DSGE Models and the Financial Crisis
Based On: QE 1 vs. 2 vs. 3... A Framework for Analyzing Large Scale Asset Purchases as a Monetary Policy Tool*
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A Brief Digression on Macro-Modeling Philosophy • No single model useful for all purposes: — Preferred Approach: Use a "suite" models (e.g. Bank of England) • DSGE models occupy a middle ground between statistical and theoretical — Finding this middle ground involves art as well as science. • No single DSGE useful for all purposes — Adjust detail to question at hand • Tools existed to incorporate financial factors well before crisis (e.g BGG 1999) — Failure to anticipate need for these tools — Literature now rapidly adjusting
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Modeling QE: background • Fed has introduced a variety of new policy tools. Response to: — Disruption of credit markets — The zero lower bound.
• Most visible new tool: Large Scale Asset Purchases (LSAPs - also known as "QE") — QE1: December 2008 (AMBS, Agency Debt, Gov’t Bonds) — QE2: October 2010 (Gov’t Bonds) — QE3: September 2012: (AMBS)
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Modeling QE: background (con’t) • Evidence from QE1 and QE2 that LSAPs have reduced long rates and rate spreads — "Large" effect of QE1 (e.g Gagnon et.al.) — "Modest" effect of QE2 ∗ 600 bill govt bonds purchase ∼15 basis point drop in 10 yr rate • Larger "size-adjusted" effect of QE1 (so type of security purchased matters) — QE1 "size adjusted" ∼ 44 basis points (based on Gagnon et.al). — QE1 also reduced AMBS and mortgage spreads
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Introduction (con’t) • Objective: Develop a unified framework for analyzing LSAPs • Perspective: LSAPs reflect central bank intermediation. — Like private banks, CB funds assets by issuing short term debt. — Interest-bearing bank reserves ≈ short term gov’t debt • Effectiveness of LSAPs depends on limits to arbitrage on private intermediation — CB bank advantage: can obtain funds elastically. — Type of security purchased matters (e.g. AMBS vs.gov’t bonds). 5
Introduction (con’t) • Alternative view: Imperfectly elastic household demand for long term securities — e.g Preferred habitat. — Asset supplies matter.
• However, behavior of the marginal investor is key — Leveraged financial institutions are natural marginal investors. — Limits to arbitrage are key.
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Table 1: Asset holdings of leveraged and non-leveraged institutions
Total Mortgages Agency MBS Treasuries & Agency debt Treasuries
Domestic net assets (Billions,$) all leveraged non-lev’d 14336 6170 8166 3590 1567 2023
% leveraged 43.0% 43.6%
non-lev’d 57.0% 56.4%
4195
1325
2870
31.6%
68.4%
1876
312
1563
16.7%
83.3%
Source: Flow of Funds, 2008 december Leveraged institutions: Commercial Banks, Savings Banks, Credit Unions, Brokers and Dealers, Government Sponsored Enterprises, Finance Companies Agency debt and Agency MBS is not published separately for different financial intermediaries. We assume each are held proportionally to their combined holdings by leveraged and non-leveraged institutions.
Macro Model • Baseline: Streamlined version of quantitative model widely used at central banks. — We keep: habit formation, investment adjustment costs, price rigidities. — We omit: wage rigidity, indexing, and variable factor utilization.
• Distinctive Features: — Banks (face endogenous financial constraints) — Central bank: conducts both LSAPs and conventional interest rate policy.
