On the stability of money demand
Robert E. Lucas, Jr. and Juan Pablo Nicolini
discussion
by
Francesco Lippi (EIEF)
The 8th Bank of Portugal monetary conference on monetary economics
Lisbon , June 2015
F. Lippi (EIEF, U. Sassari)
discussion
Lisbon , June 2015
1 / 17
Fact: the relation between M1/GDP and r changes after the 80s
breakdown mostly due to deposit (not currency)
M1/GDP VS. INTEREST RATE (3-MONTH T-BILL), 1915-2012
0.5
0.45
1915-1980
0.4
1981-2012
M1/GDP
0.35
0.3
0.25
0.2
0.15
0.1
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
INTEREST RATE
reserves and M1 central to policy yet absent in standard macro models
Money: difficult to analyze both in theory and in data
I
what assets serve as money in practice?
regulation and technical change matter
I
in particular: NOW and MMDA (interest paying deposits) in early 1980s
-
MMDA allowed for limited checking but no limits on ATM withdrawals
-
MMDA close substitute to deposit but included in M2 (not in M1)
I
relevance: e.g. M, P, Y , r relationship (and welfare)
Empirical contribution: new measure of M1
NEW-M1 VS. OPPORTUNITY COST, 1915 - 2012
0.5
0.45
1915-1980
1981-2012
0.4
NEW-M1/GDP
0.35
0.3
0.25
0.2
0.15
0.1
0
0.02
0.04
0.06
0.08
0.1
0.12
OPPORTUNITY COST (RATE)
Essentially
M1new = M1 + MMDA
0.14
account for the low reaction of M1 to
lower interest rates and higher output af0.5 percent. Outter 1980 lowers both the estimated interest elasticity
people demand
and income elasticity. The relatively low income and
sactions is highinterest elasticity in the postwar period (1947–94) are
onsistent with
significantly different from the unitary income elasage rate as outticity and relatively high interest elasticity in the premand for money
war period (1903–45), leading Ball to argue against a
nse because the
stable long run money demand.4
e
terconstraints, agents’ portfolio decisions deces.
FIGURE
2
pend
on their
liquidity preferences and the
matreturn
on the assets.
term/nonterm
Actual
and
estimated
real balances
M1/P,The
1900–2003
mand
(interest
elasticity of
of monetary
0.5)
distinction
aggregates is
icity
aligned with private agents’ incentives.
largbillions of 2 0 0 0 dollars
Motley proposed classifying all nonwer
5,0 0 0
term deposits, money that can be accessed
A
without notice and at par, as a new mone5,
4,0 0 0
tary aggregate. Poole coined the name
sisMZM (money zero maturity) for the mea1.
3,0 0 0
sure. Specifically, MZM is defined as
e we
Related empirical analysis in Teles and Zhou (2005)
to
of
od
here
ela-
The
ed
–
or
Estimated
(M1 / P)
MZM = M2 – Small
denomination
time
deposits + Institutional MMMFs.
2,0 0 0
1,0 0 0
0
1 9 0 0 ’10
’2 0
’3 0
Institutional MMMFs, currently classified in M3, are interest-bearing checkable accounts
that/ P)allow holders to get
Actual (M1
around the zero-interest demand deposits
’4 0 ’5
’ 0
’6 0 ’70
’8 0 ’9 0 2 0 0 0
restriction.
Note s: Re stricting the intere st ela sticity to be .5, the e stimated re al balance s
are  M 1 
−0.5

 = 0.05Yt i t .
 P t
The demand for money
In appendix 1, we show that it is possible to derive from a simple stochastic
general equilibrium monetary model the
equilibrium relationship
Source: Authors’ calculations and Luca s (2 0 0 0).
the
2)
−ν
Perspectives
M t 1Q / 2005, Economic
= αYt ( it − itm ) ,
Pt
FIGURE 8
Actual and estimated real balances, M1/P (1900–79)
and MZM/P (1980–2003)
(common interest elasticity of 0.24)
billions of 2 0 0 0 dollars
7,0 0 0
6,0 0 0
Estimated M1 / P (1 9 0 0–7 9),
MZM / P (1 9 8 0–2 0 0 3)
5,0 0 0
4,0 0 0
3,0 0 0
Actual M1 / P (1 9 0 0–7 9),
MZM / P (1 9 8 0–2 0 0 3)
2,0 0 0
1,0 0 0
0
1 90 0
’1 3
’2 6
’3 9
’5 2
’6 5
’7 8
’9 1
2 00 4
Note s: Estimated 1 9 0 0–7 9:  M 1  = 0.13Y i −0.24 .
t t


