On the Stability of Money Demand

Robert E. Lucas Jr., University of Chicago.
Juan Pablo Nicolini, Minneapolis Fed and U. Di Tella

July 3, 2013

A simple (old fashion!) theoretical framework• Let us start with the quantity equation
+1 +1 = +1+1• ..in growth rates =+1 + +1
+1 +  +1• Assume  = 

where  is the nominal interest rate and  is a stochastic process.

• I will interpret  as exogenous shocks to velocity (or real moneydemand).

• I assume that  is stationary with a lung run average of • This is the general case, and I will have much to say about it.
• However, for the time being, let me set  = 0 so   = • Then+1
+1 = ln• Thus, we obtain −
+1 = +1 + +1
+1

• Clearly, inflation and money growth will not be the same period byperiod, due to the shocks. However, taking averages over time



1 X
1 X
1 X
1 X


+1 =
+1 −
+1 ++1 =0 =0 =0 =0• as  grows,

1 X+1 →   =0where   is the long run growth rate of output and
1 X+1→0 =0since  is seasonally stationary.

• Then, as we average money growth and inflation, the data shouldline-up around the line
 =  − • These three variables are observable.
• How do we test this theory?
• Look at the ”long run”!!
• Vogel (1974), Lucas (1980), Barro (1990), Rolnick and Weber (1994),
McCandless and Weber (1995), Benatti (2005), Sargent and Surico(2011), etc.

• Let me show you one more: Nicolini 2012• We use data from IFS for inflation (CPI) and monetary growth (Monetary Base).

• Quarterly data from 1955.1 to 2005.4. Non-seasonally adjusted.
• Includes countries with own currency and more than 10 years of consecutive data.

• A look at the long run behavior
1. 1 observation per country per 1 year.
2. 1 observation per country per 2 years.
3. 1 observation per country per 5 years.
4. Country average• We also plot a 45 degree line with slope -0.0075.

Is this an artifact of the high inflation countries?

Am I cheating with the scale?

• The data lines-up around the lines because average inflation varied
across countries.

• Otherwise, the data should converge to a point.
• To detect the QT in the data in a time series, we need variation ofinflation over time.

• Before that, how about the ”short-run”?
• See Nicolini 2012.....

Further evidence• Average money growth and inflation for countries where inflation varied over time.

• Examples: Chile, Colombia, Peru, Argentina, Brazil, Turkey.

1990q2
1990q4
1991q2
1991q4
1992q2
1992q4
1993q2
1993q4
1994q2
1994q4
1995q2
1995q4
1996q2
1996q4
1997q2
1997q41998q2
1998q4
1999q2
1999q4
2000q2
2000q4
2001q2
2001q4
2002q2
2002q4
2003q2
2003q4
2004q2
2004q4
2005q2
2005q4
2006q2
2006q42007 Q2
2007 Q4
2008 Q2
2008 Q4
2009 Q2
2009 Q4
2010 Q2
2010 Q4
2011 Q2
2011 Q4
2012 Q2
2012 Q4

Brazil100.00

80.00

60.00

40.00

20.00

0.00

‐20.00
CPI
BaseChile
14.00

12.00

10.00

8.00

6.00

4.00

2.00

0.00

CPI

Base

1990q2
1990q4
1991q2
1991q4
1992q2
1992q4
1993q2
1993q4
1994q2
1994q4
1995q2
1995q4
1996q2
1996q4
1997q2
1997q4
1998q2
1998q4
1999q2
1999q4
2000q2
2000q4
2001q2
2001q4
2002q2
2002q42003q2
2003q4
2004q2
2004q4
2005q2
2005q4
2006q2
2006q42007 Q2
2007 Q4
2008 Q2
2008 Q4
2009 Q2
2009 Q4
2010 Q2
2010 Q4
2011 Q2
2011 Q4
2012 Q2
2012 Q4

