Discussion of “A Gains from Trade Perspective onMacroeconomic Fluctuations” by Paul Beaudry and
Franck Portier
Cosmin Ilut
Duke Univ.
International Conference on “Macroeconomic Modeling in Times ofCrisis”, Paris, 2012
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 1 / 20
Paper
Motivation:
1 Data: business cycles feature comovement and stable inflation.2 Model: depart from the stringent representative agent model.
Heterogenous agent model: main ingredients
1 some market incompleteness.2 some labor market specialization.
Main findings:
1 Model: offers a constructive way to show comovement2 Policy: revised implications for fiscal and monetary policy3 Data: ’perception’ driven cycles with stable inflation
My discussion:
1 Mechanism to get comovement.2 Nominal rigidities as an alternative.
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 2 / 20
General model
Two sectors: investment and consumption goods
Two types of agents:
I decide how much to consume C i , buy K i , work Li
Production function for sectors:
I if only one type of labor used to produce a good → specialized labormkt.
Preferences:
I per period felicity: U i (C i , 1− Li ); both normal goodsI continuation value: V i (K i ,Ω) ≡ E [βV i (K i ,S)|Ω1,Ω]I Ω1 : information used to predict exogenous state
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 3 / 20
Competitive equilibrium
Each individual i :
maxC i ,K i ,Li
U i (C i , 1− Li ) + V i (K i ,Ω)
s. t. C i + PK i = w iLi
I P relative price of capital; consumption good is numeraire; w i wage
Here assume fully specialized labor mkts: C = F (L1);K = F (L2):
maxL1
F (L1)− w1L1; maxL2
PF (L2)− w1L2
Optimality conditions: Intra Euler
U i2(C i , 1− Li ) = piF1(Li )U i
1(C i , 1− Li )
pi =
1, for i = 1P, for i = 2
and Inter Euler:V i1(K i ,Ω) = PU i
1(C i , 1− Li )
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 4 / 20
Mechanism: Intertemporal optimality
Define the change in Ω1 : such that
∂2V i (K i ,Ω)
∂K i∂Ω1> 0
UsingV i1(K i ,Ω) = PU i
1(C i , 1− Li )
then since demand for capital goes up, under general conditions priceof capital goes up.
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 5 / 20
Mechanism: Intratemporal optimality
Take agent 2:
U2(C , 1− L) = PF1(L)U1(C , 1− L)
an increase in P, acts like a production possibility frontier shifter(TFP shock)
Gains from trade: increase in the relative price for capital.
it makes possible an increase in both L2 and C 2.
This is in contrast to the standard Barro-King logic: C and L cannotcomove unless a technology shock.
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 6 / 20
Mechanism: Intratemporal optimality
−0.2 0 0.2 0.4 0.6 0.8 1 1.2−0.2
0
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LS (λt)LD (Z
t; P
t)
Labor
Wage
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 7 / 20
Shift in labor supply: Barro-King logic
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LS (λt)LD (Z
t; P
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LS (λt′ ↓ )
Labor
Wage
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 8 / 20
Shift in labor supply and demand (price ↑)
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0
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LS (λt)LD (Z
t; P
t)
LS (λt′ ↓ )
LD (Zt; P′ ↑ )
Labor
Wage
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 9 / 20
Mechanism: Intratemporal optimality
Agent 1:U2(C , 1− L) = F1(L)U1(C , 1− L)
no change in the price, so here standard Barro-King logic applies
What direction of change?
Negative wealth effect: from increase in relative price of capital−→ L1 increases and C 1 falls
I at most C 1 stays constant.
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 10 / 20
Overall: recall Proposition 1
1 Aggregate positive comovement is possible:
L2 ↑, Investment ↑, L1 ↑, ( C 1 + C 2) ↑
2 Individual positive comovement is not possible:
C 1, L1 and C 2, L2 cannot move all up.
Next, discuss the two main mechanisms:
1 increased demand for capital
2 comovement between C 2 and L2.
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 11 / 20
Discussion : 1) increased demand for capital
Intertemporal Euler in the standard dynamic optimization formulation
λt = βEtλt+1Rkt+1
I λt = LM on budget constraint; here:
βEtλt+1Rkt+1 = V i
1(K i ,Ω)
Start from: as Ω1 ↑, then V i1(K i ,Ω) ↑
It is the marginal ‘valuation’ of capital ↑In standard RBC: good news on TFP −→ βEtλt+1R
kt+1 ↓
Need the intertemporal substitution stronger than wealth effect.
Same logic if signals about future means or variances.
