Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence:...
Transcript of Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence:...
![Page 1: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/1.jpg)
Leverage Restrictions in a BusinessCycle Model
Lawrence J. ChristianoDaisuke Ikeda
Disclaimer: The views expressed are those of the authors and do not necessarily reflect
those of the Bank of Japan.
![Page 2: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/2.jpg)
Background
• Increasing interest in the following sorts of questions:
— What restrictions should be placed on bank leverage?— How should those restrictions be varied over the business cycle?— How should monetary policy react to bank leverage, if at all?
![Page 3: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/3.jpg)
Background
• Increasing interest in the following sorts of questions:
— What restrictions should be placed on bank leverage?
— How should those restrictions be varied over the business cycle?— How should monetary policy react to bank leverage, if at all?
![Page 4: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/4.jpg)
Background
• Increasing interest in the following sorts of questions:
— What restrictions should be placed on bank leverage?— How should those restrictions be varied over the business cycle?
— How should monetary policy react to bank leverage, if at all?
![Page 5: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/5.jpg)
Background
• Increasing interest in the following sorts of questions:
— What restrictions should be placed on bank leverage?— How should those restrictions be varied over the business cycle?— How should monetary policy react to bank leverage, if at all?
![Page 6: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/6.jpg)
Background
• Increasing interest in the following sorts of questions:
— What restrictions should be placed on bank leverage?— How should those restrictions be varied over the business cycle?— How should monetary policy react to bank leverage, if at all?
![Page 7: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/7.jpg)
What We Do
• Modify a standard medium-sized DSGE model to include abanking sector.
Assets LiabilitiesLoans and other securities Deposits
Banker net worth
• Job of bankers is to identify and finance good investmentprojects.
— doing this requires exerting costly effort.
• Agency problem between bank and its creditors:— banker effort is not observable.
• Consequence: leverage restrictions on banks generate a verysubstantial welfare gain in steady state.
• Explore some of the dynamic implications of the models.
![Page 8: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/8.jpg)
What We Do• Modify a standard medium-sized DSGE model to include abanking sector.
Assets LiabilitiesLoans and other securities Deposits
Banker net worth
• Job of bankers is to identify and finance good investmentprojects.
— doing this requires exerting costly effort.
• Agency problem between bank and its creditors:— banker effort is not observable.
• Consequence: leverage restrictions on banks generate a verysubstantial welfare gain in steady state.
• Explore some of the dynamic implications of the models.
![Page 9: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/9.jpg)
What We Do• Modify a standard medium-sized DSGE model to include abanking sector.
Assets LiabilitiesLoans and other securities Deposits
Banker net worth
• Job of bankers is to identify and finance good investmentprojects.
— doing this requires exerting costly effort.
• Agency problem between bank and its creditors:— banker effort is not observable.
• Consequence: leverage restrictions on banks generate a verysubstantial welfare gain in steady state.
• Explore some of the dynamic implications of the models.
![Page 10: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/10.jpg)
What We Do• Modify a standard medium-sized DSGE model to include abanking sector.
Assets LiabilitiesLoans and other securities Deposits
Banker net worth
• Job of bankers is to identify and finance good investmentprojects.
— doing this requires exerting costly effort.
• Agency problem between bank and its creditors:— banker effort is not observable.
• Consequence: leverage restrictions on banks generate a verysubstantial welfare gain in steady state.
• Explore some of the dynamic implications of the models.
![Page 11: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/11.jpg)
What We Do• Modify a standard medium-sized DSGE model to include abanking sector.
Assets LiabilitiesLoans and other securities Deposits
Banker net worth
• Job of bankers is to identify and finance good investmentprojects.
— doing this requires exerting costly effort.
• Agency problem between bank and its creditors:— banker effort is not observable.
• Consequence: leverage restrictions on banks generate a verysubstantial welfare gain in steady state.
• Explore some of the dynamic implications of the models.
![Page 12: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/12.jpg)
What We Do• Modify a standard medium-sized DSGE model to include abanking sector.
Assets LiabilitiesLoans and other securities Deposits
Banker net worth
• Job of bankers is to identify and finance good investmentprojects.
— doing this requires exerting costly effort.
• Agency problem between bank and its creditors:— banker effort is not observable.
• Consequence: leverage restrictions on banks generate a verysubstantial welfare gain in steady state.
• Explore some of the dynamic implications of the models.
![Page 13: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/13.jpg)
Outline
• Model— first, without leverage restriction
• observable effort benchmark• unobservable case
— then, with leverage restriction
• Steady state properties of leverage restrictions• Implications for dynamic effects of shocks
![Page 14: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/14.jpg)
Outline
• Model— first, without leverage restriction
• observable effort benchmark• unobservable case
— then, with leverage restriction
• Steady state properties of leverage restrictions
• Implications for dynamic effects of shocks
![Page 15: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/15.jpg)
Outline
• Model— first, without leverage restriction
• observable effort benchmark• unobservable case
— then, with leverage restriction
• Steady state properties of leverage restrictions• Implications for dynamic effects of shocks
![Page 16: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/16.jpg)
Standard Model
Firms
household
Labor market
L
![Page 17: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/17.jpg)
Standard Model
Firms
household
Market for Physical Capital
Labor market
LK
![Page 18: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/18.jpg)
Standard Model
Firms
household
Market for Physical Capital
Labor market
L
C I
K
![Page 19: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/19.jpg)
Standard Model with Banking
Firms
household
Entrepreneurs
Labor market
L K → K, ~F,t
![Page 20: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/20.jpg)
Standard Model with Banking
Firms
household
Entrepreneurs
Labor market
Capital Producers
L
C I
1 − K
Entrepreneurpays everything to the bankand has nothing.
![Page 21: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/21.jpg)
Standard Model with Banking
Firms
household
Entrepreneurs
Labor market
banks
Capital Producers
Mutual funds
![Page 22: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/22.jpg)
Entrepreneurs
• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 23: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/23.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 24: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/24.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 25: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/25.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.
— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 26: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/26.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 27: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/27.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 28: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/28.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 29: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/29.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 30: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/30.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 31: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/31.jpg)
Entrepreneurs• After goods production in period t : Purchase raw capital fromcapital producers, for price Pk′,t.
— entrepreneurs have no resources of their own and must obtainfinancing from banks.
• Entrepreneurs convert raw capital into effective capital.— Some are good at it and some are bad.
• In period t+ 1 :
— entrepreneurs rent capital to goods-producers in competitivemarkets, at rental rate, rt+1.
— after production, sell undepreciated capital back to capitalproducers at price, Pk′,t+1.