 P t
 MZM 
m −0.24
.
Estimated 1 9 8 0–2 0 0 3:  PY  = 0.17Yt ( i t − i t )

t
MZM
= M1+ MMMF + MMDA
–0.07, respectively. It would also be apparent that the
curves would be shifted down.
Next, we estimate equation 2 using M1 as the
measure of money for the period 1900–79 and MZM
model review
Model competing means of payments / deposits
∞
X
be the fraction
of total purchases paid for in cash,c expressed
as a function of the
β t U(xt ) subject to
m ≥ cθ +dθd +aθa
(3)
n,γ,δ,x,c,d,a
cuto§ level
t=0 , the cash constraints facing this consolidated household/bank are
max
nc  px(),
(4)
nd  px [()  ()] ,
(5)
na  px [1  ()] .
(6)
The law of motion for money balances is


m + T + py(1  n)  px k d (F ()  F ()) + k a (1  F ()) + 1  (c  1)c
m0 =
1+
Notice that the function F measures numbers of transactions while  measures
– Key choices: 0 <γ < δ , and # transactions n
(m unit elasticity w.r.t. y )
1
numbers of dollars. Note also that the “lost” currency  c 1
=  cc = (c  1)c
does appear as a negative item of the right. The variable T denotes the lump sum
transfers, that include these cash balances lost and increases the total quantity of
base money by 1 + . The household Bellman equation is
model review
Model competing means of payments / deposits
∞
X
be the fraction
of total purchases paid for in cash,c expressed
as a function of the
β t U(xt ) subject to
m ≥ cθ +dθd +aθa
(3)
n,γ,δ,x,c,d,a
cuto§ level
t=0 , the cash constraints facing this consolidated household/bank are
max
nc  px(),
(4)
nd  px [()  ()] ,
(5)
na  px [1  ()] .
(6)
The law of motion for money balances is


m + T + py(1  n)  px k d (F ()  F ()) + k a (1  F ()) + 1  (c  1)c
m0 =
1+
Notice that the function F measures numbers of transactions while  measures
– Key choices: 0 <γ < δ , and # transactions n
(m unit elasticity w.r.t. y )
1
numbers of dollars. Note also that the “lost” currency  c 1
=  cc = (c  1)c
a right. The variable T denotes thec lump
a
does appear
as a negative
– Costs:
φn, Fixed
cost: item
k d <ofkthe
, “reserve requirements” θ , θd , θsum
transfers, that include these cash balances lost and increases
ther total quantity
of
0
0
– “Opportunity cost” of m = c + d + a
is
λm = V (m) 1+r
base money by 1 + . The household Bellman equation is
with λm (r ) > 0
model review
Tradeoffs
A unit of consumption x made of purchases of different size z:
Z ∞
z
1=
f (z) dz
ν
0
– checks
havestate
fixed
cost per-purchase
→ convenient
for satisfy
largefeasibility
purchase
A steady
equilibrium
with positive interest
rates must also
(2), the cash-in-advance constraints (4)  (6) and the distribution of base money
condition (3) must hold with equality. The normalized base money is 1.
– pin down γ (cash-good threshold), n # transactions
We can combine all these equations and obtain



