Macroeconomics and financing frictions, [lectures 2 and 3].

Part 1: crisis narrative and the thieving banker model

Lecture to MSc Advanced Macro Students, Bristol, Spring 2014

Overview

• Schematic account of recent history of though in macro and finance

• Quick account of the financial crisis and puzzles it poses for macro

• Analytics of simplified models of credit frictions in Christiano and Ikeda.

• Some questions begged by the models; account of financial shocks

More specifically

• Banker absconds model• Lazy banker model• Bernanke-Gertler-Gilchrist model.• In each case, we will cover the story, what it does and

does not capture, and the analytics.• In case of BGG, analytics is hard, and won’t be directly

examined.• But familiarity with that model will help, and familiarity

with the analytics will help you excel.• Will try to cover all this in 2 lectures.

Useful resources

• Martin Ellison’s Oxford Mphil notes.• Literature survey by Quadrini in Min Fed Review• Christiano and Ikeda• Bernanke Gertler (1989)• Bernanke Gertler Gilchrist (1999) [sticky price

version of above]• Kiyotaki-Moore [various]. Not much covered here.• Brunnermeir et al: survey of financial frictions

models

More DSGE papers on credit frictions

• Iocoviello• Gertler-Karadi: ‘A model of unconventional mon pol’• Christiano, Motto, Rostagno: ‘Risk shocks’• Del Negro et al: ‘The great escape’• Pinter, Theodoridis, Yates: ‘Risk news shocks and the

business cycle’• Gertler-Kiyotaki: Bank runs• Carlstrom-Fuerst-Paustian ‘Optimal mon pol in a

model with agency costs’.

Narrative of the financial crisis

• ‘Great moderation’: unusually low and stable inflation; unusually high and stable growth.

• Spreads low.• Fast growing emerging economies exporting

capital into West driving up asset prices, driving down yields on risky assets.

• Financial sector innovation and deregulation.• Basle accord bases capital requirements on risk-

weighting, using banks’ own models to assess risk.

• Banks experiment with new funding models. Eg Northern Rock’s aggressive entry into mortgages with wholesale funding.

• Irish banks: heavily exposed to commercial property; there, sky high prices based on extrapolating fast convergence of Irish gdp/head to mainland levels.

• Key innovation: securitisation of mortgages.• Creation of off-balance sheet subsidiaries

called ‘special purpose vehicles to get round capital requirement regulations.

• Supposedly AAA rated securities manufactured from pools of mortgages.

• At same time vast expansion of lending into ‘sub prime’ sector in US

• ‘Sub-prime’ lending based on political pressure to extend home ownership through relaxing risk management in the Federal Agencies. [See, for example, Calomiris(various)].

• Also over-optimistic forecasts of house price growth.

• Under-recognition of the correlation of risks inherent. Ie if one fails perhaps most will.

• Complexity of sub-prime mortgage assets meant holders and credit ratings failed to appreciate risks.

• Sub-prime mortgages started to fail in 2006. Even if whole sector failed not that large.

• However, uncertainty about who exposed to what caused wholesale funders to pull money out of banks, investment banks and insurance companies.

• Fed rescues Bear Sterns.• Fed then lets Lehman’s fail, because unable to

quantify the exposure by taking on LB’s liabilities.

• Previous held view that large institutions would be supported revised sharply.

• Banks in UK, Iceland, Ireland, France, Germany, Greece look like failing without state assistance.

• Sharp, unusually synchronised downturn across western world

• Plunges sovereigns into fiscal trouble.• Financial crisis socialised by sovereigns, to differing

degrees, making explicit deposit guarantee.• Eg Ireland introduces 100% guarantee and is soon

forced to get bail out as spreads rise to levels intolerable for it to continue servicing debt.

• Same in Greece, Portugal.

Policy responses

• US fiscal stimulus package driven through Congress by new Obama administration.

• Central banks, initially doubting crisis will be so bad, worrying about inflationary pressures, don’t respond. Soon cut rates to zero. [See recently released Fed transcripts, for example].

