Fisherian Deflation, Credit Collapse and Sudden Stopsegme/econ252/files/Deflation.pdf1....
Transcript of Fisherian Deflation, Credit Collapse and Sudden Stopsegme/econ252/files/Deflation.pdf1....
Fisherian Deflation, Credit Collapse and
Sudden Stops
Enrique G. MendozaUniversity of Pennsylvania, NBER & PIER
Layout
1. Basic elements of financial crises modeling2. Principles of Fisherian models 3. Extending the small open economy model to
incorporate Fisherian deflation4. Quantitative experiments5. Policy implications
Basics of Nonlinear Financial Crises Models
A writerβs perspective
ββ¦debt happens as a result of actions occurring over time. Therefore, any debt involves a plot line: how you got into debt, what you did, said and thought while you were there, and thenβdepending on whether the ending is to be happy or sadβhow you got out of debt, or else how you go further and further into it until you became overwhelmed by it, and sank from view.β
(Margaret Atwood, βDebtorβs Prism,β WSJ, 09/20/2008)
Crises, βBlack swansβ & nonlinearities
β’ βThings are not conceptually out of control, this is not some mystery black swan we donβt understand and we need to rewrite all the paradigms because all the modeling is wrong. If people are acting using a linear model, what looks like a ten-sigma event can actually be a two-sigma event...β
β’ βMost of the models in credit, in trading desks, in macro models do quite well locally, the problem is when you stop being locally nonlinearities are really quite large,β¦If you want to see what happened in AIGβ¦they wrote a whole lot of credit default swapsβ¦the assets underlying them went down not one shock, not two shocks, not three shocks, but over and over. Each time the same size shock is going to create something even largerβ¦β
R. Merton, βObservations on the Science of Finance in the Practice of Finance,β(Muh Award Lecture, 03/05/2009)
Pricing liabilities with financial distress
Theoretical pricing function
Amplification, nonlinearities and βmacroprudentialβ policy
regular cycle
financial distress
Theoretical pricing function
local approximation
financial distress with MPP
yield
Principles of Fisherianmodels of financial crises
Fisherian models
β’ Fisher (1933): narrative of fin. amplification driven by debt-deflation mechanism & interaction of innovation and beliefsβ Modern examples: Minsky, Kiyotaki-Moore, Bernanke-Gertler,
Aiyagari-Gertler, Mendoza, Brunnermeier-Sannikovβ¦
β’ Collateral constraints: debt cannot exceed a fraction of market value of collateral (a market price affects borrowing capacity). 1. DTI models (flow constraints): debt in units of tradables limited
to a fraction of market value of total income:
2. LTV models (stock constraints): debt cannot exceed a fraction of the market value of assets:
πππ‘π‘+1 β₯ βπ π π¦π¦π‘π‘ππ + πππ‘π‘πππ¦π¦π‘π‘ππ
πππ‘π‘+1 β₯ βπ π πππ‘π‘πππ‘π‘+1
Two key features of Fisherian constraints
1. Debt-deflation mechanism: When constraints bind, agents fire sale assets/goods, prices fall, constraint tightens further forcing more fire sales
β Credit crunch causes collapse in demand, and also in supply via effects on factor demands (e.g. deflation of relative prices)
β Crises are endogenous outcomes of standard shocks not large unexpected, or financial, shocks
β Different from Keynesian disequilibrium: price flexibility, rather than rigidity and exogenously insufficient aggregate demand
2. Pecuniary externality: agents do not internalize effect of individual borrowing on collateral prices
β Dynamic externality: effect of todayβs borrowing on tomorrowβs prices if there is a financial crisis
β Market failure that justifies macroprudential regulation
Extending the SOE Model to Incorporate
Fisherian DTI Constraints
Why is this important?
