Extensions/Applications of the CSV FrameworkECON 70428: Advanced Macro: Financial Frictions

Eric Sims

University of Notre Dame

Spring 2020

1 / 22

Extensions

I The Bernanke and Gertler (1989), Carlstrom and Fuerst(1997), and Bernanke, Gertler, and Gilchrist (1999) papers arebased on the CSV framework of Townsend (1979)

I Idiosyncratic returns to entrepreneurs and the possibility ofdefault give rise to an external finance premium

I More net worth an entrepreneur has, the better access tocredit it has

I This can generate both persistence (BG 1989 and CF 1997)as well as amplification (BGG 1999) depending on theenvironment and the underlying shocks

I We will focus on two extensions of this framework:

1. Christiano, Motto, and Rostagno (2014): “Risk Shocks”2. Carlstrom, Fuerst, and Paustian (2016): “Optimal Contracts,

Aggregate Risk, and the Financial Accelerator”

2 / 22

Non-Financial Components of the CMR (2014) Model

I The CMR (2014) paper is basically BGG (1999) with a shockto the variance from which ω is drawn

I But it has lots of other bells and whistles that BGG (1999)don’t necessarily include

I Sticky wages (in addition to sticky prices)I Backward price and wage indexationI Variable capital utilizationI “I-dot” adjustment costs (as in Christiano, Eichenbaum, and

Evans 2005)I Habit formation in consumptionI Long-term bondsI Many more types of shocks (preference, investment-specific

technology)

3 / 22

Risk Shocks

I The key thing in the model is time-varying cross-sectional riskfacing entrepreneurs

I Entrepreneur borrows funds from intermediary to financepurchase of new capital, Kt+1

I i.e. it borrows QtKt+1 −Nt at some gross loan rate (the loanis intertemporal)

I It draws a value of ωt . Across entrepreneurs, E[ωt ] = 1

I This gives it capital ωtKt+1

I Enjoys entrepreneur-specific return ωtRkt+1 in t + 1, where

Rkt+1 is the aggregate return to physical capital

4 / 22

Distribution on ωt

I As in CF (1997) and BGG (1999), let:

ln(ωt) ∼ N(µ, σ2t )

I The difference is that σt is time-varying, e.g.:

σt = (1− ρσ)σ + ρσσt−1 + sσεσ,t

I The shock to σt , εσ,t , is called the risk shockI Note this is not aggregate risk, which wouldn’t have first-order

effectsI It is a shock to the cross-sectional variance of ω

5 / 22

Basic Intuition

I An increase in cross-sectional risk increases probability of anentrepreneur drawing a low ω

I Low ωs drive entrepreneurs to default

I Default is costly for lenders

I Hence, lenders demand a higher interest rate on these loans

I But this reduces the overall demand for capital and henceinvestment

I Triggering a recession

6 / 22

Anticipated vs. Unanticipated Risk

I CMR (2014) include both a “conventional” surprise risk shockbut also an anticipated risk shock, i.e. a “news shock”:

σt = (1− ρσ)σ + ρσσt−1 + sσεσ,t + sσ′εσ′,t−l

I Here, l > 0 is the anticipation horizon

I They estimate model and find that risk shocks are important,and drive out importance of marginal efficiency of investmentshocks (Justiniano, Primiceri, and Tambalotti 2010, 2011)

I Why? Risk shock does better job matching business cyclestatistics related to financial variables – in particular creditflows and stock prices (think of Qt as proxying for stockprices)

7 / 22

IRFs to Risk Shock: Unanticipated vs. Anticipated

8 / 22

Risk Shocks in the Carlstrom and Fuerst (1997) Model

I For point of comparison, it is possible to study risk shocks inthe CF (1997) model

I This helps elucidate the core mechanism in CMR (2014), butalso better highlights some of the differences between CF(1997) and the BGG (1999) approach on which CMR (2014)is based

I In particular, in CF (1997) the agency friction applies to thesupply curve for capital (because it applies to entrepreneurswho do investment)

I In BGG (1999) and related approaches the friction applies tothe demand curve for capital

I The capital supply curve is upward-sloping because ofadjustment costs, not the agency friction per se as in CF(1997)

I Entrepreneurs demand capital (from separate capital goodsproducers) to in turn lease to production firms

I Their net worth and the riskiness of their idiosyncratic returnsinfluences how much of a loan they can get, and henceinfluences how much capital they can purchase