— entrepreneurs pay all earnings to bank at end of t+ 1, keepingnothing.
— no agency problems between entrepreneurs and banks.
![Page 32: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/32.jpg)
Earnings of Entrepreneurs
• there are good entrepreneurs and bad entrepreneurs.• bad: 1 unit, raw capital → ebt units, effective capital• good: 1 unit, raw capital → egt units, effective capital
• return to capital enjoyed by entrepreneurs:
Rgt+1 = egtRk
t+1, Rbt+1 = ebtRk
t+1
Rkt+1 ≡
rkt+1Pt+1 + (1− δ)Pk,t+1
Pk′t
• In effect, entrepreneurs operate linear investment technologies,
Rgt+1 > Rb
t+1
![Page 33: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/33.jpg)
Earnings of Entrepreneurs
• there are good entrepreneurs and bad entrepreneurs.
• bad: 1 unit, raw capital → ebt units, effective capital• good: 1 unit, raw capital → egt units, effective capital
• return to capital enjoyed by entrepreneurs:
Rgt+1 = egtRk
t+1, Rbt+1 = ebtRk
t+1
Rkt+1 ≡
rkt+1Pt+1 + (1− δ)Pk,t+1
Pk′t
• In effect, entrepreneurs operate linear investment technologies,
Rgt+1 > Rb
t+1
![Page 34: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/34.jpg)
Earnings of Entrepreneurs
• there are good entrepreneurs and bad entrepreneurs.• bad: 1 unit, raw capital → ebt units, effective capital
• good: 1 unit, raw capital → egt units, effective capital
• return to capital enjoyed by entrepreneurs:
Rgt+1 = egtRk
t+1, Rbt+1 = ebtRk
t+1
Rkt+1 ≡
rkt+1Pt+1 + (1− δ)Pk,t+1
Pk′t
• In effect, entrepreneurs operate linear investment technologies,
Rgt+1 > Rb
t+1
![Page 35: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/35.jpg)
Earnings of Entrepreneurs
• there are good entrepreneurs and bad entrepreneurs.• bad: 1 unit, raw capital → ebt units, effective capital• good: 1 unit, raw capital → egt units, effective capital
• return to capital enjoyed by entrepreneurs:
Rgt+1 = egtRk
t+1, Rbt+1 = ebtRk
t+1
Rkt+1 ≡
rkt+1Pt+1 + (1− δ)Pk,t+1
Pk′t
• In effect, entrepreneurs operate linear investment technologies,
Rgt+1 > Rb
t+1
![Page 36: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/36.jpg)
Earnings of Entrepreneurs
• there are good entrepreneurs and bad entrepreneurs.• bad: 1 unit, raw capital → ebt units, effective capital• good: 1 unit, raw capital → egt units, effective capital
• return to capital enjoyed by entrepreneurs:
Rgt+1 = egtRk
t+1, Rbt+1 = ebtRk
t+1
Rkt+1 ≡
rkt+1Pt+1 + (1− δ)Pk,t+1
Pk′t
• In effect, entrepreneurs operate linear investment technologies,
Rgt+1 > Rb
t+1
![Page 37: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/37.jpg)
Earnings of Entrepreneurs
• there are good entrepreneurs and bad entrepreneurs.• bad: 1 unit, raw capital → ebt units, effective capital• good: 1 unit, raw capital → egt units, effective capital
• return to capital enjoyed by entrepreneurs:
Rgt+1 = egtRk
t+1, Rbt+1 = ebtRk
t+1
Rkt+1 ≡
rkt+1Pt+1 + (1− δ)Pk,t+1
Pk′t
• In effect, entrepreneurs operate linear investment technologies,
Rgt+1 > Rb
t+1
![Page 38: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/38.jpg)
Earnings of Entrepreneurs
• there are good entrepreneurs and bad entrepreneurs.• bad: 1 unit, raw capital → ebt units, effective capital• good: 1 unit, raw capital → egt units, effective capital
• return to capital enjoyed by entrepreneurs:
Rgt+1 = egtRk
t+1, Rbt+1 = ebtRk
t+1
Rkt+1 ≡
rkt+1Pt+1 + (1− δ)Pk,t+1
Pk′t
• In effect, entrepreneurs operate linear investment technologies,
Rgt+1 > Rb
t+1
![Page 39: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/39.jpg)
Bankers
• each has net worth, Nt.• a banker can only invest in one entrepreneur (asset side ofbanker balance sheet is risky).
• by exerting effort, et, a banker finds a good entrepreneur withprobability p :
p (et) = a+ bet
• in t, bankers seek to optimize:
Etλt+1{p (et)[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]+ (1− p (et))
[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]} − 1
2e2
t
• Bankers have a cash constraint:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
![Page 40: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/40.jpg)
Bankers• each has net worth, Nt.
• a banker can only invest in one entrepreneur (asset side ofbanker balance sheet is risky).
• by exerting effort, et, a banker finds a good entrepreneur withprobability p :
p (et) = a+ bet
• in t, bankers seek to optimize:
Etλt+1{p (et)[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]+ (1− p (et))
[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]} − 1
2e2
t
• Bankers have a cash constraint:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
![Page 41: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/41.jpg)
Bankers• each has net worth, Nt.• a banker can only invest in one entrepreneur (asset side ofbanker balance sheet is risky).
• by exerting effort, et, a banker finds a good entrepreneur withprobability p :
p (et) = a+ bet
• in t, bankers seek to optimize:
Etλt+1{p (et)[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]+ (1− p (et))
[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]} − 1
2e2
t
• Bankers have a cash constraint:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
![Page 42: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/42.jpg)
Bankers• each has net worth, Nt.• a banker can only invest in one entrepreneur (asset side ofbanker balance sheet is risky).
• by exerting effort, et, a banker finds a good entrepreneur withprobability p :
p (et) = a+ bet
• in t, bankers seek to optimize:
Etλt+1{p (et)[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]+ (1− p (et))
[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]} − 1
2e2
t
• Bankers have a cash constraint:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
![Page 43: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/43.jpg)
Bankers• each has net worth, Nt.• a banker can only invest in one entrepreneur (asset side ofbanker balance sheet is risky).
• by exerting effort, et, a banker finds a good entrepreneur withprobability p :
p (et) = a+ bet
• in t, bankers seek to optimize:
Etλt+1{p (et)[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]+ (1− p (et))
[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]} − 1
2e2
t
• Bankers have a cash constraint:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
![Page 44: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/44.jpg)
Bankers• each has net worth, Nt.• a banker can only invest in one entrepreneur (asset side ofbanker balance sheet is risky).