β’ In economies that are highly leveraged, Fisheriandeflation amplifies real effects of credit contractions
β’ Via Fisherian deflation, credit frictions induce amplification and asymmetry (i.e., βGreat Depressionsβ or βSudden Stopsβ) in response to βstandardβ shocks
β’ The transmission mechanism features a βpureβ balance sheet effect (i.e. without feedback) and Fisherβs debt-deflation process
β’ Quantitatively, the contribution of the Fisheriandeflation is substantial and Fisherian models provide a framework for macroprudential policy analysis
Fisherβs debt-deflation mechanism
β’ Example: DTI setup with debt in units of tradables, leveraged on nontradables income
πππ‘π‘+1 β₯ βπ π π¦π¦π‘π‘ππ + πππ‘π‘πππ¦π¦π‘π‘ππ
β’ Assume a period of expansion and real appreciation driven by rising relative prices (nontradables relative to tradables)
β’ Debt rises and at some point DTI constraint becomes binding
β’ Pure balance sheet effect: borrowing constraint lowers tradables consumption and rel. price of nontradables
β’ Fisherian deflation: spiral of tightening debt constraints and falling nontradables prices (feedback effect)
Adding DTI constraint to SOE model
β’ Households consume tradables and nontradables, combining them into a composite good ππ πππ‘π‘ππ , πππ‘π‘ππ . For example, if the composite good is Cobb-Douglas:
ππ πππ‘π‘ππ , πππ‘π‘ππ = (πππ‘π‘ππ)πΌπΌ(πππ‘π‘ππ)1βπΌπΌ
β’ Utility function can be log as before, with infinite life horizon:
ππ ππππ , ππππ = πΏπΏπΏπΏ ππ ππ0ππ , ππ0ππ +πΏπΏπΏπΏ ππ ππ1ππ , ππ1ππ
1 + πΏπΏ +πΏπΏπΏπΏ ππ ππ2ππ , ππ2ππ
1 + πΏπΏ 2 +. . .
β’ Budget constraint (with π π β‘ 1 + ππ & tax on nontradables purchases):
πππ‘π‘ππ + (1 + πππ‘π‘)πππ‘π‘πππππ‘π‘ππ = π¦π¦π‘π‘ππ + πππ‘π‘πππ¦π¦π‘π‘ππ β πππ‘π‘+1 + πππ‘π‘π π + πππ‘π‘
β’ DTI Fisherian credit constraint:πππ‘π‘+1 β₯ βπ π π¦π¦π‘π‘ππ + πππ‘π‘πππ¦π¦π‘π‘ππ
SOE model contnβd
β’ Government budget constraint:
πππ‘π‘πππ‘π‘πππππ‘π‘ππ = οΏ½ΜοΏ½πππ + πππ‘π‘πποΏ½ΜοΏ½πππ + πππ‘π‘
β’ Nontradables market clearing:
β’ Tradables resource constraint (obtained by combining budget constraints of households and government):
β’ Focus on the case that gave perfectly smooth consumption before (i.e. assume 1 + πΏπΏ = π π ), and for simplicity assume also π¦π¦π‘π‘ππ = οΏ½ΜοΏ½π¦ππ so that market-clearing implies οΏ½ΜοΏ½πππ = οΏ½ΜοΏ½π¦ππ - οΏ½ΜοΏ½πππ
πππ‘π‘ππ + οΏ½ΜοΏ½πππ = π¦π¦π‘π‘ππ
πππ‘π‘ππ + οΏ½ΜοΏ½πππ = π¦π¦π‘π‘ππ β πππ‘π‘+1 + π π πππ‘π‘
Frictionless perfectly smooth equilibrium (FPSE)
β’ Recall optimal savings plan equates marginal cost and benefit of savings (IMRS=R). Since bonds are in units of tradables we get:
ππππ(ππ πππ‘π‘ππ , οΏ½ΜοΏ½πππ )πππππ‘π‘ππ
=(1 + ππ)(1 + πΏπΏ)
ππππ(ππ πππ‘π‘+1ππ , οΏ½ΜοΏ½πππ )πππππ‘π‘+1ππ
β’ Hence assuming πΏπΏ = ππ still yields perfectly smooth consumption:
