Could making banks hold only liquid assets induce bank runs? Karl - PowerPoint PPT Presentation

Could making banks hold only liquid assets induce bank runs? Karl Shell James Peck Cornell University The Ohio State University Presentation by Ludovico Genovese and Alessandro Pistoni

Agenda • Contextualization • Model: assumptions (vs Diamond-Dybvig) • Banks (unified and separated system) • Welfare maximization problem • Results • Take-aways 2

Contextualization • Glass-Steagall Act (Banking Act of 1933) “To provide for the safer and more effective use of the assets of banks, to regulate interbank control, to prevent the undue diversion of funds into speculative operations [ …] .” • Repeal of Glass-Steagall Act (1999) 3

Is Glass- Steagall’s repeal to blame? • Paul Volcker (March 2009) "Maybe we ought to have a two-tier financial system ." "This institutions should not be taking extraordinary risks in the market place represented by hedge funds, equity funds, large-scale proprietary trading. Those things would put their basic functions in jeopardy" • Could making banks hold only liquid assets induce bank runs? (PS, April 2010) 4

Model • 3 periods: 𝑈 = 0 𝑈 = 1 𝑈 = 2 • Continuum of consumers: [0; 1] • Single good (costless storage) • Each endowed with 𝑧 in 𝑈 = 0 5

Model • I n 𝑈 = 0 each consumer is identical • In 𝑈 = 1 they discover their type (patient or impatient) • Private information • Sequential service constraint • Until now, same assumptions as in Diamond and Dybvig (1983) 6

Model • 𝛽 ∶ probability of being impatient • 𝛽 is a random variable with density 𝑔 • Support: 0, 𝛽 𝛽 < 1 • 𝛽 : maximum proportion of impatient consumers 7

What is the difference? Diamond-Dybvig Peck-Shell Intrinsic uncertainty 8

The utility functions 1 + 𝐷 𝐽 2 − 1 1 ≥ 1 2 = 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 1 , 𝐷 𝐽 𝑉 𝐽 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 1 < 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 2 = 1 + 𝐷 𝑄 2 − 1 1 , 𝐷 𝑄 𝑉 𝑄 𝐷 𝑄 𝑣 + 𝑣 𝐷 𝑄 9

The utility functions 1 + 𝐷 𝐽 2 − 1 1 ≥ 1 2 = 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 1 , 𝐷 𝐽 𝑉 𝐽 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 1 < 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 2 = 1 + 𝐷 𝑄 2 − 1 𝑉 𝑄 𝐷 𝑄 1 , 𝐷 𝑄 1 , 𝐷 𝑄 2 𝑉 𝑄 𝐷 𝑄 𝑣 + 𝑣 𝐷 𝑄 1 : consumption available to an impatient in 𝑈 = 1 𝐷 𝐽 : incremental utility of:  1 unit of consumption in 𝑈 = 1 for an impatient 10

The utility functions 1 + 𝐷 𝐽 2 − 1 1 ≥ 1 2 = 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 1 , 𝐷 𝐽 𝑉 𝐽 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 1 < 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 2 = 1 + 𝐷 𝑄 2 − 1 1 , 𝐷 𝑄 𝑉 𝑄 𝐷 𝑄 𝑣 + 𝑣 𝐷 𝑄 1 : consumption available to a patient in 𝑈 = 1 𝐷 𝑄 : incremental utility of:  1 unit of consumption in 𝑈 = 1 for an impatient 11

The utility functions 1 + 𝐷 𝐽 2 − 1 1 ≥ 1 2 = 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 1 , 𝐷 𝐽 𝑉 𝐽 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 1 < 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 2 = 1 + 𝐷 𝑄 2 − 1 𝑉 𝑄 𝐷 𝑄 1 , 𝐷 𝑄 1 , 𝐷 𝑄 2 𝑉 𝑄 𝐷 𝑄 𝑣 + 𝑣 𝐷 𝑄 2 : consumption available to an impatient in 𝑈 = 2 𝐷 𝐽 : incremental utility of:  1 unit of consumption in 𝑈 = 1 for an impatient 12

The utility functions 1 + 𝐷 𝐽 2 − 1 1 ≥ 1 2 = 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 1 , 𝐷 𝐽 𝑉 𝐽 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 1 < 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 2 = 1 + 𝐷 𝑄 2 − 1 1 , 𝐷 𝑄 𝑉 𝑄 𝐷 𝑄 𝑣 + 𝑣 𝐷 𝑄 2 : consumption available to a patient in 𝑈 = 2 𝐷 𝑄 : incremental utility of:  1 unit of consumption in 𝑈 = 1 for an impatient 13

