Notes Chapter 6-8
Point of the class
Math



Systems of equations
Regressions and scatterplots
Levels versus rates of change
Model building


Using data to build models, in addition to logic
Combining the results into more complete models
Economic concepts and intuition






Wage determination through collective bargaining
Cost-plus-markup pricing: role of labor and non-labor costs
Phillips Curve, Expectations-augmented Phillips Curve
Stagflation, Disinflation
Okun’s Law
Aggregate Supply- curve
Definitions







Collective bargaining
Production function
Wage-setting relation
(Wage Curve)
Phillips Curve

Okun’s Law

Homework Problems
On webpage

Bargaining power
Labor productivity
Price-Setting relation
(Price Curve)
Expectationsaugmented Phillips
Curve
Normal Growth Rate





Unemployment insurance
Markup
Natural rate of unemployment
Non-accelerating-inflation
rate of unemployment
Disinflation
Facts




When unemployment is high, wage pressures abate
When unemployment falls, wage pressures rise.
Much of wage bargaining is done collectively.
The more specialized a type of worker or the more unique a worker, the more bargaining power
he has.
Model Building
Building Blocks
Wage Determination
The theory of Efficiency Wages: Real Wages may or may not clear the Labor Market. Firms may want to
pay more than the market-clearing wage to ensure that the workers are of better quality and more loyal.
This generates unemployment … but unemployment can be a disciplining device: gets people to take
lower wages, u.  is the sensitivity of workers to the level of unemployment.
Workers care about the Real wage that they will get in the future, so they form an expectation of future
prices and ask for wages accordingly. There are also other factors that affect the desired real wage,
which we will denote by Z, such as the existence and generosity of unemployment insurance, or the degree of labor union militancy.
𝑊 = 𝑃𝑒 𝐹 (𝑢
⏟,𝑍
⏟)
− +
Think of this equation as representing the “Labor Union and Human Resources” side of a company: it is
the interaction between workers and the Personnel office that determines wages, given a host of factors. In reality, many contracts are negotiated not for a level of wages given an expected cost of living,
but for a rate of wage raises given an expected rate of inflation. Denote the rate of wage raises with the
Greek letter𝜔 =
∆𝑊
,
𝑊
omega.
Wage Curve
ω = 𝜋 𝑒 + (𝑍 − 𝛼𝑢)
This tells us that workers want their wages to grow faster (higher ) if their expectations for future inflation are higher (𝜋 𝑒 ); if unemployment insurance or labor-union militancy increases (higher Z); if they
become less sensitive to unemployment, that is, if they care less about u (a lower ) or if unemployment
is lower (lower u).
Cost-plus-markup Pricing
Price = Labor Costs + Non-Labor Costs
The labor portion of the marginal cost of production depends on two things: the cost of a unit of labor
services (e.g., the hourly wage rate), and the productivity of labor (e.g., the number of hours it takes to
produce a unit). Labor productivity in turn depends on factors such as technology as well as the availability of capital, natural resources, the human capital (skills, education) of workers, and other factors.
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐿𝑎𝑏𝑜𝑟 =
$
$
𝑤𝑜𝑟𝑘𝑒𝑟 − ℎ𝑜𝑢𝑟𝑠
=
𝑢𝑛𝑖𝑡 𝑤𝑜𝑟𝑘𝑒𝑟 − ℎ𝑜𝑢𝑟
𝑢𝑛𝑖𝑡
1
𝑊
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐿𝑎𝑏𝑜𝑟 = (𝑤𝑎𝑔𝑒) (
)=
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦
𝐴
𝑊
𝐴
is, then, “unit labor costs”: the labor cost of producing a unit.
Non-Labor Costs include profits for entrepreneurs, rent for land, interest for capital (including the availability of loans). Non-labor costs also include business taxes, etc. In particular, “Crude Producer Prices”
include