• Forced to undertake lender of last resort, unconventional monetary policy.

EZ bails out PIGS

• Eurozone: coordinated fiscal stimulus not possible. And many sovereigns under stress.

• Greek/Portuguese/Irish case threatens continuation of eurozone.

• If they can’t finance their budgets, either default and/or forced to start printing own currency again to prop up banks. (etc)

• Small peripherals ok, but worry is spreads to large ones ie Spain and Italy.

Spain and Italy

• Spanish economy hit hard in same way as Ireland.

• Spanish fiscal policy quite prudent in run up.• But banks heavily exposed by property and

construction boom, despite operating form of ‘macro pru’ [requiring more capital in a boom]

• Italian economy stagnant for 10 years already, no political consensus to sort out persistent deficits.

ECB and the EZ financial crisis

• ECB edges towards sort of lender of last resort.• Securities Market Program. Then Outright Monetary

Transactions.• Promise to buy unlimited short term securities of

troubled sovereign from secondary market.• Provided fiscal problem sorted out by country seeking

assistance from the ESM.• Spreads on peripheral bonds narrow dramatically,

quelling panic.• OMTs so far not needed.

So many causes

• Political pressure to give mortgages to people who can’t afford them.

• All blind to size and synchronisation of risks.• Complexity of securities, new financial

organisations, financial system, leads to opaqueness.

• Weak regulation, implicit subsidies through too big to fail.

• Monetary union without fiscal union.

Warning!

• That wasn’t just warm up story-telling. You’ll be expected to show knowledge of how the models relate to the crisis. If they do!

• Further reading will help. See next slide.

Narrative accounts of the crisis and its causes

• Gary Gorton-’Misunderstanding financial crises’• Calomiris ‘Fragile by design’• Robert Peston ’How do we fix this mess?’• Gillian Tett – ‘Fool’s gold’• Nouriel Roubini – ‘Crisis economics’• Andrew Haldane ‘The dog and the frisbee’, also see

‘The £xbn question’• Reinhart and Rogoff – ‘This time is different’ [a joke:

this time it’s the same]

• Reports into failings of Central Bank of Ireland to regulate its banks.

Macro and finance: hubris, then humility

• 1970s. Schism between micro advances [eg Akerlof and Yellen, Stiglitz and Weiss, Diamond and Dybvig], and macro wars.

• Lucas and Sims vs Cowles Commission.• Focus on rebuilding macro from micro.• Simplicity partly out of necessity; understanding of

competitive equilibria, and computational tools still emergent.

• But necessary simplicity morphed into RBC claim that (efficient) technology shocks drove the business cycle, and that finance ‘the plumbing’ was not important.

New Keynesian synthesis and monetary policy

• Sticky price models built around RBC core• Monetary policy seen as separable from non-

existent macro issue of financial stability

First finance in macro

• Bernanke-Gertler, Carlstrom-Fuerst, Bernanke-Gertler-Gilchrist: costly state verification model in general equilibrium.

• Kiyotaki-Moore: liquidity and resaleability constraints.

• Propagation/amplification of conventional shocks very weak. Implications for monetary/fiscal policy therefore very mild.

More recent developments• Go back to micro or partial equilibrium?

Caballero’s ‘pretence of knowledge syndrome’• Study of financial shocks in macro. ‘Wedges’.• Introduction of financing problems for banks, and bank runs.• Relaxation of rational expectations ‘irrational exuberance’;

bubbles. Eg Adam et al• Geannokoplous - Optimism, pessimism, leverage• Heterogeneous agents; eg Heathcote et al• Morris and Shin: Coordination games, imperfect knowledge.

Three models of financing frictions in Christano and Ikeda

• We will cover:– Banker absconds model. Gertler-Karadi. Banker

can run away with some of the funds deposited.– Lazy banker model. Banks can’t be bothered to

monitor their investments enough to guarantee returns.

– Costly state verification. Mutual funds have to pay something to check that banks aren’t lying about their profits. BGG.

Source: Christiano and Ikeda (2012), p88.

