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This is to certify that the
dissertation entitled

ESSAYS ON THE REAL EFFECTS OF MONETARY SHOCKS
IN CLOSED AND OPEN ECONOMIES

presented by

Scott L. Baier

has been accepted towards fulfillment
of the requirements for

Ph.Dt degree in Economics

 

Date May 3, 1996

 

MS U i: an Affirmative Action/Equal Opportunity Institution I 0-12771

 

 

 

LIBRARY
Michigan State
University

 

 

 

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To AVOID FINES Mum on or before date duo.

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ESSAYS ON THE REAL EFFECTS OF MONETARY SHOCKS
IN CLOSED AND OPEN ECONOMIES

by

Scott L. Baier

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1 996

ABSTRACT

ESSAYS ON THE REAL EFFECTS OF MONETARY SHOCKS
IN CLOSED AND OPEN ECONOMY
By

Scott L. Baier

This dissertation investigates the effects of unanticipated increases in the money
supply on real activity, and derives the optimal monetary policy for interdependent
countries. Chapters 1 and 2 derive the optimal monetary policy in a two country two
sluggish cash flow model under a variety of exchange rate regimes. It is shown that the
monetary authorities can achieve the Pareto optimal allocations by providing liquidity to
banks when the demand for loanable funds is high. Chapter 3 adds inventories and credit
goods to the basic liquidity effects model. By doing so, the dynamics of the model are
vastly improved. Chapter 4 examines the econometric work of Christiano, Eichenbaum,

and Evans. It is argued that only one of their models yields credible results.

FOR MICHELE

Acknowledgments

Many people have played a role in my development as an economist and in writing this
dissertation. First and foremost is Rowena Pecchenino who has been my committee
chairperson, mentor, and friend. Her constant encouragement, her insightful comments, and
our sometimes lively discussions have made this a better dissertation and me a better
economist. Her emphasis on the intuitionnthe economies behind the math--resulted in greater
clarity and depth of exposition in my work. She always made time to speak with me even
though it sometimes took time away from her own research. For all the time and effort she put
into this project, I am truly grateful.

My other committee members have played a major role in the completion of this
dissertation. The papers by Timothy Fuerst, at Bowling Green State University, sparked my
interest in monetary economics. Tim agreed to be on my committee and provided many
insightful comments. He also invited me to present my paper at Bowling Green State
University which was good experience for a young economist. Gerhard Glomm provided
ample comments that made the dissertation better. Gerhard also made himself available
whenever I needed to talk with him. I am thankful to Gerhard for teaching me the techniques
of dynamic optimization. Robert Rasche provided many useful comments on the dissertation.
In particular, his comments and suggestions on Chapter 4 vastly improved the empirical aspects
of the dissertation. He taught most me most of what I know about time series econometrics.

Jeffrey Wooldridge made many suggestions that have improved the dissertation. I am mostly

deeply indebted to Jeff for the three courses I took from him. Jeff's approach to teaching
econometrics made a subject that I initially had difficulty understanding much easier than it
otherwise would have been. I am certain I will be a better econometrician given the classes I
have taken from Jeff, Robert, and Richard Baillie.

I would also like to thank Steven Matusz and Peter Schmidt who took time to read
some of the essays in the dissertation and provide feedback on them. In addition, I am indebted
to Anthony Creane whose encouragement has been invaluable. His friendship has helped me
get through some of the "down times" that graduate students frequently encounter.

My fellow graduate students have been a major source of encouragement over the last
four years. I especially want to thank Kathleen Beegle, Mike Cichello, Dan Hansen, Cece
Howell, Matt Knittel, John Kooistra, and Jennifer Tracey.

The greatest debts owed here, however, are to my family. My wife Michele has been a
constant source of encouragement and inspiration. Somehow she has tolerated my moodiness
and my many, many panic attacks. Her emotional support and patience have resulted in a debt
I will never be able to repay. My parents, Paul and Lenna Baier, have always supported me
and encouraged me to do my best even when they did not agree with or understand my
decisions. For all of this and more, I am deeply indebted to them. I would also like to thank
my in-laws for their support. It is not possible to have better in-laws. I would be remiss if I
did not thank my brother and sister and their families for their friendship and love over the
years. Lastly, though she will never read this, I thank Lenora Muscetta for her love and

support throughout her lifetime.

TABLE OF CONTENTS

LIST OF TABLES .................................... ix
LIST OF FIGURES ................................... x
Introduction ........................................ 1
Chpater 0
Literature and Methodology .......................... 4
A Simple Liquidity Effects Model ...................... 6
Chapter 1
Optimal Monetary Policy in a Two Country One World Currency Model 17
The Model an Overview ............................ 18
Behavior of Economic Agents ........................ 20
Equilibrium .................................... 27
A Simulation Exercise ............................. 40
Conclusion .................................... 43
Chapter 2
Optimal Monetary Policy in a Two Country, Two Currency Model with
Fixed and Flexible Exchange Rates ..................... 48
The Model ..................................... 49
Equilibrium .................................... 62
Optimal Monetary Policy ........................... 69
Policies in a Constrained Environment ................... 79
Conclusion .................................... 83
Appendix 2.1 ................................... 87
Appendix 2.2 ................................... 90
Chapter 3
Real Effects from Unanticipated Increases in the Money Supply in a Model with
Inventories and Credit Goods ....................... 94
The Basic Christiano and Eichenbaum Model ............. 97
The Christiano and Eichenbaum Model with Inventories ...... 107

vi

Inventories and Credit Goods: Friedman Revisited ..........
Conclusion ...................................
Chapter 4
Time Series Evidence of Liquidity Effects ...............
CEE Model ...................................
CEE Model with Difference Stationary Data ...............
Other Shocks in the CEE Model ......................
Conclusion ....................................
Appendix 4.1 ..................................
References .........................................

vii

112
116

126
127
138
142
151
209
210

LIST OF TABLES

Table 2.1: Welfare Under Fixed Exchange Rate Regimes ............
Table 2.1: Welfare Under Flexible Exchange Rate Regimes ..........
Table 4.1: Augmented Dickey-Fuller Unit Root Test ..............

Table 4.2: Augmented Dickey-Fuller Unit Root Test ..............

viii

82

83

209

209

LIST OF FIGURES

Figure 1.1:The Demand for Loanable Funds: Country one ............. 32
Figure 1.2:The Demand for Loanable Funds: Country two ............. 32
Figure 1.3:The Market Demand for Loanable Funds .................. 32
Figure 1.4:The Labor Market: Country one ....................... 33
Figure 1.5:The Labor Market: Country one ....................... 33
Figure 1.6: Welfare Loss When the Average Money Growth Rate is 10 Percent
and the shocks are iid ................................. 44
Figure 1.7: Welfare Loss When the Average Money Growth Rate is 20 Percent
and the shocks are iid ................................. 45
Figure 1.8: Welfare Loss When the Average Money Growth Rate is 10 Percent
and the Shocks are Correlated ........................... 46
Figure 1.9: Welfare Loss when the Average Money Growth Rate is 20 Percent
and the shocks are Correlated ............................ 47
Figure 3.1: Change in the Interest Rate .......................... 118
Figure 3.2: Change in Output ................................ 118
Figure 3.3: Change in Employment ............................ 119
Figure 3.4: Change in Consumption ............................ 119
Figure 3.5: Change in Output ................................ 120

Figure 3.6: Change in the Interest Rate .......................... 120

ix

Figure 3.7: Change in Employment ............................ 121

Figure 3.8: Change in Consumption ............................ 121
Figure 3.9: Change in Inventories ............................. 122
Figure 3.10: Change in Output .............................. 123
Figure 3.11: Change in the Interest Rate .......................... 123
Figure 3.12: Change in Inventories ............................. 124
Figure 3.13: Change in Employment ........................... 124
Figure 3.14: Change in Consumption ........................... 125
Figure 3.14: Change in Inventories ............................ 125
Figure 4.1: GDP ........................................ 153
Figure 4.2: Federal Funds Rate ............................... 154
Figure 4.3: Nonborrowed Reserves ............................. 155
Figure 4.4: Monetary Base .................................. 156
Figure 4.5: Total Reserves .................................. 157
Figure 4.6: Price Level .................................... 158
Figure 4.7: Unemployment Rate ............................... 159
Figure 4.8: Detrended Federal Funds Rate and N onborrowed Reserves ..... 160
Figure 4.9: Detrended Federal Funds Rate and Monetary Base ........... 161
Figure 4.10: Impulse Response ............................... 162
Figure 4.11: Impulse Response ............................... 164
Figure 4.12: Impulse Response ............................... 166

