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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
Lecture to MSc Advanced Macro Students, Bristol, Spring 2014
Banks experiment with new funding models. Eg Northern Rock’s aggressive entry into mortgages with wholesale funding.
‘Sub-prime’ lending based on political pressure to extend home ownership through relaxing risk management in the Federal Agencies. [See, for example, Calomiris(various)].
Complexity of sub-prime mortgage assets meant holders and credit ratings failed to appreciate risks.
However, in bad times, when net worth is low, defaulting is more tempting.
Household maximise sum of 2 period discounted utility. Small c is period 1, big C is period 2.
Period 1 budget constraint. Consumption plus what you deposit in bank (d) can’t be more than your endowment (y)
Period 2 budget constraint. C can’t be more than What you get from your deposits, plus the bank profits.
The inter-period budget constraint.
R is the gross interest rate.
Pi are the profits from the bank.
Differentiate wrt c and C
Eliminate lagrange multiplier.
Get expression for either c or C
Substitute 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.
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.
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.
Firm issues securities s, produce quantity sR_k, no profits.
s=N+d, ie banker buys securities with net worth, plus deposits
Eqm is values for R, c, C, d, pi, such that:
1. Household and firm problem solved
2. Bank problem is solved
3. Markets for goods and deposits clear
If funding cost>return for bank, wouldn’t offer deposits.
If funding costs<returns, would wish to set deposits infinitely high.
Equilibrium solves the planning problem, ie gives the first best, if there is no financial frictions and R=R_k
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.
Interior eq only.
C>0 so lamda <>0
Inspecting the FOC wrt period 1 consumption reveals lamda not zero.
Return on securities
Cost of funding
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.
It will be an exercise for you to derive this equation from the FOC for the banker’s problem.
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.
This translates to finding the derivative of the spread wrtlamda.
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.
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 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.
Neither, as it turns out, is first period consumption, since does not involve T.
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!
But deposits d do fall as T financed injections rise.
So total intermediation unchanged.
But 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.