the cost of energy (electricity, gas),
of foodstuffs and feedstuffs (wheat, cattle, soybeans), and
of raw materials (coal, crude oil, sand, timber).
Denoting the impact of non-labor costs by 𝑝NL , this equation 𝑃 = 𝑝NL W⁄𝐴 says that prices depend on
𝑊
unit labor costs, 𝐴 , and non-labor costs, which increase the price (relative to just unit labor costs) by a
proportion 𝑝NL .
Think of this as the “Production and Marketing” side of a company. Production determines the number
of workers needed, given their level of productivity and availability of non-labor resources (including
technology). Marketing takes the cost of producing a unit and sets the price, given all sorts of competitive considerations. It is the interaction between production and customer relations that determines
prices, given a host of factors.
More realistically, firms set out a plan for raising prices (their “individual firm” level of inflation), given
the rate of increase in their costs. This “individual firm” inflation () (and therefore, the overall aggregate level of inflation) will be higher if

the rate of increase of their labor costs () is higher or if workers’ productivity rises faster gA =
A/A: both of these events would raise unit labor costs.

if the rate of increase of non-labor costs NL= pNL/pNL is higher.
Price Curve
𝜋 = ω + 𝜋𝑁𝐿 − 𝑔𝐴
Putting the Building Blocks Together
What determines inflation in equilibrium? It is given by the combination of the interaction between all
sides of the firm: the “Labor Union+Personnel” side that determines the availability and cost of labor
and the “Production+Marketing” that determines the use of labor, its combination with other factors,
and the revenue to be earned by the firm. Equilibrium is determined by the point where the two sides
of the firm agree. Plugging the Wage Curve into the Price Curve, we get
𝜋 = 𝜋 𝑒 + (𝑍 − 𝛼𝑢) + 𝜋𝑁𝐿 − 𝑔𝐴
Rearranging a little,
𝜋 = 𝜋 𝑒 − 𝛼𝑢 + (𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴 )
we find that, in equilibrium, inflation rises if expected inflation is higher (so workers want faster raises)
or if unemployment is lower (so workers’ bargaining power increases); or if it is pushed up by factors
that have to do with the “structure” of the economy, such as greater labor-union militancy or unemployment benefits (Z), faster-rising non-labor costs (𝜋𝑁𝐿 ), or slowing productivity (gA).
Examining the Result and Using the Model
Suppose that workers correctly anticipate P, so that (𝜋 = 𝜋 𝑒 ). Then (𝜋 − 𝜋 𝑒 ) = 0. The unemployment
rate that is consistent with this result is called the “natural unemployment rate,” the unemployment
rate that prevails when expectations are met.
Set 𝜋 = 𝜋 𝑒 , and then solve for u, which is the natural rate of unemployment.
𝜋 − 𝜋 𝑒 = 0 = −𝛼𝑢 + (𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴 )
𝛼𝑢𝑛 = 𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴
𝑢𝑛 =


