Inflation-Unemployment Tradeoff

1
Inflation-Unemployment Tradeoff

• Lecture 12

2
The Equation for Wage Inflation

• RWRP\1A0-A1(U-U_at_VOL)
• The rate of change of wages (RW) equals
• the rate of change in prices (RP) in the past
  year (\1) as a proxy for expected inflation
• plus a constant (A0) for productivity growth and
  other factors not defined here
• minus an adjustment for the existence of
  involuntarily unemployed workerstotal
  unemployment (U) - voluntary (U_at_VOL)

3
The Equation for Wage Inflation
Dependent Variable _at_PCH(ECIWSP) Method
Least Squares Date 03/24/00 Time
1416 Sample(adjusted) 1976
1999 Included observations 24 after
adjusting endpoints Variable Coefficient St
d. Error t-Statistic C 0.002674 0.004323 0.6
18574 (RUC-RUFE)/100 -0.446966 0.102777 4.348
886 (_at_PCH(CPI)_at_PCH(CPI(-1))_at_PCH(CPI(-2)))/3
0.809404 0.049476 16.35956 (_at_PCH(JQPERMH(-1)
)_at_PCH(JQPERMH(-2)))/2 0.466850 0.154689 3.0
17989 R-squared 0.936629 S.E. of
regression 0.005501
4
The Equation for Wage Inflation
5
A Companion Equation for Price Inflation

• If prices are a simple mark-up on wages
  adjusted for productivity QperH (wages divided
  by productivity unit labor costs)..
• P K W/QperH
• hence RP RK R(W/QperH)
• ..and this markup could fall when the economy is
  sluggish
• RK B0 - B1 (U-U_at_VOL)
• Then
• RP B0 - B1 (U-U_at_VOL) R(W/QperH)

6
A Companion Equation for Price Inflation
Dependent Variable _at_PCH(CPI) Method Least
Squares Date 03/24/00 Time
1437 Sample(adjusted) 1977
1999 Included observations 23 after
adjusting endpoints Variable Coefficient Std
. Error t-Statistic C 0.023543 0.002996 7.857
116 NEWCPI -0.006199 0.003771 -1.643598 _at_PCH(E
CIWSP/JQPERMH) .576988 0.077744 7.421618 _at_PC
H(ECIWSP(-1)/JQPERMH(-1)) 0.256860 0.067738 3
.791945 _at_PCH(IMPORTPRICES/(ECIWSP/JQPERMH)) 0.
120974 0.034859 3.470341 _at_PCH(WPI05/(ECIWSP/JQP
ERMH)) 0.065891 0.020495 3.215051 R-squared
0.969657 S.E. of regression 0.006245
7
A Companion Equation for Price Inflation
8
The Final Form Model of Wage and Price Inflation

• RP B0 - B1 (U-U_at_VOL) RW
• AND, EARLIER,
• RWRP\1A0-A1(U-U_at_VOL)
• THUS RP (A0B0) - (A1B1)(U-U_at_VOL)RP\1
• OR RP-RP\1 THE CHANGE IN INFLATION
• (A0B0) (A1B1)(U-U_at_VOL)
• SIMILARLY, THE CHANGE IN WAGE INFLATION CAN BE
  SHOWN TO BE DRIVEN BY THE LEVEL OF UNEMPLOYMENT
• RWRP\1A0-A1(U-U_at_VOL)
• B0 - B1 (U\1-U_at_VOL) RW\1 A0-A1(U-U_at_VOL)
• BRING RW\1 TO THE LEFT (and ignore the difference
  between U and U\1)
• RW - RW\1 THE CHANGE IN WAGE INFLATION
• (A0b0) - ( A1B1) (U -
  U_at_VOL)
• I.E. A FUNCTION OF THE ADJUSTED LEVEL OF
  UNEMPLOYMENT

9
The Final Form Model of Wage and Price Inflation

• RP-RP\1 (A0B0) -(A1B1)(U-U_at_VOL)
• THE CHANGE IN INFLATION A FUNCTION OF THE
  ADJUSTED LEVEL OF UNEMPLOYMENT
• A stable, low rate of inflation is a valuable
  attribute of an economy it promotes good
  decision making because economic life is
  predictable and unbiased by continually changing
  prices
• If inflation is constant, RP RP\1 and the price
  level is non-accelerating, we can compute the
  associated non-accelerating rate of
  unemployment or NAIRU.
• For this to hold, 0 (A0B0) - (A1 B1)
  (U-U_at_VOL)
• Hence, U(NAIRU) U_at_VOL (A0B0)/(A1B1)
• A0 is the excess of wage growth over price growth
  from the wage equation this tends to be the
  long-run productivity growth rate.
• B0 is the excess of price growth less wage
  growth in the price equation this tends to be
  equal to the negative of the long-run
  productivity growth rate (i.e. prices only need
  to rise as rapidly as wage growth minus
  productivity).
• Thus A0B0 0, and U(NAIRU) is the U_at_VOL.

