A model to help guide monetary (and fiscal) policy-making that isn t a sticky-price Ricardian cashless NK model David Andolfatto
Overlapping generations model Two types of young, workers and investors. Workers endowed with y t, investors have storage k t F (k t ). All agents value future consumption only (linear). Constant population, equal mass of each type. Competitive eqm k t = y t, r t = F (y t ).
Money and bonds Government issues money M t and bonds B t. R m t R t gross nominal interest rate on money, bonds, resp. Assume G t = 0, so T t + M t + B t = R t 1 B t 1 + R m t 1 M t 1. Fiscal authority determines D t = µd t 1, D t M t + B t, and T t. Monetary authority determines R t (or θ t M t /D t ) and R m t. Legal restriction: money must be held as reserves against other securities.
Workers (banks) Deposit (save) y t in portfolio of money (m t ), bonds (b t ), loans (k t ). Loans and bonds earn same real return R t (p t /p t+1 ), so indeterminate. Workers maximizes wealth: max m t {R t (p t /p t+1 ) (y t m t ) + R m t (p t /p t+1 )m t + λ t [m t σ (y t m t )] τ t } If R t > R m t, then λ t > 0 and m t = σ(1 + σ) 1 y t (NB: R m when R m < R loosens reserve constraint). If R t = R m t, then workers indifferent between money, bonds, loans.
Investors Investors subject to debt constraint R t (p t /p t+1 )k t x t, so choice problem: max k t {F (k t ) R t (p t /p t+1 )k t + ξ t [x t R t (p t /p t+1 )k t ]} F (k t ) = (1 + ξ t )R t (p t /p t+1 ) If ξ t > 0, then k t = (p t+1 /p t )x t /R t and F (k t ) > R t (p t /p t+1 ). Note: high marginal (average) return on capital is consistent with constrained investment sector (Re: Gomme, Ravikumar, Rupert).
Equilibrium: normal times In normal times, (λ t > 0, ξ t = 0) and in SS, θ = M t /D t and (p t+1 /p t ) = (D t+1 /D t ) = (M t+1 /M t ) = µ. Note: fiscal authority determines inflation in steady-state. With µ so determined and R determined by MP, eqm investment determined by F (k ) = R/µ. Eqm real money balances m = σ(1 + σ) 1 y. Real bond holdings b = y m k and price-level p t = M t/m.
Equilibrium: financial crisis Exogenous decline in x t such that ξ t > 0 (assume λ t > 0 for now). Investment collapse ˆk = (µ/r)x < k. No change in demand for real money balances m = σ(1 + σ) 1 y. Since y = m + ˆb + ˆk, implication is that ˆb > b (substitution out of loans into bonds). Downward jump in price-level, but expected inflation remains unchanged.
Equilibrium: financial crisis and monetary policy Monetary policy response: lower R (increase θ via LSAP). Effect is to loosen debt-constraint ˆk = (µ/r)x. Each step down in R associated with increase in price-level (but not inflation). So, monetary easing (lowering R) helps investors. Lump-sum transfers targeted to young (esp. investors) would help too.
Equilibrium: liquidity trap and secular stagnation Suppose debt-contraints remain binding in (new) steady-state. Suppose R has been lowered as far as it can go, so R = R m. Then LSAPs ( θ) are inconsequential (do not even affect price-level). Only effect is to increase level of reserves held by workers ( excess reserves in banking sector). Relevant (monetary) policy instrument is now reduced to R = R m (IOR).
Equilibrium: liquidity trap and secular stagnation Whereas raising R m when R m < R (weakly) welfare improving, increasing R m = R is not (unless debt constraints slack and economy is dynamically ineffi cient). When debt-constraint binds, effect is to make constraint bind more tightly. Even when debt-constraint slack, increasing R m good for workers (savers), bad for investors (borrowers). Moreover, increase in R m causes price-level to fall (long-run inflation remains determined by fiscal authority).
Conclusions By many measures, economy appears back to normal. Unemployment rate, rate of return on capital, investment/output ratio. But not normal along several dimensions. Emp/Pop and LFPR remain low, nominal and real yields remain low, inflation and inflation expectations remain low, willingness to hold cash/reserves high. Moreover, normal UR, ROR on capital, and I/Y all consistent with depressed economy.
Conclusions IF economy is depressed in manner described above (binding DCs). IF long-run inflation is indeed anchored by fiscal policy. THEN not immediately clear how raising R m helps economy (apart from savers). Tell-tale sign of normalization (slackening debt constraints) would be price-level jump (transitory inflation). But in this model, no need for MP to hedge against that event by raising R m early (Yellen s argument).
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