1
[𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴 ]
𝛼
un rises if Z or 𝜋𝑁𝐿 rises.
un falls if 𝑔𝐴 rises.
Now, notice that 𝛼𝑢𝑛 = [𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴 ]. Remember that combining the Wage Curve with the Price
Curve yielded 𝜋 = 𝜋 𝑒 − 𝛼𝑢 + [𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴 ], we can rewrite this equation as
𝜋 = 𝜋 𝑒 − 𝛼𝑢 + 𝛼𝑢𝑛
𝜋 − 𝜋 𝑒 = −𝛼(𝑢 − 𝑢𝑛 )
This equation is known as the Phillips Curve. One interesting conclusion from this equation is that the
“natural rate of unemployment” is the value of u that prevents inflation from rising above its expected
value. So another term for un is the NAIRU, the
non-accelerating-inflation rate of unemployment,
the rate of unemployment at which inflation does not accelerate.
The Phillips Curve, Expansionism and Adverse NAIRU Shocks
For years and centuries, up to the mid-1960s, inflation had been sometimes high, sometimes low, sometimes negative, averaging zero over the long run. So in 1960, it was not unreasonable to suppose that
future inflation would average 0 (or pretty darn close). People argued (and keep arguing) for “Price Stability”: zero inflation.
Suppose then 𝜋 𝑒 = 0.
𝜋 − 𝜋 𝑒 = −𝛼(𝑢 − 𝑢𝑛 )
𝜋 = −𝛼(𝑢 − 𝑢𝑛 )
𝜋
𝛼𝑢𝑛 = [𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴 ]
−𝛼
Phillips Curve
𝑢𝑛
u
5
1969
1966
3
INFLATION
4
1968
2
1967
1965
1960
1963
1962
1
1964
1961
3
4
5
UNRATE
6
7
After 1960, the government purposefully kept inflation high to lower unemployment.1 The government
“rode” the Phillips Curve, choosing where it would rather be. Higher inflation, lower unemployment. Or
… higher unemployment, lower inflation.
1
See http://www.time.com/time/covers/0,16641,19651231,00.html)
Many argued that “A little inflation is like a little fever, it quickly gets out of control.”
Get, from Fred, data on % change of CPIAUCSL and UNRATE. Then draw a scatter plot, putting inflation on the vertical axis, between 1948 and 1969. Note the very tight fit (except for 1953 and the recession of 1958).
U.S. Government's economic managers […] in 1965 […] have been pursuing a strongly expansionist policy. They carried out the second stage of
a two-stage income-tax cut, thus giving consumers $11.5 billion more to
spend and corporations $3 billion more to invest. In addition, they put
through a long-overdue reduction in excise taxes, slicing $1.5 billion this
year and another $1.5 billion in the year beginning Jan. 1. In an application of the Keynesian argument that an economy is likely to grow best
when the government pumps in more money than it takes out, they
boosted total federal spending to a record high of $121 billion and ran a
deficit of more than $5 billion. Meanwhile, the Federal Reserve Board
kept money easier and cheaper than it is in any other major nation,
though proudly independent Chairman William McChesney Martin at
year's end piloted through an increase in interest rates—thus following the
classic anti-inflationary prescription.
By and large, Keynesian public policies are working well because the private sector of the economy is making
them work. Government gave business the incentive to expand, but it was private businessmen who made the
decisions as to whether, when and where to do it. Washington gave consumers a stimulus to spend, but millions of ordinary Americans made the decisions—so vital to the economy —as to how and how much to
spend. For all that it has profited from the ideas of Lord Keynes, the U.S. economy is still the world's most
private and most free-enterprising. Were he alive, Keynes would certainly like it to stay that way.
Time Magazine, Friday, Dec. 31, 1965 "We Are All Keynesians Now",
http://www.time.com/time/printout/0,8816,842353,00.html
But then things changed. First, after years of positive inflation – of purposefully positive inflation – people figured out that inflation wasn’t going to come back down. In particular, they figured out that it was
going to remain positive and not average zero because the government wanted it to be non-positive.
Expectations of inflation became non-zero.
This led workers to factor in non-zero inflation into their wage bargaining. So we get an “expectational”