Figure 4.13: Impulse Response ............................... 168
Figure 4.14: Impulse Response ............................... 170
Figure 4.15: Impulse Response ............................... 172
Figure 4.16: Impulse Response ............................... 174
Figure 4.17: Impulse Response ............................... 176
Figure 4.18: Detrended GDP ................................. 178
Figure 4.19: Detrended Federal Funds Rate ....................... 179
Figure 4.20: Detrended Nonborrowed Reserves ..................... 180
Figure 4.21: Detrended Unemployment .......................... 181
Figure 4.22: Detrended Total Reserves .......................... 182
Figure 4.23: Detrended Commodity Prices ........................ 183
Figure 4.24: Detrended Price Level ............................. 184
Figure 4.25 Detrended Monetary Base .......................... 185
Figure 4.26: Impulse Response ............................... 186
Figure 4.27: Impulse Response ............................... 187
Figure 4.28: Impulse Response ............................... 188
Figure 4.29: Impulse Response ............................... 189
Figure 4.30: Impulse Response ............................... 190
Figure 4.31: Impulse Response ............................... 191
Figure 4.32: Impulse Response ............................... 192
Figure 4.33: Cumulative Effect ............................... 193

xi

Figure 4.34:
Figure 4.35:
Figure 4.36:
Figure 4.37:
Figure 4.38:
Figure 4.39:

Figure 4.40:

Cumulative Effect ............................... 195

Cumulative Effect ............................... 197
Cumulative Effect ............................... 199
Cumulative Effect ............................... 201
Cumulative Effect ............................... 203
Cumulative Effect ............................... 205
Cumulative Effect ............................... 207

xii

Textbook aggregate supply and demand models suggest a simple relationship between
unanticipated increases in the money supply, interest rates, and real activity: an unanticipated
increase in the money supply lowers interest rates, and the lower interest rates lead to increases in
output. Recently there has been a plethora of theoretical and empirical work that supports this
theory. The purpose of this dissertation is threefold: First the optimal monetary policy is derived
for interdependent countries in the context of a general equilibrium Optimizing model. Second to
improve the dynamic response of the variables in the basic Fuerst-Christiano and Eichenbaum
liquidity effects models by making the real side of the economy richer by including inventories
and credit goods. Third, it is my intention to quantify the liquidity effect empirically using time
series econometrics.

The recent theoretical and empirical work on the negative relationship between
unanticipated monetary injections and interest rates is significant since theoretical models and
empirical studies from the previous decade caste doubt on the existence of the liquidity effect. In
particular, from a theoretical perspective, early attempts to include money in business cycle
models led to the conclusion that monetary injections that were larger than anticipated drove
interest rates up causing output to fall (see Greenwood and Huffman, 1987). It is easy to see why
interest rates would rise: by decomposing the nominal interest rate into the sum of expected
inflation and the real rate of interest, the expected inflation component rises with the larger than
anticipated monetary innovation. If the real interest rate does not fall, then the nominal rate will

rise. Econometric studies, such as, Melvin (1983) and Mishkin (1981a,1981b), argue that the

time period the expected inflation component of the interest rate determination process
dominated the liquidity effect.

More recently the theoretical work of Lucas (1990) and Fuerst (1992) and empirical
work by Christiano, Eichenbaum, and Evans (1994), Gali (1992), and Leeper and
Gordon(1992) argue that the liquidity effect is theoretically plausible and that there does appear
to be support for this effect in the data. Theoretically, Lucas and Fuerst show that if agents
make their savings decision before the state of the world is revealed, unanticipated monetary
injections can have real effects. That is, it is possible that monetary innovations that exceed
agents' expectations will drive down the interest rate and lead to an increase in output.
Extensions of the Fuerst-Lucas model include work by Christiano and Eichenbaum (1992b,
1995), Schlagenhauf and Wrase(l995), Fuerst (1994), and Carlstrom and Fuerst (1995).

The empirical work of Christiano and Eichenbaum (1992a) show that innovations to
nonborrowed reserves decrease interest rates and cause output to increase. beeper and Gordon
(1994) also find support for the existence of the liquidity effect. Gali (1992) using a structural
VAR finds that liquidity effects do exist given his identifying restrictions.

This dissertation is two parts theoretical and two parts empirical. Chapter 0 provides a
more detailed review of the literature, as well as a Simple two country, two currency liquidity
effects model. Chapter I investigates the optimal monetary policy in a two country single
currency economy. Similarly, Chapter 2 investigates the optimal monetary policy in a two
country, two currency model with fixed and flexible exchange rates. These two theoretical
chapters demonstrate that unanticipated increases in the money supply lower interest rates and
increase output and show how the shocks in one country affect the other country. Once the
monetary transmission mechanism is understood, the optimal monetary policy is derived. It is

shown that there exists a policy rule that attains the Pareto optimal allocations.

The next two chapters are empirical investigations of the monetary transmissions
mechanism. One of the problems with the liquidity effects literature is the inability of
monetary shocks to have persistent effects. Chapter 3 attempts to remedy this deficiency by
incorporating inventories and credit consumption goods. Including these variables make the
model more consistent with the recent empirical evidence than the existing liquidity effects
models. In the model with inventories and credit goods, the interest rate stays below its steady
state value for several periods after the monetary innovation. This is not a feature of the other
liquidity effects models.

Chapter 4 is an empirical investigation of the effects of money supply shocks using
time series econometric techniques. In this chapter, a seven variable VAR investigates the
model used by Christiano, Eichenbaum, and Evans(1994a,b). Christiano, Eichenbaum, and
Evans claim that unanticipated increases in the money supply caused by monetary authority
have real effects along the lines outlined by Friedman (1975). The responses of variables to

unanticipated increases in the money supply is investigated.

All the models analyzed in Chapters 1, 2, and 3 build on a monetized, general
equilibrium, production economy with an endogenous labor supply decision. Also, there are
stochastic shocks that affect the productive opportunities of the economy. Fuerst (1992) was the
first to show that monetary innovations in these models when they incorporate " liquidity effects"
can have real effects on output. The Fuerst model begins with the notion of a representative
household. Within this household there are different agents--a worker, a saver, and a shopper for
the consumption good. Each of these individuals is responsible for carrying out distinct tasks. At
the start of each period, the household divides its money portfolio (m) and allocates money to the
agents who will need the money to conduct their daily activities. In particular, the household
allots a fixed amount of money (n) to the saver. Once the savings decision is made, the household
cannot alter its decision. The saver deposits these funds into the financial intermediary. The
remaining m-n dollars are available for the purchase consumption goods. The shopper, therefore,
is constrained by a cash—in-advance constraint given by: m—anc, where p is the price of the
consumption good, c. In addition to the funds deposited by the saver, the financial intermediary
also receives a cash injection of x dollars from the monetary authority. Thus the financial
intermediary has n+x dollars to loan out. Who demands these funds? Since the goods producing
firms do not have any funds at the start of the period, they must borrow from the financial
intermediary in order to hire inputs. That is, the goods producing firms are required to use cash

to hire workers and purchase capital for next period. If the monetary injection is larger than
4

next period. If the monetary injection is larger than anticipated, then the amount of loanable
funds held by the financial intermediary will be greater than anticipated. The increase in the
supply of loanable funds will cause the price of the loanable funds to fall; that is, the interest
rate will fall. As long as the nominal interest rate is nonnegative, the financial intermediary
will lend out all of its cash holdings to the goods producing firms. The lower interest rates
entice the firms to borrow all the cash in the financial intermediaries. The firms will use this
excess cash to hire more workers and purchase more capital leading to increases in
contemporaneous and future output. In the Fuerst model, both consumers and firms are
recipients of the additional output.

Christiano (1991) showed that the Fuerst model, when calibrated to the United States
economy, interest rates do not fall when monetary innovations exceed their anticipated values.
To remedy this shortcoming Christiano proposed the "sluggish capital" model. In this
formulation, investment decisions are made before the state of the world is revealed and
cannot be changed ex-post. With this modification, Christiano shows that, when this model is
calibrated, the interest rates fall when monetary injections exceed their anticipated values.
However, even though interest rates fall, the rise in expected inflation results in consumption
falling precipitously in subsequent periods. This contradicts the empirical findings of Sims
(1991) that monetary injections lead to a hump-shaped response of output. Also counterfactual
is the contemporaneous drop in prices that Christiano's model predicts. This is easy to see by
looking at the cash-in-advance constraint. The price is determined by p=(m-n)/c the ’

numerator on the right hand side is a constant, but since consumption increases as output

increases prices must fall. Thus a rise in consumption must imply that contemporaneous prices
fall. This fact in also inconsistent with Sims' empirical findings.

Christiano and Eichenbaum (1992b) rectify the price deflation problem by making
contemporaneous wage earnings available for the purchase of consumption goods. However,
as shown in Chapter 3 the dynamics of the model are not consistent with the time series data.
In the Christiano and Eichenbaum model, consumption increases in the period of the shock but
in the subsequent period consumption falls drastically. Again this is at odds with Sims'
findings that the dynamic response of consumption to monetary innovations is hump shaped.

Schlagenhauf and Wrase (1995) construct an open economy model with complete
capital mobility. They show that positive monetary innovations by one country can lead to a
reduction in interest rates and a depreciation of that country's currency. While these results of
their calibrated model are consistent with their reported empirical findings, their model does
not account for the variability of exchange rates in the time series data. In the next sub-
section, a simple open economy liquidity effects model is developed and the response of the

variables in the model to an unanticipated monetary injection is discussed.