1. Moral hazard via bankers absconding

Banker absconds model

• 2 periods• Simplified version of Gertler-Karadi• Easy to extend to infinite period model,

essence still there.• Consumer has to decide how much to deposit

in the bank, given that the Bank might run off with it.

• Kiyotaki tale about his Grandfather

The story of the banker absconds model

• Banker can run away with some of the money and default.

• This gives it an incentive to steal deposits made with it.

• Assume the bank has some net worth, some ‘skin in the game’.

• Can steal deposits, but not extract all its own net worth. [eg can’t steal the buildings].

• However, in bad times, when net worth is low, defaulting is more tempting.

• Causes depositors to insist on a spread over the return on capital to compensate themselves for the risk.

• Government gifts of net worth to banks restores their incentive not to steal, and eliminate spreads.

Banker absconds model set-up

uc uC

ux x 1

1

Household maximise sum of 2 period discounted utility. Small c is period 1, big C is period 2.

c d yPeriod 1 budget constraint. Consumption plus what you deposit in bank (d) can’t be more than your endowment (y)

c CR y

RThe inter-period budget constraint.R is the gross interest rate.Pi are the profits from the bank.

C Rd Period 2 budget constraint. C can’t be more than What you get from your deposits, plus the bank profits.

Solving household problem

• Dynamic optimisation.• Set up Lagrangian involving constraints.• Differentiate wrt choice variables for

consumer.• Set these derivatives to zero.• Eliminate lagrange multipliers.• Solve for choice variables, and others that

depend on them.

Lagrangian, and steps to solve the household problem

L c1

1 C1

1 c C

R y R

Differentiate wrt c and CEliminate lagrange multiplier.Get expression for either c or CSubstitute into inter-period budget constraint assuming that it holds with equality.Find either c or C.Then solve for remaining unknowns.We will see the solution in the next slide, but this will be an exercise for you.

Solutions to the household’s problem

c y

R

1 R1 /R

d y c,C Rd

Can you explain equations for d and C in words? How do we get these so simply?

c smoothing motive: consume some of the profits u r going to get in period 2, but less if the interest rate is high; R higher means denominator also larger.

Digression on Barro-Wallace irrelevance

• Barro: tax cuts will have no effect as compensating tax rises will be anticipated.

• Wallace: central bank operations to buy private sector assets [ring any bells?] will have no effect either for same reason.

• Obviously holds under only certain circumstances.

Barro-Wallace irrelevance

1 : c d y T

2 : C Rd RT

1,2 : c C/R y /R T RT/R

Govt levies taxes T, purchases deposits, earns interest, then returns the taxes in period 2 as a tax cut.Write out the period 1, 2 then interperiod budget constraints.

We are going to get RT when the govt gets its deposits out of the bank, but today we discount this at rate of return R. So the tax terms cancel.Looming q is what might break this ‘irrelevance’ to motivate government action.

No financial frictions

max sRk Rd

Eqm is values for R, c, C, d, pi, such that:1. Household and firm problem solved2. Bank problem is solved3. Markets for goods and deposits clear4. c,C>0

Firm issues securities s, produce quantity sR_k, no profits.s=N+d, ie banker buys securities with net worth, plus deposits

R Rk

R Rk d 0

R Rk d

If funding cost>return for bank, wouldn’t offer deposits.If funding costs<returns, would wish to set deposits infinitely high.

No financial frictions/ctd

maxc,C,k uc uC

ux x 1

1

s.t.c k y N,C Rkk

Equilibrium solves the planning problem, ie gives the first best, if there is no financial frictions and R=R_k

Solving the no financial frictions model

L c1

1 C1

1 c k1 R k

R CR y N

dLdk 0 1

Rk

R

R, ,C,c 0, 0 R Rk

Here we have substituted in the intertemporal budget constraint.

From FOC wrt k we can deduce that R=R_k. Only interior eq’ia.Model is the same as before. Stare at the intertemporal budget constraint.Spread drops out. As if there were no banks.