1 (c  1) + r c  d

= kd

n



ra + (c  1) + r c  d () + r(d  a )(h(r))
n2 
=
d
(1  n)
[1 + k (F (h(r))  F ()) + k a (1  F (h(r)))]
(11)
(12)
These two equations determine the steady state values of (n, ). Then we can use (10)
to solve for .
resources
spent on “trips” to the bank: φn
Given the solution, we can construct theoretical counterparts of observables, as
resources spent on banking services k d (F (δ) − F (γ)) , k d (1 − F (δ))
follows: The ratio of money to output is given by
model review
Novelty is the multiplicity of bank liabilities
cash
c/(c + d + a) = Ω(γ)
deposits
Fraction of c purchases
0.12
d/(d + a)
Fraction of d/(d+a)
1
0.9
0.1
0.8
0.7
0.08
0.6
0.06
0.5
0.4
0.04
0.3
0.2
0.02
0.1
0
0
0.05
0.1
0.15
Interest rate
0
0
0.05
0.1
Interest rate
I
both cash and deposits are used even at r = 0 if θc > 1
I
No demand for MMDA at r = 0
0.15
0.4
model review
0.4
0.3
0.2
Main results from calibration (match 1984 values)
0.2
0.1
0
1980
1985
1990
1995
2000
2005
2010
0
1980
2015
1985
1990
c/(c + d + a)
1995
2000
2005
2010
2015
d/(d + a)
Figure 5b: Currency / Demand Deposits - trend component , 1984 - 2012
Figure 5d: Demand Deposits / (Demand Deposits+MMDAs) - trend component, 1984 - 2012
DATA
MODEL
1
DATA
MODEL
1
0.9
0.8
0.8
0.6
RATIO
RATIO
0.7
0.6
0.5
0.4
0.4
0.3
0.2
0.2
0.1
0
1980
1985
1990
1995
2000
2005
2010
2015
0
1980
1985
1990
1995
2000
37
36
2005
2010
2015
0.4
model review
0.4
0.3
0.2
Main results from calibration (match 1984 values)
0.2
0.1
0
1980
1985
1990
1995
2000
2005
2010
0
1980
2015
1985
1990
c/(c + d + a)
1995
2000
2005
2010
2015
d/(d + a)
Figure 5b: Currency / Demand Deposits - trend component , 1984 - 2012
Figure 5d: Demand Deposits / (Demand Deposits+MMDAs) - trend component, 1984 - 2012
DATA
MODEL
1
DATA
MODEL
1
0.9
0.8
0.8
0.6
RATIO
RATIO
0.7
0.6
0.5
0.4
0.4
0.3
0.2
0.2
0.1
0
1980
1985
1990
1995
2000
2005
2010
2015
0
1980
Figure 6: M1/GDP vs. Interest Rate (3-Month T-Bill), 1915 - 1935 & 1983 - 2012
1985
1990 5a: Currency
1995
2000
2005
2010 - 20122015
Figure
/ Demand
Deposits,
1984
Main results from calib
37
1
MODEL
DATA
0.5
RATIO
M1 / GDP
0.8
36
0.4
0.3
0.6
M
GDP
0.4
0.2
0.1
0
mo
DATA
MODEL
c
= A 1+(✓ n(r1)⌦(
)
⇠
=
)
A
n(r )
0.2
0
0.05
0.1
INTEREST RATE
0.15
0
1980
1985
1990
1995
c
2000
2005
2010
Comments
Comments
1. some details (on interest elasticity, multipliers &
transaction-costs specification)
2. on modeling M1: beyond households?
3. what did we learn?
interest elasticity
Non-monotone M(r ) when both γ and n endogenous
n(r ) has a 1/2 elasticity w.r.t. r for given γ and θc = 1, like BT model
interest elasticity
Non-monotone M(r ) when both γ and n endogenous
n(r ) has a 1/2 elasticity w.r.t. r for given γ and θc = 1, like BT model
but n(r ) is a non-monotone function of r when γ = γ(r , θi , k i )
and for θc > 1 model has satiation at r = 0
interest elasticity
Non-monotone M(r ) when both γ and n endogenous
n(r ) has a 1/2 elasticity w.r.t. r for given γ and θc = 1, like BT model
but n(r ) is a non-monotone function of r when γ = γ(r , θi , k i )
and for θc > 1 model has satiation at r = 0
θc = 1.01
θc = 1.005
M1 / GDP vs interest rate
0.36
0.3
0.34
0.29
0.32
0.28
0.3
0.27
0.28
0.26
0.26
0.25
0.24
0.24
0.22
0
0.05
0.1
Interest rate
M1 / GDP vs interest rate
0.15
0.23
0
0.05
0.1
Interest rate
0.15
interest elasticity
Interest elasticity of M1 at low interest r < 0.01
Satiation of money balances
Interest elasticity is small
M1 / GDP vs interest rate (log scale)
0.34
0
0.33
-0.02
Interest elasticity of M1 / GDP
0.32
0.31
-0.04
0.3
-0.06
0.29
-0.08
0.28
-0.1
0.27
-0.12
0.26
0.25
10-6
10-5
10-4
Interest rate
10-3
10-2
-0.14
0
0.002
0.004
0.006
Interest rate
0.008
0.01
Multipliers
M1 and Multipliers
Let M = a + b + c and remember m = c(r , ...)θc + d(r , ...)θd + a(r , ...)θa
I
model features a money multiplier :
M = µ(θi , k i , r ) m
- look at the empirical performance of the multiplier !
Multipliers
M1 and Multipliers
Let M = a + b + c and remember m = c(r , ...)θc + d(r , ...)θd + a(r , ...)θa
I
model features a money multiplier :
M = µ(θi , k i , r ) m