S 'nII.A iml Li idi Effects Model

The models described above are based on the premise that innovations in the money
supply affect different agents in the economy differently. To demonstrate the effects of the

liquidity effects models employed in Chapter 1, 2 and 3, a simple two country, open economy

model is analyzed below. I assume there exist two countries populated with many infinitely
lived households who have identical preferences over two consumption goods el and c2. For
reasons that will be made clear below, one country is called the blue country the other country
the red country. Each household within each country begins the period with the same level of
wealth. Wealth is held in the form of nominal money balances. At the start of the period,
households hold only the currency of their respective country. Define MRl (M3,) to be the
holdings of nominal money balances held by a household of the red (blue) country at the start
of the period. Each period in the red (blue) country the gross growth rate of their currency is
given by l+xR(s,) (1 +xB(s,)), where s, is the state of the world at time t. I will return shortly
to describe the process that generates the state of the world in any time period, but first the
endowment process for each household is described.

Each household in the blue country is endowed with a perishable "raw material" E,(s.).
Similarly, each household in the red country is endowed with a perishable "raw material"
71(80- Notice that the endowment depends on the state of the world at time t. The raw
material can instantaneously and costlessly be transformed into consumption good one or
consumption good two by a linear production process. However, during the production
process the consumption good becomes discolored. In particular, when §(st) is used to make
consumption good one it turns blue and when it is used to make consumption good two it turns
red. Similarly, when n(s,) is used to make consumption good one it turns red and when 11(5.)
is used to make consumption good two it turns blue. Thus the technology for the production

process for both countries is §(s,)=cm(st) +c2R(st) and n(st)=clR(St) +cZB(St).

Households in the blue (red) country strictly prefer blue (red) consumption goods.
Also, households in both countries like consumption good one better than consumption good
two. Therefore, preferences of a household in the blue country are given by

E{>:.=.°°B‘(Iog(c‘3<s.» + vlog(c2‘3<s.)}
and of a household in the red country are given by

Ei2.=.°°B‘(log<c‘“<s.» + vlog<cm<so>r
where 0 <7 <1, and B is the discount factor. One can interpret this set-up as implying that
consumption good one is preferred because domestically produced goods are preferred to
foreign produced goods, but for good two there exists snob appeal to consuming the good
produced abroad whereas domestically produced good two is viewed as being cheaply made or
distasteful.

I now return to describing the state of the world in any time period. The state of the
world at time t, s, is a 4x1 vector drawn randomly from a compact set SCR4. The distribution
function is given (I>(ds) and the distribution function is constant over time. The four shocks
are the two monetary innovations in each country, and the endowments in each country
respectively.

Since the timing of the actions of the agents in this model is the key to understanding
the model, a discussion of when the agents make their decisions and what information they
have when they make their decisions is necessary. Each household consists of three agents: a
shopper of consumption good one, a shopper of consumption good two, and a goods trader.
At the start of each period before the state of the world is revealed, the household in the blue

(red) country allocates MBt-NB. (Mix-NR.) to the consumption of good one. By assumption if a

household in the blue (red) country wants to buy a good produced in the red (blue) country,
they must use the currency of the red (blue) country. Since households in the blue (red)
country prefer consumption good two produced in the red (blue) country, there will be a
demand for and supply of foreign currency.

After the money is allocated to consumption good one, the household separates and the
state of the world is revealed. At this point, the monetary shocks are revealed. Once the
household decides how much it wants to spend on consumption good one, it is prohibited from
altering this decision. Thus after the state of the world is revealed, the households would most
likely prefer to alter its choice of 11, but this is prohibited by assumption. This captures the fact
that it is costly for households to adjust their portfolio with every shock to the economy
without explicitly modeling the costs. The shopper for good one takes Mit-Nit (i=R,B) to the
market place to buy good one. The goods trader goes to the marketplace where his endowment
is given to him. Because he intends to buy consumption good two that is produced in the other
country, the third member (the shopper for consumption good two) carrying Nit (i =R or B)
units of currency must go to the market for foreign exchange. In the market for foreign
exchange the agents from the blue (red) country receive a cash injection of XB(S,) (XR(St)),
which gives them a total of NB,+XB(st) (NR,+XR(S,)) to exchange for the currency of the red
(blue) country. Define MS.) to be the price of foreign exchange in terms of how many units of
the red country's currency it takes to buy a unit of the blue country's currency. Market
clearing in the foreign exchange market implies that D(S,)(NB,+XB(S,)) =(NR.+XR(S,)). Once

this exchange is made, the shopper for good two travels to the goods market. At the

IO

marketplace, traders are unable to discern which agents are from their household so all
transactions must be carried out using cash.

Because the technology to transform the endowment as.) into either good one or good
two is assumed to be linear, the price for either consumption good clB(st) and c2R(st) must be
the same, say P(s,). Likewise, the price (Qt(s,)) for either c1R(st) and c236,) must be the same.

The cash-in-advance constraint for a household in the blue country then implies that; MB,-
NB,2P,(st)clB(st), and D(s,)(NB,+XB(S,))ZQ(st)cZB(S,). The cash-in-advance constraints for a
household in the red country are MR,-NR,2Q(s,)e‘R(s,), and (1/D(s,))(NR,+xR(s,))2P(s,)c2R(s,).
At the end of each period, the households reunite, consume their consumption goods and pool
their resources. These pooled resources form the basis of next period's wealth. For a
household in the blue country, wealth next period is given by

MB...=<MB.-P(s.>cm(s.) -(1/D(s.»Q<s.)c2”(s.)+XB<so+P<s.>t<s.».
and for a household in the red country wealth next period is

M“... =(MRt-Qt(st)c1R(St)-D(St)P(St)CZR+XR(St)+Q(st)n(8t)).

Now that all the agents in the economy and their daily routines have been described,
equilibria are sought. Since all agents within each country are identical, the equilibria can be
analyzed by the actions of a representative household and firm in each country. For simplicity
in this section, I restrict the analysis to cases in which the cash-in-advance constraints bind.
Also, because I am restricting the equilibria to stationary rational expectational equilibria, all
growing variables must be detrended. The only growing variables in this model are the money
stocks, so all nominal variables of a particular country can be made stationary by dividing by

the time t money supply of that country. In particular, the normalized variables are:

11

mit=1 where i=R or B,

p.=(P(s.>/MB.>. qt=<0<s.)/MR.>,
n‘,=(N‘/M‘,) where i=R or B, e,=D(s,)(MR,/MB,),
x‘(s,)=(x‘(s,)/Mi(s,)) i=R or B.

The household's problem can be written in terms of its dynamic program. At this
point, all time subscripts will be dropped and primes are used to denote next period's values.
With a value function given by J(mB), the household in country one solves

Km")=mameaxailog<cm<s>>+ylog(c23<s>> +BJ(mB’))¢(ds)}

where cB =(clB(s), czB(s)) is the vector of choice variables for the representative household in
the blue country. The household’s maximization problem is subject to the cash-in-advance
constraints, mB-nBZp(s)clB(s) and nB+xB(s)2 (l/e(s))q(s)c23(s). The transition equation is given
by next period's money balances are given by

m"' =lmB-p<s)c‘B(s)-(1/e(s»q<s)c2”<s> +xB(S)-p(8)§(S)I/I1 +xB(S)l.

The first order conditions for the representative household in the blue country are

lx‘,(s)<l>(ds)=li3,(s)cl>(ds) 0.1
<1/c‘Bts»=p<s>i>~‘l<s)+BJ'(m”')/(1+x"<s»} 0.2
0/c”(s» =<1/e<s»q(s){x21(s> +BJ'(mB')/(1 +st»} 0.3
mB-nBZp(s)clB(s) with equality if 1‘,(s) .>_ 0 0.4
a” +xB(s)Z(1/e(s))q(s)c23(s) with equality if ms) )2 0 0.5

The envelope condition is given by
J'(mB')=i[1/(p(s)cm(s))]<b(ds) 0.6.

The representative household in the red country solves the following problem

12

1(mR)=maxolmaxcn{log(C‘R(S))+Ylog(CZR(S))+BJ(mR')}
where cR=( clR(s), c2R(s)) is the vector of choice variables for the representative household in
the red country, subject to the cash-in-advance constraints
mR-nR2q(s)clR(s) and nR+xR(s)2e(s)p(s)c2R(s).
Next period's money balances are given by
m“' = [mRa(S)c‘R(S)-e(8)p(8)czR(S) +x“(s> +q<s>n<s>vll +xR(S)].

