1. How do shocks and frictions within financial markets affect the real economy?
Stephen Millard (Bank of England, Durham University Business School and Centre for Macroeconomics)
Alexandra Varadi (Bank of England)
Eran Yashiv (Tel Aviv University, CfM, and CEPR)
17 March, 2017

2. Roadmap Introduction and motivation Relevant literature Model
Effects of shocks
Effects of frictions
Conclusions and next steps

3. What is our research question?
How do financial and real frictions affect the transmission of shocks (including financial) onto the real economy
Three key question we want to consider:
How do financial frictions and frictions in the real economy, such as labour market frictions, interact in the presence of shocks?
What does this mean for the transmission of monetary and macroprudential policies?
What does this mean for the transmission of problems in the financial sector into the wider macroeconomy?

4. Where do we fit in the literature?
DSGE models with financial frictions
Gertler and Kiyotaki (2015)
Bernanke, Gertler and Gilchrist (1999)
DSGE models with labour/investment frictions
Yashiv (2015)
DSGE models with housing
Iacoviello (2015)
We incorporate all these frictions into one model to move away from studying them in isolation

5. Our Model
Two types of households – patient and impatient – who get utility out of consumption, housing and leisure. Impatient households borrow subject to a collateral constraint (mortgage borrowing).
We think of the loan-to-value ratio in this constraint as a potential policy tool and examine the effects of a temporary shock to this.
Firms subject to costs of adjusting prices, hiring costs and investment adjustment costs. Have to borrow to finance investment and hiring costs.
Banks lend to firms and households and are subject to Gertler-Kiyotaki frictions.

6. Our model: Patient Households
Mass of 1-s patient housheholds
‘Patience’ implies low discount rate
These households save via bank deposits
Get utility out of consumption and housing
Disutility from members of the household working
Nj is the proportion of household j in employment
Total employment of patient households equals NP

7. Our Model : Patient Households
Maximize:
Subject to:

8. Our model: Impatient Households
Mass of s impatient housheholds
‘Impatience’ implies high discount rate
These households borrow via mortgages
Get utility out of consumption and housing
Disutility from members of the household working
Nj is the proportion of household j in employment
Total employment of impatient households equals NI

9. Our Model : Impatient Households
Maximize:
Subject to:

10. Our model: Firms Monopolistically competitive
Owned by the patient households
Maximise present discounted utility value of dividends
Face costs of adjusting investment and hiring costs
Have to borrow from banks to finance hiring costs
Also have to borrow from banks to finance investment
Face quadratic costs of adjusting prices
Wages are set so that all the surplus of job matches goes to firms
Households will be indifferent between supplying an extra worker and not supplying an extra worker

11. Our Model : Firms
Maximize:
Subject to:

12. Our Model : Firms First-order conditions: New Keynesian Phillips curve
Value of installed capital
Investment demand

13. Our model: Firms Definition of real marginal cost
This is the usual expression for real marginal cost plus an additional term reflecting the cost of hiring additional workers and this term depends on the spread
This is the key link between financial frictions and the real economy and inflation

14. Our model: Banks
Banks are funded through capital (retained earnings) and deposits
Bank assets are loans to impatient households (mortgages) and firms
Banks are owned by the patient households
Each period banks either continue to accumulate net worth (probability z) or ‘die’ and distribute their accumulated net worth to patient households as dividends (probability 1-z)
The 1-z ‘dead’ banks are replaced by 1-z new banks with initial net worth Pn, provided lump sum by the patient households

15. Our model: Banks For a surviving bank, net worth evolves according to:
Where ey is a shock to bank profits (and, by implication, net worth)
Net worth will equal assets less liabilities (deposits)
So, aggregate net worth in the banking sector evolves according to:

16. Our model: Banks
Bankers have the opportunity to ‘run away’ overnight with a proportion, q, of the bank’s assets.
To stop them doing so, it must be more profitable for them to keep the bank open as an ongoing business than to run away with the assets.
This implies the incentive constraint:
This leads to a spread between lending and deposit rates, which is increasing in leverage and this friction, q.
We implement regulatory policy as affecting q .
We also implement a shock to bank equity prices, V, which will directly affect the spread.

