Uncertainty, Liquidity and Financial Cycles Ge Zhou Zhejiang University Jan 2019, ASSA Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 1 / 26
2500.00 Recession SP 500 Index and Fixed Capital Formation Ratio 21.50000 21.00000 2000.00 20.50000 20.00000 1500.00 19.50000 19.00000 1000.00 18.50000 18.00000 500.00 SP 500 Index 17.50000 17.00000 0.00 Fixed Capital Formation Ratio 16.50000 16.00000
50 Annual Growth Rate of SP 500 and Fixed Capital Formation Ratio 20.00000 40 30 Recession 19.50000 19.00000 20 10 18.50000 18.00000 0 2009-07 2010-01 2010-07 2011-01 2011-07 2012-01 2012-07 2013-01 2013-07 2014-01 2014-07 2015-01 17.50000-10 -20-30 Growth Rate of SP 500 Fixed Capital Formation Ratio 17.00000 16.50000
Motivation Obvious Phenomenon: Inconsistence between macroeconomic uctuations and nancial cycles After the Great Recession, a slow economic recovery together with nancial booms Macroeconomy and nancial markets often blossom together. Very FEW Theoretical Explanation Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 4 / 26
What I Do Main Question: What are the roles of Uncertainty? My Answer: An endogenous Liquidity Allocation Mechanism between real economy and nancial system A simple theory based on a tractable continuous-time DSGE model of heterogenous agents Numerical Analysis of Global Dynamics Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 6 / 26
Key Assumptions Slower Adjustment of Macroeconomy than Financial Market. Physical capital has less liquidity than its corresponding equity. Financial Frictions: Skin in the Game Entrepreneurs have to take partial risk of their own investment. This leads to entrepreneur faces a leverage constraint that depends on his capital structure investment depends on not only equity price but also the capital structure Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 7 / 26
Main Insights Net Worth of an entrepreneur determines his ability of risk tolerance a ects corporate investment Recession Stage: Risk-averse entrepreneurs who have low net worth, will disinvest and hold more nancial assets. More funds ows into nancial system from real economy. There is a nancial booms but a slow economic recovery. Booms Stage: Entrepreneurs with high net worth have high investment demand. This leads to high equity prices. Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 8 / 26
Literature Bolton, Chen, Wang (JF, 2011) Bolton, Wang, Yang (Forthcoming in JF) Brunnermeier, Eisenbach and Sannikov (2013) Brunnermeier and Sannikov (AER 2014, 2017) Di Tella (JPE, 2017) He and Kondor (Econometrica, 2016) Kiyotaky and Moore (2012) Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 9 / 26
The Model: Environment Infinite identical risk-averse entrepreneurs that totally measured by 1. Infinite identical risk-neutral investors that totally measured by 1. ONLY entrepreneurs can run physical capital. Entrepreneurs raise funds by issuing equity and debt. Investors can buy equity and risk-free bonds. Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 10 / 26
Output Market Equity Market Entrepreneurs Investors Capital Market Bond Market Real Economy Financial System The Economic Structure
The Model: Entrepreneur s Balance Sheet Assets Liabilities Capital: qk (Outside) Equity: (1 χ) qk (Others ) Equity: qh Bond: (ν 1)W Net Worth: W Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 12 / 26
The Model: Key Assumption Less liquidity of physical capital because of transaction cost: Ψ (κ) < κ This implies that capital and equity are imperfect substitutive. The market price of physical capital is denoted by p. The evolving process of capital is given by dk = [Φ (ι) + Ψ (κ) δ] Kdt + σkdz Entrepreneurs face equity issuance constraint: χ χ. This leads to a leverage constraint for entrepreneurs from the equity issuance constraint the optimal investment choice depends on equity price, q, and the capital structure Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 13 / 26