Figuring out that lamda is not zero

dLdc

0 c Interior eq only.C>0 so lamda <>0

Inspecting the FOC wrt period 1 consumption reveals lamda not zero.

Adding in financial frictions to the banks’ problem

max sRk Rd

s.t.

N dRk Rd N dRk

1 N dRk Rd

Now we have a no-default condition.LHS=what banks get-what they pay.RHS=what they can steal if default.

Which re-written reads ‘i won’t default provided it makes depositors worse off’

Theta here is the fraction of resources that the banker can get away with if there is a default.Second line just a re-writing of the first.

Return on securities

Cost of funding

Digression on model solution methods

• 2 ways to equivalent ways solve a microfounded macro model with no ‘distortions’.

• 1: a)solve the problem of firms and consumers and banks [or whatever agents you have]. b) solve resulting system of FOCs and resource constraints, market clearing conditions.

• 2: pose a planning problem. Benevolent dictator decides on consumption, work, production, profits, everything, one set of its FOCs, plus resource constraints.

Eqm spread in a no-default equilibrium

Rk R 1

Rk

If constraint binds, this means lamda>0, and this implies that the spread is positive. [Ex – why?]But, importantly, note that constraint binds in bad times, so spreads rise [strictly, emerge] in a recession.

It will be an exercise for you to derive this equation from the FOC for the banker’s problem.

How does the spread change with banks cash position?

Rk R1

1

RRk

1 1

11 2

0

This translates to finding the derivative of the spread wrt lamda.So solve for the ratio of the two interest rates and then differentiate.

What’s going on? As cash position of banks worsens, the benefits to them of keeping the bank as a going concern fall, so to restore those benefits the funding cost has to fall.

Explaining why funding rate R falls relative to Rk

max sRk Rd

s.t.

N dRk Rd N dRk

1 N dRk Rd

This was the bank’s problem with financial conditions, when it can run off with theta*resources left.

See how if N falls, we have to find another way to increase the LHS of the inequality in order to relax the no default constraint.

And lowering R does just this.

Government policy that breaks Barro-Wallace irrelevance

N T dRk Rd RkT N dRk Rd

Government taxes households by T, gives to banks, expects RkT in return in period 2.

So bank profits not affeted by the tax financed equity injection.

c N yR k

R1/ R kNeither, as it turns out, is first period consumption, since does not involve T.

The zero effect on period 1 consumption of T

c y

R

1 R1/

R

c y T

R RkTR

1 R1/

R

c y T NdRk Rd

R RkTR

1 R1/

R

This was our old expression for c without T financed equity injections into banks.

Now we have an extra term, funds from government investment. And doesn’t cancel with taxes due to the different rate of return.

Now if we substitute in our unchanged equation for bank profits as we have here, and then note that d=y-c-T…. We end up with that equation not involving T!

Taxes reduce deposits, which the bank can run away with

d y c T But deposits d do fall as T financed injections rise.So total intermediation unchanged.

N dRk Rd N dRkBut if the no-default condition binds, then the fall in deposits does have an effect.

Both sides of this inequality fall, since both involve d

But LHS falls by less than RHS.LHS involves spread*; RHS involves Rk*d

So fall in d relaxes constraint.

Another government policy that works

• Govt taxes consumers in period 1, invests directly in firms, returns Rk*T to consumers in period 2.

• Consumers understand this substitutes for their deposits, so they reduce their demand for deposits, wiping out the spread, since R then rises back towards the Rk.

Government policy that doesn’t work.

• Government taxes consumers, then places the money on deposit in the Bank.

• Bank can run away with these too.• Total deposits unchanged. Immaterial where

they come from. Spreads unchanged.

Does the model ‘get’ the crisis?

• Banks did suffer reductions in net worth. Illustrated by fall in market capitalisation.

• Funding costs probably rose relative to rok though. Eg change in CDS spreads.

• Threat for banks was not being able to meet obligations, not the worry of expropriation by the managers.

• [OK, there was libor rigging, misselling of payment protection insurance, but this didn’t increase in the crisis].