ππππ(ππ πππ‘π‘ππ, Μππππ )πππππ‘π‘ππ
= ππππ(ππ πππ‘π‘+1ππ , Μππππ )πππππ‘π‘+1ππ β πππ‘π‘ππ= πππ‘π‘+1ππ = οΏ½ΜοΏ½πππ
β’ Tradables intertemporal resource constraint implies same result as before: πππ‘π‘ππ is a constant fraction of tradables wealth
οΏ½ΜοΏ½πππ = 1 β π½π½ ππ0 + π π ππ0 β οΏ½ΜοΏ½πππ π€π€π€π€π€π€π€ ππ0 β‘οΏ½π‘π‘=0
β
π π βπ‘π‘ π¦π¦π‘π‘ππ
FPSE contnβd
β’ New item we need to determine is the equilibrium πππ‘π‘ππ
β’ Optimal choices of πππ‘π‘ππ and πππ‘π‘ππ equate marginal cost and benefit of reallocating consumption:
ππππ(ππ πππ‘π‘ππ,πππ‘π‘ππ )πππππ‘π‘ππ
= ππππ(ππ πππ‘π‘ππ,πππ‘π‘ππ )πππππ‘π‘ππ
1 + πππ‘π‘ πππ‘π‘ππ
Ξ¦ πππ‘π‘ππ/πππ‘π‘ππ β‘ οΏ½ππππ(ππ πππ‘π‘ππ,πππ‘π‘ππ )πππππ‘π‘ππ
ππππ(ππ πππ‘π‘ππ,πππ‘π‘ππ )πππππ‘π‘ππ
= 1 + πππ‘π‘ πππ‘π‘ππ
Ξ¦ πππ‘π‘ππ/πππ‘π‘ππ is the MRS between the two goods
β’ Using solutions for πππ‘π‘ππ & πππ‘π‘ππ we get : πππ‘π‘ππ = οΏ½ΜοΏ½πππ = Ξ¦ οΏ½ΜοΏ½πππ/οΏ½ΜοΏ½πππ 1 + πππ‘π‘ β1
π€π€π€π€π€π€π€ Ξ¦ οΏ½ΜοΏ½πππ/οΏ½ΜοΏ½πππ =1 β πΌπΌπΌπΌ
οΏ½ΜοΏ½πππ
οΏ½ΜοΏ½πππππππππ πΆπΆππππππ β π·π·πππππππ·π·π·π·π·π· ππ(. )
FPSE summary(see Mendoza (2005) for details)
β’ Frictionless perfectly-smooth equilibrium (if credit constraint never binds):
οΏ½ΜοΏ½πππ = οΏ½ΜοΏ½π¦ππ - οΏ½ΜοΏ½πππ
οΏ½ΜοΏ½πππ = 1 β π½π½ ππ0 + π π ππ0 β οΏ½ΜοΏ½πππ , ππ0β‘οΏ½π‘π‘=0
β
π π βπ‘π‘ π¦π¦π‘π‘ππ
οΏ½ΜοΏ½πππ =Ξ¦ οΏ½ΜοΏ½πππ/οΏ½ΜοΏ½πππ
1 + ππ
πππ‘π‘+1 = π¦π¦π‘π‘ππ + π π πππ‘π‘ β 1 β π½π½ ππ0 + π π ππ0β This a βsocial optimum:β yields the highest welfare
the economy can attain given its resources
Wealth-neutral shocks (WNS) to π¦π¦0ππ
β’ π¦π¦0ππ ,π¦π¦1ππ such that β π¦π¦0ππ & β π¦π¦1ππ relative to οΏ½ΜοΏ½π¦ππ keeping ππ0 constant:
β’ In the FPSE, WNS shocks are irrelevant for consumption, prices and welfare. They only alter pattern of borrowing and lending:
β’ If for a given WNS the Fisherian credit constraint does not bind we preserve FPSE: Agents borrow at 0, repay at 1. But if it binds, FPSE cannot be maintained (credit is constrained)
οΏ½ππ1 β ππ0 = π¦π¦0ππ β οΏ½ΜοΏ½π¦ππ < 0
οΏ½ππ2 βοΏ½ππ1 = β οΏ½ππ1 β ππ0 > 0,
οΏ½ΜοΏ½ππ‘π‘= ππ0 ππππππ π€π€ β₯ 2
π¦π¦1ππ β οΏ½ΜοΏ½π¦ππ
1 + ππ = οΏ½ΜοΏ½π¦ππ β π¦π¦0ππ π€π€π€π€π€π€π€ οΏ½ΜοΏ½π¦ππ β‘ππππ0
1 + ππ π€π€π·π· πππππππππ·π·πΏπΏπππΏπΏπ€π€ π€π€πΏπΏππππππππ
Fisherian deflation equilibrium (FDE)
β’ Unanticipated wealth neutral shock β π¦π¦0ππ
β’ As π¦π¦0ππ falls agents borrow more, and if π¦π¦0ππ falls below critical level οΏ½π¦π¦ππ, credit constraint becomes binding
β’ A devaluation of the real ex. rate can be proxied as a tax hike (β ππ ββ οΏ½ΜοΏ½π0ππ ). This increases οΏ½π¦π¦ππ, so βreal devaluationsβ can trigger credit constraints for smaller shocks to π¦π¦0ππ
β’ k has an upper bound, above which the credit constraint never binds for positive income, and a lower bound below which ππ0ππ β€ 0.
