Heterogenous Regulation Europlace Insitute of Finance Grant Frdric - - PowerPoint PPT Presentation

Heterogenous Regulation

Europlace Insitute of Finance Grant Frédéric Malherbe and Wolf Wagner LBS & Tilburg

Malherbe and Wagner () Heterogenous Regulation LBS & Tilburg 1 / 27

Recent regulatory initiatives aim to increase the reach of banking regulation

Following the experience of the crisis of 2007-2008, there is debate on whether to extend banking-style regulation beyond the traditional banking

• sector. Some examples:

Dodd-Frank gives FED the power to regulate all institutions of systemic importance Regulating shadow banking system is top priority for FSB G20 leaders consider regulation of securitization and money market funds Investment banks became BHCs and are now in the regulated depository sphere Solvency II requires insurance companies to hold capital like banks ("Basel for insurers")

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Rationale for increasing bank-style regulation:

Avoid regulatory arbitrage Make sure all parts of …nancial systemic are regulated . . However, it is not necessarily optimal to regulate all parts of …nancial system in same way

1

More homogeneity in …nancial system leads to similar behaviour (ex-post)

2

We may want a diversity of activities being undertaken in the …nancial system (ex-ante)

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Homogeneity has increased in recent years

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A model of heterogenous regulation

If di¤erent activities can be undertaken in the …nancial system, it may be

• ptimal to regulate them di¤erently

Traditional activity:

Requires less unique skills and less susceptible to incentive problems Safe but low return Examples: community bank lending, mortgage and consumer loan lending (institutions that carry out such activities: commercial banks)

Fancy activity:

Highly dependent on e¤orts and skills of managers High start-up cost and potentially high return Examples: …nancial innovation, funding of new and high-risk activities (institutions that carry out such activities: hedge funds, investment banks, private equity funds)

) Optimal regulation of institutions (considered in isolation) may hence depend on which activities they carry out

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A model of heterogenous regulation

Institutions that specialize in these activities will also interact with each

• ther, in particular in times of crisis:

1

Access to common pools of liquidity for liquidation of assets

2

Institutions may buy assets from each other Optimal sectoral regulation not determined in isolation. In particular, it may be optimal to design di¤erent regulatory environments, one with light regulation and another one with strict regulation

1

Light regulation provides environment for fancy activities to be undertaken

2

But light regulation is only optimal because at the same time there is a traditional sector is heavily regulated. Traditional sector acts as "backstop".

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Existing work on shadow banking and regulation

Allen and Carletti (2006) and Allen and Gale (2005), credit risk transfer between the banking sector and the insurance sector can cause spillbacks to the banking sector when there are failures in the insurance sector. This is because following the transfer of risk, the insurance sector invests in the same assets as the banking sector. When there is a systemic event in the insurance sector, these assets are then liquidated. This depresses their price and can, in turn, cause bankruptcies in the banking sector. Gennaioli, Shleifer, and Vishny (2012) show that an increase in investors’ wealth drives up securitization. This also introduces fragility because banks become interconnected and more exposed to systemic

• risk. In their model, securitization is also welfare improving and only

subject to crises when agents neglect those systemic risk.

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Existing work on shadow banking and regulation

Acharya, Schnabl, and Suarez (2013) show that the banks that used ABCP more intensively before the recent crisis were also the banks that were more heavily constrained by regulation, hence arguing that these conduits were e¤ectively used to avoid regulatory pressures and to reduce capital requirements Plantin (2012): If shadow banking cannot be perfectly regulated, it may be optimal not to regulate traditional banking system too much because risk is then pushed in shadow banking system Ordonez (2013): Shadow banking spurs when outside investors believe that capital requirements are not critical to guarantee the quality of banks’ assets (reputation concerns -discipline bank behavior). However, reputation concerns collapse when bad news about the future arise. Investors stop believing in the self-discipline of banks, moving their funds to a less e¢cient, but safer, traditional banking.

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Setup

There are three dates: t = 0, 1, 2 There is a measure 1 of bankers endowed with two investment

• pportunities, scaleable up to one unit.

The liability side of banks is given: equity e and (demand) deposits d = 1 e The two long-term technologies convert date-0 funds into funds at date 2

traditional activity: unit return of R > 1 at date 2 fancy activity: unit return of R + b at date 2 but requires private …xed cost of k < b (that is, if operated at full scale, fancy project dominates the traditional one) choice of activity is private information but the scale of the activity is not.