Colombia

9.00

8.00

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.00

CPI
M1

Peru
25.00

20.00

15.00

CPI
10.00

5.00

0.00

M1

1990q2
1990q4
1991q2
1991q4
1992q2
1992q4
1993q2
1993q4
1994q2
1994q4
1995q2
1995q4
1996q2
1996q4
1997q2
1997q4
1998q2
1998q4
1999q2
1999q4
2000q2
2000q4
2001q2
2001q4
2002q2
2002q4
2003q2
2003q4
2004q2
2004q4
2005q2
2005q4
2006q2
2006q42007 Q2
2007 Q4
2008 Q2
2008 Q4
2009 Q2
2009 Q4
2010 Q2
2010 Q4
2011 Q2
2011 Q4
2012 Q2
2012 Q4

Turkey

20.00

18.00

16.00

14.00

12.00

10.00

8.00

6.00

4.00

2.00

0.00

CPIM1

• A more serious analysis of velocity• By setting  = 0 in the equation  = 
I treated velocity as purely exogenous.

• However, a long literature pioneered by Baumol and Tobin served as
the theoretical framework for a series of empirical papers, mainly byMeltzer (1962) and Lucas (1988).

• Both theory and data supported a negative relationship between realmoney balances and the short term interest rate.

• In the US, this conceptual framework was abandoned as a tool to understand the relationship between monetary policy and inflation sometime in the late 80’s or early 90’s.
• By the late 90’s, a new conceptual framework, the New Keynesianmodel, became the workhorse in central banking theory and practice.
• But the failure of Lehman Brothers in 2008 was a challenge: it led theFed to increase the level of bank reserves from some $40 b. $800 b.
in 4 months.
• None of the leading models–including the New Keynesian model inuse by the Fed itself–had anything to contribute to the Fed’s responseto the liquidity crisis.

• By the time of the outburst of the crisis, a broad consensus was reachedthat no measure of “liquidity” in an economy was of any value in
conducting monetary policy.

• There were good reasons behind this consensus.
• Long standing empirical relations connecting monetary aggregates tomovements in prices and interest rates began to fall apart in the 1980s
and have not been restored since.

• Our first objective in this paper is to oﬀer a diagnosis of this empiricalbreakdown.

• Changes in the regulation of interest payments on commercial bankdeposits 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 insidemoney model and propose a monetary aggregate the oﬀers a unified
treatment of monetary facts preceding and following 1980.

Plan• Document the empirical break-down.
• Discuss changes in regulation.
• Briefly discuss the model.
• Show the performance of the model.
• Discuss the implications of the model for the evolution of inflation inthe US.

M1 AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 - 1980
0.5

0.45

0.4

M1 / GDP

0.35

0.3

0.25

0.2

0.15

0.1
00.02

0.04

0.06

0.08
INTEREST RATE

0.1

0.12

0.14

0.16

• Why 1?
• No theoretical attempts at modeling the households decision between
the components.

• No apparent need to: some ”proportions” did not seem to changemuch over time.

CURRENCY AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 - 1980
0.12

0.110.1CURR / GDP

0.09

0.08

0.07

0.06

0.05

0.04

0.03
00.02

0.04

0.06

0.08
INTEREST RATE

0.1

0.12

0.14

0.16

DEMAND DEPOSITS AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 - 1980
0.4

0.35

0.3

DEP / GDP

0.25

0.2

0.15

0.1

0.05
00.02

0.04

0.06

0.08
INTEREST RATE

0.1

0.12

0.14

0.16

Evidence since 1980.

M1 AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 - 1980
0.5
1915-1980
1981-2008
0.45

0.4

M1 / GDP

0.35

0.3

0.25

0.2

0.15

0.1
00.02

0.04

0.06

0.08
INTEREST RATE

0.1

0.12

0.140.16

CURRENCY AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 - 1980
0.12
1915-1980
1981-2008
0.110.1

CURR / GDP

0.09

0.08

0.07

0.06

0.05

0.04

0.03
00.02

0.04

0.06

0.08
INTEREST RATE

0.1

0.12

0.14

0.16

DEMAND DEPOSITS AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 - 1980
0.4
1915-1980
1981-2008

0.35

0.3

DEP / GDP

0.25

0.2

0.15

0.1

0.05
00.02

0.04

0.06

0.08
INTEREST RATE

0.1

0.12

0.140.16

Key changes in legislation• After Great Depression, Regulation Q: Prohibited Commercial Banks
paying interest rates on checking accounts.