Phillips curve.
𝜋 − 𝜋 𝑒 = −𝛼(𝑢 − 𝑢𝑛 )
6
where 𝜋 𝑒 > 0. The result was that unemployment rose. If the Phillips Curve had not shifted, one would
have thought that inflation would fall (a movement down and to the right along the Phillips Curve). But
inflation stayed up even as unemployment returned to its natural rate (around 5%). In hindsight, we
recognize the shift up and to the right of the Phillips Curve.
1970
5
1969
1971
4
1972
3
1966
2
1967
1965
1964
1960
1963
1962
1
INFLATION
1968
1961
3
4
5
UNRATE
6
7
𝜋
𝜋 𝑒 + 𝛼𝑢𝑛
𝛼𝑢𝑛
Phillips Curve
𝑢𝑛 𝜋 𝑒
+ 𝑢𝑛
𝛼
u
15
Second, the NAIRU also changed.
 Oil shocks: oil prices went up significantly: 𝜋𝑁𝐿 rose quickly.
 The growth rate of productivity 𝑔𝐴 fell between 1973 and 1995.
 Entitlements and welfare expanded: Z grew.
1980
10
1981
1975
5
1978
1977
1973
1970
1969
1976
1982
1971
1968
1972
1966
1967
1965
1964 1960
1963
1962
1961
0
INFLATION
1979
1974
4
6
8
10
UNRATE
The result was more inflation and more1960-1969
unemployment.1970-1972
Monetary Policy responded to these develop1973-1975
1976-1979
ments by accommodating, that is, by letting inflation rise in order to keep unemployment from rising
1980-1982
even more.
𝜋
1975, 1980-1982
1974, 1976-1979
𝜋 𝑒 + [𝑍 + 𝜋𝑁𝐿 − 𝑔𝐴 ]
1970-1973
1960-1969
Phillips Curve
𝑢𝑛
𝜋𝑒
+ 𝑢𝑛
𝛼
u
In sum: the Phillips Curve shifted for two reasons: expected inflation changed and the natural rate of
unemployment (the NAIRU) changed adversely.
Monetary Disinflation and Favorable NAIRU Shocks
Between 1979 and 1984, the Federal Reserve embarked on a very aggressive anti-inflation program.
This eventually changed expectations of inflation. At the same time, oil shocks receded – oil prices fell
repeatedly. The combination shifited the Phillips Curve downward.
Continued anti-inflation policy – and a resumption of high productivity growth – succeeded in bringing
the Phillips Curve down once more in the mid-late 1990s. (Note that in 2008 oil shocks have put the
economy at higher inflation-unemployment combination, more like the Phillips Curve of the late-1980s.)
15
1980
10
1981
1982
5
1990
1989
1988
1984
1991
1987
1996
1995
1985
1993
1994
1983
1992
0
1986
6
7
8
Unemployment Rate, %
9
10
6
5
5
1990
1989
2008
1991
4
1988
1987
2000
2005
3
2006
2007
2001
1997
1992
1994
2003
2
1999
1993
1996
1995
2004
1986
2002
1
1998
4
5
6
Unemployment Rate, %
7
8
The Expectationsaugmented Phillips
Curve
The Phillips Curve had
shifted for two reasons: a)
changes in expectations
and b) changes in the
NAIRU. We’d like to separate these two effects. To
do this, we need to come
up with a model for expected inflation so we can
take it into account explicitly and put it on the axes.
That way changes in expected inflation won’t cause shifts of the curve. This will allow us to calculate the NAIRU and see how it
changes over time. What is a good model for Expected Inflation? What do people expect inflation to
be?2
Instead of assuming that prices would be stable (𝑃𝑒 = 𝑃𝑡−1 ) or (𝜋 𝑒 = 0), perhaps it is reasonable to
think that people expect that inflation, not prices, would be stable (𝜋 𝑒 = 𝜋𝑡−1 ). Suppose, then, 𝜋 𝑒 =
𝜋𝑡−1 .
𝜋 − 𝜋 𝑒 = −𝛼(𝑢 − 𝑢𝑛 )
𝜋𝑡 − 𝜋𝑡−1 = −𝛼(𝑢 − 𝑢𝑛 )
∆𝜋𝑡 = −𝛼(𝑢 − 𝑢𝑛 )
We call this an Expectations-augmented Phillips Curve (E-PC for short) because it takes expectations into
account explicitly, right on the axis. Graphing the change in annual inflation versus the unemployment
rate we see a pretty robust medium-term relation. We can use regression tools (from econometrics) to
estimate the correct relation between the change in inflation and the unemployment rate. That is, we
want to estimate the parameters of this model:
∆𝜋𝑡 = 𝛼
̂0 − 𝛼
̂𝑢
1
2
Here’s a useful report on the impact of changes of inflation rates for different types of goods on different kinds of
households: http://www.sca.isr.umich.edu/documents.php?c=r.
4
1974
1979
1980
1957
1956
1968
1966
1969 2000
-2
0
2
1973
2008
1987
1978
2005
1989 1990 2003
1999
1988
1960
1965 1970 2004
1962
1995
1996
1963
2006 1964
1967
2007
1954 1994
1955 2001
1997
1998
1972
2002
1959 1971
1984
1977
1993
1961
19581985
1992
1991
1986
1975
1983
-4
1981
1976
1982
4
6
8
Unemployment Rate %
10
. reg chinflation unrate if time >1953