There is also a standard storage technology (liquid asset) which translates one unit of funds at t into one unit at t + 1

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Setup

Liquidity risk

With probability π (2 (0, 1)) no depositor withdraws at date 1 With probability 1 π, a mass λ (2 (0, d)) of depositors withdraws

Liquidation technology and externality

There is a liquidation technology which at date 1 transforms 1 unit of the long-term project into φ(l) 1 units of the consumption good, where l is the aggregate amount liquidated The function φ(.) is decreasing. The liquidation technology creates an externality as individual bankers take φ as given (externality could for instance arise from …re-sales)

We assume no insolvency.

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Homogenous regulation

The regulator sets a single regulatory requirement that applies to all bankers. We denote with x a banker’s investment in liquid assets. Total investment in illiquid projects is hence y = 1 x. We can think of regulation as either a liquidity requirement x or a constraint on illiquid activities y = 1 x.

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Banker’s optimization problem

A banker has to decide how much to invest in illiquid activities and how to split this investment among the two technologies. Due to liquidation externality, the banker’s private bene…ts from investing in illiquid activities are higher than the social ones. It follows that the regulatory constraint y will be binding for the banker. The banker hence chooses the maximum permissible extent of illiquidity: y = y. In addition, a banker will never mix fancy with traditional projects due to the …xed cost of investing in fancy projects. His optimization problems thus boils down to choosing whether to invest y in the traditional of the fancy activity. The expected utility from undertaking the traditional activity is given by vT = π (yR + x d) + (1 π) ((y l)R + x (d λ)) , (1) where l denotes amount that has to be liquidated at t = 1 in case depositors withdraw.

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Banker’s optimization problem

How much has to be liquidated? Liquidity needs are λ x and liquidation proceeds are lφ, thus liquidations are given by l = λ x φ . (2) Using that x = 1 y and y = y, we can simplify (1) to vT = yR + 1 y d (1 π) (lR λ) , (3) where (1 π) (lR λ) is the expected cost due to liquidations.

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Banker’s optimization problem

Similarly, we can derive the expected utility from undertaking the fancy activity vF = y(R + b) + 1 y d (1 π) (lR λ) k. (4) It follows that the banker will choose the fancy activity i¤ yb k. (5) This gives a critical threshold b y = k

b such that banker "goes for

fancy" if y b y, and undertakes traditional activities if y < b y.

Intuition: Given that there are …xed costs of undertaking the fancy activity, the banker has to get su¢cient bene…ts from undertaking this activity in order to make it worth his while. This means that regulation has to be su¢ciently light to allow him to operate the fancy activity a large scale.

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The regulator’s problem

Welfare in the economy consists of the sum of bankers’ utilities plus the pay-o¤s to depositors Let us assume that only a fraction α (2 (0, 1)) of the private costs k from choosing the fancy project enters welfare. The banker may hence choose the traditional activity even if this is not socially optimal. Welfare is given by W (y) = yR + 1 y (1 π) (lR λ) if y < b y y(R + b) + 1 y (1 π) (lR λ) αk if y b y. (6)

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The regulator’s problem

Denote with y

F and y T the (socially) optimal investment levels when the

banker chooses the fancy and the traditional technology, respectively. We have y

F > y T , since the marginal bene…ts from the fancy technology are

higher. Two cases arise:

• 1. y

F b

y The banker chooses the fancy activity at the socially optimal investment level for fancy projects y

F . ) The regulator will then set y F and the

banker chooses the fancy activity.

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The regulator’s problem

• 2. y

F < b

y The banker chooses the traditional activity if the regulator imposes y

F .

There are then two possibilities for the regulator: The regulator imposes the highest activity restriction that is still consistent with the choice of the fancy project: y = b y. The regulator chooses a stricter restriction (y < b y). The banker will then choose the traditional project. Given this, the regulator chooses y

T .

The regulator hence faces a trade-o¤: Strict regulation (low y) lead to more e¢cient liquidity holdings in the economy and hence lower liquidation externalities. But it also means that the banker may not choose the fancy activity. Depending on the model’s parameters, either choice can be optimal.

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Heterogenous regulation

Consider that the regulator o¤ers two menus to bankers: Menu A (strict regulation): activity restriction yA (< b y) and a subsidy s Menu B (light regulation): activity restriction yB ( b y) Bankers will …rst choose menu ("sector" to operate in) and following this, choose activity

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Banker’s optimization problem

Given activity restrictions yA and yB, the representative banker will choose the traditional activity in the heavily regulated sector and the fancy activity in the lightly regulated sector. We focus on an “interior” equilibrium where both sectors are

• perative. An individual banker is then indi¤erent between sector A

and B: (yB yA)(R 1 (1 π)(R φ 1)) = s (yBb k) (7) Private choices of bankers determine the mass n (2 (0, 1)) of agents in the light sector.