• by exerting effort, et, a banker finds a good entrepreneur withprobability p :
p (et) = a+ bet
• in t, bankers seek to optimize:
Etλt+1{p (et)[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]+ (1− p (et))
[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]} − 1
2e2
t
• Bankers have a cash constraint:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
![Page 45: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/45.jpg)
Bankers and their Creditors
• Bankers and Mutual Funds interact in competitive markets forloan contracts: (
dt, et, Rdg,t+1, Rd
b,t+1
)
• Free entry and competition among mutual funds implies:
p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt
• Two scenarios:— banker effort, et, is observed by mutual fund— banker effort, et, is unobserved.
![Page 46: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/46.jpg)
Bankers and their Creditors
• Bankers and Mutual Funds interact in competitive markets forloan contracts: (
dt, et, Rdg,t+1, Rd
b,t+1
)• Free entry and competition among mutual funds implies:
p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt
• Two scenarios:— banker effort, et, is observed by mutual fund— banker effort, et, is unobserved.
![Page 47: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/47.jpg)
Bankers and their Creditors
• Bankers and Mutual Funds interact in competitive markets forloan contracts: (
dt, et, Rdg,t+1, Rd
b,t+1
)• Free entry and competition among mutual funds implies:
p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt
• Two scenarios:— banker effort, et, is observed by mutual fund
— banker effort, et, is unobserved.
![Page 48: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/48.jpg)
Bankers and their Creditors
• Bankers and Mutual Funds interact in competitive markets forloan contracts: (
dt, et, Rdg,t+1, Rd
b,t+1
)• Free entry and competition among mutual funds implies:
p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt
• Two scenarios:— banker effort, et, is observed by mutual fund— banker effort, et, is unobserved.
![Page 49: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/49.jpg)
Observed Effort Benchmark
• Set of contracts available to bankers is the(dt, et, Rd
g,t+1, Rdb,t+1
)’s that satisfy
MF zero profits : p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt,
cash constraint : Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
• Each banker chooses the most preferred contract from themenu.
• Key feature of observed effort equilibrium:
et = Etλt+1p′t (et+1)(
Rgt+1 − Rb
t+1
)(Nt + dt)
![Page 50: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/50.jpg)
Observed Effort Benchmark
• Set of contracts available to bankers is the(dt, et, Rd
g,t+1, Rdb,t+1
)’s that satisfy
MF zero profits : p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt,
cash constraint : Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
• Each banker chooses the most preferred contract from themenu.
• Key feature of observed effort equilibrium:
et = Etλt+1p′t (et+1)(
Rgt+1 − Rb
t+1
)(Nt + dt)
![Page 51: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/51.jpg)
Observed Effort Benchmark
• Set of contracts available to bankers is the(dt, et, Rd
g,t+1, Rdb,t+1
)’s that satisfy
MF zero profits : p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt,
cash constraint : Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
• Each banker chooses the most preferred contract from themenu.
• Key feature of observed effort equilibrium:
et = Etλt+1p′t (et+1)(
Rgt+1 − Rb
t+1
)(Nt + dt)
![Page 52: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/52.jpg)
Unobserved Effort• In this case, banker always sets et to its privately optimal level,whatever et is specified in the loan contract:
incentive : et = Etλt+1p′t (et) [(
Rgt+1 − Rb
t+1
)(Nt + dt)
−(
Rdg,t+1 − Rd
b,t+1
)dt].
• Set of contracts available to bankers is the(dt, et, Rd
g,t+1, Rdb,t+1
)’s that satisfy ‘incentive’in addition to:
MF zero profits : p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt,
cash constraint : Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
• Two factors can make et ineffi ciently low:— Rd
g,t+1 > Rdb,t+1
— Nt + dt low.
![Page 53: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/53.jpg)
Unobserved Effort• In this case, banker always sets et to its privately optimal level,whatever et is specified in the loan contract:
incentive : et = Etλt+1p′t (et) [(
Rgt+1 − Rb
t+1
)(Nt + dt)
−(
Rdg,t+1 − Rd
b,t+1
)dt].
• Set of contracts available to bankers is the(dt, et, Rd
g,t+1, Rdb,t+1
)’s that satisfy ‘incentive’in addition to:
MF zero profits : p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt,
cash constraint : Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
• Two factors can make et ineffi ciently low:— Rd
g,t+1 > Rdb,t+1
— Nt + dt low.
![Page 54: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/54.jpg)
Unobserved Effort• In this case, banker always sets et to its privately optimal level,whatever et is specified in the loan contract:
incentive : et = Etλt+1p′t (et) [(
Rgt+1 − Rb
t+1
)(Nt + dt)
−(
Rdg,t+1 − Rd
b,t+1
)dt].
• Set of contracts available to bankers is the(dt, et, Rd
g,t+1, Rdb,t+1
)’s that satisfy ‘incentive’in addition to:
MF zero profits : p (et)Rdg,t+1 + (1− p (et))Rd
b,t+1 = Rt,
cash constraint : Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt
• Two factors can make et ineffi ciently low:— Rd
g,t+1 > Rdb,t+1
— Nt + dt low.
![Page 55: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/55.jpg)
Law of Motion of Net Worth• Bankers live in a large representative household, with workers(as in Gertler-Karadi, Gertler-Kiyotaki).— Bankers pool their net worth at the end of each period (weavoid worrying about banker heterogeneity)
• Law of motion of banker net worth
Nt+1 = γt+1{p (et)
profits when bank assets good︷ ︸︸ ︷[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]
+ (1− p (et))
profits when bank assets are bad︷ ︸︸ ︷[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]}
+
lump sum transfer, households to their bankers︷︸︸︷Tt+1
![Page 56: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/56.jpg)
Law of Motion of Net Worth• Bankers live in a large representative household, with workers(as in Gertler-Karadi, Gertler-Kiyotaki).— Bankers pool their net worth at the end of each period (weavoid worrying about banker heterogeneity)
• Law of motion of banker net worth
Nt+1 = γt+1{p (et)
profits when bank assets good︷ ︸︸ ︷[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]
+ (1− p (et))
profits when bank assets are bad︷ ︸︸ ︷[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]}
+
lump sum transfer, households to their bankers︷︸︸︷Tt+1
![Page 57: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/57.jpg)
Law of Motion of Net Worth• Bankers live in a large representative household, with workers(as in Gertler-Karadi, Gertler-Kiyotaki).— Bankers pool their net worth at the end of each period (weavoid worrying about banker heterogeneity)
• Law of motion of banker net worth
Nt+1 = γt+1{p (et)
profits when bank assets good︷ ︸︸ ︷[Rg
t+1 (Nt + dt)− Rdg,t+1dt
]
+ (1− p (et))
profits when bank assets are bad︷ ︸︸ ︷[Rb
t+1 (Nt + dt)− Rdb,t+1dt
]}
+
lump sum transfer, households to their bankers︷︸︸︷Tt+1
![Page 58: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/58.jpg)
• The model assumes that when bankers want funds, issuing equity is not an option.