Source |
SS
df
MS
-------------+-----------------------------Model | 40.5691121
1 40.5691121
Residual | 102.886955
53
1.9412633
-------------+-----------------------------Total | 143.456067
54 2.65659383
Number of obs
F( 1,
53)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
55
20.90
0.0000
0.2828
0.2693
1.3933
-----------------------------------------------------------------------------chinflation |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------unrate | -.6250665
.1367322
-4.57
0.000
-.8993165
-.3508165
_cons |
3.667031
.8093325
4.53
0.000
2.043715
5.290346
-----------------------------------------------------------------------------PhilCurveAnnual.dta
This output tells us that
𝐶𝐻_𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁 = 3.667 − 0.625 𝑈𝑁𝑅𝐴𝑇𝐸
On the basis of this estimated equation, what is the natural rate of unemployment? That is, the value of
unemployment where inflation does not change?
∆𝜋𝑡 = 𝛼
̂0 − 𝛼
̂𝑢
1
0=𝛼
̂0 − 𝛼
̂𝑢
1 𝑛
0 = 3.667 − 0.625 𝑈𝑁𝑅𝐴𝑇𝐸𝑛
0.625 𝑢𝑛 = 3.667
𝑢𝑛 = 5.8672
So 5.86% is the NAIRU between 1953 and 2008, but without taking into account NAIRU shocks.
We are also interested in knowing how the natural rate of unemployment has changed over the years.
To see this, we have to allow the Expectations-augmented Phillips curve to shift – we do this by looking
at the data in a bit more detail. We find that there was one E-PC between the mid-1950s and the early
1970s. Remember that the regular Phillips Curve shifted between 1969 and 1970 because expectations
changed (not a change in the NAIRU). Here we are taking expectations into account, so the 1970-1972
years (which had a separate PC) are described by the same E-PC as the 1960s. That’s the advantage of
modeling expectations explicitly.
4
1974
1979
-2
0
2
1973
1980
1957
1956
1968
1966
1969 2000
2008
1987
1978
2005
1989 1990 2003
1999
1988
1960
1965 1970 2004
1962
1995
1996
1963
1964
2006
1967
1994
2007
1954
1955 2001
1997
1998
1972
2002
1959 1971
1984
1977
1993
1961
19581985
1992
1991
1986
-4
1981
1976
1975
1983
1982
4
6
8
Unemployment Rate %
10
There was another curve after the 1973 oil shock and we were on it until 1984. Notice that the 19801982 monetary contraction, which caused the PC to shift, simply causes a movement along the E-PC.
The monetary contraction caused expectations to change, and expectations are already taken into account in the E-PC, so we just move along it. But as oil prices fell, and fell, and fell during the 1980s (especially in real terms), the E-PC shifted in.
In 1990, oil prices rose again, but the Fed did not accommodate. Instead, it fought the incipient inflation
with higher interest rates, which raised unemployment and lowered expectations of inflation and shifted … the PC curve, but kept the economy on the same E-PC curve (thankfully). By the time that the recession was over and oil prices had receded, the economy was ready for a shift of the E-PC curve, back
to the original (60s) E-PC. To this we returned in the late 1990s as a) oil prices fell, b) productivity rose,
and c) Clinton and the Republican Congress ended welfare as-we-knew-it in 1996.
Then, how has the natural rate changed? Between 1954-1972 and again between 1997-2002 and 20062007, the expectations-augmented Phillips Curve could have been described by
𝐶𝐻_𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁1 = 3.491 − 0.707 𝑈𝑁𝑅𝐴𝑇𝐸
So 𝑢𝑛 = 4.937. Between 1973 and 1984, the expectations-augmented Phillips Curve could have been
described by
𝐶𝐻_𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁2 = 12.639 − 1.723 𝑈𝑁𝑅𝐴𝑇𝐸
So 𝑢𝑛 = 7.323. Between 1985-1996, 2003-2005, and in 2008, the expectations-augmented Phillips
Curve could have been described by
𝐶𝐻_𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁3 = 5.707 − 0.920 𝑈𝑁𝑅𝐴𝑇𝐸
So 𝑢𝑛 = 6.200. In sum: Why did the natural rate of unemployment change? As mentioned above, a
combination of oil shocks3 (notice for example, the oil shocks of 2003 and 2004, which put the economy
temporarily on a higher expectations-augmented Phillips Curve from 2003 to 2005); changes in productivity4; and changes to unemployment insurance and labor-union militancy.
3
4