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 12 / 20
Discussion : 2) comovement between C and L
Irrespective of effect on U1(C , 1− L), need C and L to comove:
U2(C , 1− L) = PF1(L)U1(C , 1− L)
Change in P: essential; shifts labor demand
Other solutions:
1 internal habit formation: λt = f ( Ct︸︷︷︸−
,EtCt+1︸ ︷︷ ︸+
)
I can have Ct ↑, and still λt ↑, so Lt can ↑2 nominal rigidities: countercyclical markups:
U2(C , 1− L) =1
µF1(L)U1(C , 1− L)
I C ↑, Lsupply ↓, real wage ↑, markup over mg. cost µ ↓, labor demand ↑3 other shocks (eg. demand), act like TFP shocks (eg. Bai et al., 2012)
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 13 / 20
Sticky prices: Shift in supply and demand (markup ↓)
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LS (λt)LD (Z
t; µ
t)
LS (λt′ ↓ )
LD (Zt; µ
t′ ↓ )
Labor
Wage
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 14 / 20
Back to motivation: inflationary ’perception-driven’booms?
BP’s argument: standard New Keynesian model, ’perception’ shockswill be highly inflationary (act like ’demand’ shocks)
In the data: inflation roughly constant in last 3 cycles−→ not a priori plausible
their model, ’perception’ shock not inflationary because affectspotential output
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 15 / 20
Disinflationary ’perception-driven’ booms?
Christiano, Ilut, Motto, Rostagno (2008, 2010): news about TFP in areal and monetary model.
Document that inflation tends to be low during (stock market) booms
Table 3: Variables Over Various Sub-periods, 1919Q1-2010Q1Periods CPI Credit GNP Stock PriceBoom 1.8 5.3 4.6 13.8Other 4.0 2.3 0.2 -11.7
Whole period 2.7 4.0 2.7 2.7Notes: (1) numbers represent 100 tim es average of log rst d i¤erence of ind icated variab le over in -d icated p eriod .(2) Boom periods are the union of the trough to p eak p eriods enumerated in Tablexx.(3) O ther are p eriods that are not b oom s and that exclude World War II (1939Q4-1945Q4).Whole p eriod corresp onds to the fu ll sample, exclud ing World War II.
Table 4: Variables in Stock Market Boom EpisodesA. Non-boom, non-World War II, 1919Q1-2010Q1
CPI Credit GNP Stock Price4.0 2.3 0.2 -11.7
B. Boom episodestrough-peak CPI Credit GNP Stock Price
1921Q3-1929Q3 -0.2 5.7 5.9 19.31932Q2-1937Q2 0.6 -2.1 6.5 24.21949Q2-1968Q2 2.0 6.3 4.2 8.11982Q3-1987Q3 3.2 7.5 4.3 17.51994Q2-2000Q2 2.5 6.1 3.9 16.42003Q1-2007Q1 3.0 4.6 3.0 10.1Notes: (1) numbers represent 100 tim es average of log rst d i¤erence of ind icated variab le over ind i-cated p eriod . (2) panel A : data averaged over p eriod 1919Q1-2010Q1, sk ipp ing 1939Q4-1945Q4 andtrough to p eak years. (3) panel B : data averaged only over the ind icated trough-p eak years. (4) Panicso ccur after sto ck market p eak.
2
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 16 / 20
Disinflationary ’perception-driven’ booms
Monetary model: following positive news about future TFP
I positive comovement: C ,H, I and price of capital all ↑I inflation is low.
Why can inflation be low? Two counter effects
1 Standard, inflationary: because current marginal cost ↑2 Disinflationary: future marginal costs ↓, since expected TFP ↑
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 17 / 20
Disinflationary ’perception-driven’ booms
For the textbook CGG model, analytical results:
I perfect signal st about TFP
at+1 = ρat + ξt+1 + st
Closed form solution for output gap and inflation:
yt = ηyat + φy st ; πt = ηπat + φπst
1 Proposition: ηy , ηπ < 0
2 For wide parameterization: φy > 0, φπ < 0
Inside coefficient φπ : sum of the two counter effects
πt = λyt + βEt πt+1
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 18 / 20
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Figure 6: Response of Baseline and Perturbed Model to Signal Shock (Signal not realized); Perturbation = Ramsey
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Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 19 / 20
Conclusion
Very rich paper.
Heterogeneity is important.
Labor market specialization can deliver many new insights:
1 comovement driven by perception
2 demand vs supply shocks
3 redistribution effects of fiscal policy
Cosmin Ilut (Duke Univ.) Discussion of Beaudry and Portier Oct. 2012 20 / 20