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Households • Within each household, 1 − "workers" and "bankers". — Workers earn wages — Bankers manage financial intermediaries and pay dividends
• Perfect consumption insurance within the family. • Bankers have finite expected horizons 1 ) — With i.i.d prob. 1 − , a banker exits next period. (Expected horizon = 1−
— Replaced by new bankers who receive a start-up transfer from the family. 8
CAPITAL PRODUCERS
NONFINANCIAL FIRMS
Dh Q Sp
q Bp GOVERNMENT
HOUSEHOLDS
N
Banks • Balance Sheet + = +
• Net worth = −1−1 + −1−1 − −1 with
Banks (con’t) • With Frictionless Capital Markets Λ+1+1 = Λ+1+1 = Λ+1+1
• With Capital Market Frictions
Λ+1+1 ≥ Λ+1+1
Λ+1+1 ≥ Λ+1+1 11
Limits to Bank Arbitrage • Agency Problem: After the banker/intermediary borrows funds at the end of period it may divert: — a fraction of of loans — a fraction and ∆ of gov’t bonds, with 0 ≤ ∆ ≤ 1. • If the bank does not honor its debt, creditors can recover the residual funds and shut the bank down. ⇒ • Incentive constraint ≥ + ∆ 12
Bank Optimization Problem: Solution • Balance sheet constraint + ∆ ≤ ≡ maximum "adjusted" leverage ratio: Depends positively on excess returns • Arbitrage e e Λ +1(+1 − +1) = ∆Λ+1(+1 − +1)
LSAPs • Central bank intermediation supplements private intermediation: + =
• The central bank issues government debt that pays +1 and then buys private securities and government bonds at market prices • Central bank less efficient at intermediating securities than private banks — cost of per unit for private securities; for gov’t bonds. • Unlike private intermediaries, the central bank is not "balance-sheet" constrained. 15
LSAPs (con’t) • Total asset demands = + = + =⇒ • Effects of LSAPs on total private securities demand: ≤ − ∆ + ( + ∆)
Since ∆ 1 per dollar, has a weaker effect on asset demand than
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CAPITAL PRODUCERS
NONFINANCIAL FIRMS
Dh Q Sp
q Bp
HOUSEHOLDS
N
GOVERNMENT
Q Sg q Bg
Dg
Direct Household Asset Holdings • Households can directly hold and subject to proportional holding costs: — Private securities: 12 ( − )2 for ≥ — Gov’t bonds: 12 ( − )2 for ≥ • Household asset demands Λ+1(+1 − +1) = + Λ+1(+1 − +1) = +
• Qualitative effects of LSAPs similar to baseline case — Relative strength depends inversely on Hh demand elasticities — For LSAPs to matter need limits to arbitrage for both Hh and banks 18
Non-financial Business Sector • Intermediate goods producers make output using capital and labor — Finance capital by issuing risky securities at price
Figure 1: Private and government asset purchase shocks. Purchases are calibrated to a peak effect of 2.5% of GDP and interest rates are kept unchanged for 4 periods.
2.5
1
2 1.5
0.8
2 1.5 1
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% of GDP
Shocks 3
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Government bond purchase
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Monetary policy shock
Figure 2: Monetary and government bond purchase shocks. The government bond purchase shock is calibrated to a peak effect of 2.5% of GDP with interest rates kept unchanged for 4 periods. The monetary policy shock reduces the nominal interest rate by 40 basis-points below its steady state value for 4 periods.
2.5
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0.6 0.5 0.4 0.2
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Y 1.2
%∆ from ss
% of GDP
CB purchases 3
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0 0
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Interest rate response
Figure 3: Government bond purchase shocks with and without interest rate responses. The bond policy is calibrated to a peak effect of 2.5% of GDP. The interest rate is kept unchanged for 4 periods.
Figure 4: Government bond purchase shocks with and without segmented household asset markets. Purchases are calibrated to a peak effect of 2.5% of GDP and interest rates are kept unchanged for 4 periods.
eξ
4 2
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−2
−5
0 −5
−3 0
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40
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R
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% of GDP
%∆ from ss
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Y
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Private asset purchase
20 Quarters
40
6 4 2 0
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Government bond purchase
Figure 5: Crisis experiment. Reactions to two consecutive unexpected capital quality shocks with gradual private and government asset purchases with the zero-lower bound.
Purchases
π
Y
7 6
4
5
3
4
%∆ from ss
% of GDP
5 4 3
3 2 2 1 1
2 0
1 0
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ib10
i 4
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20 Quarters
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−0.4 20 40 0 20 Quarters Quarters Private asset purchase Government bond purchase 40
−0.4
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ik10−ib10
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Figure 6: Effects of private and government asset purchases following the crisis experiment. The figures plot the differences from a no-policy-response case.
Concluding Remarks • LSAPS reflect CB intermediation and not "money creation" per se. — Effective if limits to arbitrage in private financial intermediation • Like conventional policy, LSAPs stimulate the economy by reducing credit costs — Transmission to real output and inflation very similar — Unlike conventional policy, effective at the ZLB • Variations of LSAPs fit within our framework — "Sterilzed" QE — LTROs (by the ECB) • DSGE models can be adapted to meet current needs of central bankers! 21
