Presentation from ASSA2021 The paper studies the implication of initial beliefs and associated confidence under adaptive learning. We first illustrate how prior beliefs determine learning dynamics and the evolution of endogenous variables in a small DSGE model with credit-constrained agents, in which rational expectations are replaced by constant-gain adaptive learning. We then examine how discretionary experimenting with new macroeconomic policies is affected by expectations that agents have in relation to these policies. More specifically, we show that a newly introduced macro-prudential policy that aims at making leverage counter-cyclical can lead to substantial increase in fluctuations under learning, when the economy is hit by financial shocks, if beliefs reflect imperfect information about the policy experiment.

1. The danger of policy experiments:
initial beliefs under adaptive learning
Patrick A. Pintus Jacek Suda Burak Turgut
CNRS - InSHS and Aix-Marseille University SGH, Warsaw School of Economics and FAME|GRAPE University of Warsaw and CASE
What we do
•Allow agents’ perception about
• the structure of the economy and
• the policy
to evolve over time.
•Examine how financial shocks affect the
macroeconomy when perceptions updated in
real time.
•Study effect of change of / introduction of new
macroeconomic policy under learning
• announced/undestood vs surprised/misunderstood
May you leave in interesting times
•Turbulent times
• Global Financial Crisis, economic crises, Sovereign Debt
crisis,...
• COVID-19
•New policy instruments
• Monetary policy: QE, credit easing, APP, FG,...
+ nominal interest rate at ZLB/ELB
• Macroprudential policy: LtV, debt-service ratio,...
• Fiscal policy: employment programs, subsidies, transfers...
Policy and expectations
•The success of new tools/policies depends on
communication and expectations (Lucas)
•Check how formation of expectation and beliefs
about new policy affects its outcome
• RE versus bounded rationality (adaptive learning)
Model: Pintus and Suda (2019)
Representative agent
max E∗
0
∞
X
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
Θ̃tE∗
t [Qt+1]Lt+1 ≥ (1 + R)Bt+1,
where
Θ̃t ≡ Θt
(
E∗
t [Qt+1]
Q
)ε
.
•Θt is exogenous and subject to random shocks
log Θt = (1 − ρθ) log Θ + ρθ log Θt−1 + ξt.
•Leverage can respond to changes in the land price
— ε 0 agrees with evidence in Mian and Sufi (2011)
System
Linearized expectational system (in log levels):
Xt = AXt−1 + BE∗
t−1[Xt] + CE∗
t [Xt+1] + N + Dξt,
•E∗
t 6= Et =⇒ expectations may differ from RE
How we do it
•Use RBC model with collateral constraint:
• variant of Kiyotaki and Moore (1997) and Pintus and
Suda (2019).
•Replace rational expectations (RE) with
adaptive learning.
•Calibrate the model using US data from
1996Q1-2008Q4 period.
•Consider new macro-prudential policy
• make leverage counter-cyclical
•Focus on initial beliefs regarding the policy
Learning process
•Agents as econometricians:
• Endow agents with a perception of the equilibrium law of
motion (PLM)
Xt = MXt−1 + H + Gξt + Jψt,
• has the same VAR(1) structure as RE equilibrium, but
admits M 6= Mre
, H 6= Hre
, G 6= Gre
, J 6= Jre
.
• Agents update their “beliefs” by estimating a VAR(1).
• Agents use PLM to form expectations
EτXτ+1 = Mτ−1Xτ + Hτ−1
•Model is E-stable, i.e. limt→∞ Mt → Mre
.
Experiment
•Assume that, in the decade preceding 2008Q4,
agents have learned the economy and the policy
• the associated matrix in PLM is M2008Q4,
• beliefs about ρθ, ε are reflected in matrix M2008Q4.
•Key equation: AR(1) process for leverage:
• RE corresponds to OLS estimates for 1975-2010 for ρθ,
ρθ = 0.976, Θ̄ = 0.88.
• Agents’ initial beliefs given by 2008Q4 CG estimates,
ρCG
θ = 0.9904 for νt = 0.004.
• Agents (both RE and AL) use ε = 0.5.
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.
What we find
•Agents gradually learn the economy.
•Initial beliefs matter a lot!
• priors affect the evolution of beliefs,
... and dynamics of endogenous variables.
•When understood macro-prudential policies
enforcing counter- cyclical leverage have
stabilizing effect.
•But if not, change or the introduction of new
policy that reduces volatility and exposure to
shocks under learning may not work.
Macroprudential policy
Regulation that makes leverage countercyclical
•Set ε = −0.5 (leverage goes down when land price
goes up).
•Assume that agents “know” (or has learnt) it:
• DGP (MRE
) and beliefs (M2008Q4) use ε = −0.5
Agents “know” (or learnt) policy
Result:
•Countercyclical leverage dampens responses to
financial shocks.
•Smaller recession follows a negative leverage shock
•Learning dynamics closer to its rational
expectations counterpart.
10 20 30 40 50
Time
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
%
Output
pro-cyclical (ε = 0.5) leverage under learning (solid red) and RE (dotted blue)
counter-cyclical (ε = −0.5) leverage under learning (dashed purple) and RE (dashed-dotted)
Unannounced/misperceived policy
•But if new policy is unannounced/misunderstood?
• incorrect beliefs regarding the macro-prudential policy.
• MRE
for 0 but M2008Q4 reflects 0
Result:
•Policy change designed to reduce volatility can
lead to opposite results
•Reduction of confidence in the policy makes
reaction under learning even larger
20 40 60 80 100
Time
-1.0
-0.5
0.5
1.0
1.5
2.0
%
Output
counter-cyclical (ε = −0.5%) leverage under learning (solid red) and RE (dotted blue)
strongly counter-cyclical (ε = −1.5%) leverage under learning (dashed purple) and RE