17. Our model: Banks Dividends will be given by
So, banks will solve the following profit maximisation problem:
Maximise
Subject to

18. Our model: Banks The Bellman equation for this problem implies:
That is, the spread is increasing in leverage j, the (expected value of) the shock, ey, and the friction, q

19. Our model: Public sector and market clearing
The government is assumed to run a balanced budget:
The Central Bank operates a Taylor rule:
Finally, market clearing implies:

20. Effects of frictions We compare results from four models:
1. Model with no other friction than sticky prices
Firms are 100% equity financed and face no investment or hiring adjustment costs
No role for banks, one representative household
2. Model with hiring and investment frictions
Same as Model 1, but firms face costs of hiring and adjusting investment
3. Model with financial frictions
Firms have to borrow to finance investment
Impatient households borrow for housing purchases
4. Model with all the frictions
Financial frictions : LTV ratios, leverage constraint, firms have to borrow to finance investment, costs of adjusting investment, and hiring costs , and impatient households borrow for housing purchases
Hiring and investment frictions
To compare the impact of different frictions, we start with a model of no frictions and start adding frictions gradually to be able to observe their impact.
No friction model
Firms are 100% equity financed
There are no costs to adjusting investment or labour, but we do allow for price adjustment to be costly
There is no role for banks, because there is no borrowing
One representative household that chooses between investing in housing, consumption or leisure
Model with hiring and investment frictions
This is the same as model 1, but firms face costs of adjusting investment and labour
Model with financial frictions
This is similar to the model presented by Steve, but there are no frictions in the real economy, apart from sticky prices
Model with all the frictions
This is the full model, as presented by Steve
Financial frictions : LTV ratios that restrict household borrowing, regulatory capital constraints imposed exogenously on banks, and firms can borrow prior to production
Hiring and investment frictions
Price adjustment costs

21. Effects of a monetary policy shock
We use the monetary policy shock to illustrate what frictions do in each of the four models.
In all models, the loosening in policy leads to a drop in the policy rate. In models 3 and 4, where we have a banking sector, the drop in policy rate decreases banks financing costs, which incentivises banks to reduce the bank spreads. This increases both corporate and mortgage lending which leads to higher investment, employment, and house prices. The result is a positive rise in output and inflation. In Models 1 and 2 is the drop in the risk free rate that incentivises the a change in asset allocations and boosts firm production.
But the magnitude of responses is very different.
Comparing models 1 and 2:
Hiring/investment frictions leads to hump shaped results. That is because costs on adjusting investment and employment imply that these two cannot adjust fully and quickly to the monetary policy shock.
As a consequence, investment and employment increases by less than 0.1% in model 2 versus 2% and 1% respectively in Model 1. House prices and consumption have a similar magnitude.
Comparing models 1 and 3:
The lack of real economy frictions leads to a sudden jump in investment and employment, but to a lower extend compared to Model 1. That is because in model 3, the firms’ decision on how much to invest depends on the bank spread, as opposed to just the risk-free rate in Model 1. And the bank spread in Model 3 is higher than the risk free rate in Model 1, which implies that effect on investment and employment is reduced. This means that the transmission mechanism of monetary policy to the real economy is reduced in the presence of financial frictions.
Model 3 delivers a higher response of house prices. Similar to the firm decision, the household’s decision to invest in housing depends on the cost of obtaining finance today, that is on bank lending rates. The lower this is, as a consequence of the monetary policy, the more available finance is and the higher the demand for mortgages, which will increase asset prices today and in the future.
Comparing all of this with model 4: Model 4 delivers magnitudes somewhere between model 2 and 3. In this mode, the bank spread is directly linked to hiring and investment frictions. The lower the financial frictions, the spread, and cheaper it is for firms to finance real economy frictions. As a consequence, investment, employment and output will be higher than they are in Model 2.

22. Effects of shocks Look at shocks to: Bank equity prices, ey
Mortgage loan-to-value ratio, ltv
Banking regulation (proxied by q)

23. Effects of a bank equity price shock
The second shock we wanted to show is a 0.5% drop in regulatory capital. We think this could be interesting to help draw parallels to the release in countercyclical capital buffer in July this year.
The loosening in capital requirements has a positive effect on banks’ lending to households and corporates. Overall, total lending raises almost 1 for 1 with the change in capital requirements
On impact, bank lending rates and spreads fall. Since the spread matters for firms decisions on how much to borrow to invest and hire, a fall in spreads leads to a higher demand for corporate loans which boosts employment. Mortgage lending raises as well. That is because, impatient households take advantage of lower lending rates to increase their housing purchases by buying from the patient households. In turn, patient households use the extra wealth this generates for them to increase both their consumption and bank deposits.
As a result, output raise, which raises inflation and determines the central bank to increases the policy rate.
There 2 interesting results coming from this experiment:
1) This exercise brings out the interaction between monetary and macroprudential policies. A loosening in macropru triggers a monetary policy tightening to lower inflation. This reduces the benefits from the positive macropru shock on the real economy, as output, employment, consumption return to steady state in the short term. [This move ensures a temporary impact on some real economy aspects, such as consumption, output, employment. But macroprudential policy lead to permanently higher asset prices and total lending.]
2) The second interesting aspect is the behaviour of banks’ net worth, which goes down following the policy change. Given the change in capital requirements, banks can do 2 things:
First, banks can expand their balance sheet until they hit the new constraint. But this will leave net worth unchanged, with a move in just lending and deposits.
So for the net worth to go down, banks have to use some or all of the capital surplus to pay dividends to their owners. This payment of dividends will lower banks net worth.
We have evidence that banks do a bit of both as lending goes up and net worth goes down.

