Intro Model Equilibrium Results Fed Model Liquidity crises Conclusion Appx. A Model of Monetary Exchange in Over-the-Counter Markets

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1 A Model of Monetary Exchange in Over-the-Counter Markets Ricardo Lagos New York University Shengxing Zhang London School of Economics

2 Money in financial over-the-counter markets Broad question: Quantity of money and performance of OTC markets What we do: Build model of fiat money used as medium of exchange in OTC markets Study effects of monetary policy on asset prices and financial liquidity How we do it: Embed the OTC market structure and gains from trade in financial assets of Duffi e, Gârleanu and Pedersen (2005) into the monetary framework of Lagos and Wright (2005)

3 Applications and results We show that the quantity of money and market microstructure: 1 Determine asset prices and standard measures of financial liquidity (spreads, trade volume, dealer supply of immediacy)

4 Applications and results We show that the quantity of money and market microstructure: 1 Determine asset prices and standard measures of financial liquidity (spreads, trade volume, dealer supply of immediacy) 2 Generate a speculative premium (or speculative bubble )

5 Applications and results We show that the quantity of money and market microstructure: 1 Determine asset prices and standard measures of financial liquidity (spreads, trade volume, dealer supply of immediacy) 2 Generate a speculative premium (or speculative bubble ) 3 Explain positive correlation between real stock yield and nominal Treasury yield (the Fed Model)

6 Applications and results We show that the quantity of money and market microstructure: 1 Determine asset prices and standard measures of financial liquidity (spreads, trade volume, dealer supply of immediacy) 2 Generate a speculative premium (or speculative bubble ) 3 Explain positive correlation between real stock yield and nominal Treasury yield (the Fed Model) 4 Lead to equilibria with recurrent belief driven liquidity crises (times of sudden large increases in trading delays and spreads, and sharp persistent declines in asset prices, trade volume, and dealer participation in marketmaking)

7 Environment Time. Discrete, infinite horizon, two subperiods per period Population. [0, 1] investors, [0, v] dealers (both infinitely lived) Commodities. Two divisible, nonstorable consumption goods: dividend good general good

8 Preferences Dealers: E 0 t=0 β t (c td h td ) Investors: E 0 t=0 β t (ε ti y ti + c ti h ti ) β (0, 1) : discount factor c td, c ti : consumption of general good h td, h ti : effort to produce general good y ti : consumption of dividend good ε ti : preference shock, i.i.d. over time, cdf G ( ) on [ε L, ε H ]

9 Endowments and production technology First subperiod A s productive units (trees) Each unit yields y dividend goods at the end of the first subperiod Each unit permanently fails with probability 1 π at the beginning of the period Failed units immediately replaced by new units (allocated uniformly to investors) Second subperiod Linear technology allows dealers and investors to transform effort into general goods

10 Assets Equity shares A s equity shares At the beginning of period t: (1 π) A s shares of failed trees disappear (1 π) A s shares of new trees allocated uniformly to investors Fiat money Money supply: A m t dollars Monetary policy: A m t+1 = µam t, µ R ++ (implemented with lump-sum injections/withdrawals)

11 Market structure First subperiod: OTC market money, equity (cum dividend) dealer-investor pairwise trade Walrasian trade between all dealers Second subperiod: centralized market general good, money, equity (ex dividend) Walrasian trade between all dealers and investors Anonymity quid pro quo trade money serves as means of payment

12 OTC market structure Investors Contact a dealer with probability δ Dealers Contact an investor with probability κ δ/v Have access to a competitive interdealer market Bilateral terms of trade Investor makes offer with probability θ Dealer makes offer with probability 1 θ

13 Timeline and marketstructure

14 Value functions Dealers W D t (a t ) : value of entering CM with a t (a m t, a s t ) Ŵ D t (a t ) : value of rebalancing portfolio a t in OTCM V D t (a t ) : value of entering OTCM Investors W I t (a t ) : value of entering CM V I t (a t, ε t ) : value of entering OTCM

