgages
• The U. S. Treasury
• Borrowers in general
• Anyone who had an obligation to pay $

• The big losers in the 70s were lenders
• Savings and Loans
• Banks
• Owners of US Treasury bonds
• Those on fixed pensions.
• Anyone promised fixed payments,

Then parties could agree on payments that increase with inflation.

• A contract stating that payments be adjusted regularly depending on future changes in the CPI.

• Social Security payments are indexed.
• Wage contracts may include a cost of living adjustment, or COLA, based on the CPI.
• Leases on commercial property often provide rent adjustment based on the CPI.
• ARMs, protect lenders by indexing the interest payment to the short interest rate.
• Income tax brackets adjusted annually.

• COLA clauses affected.
• Tax brackets adjusted more slowly.
• Baby Boomers would receive much smaller Social Security checks.
• 1.1% compounded for 20 years is 25%!
• Big politics here!

• If you purchase bond yielding 6%,
  and inflation is 6%,
  your purchasing power gain is zero .
• In that case, we say the real yield is zero.
• If inflation < 6%, you gain in real terms.
• If inflation > 6%, you lose in real terms.
• Stated yield is the nominal interest rate.

• Deflate amount invested by CPI year ago.
• Deflate amount received by CPI today.
• Percentage gain is the real rate of interest.
• The real rate is approximately
  the nominal rate minus the inflation rate.
• Why?

• % change in real terms is approximately
  the nominal % change
  minus the CPI % change.
• Applied to interest rates:
  Real Interest Rate =
  Nominal Rate minus Rate of Inflation
• Works well only if rates of interest and inflation are small!

• Lenders and borrowers do not know what the real interest rate will be.
• But they have an expectation of it,
  based on their expectation of inflation.

• the expected or ex ante real interest rate =
  nominal interest rate - expected inflation
  
• the realized or ex post real interest rate=
  nominal interest rate - actual inflation

• A forecast, different across individuals
• Invariably wrong, ex post!
• If you expect the CPI to rise 3%,
  your ex ante real rate is 6% - 3% = 3%.
• If inflation turns out to be 5%,
  your ex post real rate is only 1%.

• What matters is the real interest rate.
• If inflation is higher than expected,
  bond holders lose,
  borrowers win;
• and vice versa.

• How to measure expected inflation?
• Inflation over past year is a "rule of thumb"
• Using that measure, the real T bill yield is:

• Ex post fluctuates more than ex ante.
• Fairly steady during the 60s, at about 1%.
• Mid 70s-1980 very low and even negative.
• 1980s real rates higher high, then declining.

• First issued Jan 97.
• Maturity range from 2002 to 2029.
• Payments are indexed to the CPI.
• The yield is a real interest rate.
• Quoted in the WSJ table.
• For the first time, we observe an ex ante real interest rate in the US.

• By supply and demand, of course.
• Savers supply loans
• The higher the real rate, the greater the supply
  from households and ROW.
• Issuers of bonds demand loans:
• The higher the real rate, the lower the demand.
• The equilibrium real interest rate equates the supply of loans with the demand.

• Large federal deficits required large loans.
• That helped push real interest rates up.
• What would happen to real interest rates if Congress balanced the budget?
• That happened in 1998, rates fell.
• Now headed back up!

• Yuppies of the 80’s now middle aged savers.
• Helping lower real interest rate
• The Fed buys and sells T bonds,
  so the Fed can move the real rate too.
• "Tight money policy" of the early 80’s,
  a factor in high real interest rates.
• Fed has been tightening lately!

• Nominal rate = real rate + expected inflation (the "Fisher equation")
• Variables affecting real rate change slowly, like demographics,
• but inflation rates vary widely.
• So, variation in the nominal rate reflects mainly variation in inflation.

• Nominal interest income is taxed.
• In 1980 T bill yield was about 12%
  and so was inflation.
• What was the real rate?
• Before taxes it was zero, 12% - 12% = 0%!
• Good for borrowers, bad for lenders!

• Call the tax rate "t" so
  after tax nominal yield = 12% • (1-t)
• But now we subtract inflation rate of 12%!
• After tax real yield =
  12% • (1-t) - 12% = - t • 12%
• For someone in the 50% tax bracket,
  after tax yield was negative 6%!

• You bet!
• Not only did it pay a zero real rate,
  it collected half of it back in taxes!
• It made 6% on money it borrowed!
• How could the tax law be fixed?

• Capital gain = sale price - cost.
• You bought Widgets Inc. stock in 1983
  Cost $100/ share, sold today for $168
  Taxable gain is $68 per share.
• What is the real gain?
• What is the real gain after taxes?
• What would fix this distortion?