A model to help guide monetary (and …scal)
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 yt; investors have storage kt ! F (kt):
All agents value future consumption only (linear).
Constant population, equal mass of each type.
Competitive eqm kt = yt; rt = F 0(yt):
Money and bonds
Government issues money Mt and bonds Bt:
Rtm
Rt gross nominal interest rate on money, bonds, resp.
Assume Gt = 0; so Tt + Mt + Bt = Rt 1Bt 1 + Rtm 1Mt 1:
Fiscal authority determines Dt = Dt 1; Dt
Monetary authority determines Rt (or t
Mt + Bt; and Tt:
Mt=Dt) and Rtm:
Legal restriction: money must be held as reserves against other securities.
Workers (banks)
Deposit (save) yt in portfolio of money (mt); bonds (bt), loans (kt):
Loans and bonds earn same real return Rt(pt=pt+1); so indeterminate.
Workers maximizes wealth:
max fRt(pt=pt+1) (yt
mt
mt) + Rtm(pt=pt+1)mt + t [mt
If Rt > Rtm; then t > 0 and mt =
Rm < R loosens reserve constraint).
(yt
mt)]
(1 + ) 1yt (NB: " Rm when
If Rt = Rtm; then workers indi¤erent between money, bonds, loans.
tg
Investors
Investors subject to debt constraint Rt(pt=pt+1)kt
lem:
max fF (kt)
kt
Rt(pt=pt+1)kt + t [xt
xt; so choice prob-
Rt(pt=pt+1)kt]g
F 0(kt) = (1 + t)Rt(pt=pt+1)
If t > 0; then kt = (pt+1=pt)xt=Rt and F 0(kt) > Rt(pt=pt+1):
Note: high marginal (average) return on capital is consistent with constrained investment sector (Re: Gomme, Ravikumar, Rupert).
Equilibrium: normal times
In “normal” times, ( t > 0; t = 0) and in SS,
(pt+1=pt) = (Dt+1=Dt) = (Mt+1=Mt) = :
= Mt=Dt and
Note: …scal authority determines in‡ation in steady-state.
With so determined and R determined by MP, eqm investment determined by F 0(k ) = R= :
Eqm real money balances m = (1 + ) 1y:
Real bond holdings b = y
m
k and price-level pt = Mt=m :
Equilibrium: …nancial crisis
Exogenous decline in xt such that t > 0 (assume t > 0 for now).
^ = ( =R)x < k :
Investment collapse k
No change in demand for real money balances m = (1 + ) 1y:
^ implication is that ^b > b (substitution out of
Since y = m + ^b + k;
loans into bonds).
Downward jump in price-level, but expected in‡ation remains unchanged.
Equilibrium: …nancial crisis and monetary policy
Monetary policy response: lower R (increase
via LSAP).
^ = ( =R)x:
E¤ect is to loosen debt-constraint k
Each step down in R associated with increase in price-level (but not in‡ation).
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 = Rm:
Then LSAPs (" ) are inconsequential (do not even a¤ect price-level).
Only e¤ect is to increase level of reserves held by workers (“excess reserves” in banking sector).
Relevant (monetary) policy instrument is now reduced to R = Rm (IOR).
Equilibrium: liquidity trap and secular stagnation
Whereas raising Rm when Rm < R (weakly) welfare improving, increasing
Rm = R is not (unless debt constraints slack and economy is dynamically
ine¢ cient).
When debt-constraint binds, e¤ect is to make constraint bind more tightly.
Even when debt-constraint slack, increasing Rm good for workers (savers),
bad for investors (borrowers).
Moreover, increase in Rm causes price-level to fall (long-run in‡ation remains determined by …scal 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,
in‡ation and in‡ation 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 in‡ation is indeed anchored by …scal policy.
THEN not immediately clear how raising Rm helps economy (apart from
savers).
Tell-tale sign of “normalization” (slackening debt constraints) would be
price-level jump (transitory in‡ation).
But in this model, no need for MP to hedge against that event by raising
Rm early (Yellen’s argument).
Unemployment rate
Employment to population
Labor force participation rate