10
The Link Between Unemployment and Real Output

• The unemployment rate reflects the difference
  between the demand for and the supply of labor.
• The demand for labor is the number of employees
  (E) needed, with a given productivity (GDP/E) to
  produce a given output (GDP)
• or, E GDP / (GDP/E)
• The supply of labor is the number of workers (L)
  seeking to work at a given real wage
• The Potential output they can produce in a Fully
  Employed economy an economy operating at the
  NAIRU is called Potential GDP (GDP_at_ FE)
• GDP_at_FEL (1-NAIRU) (Productivity)
• substituting from above for productivity L (
  1-NAIRU) (GDP/E)
• hence L GDP_at_FE / (1-NAIRU)(GDP/E)
• Unemployment Rate U/L (L-E) /L 1 - E / L
• 1- GDP/ (GDP/E) / GDP_at_FE / (1-NAIRU)
  (GDP/E)
• 1- GDP / GDP_at_FE x (1-NAIRU)
• (APPROX.) NAIRU THE GDP GAP VS
  GDP_at_FE ((GDP-GDP_at_FE)/GDP_at_FE)

11
The Link Between Unemployment and Real Output

• A small adjustment to this is required to reflect
  the short-run increases in productivity that
  occur during booms, and the symmetric short-run
  loss during recessions
• Specifically, the prior formula indicates the
  unemployment rate would fall a full 1 for each
  1 increase in GDP (for any given GDP_at_FE)
• In fact, due to temporary shifts in productivity,
  the actual change is roughly 1/2 of this
• In other words, on a cyclical basis, a 1 boost
  in output is met by firms with a 1/2 boost in
  employees and a 1/2 boost in temporary
  productivity
• This relationship is known as Okuns Law
• the change in Unemployment Rate
• about half the growth rate difference between
  potential and actual GDP growth
• or, the level of the Unemployment Rate
• about half the gap between potential and actual
  GDP

12
The Full Links AmongInflation, Unemployment and
Real Output

• The critical relationships are
• 1. The change in inflation responds (with a
  negative derivative) to the unemployment rate
• 2. The unemployment rate responds (with a
  negative derivative) to the GDP level, given
  GDP_at_FE
• Therefore,
• 3. The change in inflation responds (with a
  positive derivative) to the GDP level, given
  GDP_at_FE

change in inflation
GDP level
GDP_at_FE
13
The Full Links AmongInflation, Unemployment and
Real Output

• The change in inflation responds (with a positive
  derivative) to the GDP level, given GDP_at_FE.
• A favorable external shock, such as a drop in oil
  prices or imported goods prices, effective
  reduces the NAIRU (the unemployment rate required
  to keep inflation unchanged), and thereby raises
  GDP_at_FE.

change in inflation
GDP level
GDP_at_FE with NAIRU (1)
GDP_at_FE with NAIRU (2)
14
The Determination of Trend Potential GDP

• GDP_at_FE expands in predictable ways (see Growth
  lectures)
• GDP requires capital, labor, and technology
• If we use a narrow definition of capital as
  physical capital, then trend GDP growth is the
  weighted average of capital and labor growth
  rates, plus the total factor productivity growth
  created by advancing technology
• A broader definition of capital changes the
  defined labor and capital growth rates and hence
  the residual left for technology

15
Recall the Determinants of Labor Productivity

• What enables an employee to produce more or less
  per hour?
• The state of the art potentially available
  (the production possibility frontier).
• His/ Her own education and training to absorb the
  state of the art.
• The quantity and quality of available,
  complementary tools such as computers, assembly
  machines.

16
The Determinants of Labor Productivity

• What infrastructure can the nation provide to
  influence
• the level of output in a workplace?
• education, health, attitudes toward work,
  regulation, taxation
• the efficiency of connections between
  workplaces?
• communication, transportation, common language,
  anti-monopoly regulation, global access

17
The Determinants of Labor Productivity

• Economists can refer to almost all of these
  factors as simply different types of capital
• Capital in this context simply means something
  that is long-lasting and not used up by the
  process of production
• More narrowly, capital sometimes only means
  tangible goods such as equipment, buildings,
  highways

18
The Determinants of Labor Productivity

• Types of Capital
• Tangible equipment and structures
• Human, from brains through brawn
• Technological, e.g. accumulated RD
• Infrastructure, i.e. tangible goods not owned by
  one enterprise