15 Centralized market Dealers [ ] Wt D (a t ) = max c t h t + βvt+1 D (a t+1 ) c t,h t,ã t+1 c t + φ t ã t+1 h t + φ t a t a t+1 = (ã m t+1, πã s t+1) Investors [ Wt I (a t ) = max c t h t + β c t,h t,ã t+1 Vt+1 I ( at+1, ε ) ] dg (ε ) c t + φ t ã t+1 h t + φ t a t + T t a t+1 = (ã m t+1, πã s t+1 + (1 π) A s )

16 Dealer problem in OTCM where Vt D (a td ) = κθ Ŵ D Ŵ D t (a m td, as td ) dh t (a ti, ε) +κ (1 θ) + (1 κ) Ŵ D t (a td ) t (a t ) = max Ŵ D t (a m td, as td ) dh t (a ti, ε) â m t,â s t â m t + p t â s t a m t + p t a s t W D t (â m t, â s t ) p t : nominal equity price in the OTC interdealer market

17 Investor problem in OTCM Vt I (a ti, ε i ) = [ ] δθ ε i ya s ti + W t I (a m ti, as ti ) df D [ +δ (1 θ) ε i ya s ti + Wt I (a m ti, a s ti ) [ ] + (1 δ) ε i yati s + Wt I (a ti ) t (a td ) ] df D t (a td )

18 Trading situations in OTCM 1 Dealer with interdealer market 2 Dealer-investor trade investor offers w.p. θ dealer offers w.p. 1 θ

19 Dealer with interdealer market Dealer with a t = (a m t, a s t ) chooses (â m td, âs td ) â m td = { 0 if pt φ m t < φ s t a m t + p t a s t if φ s t < p t φ m t â s td = { a s t + 1 p t a m t if p t φ m t < φ s t 0 if φ s t < p t φ m t

20 Dealer-investor trade: formulation Investor with type ε and (a m ti, as ti ) contacts dealer with (am td, as td )

21 Dealer-investor trade: formulation Investor with type ε and (a m ti, as ti ) contacts dealer with (am td, as td ) w.p. θ investor offers (a m ti, as ti ), (am td, as td ), solves: [ ] εya s ti + W t I (a m ti, as ti ) max a m ti,a s ti,a m td,as td a m ti + am td + p t (a s ti + as td ) a m ti + a m td + p t (a s ti + a s td ) Ŵ D t (a m td, as td ) Ŵ D t (a m td, as td )

22 Dealer-investor trade: formulation Investor with type ε and (a m ti, as ti ) contacts dealer with (am td, as td ) w.p. θ investor offers (a m ti, as ti ), (am td, as td ), solves: [ ] εya s ti + W t I (a m ti, as ti ) max a m ti,a s ti,a m td,as td a m ti + am td + p t (a s ti + as td ) a m ti + a m td + p t (a s ti + a s td ) Ŵ D t (a m td, as td ) Ŵ D t (a m td, as td ) w.p. 1 θ dealer offers (a m ti, as ti ), (am td, a s td ), solves: max Ŵ a m ti,as ti,am td,a s t D (a m td, as td ) td a m ti + a m td + p t(a s ti + a s td ) am ti + a m td + p t (a s ti + a s td ) εya s ti + W I t (a m ti, a s ti ) εya s ti + W I t (a m ti, a s ti )

23 Dealer-investor trade: solution when investor offers { a m 0 if ε ti = t < ε ati m + p t ati s if ε < εt where a s ti = { a s ti + 1 p t a m ti if ε t < ε 0 if ε < ε t εt p t φ m t φ s t y

24 Dealer-investor trade: solution when dealer offers a m ti = { 0 if ε t < ε a m ti + p o t (ε) a s ti if ε < ε t a s ti = { a s ti + 1 pt o (ε) am ti if εt < ε 0 if ε < εt where ( εy + φ pt o s ) (ε) t εt y + φ s p t t

25 Euler equations: dealers φ m t β max ( φ m t+1, φs t+1 /p ) t+1 φ s t βπ max ( p t+1 φ m t+1, ) φs t+1

26 Euler equations: investors φ m t β [ φ m t+1 + δθ εh ε t+1 ( εi y + φ s ) ] t+1 φ m t+1 dg (ε i ) p t+1

27 Euler equations: investors φ m t β [ φ m t+1 + δθ εh ε t+1 ( εi y + φ s ) ] t+1 φ m t+1 dg (ε i ) p t+1 [ ε φ s t βπ εy + φ s t+1 + δθ t+1 [ pt+1 φ m t+1 ( ] ε i y + φ s )] t+1 dg (εi ) ε L

28 Nonmonetary equilibrium Proposition (i) A nonmonetary equilibrium exists for any parametrization. (ii) In the nonmonetary equilibrium: there is no trade in the OTC market A s I = A s A s D = As (only investors hold equity shares) the equity price is: φ s = βπ 1 βπ εy.

