1. The output market Short and medium run equilibria
Output Gap detection: all the different approaches Luxembourg, 8-10 June 2016
CONTRACTOR IS ACTING UNDER A FRAMEWORK CONTRACT CONCLUDED WITH THE EUROPEAN COMMISSION

2. Outline Determination of Output in the short-run and medium-run
Requires equilibrium in the good, financial and labor markets
Aggregate supply focuses on equilibrium in the labor market
Aggregate demand focuses on equilibrium in the goods and financial markets
We abstract from financial markets
Determination of Output dynamics, from short-run to medium-run equilibria

3. Aggregate Supply Captures the effects of output on the price level
It is derived from equilibrium in the labor market.
The labor market equilibrium is the pair (Y,W/P) such that, given price expectations 𝑃 𝑒 ,
Substituting, the (inverse) aggregate supply function is, AS

4. Pe  W= Pe F(.)   P =(1+µ)W 
Aggregate Supply
The AS determines the output price P, set optimally by firms that decide to supply Y units of output, at given price expectations Pe in a certain economy (z,µ(.),F(.),…)
Higher Pe  higher P
Pe  W= Pe F(.)   P =(1+µ)W 
Higher output  higher P
This captures the fact that higher Y (u) implies higher W = Pe F(Y/L,.)

5. AS graphical representation
By definition of natural rate, 𝑃= 𝑃 𝑒 ⟹𝑌= 𝑌 𝑛 AS
Output, Y
Price Level, P
P > Pe
Given Pe an increase in Y
increases P ⇒𝑷> 𝑷 𝒆 .
The reverse is also true.
Forecast errors
are associated to changes of
real output:
Y > Yn ⟺ P > Pe
Y < Yn ⟺ P < Pe A Pe
P < Pe Yn

6. A story of why forcast errors have real effects 𝑃> 𝑃 𝑒 ⟹𝑌> 𝑌 𝑛
Suppose the economy starts at (𝑌 𝑛 , 𝑃 𝑒 )
Workers are imperfectly informed about output prices and set wages 𝑊 using forecasted price 𝑃 𝑒 = 𝑃 −1
Suppose they make a forecast error, 𝑃>𝑃 𝑒 = 𝑃 −1 , which they do not realize until next period. Then, they will perceive any increase in the nominal wage 𝑊− 𝑊 as an increase in the real wage rate (even if this does not exceed the increase of 𝑃 over 𝑃 −1 )
Hence, workers will increase their supply of labor.
Firms, who exactly observe 𝑃, will hire workers at any real wage rate
𝑊 𝑃 ≤ 𝑊 𝑃 −1
and increase Y above its natural level 𝑌 𝑛 .

7. AS when Pe changes Price Level, P Output, Y AS´ (Pe´ > Pe) AS (Pe)Yn Pe A
AS (Pe)
Observation:
Given Yn: changes in Pe
shift the AS curve A´
Pe´
Hint: If an increase in 𝑷 𝒆 is perfectly forecasted and matched by an increase of wages,
constant 𝑾/ 𝑷 𝒆 , no change in labor supply (u)
constant 𝑾/𝑷 no change in labor cost and labor demand
𝑌= 𝑌 𝑛

8. Aggregate demand 𝑌=𝐴𝐷 𝑃,.
Output, Y
Price. P AD Y P A
Initial
Equilibrium A´ P’ Y´

9. Aggregate demand determinants
What does affect the AD, beside P? 𝑨𝑫≡𝑪+𝑰+𝑮
𝑪=𝑪 𝒀,𝑻,𝒊− 𝝅 𝒆 , 𝑰=𝑰 𝒀,𝑻,𝒊− 𝝅 𝒆 , 𝝅 𝒆 ≡ 𝑷 𝒆 𝑷 −𝟏
↑𝑌, as output increases, ↑𝐶 (Keynesian multiplier) ↑𝐼 is also possible (firms confidence and market opportunities are pro-cyclical)
↑(𝑖− 𝜋 𝑒 ) depresses the demand for (durable) consumption and capital investments. A restrictive monetary policy ↓𝑀 (given P), increases interest rates, reduces the AD.
↑𝐺 (given taxes T) has a positive direct effect on the AD and possibly negative effects on the interest rate (crowding out).
↑𝑇 (given G) has negative effects on purchases (income or sale taxes)

10. Equilibrium Output Short and Medium Run
Short Run equil.: 𝑃 𝑒 might be different from 𝑃 and output 𝑌 can be above or below 𝑌 𝑛
Medium Run equil.: 𝑃 𝑒 =𝑃 & 𝑌= 𝑌 𝑛
AD : 𝑌=𝐴𝐷 ( 𝑃 − , 𝑀 + , 𝐺 + , 𝑇 − )
In the AD, we have implicitelly assumed that the central bank controls the interest rate through money supply.