9 / 22

CF (1997) IRFs to a Risk Shock

0 10 20-0.4

-0.2

0Y

0 10 20-0.02

0

0.02

0.04

C

0 10 20-2

-1

0I

0 10 20

-0.4

-0.2

0H

0 10 200

0.1

0.2

q

0 10 20-10

-5

0

10-3 r

0 10 200

1

2Net Worth

0 10 200

0.05

0.1

0.15Bankruptcy Rate

0 10 200

0.02

0.04

0.06

Spread

10 / 22

Mechanism of Risk in CF (1997) Model

I An increase in risk:I Increases probability of a low ω drawI Results in tightening credit and less investmentI Higher risk spread and higher bankruptcy rateI But higher price of capital, qt , and hence net worth

I Effectively, an increase in risk reduces the supply of newcapital goods

11 / 22

CF (1997) and Risk: Demand-Supply Interpretation

𝑞𝑡

𝑘𝑡+1

𝑞0

𝑘0

1

𝑘𝑑

𝑘𝑠

𝑘𝑠′

𝑞1

𝑘1

12 / 22

CMR (2014) and Risk: Demand-Supply Interpretation

𝑞𝑡

𝑘𝑡+1

𝑞0

𝑘0

𝑘𝑑

𝑘𝑠

𝑞1

𝑘1

𝑘𝑑′

13 / 22

Discussion

I An increase in risk causes capital supply to contract in CF(1997), resulting in an increase in qt (i.e. countercyclicalstock prices)

I But in CMR (2014), based on BGG (1999), it is the capitaldemand curve that is shifting, so qt falls (i.e. procyclical stockprices, consistent with data)

I You see this same dynamic at work when looking at net worthshocks in CF (1997) compared to BGG (1999) – differentimplications for qt – see next slides

I CMR (2014) refer to the net worth shock as an equity shock.They show, because of general equilibrium considerations, theequity shock has counterfactual implications for the cyclicalityof credit

14 / 22

Net Worth Shock: Countercyclical qt in CF (1997)

0 5 10 15 200

0.05

0.1

Output

0 5 10 15 200

0.005

0.01

Consumption

0 5 10 15 200

0.1

0.2

0.3

0.4Investment

0 5 10 15 200

0.05

0.1

0.15

0.2Hours

0 5 10 15 20

-0.06

-0.04

-0.02

0q

0 5 10 15 20

0

1

2

3

410-3 r

0 5 10 15 200

0.5

1Net Worth

0 5 10 15 20-0.04

-0.03

-0.02

-0.01

0Bankruptcy Rate

0 5 10 15 20-20

-15

-10

-5

010-3 Spread

Net Worth Shock

15 / 22

Net Worth Shock: Procyclical Qt in BGG (1999)

0 5 100

0.5

1

1.5Monetary Shock

0 5 100

0.5

1

Productivity Shock

0 5 100

0.1

0.2

0.3Gov. Spending Shock

0 5 100

0.5

1Net Worth Shock

16 / 22

Optimal Contracts, Aggregate Risk, and the FinancialAccelerator

I Carlstrom, Fuerst, and Paustian (2016, AEJ: Macro), throwsome cold water on the celebrated financial acceleratormechanism of BGG (1999)

I In BGG (1999), the lender’s return on a loan to entrepreneursis predetermined at the riskless, one-period (gross) rate, Rt

I This predetermined return is what drives the financialaccelerator

I Consider a shock that raises the aggregate return to capital(e.g. productivity)

I Because the lender’s return is predetermined, this results in alarge increase in entrepreneurial net worth

I But this increase in net worth lowers agency costs – this resultsin lower leverage, a lower risk spread, more investment, andthe virtuous cycle of the financial accelerator

17 / 22

Privately Optimal Contract

I CFP (2016) show that the BGG (1999) contract is notprivately optimal

I Basically, idea is that contract should be written to provideinsurance to households for aggregate shocks

I The privately optimal contract has debt repayment linked toinnovations in the aggregate return to capital, the level ofhousehold consumption, and entrepreneur’s valuation of networth

I Under the privately optimal contract, the gains from positiveaggregate shocks to the return to capital are, in effect, sharedby the lender and the entrepreneur

I But this dampens the reallocation of net worth toentrepreneurs from these shocks, thus largely eliminating thefinancial accelerator

18 / 22

The Details

I The details get rather messy, and I’m not going to go intothem

I The privately optimal contract and the BGG (1999) contractonly differ in innovations

I The relationship between the risk spread and leverage is thesame

I The difference is net worthI With predetermined lender returns, aggregate shocks cause

sharp movements in entrepreneurial net worthI Which is what gives rise to the financial acceleratorI With the optimal contract, this doesn’t happen, and the

financial accelerator is largely eliminated

19 / 22

Net Worth Shock: Optimal Contract vs. BBG

20 / 22

Productivity Shock: Optimal Contract vs. BBG

21 / 22

Monetary Shock: Optimal Contract vs. BBG

22 / 22