The utility functions 1 + 𝐷 𝐽 2 − 1 1 ≥ 1 2 = 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 1 , 𝐷 𝐽 𝑉 𝐽 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 1 < 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 2 = 1 + 𝐷 𝑄 2 − 1 1 , 𝐷 𝑄 𝑉 𝑄 𝐷 𝑄 𝑣 + 𝑣 𝐷 𝑄 𝑣 : incremental utility of:  1 unit of consumption in 𝑈 = 1 for an impatient  1 unit of consumption in 𝑈 = 2 for a patient 14

The utility functions 1 + 𝐷 𝐽 2 − 1 1 ≥ 1 2 = 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 1 , 𝐷 𝐽 𝑉 𝐽 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 1 < 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 𝑗𝑔 𝐷 𝐽 2 = 1 + 𝐷 𝑄 2 − 1 𝑉 𝑄 𝐷 𝑄 1 , 𝐷 𝑄 1 , 𝐷 𝑄 2 𝑉 𝑄 𝐷 𝑄 𝑣 + 𝑣 𝐷 𝑄 𝛾 𝑣 : incremental utility of 1 unit of consumption in 𝑈 = 2 for an impatient: incremental utility of:  1 unit of consumption in 𝑈 = 1 for an impatient  1 unit of consumption in 𝑈 = 2 for a patient 15

The utility functions 𝑣 𝐷 1 + 𝐷 2 − 1 : utility from “ left−over” consumption 16

The utility functions 𝑣(𝑦) 1 + 𝐷 𝐽 2 − 1 𝑣 𝐷 𝐽 𝐷 1 + 𝐷 2 − 1 17

The utility functions 𝑣(𝑦) 1 + 𝐷 𝐽 2 − 1 𝑣 𝐷 𝐽 𝑣 𝛾 𝑣 𝐷 1 + 𝐷 2 − 1 18

The utility functions 𝑣(𝑦) 𝑣 + 𝑣 𝐷 1 + 𝐷 2 − 1 1 + 𝐷 𝐽 2 − 1 𝛾 𝑣 + 𝑣 𝐷 𝐽 1 + 𝐷 𝐽 2 − 1 𝑣 𝐷 𝐽 𝑣 𝛾 𝑣 𝐷 1 + 𝐷 2 − 1 19

One more assumption Constant-return-to-scale technologies • 𝑗 : illiquid (higher-yield technology) 1 < 𝑆 𝑚 < 𝑆 𝑗 • 𝑚 : liquid (lower-yield technology) 𝑈: 0 1 2 𝑗 : −1 𝑆 𝑗 −1 1 𝑚 : −1 𝑆 𝑚 20

Recap ( What’s new?) • 𝛽 ∽ 𝑔 𝛽 𝛽 ∗ 1 0, 𝛽 𝛽 𝑣 𝑣 𝐷 1 + 𝐷 2 − 1 • 𝑉 𝑦 = + or 𝛾 𝑣 • 𝑗 (illiquid) returns 𝑆 𝑗 in 𝑈 = 2 • 𝑚 (liquid) returns 𝑆 𝑚 in 𝑈 = 2 21

Banks Separated system Unified system (only 𝑚 ) (both 𝑚 and 𝑗 ) 22

Contract 𝛿 𝑑 1 𝑨 𝑡𝑞𝑓𝑑𝑗𝑔𝑗𝑓𝑡 2 (α 1 ) 𝑑 𝐽 2 α 1 𝑑 𝑄 𝛿 = % of endowment in 𝑚 𝑑 1 𝑨 = withdrawal in 𝑈 = 1 2 𝛽 1 = withdrawal in 𝑈 = 2 if he also withdrew in 𝑈 = 1 𝑑 𝐽 2 𝛽 1 = withdrawal in 𝑈 = 2 if he did not withdraw 𝑑 𝑄 in 𝑈 = 1 23

Welfare No entry costs Perfect competition Maximize utility 24

Welfare Remarks: • 𝑑 1 𝑨 = 1 Maximum withdrawal in 𝑈 = 1 • 𝛿𝑧 ≤ 𝛽 ∗ 1 Maximum investment in 𝑚 25

Welfare 𝛽 • 𝛽 ≤ 𝛿𝑧 All impatient agents satisfied 26

Welfare 𝛽 • 𝛽 ≤ 𝛿𝑧 All impatient agents satisfied • 𝛽 > 𝛿𝑧 Only 𝛿𝑧 impatient agents satisfied 27