οΏ½π¦π¦ππ =οΏ½ΜοΏ½π¦ππ β ππ0 β π π οΏ½ΜοΏ½π0πποΏ½ΜοΏ½π¦ππ
1 + π π
Solving Fisherian deflation equilibrium (FDE)
β’ FDE yields an equilibrium with βSudden Stop.β The solution follows from two equations:
1. Date-0 tradables resource constraint implies:
2. Date-0 price of nontradables implies:
β’ The above two form a possibly non-linear eq. in ππ0ππ:
ππ0ππ = π¦π¦0ππ β οΏ½ΜοΏ½πππ + π π π¦π¦0ππ + Ξ¦ππ0ππ
οΏ½ΜοΏ½π¦ππ β οΏ½ΜοΏ½πππ1 + ππ0 β1 οΏ½ΜοΏ½π¦ππ + π π ππ0
β’ The date-0 current account implies:
ππ0ππ = π¦π¦0ππ β οΏ½ΜοΏ½πππ + π π π¦π¦0ππ + ππ0πποΏ½ΜοΏ½π¦ππ + π π ππ0 < οΏ½ΜοΏ½πππ
ππ0ππ = Ξ¦ππ0ππ
οΏ½ΜοΏ½π¦ππ β οΏ½ΜοΏ½πππ 1 + ππ0 β1 < οΏ½ΜοΏ½π0ππ
ππ1 β ππ0 = βπ π π¦π¦0ππ + ππ0πποΏ½ΜοΏ½π¦ππ β ππ0 > οΏ½ππ1 β ππ0
Graph of Frictionless Perfectly Smooth Equilibrium
οΏ½ΜοΏ½πππ = 1 β π½π½ ππ0 + π π ππ0 β οΏ½ΜοΏ½πππ
ππ0ππ =Ξ¦ ππ0ππ/οΏ½ΜοΏ½πππ
1 + ππ
ππ0ππ = οΏ½π¦π¦ππ β οΏ½ΜοΏ½πππ + π π οΏ½π¦π¦ππ + ππ0πποΏ½ΜοΏ½π¦ππ+π π ππ0
Graph of Equilibrium with Fisherian deflation
ππ0ππ = π¦π¦0ππ β οΏ½ΜοΏ½πππ + π π π¦π¦0ππ + ππ0πποΏ½ΜοΏ½π¦ππ + π π ππ0π¦π¦0ππ< οΏ½π¦π¦ππ
ππ0ππ =Ξ¦ ππ0ππ/οΏ½ΜοΏ½πππ
1 + ππ
β ππ0ππ
β ππ0ππ
Main features of FDE
β’ Asymmetric response to positive v. negative shocks
β’ FDE amplifies response to negative shocks beyond βpureβ balance sheet effect
β’ βDevaluationβ or price shocks neutral for FPSE, not FDE
β’ Nonexistence and multiplicity:β If shock is βtoo largeβ, economy cannot borrow (no FDE
exists) and moves to autarky solutionβ Unique equilibrium guaranteed if SS is steeper than PP
around PSE (point A)
β’ Endogenous volatility of pn drives volatility of rer and causes Sudden Stops
Quantitative Experiments
Functional forms & calibration
β’ Functional forms:
β’ Parameter values:β Ξ² = 0.96, Ο = 2
β a = 0.342 Mendozaβs (02) estimate for Mexico
β Β΅ = 0.204, 1/(1+ Β΅) = 0.83 at upper bound of range of existing estimates for Latin America
β yT/(pNyN) = 1.543, cT/yT = 0.66, cN/yN = 0.71 from Mendozaβs (02) estimates for Mexico
β Initial debt set at 1/3 of GDP
β βPermanentβ output normalized to 1 (results as shares)
ππ(ππ) = ππ1βππ /(1 β ππ) ππ = π·π·(ππππ)βππ + (1 β π·π·)(ππππ)βππ β1/ππ
Wealth Neutral Shocks to y0T with ΞΊ=0.34
Wealth Neutral Shocks to y0T with ΞΊ=0.34
β¦and it gets worse (output & employment effects)
β’ Firms that produce NT goods experience a collapse of the relative price of their output and sales
β’ Value of marginal product (i.e. demand) for inputs they use (capital, labor, int. goods) falls, and so does output
β’ Falling supply of NT goods has two effects:β Weakens deflation by reducing supply
β Worsens the credit crunch as now both prices and output fall
β’ βVulnerableβ agents that were βo.k.β before are hit by the crisis as they become unemployed and/or hit credit constraint because of falling incomes and prices