2006 2007 2008 2009 2010 2011
100
200
300
400
500
600
700
800
billio
ns o
f dol
lars
Borrowing by Private Depository Institutions (Table F.109, Flow of Funds)
open market paper, bonds, other loans, deposits
2006 2007 2008 2009 2010 2011
7
8
9
10
11
12
billio
ns o
f dol
lars
Equity as a source of funds, Private Depository Institutions (F.109, F of F)
This shows how major debt instruments were used at private depository institutions in the wake of the crisis.
![Page 59: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/59.jpg)
• The model assumes that when bankers want funds, issuing equity is not an option.
2006 2007 2008 2009 2010 2011
100
200
300
400
500
600
700
800
billio
ns o
f dol
lars
Borrowing by Private Depository Institutions (Table F.109, Flow of Funds)
open market paper, bonds, other loans, deposits
2006 2007 2008 2009 2010 2011
7
8
9
10
11
12
billio
ns o
f dol
lars
Equity as a source of funds, Private Depository Institutions (F.109, F of F)
![Page 60: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/60.jpg)
‘Crisis’
• Suppose something makes banker net worth, Nt, drop.
• For given dt, bank cash constraint gets tighter:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt.
• So, Rdb,t+1 has to be low
— when Nt is low, banks with bad assets cannot cover their ownlosses and creditors must share in losses.
— then, creditors require Rdg,t+1 high
• So, interest rate spread, Rdg,t+1 − Rt, high, banker effort low.
• Banks get riskier (cross sectional mean return down, standarddeviation up).
![Page 61: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/61.jpg)
‘Crisis’
• Suppose something makes banker net worth, Nt, drop.• For given dt, bank cash constraint gets tighter:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt.
• So, Rdb,t+1 has to be low
— when Nt is low, banks with bad assets cannot cover their ownlosses and creditors must share in losses.
— then, creditors require Rdg,t+1 high
• So, interest rate spread, Rdg,t+1 − Rt, high, banker effort low.
• Banks get riskier (cross sectional mean return down, standarddeviation up).
![Page 62: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/62.jpg)
‘Crisis’
• Suppose something makes banker net worth, Nt, drop.• For given dt, bank cash constraint gets tighter:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt.
• So, Rdb,t+1 has to be low
— when Nt is low, banks with bad assets cannot cover their ownlosses and creditors must share in losses.
— then, creditors require Rdg,t+1 high
• So, interest rate spread, Rdg,t+1 − Rt, high, banker effort low.
• Banks get riskier (cross sectional mean return down, standarddeviation up).
![Page 63: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/63.jpg)
‘Crisis’
• Suppose something makes banker net worth, Nt, drop.• For given dt, bank cash constraint gets tighter:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt.
• So, Rdb,t+1 has to be low
— when Nt is low, banks with bad assets cannot cover their ownlosses and creditors must share in losses.
— then, creditors require Rdg,t+1 high
• So, interest rate spread, Rdg,t+1 − Rt, high, banker effort low.
• Banks get riskier (cross sectional mean return down, standarddeviation up).
![Page 64: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/64.jpg)
‘Crisis’
• Suppose something makes banker net worth, Nt, drop.• For given dt, bank cash constraint gets tighter:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt.
• So, Rdb,t+1 has to be low
— when Nt is low, banks with bad assets cannot cover their ownlosses and creditors must share in losses.
— then, creditors require Rdg,t+1 high
• So, interest rate spread, Rdg,t+1 − Rt, high, banker effort low.
• Banks get riskier (cross sectional mean return down, standarddeviation up).
![Page 65: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/65.jpg)
‘Crisis’
• Suppose something makes banker net worth, Nt, drop.• For given dt, bank cash constraint gets tighter:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt.
• So, Rdb,t+1 has to be low
— when Nt is low, banks with bad assets cannot cover their ownlosses and creditors must share in losses.
— then, creditors require Rdg,t+1 high
• So, interest rate spread, Rdg,t+1 − Rt, high, banker effort low.
• Banks get riskier (cross sectional mean return down, standarddeviation up).
![Page 66: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/66.jpg)
‘Crisis’
• Suppose something makes banker net worth, Nt, drop.• For given dt, bank cash constraint gets tighter:
Rbt+1 (Nt + dt) ≥ Rd
b,t+1dt.
• So, Rdb,t+1 has to be low
— when Nt is low, banks with bad assets cannot cover their ownlosses and creditors must share in losses.
— then, creditors require Rdg,t+1 high
• So, interest rate spread, Rdg,t+1 − Rt, high, banker effort low.
• Banks get riskier (cross sectional mean return down, standarddeviation up).
![Page 67: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/67.jpg)
Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
![Page 68: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/68.jpg)
Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?
— With less dt, banks with bad assets more able to cover losses• interest rate spread, Rd
b − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
![Page 69: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/69.jpg)
Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
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Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
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Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,
• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
![Page 72: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/72.jpg)
Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
![Page 73: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/73.jpg)
Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists
• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
![Page 74: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/74.jpg)
Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
![Page 75: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/75.jpg)
Leverage Restrictions• Banks face the following restriction:
Lt ≥Nt + dt
Nt.
• What is the consequence of this restriction?— With less dt, banks with bad assets more able to cover losses
• interest rate spread, Rdb − R, falls, so banker effort rises.
— Second effect of leverage restriction,• leverage restriction in effect implements collusion amongbankers
• allows them to behave as monopsonists• make profits on demand deposits....lots of profits:
[p (et)
(Rg
t+1 − Rdg,t+1
)+ (1− p (et))
(Rb
t+1 − Rdb,t+1
)] big︷︸︸︷dtNt
• makes Nt grow, offseting incentive effects of decline in dt.
