Liquidity, Business Cycles, and Monetary Policy. Nobuhiro Kiyotaki and John Moore

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1 Liquidity, Business Cycles, and Monetary Policy Nobuhiro Kiyotaki and John Moore

2 1 Question How does economy uctuate with shocks to productivity and liquidity?! Want to develop a canonical model of monetary economy in which money is essential for smooth running of the economy What are the roles of monetary policy?

3 Approach: Real business cycles model + limited commitment present goods original lender borrower resell &claim claim to future goods new lenders How much can the original lender enforce the borrower to repay?! borrowing constraint How much can new lenders enforce the borrower to repay?! limited resaleability

4 2 Model homogeneous output Y t, capital K t and at money M t at each date agents, measure 1: E t P 1 s=t s t log c s All agent use their capital to produce goods: k t capital! r t k t goods >: k t capital start of date t 99K end of date t individually constant returns & decreasing returns in aggregate 8 >< r t = a t Kt 1 ; = r t K t = a t Kt Y t

5 Fraction of agents can invest in producing new capital: i t goods! i t new capital start of date t 99K end of date t investment opportunities are i.i.d., across people, through time no insurance market against arrival of investment opportunity

6 Equity: capital is speci c to the agent who produce it, but he can mortgage future returns by issuing equity one unit of equity issued at date t promises r t+1 ; r t+2 ; 2 r t+3 ; ::: Borrowing Constraint: an investing agent can mortgage at most fraction of the future returns from his new capital production Resaleability Constraint: at each date, an agent can resell at most t fraction of his equity holdings! (a t ; t ) follows a stationary Markov process

7 balance sheet at the end of date t money: p t m t+1 own equity issued: q i tn i t+1 equity of others: q o t n o t+1 own capital stock: q i tk t+1 net worth Simpli cation: at every date, an agent can mortgage up to a fraction t of his unmortgaged capital stock! equity of the others and unmortgaged capital stock become perfect substitutes: qt o = qt i = q t & n o t + k t n i t = n t Flow-of-funds and liquidity constraints: c t + i t + q t (n t+1 i t ) + p t m t+1 = (r t + q t )n t + p t m t n t+1 (1 )i t + (1 t )n t m t+1 0

8 Government chooses M t+1 (money supply), N g t+1 (government equity holding) and G t (government net spending/transfers), subject to the budget constraint: G t + q t (N g t+1 N g t ) = r t N g t + p t (M t+1 M t ) Claim 1: In the neighborhood of the steady state, (1 ) + (1 )(1 ), unconstrained, rst best allocation, no money E t MP K = rate of return on equity ' time preference rate (1 ) + < ( )(1 ) ) liquidity constrained, monetary equilibrium exists

9 Equilibrium: (p t ; q t ; I t ; K t+1 ; M t+1 ) as functions of aggregate state (K t ; a t ; t ; G t ; N g t+1) satisfying: a t K t = I t + G t + (1 )f[r t + (1 + t )q t + (1- t )q R t ]N t + p t M t g I t = [(r t + t q t )N t + p t M t ] (1 )(1 t )q R t N t 1 q t (1 )E t = E t (r t+1 + q t+1 )=q t p t+1 =p t C ss t+1 p t+1 =p t [r t+1 + t+1 q t+1 + (1 t+1 )qt+1]=q R t Ct+1 si K t+1 = K t + I t = N t+1 + N g t+1 q R t 1 q t 1 <

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16 Normal features of "monetary economy" interest rates spread between assets with di erent liquidity rate of return on money < rate of return on equity < time preference rate < expected marginal product of capital quantities and asset prices react to liquidity shock Policy: Can use open market operation to accommodate productivity shock and to o set shocks to liquidity (resaleability) Needs to buy (or lend against) partially resaleable assets which has liquidity premium