http://research.stlouisfed.org/fred2/
http://pwt.econ.upenn.edu/php_site/pwt62/pwt62_form.php
𝑢𝑡 − 𝑢𝑡−1 =
𝑌 −𝑌
−𝛽 ( 𝑡 𝑌 𝑡−1
𝑡
−
𝑌𝑡,𝑛 −𝑌𝑡−1,𝑛
𝑌𝑡,𝑛
3
2
1975
1954
1958
1970
1980
1991
1974
)
𝑌𝑡,𝑛
1961
2002
-1
= 3.42.
1971
2001
0
Estimating this equation yields CHUNRATE=1.32-0.39(GROWTHGDP). So
𝑌𝑡,𝑛 −𝑌𝑡−1,𝑛
1982
1
Change in the Unemployment Rate, %
Okun’s Law
Arthur Okun noticed this relation between the change in the unemployment rate and the percentage deviation of Real GDP from Potential GDP.
1992
1981
1990
2003
1957
19602007
1963
1967
1969
1953
1996 1983
1986
1989
1956
2000
1952 1979
1968
1999
1985
1972
2004
1997
20051998
1964
19952006
1993
1977 1966
1965
1988
1973
1994 1976
1987
1978
1962
1950
1955
1959
-2
1951
In Principles of Macroeconomics we
1984
-5
0
5
studied another version Okun’s Law
Real GDP Growth Rate - Potential GDP Growth Rate, %
(quite consistent with the above),
which says that cyclical unemployment (𝑢𝑡 − 𝑢𝑛 ) is lower if output is above the natural level of output
𝑌𝑡 −𝑌𝑛
).
𝑌𝑛
(
𝑌𝑛 −𝑌𝑡
)
𝑌𝑛
This can be expressed thus (
1
= 𝜃 (𝑢𝑡 − 𝑢𝑛 ) or
𝑌𝑛 − 𝑌𝑡
𝑢𝑡 − 𝑢𝑛 = 𝜃 (
)
𝑌𝑛
If we remember that above we found that 𝑢𝑛 = 5.8672, we can define “cyclical unemployment” as
𝑢𝑡 − 𝑢𝑛 = 𝑢𝑡 − 5.8672. With that definition, we run a regression
. reg cyclical
outputgap
Source |
SS
df
MS
-------------+-----------------------------Model | 96.1023019
1 96.1023019
Residual | 28.4946018
57 .499905295
-------------+-----------------------------Total | 124.596904
58 2.14822248
Number of obs
F( 1,
57)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
59
192.24
0.0000
0.7713
0.7673
.70704
-----------------------------------------------------------------------------cyclical |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------outputgap |
.5500022
3.96681
13.87
0.000
47.05682
62.94362
_cons | -.2958689
.0921275
-3.21
0.002
-.4803511
-.1113866
-----------------------------------------------------------------------------𝑌𝑛 −𝑌𝑡
)
𝑌𝑛
So we find that 𝜃 = 0.55, which confirms what we knew from ECON 201: (
≈ 2(𝑢𝑡 − 𝑢𝑛 ).
Notice that Okun’s Law assumes that there is a close relation between the natural level of output 𝑌𝑛
and the natural rate of unemployment 𝑢𝑛 . For example, if workers become less productive, the natural
level of output will fall (less can be produced even in the long-run), and fewer workers will end up being
hired (hire long-run, natural unemployment). Perhaps we can think of the relationship this way
𝑌𝑛 = 𝐴𝐿(1 − 𝑢𝑛 )
where L is the labor force (assume constant) and A is the given level of productivity.
Aggregate Supply-Inflation: AS-
We know that the Phillips Curve is
𝜋𝑡 = 𝜋 𝑒 − 𝛼(𝑢 − 𝑢𝑛 )
And that a familiar version of Okun’s Law is
𝑌𝑛 − 𝑌𝑡
𝑢𝑡 − 𝑢𝑛 = 𝜃 (
)
𝑌𝑛
We can combine these two and get
𝜋𝑡 = 𝜋 𝑒 − 𝛼𝜃 (
𝑌𝑛 − 𝑌𝑡
)
𝑌𝑛
This is great, but wouldn’t it be nice to focus on the relation between inflation and Yt? We do some very
simple rearranging and get
𝛼𝜃
𝜋𝑡 = 𝜋 𝑒 − 𝛼𝜃 + ( ) 𝑌𝑡
𝑌𝑛
We can think of this as the Aggregate Supply-Inflation equation (AS-).
If we use past inflation as a proxy for expected inflation (𝜋 𝑒 = 𝜋𝑡−1 ), we can use the expectationsaugmented Phillips curve and write ∆𝜋𝑡 = 𝛼𝜃
𝑌𝑡
𝑌𝑛
− 𝛼𝜃. If our equation is correct, then the “intercept”
term should be equal in size to the “slope” term, but of opposite sign … as it is!
. reg chinflation outputratio
Source |
SS
df
MS
-------------+-----------------------------Model | 58.3944444
1 58.3944444
Residual | 245.028133
57 4.29873918
-------------+-----------------------------Total | 303.422578
58 5.23142376
Number of obs
F( 1,
57)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
59
13.58
0.0005
0.1925
0.1783
2.0733
-----------------------------------------------------------------------------chinflation |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------outputratio |
42.87295
11.63237
3.69
0.001
19.57953
66.16636
_cons | -42.91497
11.62433
-3.69
0.000
-66.19229
-19.63764
------------------------------------------------------------------------------
Appendix: A graphical analysis of the Wage Curve and the Price Curve.
Add inflation to both sides of the wage curve.
∆𝑊
− 𝜋 = (𝜋 𝑒 − 𝜋) + (𝑍 − 𝛼𝑢)
𝑊
Then you can draw this:
∆𝑊
−𝜋
𝑊
[𝜋 𝑒 − 𝜋 + 𝑍]

