The I Theory of Money Markus K. Brunnermeier & Yuliy Sannikov - PowerPoint PPT Presentation

The I Theory of Money Markus K. Brunnermeier & Yuliy Sannikov Brunnermeier & Sannikov Princeton University Capri, June 24 th , 2015 CSEF-IGIER Symposium

Motivation  Framework to study monetary and fin financial stability  Interaction between monetary and macroprudential policy  Connect th theory of f value and th theory of f money  Intermediation (credit) • “Excessive” leverage and liquidity mismatch  Inside money – as store of value • Demand for money rises with endogenous volatility • In downturns, intermediaries create less inside money  Endogenous money multiplier = f(capitalization of critical sector) • Value of money goes up – Disinflation spiral a la Fisher (1933) • Fire-sales of assets – Liquidity spiral Brunnermeier & Sannikov  Flight to safety  Time-varying risk premium and endogenous volatility dynamics

Some literature  Macro-friction models without money • Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015  “Money models” without intermediaries • Money pays no dividend and is a bubble – store of value Brunnermeier & Sannikov  With intermediaries/inside money • “Money view” (Friedman & Schwartz) vs. “Credit view”(Tobin)  New Keynesian Models: BGG, Christian et al., … money in utility function

Some literature  Macro-friction models without money • Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015  “Money models” without intermediaries • Store of value: Money pays no dividend and is a bubble Brunnermeier & Sannikov  With intermediaries/inside money • “Money view” (Friedman & Schwartz) vs. “Credit view”(Tobin)  New Keynesian Models: BGG, Christian et al., … money in utility function

Some literature  Macro-friction models without money • Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015  “Money models” without intermediaries • Store of value: Money pays no dividend and is a bubble Frictio Fric ion OL OLG deterministic endowment risk borrowing constraint Only money Samuelson With capital Diamond Brunnermeier & Sannikov  With intermediaries/inside money • “Money view” (Friedman & Schwartz) vs. “Credit view”(Tobin)  New Keynesian Models: BGG, Christian et al., … money in utility function

Some literature  Macro-friction models without money • Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015  “Money models” without intermediaries • Store of value: Money pays no dividend and is a bubble Fric Frictio ion OLG OL Incomple Inc lete Mark arkets + + idiosyncratic ic ri risk sk Risk deterministic endowment risk borrowing constraint Only money Samuelson Bewley With capital Diamond Ayagari, Krusell-Smith Brunnermeier & Sannikov  With intermediaries/inside money • “Money view” (Friedman & Schwartz) vs. “Credit view”(Tobin)  New Keynesian Models: BGG, Christian et al., … money in utility function

Some literature  Macro-friction models without money • Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015  “Money models” without intermediaries • Store of value: Money pays no dividend and is a bubble Fric Frictio ion OLG OL Inc Incomple lete Mark arkets + + idiosyncratic ic ri risk sk Risk deterministic endowment risk investment risk borrowing constraint Only money Samuelson Bewley With capital Diamond Ayagari, Krusell-Smith Basic “I Theory” Brunnermeier & Sannikov  With intermediaries/inside money • “Money view” (Friedman & Schwartz) vs. “Credit view”(Tobin)  New Keynesian Models: BGG, Christian et al., … money in utility function

Some literature  Macro-friction models without money • Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015  “Money models” without intermediaries • Store of value: Money pays no dividend and is a bubble Fric Frictio ion OLG OL Inc Incomple lete Mark arkets + + idiosyncratic ic ri risk sk Risk deterministic endowment risk investment risk borrowing constraint Only money Samuelson Bewley With capital Diamond Ayagari, Krusell-Smith Basic “I Theory” Brunnermeier & Sannikov  With intermediaries/inside money • “Money view” ( Friedman & Schwartz ) vs. “Credit view ”(Tobin)  New Keynesian Models: BGG, Christian et al., … money in utility function

Some literature  Macro-friction models without money • Kiyotaki & Moore, BruSan2014, He & Krishnamurthy, DSS2015  “Money models” without intermediaries • Store of value: Money pays no dividend and is a bubble Fric Frictio ion OLG OL Inc Incomple lete Mark arkets + + idiosyncratic ic ri risk sk Risk deterministic endowment risk investment risk borrowing constraint Only money Samuelson Bewley With capital Diamond Ayagari, Krusell-Smith Basic “I Theory” Brunnermeier & Sannikov  With intermediaries/inside money • “Money view” ( Friedman & Schwartz ) vs. “Credit view ”(Tobin)  New Keynesian Models: BGG, Christian et al., … money in utility function

Roadmap  Model absent monetary policy • Toy model: one sector with outside money • Two sector model • Adding intermediary sector and inside money  Model with monetary policy  Model with macro-prudential policy Brunnermeier & Sannikov

One sector basic model  Technologies 𝑏 𝐵 1  Each households can only operate one firm Brunnermeier & Sannikov • Physical capital 𝑒𝑙 𝑢 𝑏 + = (Φ 𝜅 𝑢 − 𝜀)𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝜏𝑒 𝑏 𝑎 𝑢 𝑙 𝑢 • Output sector idiosyncratic risk 𝑧 𝑢 = 𝐵𝑙 𝑢  Demand for money