![Page 76: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/76.jpg)
Macro Model
• Sticky wages and prices• Investment adjustment costs• Habit persistence in consumption• Monetary policy rule
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Calibration targets
Table 2: Steady state calibration targets for baseline modelVariable meaning variable name magnitude
Cross-sectional standard deviation of quarterly non-financial firm equity returns sb 0.20Fnancial firm interest rate spreads (APR) 400Rg
d − R 0.60Financial firm leverage L 20.00Allocative efficiency of the banking system peeg 1 − peeb 1Profits of intermediate good producers (controled by fixed cost, ) 0Government consumption relative to GDP (controlled by g) 0.20Growth rate of per capita GDP (APR) 400z
∗ − 1 1.65Rate of decline in real price of capital (APR) 400 − 1 1.69
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Data behind calibration targets
Q3‐1962 Q1‐1968 Q2‐1973 Q4‐1978 Q1‐1984 Q2‐1989 Q4‐1994 Q1‐2000 Q3‐2005 Q4‐20100
0.1
0.2
0.3
0.4
quarterly data
Figure 1: Cross-section standard deviation financial firm quarterly return on equity, HP-filtered US real GDP
-0.1
-0.05
0
0.05
0.1
Cross‐section volatility (left scale)
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Data behind calibration targets
Q3‐1962 Q1‐1968 Q2‐1973 Q4‐1978 Q1‐1984 Q2‐1989 Q4‐1994 Q1‐2000 Q3‐2005 Q4‐20100
0.1
0.2
0.3
0.4
quarterly data
Figure 1: Cross-section standard deviation financial firm quarterly return on equity, HP-filtered US real GDP
-0.1
-0.05
0
0.05
0.1
Cross‐section volatility (left scale)
HP‐filtered GDP (right scale)
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Parameter Values
Table 1: Baseline Model Parameter ValuesMeaning Name ValuePanel A: financial parameters
return parameter, bad entrepreneur b -0.09return parameter, good entrepreneur g 0.00constant, effort function ā 0.83slope, effort function b 0.30lump-sum transfer from households to bankers T 0.38fraction of banker net worth that stays with bankers 0.85
Panel B: Parameters that do not affect steady statesteady state inflation (APR) 400 − 1 2.40Taylor rule weight on inflation 1.50Taylor rule weight on output growth Δy 0.50smoothing parameter in Taylor rule p 0.80curvature on investment adjustment costs S′′ 5.00Calvo sticky price parameter p 0.75Calvo sticky wage parameter w 0.75
Panel C: Nonfinancial parameterssteady state gdp growth (APR) z∗ 1.65steady state rate of decline in investment good price (APR) 1.69capital depreciation rate 0.03production fixed cost 0.89capital share 0.40steady state markup, intermediate good producers f 1.20habit parameter bu 0.74household discount rate 100−4 − 1 0.52steady state markup, workers w 1.05Frisch labor supply elasticity 1/L 1.00weight on labor disutility L 1.00steady state scaled government spending g 0.89
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Steady State Calculations
• Next study steady state impact of leverage— Quantify role of hidden effort in the analysis (essential!)
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Table 3: Steady State Properties of the ModelVariable meaning Variable name Unobserved Effort Observed Effort
Leverage Restriction Leverage Restrictionnon-binding binding non-binding binding
Spread 400Rgd − R 0.600 0.211 NA NA
scaled consumption c 1.84 1.88 2.01 1.95labor h 1.18 1.16 1.15 1.14scaled capital stock k 51.52 51.40 59.75 53.86bank assets N d 51.52 51.31 59.55 53.68bank net worth N 2.58 3.02 2.58 3.16bank deposits d 48.94 48.29 56.98 50.52bank leverage N d/N 20.00 17.00 23.12 17.00
bank return on equity (APR) 400petRt1
g 1−petRt1b Ntdt−Rtdt
Nt− 1 4.59 14.96 4.59 17.63
fraction of firms with good balance sheets pe 0.962 0.982 1.000 1.000Benefit of leverage (in c units) 100 NA 1.19 NA -2.70Benefit of making effort observable (in c units) 100 NA NA 6.11 2.03Note: (i) NA, not applicable, indicates that the number is not defined. (ii) All calculations based on a single set of parameter values, reported in Table 1.
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Table 3: Steady State Properties of the ModelVariable meaning Variable name Unobserved Effort Observed Effort
Leverage Restriction Leverage Restrictionnon-binding binding non-binding binding
Spread 400Rgd − R 0.600 0.211 NA NA
scaled consumption c 1.84 1.88 2.01 1.95labor h 1.18 1.16 1.15 1.14scaled capital stock k 51.52 51.40 59.75 53.86bank assets N d 51.52 51.31 59.55 53.68bank net worth N 2.58 3.02 2.58 3.16bank deposits d 48.94 48.29 56.98 50.52bank leverage N d/N 20.00 17.00 23.12 17.00
bank return on equity (APR) 400petRt1
g 1−petRt1b Ntdt−Rtdt
Nt− 1 4.59 14.96 4.59 17.63
fraction of firms with good balance sheets pe 0.962 0.982 1.000 1.000Benefit of leverage (in c units) 100 NA 1.19 NA -2.70Benefit of making effort observable (in c units) 100 NA NA 6.11 2.03Note: (i) NA, not applicable, indicates that the number is not defined. (ii) All calculations based on a single set of parameter values, reported in Table 1.
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Table 3: Steady State Properties of the ModelVariable meaning Variable name Unobserved Effort Observed Effort
Leverage Restriction Leverage Restrictionnon-binding binding non-binding binding
Spread 400Rgd − R 0.600 0.211 NA NA
scaled consumption c 1.84 1.88 2.01 1.95labor h 1.18 1.16 1.15 1.14scaled capital stock k 51.52 51.40 59.75 53.86bank assets N d 51.52 51.31 59.55 53.68bank net worth N 2.58 3.02 2.58 3.16bank deposits d 48.94 48.29 56.98 50.52bank leverage N d/N 20.00 17.00 23.12 17.00
bank return on equity (APR) 400petRt1
g 1−petRt1b Ntdt−Rtdt
Nt− 1 4.59 14.96 4.59 17.63
fraction of firms with good balance sheets pe 0.962 0.982 1.000 1.000Benefit of leverage (in c units) 100 NA 1.19 NA -2.70Benefit of making effort observable (in c units) 100 NA NA 6.11 2.03Note: (i) NA, not applicable, indicates that the number is not defined. (ii) All calculations based on a single set of parameter values, reported in Table 1.