The first order conditions for the representative household in the red country are given by

1112(s)<l>(ds) =l>.22(s)¢(ds) 0.7
(1/c‘Rts» =q(s){7~‘2(s) +BJ'(mR’)/(1 +x“<s»} 0.8
(t/cZRts»=p<s>e<s>ix22<s>+ 131'(mR')/(1+x“(s))} 0.9
mR-nR2q(s)e‘R(s) with equality if 112(s)20 0.10
nR+xR(S)Ze(s)p(s)c2R(s) with equality if 122(920 0.11

The envelope condition is given by

J'(mR)=l[1/(q(s)clR(s))] <b(ds). 0.12

An equilibrium for this economy is found by solving for functions p(s), q(s), c18 (S),

c‘R(s), c28(s), c2R(s), 111(s), 71‘2“), 121(5), 122a), e(s) and constants J'(mB), J‘(mR), nR, and nB
that solve eq. 0.1 - eq. 0.12 and the market clearing conditions. The market clearing
conditions are

6%.) +c2R(s) =§(s) 0.13

c1R(s) +cZB(s) =n(s) 0. l4

t(s)(nB +xB(s)) =(nR+xR(S)) 0. 15

13

and mB=1, mR =1. I now search for an equilibrium in which the cash-in-advance constraints
bind. In order for the cash-in-advance constraints to bind, restrictions are placed on nB, 11R and
the money growth process. These restrictions also imply that the equilibrium, if one exists, is

unique.

Assumption 0.1; Let 0 < xi <y for (1: 1,2), and
lYB(1-maX(X)){(r(1 +x<s»(1+max<x>+B<max<x>—x<s»i“> 1,
where max(x) is the largest possible monetary shock in the red country or the

blue country.

Assumption 0.1 guarantees that the lagrange multiplier on the cash-in-advance constraint is

positive.

Proposition 9,1: For xB(s) and xR(s) less than 7, there exists a unique equilibrium in which all

constraints bind, households maximize utility and all markets clear.

m The proof proceeds as follows: First, assuming the constraints bind, I show that there

exist constants nB and 11R that are unique. Then the constants J '(mR) and J '(mB) can be

recovered, as well as the equilibrium prices and quantities. Finally I solve for the lagrange

multipliers. If they are found to be positive the constraints are binding and existence is proved.
Imposing the cash-in-advance constraints, eq. 0.1 - eq. 0.3 imply

l =l{y(1—nB)/(nB +xB(s))}(D(ds) 0.16

14

and, similarly, eq. 0.7 - eq 0.9 imply
l =l{y(1-nR)/(nR +xR(s))}<D(ds). 0.17
Note that eq. 0.16 and eq. 0.17 are strictly decreasing in 11B and nR respectively. Moreover,
notice if nB(nR)=1 the right hand Side of eq. 0.16 (0.17) equals zero and if nB (nR)=0 then the
right hand side of eq. 0.16 (0.17) exceeds unity since xB(s) <y (xR(s) <7). Therefore, there
exist unique nRe(0,1) and nBs(O,1) satisfying eq. 0.16 and 0.17 respectively.
Given these values for the n's the derivatives of the value function are easily recovered
and are given by
J'(mB)=(1/(l-nB)), and
J'(mR)=(l/(l-nR)).
Prices are given by
p(s) =<1 +x"<s»/§<s>.
q<s>=0 +xR(S))/n(8). and
e(s)=(nR+xR(s))/(nB+xB(s)).
Equilibrium quantities are given by
c”’(s>=l(1-n”>/<1 +xB(S))]§(S),
c‘“(s) =[(1-nR)/(1 +xR(S))ln(S).
028(8) = [(nR+xR(S))/(1 +xR(S))ln(S).and
02R(s) = Kn" +x“(s»/(1 +xB(S))]§(S).
The shadow prices are then given by
1‘,(s) =[1-B/(1 +xB(S))]/(1-n) 0.18

i.‘,(s) = [1-0/(1 +xR(s))]/(l-n) 0.19

15

A21(S)={y/(nB+xB(s)) + [(1-nB)(1+xB(s))]"} 0.20
fists>=ivl<nR+xats>> + ltl-n"x1+x“<s»l“} 0.21
Clearly, 731(3) and A12(S) are greater than zero since xB(s) and xR(s) are constrained to be
nonnegative. Also, 121(3) and 122(5) are positive if and only if:
nB <{(y(1+ max xB(S))-B(max xB(S)))/(y(1 + max xB(s)) +B)}, and
nR <{(y(1+ max xR(S))-B(max xR(S)))/(y(1+ max xR(s))+B)}, where max xB(S)
and max XR(S) are the largest magnitudes of the monetary shocks. This holds by Assumption
0.1.

AS one would expect, prices are positively related to monetary injections. The
exchange rate is decreasing in monetary injections in the blue country and increasing in
monetary injections in the red country. In particular, a larger than average increase in the
money supply in the blue country leads to a decrease in the exchange rate. The lower exchange
rate makes consumption good two cheaper for people in the red country since they pay
e(s)p(s), which is decreasing in the monetary innovations in the blue country. Moreover, the
consumption of good one becomes more expensive--p(s) is increasing in the monetary
innovations in the blue country--for members of the blue country because of the higher prices.
Thus there will be an increase in the demand for consumption good two by members of the
red country and a decrease in the demand for good one by members of the blue country.
Consequently, production will be altered by the trader of €(S). This trader will shift the
production schedule to making more consumption good two. Unexpected cash injections
leading to changes in the consumption allocation and production are precisely the liquidity .

effect-—monetary policy has real effects. Monetary injections/withdrawals that differ from their

l6

expected values will have affects on consumers' and producers' behavior that differ from what
would have occurred with full contemporaneous information. Chapters 1, 2, and 3 employ the

basic concepts used above to show how monetary innovations have real effects.

0:

 

As countries have become increasingly more interdependent due to the liberalization of
trade policies, policy makers have been considering the benefits to be gained by coordinating
policies across countries. Perhaps the most frequently proposed coordinated policy is
establishing an optimal currency region. The idea here is to have only one currency in circulation
for a specific group of countries. Moreover, the supply of currency would be controlled by a
single central bank. The European Union is a prime example of a region that is considering the
adoption of a single currency to be used by the members of the union.

The benefits of the optimal currency area include the elimination of exchange rate
uncertainty and a reduction in transactions costs involved with exchanging currencies. The main
argument against the adoption of an optimal currency area is that the monetary authority can not
react to country specific shocks. This loss of autonomy, it is argued, may make the outcomes in
optimal currency regions less efficient than the established flexible exchange rate regimes.

This chapter is a theoretical investigation of the optimal monetary policy in a two country,
one currency, liquidity effects model]. I assume that each country specializes in the production of

a Single good. The monetary authority injects currency into the financial intermediaries. It is first
established that monetary innovations have real effects in both countries. Then given the fact that
the actions taken by the monetary authority has real effects, the optimal monetary policy is
derived. It is shown that the optimal monetary policy involves contracting the money supply On

average at rate equal to the household’s subjective rate of time preference. However, if the

 

' These models have been popularized by Lucas (1990), Fuerst (1992), and Christaino and Eichenbaum (19921))
17

'I.
an

Iii

the :

tap:

it»).

18

countries are “more” (“less”) productive than usual, the monetary authority should increase
(decrease) the growth rate of the money supply above (below) the average contraction rate. This
procyclical policy accommodates money demand shocks. The ability to attain the Pareto optimal
allocation hinges on the monetary authority being able to contract the money supply on average.
In addition to deriving the optimal monetary policy when the growth rate of the money supply is
unconstrained, I also look at the best monetary policy in the case were the money growth rate is
constrained to be positive on average. In this case, a procyclical policy is still preferred. That is,
the monetary authority should provide liquidity when firms are most productive. Therefore, this
paper shows that the monetary authority in a single currency region can attain the Pareto optimal
allocations by simply responding to the “average” level of technology.

The rest of the chapter proceeds as follows: Section I provides an overview of the model.
Section 11 describes the behavior of the agents. In Section III, a competitive equilibrium is
derived and it shown to be unique. The qualitative features of the competitive equilibrium are
also investigated. Finally, in this section, the optimal monetary policy is derived. In Section IV,
the “best” policy is investigated when the money supply is constrained to be positive on average.

Section V concludes.

5 . I I] l I i l' D .
In this chapter, a two country, liquidity effects model with a Single currency is
investigated. It is shown that with identically distributed shocks that a competitive equilibrium

exists where all constraints bind. A property of this equilibrium is that the interest rate is

decreasing in monetary innovations, and employment is a decreasing function of the interest rates.

in

3.11

l .. ._:_. (‘7

19

Therefore, monetary injections that differ from agents' expectations will cause interest rates to
differ from their fundamentals and have real effects. Since monetary innovations can have real
effects, the optimal monetary policy is derived. It is shown that the role of the monetary authority
is non-trivial. Indeed, the monetary authority, by responding to shocks, can make the competitive
equilibrium Pareto optimal.