11. Equilibrium Output Short and Medium RunAS AD
Observation:
A is a short – run equil.
B is a medium – run equil.
Price Level, P A P Y
Short- run Equilibrium Pe Yn B
Output, Y

12. Equilibrium Output dynamics
Suppose that 𝑃 𝑒 ≠𝑃 & 𝑌≠ 𝑌 𝑛 , will the economy automatically move to the medium run equilibrium over time [i.e. is the medium – run equil. stable] ?
Let,
𝑃 𝑡 𝑒 ≡ 𝐸 𝑡 𝑃 𝑡+1
denote the expectation of 𝑃 𝑡+1 computed with the information available at t.
Assume that, at all 𝑡, 𝐸 𝑡 𝑃 𝑡+1 = 𝑃 𝑡 (i.e. P has martingale property)

13. Price-income dynamics: from the short to the medium run equilibrium
Pte = Pt-1
µ,z,G,M,T (and ρ) are assumed to be given & constant

14. Dynamics graphically Price Level, P Output, Y AS´ (t+1) AS(t) AD(t) Yt
Pet+1 = Pt A Yn
s.r. equilibrium Year t
At A:
Yt > Yn & Pt > Pet = Pt-1
Pet = Pt-1 B A´
In t+1, AS shifts to AS´ as Pe adjust upwards
Pt+1 B´
s.r. equilibrium Year t + 1
At A’:
Yt+1 > Yn & Pt+1 > Pet+1 = Pt
Yt+1

15. Dynamics graphically (cont.)
AS´
AS´´
Dynamics after t + 1
As output continues to fall to 𝒀 𝒏
At period T>t+1, point A’’ is riched:
𝒀 𝑻 , 𝑷 𝑻 = 𝒀 𝒏 , 𝑷 𝒏 , 𝑷 𝒏 =𝑷 𝑻 𝒆
Aggregate supply
continues to shift to AS´´
As price level continues
to increase, 𝑷 𝒕+𝟏+𝒔 > 𝑷 𝒕+𝟏+𝒔 𝒆 AS
Output, Y
Price Level, P AD Yt Pt A Yn Pn
A´´ A´
Pt+1
Yt+1
Medium run equilibrium

16. Observations
The above analysis can be repeated assuming that expectation form differently (different information set). What matters is to consider the effect of forecast errors.
Forecast errors are temporary, characterize short run equilibria and produce adjustment dynamics.
Adjustment dynamics involve real effects: changes in output, consumption, etc.

17. The Effects of a Monetary Expansion
AS´´ 𝑷 𝒕+𝟏 𝒆 = 𝑷 𝒏 ′
A´´
Pn´
AD´ AD
AS 𝑷 𝒕 𝒆 = 𝑷 𝒕−𝟏
Output, Y
Price Level, P Yn Pn A
M: Yt = Y( , G, T)
AD shifts to AD´
A´ equilibrium (Yt > Yn & 𝑷 𝒕 𝒆 < 𝑷 𝒕 )
AS shifts to AS´´ Pt A´ Yt
Equilibrium Yn at P’n
10% increase in M
leads to 10%
increase in P

18. The effects of a monetary expansion
Summing up:
Short-run: M  Y & P  The relative change in P and Y depends on the slope of AS (e.g. if P are fixed in the short run, the AS is horizontal and Y is the only one to adjust)
Medium run: Prices continue to increase until P and Y return to their original level, i.e., money is “neutral”; i.e. it does not affect real variables (Y,C,I,..,M/P), only the price level

19. How long lasting is the “short run”, when it comes for a monetary expansion?
Quarters
Effects on output
Anticipated
Unanticipated
Mishkin Model

20. A negative productivity shock in the labor market
Real Wage, W/P WS
𝑷𝑺(𝝆) un
Unemployment Rate, u A
Assume a negative, persistent, productivity shock
𝝆 ′ <𝝆
un´ A´
𝑷𝑺(𝝆′)

21. A negative productivity shock in the output market
AS´´ AS
Output, Y
Price Level, P AD A
Pt-1 Yn
AS´ B
Y´n
When oil prices increase:
Pt+n
A´´
ρ decreases A´ P´ Y´
Yn decreases to Yn´
AS shifts up (ρ effect)
From B, P adjusts to compensate AD>AS ( 𝑃 𝒆 given). A s.r. equil is in A’
A’ to A’’ medium-run
adjustment ( 𝑃 𝒆 )

22. AD through IS-LM 𝑌=𝐴𝐷 ( 𝑃 − , 𝑀 + , 𝐺 + , 𝑇 − ) Good market 𝑌=𝐴𝐷≡𝐶+𝐼+𝐺
𝐶=𝐶 𝑌,𝑇,𝑖− 𝜋 𝑒 𝐼=𝐼 𝑌,𝑇,𝑖− 𝜋 𝑒
𝜋 𝑒 ≡ 𝑃 𝑒 𝑃 −1 −1
The IS representation
𝑌=Ψ 𝐺,𝑇,𝑖− 𝜋 𝑒
Monetary market (LM)
𝑖=Φ( 𝑀/𝑃 − , 𝑌 + )
IS-LM-AD
𝑌=𝐴𝐷 ( 𝑃 − , 𝑀 + , 𝐺 + , 𝑇 − )

23. Summary
Short-run equilibrium (at given 𝑃 𝑒 ). Price expectations may be wrong and this causes real effects, 𝑃≥ 𝑃 𝑒 ⟹𝑌≥ 𝑌 𝑛 , resulting in an output-gap.
Forcast errors may be determined by demand or supply shocks (e.g. unforseen changes in fiscal or monetary policy, productivity shocks).
Medium-run equilibrium, by definition, entails no forcast errors and 𝑌= 𝑌 𝑛 .
The dynamic effects from short- to medium-run (propagation mechanisms) vary in accordance to the shock
Permanent monetary shocks have temporary effects
Permanent productivity shocks have permanent effects. «Real Business Cycle» literature uses temporary productivity shocks to replicate business-cycles – lasting btw. 2 quarters and 8 years (NBER).