Euler equation poster
1
L A T E X Tik Zposter The walking dead Euler equation A reconciliation of consumption, interest rates and expectations Aur ´ elien Poissonnier Insee & Crest-LMA & ´ Ecole Polytechnique The walking dead Euler equation A reconciliation of consumption, interest rates and expectations Aur ´ elien Poissonnier Insee & Crest-LMA & ´ Ecole Polytechnique A baseline rejection of the Euler equation The Euler equation relating consumption, interest rates and expectations is a cornerstone of monetary policy models. Canzoneri, Cumbi and Diba (2007) compare the Marginal Rate of intertemporal Substitution of consumption (MRS) with the Fedfunds using ex ante estimated (VARX) for expectations and find null or negative correlation (in real terms). Fedfunds and MRS misalignment 1970 1975 1980 1985 1990 1995 2000 2005 2010 -1 0 1 2 3 4 5 MRS without habit with habit fedfund Rejection of Euler equation is conditional on VARX expectations and monetary policy rate • Baseline has a very low fit to the data (R 2 < 20%) • Interest rates specific to households’ savings and bor- rowing markedly improve the model’s fit (R 2 > 50%) • Considering households expectations departing from optimality further improves the models fit (R 2 > 80%). Methodology Full model = Euler equation + expectations: i fed t - E t π t+1 = δ + σE t Δc t+1 + X x6=fed γ x i x t - i fed t + ζ t (Euler) Y t+1 =[c t+1 ,π t+1 ]= E t Y t+1 + t+1 = Λ(L)Y t +ΓX t + t+1 (VARX) Baseline • Hyp. expectation errors = VARX residuals • Hyp. households react to Fedfunds (γ x = 0) • Method first MLE (VARX) then MLE (Euler) New tests • households may react to a different in- terest rate ⇒ γ x 6=0 • Baseline method is bias towards re- jecting (Euler) ⇒ joint MLE (Eu- ler+VARX) Households specific interest rates better describe consumption-savings arbitrage Fedfunds only or with mortgage rate + car loans rate + personal loans rate + deposit rate + 3 month treasury bill ⇒ markedly improves the fit to the data 1 rate 6 rates Stdev 0.74 0.58 log-lik. 1947.81 1999.79 R2 (Euler) 17 56 Optimal rate linear combination: cannot reject ” H 0 : zero weight on Fedfunds” ; sensible mix of actual rates (correlated between 40% and 90% with other rates). Joint estimation (Euler+VARX) The expectation VARX is jointly estimated with the Euler equation by maxi- mum likelihood over the full sample (1972-2013) Interest rates and MRS from a joint estimation 1975 1980 1985 1990 1995 2000 2005 2010 0 1 2 3 4 Fedfunds Pers. Loans MRS Optimal rate combination Households respond to an interest rate close to the interest rate on personal loans. Graph is quite different from baseline rejection (cf. above). Optimal (Rational ) expectations ? Full sample (R 2 = 83%) Expectations are • non statistically 6= from VARX for π ⇒ optimal • statistically 6= from VARX for Δc ⇒ suboptimal Before/after 1990 (R 2 = 87% / 89%) Expectations are • non statistically 6= from VARX before 1990 for π and Δc ⇒ optimal • flat for π after 1990 ⇒ suboptimal Break in expectation formation process after great moderation before 1990 1975 1980 1985 1990 1995 2000 2005 2010 -1.0 -0.5 0.0 0.5 1.0 1.5 after 1990 1975 1980 1985 1990 1995 2000 2005 2010 -1.0 -0.5 0.0 0.5 1.0 1.5 dc Edc optimal forecast before 1990 1975 1980 1985 1990 1995 2000 2005 2010 -1 0 1 2 3 after 1990 1975 1980 1985 1990 1995 2000 2005 2010 -1 0 1 2 3 pi Epi optimal forecast → behave like inattentive consumers: when inflation is steadily low, it can be optimal to form naive expectations. Robustness Results are robust to: • habit formation, rule of thumb consumers, Uzawa pref- erences, animal spirit and precautionary savings • measures of expectations and interest rate through households surveys • the use of French data and other definitions of consump- tion bundle Results and interpretation • By and large, US households respond to the interest rate on personal loans (lower savings, widespread use of credit cards) • French households respond to the interest rate on regulated savings (90% pop. holds a livret ) ⇒ weaker transmission of monetary policy • Expectations are optimal for consumption but flat for inflation. Behaviour interpretable as inattentiveness: for house- holds, forecasting consumption is relatively costless, but inflation is more complex. When the latter is steadily low, it can be optimal to form naive expectations. contact: [email protected] acknowledgments: Edouard Challe (PhD advisor), Behzad Diba, Xavier Ragot download: http://sites.google.com/site/apoissonnierrandt/home/research
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Transcript of Euler equation poster
LATEX TikZposter
The walking dead Euler equationA reconciliation of consumption, interest rates and
expectations
Aurelien Poissonnier
Insee & Crest-LMA & Ecole Polytechnique
The walking dead Euler equationA reconciliation of consumption, interest rates and
expectations
Aurelien Poissonnier
Insee & Crest-LMA & Ecole Polytechnique
A baseline rejection of the Euler equation
The Euler equation relating consumption, interest ratesand expectations is a cornerstone of monetary policy models.
