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O M O Guillaume Rocheteau, Randall Wright, - PowerPoint PPT Presentation

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O M O Guillaume Rocheteau, Randall Wright, Sylvia Xiaolin Xiao UC-Irvine, UW-Madison, UT-Sydney Presentation to the NBER, May, 2015 May 15, 2015 Rocheteau, Wright & Xiao () OMOs May

  1. O��� M����� O��������� Guillaume Rocheteau, Randall Wright, Sylvia Xiaolin Xiao UC-Irvine, UW-Madison, UT-Sydney Presentation to the NBER, May, 2015 May 15, 2015 Rocheteau, Wright & Xiao () OMO’s May 15, 2015 1 / 32

  2. Introduction New Monetarist model with money and bonds, A m and A b study two policies: LR inflation and a one-time OMO assets can differ in acceptability or pledgeability these differences are microfounded in information theory with random or directed search, and bargaining, price taking or posting Results: negative nominal rate, liquidity trap, sluggish prices, multiplicity OMO’s work, unless liquidity is not scarce or if the economy is in a trap, but what matters is ∆ A b and not ∆ A m Rocheteau, Wright & Xiao () OMO’s May 15, 2015 2 / 32

  3. Related Literature NM surveys: Williamson & Wright (2010), Nosal & Rocheteau (2011), Lagos et al (2014) Related monetary policy analyses: Williamson (2012,2013), Rocheteau & Rodriguez-Lopez (2013), Dong & Xiao (2014), Han (2014) McAndrews (May 8 speech): The Swiss National Bank, the European Central Bank, Danmarks Nationalbank, and Swedish Riksbank recently have pushed short-term interest rates below zero. This is ... unprecedented. Rocheteau, Wright & Xiao () OMO’s May 15, 2015 3 / 32

  4. Environment Each period in discrete time has two subperiods : in DM, sellers produce q ; buyers consume q in CM, all agents work � , consume x and adjust portfolios Period payoffs for buyers and sellers: U b ( x , � , q ) = U ( x ) − � + u ( q ) U s ( x , � , q ) = U ( x ) − � − c ( q ) NB: the buyers can be households, firms or financial institutions. Rocheteau, Wright & Xiao () OMO’s May 15, 2015 4 / 32

  5. Assets A m and A b can be used as payment instruments (Kiyotaki-Wright), collateral for loans (Kiyotaki-Moore) or repos (combination). asset prices: φ m and φ b pledgeability parameters: χ m and χ b Nominal returns: real liquid bonds: 1 + ρ = ( 1 + π ) / φ b nominal liquid bonds: 1 + ν = φ m / φ b nominal illiquid bonds: 1 + ι = ( 1 + π ) ( 1 + r ) Rocheteau, Wright & Xiao () OMO’s May 15, 2015 5 / 32

  6. Acceptability 3 types of DM meetings or trading needs/opportunities: α m = prob (type- m mtg): seller accepts only money α b = prob (type- b mtg): seller accepts only bonds α 2 = prob (type-2 mtg): seller accepts both Special cases: α b = 0: no one takes only bonds α b = α 2 = 0: no one takes bonds α b = α m = 0: perfect subs Rocheteau, Wright & Xiao () OMO’s May 15, 2015 6 / 32

  7. Policy Policy instruments: money growth rate = inflation rate: π liquid real bond supply: A b nominal bonds: omitted for talk but results (in paper) are similar tax: T adjusts to satisfy GBC after ∆ monetary policy NB: trading A b for A m ⇔ changing A b with A m fixed due to the ‘radical’ assumption that prices clear markets classical neutrality holds, but OMO’s can still matter NB: A b can be used to target ρ within bdds [ ρ , ι ] Rocheteau, Wright & Xiao () OMO’s May 15, 2015 7 / 32

  8. CM problem Let z m = φ m a m and z b = a b . Then W ( z m + z b ) = max { U ( x ) − � + β V ( ˆ z m , ˆ z b ) } st x + T = z m + z b + � − ( 1 + π ) ˆ z m − φ b ˆ z b Lemma (history independence): ( ˆ z m , ˆ z b ) ⊥ ( z m , z b ) Lemma (linear CM value function): W � ( · ) = 1 Rocheteau, Wright & Xiao () OMO’s May 15, 2015 8 / 32

  9. DM problem Let the terms of trade be given by p = v ( q ) where v is a mechanism (e.g., Walras, Nash, Kalai...). Then V ( z m , z b ) = W ( z m + z b ) + α m [ u ( q m ) − p m ] + α b [ u ( q b ) − p b ] + α 2 [ u ( q 2 ) − p 2 ] Liquidity constraint: p j ≤ ¯ p j , where p m = χ m z m , ¯ ¯ p b = χ b z b and ¯ p 2 = χ m z m + χ b z b Rocheteau, Wright & Xiao () OMO’s May 15, 2015 9 / 32

  10. Types of equilibria Lemma: We always have p m = ¯ p m but we can have either p 2 = ¯ p 2 , p b = ¯ p b (constraint binds in all mtgs) 1 p 2 < ¯ p 2 , p b = ¯ p b (constraint slack in type-2 mtgs) 2 p 2 < ¯ p 2 , p b < ¯ p b (constraint slack in type-2 & type- b mtgs) 3 Consider Case 1, where v ( q m ) = χ m z m , v ( q b ) = χ b z b and v ( q 2 ) = χ m z m + χ b z b Rocheteau, Wright & Xiao () OMO’s May 15, 2015 10 / 32