24. Effects of a mortgage loan-to-value shock
The second shock we wanted to show is a 0.5% drop in regulatory capital. We think this could be interesting to help draw parallels to the release in countercyclical capital buffer in July this year.
The loosening in capital requirements has a positive effect on banks’ lending to households and corporates. Overall, total lending raises almost 1 for 1 with the change in capital requirements
On impact, bank lending rates and spreads fall. Since the spread matters for firms decisions on how much to borrow to invest and hire, a fall in spreads leads to a higher demand for corporate loans which boosts employment. Mortgage lending raises as well. That is because, impatient households take advantage of lower lending rates to increase their housing purchases by buying from the patient households. In turn, patient households use the extra wealth this generates for them to increase both their consumption and bank deposits.
As a result, output raise, which raises inflation and determines the central bank to increases the policy rate.
There 2 interesting results coming from this experiment:
1) This exercise brings out the interaction between monetary and macroprudential policies. A loosening in macropru triggers a monetary policy tightening to lower inflation. This reduces the benefits from the positive macropru shock on the real economy, as output, employment, consumption return to steady state in the short term. [This move ensures a temporary impact on some real economy aspects, such as consumption, output, employment. But macroprudential policy lead to permanently higher asset prices and total lending.]
2) The second interesting aspect is the behaviour of banks’ net worth, which goes down following the policy change. Given the change in capital requirements, banks can do 2 things:
First, banks can expand their balance sheet until they hit the new constraint. But this will leave net worth unchanged, with a move in just lending and deposits.
So for the net worth to go down, banks have to use some or all of the capital surplus to pay dividends to their owners. This payment of dividends will lower banks net worth.
We have evidence that banks do a bit of both as lending goes up and net worth goes down.

25. Effects of a loosening in regulation (q)
The second shock we wanted to show is a 0.5% drop in regulatory capital. We think this could be interesting to help draw parallels to the release in countercyclical capital buffer in July this year.
The loosening in capital requirements has a positive effect on banks’ lending to households and corporates. Overall, total lending raises almost 1 for 1 with the change in capital requirements
On impact, bank lending rates and spreads fall. Since the spread matters for firms decisions on how much to borrow to invest and hire, a fall in spreads leads to a higher demand for corporate loans which boosts employment. Mortgage lending raises as well. That is because, impatient households take advantage of lower lending rates to increase their housing purchases by buying from the patient households. In turn, patient households use the extra wealth this generates for them to increase both their consumption and bank deposits.
As a result, output raise, which raises inflation and determines the central bank to increases the policy rate.
There 2 interesting results coming from this experiment:
1) This exercise brings out the interaction between monetary and macroprudential policies. A loosening in macropru triggers a monetary policy tightening to lower inflation. This reduces the benefits from the positive macropru shock on the real economy, as output, employment, consumption return to steady state in the short term. [This move ensures a temporary impact on some real economy aspects, such as consumption, output, employment. But macroprudential policy lead to permanently higher asset prices and total lending.]
2) The second interesting aspect is the behaviour of banks’ net worth, which goes down following the policy change. Given the change in capital requirements, banks can do 2 things:
First, banks can expand their balance sheet until they hit the new constraint. But this will leave net worth unchanged, with a move in just lending and deposits.
So for the net worth to go down, banks have to use some or all of the capital surplus to pay dividends to their owners. This payment of dividends will lower banks net worth.
We have evidence that banks do a bit of both as lending goes up and net worth goes down.

26. Conclusions
According to our model, a loosening of bank regulation leads banks to lend more while allowing their net worth (capital) to fall
A shock to bank equity valuations leads to a marked rise in the spread but a relatively small fall in output
Raising the LTV ratio on mortgage lending leads to a rise in mortgage lending but only a small rise in house prices
But we are still not happy with the quantitative implications of the model: in particular, for the spread
Need for a more careful calibration of the model
In future work we hope to estimate the model!
Three takeaways:
Investment and hiring frictions enable hump shaped responses but effects on the real economy are very much reduced due to adjustment costs
Financial frictions can amplify effects of shocks on some asset prices, such as housing, because of cheap borrowing available in periods of boom. Their presence however can dampen the impact of shocks on employment, investment and output, because the firm’s decision on how much to produce depends on the relative cost of borrowing to the risk free rate.
Interaction between macrprudential and monetary policy may require coordination in some circumstances – we’ve seen that in the absence of coordination, one policy can offset the effects of the other one
Further work:
Model banking frictions as in Gertler and Kiyotaki (2015) – to obtain an endogenous leverage rate
Add wage bargaining (Yashiv (2015)) – to model hiring frictions more explicitly
Estimate the model – currently the model is just calibrated and we plan to bring it to the data