There exist two spatially separated, infinitely lived countries populated with three types of
agents: households, goods producing firms, and a financial intermediaryz. There are many
identical infinitely lived households. It is assumed that wealth is distributed uniformly across
households. These households have preferences over lifetime consumption and leisure given by

Utah-£31,)=x=o°°{B‘<u(c‘,..c2,-o + V(T-Lj0)}
where cij, is consumption of good i by household j at time t, Lj, is the amount of labor supplied at
time t, T is the fixed time endowment each period3. Then (T-Ljo is the amount of leisure at time t
for household j (j = 1,2). It is assumed that u(., .) is twice continuously differentiable, increasing
and concave. V(.) is also increasing and concave. When the competitive equilibrium and the
optimal monetary policy are derived, the following functional form is imposed
U(e‘j,c2j,L,-)=E-o°°{13‘(ln(e‘,-,(s)) + 1n(e2j,(s)) + (T-ij. 1.1
This specification, along with the specification of the production function, permits closed form
solutions. Thus, the economic interpretations are easily understood.
Since all households are identical, I will solve for equilibria in terms of a representative

household in each country. Furthermore since households in country one and households in

 

2 Allowing for a finical intermediary in each country would not change the results as long as the individuals could
choose where to deposit their funds after the state of the world is revealed or if the banks could make inter-bank
loans after the state of the world is known.

3 It is assumed that T > 2, so that the Pareto optimal labor supply is feasible.

11}:

E?

US

is

3'1)!

its.
1

20

country two are ex—ante identical, attention is restricted to the description of a representative
household and firm in country one. The reader should keep in mind similar constructs hold for

households and firms in country two.

I] I l l E. l g I . .
There exists a single monetary authority in this model“. The monetary authority injects

x(s) units of currency into the financial intermediary. The monetary injection in this section is

assumed to be a stochastic process. In particular, x(s)e X where x(s) is iid and X c R + . When

the optimal monetary policy is derived, the monetary injections are a function of the state of the
world. The fiscal authority in this economy collects taxes (pays transfers) in order to keep wealth
constant over time. Absent this tax transfer scheme, households’ wealth would change from
period to period due to the technology and monetary shocks--these shocks will be discussed in
greater detail below. Households prefer this tax/transfer scheme because the variability in wealth
would yield lower expected lifetime utility. It is shown below that average tax/transfer is zero.
Also, each period the government maintains a balanced budget. That is, it is shown below that
the taxes collected from one country are equal to the transfer payments in the other country.
These taxes are a form of coinsurance as suggested by Ingram (1959). That is, there are transfers
that shift funds from the region which has experienced a beneficial idiosyncratic shock to the less

fortunate region.

 

‘ Given the equal wealth distribution and that all agents are ex-ante identical, it is possible to think of this model as a
model of fixed exchange rates, as well as a single currency area.

21

Hmholds

What is important in these liquidity effects models is the timing of decisions relative to the
realization of the shocks, and that some decisions cannot be altered ex post. In this model, the
household, which consists of a worker, and a shopper for goods one and two, begins each period
with Mlt money balances carried over from the previous period. Before the state of the world is
revealed, the household chooses how much of its money balances to place in savings (Nu). Once
this decision is made, it cannot be altered ex-post, and the worker-shopper pair separates. With
full contemporaneous information, the worker offers labor services in the labor market5 and the
shopper purchases goods in the goods market. The Shopper’s purchases are constrained by the
amount of cash that is brought into the trading session. The cash—in-advance constraints on goods
purchases are given by

Mlt'Nlt'Qltzpltcllt
QItZletczlta
where Q1t is the dollar allocation for consumption of good two, and Pi is the price of good i.

At the end of the period, the household reunites consumes the consumption goods and
pools its resources. The pooled resources are denominated in home currency temrs and this
becomes the representative household's wealth in the subsequent period. More formally

M‘,,,={(M‘,- N1t -l>‘,e‘,l - 19,81.) +(N,,(1+Rw) + w,,L,,) + (r1f1 +113) + 1:, M1,}
The first term in parentheses is the residual from the cash-in-advance constraints. The second

term in parentheses is the return on savings deposits and labor compensation. The third set of

 

5The worker in country one (two) offers her labor services to the representative firm in country one (two). By
assumption, the worker in country one (two) can not work for the representative firm in country two (one).

{6111‘

22

terms are the dividends the household receives from owning country one's (two’s) good producing
firm and dividends from owning one half of the international financial intermediary. Finally It is
the end of the period transfer (tax). This transfer (tax) which is paid (collected) by the
government maintains a constant wealth distribution across households and across countries for all
time periods. Households prefer this policy to a system without these transfers (taxes) because
this transfer/tax scheme yields higher expected utility.

Once the nature of the shocks is described and all nominal variables are made stationary,
it is possible to solve the household's problem. The shocks are independently and identically
distributed random variables drawn from a compact set S. The shock at time t is given by stst
and the distribution function is given by (I>(ds). Since monetary injections cause the money supply
to vary over time, nominal variables will also vary over time. Because I am only concerned with
stationary rational expectational equilibria, it is necessary to rescale all nominal variables by the
contemporaneous money stock to make them stationary. Let the money growth process be given
by (M1,+1/M1,)=(1+x(s,)), where x(s,) is the time t monetary injection. The stationary variables

are denoted by lowercase letters. These variables are defined as follows

pl(s)=Plt/Mlt p2(3)=P21/Mlt Wl(5)=wll/Mlt w2(s)=wzr/Mlt
q‘ts)=Q‘./M‘. q2(S)=Q21/M‘t n‘=N‘./M‘. n2=N2./M‘.
x(s)=x,/M‘,.

From this point on, unless otherwise noted, time subscripts are dropped and primes are
used to denote next period’s values. Given the properties of the utility function and the fact that
the constraint set is compact, the household's infinite horizon maximization problem can be
written as a dynamic programming problem. The household's dynamic program is given by p

J<m>=max.l. maxq,..l{u<c‘1(s),c2.<s» + V(T-L(S)) + (surnames)

CI}

23

subject to the two cash-in—advance constraints
m‘mtsh .>. p‘tslc‘ns) 1.2
qlts) 2 p21slcztts) 1.3
and the transition equation
in" =(ml-pl(s)cl1(s)-p2(s)c21(s)+anw +w‘(s)L,(s)+1t"1 +16” +t‘)/(l +x(s)).

The first order conditions are

I. [J'<m)R‘”/<1 +x<s>>1<I><ds> = I. xttslcbtds) 1.4
711(8) = 12(8) 1.5
u.(c‘.(s).c21(s» = p‘tsliwm-(m'>/(1+x(s» + 11(8)} 1.6
u.(c‘.(s).czi(s» = p2(S){BJm'(m')/(1+X(S)) + rats» 1.7
via-us» = mm-(m')wt(s>/(1+xts» 1.8
m1 - nl - q,(s)2 p‘(s)e‘,(s) with equality if 7L1(s) > 0 1.9
91(S)sz(S)C(S)21(S) with equality if MS) > 0 1.10

where the Ai's are the multiplier's on the cash—in-advance constraints. The envelope condition is
given by

J..(m)=l. lul<c‘.(s>.czt(s»/p‘(s)1<b(ds). 1.11

Before the firms' and the financial intermediary's problem is solved, I will discuss the
first order conditions. In order to aid in the discussion and avoid confusion, I renorrnalize by the
time t money supply and reintroduce time subscripts. Combining equations 1.5-1.7 yields

u1(c11,,c210/u2(c1n,c2n)=P1,/P2,.

Thus equations 1.5-1.7 give the standard result that at any point in time the marginal rate of
substitution between goods is equal to the ratio of their prices. Next by combining the envelope

condition and 1.8 yields the optimal labor supply decision is obtained. That is,

fir‘.
, UV

A‘t‘n'
§\ I s

It};

£03

iI‘t‘:

-w. .
o—d

24

V'(T'th)=EtB{ul(Cllt+ltczlt+l)wlt/Plt+l}
According to the above expression, today's labor supply is a function of the ratio of the
contemporaneous nominal wage to tomorrow's price level. This implies that today's labor supply
depends on the contemporaneous wage and the expected price of good one next period. The
reason for this is simple: today's wages are not available for current consumption only future
consumption. This equation can be rewritten so that the labor supply curve can be drawn in real
wage space. To do this multiply and divide the right hand side by P1,. This yields
V'(T'th)/Etl3{ul(cllt+laczlt+l)Plt/Plt+1}= wlt/Plt.
Note that the labor supply equation written this way implies that increases in expected inflation
will cause the labor supply curve to shift to the left.
Combining equations 1.4, 1.6, and the envelope condition yields
Et—lul(c1ltvczltyplt=Et-l{(l+Rw)B{ul(cllt+19C21t+l)/Plt+l}'
This is the household's intertemporal decision rule for savings and consumption. This
intertemporal condition is interpreted as follows: before the realization of the current period's
shocks, the representative household allocates funds to savings so that, in expectation, the
marginal cost of allocating an additional dollar to savings is equal to the marginal benefit received
next period. This decision rule captures the liquidity effect. Shocks that cause the actual
valuation to differ from the representative household's expected valuation will cause the interest
rate to differ from Fisherian fundamentals. Therefore, cash injections into the financial
intermediary that exceed the household's expectations increase the supply of loanable funds. The
increase in the supply of loanable funds will cause the price of loanable funds to fall; that is, the
interest rate should fall. Traditional models of this nature only capture the expected inflation effect

of the monetary innovations. That is, they predict interest rates will rise with monetary

C.)