Wage Curve
u
Change the price curve 𝜋 =
∆𝑊
𝑊
+
∆(1+𝑚)
(1+𝑚)
−
∆𝐴
𝐴
so that it has real wage growth on the left hand side:
∆𝑊
∆𝐴 ∆(1 + 𝑚)
−𝜋 =
−
𝑊
𝐴
(1 + 𝑚)
Then you can draw this:
∆𝑊
−𝜋
𝑊
∆𝐴 ∆(1 + 𝑚)
−
𝐴
(1 + 𝑚)
Price Curve
u
Equilibrium is determined by the point where the two curves intersect, or by the solution to the system
of equations formed by the Wage Curve and the Price Curve.
∆𝑊
−𝜋
𝑊
[𝜋 𝑒 − 𝜋 + 𝑍]
∆𝐴 ∆(1 + 𝑚)
−
𝐴
(1 + 𝑚)

Price Curve
Wage Curve
u
To find equilibrium unemployment, we need to combine the Wage Curve with the Price Curve, and
solve.
(𝜋 𝑒 − 𝜋) + (𝑍 − 𝛼𝑢) = (
𝑢=


∆𝐴 ∆(1 + 𝑚)
−
)
𝐴
(1 + 𝑚)
1
∆𝐴 ∆(1 + 𝑚)
)]
[𝑍 − (𝜋 − 𝜋 𝑒 ) − ( −
𝛼
𝐴
(1 + 𝑚)
If actual inflation exceeds expected inflation (𝜋 > 𝜋 𝑒 ), that is, if workers expect inflation to be
lower than it actually is, workers’ requests for raises will be relatively moderate compared to increases in prices. Firms will be able to afford the raises and even to expand payroll. So unemployment falls.
o If expected inflation exceeds actual inflation (𝜋 < 𝜋 𝑒 ), workers will demand faster raises but firms won’t be able to afford them. Layoffs will moderate wage demands: unemployment rises.
If unemployment benefits, Z, rise, workers will be less scared of unemployment: unemployment
rises.
o For example, a union negotiates both the wage for its members and the amount of
workers that are hired; or knows that by asking for high wages for members, it will lead
to more unemployment among non-members, who will now be mad at the union. If
unemployment benefits rise, the pain for unemployed members or non-members is not
too great, and the union will be emboldened to ask for more.
∆𝑊
−𝜋
𝑊
[𝜋 𝑒 − 𝜋 + 𝑍′]
[𝜋 𝑒 − 𝜋 + 𝑍]
Price Curve
∆𝐴 ∆(1 + 𝑚)
−
𝐴
(1 + 𝑚)
Wage Curve
u
o
If workers become more sensitive to unemployment (higher ), the Wage Curve will become steeper. Because they are more sensitive, they will be willing to take the same
W/P with lower unemployment, so u falls.
∆𝑊
−𝜋
𝑊
[𝜋 𝑒 − 𝜋 + 𝑍]
∆𝐴 ∆(1 + 𝑚)
−
𝐴
(1 + 𝑚)