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The regulator’s problem

The regulator chooses activity restrictions in both sectors, yA and yB, as well as the subsidy s. Welfare is now determined by the weighted sum of pay-o¤s of the two sectors: W (yA, yB, n) = (1 n)

• yAR + 1 yA (1 π) (lR λ(l))
• +

n

• yB(R + b) + 1 yB (1 π) (lR λ(l)) αk
• ,

(8) The gains from choosing light regulation fall in s, hence an increase in s will lead to lower n. We can hence think of the regulator directly choosing n.

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The regulator’s problem

The light sector has a comparative advantage in carrying out illiquid projects (and hence a comparative disadvantage in holding liquidity) because:

1

The return from undertaking activities in the light sector is higher

2

Undertaking more illiquid projects in the light sector alleviates the incentive constraint of the banker (yBb k) as projects can then be

• perated at greater scale.

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The regulator’s problem

It follows that all illiquid activities in the economy should be carried

• ut in the light sector (yB = 1) and all liquid assets should be held in

the strictly regulated sector (yA = 0). The level of illiquid and liquid investment in the economy is hence y = n and x = 1 n. (9) Using this, we can write welfare in the economy as W (n) = y(R + b) + 1 y (1 π) (l(y)R λ) yαk. (10) The incentive constraint is now trivially ful…lled: b k. (11) Note that the welfare expression is the same as in the case of a fancy activity under homogenous regulation, except that the cost of carrying out y units of fancy activities is now y αk instead of ak.

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Heterogenous versus homogenous regulation

Welfare is always higher than under heterogenous regulation:

1

By letting bankers specialize, heterogenous regulation minimizes the …xed costs from undertaking fancy projects. A number y of fancy projects can now be undertaken at cost y αk instead of αk.

2

Heterogenous regulation alleviates the incentive constraint by allowing fancy bankers to operate at a larger scale. This has bene…ts whenever the incentive constraint was previously binding (Case 2). Heterogenous regulation thus always dominates homogenous regulation. In fact, optimal heterogenous regulation achieves the …rst-best in the economy.

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Implications for regulation

Optimal regulation in one sector depends on regulation in the other

• sector. The fact that Sector A is heavily regulated allows Sector B to

be lightly regulated. One should hence not judge a particular part of the …nancial system as "too risky". Risk has to be evaluated at the level of the entire …nancial system. Interactions among di¤erent sectors in crisis can reduce cost of shocks ("spillovers" can be optimal). Note that this is even though there is no rationale for risk-sharing across sectors here. "Regulatory" arbitrage can be optimal. For example, we can allow banks to trade with each other at t = 0. A bank could then decide to become heavily regulated (in order to get the subsidy s) and sell projects to another bank that is lightly regulated in order to pro…t from lower activity restrictions there. This however is not di¤erent to sourcing the activity right away in the lightly regulated sector and hence does not undermine e¢ciency.

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Conclusions

Uniform regulation not necessarily optimal Regulatory di¤erences across sectors should be set with a view on how the bene…ts and costs di¤er across sectors. Regulatory arbitrage at the activity level has to be seen in connection with subsidies/taxation at the institutional level. In order to be

• ptimal, they should go in di¤erent directions.

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The regulator’s problem

The FOC for y is (when y 6= b y) W 0(y) = R 1 (1 π)l0(y)R = 0 for y < b y W 0(y) = R + b 1 (1 π)l0(y)R = 0 for y b y, (12) where l0(y) = 1 φ(l) + l ∂φ(l)

∂l

> 0. (13) Note: the expression ∂φ(l)

∂l

arises because higher liquidations in the economy increase liquidation costs (reduce φ). This e¤ect would be ignored by a single bank, creating a systemic externality.

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The regulator’s problem

The FOC for y(n) is W 0(y) = R + b 1 (1 π)

• l0(y)R λ

αk = 0. (14) The marginal cost of undertaking fancy activities is now higher (e¤ectively, the …xed cost has become a variable cost). However, at least some fancy activities are always undertaken as there is no longer a …xed cost at the aggregate. Compared to Case 2 of homogenous regulation, more or less illiquid activities may be undertaken (this depends on whether in Case 2 it was

• ptimal to implement fancy or traditional activities).

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