Bubbles, Money and Liquidity Traps: an Analytical Perspective

Transcription

1 Bubbles, Money and Liquidity Traps: an Analytical Perspective Vladimir Asriyan, Luca Fornaro, Alberto Martin and Jaume Ventura CRE, UPF and Barcelona GSE 18th June, 2015 AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

2 Facts and Questions Key features of the last two decades: large uctuations in net worth large uctuations in money holdings low nominal and real interest rates: liquidity trap macro aggregates correlated with net worth AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

3 Net Worth, AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

4 Money, AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

5 Real nterest Rates, AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

6 n ation Rate, AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

7 Nominal nterest Rates, AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

8 Macro aggregates, AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

9 Facts and questions Key features of the last two decades: large uctuations in net worth large uctuations in money holdings low nominal and real interest rates: liquidity trap macro aggregates correlated with net worth Key questions why have uctuations in net worth and money holdings become so large? how are they connected to low interest rates? what are their e ects on output, consumption and investment? AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

10 This paper Model of bubbles, money and investment Theoretical framework with the following features: liquidity traps appear when there is a shortage of stores of value money holdings expand at the expense of investment in capital bubbles raise collateral, crowd out money and crowd in investment Application to recent events: several factors have put downward pressure on interest rates dot.com and housing bubbles temporarily alleviated these pressures after their collapse the economy entered into a liquidity trap AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

11 This paper Model of bubbles, money and investment Theoretical framework with the following features: liquidity traps appear when there is a shortage of stores of value money holdings expand at the expense of investment in capital bubbles raise collateral, crowd out money and crowd in investment Application to recent events: several factors have put downward pressure on interest rates dot.com and housing bubbles temporarily alleviated these pressures after their collapse the economy entered into a liquidity trap AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

12 Related literature Rational bubbles Samuelson (1958), Tirole (1985) Bubbles and nancial frictions Caballero and Krishnamurthy (2006), Farhi and Tirole (2010), Miao and Wang (2011), Aoki and Nikolov (2011), Kraay and Ventura (2007), Kocherlakota (2010), Martin and Ventura (2011, 2012, forthcoming), Ventura (2011) Liquidity traps Krugman (1998), Eggertson and Woodford (2003), Werning (2011), Eggertson and Mehrotra (2014), Buera and Nicolini (2014), Benigno and Fornaro (2015) AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

13 Model Two-period OLG structure All individuals maximize: U i t = E t C i t,t+1 Savers: Supply one unit of labor when young and receive wage Wt Save by leding to entrepreneurs Ft and by holding money M t Entrepreneurs (or bankers?): Supply one unit of labor when young and receive wage Wt Construct portfolios of capital and bubbles, Kt and B t Finance their activities by selling credit contracts, Ft AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

14 Capital and bubbles Capital: nvestment by entrepreneurs, full depreciation Production: F (Kt, N t ) = Kt α (γ t N t ) 1 α, where γ 1 Bubbles: ntrinsically useless assets only held for resale nitiated and traded by entrepreneurs Law of motion: Bt+1 = g t+1 B t + N t+1 F F g t+1 is growth in the value of old bubbles N t+1 value of new bubbles AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

15 Money Used to facilitate transactions and as store of value Rate of money growth set by government seignorage rebated lump-sum M t+1 = µ M t and T t+1 = M t+1 M t p t+1 Savers subject to cash-in-advance constraint M t 1 ν p t+1 C S t+1 AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

16 Credit Entrepreneurs sell credit contracts to savers Promise a contingent gross return Rt+1 Et R t+1 is the real interest rate Credit contracts need to be collateralized: R t+1 F t φ r t+1 K t+1 + B t+1 where r t+1 denotes the rental price of capital One constraint for each possible future AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

17 Market equilibria Factor markets: w t = (1 α) k α t and r t = α k α 1 t Market for bubbles: E t g t+1 = E t R t+1 Money market clears: 1 π t+1 R t+1 (1 ε) (1 α) kα t m t (ν µ) m t and E t where π t+1 denotes the in ation rate Credit market clears: R t+1 = γ φ α kt+1 α + b t+1 (1 ε) (1 α) kt α m t where the borrowing constraint binds 1 E t R t+1 π t+1 AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

18 Equilibrium dynamics From aggregate resource constraint: γ k t+1 = (1 α) kt α m t b t Existence of bubbles requires low interest rates: possible sources ne cient investment (traditional view) Financial frictions (this paper) F here, low rates can also give rise to liquidity traps Finding equilibria: Propose process fgt, n t, π t g such that E t g t+1 = E t R t+1 and n t 0 Determine all possible sequences for state variables fkt, b t, m t g Check that all sequences satisfy kt 0, b t 0 and m t 0 AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

19 Case 1: Bubbleless Economy f b t = 0 for all t, 8 9 < µ φ α = m t = max, (1 ε) (1 α) µ φ α : ν µ {z }; kα t {z } CA Regime Liquidity Trap The economy is in a liquidity trap if: Transaction needs are low: high ν Credit supply is high relative to credit demand: low ε and φ n ation tax is low and return on money is high: low µ AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

20 Case 1: Bubbleless Economy AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

21 Case 2: Bubbly Economy f b 0 = 0 and n t = x kt α for all t, then the bubble grows and the economy transitions to a steady state fb, mg, where 8 < µ φ α + x B m = max, (1 ε) (1 α) µ φ 9 = α + x B : ν µ {z } {z } ; kα CA Regime Liquidity Trap where b = x B k α. AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

22 Case 2: Bubbly Economy AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

23 Facts and questions Key features of the last two decades: large uctuations in net worth large uctuations in money holdings low nominal and real interest rates: liquidity trap macro aggregates correlated with net worth Key questions: why have uctuations in net worth and money holdings become so large? how are they connected to low interest rates? what are their e ects on output, consumption and investment? AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

24 Facts and questions Key features of the last two decades: large uctuations in net worth large uctuations in money holdings low nominal and real interest rates: liquidity trap macro aggregates correlated with net worth Key questions: why have uctuations in net worth and money holdings become so large? how are they connected to low interest rates? what are their e ects on output, consumption and investment? AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

25 General narrative Declining real and nominal interest rates: nancial globalization (increase in 1 ε) improvement in transactions technology (increase in ν) decline of in ation (fall in µ) Conditions for liquidity traps, but also for bubbles, to arise AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

26 Factors that have put downward pressure on interest rates AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

27 Dot.com, housing bubbles hid these pressures AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

28 When bubble bursts, economy enters liquidity trap AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

29 Conclusions Model of bubbles, money and investment Theoretical framework with the following features: liquidity traps appear when there is a shortage of stores of value money holdings expand at the expense of investment in capital bubbles raise collateral, crowd out money and crowd in investment Application to recent events: several factors have put downward pressure on interest rates dot.com and housing bubbles temporarily alleviated these pressures after their collapse the economy entered into a liquidity trap AFMV (CRE, UPF and Barcelona GSE) Secular Stagnation, Growth and Real nterest Rates 18th June, / 29

30 x M BB CA x CA x LT MM x B x M BB x LT MM x CA CA x B x M BB CA x CA x LT MM x B Figure 9