4 Money Demand

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On the Stability of Money Demand
Robert E. Lucas Jr, University of Chicago.
Juan P. Nicolini, Minneapolis Fed and Universidad Di Tella.
November 19, 2014
• Central Bank leading models–including the one in use by the Fed
itself–have no role for monetary aggregates.
• The result of a relatively broad consensus: no measure of “liquidity”
is of any value in conducting monetary policy.
• There were good reasons behind this consensus.
• Long standing empirical relations connecting monetary aggregates,
output and interest rates to movements in prices began to fall apart
in the 1980s and have not been restored ever since.
• Our first objective in this paper is to offer a diagnosis of this empirical
breakdown.
• Changes in the regulation (Regulation Q) of interest payments on
commercial bank deposits in 1980 and 1982. (Teles and Zhou (2005)).
• Our second is to propose a fix.
• We evaluate the effects of these policy changes using a simple inside-
money model and propose a monetary aggregate the offers a unified
treatment of monetary facts preceding and following 1980.
Plan
• Document the empirical break-down.
• Briefly discuss changes in regulation.
• Present the Model without the regulation.
• Explain the effect of regulation.
• Calibrate for 1984. Skip.
• Compare with US data without regulation Q (1915-1935 plus 1982-
2012).
• Propose model of Bank competition during Regulation Q and compare
with data (1935 - 1982). Skip.
• Implications for US monetary policy debate.
• Why 1?
• No theoretical attempts at modeling the households decision between
the components.
• No apparent need to: some ”proportions” did not seem to change
much over time.
Evidence since 1980.
Key changes in legislation
• Regulation Q in place after 1933. But it was relaxed in early 80’s.
— NOW accounts allowed in 1980. Checking accounts that could pay
interest. Restricted to individuals. Included in M1.
— Money Market Deposit Accounts allowed in 1982. Restricted check-
ing accounts. NOT included in M1.
• How were the households decisions regarding the ”components” of M1
affected?
• We will use the theory to answer this question.
• Answer: regulation changes in the early 80’s increased the availability
of close substitutes for deposits, but not for cash.
• The theory implies that once the close substitutes are allowed they
should be added to cash and demand deposits.
• As a preview of the results, we reproduce the previous figures we did
for M1, but adding the newly created deposits
1 =1 +
The model
• Prescott (1987) and Freeman and Kydland (2000).
• Application of Baumol-Tobin trade-off to inside money.
• All households have the common preferences of the form
∞X
=0
()
• where  is an aggregate of a continuum of different perishable goods
in fixed proportions.
• Goods come in different “sizes“,  ∈ [0∞) with production costs and
prices that vary in proportion to size.
• We let () be the size distribution of goods and  () the correspond-
ing CDF.
• Each household has one unit of labor each period, to be divided be-
tween producing goods and cash management.
• Cash-management involves trips to the bank (standard BT) plus a
choice of asset to make transactions (non-standard BT).
• Let me describe first the non-standard BT.
• There are three payment technologies available to agents.
• One is cash (currency), which pays no interest. It costs a fraction 1+
(lost or stolen).
• There are two different deposit types,  (demand deposits) and 
(money market deposit accounts).
• Transactions with deposits involve fixed costs that are proportional to
the number (not the value) of transactions,  and 
• In addition, both require a fraction of reserves to be held,  and 
• We assume that
   but   
In equilibrium there will be two cutoff sizes 0 ≤  ≤  such that
1. transactions lower than  are paid for with 
2. transactions lager than  but lower than  are paid for with 
3. transactions larger than  are paid for with 
The standard BT
• Households also choose the number  of “trips to the bank” they take
during a period. In each trip they replenish cash and deposits.
• Each trip to the Bank costs  units of time. Thus, production is
(1− )− 
h
 ( ()−  ()) +  (1−  ())
i
= 
where  is the MgP of labor.
• A cash-in-advance constraint implies all payments must be made by
either  or .
• In equilibrium, the nominal interest rate satisfies (1 + ) = 1 + 
•  is the inflation rate.
•  is determined by monetary policy.
Given  there are two relevant margins.
1. How many trips to the Bank per period (choice of ).
2. The portfolio decision between the three asset types. (choice of  and
)
• The first order and envelope conditions imply (for  = 0)
 = 
(1− )³
 − 
´
³
 − 
´

• so the two thresholds are proportional.
• In addition, if we let
Ω() =
R 
0 ()R∞
0 ()
• conditions
2
(1− )
= 
h
Ω() +  [Ω()−Ω()] +  [1−Ω()]
i
(1 +
h
 ( ()−  ()) +  (1−  ())
i
)
 = 
(1− )


• solve for () and ()
• The theoretical counterpart to observables are


=
Ω()
[Ω()−Ω()]
and


=
[Ω()− Ω()]
[1−Ω()]
• plus


=
 + +

=
∆
()

• Effect of Regulation Q?
Numerical solutions
• We set the reserve requirements  = 01 and  = 001
• We set  = 001 (Alvarez and Lippi (2010))
• We let  ∈ [0∞) and
() =
 − 1
(1 + )
   2
• We need values for the parameters,     and ∆
• We match the 1984 ratios (the first year for which we have data on
MMDA’s)

