We build a simple theoretical model featuring financial markets and imperfect information: consumers, workers, and firms observe and learn continuously about the world they live in. We find that not only financial shock but also what people thought of it mattered for the economy.

1. Learning Financial Shocks and the Great Recession
Patrick A. Pintus Jacek Suda
Banque de France Narodowy Bank Polski
Financial Crisis and RE
• 2007-08 US financial crisis reinforced interest in
relaxing rational expectations assumption.
• Who had a decent approximation of crisis
probability at the end of the “Great Moderation”?
• Assumption that agents know probability
distributions rather strong!
Leverage ratio
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
US Household Leverage Ratio 1980Q1-2010Q3
0.4
0.5
0.6
1980Q1
1984Q1
1988Q1
1992Q1
1996Q1
2000Q1
2004Q1
2008Q1
• 1996-2006 decade witnessed huge rise in housing
prices index.
• By the end of 2008 household leverage ratio rose
from about 0.64 to about 1.26!
• This is in stark contrasts with flat leverage during
1980-1995 period.
What we do
• Allow agents’ perception about the structure of
the economy to evolve over time.
• Study how financial shocks affect the
macroeconomy when perceptions updated in
real time.
Adaptive learning
Consider linearized expectational system:
Xt = AXt−1 + BE∗
t−1[Xt] + CE∗
t [Xt+1] + N + Dξt,
• Under REE, E∗
t = Et,
Xt = Mre
Xt−1 + Hre
+ Gre
ξt,
where Mre
solves
Mre
= [I8 − CMre
]−1
[A + BMre
].
• Under learning, agents are econometricians:
• Agents’ perception of the equilibrium law of motion (PLM)
Xt = MXt−1 + H + Gξt,
• has the same VAR(1) structure as RE equilibrium, but
• admits M = Mre
, H = Hre
, G = Gre
.
• Agents use PLM to form expectations
EτXτ+1 = Mτ−1Xτ + Hτ−1
• Actual low of motion (ALM)
[I8 − CMt−1]Xt = [A + BMt−2]Xt−1 + CHt−1 + BHt−2 + N + Dξt.
• Agents update their “beliefs” by estimating a VAR(1).
• Assume recursive updating of the perceived law of motion
Mt = Mt−1 + νtR−1
t Xt−1(Xt − Mt−1Xt−1)
Rt = Rt−1 + νt(Xt−1Xt−1 − Rt−1)
• OLS/RLS if νt = 1/t,
• constant gain if νt = ν.
• REE: PLM and ALM coincide.
How we do it
• Use RBC model with collateral constraint:
• variant of Kiyotaki and Moore (1997).
• Replace rational expectations (RE) with
adaptive learning.
• Calibrate the model using US data from
1996Q1-2008Q4 period.
• Focus on financial shocks driving leverage:
• a large temporary negative shock to leverage in 2008Q4,
Representative agent
max E∗
0
∞
t=0
βt
Ct − ψN1+χ
t
1+χ
1−σ
− 1
1 − σ
,
• E∗
t denotes expectations at time t.
• Budget constraint:
Ct+Kt+1−(1−δ)Kt+TtQt(Lt+1−Lt)+(1+R)Bt = Bt+1+AKα
t Lγ
t N1−α−γ
t
• exogenous interest rate (SOE)
Borrowing constraint and leverage
Agents face borrowing constraint
˜ΘtE∗
t [Qt+1]Lt+1 ≥ (1 + R)Bt+1,
where
˜Θt ≡ Θt



E∗
t [Qt+1]
Q



ε
.
• leverage can respond to changes in the land price
• ε > 0 agrees with evidence in Mian and Sufi (2011)
• Θt is exogenous and subject to random shocks
log Θt = (1 − ρθ) log Θ + ρθ log Θt−1 + ξt.
Learning process
⇐=linearized expectational system with
Xt ≡ (ct, qt, λt, φt, bt, kt, θt, τt)
• E∗
t = Et: agents “beliefs” given by PLM and
updated with constant gain learning.
• Model is E-stable, i.e. limt→∞ Mt → Mre
.
• Expectations may differ from RE.
Experiment
• Assume that, in the decade preceding 2008Q4,
agents have learned the economy and
• the associated matrix in PLM is M2008Q4,
• agents’ beliefs about ρθ is reflected in matrix M2008Q4.
• Key equation: AR(1) process for leverage:
• RE corresponds to OLS estimates for 1975-2010 for ρθ,
ρθ = 0.976, ¯Θ = 0.88.
• Agents’ initial beliefs given by 2008Q4 CG estimates,
ρCG
θ = 0.9904 for νt = 0.004.
2000 2005 2010
0.970
0.975
0.980
0.985
0.990
CG and OLS estimates of persistence of leverage
What we find
• Agents gradually learn the economy.
• Learning amplifies effects of leverage shocks by
a factor of 2.5–3 (relative to RE).
• Magnitude of the recession also depends on the
level of leverage.
• Macro-prudential policies enforcing counter-
cyclical leverage have stabilizing effect.
Impulse response functions
10 20 30 40 50 60
Time
3.0
2.5
2.0
1.5
1.0
0.5
Output
• A −5% leverage shock, observed in 2008Q4, causes:
• fall in output by 3.3%, in consumption by 3.6%, and in
capital stock by about 5%,
• severe deleveraging (3× larger under learning).
• Response of economy leads to overshooting.
• Effect of leverage shocks larger in economies that
are more levered.
• Key: land price variations in borrowing constraint.
• Countercyclical leverage dampens responses to
financial shocks.
Great Recession
• Learning model predicts Great Recession and a
significant boom prior to that.
• Magnitude of recession almost matches data
(4.7% between 2007Q3 and 2010Q1)
Procedure
• Feed RE and learning models with
• calibrated iid land price shocks to match observed prices,
• estimated innovations/shocks to leverage.
2000 2002 2004 2006 2008 2010
80
60
40
20
0
Land Price Deviations From 2007Q4
2000 2002 2004 2006 2008 2010
0.05
0.00
0.05
Innovations OLS and CG
• Let agents update their beliefs, Ht and Mt
• H0 = HRE
and M0 = MRE
2000 2002 2004 2006 2008 2010
4
2
0
2
4
Output Response Over Time Deviations From 2007Q4