Welfare 𝛿𝑧 2 𝛽 − 1 + 𝛽𝑣 2 𝛽 𝑋 = 𝑣 + 1 − 𝛽 𝑣 1 − 𝛿 𝑧𝑆 𝑗 + 𝑑 𝑄 1 − 𝛿 𝑧𝑆 𝑗 + 𝑑 𝐽 𝑔 𝛽 𝑒𝛽 + 0 𝛽 2 𝛽 − 1 + + [ 1 − 𝛽 + 𝛿𝑧 𝑣 + 𝛽 − 𝛿𝑧 𝛾 𝑣 + 1 − 𝛽 𝑣 1 − 𝛿 𝑧𝑆 𝑗 + 𝑑 𝑄 𝛿𝑧 2 𝛽 − 1 + 𝛿𝑧𝑣 2 𝛽 + 𝛽 − 𝛿𝑧 𝑣 1 − 𝛿 𝑧𝑆 𝑗 + 𝑑 𝑄 1 − 𝛿 𝑧𝑆 𝑗 + 𝑑 𝐽 ]𝑔 𝛽 𝑒𝛽 28

Welfare Nobody is rationed 𝛿𝑧 𝑈 𝑈 𝛽 𝑣 + 𝑣 𝐷 𝐽 + 1 − 𝛽 𝑣 + 𝑣 𝐷 𝑄 𝑔 𝛽 𝑒𝛽 0 𝑈 𝛽 𝑣 + 𝑣 𝐷 𝐽 : utility of all impatient agents 𝑈 1 − 𝛽 𝑣 + 𝑣 𝐷 𝑄 : utility of all patient agents 29

Welfare 𝜷 − 𝜹𝒛 𝐛𝐬𝐟 rationed 𝛽 𝑈 𝑈 𝑈 𝛿𝑧 𝑣 + 𝑣 𝐷 𝐽 + 1 − 𝛽 𝑣 + 𝑣 𝐷 𝑄 + 𝛽 − 𝛿𝑧 𝛾 𝑣 + 𝑣 𝐷 𝑄 𝑔 𝛽 𝑒𝛽 𝛿𝑧 𝑈 𝛿𝑧 𝑣 + 𝑣 𝐷 𝐽 : utility of all satisfied impatient agents 𝑈 1 − 𝛽 𝑣 + 𝑣 𝐷 𝑄 : utility of all patient agents 𝑈 𝛽 − 𝛿𝑧 𝛾 𝑣 + 𝑣 𝐷 𝑄 : utility of all rationed impatient agents 30

Welfare 𝑔 𝛽 If it was discrete: 𝑋 = 𝑋 𝛽 1 𝑄 𝛽 1 + 𝑋 𝛽 2 𝑄 𝛽 2 + ⋯ But it is continuous: 𝛽 𝑋 = … 𝑔 𝛽 𝑒𝛽 0 𝛽 1 𝛽 2 𝛽 𝑋 𝛽 1 𝑋 𝛽 2 31

Constraints Resource constraint (only 𝑚 ) 2 𝛽 1 + 1 − 𝛽 1 𝑑 𝑄 2 𝛽 1 = 𝛿𝑧 − 𝛽 1 𝑆 𝑚 𝛽 1 ≤ 𝛿𝑧 𝛽 1 𝑑 𝐽 2 𝛽 1 + 1 − 𝛿𝑧 𝑑 𝑄 2 𝛽 1 = 0 𝛽 1 > 𝛿𝑧 𝛿𝑧𝑑 𝐽 32

Constraints Resource constraint (only 𝑚 ) 2 𝛽 1 + 1 − 𝛽 1 𝑑 𝑄 2 𝛽 1 = 𝛿𝑧 − 𝛽 1 𝑆 𝑚 𝛽 1 ≤ 𝛿𝑧 𝛽 1 𝑑 𝐽 2 𝛽 1 + 1 − 𝛿𝑧 𝑑 𝑄 2 𝛽 1 = 0 𝛽 1 > 𝛿𝑧 𝛿𝑧𝑑 𝐽 LHS: amount of withdrawals in 𝑈 = 2 RHS: resources that can be withdrawn in 𝑈 = 2 33

Constraints Resource constraint (only 𝑚 ) 2 𝛽 1 + 1 − 𝛽 1 𝑑 𝑄 2 𝛽 1 = 𝛿𝑧 − 𝛽 1 𝑆 𝑚 𝛽 1 ≤ 𝛿𝑧 𝛽 1 𝑑 𝐽 2 𝛽 1 + 1 − 𝛿𝑧 𝑑 𝑄 2 𝛽 1 = 0 𝛽 1 > 𝛿𝑧 𝛿𝑧𝑑 𝐽 2 𝛽 1 : withdrawals of impatient agents in 𝑈 = 2 𝛽 1 𝑑 𝐽 2 𝛽 1 : withdrawals of patient agents in 𝑈 = 2 1 − 𝛽 1 𝑑 𝑄 34