29 Monetary equilibrium Proposition (i) If µ (β, µ), there is one stationary monetary equilibrium. (ii) For any µ (β, µ), ε (ε L, ε H ) is the unique solution to (1 βπ) ε H ε [1 G (ε)] dε ε + βπ [ ε ε + δθ ] µ β ε G (ε) dε I βδθ = 0. { ˆµ<µ} (iii) As µ µ, ε ε L and φ s (iv) As µ β, ε ε H and φ s ε L βπ 1 βπ εy. βπ 1 βπ ε H y.

30 Stationary monetary equilibrium

31 Asset prices and inflation Proposition In the stationary monetary equilibrium: φ s / µ < 0

32 Asset prices and inflation: equity 12 x 105 Equity prices (ex dividend, daily) t (years)

33 Asset prices and OTC frictions (delays and market power) Proposition In the stationary monetary equilibrium: (i) φ s / (δθ) > 0 (ii) Z / δ > 0, for µ ( ˆµ, µ)

34 Asset prices and OTC frictions: equity 7 x 105 Equity prices (ex dividend, daily) t (years)

35 Asset prices and OTC frictions: real balances 2 x 106 Real balances t (years)

36 Measures of financial liquidity Trade volume Bid-ask spreads Liquidity provision by dealers

37 Speculation (e.g., Harrison and Kreps, 1978) Define the speculative premium as P = φ s βπ 1 βπ εy

38 Speculative premium 6 x 105 Speculative premium t (years)

39 The Fed Model

40 Log dividend yield in the nonmonetary equilibrium: log D t+1 log φ s t = log [(1 + r) γπ] where D t = εy t and D t+1 γπd t

41 Log dividend yield in the nonmonetary equilibrium: log D t+1 log φ s t = log [(1 + r) γπ] where D t = εy t and D t+1 γπd t Modigliani-Cohn hypothesis: log D t+1 log φ s t = log [(1 + ι) γπ] "Explanation" of positive relation between nominal bond yield ι = (µ β γ)/β γ and dividend yield

42 Log dividend yield in the nonmonetary equilibrium: log D t+1 log φ s t = log [(1 + r) γπ] where D t = εy t and D t+1 γπd t Modigliani-Cohn hypothesis: log D t+1 log φ s t = log [(1 + ι) γπ] "Explanation" of positive relation between nominal bond yield ι = (µ β γ)/β γ and dividend yield Liquidity/monetary considerations + resale option: log D t+1 log φ s t = log [(1 + r) γπ] log ɛ (ι) { ε } ɛ (ι) max ε, ε + δθ G (ε) dε with ɛ (ι) < 0 ε L

43 Log dividend yield in the nonmonetary equilibrium: log D t+1 log φ s t = log [(1 + r) γπ] where D t = εy t and D t+1 γπd t Modigliani-Cohn hypothesis: log D t+1 log φ s t = log [(1 + ι) γπ] "Explanation" of positive relation between nominal bond yield ι = (µ β γ)/β γ and dividend yield Liquidity/monetary considerations + resale option: log D t+1 log φ s t = log [(1 + r) γπ] log ɛ (ι) { ε } ɛ (ι) max ε, ε + δθ G (ε) dε with ɛ (ι) < 0 ε L

44 Endogenous trading delays: dealer entry δ (v) : probability investor contacts a dealer κ (v) δ (v) /v: probability dealer contacts an investor κ (v) < 0 < δ (v) Free entry: to participate in OTCM of t + 1 dealer must pay k > 0 general goods in the CM of t

