Chapter 17. Inflation, unemployment and aggregate

supply

ECON320Prof Mike Kennedy

Inflation and unemployment is a major macroeconomic concern:

A look at the Canadian experience

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1Recession CanadaUnemployment rateInflation rate

The Phillips curve• In the late 1950s and early 1960s, most economists believed that

there was a stable relationship between the rate of inflation and the unemployment rate, called the Phillips curve

• If policy makers chose a particular rate of unemployment they would have to accept the inflation rate given by the curve – there was a trade-off between one and the other (see next slide for Canada)

• While the curve appeared to be stable for a number of decades, it proved to be anything but when policy makers tried to exploit it

• In this chapter, explanations of why it was both stable and then later shifted will be examined

• The relationship explaining this will be the expectations-augmented Phillips curve

The Phillips curve for Canada when it appeared to be stable

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f(x) = − 0.673950772119679 x + 6.09839700434516R² = 0.481692725190331

Inflation

Unemployment

The stable Phillips curve disappears

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1971 startof breakdown(blue square)

1973 1st oil price shock

1974-75 recession startsProductivityslowdown

1979 2nd oil price shock

1981-82 recession starts

Crow becomes GovBoC 1987 to 1994

1990-92 recession starts

1992 Inflation target introduced

Thiessen becomes Gov BoC 1994 to 2001

19982008-09Recession starts (black diamond)

2013

Inflation

Unemployment rate

The expectations-augmented Phillips curve• We will first show how the curve works and then go on to discuss

the underlying micro foundations• Labour demand is sector i is given by where

• Assume that there is a union for each sector (i) in the economy which has the power to set the nominal wage rate (Wi)

where the term mw > 1 is the mark-up over the opportunity cost

of working (b) which is equal to unemployment benefits• Note that the union in setting the wage rate must form an

expectation of the price level that will prevail over the life of the contract – this will be key

€

Wi = P e ⋅m wb

The expectations-augmented Phillips curve con’t

• We can substitute into the labour demand equation, the union’s wage setting relationship

• At the aggregate level of the economy production is given by

• Substituting this into the expression for labour in sector (i) and putting Li on the left hand side we get

and for the aggregate amount of labour

€

Y = nYi = nBLi1−α

€

Liαε =

B(1−α )

m pmWb

P

P e

⎛

⎝ ⎜

⎞

⎠ ⎟ε

The expectations-augmented Phillips curve con’t• The previous equation (reproduced here) can be thought of as the

short-run demand for labour and at the aggregate level it is

• In the long run actual and expected prices are equal and long-run employment is given by

• If we divide the long-run equation into the short run relationship we get something very simple

The expectations-augmented Phillips curve con’t

• Actual and potential employment are given by, respectively,

• Putting these into the above equation and taking natural logs, where we have assumed that N = n we get

• Finally we assume (quite correctly) that everybody knows the price level in the previous period P-1

• Subtracting the log of P-1 from both sides of the above we get

• This is the expectations augmented Phillips curve• It can be used to explain both why the curve was stable for so

long and why it shifted from the 1970s onward (see slide 18)

€

L = (1−u)N and L = (1−u )N

How did we get the underlying relationships:The plan of attack

• Inflation is a continuous rise in the price level• In the short run, wages are the most important factor

determining prices so we start there• We will assume that there is imperfect competition

in the goods market (monopolistic competition among firms) and the labour market (a union in each sector which sets the nominal wage)

• Employers determine how many people to employ• We will also assume (realistically) that people do not

have perfect information about the current price level

The origins of nominal rigidities

• Assume a large number of firms, each of which has a monopoly in its local market – monopolistic competition.

• Workers have skills that apply to a specific firm where they are employed.

• If they lose their job they cannot transfer to another firm and so are unemployed, in which case they earn b, real benefits.

• When employed, they earn wi = Wi/P real wages.

• The worker’s net income would be (wi  – b). • At the same time there is a union for sector i which cares about

both the net income of the employee plus employment. • The parameter η > 0 reflects the weight the union attaches to

employment in its sector (Li).