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Table 3: Steady State Properties of the ModelVariable meaning Variable name Unobserved Effort Observed Effort
Leverage Restriction Leverage Restrictionnon-binding binding non-binding binding
Spread 400Rgd − R 0.600 0.211 NA NA
scaled consumption c 1.84 1.88 2.01 1.95labor h 1.18 1.16 1.15 1.14scaled capital stock k 51.52 51.40 59.75 53.86bank assets N d 51.52 51.31 59.55 53.68bank net worth N 2.58 3.02 2.58 3.16bank deposits d 48.94 48.29 56.98 50.52bank leverage N d/N 20.00 17.00 23.12 17.00
bank return on equity (APR) 400petRt1
g 1−petRt1b Ntdt−Rtdt
Nt− 1 4.59 14.96 4.59 17.63
fraction of firms with good balance sheets pe 0.962 0.982 1.000 1.000Benefit of leverage (in c units) 100 NA 1.19 NA -2.70Benefit of making effort observable (in c units) 100 NA NA 6.11 2.03Note: (i) NA, not applicable, indicates that the number is not defined. (ii) All calculations based on a single set of parameter values, reported in Table 1.
Making effort observable makes things a lot better, equivalent to a 6% permanent jump in consumption!Interestingly, leverage goes up.
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Table 3: Steady State Properties of the ModelVariable meaning Variable name Unobserved Effort Observed Effort
Leverage Restriction Leverage Restrictionnon-binding binding non-binding binding
Spread 400Rgd − R 0.600 0.211 NA NA
scaled consumption c 1.84 1.88 2.01 1.95labor h 1.18 1.16 1.15 1.14scaled capital stock k 51.52 51.40 59.75 53.86bank assets N d 51.52 51.31 59.55 53.68bank net worth N 2.58 3.02 2.58 3.16bank deposits d 48.94 48.29 56.98 50.52bank leverage N d/N 20.00 17.00 23.12 17.00
bank return on equity (APR) 400petRt1
g 1−petRt1b Ntdt−Rtdt
Nt− 1 4.59 14.96 4.59 17.63
fraction of firms with good balance sheets pe 0.962 0.982 1.000 1.000Benefit of leverage (in c units) 100 NA 1.19 NA -2.70Benefit of making effort observable (in c units) 100 NA NA 6.11 2.03Note: (i) NA, not applicable, indicates that the number is not defined. (ii) All calculations based on a single set of parameter values, reported in Table 1.
Making effort observable makes things a lot better, equivalent to a 6% permanent jump in consumption!Interestingly, leverage goes up.
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Table 3: Steady State Properties of the ModelVariable meaning Variable name Unobserved Effort Observed Effort
Leverage Restriction Leverage Restrictionnon-binding binding non-binding binding
Spread 400Rgd − R 0.600 0.211 NA NA
scaled consumption c 1.84 1.88 2.01 1.95labor h 1.18 1.16 1.15 1.14scaled capital stock k 51.52 51.40 59.75 53.86bank assets N d 51.52 51.31 59.55 53.68bank net worth N 2.58 3.02 2.58 3.16bank deposits d 48.94 48.29 56.98 50.52bank leverage N d/N 20.00 17.00 23.12 17.00
bank return on equity (APR) 400petRt1
g 1−petRt1b Ntdt−Rtdt
Nt− 1 4.59 14.96 4.59 17.63
fraction of firms with good balance sheets pe 0.962 0.982 1.000 1.000Benefit of leverage (in c units) 100 NA 1.19 NA -2.70Benefit of making effort observable (in c units) 100 NA NA 6.11 2.03Note: (i) NA, not applicable, indicates that the number is not defined. (ii) All calculations based on a single set of parameter values, reported in Table 1.
Cut in leverage in the unobserved effort economy moves things towards observed effort.
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Table 3: Steady State Properties of the ModelVariable meaning Variable name Unobserved Effort Observed Effort
Leverage Restriction Leverage Restrictionnon-binding binding non-binding binding
Spread 400Rgd − R 0.600 0.211 NA NA
scaled consumption c 1.84 1.88 2.01 1.95labor h 1.18 1.16 1.15 1.14scaled capital stock k 51.52 51.40 59.75 53.86bank assets N d 51.52 51.31 59.55 53.68bank net worth N 2.58 3.02 2.58 3.16bank deposits d 48.94 48.29 56.98 50.52bank leverage N d/N 20.00 17.00 23.12 17.00
bank return on equity (APR) 400petRt1
g 1−petRt1b Ntdt−Rtdt
Nt− 1 4.59 14.96 4.59 17.63
fraction of firms with good balance sheets pe 0.962 0.982 1.000 1.000Benefit of leverage (in c units) 100 NA 1.19 NA -2.70Benefit of making effort observable (in c units) 100 NA NA 6.11 2.03Note: (i) NA, not applicable, indicates that the number is not defined. (ii) All calculations based on a single set of parameter values, reported in Table 1.
Hidden effort assumption is essential. Otherwise, leverage restriction reduces utility.