Price Curve
Wage Curve
u

If markups increase or if Non-Labor Cost inflation speeds up, unemployment rises
o Higher costs or monopoly power leads to higher Prices. If (𝜋 − 𝜋 𝑒 ) doesn’t change
(that is, if workers change their expectations to match the change in P), then the real
∆𝑊
𝑊
expected wage (
ployment must rise.
− 𝜋 𝑒 ) has to fall. To get workers to accept a real wage cut, unem-
∆𝑊
−𝜋
𝑊
[𝜋 𝑒 − 𝜋 + 𝑍]
∆𝐴 ∆(1 + 𝑚)
−
𝐴
(1 + 𝑚)
Price Curve
∆𝐴 ∆(1 + 𝑚)
−
𝐴
(1 + 𝑚)
Wage Curve
u
o
If productivity rises, unit costs will be lower, leading to lower prices and unemployment.
This is a shift up of the Price Curve and leads to a decrease in equilibrium unemployment.
Appendix: Deriving the Price Curve from monopolistic-competitor behavior
The marginal cost of labor depends on two things: The cost of a unit of labor services (e.g., the hourly
wage rate), and the productivity of labor (e.g., the number of hours it takes to produce a unit). Labor
productivity in turn depends on factors such as technology as well as the availability of capital, natural
resources, the human capital (skills, education) of workers, and other factors.
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 =
$
$
𝑤𝑜𝑟𝑘𝑒𝑟 − ℎ𝑜𝑢𝑟𝑠
=
𝑢𝑛𝑖𝑡 𝑤𝑜𝑟𝑘𝑒𝑟 − ℎ𝑜𝑢𝑟
𝑢𝑛𝑖𝑡
1
𝑊
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 = (𝑤𝑎𝑔𝑒) (
)=
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦
𝐴
$
A profit-maximizing firm will set marginal revenue equal to marginal cost, 𝑀𝑅 = 𝑢𝑛𝑖𝑡 = 𝑀𝐶. But because most firms are not perfect competitors, price typically exceeds marginal revenue and therefore
marginal cost: 𝑃 > 𝑀𝑅 = 𝑀𝐶. We can think of the gap between MC and P as representing the economic-profit-per-unit, and call that (1 + 𝑚), the markup of prices over costs.
𝑃 = (1 + 𝑚)𝑀𝐶
What determines m? The monopolistic (market) power of firms, which yields economic profits for entrepreneurs. Whether markups are pro- or counter-cyclical is a controversial point, see
http://findarticles.com/p/articles/mi_m0PAO/is_/ai_n6152614)
If we decide that MC will only represent labor costs, then 𝑀𝐶 =
𝑊
,
𝐴
then (1 + 𝑚) also includes non-
labor costs. Non-labor costs depend on the price of energy (e.g., oil), the availability and cost of loans,
𝑊
business taxes, etc. 𝑃 = (1 + 𝑚) 𝐴 .