Adding outside money Outside Money  Technologies 𝑏  𝑟 𝑢 𝐿 𝑢 value of physical capital 𝑐 + 𝜏𝑒 𝑟 𝑒𝑢 + Φ(𝜅 − 𝜀) 𝑒𝑢 + 𝜏 𝑐 𝑒𝑎 𝑢 𝑐 • Postulate constant 𝑟 𝑢 𝐵−𝜅 𝑎 𝑢 A L  𝑞 𝑢 𝐿 𝑢 value of outside money A L A L • Postulate value of money changes proportional to 𝐿 𝑢 A L Net worth Money 𝐵 1  Each households can only operate one firm Brunnermeier & Sannikov • Physical capital 𝑒𝑙 𝑢 𝑏 + = (Φ 𝜅 𝑢 − 𝜀)𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝜏𝑒 𝑏 𝑎 𝑢 𝑙 𝑢 • Output sector idiosyncratic risk 𝑧 𝑢 = 𝐵𝑙 𝑢  Demand for money

Adding outside money Outside Money  Technologies 𝑏  𝑟𝐿 𝑢 value of physical capital • 𝑒𝑠 𝑏 = 𝐵−𝜅 𝑏 + 𝜏𝑒 𝑟 𝑒𝑢 + Φ(𝜅 − 𝜀) 𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝑏 𝑎 𝑢 A L  𝑞𝐿 𝑢 value of outside money A L A L • 𝑒𝑠 𝑁 = Φ(𝜅 − 𝜀) 𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝑏 A L 𝑕 Net worth Money 𝐵 1  Each households can only operate one firm Brunnermeier & Sannikov • Physical capital 𝑒𝑙 𝑢 𝑏 + = (Φ 𝜅 𝑢 − 𝜀)𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝜏𝑒 𝑏 𝑎 𝑢 𝑙 𝑢 • Output sector idiosyncratic risk 𝑧 𝑢 = 𝐵𝑙 𝑢  Demand for money

∞ 𝑓 −𝜍𝑢 log 𝑑 𝑢 𝑒𝑢 Demand with 𝐹 Outside Money 0  Technologies 𝑏  𝑟𝐿 𝑢 value of physical capital 𝑏 + • 𝑒𝑠 𝑏 = 𝐵−𝜅 𝜏𝑒 𝑏 𝑟 𝑒𝑢 + Φ(𝜅 − 𝜀) 𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝑎 𝑢  𝑞𝐿 𝑢 value of outside money A L A L • 𝑒𝑠 𝑁 = Φ(𝜅 − 𝜀) A L 𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝑏 A L 𝑕 Net worth Money  Consumption demand: 𝜍 𝑞 + 𝑟 𝐿 𝑢 = 𝐵 − 𝜅 𝐿 𝑢 𝐵 1  Asset (share) demand 𝑦 𝑏 : 𝑏 𝑒𝑜 𝑢 𝐹 𝑒𝑠 𝑏 − 𝑒𝑠 𝑁 /𝑒𝑢 = 𝐷𝑝𝑤[𝑒𝑠 𝑏 − 𝑒𝑠 𝑁 , ] = 𝑦 𝑏 𝜏 2 𝑏 𝑜 𝑢 𝑒𝑠 𝑁 +𝑦 𝑏 𝑒𝑠 𝑏 −𝑒𝑠 𝑁 Brunnermeier & Sannikov 𝑦 𝑏 = 𝐹 𝑒𝑠 𝑏 −𝑒𝑠 𝑁 /𝑒𝑢 = (𝐵−𝜅)/𝑟 𝑟 = 𝜏 2 𝜏 2 𝑟+𝑞 Φ ′ 𝜅 = 1/𝑟  Investment rate: (Tobin’s q) 𝜆 log(𝜆𝜅 + 1) ⇒ 𝜅 ∗ = 𝑟−1 • For Φ 𝜅 = 1 𝜆

Demand with log-utility Outside Money  Technologies 𝑏  𝑟𝐿 𝑢 value of physical capital 𝑏 + • 𝑒𝑠 𝑏 = 𝐵−𝜅 𝜏𝑒 𝑏 𝑟 𝑒𝑢 + Φ(𝜅 − 𝜀) 𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝑎 𝑢  𝑞𝐿 𝑢 value of outside money A L A L • 𝑒𝑠 𝑁 = Φ(𝜅 − 𝜀) A L 𝑒𝑢 + 𝜏 𝑏 𝑒𝑎 𝑢 𝑏 A L 𝑕 Net worth Money  Consumption demand: 𝜍 𝑞 + 𝑟 𝐿 𝑢 = 𝐵 − 𝜅 𝐿 𝑢 𝐵 1  Asset (share) demand 𝑦 𝑏 : 𝑏 𝑒𝑜 𝑢 𝐹 𝑒𝑠 𝑏 − 𝑒𝑠 𝑁 /𝑒𝑢 = 𝐷𝑝𝑤[𝑒𝑠 𝑏 − 𝑒𝑠 𝑁 , ] = 𝑦 𝑏 𝜏 2 𝑏 𝑜 𝑢 𝑒𝑠 𝑁 +𝑦 𝑏 𝑒𝑠 𝑏 −𝑒𝑠 𝑁 Brunnermeier & Sannikov 𝑦 𝑏 = 𝐹 𝑒𝑠 𝑏 −𝑒𝑠 𝑁 /𝑒𝑢 = (𝐵−𝜅)/𝑟 𝑟 = 𝜏 2 𝜏 2 𝑟+𝑞 Φ ′ 𝜅 = 1/𝑟  Investment rate: (Tobin’s q) 𝜆 log(𝜆𝜅 + 1) ⇒ 𝜅 ∗ = 𝑟−1 • For Φ 𝜅 = 1 𝜆