Price setting• In the short run we assume that K does not change so it can be

ignore and the production function is given by

• The demand for the firm’s output Yi is:

where σ > 1 is the price

elasticity of demand

• Since the firm’s total revenue equals TRi = PiYi marginal revenue is

• The marginal cost of producing one unit of output (MCi) is the wage rate paid divided by the MPLi.

€

MCi =Wi

MPLi

=Wi

(1−α )BLi−α

Price setting con’t• We get a price-setting equation by MRi = MCi and solving for Pi

and is the

mark-up of prices over marginal costs• To derive a demand for labour equation, we re-write the demand for

Yi in terms of Pi

• Now use the production function to eliminate Yi

• For convenience we have separated out Li

Price setting con’t

• Next set the first and last equation on the previous slide equal to each other so as to eliminate Pi

• Note that we have isolated the real wage (Wi/P)

• Dividing each side by we get:

• Inverting this equation and solving for Li yields the demand for labour

where

and -ε is the elasticity of labour demand wrt the real wage

€

Liα

Wage setting• The union’s utility curve is:

• Maximizing wrt wi (the real wage in sector i) yields

• Which becomes

• Solving for wages and noting that the term in large brackets is the elasticity of labour demand wrt wages (ε) we get

• The real wage that the union sets is a mark-up over the opportunity cost of not working (the outside option)

• Note we are assuming for the moment that the union knows the price level€

wi = m w ⋅b m w =ηε

ηε −1

Wage setting con’t• The mark-up factor is greater than one, provided that σ > 1,

which it is by assumption• We also assume that ηε > 1• We have already shown how using both wage setting and the

price setting equations we can arrive at the expectations-augmented Phillips curve

The acceleration view and the natural rate of unemployment

• Look again at the expectations-augmented Phillips curve

• Now let’s suppose that expected inflation equals last period’s inflation rate

• Putting this into the above we get

• The implication from this equation is that when the unemployment rate is below the natural rate inflation will accelerate (actually it is the price level that accelerates!)

• To keep inflation constant policy should be aimed at keeping the unemployment rate equal to the natural rate.

• Such an unemployment rate is often labelled the Non-Accelerating Inflation Rate of Unemployment (NAIRU)

€

π e = π −1

€

π =π−1 +α (u −u) → Δπ = α (u −u)€

π =π e +α (u −u)

The expectations augmented Phillips curve will shift with changes in expected inflation, the long run curve is

vertical

A structural definition of the natural rate

• Recall the equation in slide 8 for long-run employment (when the actual price level was equal to the expected)

• Now define• Then from the above we have

• Finally assume that unemployment benefits grow with productivity where c < 1 which yields

€

L = nB(1−α )

m pmWb

⎛

⎝ ⎜

⎞

⎠ ⎟

1/α

€

b = cB

€

u =1−(1−α )

m pmWc

⎛

⎝ ⎜

⎞

⎠ ⎟

1/α

€

L = (1−u )N = (1−u )n

A structural definition of the natural rate con’t• From our definition of the natural rate as

• We can see that it will be higher, the larger are the mark-ups for both firms and unions

• Note as well the an increase in c, the amount by which benefits are raised when growth improves, will also raises the natural rate

• Policies aimed at raising the degree of competition in the economy will lower the natural rate by raising σ, the demand elasticity wrt prices

• If the power of unions to set wages were to decline then so would the natural rate

• Note that a greater union concern about employment (an increase in η) will also lower the natural rate by lowering the wage mark up

€

u =1−(1−α )

m pmWc

⎛

⎝ ⎜

⎞

⎠ ⎟

1/α

Would improving competition raise growth?

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f(x) = − 2.78657661353589 ln(x) + 2.74802218871749R² = 0.370573888544874

The case for product market reform(a very simple result)

PMR 2003

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ntial

gro

wth

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4-15

Is pursuing labour market reform worth the effort?