• Regulation Q was relaxed in early 80’s.
— In 1980, noncommercial checking accounts (NOW) that pay interests were allowed. Included in M1. We will treat demand deposits
and NOW accounts as a single aggregate.
— A new Act in 1982 allowed for Money Market Deposit Accounts(Restricted checking accounts). NOT included in M1.

• How did this change aﬀected households decisions regarding the ”components” of M1?

• We need a model to answer this question.
• In the 90’s, introduction of Sweep technology. We will ignore thischange in our analysis - and will pay a price for that!

• Natural candidate theory given the evidence: regulation changes in theearly 80’s increased the availability of close substitutes for deposits,
but not for cash.

• Once the close substitutes are allowed, they should be added to cash
and demand deposits.

• This is what the simple model implies.
• As a preview of the results, we reproduce the previous figures we didfor M1, but adding the newly created deposits 1 =  1 + 

NEW-M1 VS. OPPORTUNITY COST, 1915 - 2008
0.5
1915-1980
1981-2008
0.45

0.4

M1J / GDP

0.35

0.3

0.25

0.2

0.15

0.1
00.02

0.04

0.06

0.08
OPPORTUNITY COST

0.1

0.12

0.14

0.16

The model• Prescott (1987) and Freeman and Kydland (2000).
• Application of Baumol-Tobin to inside money.
• It is a theory of the ”money multiplier”.

• Households consume a continuum of diﬀerent perishable goods in fixedproportions.

• Goods come in diﬀerent “sizes“,  ∈ [0 ∞) with production costs andprices that vary in proportion to size.

• We let  () be the size distribution of goods and  () the corresponding CDF.

• There are three payment technologies available to agents.
• One is cash (currency) , which pays no interest. But there is nofixed cost of dong transactions.

•  (demand deposits) pay some interest rate but there is a fixed costto make transactions.

•  (money market deposit accounts) pay a higher interest rate but areless liquid than demand deposits.

• We interpret this relative illiquidity with a higher fixed cost of transactions.

• We will look for equilibria with 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 • Households also choose the number  of “trips to the bank” they takeduring a period.

• In each trip they replenish cash and deposits.
• Each trip to the Bank costs  units of time, as in Baumol-Tobin.
• We solve for steady states, where the nominal interest rate (and therefore inflation and the growth rate of the monetary base) are all constant.

• There are two relevant margins
1. How many trips to the Banks per period (choice of ): The higher
 the higher the number of trips to the bank and the lower thereal money balances.
2. The portfolio decision between the three asset types: the higher ,
the larger the use of deposits.

• Note that the second eﬀect implies changes in the money multiplier.

• The theoretical counterpart to observables are== () = ()()•  is a parameter that makes the units of real money holdings consistent with our choice of yearly interest rates.

Numerical solutions• To be precise, we get some numbers for the (few) parameters andsolve the model, using data for the year 1984.

• We need to specify the form and parameters of the transaction size
distribution • We let  ∈ [0 ∞) and−1 () =
  2(1 + )f(z) = (η−1)/(1+z)η
3

η = 2.5
η = 3.0
η = 4.0

2.5

f(z)

2

1.5

10.5

0
0

0.5

11.5

2z

2.5

33.5

4• We can now solve for real money balances over GDP, and for thebehavior of the ratios between the components   and • We compare the predictions of the model with the data.
• Simple illustration to show the ability of the model to capture someessential features of the data.

MONEY BALANCES AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1915 - 1935 & 1984 - 2008
0.5
1915-1935
1984-2008

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

RATIO CURRENCY TO DEPOSITS (TREND COMPONENT) , 1984 - 2008
1DATA
MODEL
0.9

0.8

0.7

0.6

0.50.40.3

0.2

0.101980

1985

1990

1995

2000

2005

2010

RATIO DEP / (DEP + MMDAS) (TREND COMPONENT), 1984 - 2008
1DATA
MODEL
0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.101980

1985

1990

1995

2000

2005

2010

Decentralization• How about the Regulation Q period?
• Deposits could not pay interest, so changes in  do not necessarily
aﬀect the incentives to use deposits.
• Explains why focusing on each component of M1 did not matter muchtill 1980.
• How did Banks compete during Reg Q?
• We assume that for low interest rates, banks could oﬀer reduced fees.