How bad can it get in the U.S.?: The Great Depression
Deflation during the U.S. Great Depression
Policy Implications
Macroprudential pecuniary externality
β’ Optimality condition equating costs and benefits of borrowing/saving without regulation:
β πππ‘π‘ is Lagrange multiplier of credit constraint. It is >0 if it binds. In normal times, πππ‘π‘=0 => standard condition
β’ Macroprudential pecuniary externality: Regulator considers how πππ‘π‘+1ππ responds to debt chosen at t if constraint binds at t+1. Its optimality condition in normal times is:
ππππ(ππ πππ‘π‘ππ , οΏ½ΜοΏ½πππ )πππππ‘π‘ππ
=(1 + ππ)(1 + πΏπΏ)
πΈπΈπ‘π‘ππππ(ππ πππ‘π‘+1ππ , οΏ½ΜοΏ½πππ )
πππππ‘π‘+1ππ + πππ‘π‘+1π π οΏ½ΜοΏ½π¦πππππππ‘π‘+1ππ
πππππ‘π‘+1ππ
β’ Social marginal cost of borrowing exceeds private one, causing overborrowing in the absence of regulation!
ππππ(ππ πππ‘π‘ππ , οΏ½ΜοΏ½πππ )πππππ‘π‘ππ
=(1 + ππ)(1 + πΏπΏ)
πΈπΈπ‘π‘ππππ(ππ πππ‘π‘+1ππ , οΏ½ΜοΏ½πππ )
πππππ‘π‘+1ππ + πππ‘π‘ππππ(ππ πππ‘π‘ππ , οΏ½ΜοΏ½πππ )
πππππ‘π‘ππ=
(1 + ππ)(1 + πΏπΏ)
πΈπΈπ‘π‘ππππ(ππ πππ‘π‘+1ππ , οΏ½ΜοΏ½πππ )
πππππ‘π‘+1ππ
Optimal Macroprudential policy
β’ βMacroprudentialβ debt tax: Assume borrowing carries a tax to make debt costlier so as to prevent credit booms.
β’ The optimal tax would make the private marginal cost of borrowing match social MC of borrowing:
πππ‘π‘ = οΏ½πΈπΈπ‘π‘ πππ‘π‘+1π π οΏ½ΜοΏ½π¦πππππππ‘π‘+1ππ
πππππ‘π‘+1ππ πΈπΈπ‘π‘ππππ(ππ πππ‘π‘+1ππ , οΏ½ΜοΏ½πππ )
πππππ‘π‘+1ππ
β πππ‘π‘ > 0 only if the constraint is expected to bind with some probability at t+1 (this is why it is βprudentialβ).
β’ Equivalent instruments: capital requirements, new CCyBof the BIS, regulatory LTV or DTI ratios.
Optimism and βFisherian inflationβ
β’ Technological and/or financial innovation can lead to optimistic valuation of collateral
β’ Rising collateral values trigger credit boom (the constraint binds also in the upswing)
β’ Shocks that trigger the constraint have even larger effects because of higher leverage
β’ Recessions can be even deeper if they cause pessimistic valuation of collateral
β’ But modeling optimism/pessimism requires additional structure (e.g. Bayesian learning)
β’ Boz and Mendoza (2014) proposed a model of the U.S. crisis with these features
Conclusions
1. In highly leveraged economies with credit frictions, endogenous deflation of relative prices causes Sudden Stops (deep recessions, CA reversals)
2. Credit frictions induce amplification and asymmetry in response to βstandardβ shocks
3. The contribution of the Fisherian deflation is substantial, and it has large adverse welfare effects
4. Pecuniary externality via collateral values justifies macroprudential regulation (but optimal policy is complex and simple rules are much les effective)