 + +
= 017

 +
= 05
and
 ( ()−  ()) +  (1−  ()) = 001
 = 001
• Finally, we use the free scale parameter ∆ so real balances are 25% of
GDP when  = 6%.
Figure 3.3.1
0 0.05 0.1 0.15
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
MONEY BALANCES AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 − 1935 & 1983 − 2012
 
 
1915−1935
1983−2012
Figure 3.3.2
1980 1985 1990 1995 2000 2005 2010 2015
0
0.2
0.4
0.6
0.8
1
RATIO CURRENCY TO DEPOSITS (TREND COMPONENT) , 1984 − 2012
 
 
DATA
MODEL
Figure 3.3.3
1980 1985 1990 1995 2000 2005 2010 2015
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RATIO DEP / (DEP + MMDAS) (TREND COMPONENT), 1984 − 2012
 
 
DATA
MODEL
• Sweep technology?
• In the model, the behavior of components is very sensitive to changes
in parameters. But the behavior of the aggregate is not.
• The same happens in the data: large substitutions within, without
affecting the aggregate.
Figure 5.6
Figure 5.7
Conclusions
• Money demand is remarkably stable.
• There are large movements ”within” NewM1 - some missed by the
model. Very sensitive to small changes in
    
• But the behavior of the aggregate is not sensitive to those changes.
The Future of US Inflation: The role of Monetary Aggregates
Juan Pablo Nicolini
Minneapolis Fed and Universidad Di Tella
Time Series NewM and TBRate, Quarterly
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
0.00
2.00
4.00
6.00
8.00
10.00
12.00
19
84
_1
19
84
_4
19
85
_3
19
86
_2
19
87
_1
19
87
_4
19
88
_3
19
89
_2
19
90
_1
19
90
_4
19
91
_3
19
92
_2
19
93
_1
19
93
_4
19
94
_3
19
95
_2
19
96
_1
19
96
_4
19
97
_3
19
98
_2
19
99
_1
19
99
_4
20
00
_3
20
01
_2
20
02
_1
20
02
_4
20
03
_3
20
04
_2
20
05
_1
20
05
_4
20
06
_3
20
07
_2
20
08
_1
20
08
_4
20
09
_3
20
10
_2
20
11
_1
20
11
_4
20
12
_3
Interest Rate NewM on GDP
Recent behavior of components NewM
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
20
03
_1
20
03
_2
20
03
_3
20
03
_4
20
04
_1
20
04
_2
20
04
_3
20
04
_4
20
05
_1
20
05
_2
20
05
_3
20
05
_4
20
06
_1
20
06
_2
20
06
_3
20
06
_4
20
07
_1
20
07
_2
20
07
_3
20
07
_4
20
08
_1
20
08
_2
20
08
_3
20
08
_4
20
09
_1
20
09
_2
2009
_3
20
09
_4
20
10
_1
20
10
_2
20
10
_3
20
10
_4
20
11
_1
20
11
_2
20
11
_3
20
11
_4
20
12
_1
20
12
_2
20
12
_3
20
12
_4
20
13
_1
currsl ddsl ir_3tbill mmdas
• Once interest rates become positive, say at 4%, the model implies that
NewM1 should be around 27% of GDP.
• Now, NewM1 is around 48% of GDP.
• How will the reduction in NewM1 be achieved?
• Can use the model to simulate the evolution of money balances, and
its components that are consistent with price stability.
• Use the forecasts made by the FOMC for  and 
• Impose a target for the price level (2% explicit target).
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
15Q1 15Q2 15Q3 15Q4 16Q1 16Q2 16Q3 16Q4 17Q1 17Q2 17Q3 17Q4
My R FOMC forecast
• Compute the evolution of money (NewM1) and its components (cash)
from


= ()
and


= ()Ω(())
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
14Q4 15Q1 15Q2 15Q3 15Q4 16Q1 16Q2 16Q3 16Q4 17Q1 17Q2 17Q3 17Q4
NewM1 in Billions U$
800
900
1000
1100
1200
1300
1400
1500
14Q4 15Q1 15Q2 15Q3 15Q4 16Q1 16Q2 16Q3 16Q4 17Q1 17Q2 17Q3 17Q4
Cash Holdings Model Cash Holdings Data
y = 0.0156ln(x) + 0.2295
R² = 0.6751
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 1 2 3 4 5 6 7
Ratio c and Tbill Rate Log. (Ratio c and Tbill Rate)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
14Q4 15Q1 15Q2 15Q3 15Q4 16Q1 16Q2 16Q3 16Q4 17Q1 17Q2 17Q3 17Q4
Ratio c Data Model
Policy implications
1. Can write down models where by properly managing the short term
interest rate, the evolution of the price level is (locally) unique.
2. Money adjusts endogenously so monetary aggregates provide no rele-
vant information regarding the ”stance” of monetary policy.
3. But can also write down models where this is not the case and expec-
tations by the private sector regarding Fed doing the right thing are
crucial.
4. There are several measures put in place to make sure that excess
reserves do not translate into measures of money (draining reserves).
5. Only make sense if worried about scenario in 2.
6. How about measures to drain cash?