.57"

Li

25

innovations. In the liquidity effects models, if the liquidity effect dominates the expected inflation
effect then interest rates will fall. Since the firms, by assumption, must finance their expenses at
least in part by loans, the lower interest rates will lower the cost of inputs and firms may employ
more inputs. If this is the case, the reduction in interest rates will lead to increases in real

activity.

There exists one firm in each country which is endowed at time zero a with fixed supply
of capital. Production is carried out by combining capital and labor supplied by households. The
capital stock endowed to each country does not depreciate nor can it be augmented. There are
two shocks that affect the production function directly. The first shock is a shock to total factor
productivity (0,(s), i=1,2). It is assumed that 0i(s)eR+ +. The other shock that affects the firms
directly is a marginal productivity shock (0t,(s), i=1,2). The marginal productivity shocks falls in
the range (1/2,1).

Firms must pay their workers with cash. Since households and the financial intermediary
are the only ones that hold cash, firms must borrow in order to finance their wage bill. By
assumption, direct borrowing from households is ruled out, so firms must obtain their funds from
the financial intermediary. Therefore, firms maximize profits subject to a borrowing constraint.

Given this constraint the firrn's problem is given by
n“ =maxn1p'tsletts) H. 6W - w.(s)Hl(s>-b(s)R‘"}.
where w1(s) is the wage paid to a worker in country one (rescaled by the money supply in order

to make it stationary), H1 is the amount of labor employed, b is the level of borrowing to finance

the

in:

Bill

F51

.101

of i

RF.

in:

26

the wage bill, RW is the world interest rate, and 01(5), and a1(s) are shocks to the firms production
function. The profits of the firm are paid to the representative household in country one at the

end of the period6. The first order condition for profit maximization is given by
at(5)pl(8)91(8)H1(S)“"“"‘ =wl<s)(1+R‘”).

The firm's labor demand schedule is given by this first order condition.

The financial intermediary receives n1 dollars deposited by the representative household.
in country one and n2 dollars deposited by the representative household in country two. The
financial intermediary is also the sole recipient of monetary injections from the monetary
authority. As long as the interest rate is nonnegative, the financial intermediary will lend out all
of its cash balances. Its profits are given by

TEE =(nl + n2 + x(s))(1+Rw)-(n1 + n2)(1+Rw),
where the first term is the return from lending funds to the firms for production and the second
term is the amount the financial intermediary owes to the household for the deposits. Clearly,
profits can be simplified to: 1tB = (1+Rw)x(s). These profits are divided in half and distributed to

the representative households in country one and two at the end of the period.

 

(The profits for the firm operating in country two are distributed to the representative household in country two at the
end of the period.

27

S . IIIE 'l’l'

Definition; A competitive equilibrium in this economy is a sequence of prices {pl(s),p2(s),
(1 +Rw), wl(s),w2(s)}, allocations {cl1(s),c21(s),c12(s),c22(s),Lz(s),L1(s)} and constants Jm.(m), n1,
n2, such that

i) the prices and allocations solve the households' problem,

ii) the prices and allocations solve the firms' problem,

iii) the prices and allocations solve the financial intermediary's problem,

iv) the governments' budget constraints are balanced, and

v) all markets clear.

The market clearing conditions are:
c'l(s>+ c'a(s> = 9.1s)H.<s)°"“’ ,
191(8) + else) = 9.191126%“) .
Ll(s) = Hi(s).

L2 (3): H2(S).

n1 + n2 + x(s) 2 b1(s)+b2(s), and

In order to guarantee an interior solution, a restriction must be placed on the monetary shocks.

28

AssumptionIL

Assume that x(s)20. I 13111121915416» - a1(S)q(S))][(X(S)(1 +1x<s>/2»1"<I>(ds> > 1

This assumption ensures that the households will deposit funds into the financial
intermediary. If not, the interest rate offered by the intermediary will exceed the discount rate.
Since there is no growth in the real factors, zero deposits cannot be optimal.

Given Assumption 1.1, it is easy to show that there exists a competitive equilibrium and
it is unique. In a competitive equilibrium, all markets must clear. Given the initial wealth
distribution the representative household in each country will have exactly one half the total

money supply. Existence of the a competitive equilibrium is stated and proven below.

Proposition“ Given Assumption 1.1, the functional form of the utility function defined in 1.1,
then in the class of competitive equilibria in which all constraints bind, the competitive

equilibrium exists and is unique.

Emof; The solution strategy is as follows: first show that there exist constants n1 and n2 satisfying
the households' first order condition. Then given the solutions for the ni's the prices and wages
can be derived from the first-order conditions and the market clearing conditions.

First solutions to the constants n, and n2 are found. Recall that a household in country

one is isomorphic to a household in country two so that 111 = ti; and q,(s) = q2(s). Also, by

29

combining equations 1.5, 1.6, 1.7 by the symmetry of the model, and using the binding cash-in-
advance constraints yield ql(s) =q2(s)=(l/2-n)/2. Also, exploiting the symmetry and given that
the shocks are iid equation 1.4 can be rewritten as:

1 = l, { B(a1(s)+a2(s))((l -2 n)/4)}{(1+x(s))(n+x(s)/2)}'1<D(ds). 1.4'

Notice that the right-hand-side of this equation is strictly decreasing in n, and when n= .5
the right hand side must equal zero. Furthermore when n=0, the right hand sides exceeds unity
(from Assumption 1.1). By continuity, there exists an n‘, such that n.6(0, .5), that is, a fixed
point of this mapping in the region of zero and one-half that solves eq. 1.4'. These values for the
n's imply that Jm~(m)=(4/(1-2n)) for logarithmic preferences.

The equilibrium interest rate and prices are given by

p'(s)=<1 -2n)/29.(s>L,<s>"":’

p2(s)= (1 -2n)/202(s)L,(s)“2‘5’

(1 +Rw)= {(011(s) +012(s))(1-2n)}/{2(2n+x(s))}. 1.15
Consumption allocations are given by

cij(s)=(1/2)91(S)Li(s)“*(s) i,j=1,2
The equilibrium wage rate and labor supply are given by

w,(s)=(1+x(s))(1-2n)/4B for i= 1,2 1.16 a,b

and letting A(s) = {011(s)/(011(s)+a2(s))} then

L1(S)=A(S){(nl +02 + X(S))l34/(1-2n)(1 + X(S))}

14(S)=(1-A(s)){(n1+n2 +x(s))B4/(1-2n)(1 + x(s))}. 1.16 c,d
The transfers are given by

TI ={1((a1(S)-a2(8))((1-n)/2))] - ((1-211)/4+( A(S)(211+X(S)) + (1 +X(S))))}

30

12={((a2(8)411(8)))((1-n)/2))- ((1-2n)/4+(1-A(S))(2n+X(S)) + (1 +X(S))))}

This completes the proof.

Eropositiomiz; Given these equilibrium values, monetary injections that exceed their expected
values lead to a reduction in interest rates, an increase in equilibrium employment, and an

increase in output.

Emmi; The reduction in interest rates follows from differentiating equation 1.15 and the fact that
n is constant. Similarly, the increase in equilibrium employment follows from differentiating
equation l.16c,d. Given the production function and the fact that output is monotonically
increasing in the labor, output will increase with larger than anticipated monetary innovations.

This completes the proof.

As shown above, the interest rate is decreasing in x(s) and the employment level in both
countries is increasing in x(s). Therefore, a monetary innovation that exceeds the households'
expectations will lead to a reduction in the interest rate, an increase in employment, and thus
higher output. This implies that the monetary authority can potentially alter output. The next
natural question to pose is: Is this competitive outcome Pareto optimal? If not, then can the
monetary authority attain a Pareto improving allocation? It seems plausible that if actions of the
monetary authority can have real effects, then the monetary authority can play an important role
in this economy. There are two frictions which the monetary authority may attempt to mitigate.
First and most obvious, since it is common to most cash-in—advance models, is that there is an

inflation tax “levied” on consumption purchases and on the firm's labor bill. Common sense

31

would lead one to believe that the way to eliminate this distortion is through a Friedman type
deflation rule. In fact, the optimal monetary policy derived below is to contract, on average, the
money supply at a rate equal to the household's subjective rate of time preference. The second
distortion, and particular to the liquidity effects models, is the "sluggish" cash flow that prohibits
the representative household from readjusting its portfolio after the state of the world is revealed.
A monetary policy that can respond to the shocks and mitigate this second distortion is welfare
improving.

It is shown below that the monetary authority can attain the Pareto optimal allocations in
this stochastic environment by responding to the realizations of the stochastic variables. Notice
from equations 1.15 and 1.16c,d that the marginal productivity shocks, the 01i(s)'s, affect the
interest rates and labor supply but shocks to total factor productivity do not. Accordingly the
monetary authority will respond to the marginal productivity shocks, the (Xi(S)'S, but not the
shocks to total factor productivity.