  11. Case 1 (bonds are scarce) Euler equations, ι = α m χ m λ ( q m ) + α 2 χ m λ ( q 2 ) s = α b χ b λ ( q b ) + α 2 χ b λ ( q 2 ) , where ι = nominal rate on an illiquid bond s = spread between yields on illiquid and liquid bonds λ ( q j ) = Lagrange multiplier on p j ≤ ¯ p j Rocheteau, Wright & Xiao () OMO’s May 15, 2015 11 / 32

  12. Nominal yield on liquid bond Standard accounting yields ρ = α m χ m λ ( q m ) − α b χ b λ ( q b ) + ( χ m − χ b ) α 2 λ ( q 2 ) 1 + α b χ b λ ( q b ) + α 2 χ b λ ( q 2 ) While ι > 0 is impossible, ρ < 0 is possible when, e.g., χ m = χ b and α m λ ( q m ) < α b λ ( q b ) ( A b has higher liquidity premium) or α m λ ( q m ) = α b λ ( q b ) and χ m < χ b ( A b is more pledgeable). Rocheteau, Wright & Xiao () OMO’s May 15, 2015 12 / 32

  13. Negative rates in practice Not all Treasury securities are equal; some are more attractive for repo financing than others... Those desirable Treasuries can be hard to find: some short-term debt can trade on a negative yield because they are so sought after. The Economist Interest rates on Swiss government bonds have been negative for a while. These bonds can be used as collateral in some markets outside of Switzerland where the Swiss franc cannot. Aleks Berentsen Rocheteau, Wright & Xiao () OMO’s May 15, 2015 13 / 32

  14. Case 1 policy results Effects of LR inflation: ∆ π > 0 ⇒ no effect on q b and z m � q m � q 2 � s � φ b � and ρ � (Fisher vs Mundell) Effects of one-time OMO: ∆ A b > 0 ⇒ z m � q m � q 2 � q b � s � φ b � and ρ � Sluggish prices: ∆ A m > 0 and ∆ A b < 0 ⇒ ∆ z m > 0 ⇒ P goes up by less than A m (quantity eqn fails for OMO) Rocheteau, Wright & Xiao () OMO’s May 15, 2015 14 / 32

  15. Other cases Case 2: p 2 < ¯ p 2 and p b = ¯ p b ∆ π > 0 ⇒ z m � q m � s � and no effect on q b or q 2 ∆ A b > 0 ⇒ q b � s � and no effects on z m , q m or q 2 Case 3: p 2 < ¯ p 2 and p b < ¯ p b ∆ π > 0 ⇒ z m � q m � but no other effects ∆ A b > 0 ⇒ no effect on anything (Ricardian equivalence) Cases 1, 2 or 3 obtain when A b is low, medium or high, resp. Rocheteau, Wright & Xiao () OMO’s May 15, 2015 15 / 32

  16. Effects of inflation

  17. Effects of OMO’s

  18. Variations Nominal bonds: A b and A m grow at rate π and OMO is a one-time change in levels Results are the same except ∂ q b / ∂π < 0 in Case 1 Long-term bonds: imply multiplier effects, but not big enough to generate multiple equilibria still, ∂ z m / ∂ A b is bigger, so prices look even more sluggish after injections of cash by OMO Rocheteau, Wright & Xiao () OMO’s May 15, 2015 18 / 32

  19. Liquidity trap Injections of cash... by a central bank fail to decrease interest rates and hence make monetary policy ineffective.” Wikipedia After the rate of interest has fallen to a certain level, liquidity- preference may become virtually absolute in the sense that almost everyone prefers cash to holding a debt which yields so low a rate of interest. In this event the monetary authority would have lost effective control over the rate of interest.” Keynes Rocheteau, Wright & Xiao () OMO’s May 15, 2015 19 / 32

  20. Liquidity trap with heterogeneous buyers Type- i buyers have α i j = prob (type- j mtg) For some type- i (e.g., banks) α i 2 > 0 = α i m = α i b They hold bonds and hold money iff A b < ¯ A b A m , A b > 0 ⇒ they must have same return adjusted for χ ’s Hence, ∀ A b < ¯ A b we get the lower bdd ρ ≡ ( χ m − χ b ) ι ι + χ b NB: In this economy ρ = 0 iff χ m = χ b or ι = 0 (Friedman rule). Rocheteau, Wright & Xiao () OMO’s May 15, 2015 20 / 32

  21. Liquidity trap with random search: Example Rocheteau, Wright & Xiao () OMO’s May 15, 2015 21 / 32

  22. Directed search with heterogeneous sellers Type- m and type-2 sellers sort into segmented submarkets Buyers can go to any submarket and are indifferent if both open We consider bargaining and posting terms of trade Generates a liquidity trap but now buyers choose their types Arrival rates are endogenous fns of submarket seller/buyer ratio σ ⇒ policy affects output on extensive and intensive margins ⇒ effect of money injection on E q is ambiguous Rocheteau, Wright & Xiao () OMO’s May 15, 2015 22 / 32

  23. Liquidity trap with directed search: Example Rocheteau, Wright & Xiao () OMO’s May 15, 2015 23 / 32

  24. Endogenous acceptability As in LPW, set χ j = 1 and let buyers produce bad assets at 0 cost all sellers recognize A m (for simplicity) but have cost κ to recognize A b , where κ differs by seller Sellers’ benefit of being informed is ∆ = ∆ ( z m ) If α = prob ( seller mtg ) and θ = buyers’ bargaining power, e.g., ∆ ( z m ) = α ( 1 − θ ) [ u ◦ q 2 ( z m ) − u ◦ q m ( z m ) − z b ] . θ Rocheteau, Wright & Xiao () OMO’s May 15, 2015 24 / 32

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