- look at the empirical performance of the multiplier !
I
Money M to GDP in model is
M
p y (1 − φn)
Multipliers
M1 and Multipliers
Let M = a + b + c and remember m = c(r , ...)θc + d(r , ...)θd + a(r , ...)θa
I
model features a money multiplier :
M = µ(θi , k i , r ) m
- look at the empirical performance of the multiplier !
I
Money M to GDP in model is
M
M
x
=
p y (1 − φn)
px p y (1 − φn)
|{z}
eq. 13
Multipliers
M1 and Multipliers
Let M = a + b + c and remember m = c(r , ...)θc + d(r , ...)θd + a(r , ...)θa
I
model features a money multiplier :
M = µ(θi , k i , r ) m
- look at the empirical performance of the multiplier !
I
Money M to GDP in model is
M
M
x
M
=
=
(1 − transaction service)
p y (1 − φn)
px p y (1 − φn)
px
|{z}
eq. 13
transaction cost
Dissociated transaction costs:
φi → ni ?
model assumes once φ is “paid” c, d, a are rebalanced
hence n the same for all instruments
transaction cost
Dissociated transaction costs:
φi → ni ?
model assumes once φ is “paid” c, d, a are rebalanced
hence n the same for all instruments
In data (Italy, 2002) transaction frequency varies across assets:
# currency transactions (from d to c)
# deposits transactions (from Wealth to d)
mean
22 (60 w. ATM)
14 (+12 Auto)
Source Italian households survey data (Bank of Italy)
median
12 (48 w. ATM)
2 (+12 Auto)
sectorization
Sectoral breakdown of M1: HH and (non-fin) Firms
M1 and cash plus checking of firms and households
(1982 Dollars)
1400
1200
M1
Firm
Household
$ Billions
1000
800
600
400
200
0
1980
1985
1990
1995
2000
2005
2010
Notes: M1 is from the Federal Reserve Board of Governors Release H.6 at the end of the period. Firm cash+checking is from the Flow of Funds
L.102(A): Nonfinancial business; checkable deposits and currency; asset. Household cash+checking is from the Flow of Funds L.101(A):
Households and nonprofit organizations; checkable deposits and currency; asset. All data is not seasonally adjusted and deflated using CPI
(CPIAUCNS) from the BLS.
2015
what did we learn?
Why do we care about a “stable” M/P = L(r , y )?
I
“Giving colorful names to statistical relationships
is not a substitute for economic theory”
what did we learn?
Why do we care about a “stable” M/P = L(r , y )?
I
“Giving colorful names to statistical relationships
is not a substitute for economic theory”
- theory of L(r , y ) is key to quantify costs of anticipated inflation
what did we learn?
Why do we care about a “stable” M/P = L(r , y )?
I
“Giving colorful names to statistical relationships
is not a substitute for economic theory”
- theory of L(r , y ) is key to quantify costs of anticipated inflation
- Lucas-Nicolini might serve that role (cost: GDP wasted in cash management)
........ all the ingredients for coherent welfare analysis are there . . . use them?
what did we learn?
Why do we care about a “stable” M/P = L(r , y )?
I
“Giving colorful names to statistical relationships
is not a substitute for economic theory”
- theory of L(r , y ) is key to quantify costs of anticipated inflation
- Lucas-Nicolini might serve that role (cost: GDP wasted in cash management)
........ all the ingredients for coherent welfare analysis are there . . . use them?
I
A test of our ability to understand (account for) data we observe
- My work with Alvarez on BT data + model
what did we learn?
Why do we care about a “stable” M/P = L(r , y )?
I
“Giving colorful names to statistical relationships
is not a substitute for economic theory”
- theory of L(r , y ) is key to quantify costs of anticipated inflation
- Lucas-Nicolini might serve that role (cost: GDP wasted in cash management)
........ all the ingredients for coherent welfare analysis are there . . . use them?
I
A test of our ability to understand (account for) data we observe
- My work with Alvarez on BT data + model
I
fine tuning control of reserves, M, P, y , r ?
- Great motivation but not fully developed
what did we learn?
Conclusions
Very useful measurement
Simple clean theoretical model to think through data
Several implications can be expanded and refined . . . . . I look forward to it!