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Dynamics
• Here, we consider the dynamic effects of two shocks— shock to monetary policy— lump sum shock to net worth
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5 10 15
-0.3
-0.25
-0.2
-0.15
GDP
% d
ev fr
om s
s
5 10 15-0.35
-0.3
-0.25
-0.2
-0.15
Consumption
% d
ev fr
om s
s
5 10 15
-0.5
-0.4
-0.3
Investment
% d
ev fr
om s
s
5 10 152.322.342.362.382.4
2.422.44
Inflation (APR)
5 10 15
4.6
4.65
4.7
4.75
Risk free rate (APR)
leve
l
5 10 15-0.1
0
0.1
0.2
Interest rate spread (APR)
5 10 15
0.956
0.958
0.96
0.962
Prob of success
leve
l
5 10 15
0.2
0.205
0.21
0.215
0.22
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
Leverage (N+d)/N
leve
l
5 10 15
-6
-4
-2
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Contractionary M policy shock:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
Rt 0.80Rt−1 1 − 0.801.5 t1 0.5gy,t tp
0p 25 annual basis points
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5 10 15
-0.3
-0.25
-0.2
-0.15
GDP
% d
ev fr
om s
s
5 10 15-0.35
-0.3
-0.25
-0.2
-0.15
Consumption
% d
ev fr
om s
s
5 10 15
-0.5
-0.4
-0.3
Investment
% d
ev fr
om s
s
5 10 152.322.342.362.382.4
2.422.44
Inflation (APR)
5 10 15
4.6
4.65
4.7
4.75
Risk free rate (APR)
leve
l
5 10 15-0.1
0
0.1
0.2
Interest rate spread (APR)
5 10 15
0.956
0.958
0.96
0.962
Prob of success
leve
l
5 10 15
0.2
0.205
0.21
0.215
0.22
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
Leverage (N+d)/N
leve
l
5 10 15
-6
-4
-2
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Contractionary M policy shock:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
Rt 0.80Rt−1 1 − 0.801.5 t1 0.5gy,t tp
0p 25 annual basis points
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5 10 15
-0.3
-0.25
-0.2
-0.15
GDP
% d
ev fr
om s
s
5 10 15-0.35
-0.3
-0.25
-0.2
-0.15
Consumption
% d
ev fr
om s
s
5 10 15
-0.5
-0.4
-0.3
Investment
% d
ev fr
om s
s
5 10 152.322.342.362.382.4
2.422.44
Inflation (APR)
5 10 15
4.6
4.65
4.7
4.75
Risk free rate (APR)
leve
l
5 10 15-0.1
0
0.1
0.2
Interest rate spread (APR)
5 10 15
0.956
0.958
0.96
0.962
Prob of success
leve
l
5 10 15
0.2
0.205
0.21
0.215
0.22
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
Leverage (N+d)/N
leve
l
5 10 15
-6
-4
-2
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Contractionary M policy shock:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
Rt 0.80Rt−1 1 − 0.801.5 t1 0.5gy,t tp
0p 25 annual basis points
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5 10 15
-0.3
-0.25
-0.2
-0.15
GDP
% d
ev fr
om s
s
5 10 15-0.35
-0.3
-0.25
-0.2
-0.15
Consumption
% d
ev fr
om s
s
5 10 15
-0.5
-0.4
-0.3
Investment
% d
ev fr
om s
s
5 10 152.322.342.362.382.4
2.422.44
Inflation (APR)
5 10 15
4.6
4.65
4.7
4.75
Risk free rate (APR)
leve
l
5 10 15-0.1
0
0.1
0.2
Interest rate spread (APR)
5 10 15
0.956
0.958
0.96
0.962
Prob of success
leve
l
5 10 15
0.2
0.205
0.21
0.215
0.22
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
Leverage (N+d)/N
leve
l
5 10 15
-6
-4
-2
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Contractionary M policy shock:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
Rt 0.80Rt−1 1 − 0.801.5 t1 0.5gy,t tp
0p 25 annual basis points
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5 10 15
-0.8
-0.6
-0.4
GDP
% d
ev fr
om s
s
5 10 15
-1
-0.8
-0.6
-0.4
-0.2Consumption
% d
ev fr
om s
s
5 10 15
-1.2
-1
-0.8
-0.6
-0.4Investment
% d
ev fr
om s
s
5 10 15
2.1
2.2
2.3
2.4
Inflation (APR)
5 10 154.2
4.3
4.4
4.5
Risk free rate (APR)
leve
l
5 10 15
0.15
0.2
0.25
0.3
0.35
Interest rate spread (APR)
5 10 15
0.9520.9540.956
0.9580.96
0.962Prob of success
leve
l
5 10 150.2
0.21
0.22
0.23
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
22
Leverage (N+d)/N
leve
l
5 10 15-11
-10
-9
-8
-7
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Negative shock to bank net worth:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
log TtT 0.95 log Tt−1
T tT
0T −0.10
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5 10 15
-0.8
-0.6
-0.4
GDP
% d
ev fr
om s
s
5 10 15
-1
-0.8
-0.6
-0.4
-0.2Consumption
% d
ev fr
om s
s
5 10 15
-1.2
-1
-0.8
-0.6
-0.4Investment
% d
ev fr
om s
s
5 10 15
2.1
2.2
2.3
2.4
Inflation (APR)
5 10 154.2
4.3
4.4
4.5
Risk free rate (APR)
leve
l
5 10 15
0.15
0.2
0.25
0.3
0.35
Interest rate spread (APR)
5 10 15
0.9520.9540.956
0.9580.96
0.962Prob of success
leve
l
5 10 150.2
0.21
0.22
0.23
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
22
Leverage (N+d)/N
leve
l
5 10 15-11
-10
-9
-8
-7
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Negative shock to bank net worth:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
log TtT 0.95 log Tt−1
T tT
0T −0.10
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5 10 15
-0.8
-0.6
-0.4
GDP
% d
ev fr
om s
s
5 10 15
-1
-0.8
-0.6
-0.4
-0.2Consumption
% d
ev fr
om s
s
5 10 15
-1.2
-1
-0.8
-0.6
-0.4Investment
% d
ev fr
om s
s
5 10 15
2.1
2.2
2.3
2.4
Inflation (APR)
5 10 154.2
4.3
4.4
4.5
Risk free rate (APR)
leve
l
5 10 15
0.15
0.2
0.25
0.3
0.35
Interest rate spread (APR)
5 10 15
0.9520.9540.956
0.9580.96
0.962Prob of success
leve
l
5 10 150.2
0.21
0.22
0.23
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
22
Leverage (N+d)/N
leve
l
5 10 15-11
-10
-9
-8
-7
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Negative shock to bank net worth:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
log TtT 0.95 log Tt−1
T tT
0T −0.10
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5 10 15
-0.8
-0.6
-0.4
GDP
% d
ev fr
om s
s
5 10 15
-1
-0.8
-0.6
-0.4
-0.2Consumption
% d
ev fr
om s
s
5 10 15
-1.2
-1
-0.8
-0.6
-0.4Investment
% d
ev fr
om s
s
5 10 15
2.1
2.2
2.3
2.4
Inflation (APR)
5 10 154.2
4.3
4.4
4.5
Risk free rate (APR)
leve
l
5 10 15
0.15
0.2
0.25
0.3
0.35
Interest rate spread (APR)
5 10 15
0.9520.9540.956
0.9580.96
0.962Prob of success
leve
l
5 10 150.2
0.21
0.22
0.23
Cross-section std dev,Bank return on equity
quar
terly
, lev
el
5 10 15
20
20.5
21
21.5
22
Leverage (N+d)/N
leve
l
5 10 15-11
-10
-9
-8
-7
Bank net worth (N)
% p
oint
s de
v fro
m s
s
Negative shock to bank net worth:fall in:
c, i, y, bank net worth, N,inflation
Rise in:leveragecross‐sectional dispersion of bank performance
log TtT 0.95 log Tt−1
T tT
0T −0.10
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Cyclicality of Leverage
• The model appears to imply countercyclical leverage.
• We took data from the Flow of Funds accounts to measureleverage.
— Problem: only report financial assets (af ) and liabilities (lf )
Lf =af
af − lf
— This measure of leverage can be negative or gigantic.
• We took measures of Lf for three components of financialbusiness, over a period for which Lf does not behave strangely,the 2000s.