• This reduction in fees made deposits relatively more attractive thancash, so it acted as an increase in the interest on deposits.

• But this had some limits once fees became zero.
• Thus, Reg Q became binding, once the interest rate increased by theend of the 60’s.

• We impose this restriction into the model and solve it, using the calibration of 1984.

MONEY BALANCES AS A % OF GDP VS. INTEREST RATE 3MTBILL, 1935 - 1982
0.8

0.7

0.6

0.50.4

0.3

0.2

0.1

00

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Conclusions• Money demand is remarkably stable.
• We overpredict money balances for low interest rates.
• After regulation Q, the model matches the trend of each deposit typereasonably well for over a decade, but misses the observed substitution
between MMDA and DD that started in the late 90’s.

• Is the assumption that operating costs are constant consistent with
the Sweep technology?

• During Reg Q, the model can match the U-shape pattern of the cash tomoney balances ratio, but over-predicts its level. (Very sensitive to ourassumptions regarding the ”size” of transactions cost in calibration).

• The model of banking is very stark (misses by far the behavior ofinterest rates on deposits after 1983).

• A better theory of banking is needed.
• On the good side, in the model - and in the data - the behavior of
the aggregate is not very sensitive to the behavior of each component:large substitutions within, without aﬀecting the aggregate.

• We started the discussion mentioning the recent financial crisis, butthe evidence we used is all pre-crisis data and the analysis is all basedon theoretical steady states.

• We are trying to get the quantity theory of money back to where it
seemed to be in 1980, but after all the older theories were as silent on
financial crises as is this one is.

The recent behavior of NewM

• What happened since 2008?
• At the zero lower bound, the components of NewM are perfect substitutes of short term government bonds.

• Inflation is given by the negative real interest rate.
• We expect a large increase in NewM. We expect a large increase in allcomponents.

1984_1
1984_4
1985_3
1986_2
1987_1
1987_4
1988_3
1989_2
1990_1
1990_4
1991_3
1992_2
1993_1
1993_4
1994_3
1995_2
1996_1
1996_4
1997_3
1998_2
1999_1
1999_4
2000_3
2001_2
2002_1
2002_4
2003_3
2004_2
2005_1
2005_4
2006_3
2007_2
2008_1
2008_4
2009_3
2010_2
2011_1
2011_4
2012_3Time Series NewM and TBRate, QuarterlyInterest Rate
NewM on GDP

12.00
50.0

45.0

10.00
40.0

8.00
35.0

30.0

6.00
25.0

20.0

4.00
15.0

2.00
10.0

5.0

0.00
0.0

9.00

2003_1
2003_2
2003_3
2003_4
2004_1
2004_2
2004_3
2004_4
2005_1
2005_2
2005_3
2005_4
2006_1
2006_2
2006_3
2006_4
2007_1
2007_2
2007_3
2007_4
2008_1
2008_2
2008_3
2008_4
2009_1
2009_2
2009_3
2009_4
2010_1
2010_2
2010_3
2010_4
2011_1
2011_2
2011_3
2011_4
2012_1
2012_2
2012_3
2012_4
2013_1

Recent behavior of components NewM
currslddsl
ir_3tbill
mmdas

5.00

4.00

0.00
35.0

8.00
30.0

7.00
25.0

6.00

20.0

15.0

3.00
10.0

2.00

1.00
5.0

0.0

• Once interest rates become positive, say at 4%, I argue that NewM
should be around 25% of GDP.

• The monetary base should be• Cash should be around 5% of GDP.
• Now, NewM is around 48% of GDP.
• How will the reduction in NewM be achieved?
• The nominal value of NewM goes down, or the price level goes up.

• Assume that all reduction in deposits comes about private agents buying short term government bonds (nominal value of deposits comingdown).
• Assume also that bank reserves go down accordingly, due to open
market operations of the Fed.
• Cash may be 7,5% of GDP at the time of the ”exit”.
• But cash was 90% of the base.
• If all this cash stays in the system, the monetary base will increase by
75× 09 = 0455

• It is a 45% increase in the monetary base which would imply, in a ss,
a 45% in prices.

• High standard deviation on this forecast!
• Changes in the multiplier?