To illustrate the potential role of the monetary authority, first consider the case where the
monetary authority does not respond to the productivity shocks, and follows a constant growth
rate rule. (Figures 1.1-1.5 depict this analysis graphically.) That is, the monetary authority
increases the money supply by x percent each period. Also, assume that country one has a larger
than anticipated marginal productivity shock while the marginal productivity shock in country two
is equal to the representative household's expectation. The marginal productivity shock in country
one will shift country one's demand for loanable funds to the right (See Figure 1.1). Country
two's demand for loanable funds will be unaffected (Figure 1.2). The increase in country one's
demand for loanable funds causes the market demand for loanable funds to shift to the right

(Figure 1.3). Since the supply of loanable funds is fixed the rightward shift in the demand for

32

 

 

 

 

 

 

 

WW8;
Country One: Country Two:
(1+R
" . . (HR).
(1+R) f
o (1+R)0 .
b0 bl bl b0
Figure 1.1 Figure 1.2
Williams;
Loans
(1 +R),
(1 +R)0 ‘21!“

 

 

 

Figure 1.3 Loanable Funds

33

Country Two:

(W/P)0
(W/P)1

(“I/PM

(W/P)o

   

 

 

 

 

Figure 1.4 Figure 1.5

loanable funds will result in an increase in the interest rate. The higher interest rate implies that
country one will get a larger portion of the loanable funds. To determine what happens to the
equilibrium level of employment, recall that the firm's demand for employment is a decreasing
function of the interest rate. (Figures 1.4 and 1.5 depict the labor supply and labor demand
curves for countries one and two respectively. Also depicted are the Pareto optimal levels of
employment when shocks are equal to their expected value (11,01) and when country one's
marginal productivity shock is larger than anticipated (Lpoz)).

The representative firm in country one's labor demand curve shifts to the right due to the
larger than anticipated marginal productivity shock, while the increase in the interest rate shifts
the labor demand curve to the left. The leftward shift arising from the increase in the interest rate

is not enough to offset the rightward shift due to the marginal productivity shock. Therefore,

34

is not enough to offset the rightward shift due to the marginal productivity shock. Therefore,
equilibrium employment in country one will be greater than if the shock were equal to the
households' expectation.

For the representative firm in country two, the higher interest rate shifts the labor demand
curve to the left. Thus equilibrium employment in country two decreases. However, note that if
the monetary authority would take an active role and increase the money supply in response to the
shocks, the equilibrium interest rate would be lower than if the monetary authority followed a
constant growth rate rule. The lower interest rate would allow for equilibrium employment to
increase in both countries. If the monetary authority increases the money supply “just enough” the
Pareto optimal allocations can be attained. Thus the role of the monetary authority is to find the
Pareto optimal employment level and a money supply rule that ensures that the competitive
equilibrium employment level is the Pareto optimal level of employment. To this end, the role of
a fictitious social planner is postulated.

The social planner maximizes the welfare of both representative households. The only
constraint the social planner faces is that consumption of goods cannot exceed production of the
goods. More formally, the social planner places equal weight on each household’s utility and
chooses c11(s),c21(s), c12(s),and c22(s) to maximize the per period utility function given by
Wtc..c2.Ll.La)= u(c‘ttsls’tts» + V(T-Lns» + U(C12(S).022(S)) + V(I-Lats»
subject to the resource constraints;

c'its) + c'ats)= 911s) new” . and c216) + 022(S)= 621s) L2(S)“’“’

Carrying out this maximization, yields the following efficiency conditions,

v'(T-Lttswtu(c‘t(s>,c2.(s»=al(s)et(s) L. (S)“"s"' for i=1.2.

35

V'(T-L.(s»/u2(c‘icicle»=oe<s>62<s1 1., (oil‘sH for 1:12.
Referring back to the consumer's problem, combining 1.6 and 1.8 yields
V'(T-Lt(s))/ut(clt(8).czi(s))
=(witsllp'ts)){BJm.<m'>/(1+x<s>>ilBJm.(m')/(1+x<s>>+xa<s)1“} 1.19.
Substituting for the w,(s)/p'(s) from the firm's problem yields:

V'(T-Lt)/U.<c'.(s).c’t(s»=

101110616) L.(s)°‘”5’" /(1 +R")l{(alm.(m')/(1 +X(S)))I(BJm-(m')/(1 +x(s»+12(s)1"} 1 .19'.
It is obvious that equation 1.19' equals equation 1.18 if and only if AQ(S)=0 and RW =0 for all t.
This implies that the cash-in-advance constraint cannot bind and the gross nominal interest rate
should equal unity. Therefore, if the monetary authority can satiate households with cash balances
and drive the nominal interest rate to unity, the monetary authority can improve upon the
competitive allocation. Note also since the firm's output is constrained by how much money is
held by the financial intermediary (n, +n2+x(s)), the monetary authority may be able to
accommodate shocks to the production function. For example, suppose the production function
experiences a positive technology shock, the firm's output is constrained by the amount it can
borrow, it seems that the monetary authority could improve welfare by injecting cash into the
financial intermediary. With a positive technology shock, the firm would like to borrow more
than normal, but would be unable to do so unless the monetary authority responded to the shock.
In order to accommodate fimis, the monetary authority should increase its cash injection x(s).
Recall optimality implies that Aij(S) =0 (for j = 1,2) and that (l +Rw) =1 implies that the
cash-in-advance constraints on the households and the firms "just" bind or do not bind. Thus the

level of cash balances is indeterminate. This is true because the zero values on the lagrange ‘

36

multipliers imply that if M units of real cash balances satiates agents and an equilibrium is attained
then clearly for any a > 0, M +8 units of real balances will also yield that equilibrium. A way
around this problem is to assume that all the constraints "just" bind, however, this implies that
system will be overidentified. Instead I assume, following Fuerst (1994), that the cash constraints
are non-binding and the borrowing constraint just binds. This is similar to the real bills doctrine
in which the monetary authority stands ready to alter the money supply to suit the needs of the

borrowers.

Eropositionil; Given the above restrictions, and for the preferences given by equation 1.1, an
equilibrium exists and is characterized by non-binding cash-in-advance constraints, a gross interest
rate equal to unity, functions pi(s), wi(s), and constants ni, and Jm(m) that solve the social

planner's problem.

Proof; Since the cash-in-advance constraints do not bind, prices with the logarithmic preferences
are given by

p'(s)=(1+x(s»/(c'.(s)BJm(m» and

p2<s>=11+x<s»/(czt(s) 131mm».
By the symmetry of the households and using the goods market clearing condition, the optimal

consumption allocation for each household is given by
disl= .59.<s)L.(s)“i‘-” , i.i=1.2

p'(s)=2<1+x<s>>l<BJm-(mlet<s)Laue“) ), i=1,2 1.20 a,b

The]

Next

”111' n

{1‘ (in);

Time If:

37

These prices can be substituted back into the envelope conditions for the representative household
which yields

1 =l,(B/(1 +x(s)))<l>(ds). 1.21
Equation 1.21 states that the inverse of the household’s subjective rate of time preferences (0")
equals the inverse of the expected gross growth rate of money supply7.

Wages are given by

W1(S)={(1+X(S))/Blm(m)} and

W2(S)={(1+X(S))/BJm(m)}. 1.22 a,b
Recall Pareto optimal labor supply is given by

L1(s)=20t1(s) and

[4(3) =2012(s). 1.23 a,b
Substituting these values into the non—binding cash-in-advance constraint and the borrowing
constraint places restrictions on the constants Jm(m) and the ni's. Thus the constraints are now
given by

BJm(m)/(1 + x(s))2( . 5-n/ 2)

film(m)/(1 +X(S)) =2(ai(8) +a2(8)/((2n+X(S)))
The borrowing constraint can be rearranged and substituted back into eq. 1.21 to yield

Jm-(m)=l {2(011(s)+012(s))/(2n+x(s))}<l)(ds).

Next substitute into the non-binding cash-in-advance constraints for film(m) and rearranging yields

fl2(-5(al(8)+02(8) - x(s))/(2+0ll(8)+<12(8)).

 

7 This implies that agents expect the money supply to contract at a rate equal to the rate of time preference. This is just a
stochastic version of the Friedman rule for the optimal quantity of money; that is, to contract the money supply equal to
some real variable such as the real rate of interest or the subjective rate of time preference.

II.

In

No:

LIT-Ill
ripe
til. 1
Chin

Ioihl‘

38

Leta be the smallest 0t(s) in the distribution and x to be the largest x(s) in the distribution, and
assuming the cash-in-advance constraint just binds at these values puts a restriction on the n's. The
n’s are given by
ni =(Ot-x)/(2(l +61» 1: 1,2
Given these constants Jmo(m) and n, rearranging the borrowing constraint gives the period by
period money supply rule. That is, the money supply rule for any period is given by
X(S)=[Bim(m)(Zn-2(a1(8)+a2(8)))l/[2(a1(8)+az(S))-l31m(m)l 69- 1-24

This completes the proof.