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Cyclicality of Leverage
• The model appears to imply countercyclical leverage.• We took data from the Flow of Funds accounts to measureleverage.
— Problem: only report financial assets (af ) and liabilities (lf )
Lf =af
af − lf
— This measure of leverage can be negative or gigantic.
• We took measures of Lf for three components of financialbusiness, over a period for which Lf does not behave strangely,the 2000s.
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Cyclicality of Leverage
• The model appears to imply countercyclical leverage.• We took data from the Flow of Funds accounts to measureleverage.
— Problem: only report financial assets (af ) and liabilities (lf )
Lf =af
af − lf
— This measure of leverage can be negative or gigantic.
• We took measures of Lf for three components of financialbusiness, over a period for which Lf does not behave strangely,the 2000s.
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Cyclicality of Leverage
• The model appears to imply countercyclical leverage.• We took data from the Flow of Funds accounts to measureleverage.
— Problem: only report financial assets (af ) and liabilities (lf )
Lf =af
af − lf
— This measure of leverage can be negative or gigantic.
• We took measures of Lf for three components of financialbusiness, over a period for which Lf does not behave strangely,the 2000s.
![Page 102: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/102.jpg)
Cyclicality of Leverage
• The model appears to imply countercyclical leverage.• We took data from the Flow of Funds accounts to measureleverage.
— Problem: only report financial assets (af ) and liabilities (lf )
Lf =af
af − lf
— This measure of leverage can be negative or gigantic.
• We took measures of Lf for three components of financialbusiness, over a period for which Lf does not behave strangely,the 2000s.
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1975 1980 1985 1990 1995 2000 2005 2010-15
-10
-5
0
5
10
15
Holding Companies (L.128)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010
-20
0
20
40
60
80
100liability growth - S&P500 growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
Private Depository Institutions (L.109)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010
-20
0
20
40
60
80
100liability growth - S&P500 growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-8
-6
-4
-2
0
2
4
6
8
10
Security Brokers and Dealers (L.127)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-40
-30
-20
-10
0
10
20
30
40
50liability growth - S&P500 growth (yoy)
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1975 1980 1985 1990 1995 2000 2005 2010-15
-10
-5
0
5
10
15
Holding Companies (L.128)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010
-20
0
20
40
60
80
100liability growth - S&P500 growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
Private Depository Institutions (L.109)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010
-20
0
20
40
60
80
100liability growth - S&P500 growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-8
-6
-4
-2
0
2
4
6
8
10
Security Brokers and Dealers (L.127)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-40
-30
-20
-10
0
10
20
30
40
50liability growth - S&P500 growth (yoy)
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1975 1980 1985 1990 1995 2000 2005 2010-15
-10
-5
0
5
10
15
Holding Companies (L.128)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010
-20
0
20
40
60
80
100liability growth - S&P500 growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
Private Depository Institutions (L.109)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010
-20
0
20
40
60
80
100liability growth - S&P500 growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-8
-6
-4
-2
0
2
4
6
8
10
Security Brokers and Dealers (L.127)liability growth - asset growth (yoy)
1975 1980 1985 1990 1995 2000 2005 2010-40
-30
-20
-10
0
10
20
30
40
50liability growth - S&P500 growth (yoy)
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Conclusion
• Described a model in which there is a problem that is mitigatedby the introduction of leverage restrictions.
• Described some loose tests of the model by looking at itsdynamic implications.
• Plan to study implications of the model for a broader class ofleverage rules.
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Bankers and their Creditors
Assets LiabilitiesLoans and other securities Deposits, dtNt + dt Banker net worth, Nt
• No agency problems on asset side of bank balance sheet.• Problems are on liability side.• Bankers receive credit, dt, from mutual funds.
— Mutual funds deal with households.
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Bankers and their Creditors
Assets LiabilitiesLoans and other securities Deposits, dtNt + dt Banker net worth, Nt
• No agency problems on asset side of bank balance sheet.
• Problems are on liability side.• Bankers receive credit, dt, from mutual funds.
— Mutual funds deal with households.
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Bankers and their Creditors
Assets LiabilitiesLoans and other securities Deposits, dtNt + dt Banker net worth, Nt
• No agency problems on asset side of bank balance sheet.• Problems are on liability side.
• Bankers receive credit, dt, from mutual funds.
— Mutual funds deal with households.
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Bankers and their Creditors
Assets LiabilitiesLoans and other securities Deposits, dtNt + dt Banker net worth, Nt
• No agency problems on asset side of bank balance sheet.• Problems are on liability side.• Bankers receive credit, dt, from mutual funds.
— Mutual funds deal with households.
![Page 111: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/111.jpg)
Bankers and their Creditors
Assets LiabilitiesLoans and other securities Deposits, dtNt + dt Banker net worth, Nt
• No agency problems on asset side of bank balance sheet.• Problems are on liability side.• Bankers receive credit, dt, from mutual funds.
— Mutual funds deal with households.
![Page 112: Leverage Restrictions in a Business Cycle Modellchrist/course/IMF_Laxton_20… · Consequence: leverage restrictions on banks generate a very substantial welfare gain in steady state.](https://reader033.fdocuments.us/reader033/viewer/2022050106/5f44abd49c03152c1b3ab803/html5/thumbnails/112.jpg)
Risky Bankers Funded By Mutual Funds
Diversified,competitivemutual funds
Household
banker
banker
banker
banker
Household
Household
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Let =
aft
aft − lft
dLet =
daft
af − lf− af
t(af − lf
)2
(daf
t − dlft)
=af
af − lfaf
t −af
t(af − lf
)2
(af af
t − lf lft)
Let = af
t −1
af − lf(
af aft − lf lft
)=
lf
af − lf(
lft − aft
)
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Lt =anf
t + aft
anft + af
t − lft
LLt =anf
anf + af − lfanf
t +af
anf + af − lfaf
t
− anf + af(anf + af − lf
)2
(anf anf
t + af aft − lf lft
)Lt =
anf
anf + af anft +
af
anf + af aft −
1anf + af − lf
(anf anf
t + af aft − lf lft
)=
[anf
anf + af −anf
anf + af − lf
]anf
t +
[af
anf + af −af
anf + af − lf
]af
t +1
anf + af − lflf lft
=
[anf
anf + af −anf
anf + af − lf
]anf
t −lf(
anf + af − lf) (
anf + af)af af
t +1
anf + af − lflf lft
= − lf anf(anf + af
) (anf + af − lf
) anft −
lf af(anf + af
) (anf + af − lf
) aft +
lf
anf + af − lflft