45 Free-entry equilibrium Equilibrium conditions as before, plus the free-entry condition where Φ t+1 = βκ (v t+1 ) (1 θ) Φ t+1 k 0, with = if v t+1 > 0 { G (ε t+1) S b t+1 + [1 G (ε t+1)] S a t+1} φ t+1 S b t+1 ε t+1 [p t+1 pt+1 o (ε)]a I dg (ε) t+1 ε L G ( εt+1 ) S a t+1 εh ε t+1 A m It+1 [pt+1 o dg (ε) (ε) p t+1 ] pt+1 o (ε) 1 G ( εt+1 ) φ t+1 max ( φ m t+1, φs t+1 /p ) t+1

46 Sunspots σ ij Pr (S t+1 = S j S t = S i ) (S i is a sunspot) ] εh ε ε j Z i = β γ µ σ ij [1 + δθ j εj εj + φ s dg (ε) Z j j [ ( ε φ s i = β γπ σ ij φ s )] j + max εj j, ε + δθ (εj ε)dg (ε) j ε L [ ] k = (1 θ) β γ δ (v j ) ε A s j Ij (ε εh ε εj j ε)dg (ε) + Z j v j ε L εj ε+ φ s dg (ε) j ε A s Ij = A s if εj j < ε + δθ (εj ε)dg (ε) ( = (1 π) A s otherwise) ε L Z j = A s Dj +δ(v j )G (ε j )As Ij δ(v j )θ[1 G (εj )] 1 ε j + φ s +δ(v j )(1 θ) ε H j ε j 1 ε+ φ s dg (ε) j

47 12 Equity prices (ex dividend, daily) t (years)

48 Equity prices (ex dividend, daily) Investor`s trading probability in the OTC market Dealers` overnight asset holding t (years) t (years) t (years) 12 Trade volume (value, in terms of numeraire good) 1.5 x 10 4 Average real spread 12 Real balances t (years) t (years) t (years)

49

50 Summary A model of monetary exchange in OTC markets Liquidity and asset prices in OTC markets Inflation: distorts the asset allocation across investors reduces trade volume reduces dealers incentives to provide liquidity increases ask-spreads Asset prices contain a speculative premium that: decreases with inflation decreases with OTC frictions (trading delays, power of dealers)

51 Summary Dynamic stochastic equilibria with episodes that resemble crises: speculative premium bursts sudden, sharp decline in asset price liquidity dries up sudden, sharp decline in marketmaking and trade volume sudden, sharp increase in trading delays and spreads per share

52 Summary Dynamic stochastic equilibria with episodes that resemble crises: speculative premium bursts sudden, sharp decline in asset price liquidity dries up sudden, sharp decline in marketmaking and trade volume sudden, sharp increase in trading delays and spreads per share

53 Summary Dynamic stochastic equilibria with episodes that resemble crises: speculative premium bursts sudden, sharp decline in asset price liquidity dries up sudden, sharp decline in marketmaking and trade volume sudden, sharp increase in trading delays and spreads per share

54 Summary Dynamic stochastic equilibria with episodes that resemble crises: speculative premium bursts sudden, sharp decline in asset price liquidity dries up sudden, sharp decline in marketmaking and trade volume sudden, sharp increase in trading delays and spreads per share

55 Summary Dynamic stochastic equilibria with episodes that resemble crises: speculative premium bursts sudden, sharp decline in asset price liquidity dries up sudden, sharp decline in marketmaking and trade volume sudden, sharp increase in trading delays and spreads per share

56 end.

57 Sunspots example β = (0.99) 1/365 γ = E ( ) yt+1 y t ε U [0.01, 20] Σ = SD ( yt+1 y t = (1.04) 1/365 y t ) = δ (v) = 1 e (0.1)v π = (0.9) 1/365 k = 0.1 θ = 0.5 y t+1 = µe x t+1 y t µ = (1.03) 1/365 x t+1 N ( Σ 2 /2, Σ 2) σ 00 = (0.996) 1/365 ; σ 11 1 φ s 0 /φs 1 δ (v 0 ) δ (v 1 ) Z 0 /Z 1 ε 0 /ε 1 A s D0 A s D

58 The Fed Model