Canzoneri, Cumbi and Diba (2007) compare theMarginal Rate of intertemporal Substitution of consumption(MRS) with the Fedfunds using ex ante estimated (VARX)for expectations and find null or negative correlation (in realterms).
Fedfunds and MRS misalignment
1970 1975 1980 1985 1990 1995 2000 2005 2010
−1
0
1
2
3
4
5
MRS without habitwith habitfedfund
Rejection of Euler equation is conditional on VARXexpectations and monetary policy rate
•Baseline has a very low fit to the data (R2 < 20%)
• Interest rates specific to households’ savings and bor-rowing markedly improve the model’s fit (R2 > 50%)
•Considering households expectations departing fromoptimality further improves the models fit (R2 > 80%).
Methodology
Full model = Euler equation + expectations:
ifedt − Etπt+1 = δ + σEt∆ct+1 +∑x 6=fed
γx(ixt − i
fedt
)+ ζt (Euler)
Yt+1 = [ct+1, πt+1] = EtYt+1 + εt+1 = Λ(L)Yt + ΓXt + εt+1 (VARX)
Baseline
•Hyp. expectation errors = VARXresiduals
•Hyp. households react to Fedfunds(γx = 0)
•Method first MLE (VARX) then MLE(Euler)
New tests
• households may react to a different in-terest rate ⇒ γx 6= 0
•Baseline method is bias towards re-jecting (Euler) ⇒ joint MLE (Eu-ler+VARX)
Households specific interest rates better describe
consumption-savings arbitrage
Fedfunds only or with mortgage rate + car loans rate + personal loans rate + depositrate + 3 month treasury bill ⇒ markedly improves the fit to the data
1 rate 6 rates
Stdev 0.74 0.58log-lik. 1947.81 1999.79R2 (Euler) 17 56
Optimal rate linear combination: cannot reject ”H0: zero weight on Fedfunds”; sensiblemix of actual rates (correlated between 40% and 90% with other rates).
Joint estimation (Euler+VARX)
The expectation VARX is jointly estimated with the Euler equation by maxi-mum likelihood over the full sample (1972-2013)
Interest rates and MRS from a joint estimation
1975 1980 1985 1990 1995 2000 2005 2010
0
1
2
3
4
FedfundsPers. LoansMRSOptimal rate combination
Households respond to an interest rate close to the interest rate on personal loans.Graph is quite different from baseline rejection (cf. above).
Optimal (Rational) expectations ?
Full sample (R2 = 83%)
Expectations are
• non statistically 6= from VARX for π⇒ optimal
• statistically 6= from VARX for ∆c⇒ suboptimal
Before/after 1990 (R2 = 87% / 89%)
Expectations are
• non statistically 6= from VARX before1990 for π and ∆c ⇒ optimal
• flat for π after 1990 ⇒ suboptimal
Break in expectation formation process after great moderationbefore 1990
1975 1980 1985 1990 1995 2000 2005 2010
−1.0
−0.5
0.0
0.5
1.0
1.5
after 1990
1975 1980 1985 1990 1995 2000 2005 2010
−1.0
−0.5
0.0
0.5
1.0
1.5
dcEdcoptimal forecast
before 1990
1975 1980 1985 1990 1995 2000 2005 2010
−1
0
1
2
3
after 1990
1975 1980 1985 1990 1995 2000 2005 2010
−1
0
1
2
3 piEpioptimal forecast
→ behave like inattentive consumers: when inflation is steadily low, it can be optimalto form naive expectations.
Robustness
Results are robust to:
• habit formation, rule of thumb consumers, Uzawa pref-erences, animal spirit and precautionary savings
•measures of expectations and interest rate throughhouseholds surveys
• the use of French data and other definitions of consump-tion bundle
Results and interpretation
•By and large, US households respond to the interest rate on personal loans (lower savings, widespread use ofcredit cards)
•French households respond to the interest rate on regulated savings (90% pop. holds a livret)
⇒weaker transmission of monetary policy
•Expectations are optimal for consumption but flat for inflation. Behaviour interpretable as inattentiveness: for house-holds, forecasting consumption is relatively costless, but inflation is more complex. When the latter is steadily low, it canbe optimal to form naive expectations.
contact: [email protected]: Edouard Challe (PhD advisor), Behzad Diba, Xavier Ragotdownload: http://sites.google.com/site/apoissonnierrandt/home/research