The Model: Entrepreneurs s.t. Z max E fc,χ,ι,κ,ν,ζg χ χ qh 0 e ρt C 1 γ 1 γ dt νw χqk + qh dw = νwdr + (1 ν) Wrdt Cdt d (qh) qh = (ζ δ + µq + σσ q ) dt + (σ + σ q ) dz d (qk ) qk = [Φ (ι) + Ψ (κ) δ + µq + σσ q ] dt + (σ + σ q ) dz where A ι pκ dr = dt + [Φ (ι) + Ψ (κ) δ + µ q + σσ q ] dt + (σ + σ q ) dz q Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 14 / 26
The Model: Entrepreneurs Optimal Investment Ratio: (1 γ) ϕ (w) w ϕ 0 (w) νw ϕ 0 (w) + 1 Φ 0 (ι) = 1 q w qk W : the capital ratio; ϕ (w) J (W, qk ) / (qk )1 γ Relative Price between capital and equity valued by entrepreneurs: (1 γ) ϕ (w) w ϕ 0 (w) νw ϕ 0 (w) + 1 = qkj0 qk + νwj0 W νwj 0 W Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 15 / 26
The Model: Entrepreneurs Trade-O between Producing Capital and Purchasing Capital: Φ 0 (ι) K {z } = Ψ 0 (κ) K /p {z } Capital Formation by Producing Capital Formation by Purchasing Asset Pricing of Inside Equity: = A ι pκ + Φ (ι) + Ψ (κ) δ + µ q + σσ q q {z } γ + (1 ν) w ϕ00 ϕ 0 E (dr )/dt (σ + σ q ) 2 r + λ 2 V γ ϕ 0 {z } Liquidity Premium λ 2 : the Lagrangian multiplier of equity issuance constraint χ χ Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 16 / 26
The Model: Di erences with BS (2014, 2017) BS(2014, 2017): physical capital, equity: relative price is 1 Φ 0 (ι) K {z } = K /q {z} Capital Formation by Producing New Capital by Purchasing Non-Arbitrage Condition: one more unit of investment ratio Φ 0 (ι) K {z } = Ψ 0 (κ) K /p {z } Capital Formation by Producing Capital Formation by Purchasing Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 17 / 26
The Model: Investors s.t. max fc I 0,νg E 0 Z 0 e rt Cdt dw = νw dr + r (1 ν) W dt Cdt Asset Pricing of (Outside) Equity: A ι + Φ(ι) + Ψ (κ) δ + µ q + σσ q = r q {z } E (dr /dt) Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 18 / 26
Markov Equilibrium: 2nd-Order ODEs µ q q = q 0 (η) µ η η + 1 2 q00 (η) (σ η η) 2 n h ρ (1 γ) Φ(ι) δ + µ q + σ q γ σ 2 (σ + σq ) 2io ϕ (cη) 1 γ = max fc,ι,νg 1 γ + 1 2 (ν 1)2 (σ + σ q ) 2 η 2 ϕ 00 ( ) ν A ι q + (ν 1) [Φ(ι) δ + µ q + σ q σ] + + (1 ν) r c + (1 ν) γ (σ + σ q ) 2 ηϕ 0 η R 1 0 W i di R 1 0 qk i di : entrepreneurs wealth ratio over the aggregate wealth Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 19 / 26
Markov Equilibrium: Parameterization Set Similar Parameters Values as Brunnermeier and Sannikov (2014): Parameter Meaning Value ρ time discount rate of entrepreneurs 6% r time discount rate of investors 5% γ entrepreneur s risk aversion 2 A productivity level 12% δ depreciation rate 3% σ capital quality shock 2% φ investment function 10 χ equity issuance constraint 70% Investment function: Φ (ι) 1 φ p1 + 2φι 1 Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 20 / 26
Investment Ratio, Equity Price Growth and Equity Market Risk 0.25 0.2 q q q q 0.15 0.1 0.05 0 0.05 0.1 0 0.2 0.4 0.6 0.8 1 Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 21 / 26
Equity Price Growth and Net Liquidity to Financial System Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 22 / 26
Global Dynamics with Di erent Extents of Equity Issuance Constraint Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 23 / 26
Conclusion A tractable DSGE model of an endogenous liquidity allocation mechanism between real economy and nancial markets. The endogenous risks and liquidity allocation are helpful to understand the inconsistency between macroeconomic uctuations and nancial cycles. Ge Zhou (Zhejiang University) Uncertainty, Liquidity and Financial Cycles Jan 2019 24 / 26