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f(x) = − 1.00691718313878 ln(x) + 3.3952635667638R² = 0.318209332728991

Strutural unemployment rate (2014-15)

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Sticky prices• So far we have assumed that prices of goods adjust instantly

while wages are slow to adjust• There is lots of evidence that firms in certain sectors adjust

prices infrequently – possibly due to “menu costs”• The model above can be modified to take account of this

feature of the economy (see Chap 17 pp 489 to 491)• When this is done the Phillips curve becomes where ϖ is the fraction of firms that adjust their prices

infrequently• Of note is that is that the basic equation has not changed but

the slope of the curve has – it is now smaller€

π =π e +α (1−ω )(u −u)

Supply shocks• The Phillips curve can also be affected by supply shocks that take the

form of short-run changes in the mark-ups (mp and mW) and to productivity (B)

• To see how this works we first note that unemployment benefits (b) do not tend to move with short-run short-run changes in B but rather with its trend, implying

• Substituting this into the equation for the actual level of employment (slide 8, first equation) we get

• Next we develop an equation for long-run employment, using the equation from slide 8, and remembering that

€

b = cB

€

L = nB(1−α )

m pmWcB

P

Pe

⎛

⎝ ⎜

⎞

⎠ ⎟

1/α

€

L = n(1−α )

m pm Wc

⎛

⎝ ⎜

⎞

⎠ ⎟

1/α

€

b = cB

Supply shocks con’t• As before we can divide the long-run employment equation into

the short-run version and get

• Remembering that and• This becomes

where represents supply shocks

• The next 7 slides show the importance of taking into account supply shocks

€

π =π e +α (u −u) + ˜ s

€

˜ s = lnm p

m p ⎛

⎝ ⎜

⎞

⎠ ⎟+ ln

mW

m W ⎛

⎝ ⎜

⎞

⎠ ⎟− ln

B

B

⎛

⎝ ⎜

⎞

⎠ ⎟

In Canada the Phillips appears to have shifted inward

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Unemployment

Infla

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The Phillips curve for Canada(A simple accelerationist model assuming no

change in the natural unemployment rate)

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The implied natural rate over the period is 1.6/0.21

= 7.62

f(x) = − 0.329726411466526 x + 2.62743709149666R² = 0.179585371910048

π-πe

U

We do know that the natural rate or NAIRU has changed – it seems to have fallen

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NAIRUUnemployment rate

The Phillips curve for Canada (Taking account of a changing

natural rate of unemployment)

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f(x) = − 0.484012276686362 x − 0.0881413149065197R² = 0.147165233508031

π-πe

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The importance of supply shocks in explaining inflation

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10Dynamic simulation

Actual inflation (π)

π forecast assuming constant NAIRU

π forecast assuming changing NAIRU

Each equation is estimated up to 2002 and then dynamically simulated up to 2013

What could have caused the NAIRU to shift down?Possibly a decline in unionisation…

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NAIRU

Unemployment rate

Unionisation rate

… or an improvement in competition

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Product Market Regulation index for Canada

Source OECD: A decrease in the measure implies a reduction in regulations which negatively affect competition

The aggregate supply curve• The theory of inflation and unemployment implies a systematic

relationship between inflation and the output gap• Our strategy is to find short-run and long-run equations for each

unemployment rate and substitute them into the expectations augmented Phillips curve

• We start from the production function (a supply concept) for GDP

• In logs this becomes

which takes care of actual u

The aggregate supply curve con’t

• Next we find the “natural” or long-run equilibrium level of the supply of output, where long-run values are denoted by “bars”

• Using a similar procedure as in the previous slide we get

• The expectations augmented Phillips curve is reproduced here from slide 25

• Next, use the production relationships and compute€

u = ln N +ln nα + ln B − y

1−α

€

u −u =y − y

1−α−

ln(B / B )

1−α€

π =π e +α (u −u) + ˜ s

The aggregate supply curve con’t• We can substitute the equation we have for cyclical unemployment (the

difference between actual and long-run or structural unemployment) into the expectations augmented Phillips curve to get

• This is the short-run aggregate supply curve (SRAS) where

• An increase in the output gap will raise inflation in the short run because:– The increase requires an increase in employment– Because of diminishing marginal product, marginal costs rise– This ends up in higher prices due to the mark up (mp)– Inflation is also affected by supply shocks (s)

• The figure (next slide) shows that the position of the SRAS depends of πe

€

π =π e +γ(y − y ) + s

The SRAS curve slopes upward and shifts with πe and supply shocks, the LRAS curve is vertical