Notice that 6x(s)/60ti(s) > 0 which is what we would have suspected given the optimal labor supply
in eq. 1.23 a,b. Thus the monetary authority will respond to shocks to the production function for
high ai(S)'S by injecting cash into the system.

In general, the monetary authority expects to follow a policy given eq. 1.21; a monetary
contraction at a rate equal to the subjective rate of time preference. The 01,(s)'s deviating from the
expected value will lead the monetary authority to deviate from this exact plan. By inspection of
eq. 1.24 one may think that the monetary authority's hands are tied if both country's 0t,(s)'s
change by equal magnitudes but in opposite directions. In this case the monetary authority should
follow the Friedman deflation rule since the market mechanism channels the funds to the
appropriate country. Furthermore, notice that the monetary authority does not respond to shocks
to 0,(s). This is not a failure of the model but rather due to the specification of preferences which
yields that the Pareto optimal level of work effort is independent of the EMS). With more general
preferences the monetary authority does respond to 0,(s) shocks to achieve the Pareto optimal.

allocations. Thus the lack of monetary independence does not inhibit the Pareto optimal

39

allocations from being attained. That is, a single monetary authority can attain the Pareto optimal

allocations.

L132

10:

Clunl

[he :11

Since countries in general do not contract their money supplies, this section investigates
the monetary policy when the money growth rate is constrained to be non-negative on average.
Positive money growth rates may be required to generate a level of seigniorage. The idea in this
section is to choose a money growth rate that corresponds to the realization of the shocks; that is,
the monetary authority chooses the degree of correlation between money growth and the
realization of the shock.

To keep matters simple, I restrict attention to two realizations of the 01 shocks. I assume
0t takes on the values .65 or .75 with equal probability. For this set of simulations I fix 9 =2 and
B= .95. The experiment is to calculate how much a household would, in expectation, need to be
compensated in terms of consumption goods to attain the expected Pareto optimal welfare for a
given correlation between money growth rates and marginal productivity shocks. That is, I solve
for Ac in the following problem:

Eiutc't"°.c21"°)+(T-I.-"°)} =E{u(c'f'°+ Ac.c2f°+ Ac)+(T—L.C°>},
where Po stand for allocations in the Pareto optimal case and Ce stands for the allocations in the
competitive equilibrium.

Figures 1.6 through 1.9 depict the welfare loss (Ac) for 01 stochastic. The welfare loss is
plotted on the vertical axis and the money growth rate if the bad state (01(3)= .65) occurs in both
countries is plotted on the horizontal axis. The interpretation of this graph is as follows. Suppose

the average money growth is set to Y percent, then if the bad state arises in both countries, the

more

rule 11

II-X

IIIC

' r'J
7 '

41

money growth rate rule is to increase the money supply by X percent. The money growth rate
rule in the good state (that is if 01(s)= .75 for both countries) is to increase the money supply by
2Y-X percent. Finally, if 01(s)= .75 for one country and 0t(s) = .65 for the other country by
default the monetary authority chooses to increase the money supply by its expected value (Y).
This monetary rule guarantees the average growth rate of the money supply is Y percent. Thus a
high x value implies a countercyclical policy. That is if the bad state occurs the growth rate of the
money supply is high.

Before the simulations are analyzed, a few comments should be made about how the
figures would appear in the absence of the portfolio rigidity with the only stochastic variable being
the money growth process. For lack of a better label, this case is referred to as the base model.
The graph for the base model would actually be symmetric and hump—shaped, which implies
monetary variance is preferred. This is true because work effort in the competitive equilibrium is
given by

V'tT-L.<s))/u<c‘.,c2.>= 01.1.9916) L. (S)“"’“ /(1+R)2,
and the interest rate is given by

(1 +R) = [1(13/(1 + x(s))<l>(ds)]".
Recall in the previous section, it was shown that the Pareto optimal interest rate is unity.
Therefore, in this model the closer the interest rate is to unity the closer the economy is to the
Pareto optimal allocations and the lower Ac will be. The above equation for the interest rate
implies that the larger the variance in the money growth process the lower interest rate will be.

Therefore, the more variable the money growth process is the lower the interest rate. Higher

("Cl
‘3’

(71:9
(9

r":
l g.

The

firth

“1h:

42

money supply variance, therefore, would be preferred by households. In the simulations, 1 look
for significant deviations from the base model.

As stated above, Figures 1.6 through 1.9 depict the welfare loss for the case where 0 is
fixed and or variable. Figure 1.6 shows the welfare loss when the shocks are iid and the average
growth rate is 10 percent. The variable on the horizontal axis is the money growth rate if the bad
state occurs in both countries. This implies that the growth rate of the money supply in case the
good state occurs in both countries is .20—x, and the money growth rate will be 10 percent if a
good state occurs in one country and a bad state in the other. This policy yields an expected
money growth rate of 10 percent. As can be seen from the figure, the graph is hardly symmetric
or hump shaped. In fact, the peak has shifted well to the right. Therefore, a procyoiioal policy is
favored. Note the role of the monetary authority in this case is to smooth interest rates. This is
easy to see. Recall the definition of interest rates:

(1 +R) =(011(s)+012(s))(1-2n)[2(2n+x)]'1.
Looking at the effect on interest rates from this procyclical policy, if the 01 shocks are high (low)
then the above policy recommendation is to increase (decrease) the money growth rate. The large
(small) 01's would drive up (down) interest rates, while the increase in the money supply above.
(below) its expected value would counteract the upward (downward) pressure on interest rates.

Figure 1.7 depicts the welfare loss when the money growth rate is constrained to be 20
percent on average. In this figure, the graph is more "hump-shaped" but it is hardly symmetric.
The implication is the same; a procyclical monetary policy is preferred.

Figures 1.8 and 1.9 show the expected welfare loss when the shocks are correlated with
each other but independent of all other factors. That is 01,(s)=0t2(s) = .65 or (11(3) =012(s)= .75

with equal probability. Again the results are the same that a procyclical policy is preferred.

43

Conclusion

It was shown in this open economy liquidity effects model with a single currency used for
exchange that under certain restrictions, there exists a competitive equilibrium in which all
constraints bind and cash injections lead to a reduction in the interest rate and an increase in real
activity. Furthermore, the competitive outcome could be improved upon by a procyclical
monetary policy rule that smooths interest rates. More specifically, the role of the monetary
authority is to satiate consumers with cash balances and, on average, contract the money supply at
a rate equal to the subjective rate of time preference. Moreover, the monetary authority increases
household's expected lifetime welfare in by responding to positive (negative) shocks to marginal
productivity by decreasing (increasing) the cash contraction. These policy rules keep the interest
rate at its Pareto optimal level--unity.

For policy advice, the monetary authority is not restricted by using only one currency. In
this model, the monetary authority reacts to the average marginal productivity shock. Then the
firms bid for the loanable funds. The more productive firm will receive the lion’s share of the
funds and thus the efficient allocation can be achieved. However, for this analysis to go through it
must be the case that the monetary authority can respond quickly to shocks households can not

respond to.

Figure 1.6: Welfare Loss When the Average Growth Rate of the Money Supply
is 10 Percent and the Shocks are iid

 

0.036 f I I

0.034

0.032

wcl(n.x) 0.03
-9-

0.028

0.026

 

 

 

 

0.024

x is the growth rate of the money supply when the bad State occurs

45

Figure 1.7: Welfare Loss When the Average Growth Rate of the Money Supply
is 20 Percent and the Shocks are iid

 

O.l05 l T— W
0.1 '—

0095 l—

0.09 '—

we2(n,x)
-0—

0.085 '-

 

008 — L

0075 '- —'

 

 

 

x is the growth rate of the money supply when the bad state occurs

Figure 1.8:

0.035

0.03

Wel(n,x)
-9—

0.025

46

Welfare Loss When the Average Growth Rate of the Money Supply
is 10 Percent and the Shocks are Correlated

 

 

 

 

0 0.05 0.1 0.15 0.2

x is the growth rate of the money supply when the bad state occurs

47

Figure 1.9: Welfare Loss When the Average Growth Rate of the Money Supply
is 20 Percent and the Shocks are Correlated

 

 

 

 

0107 l I j l I I
Wcl(n,x)0,079 ”‘ _
—a—

0105] l l l L l l l

0 0.05 0.! 0.l5 0.2 0.25 0 3 0 35 0.4

X

x is the growth rate of the money supply when the bad state occurs

the

2m

ter 2: tim Monetar Polic in a Two Coun Two C rrenc Model with Fixed and

Floxible Exohonge Rotes

In developed economies, where goods and assets are traded across borders, events that
happen in one country generally affect the production possibilities and the welfare of agents in
other countries. Therefore, the post World War II adage can be generalized to “when a
developed economy sneezes the world is susceptible to a cold.” Acknowledging the increased
economic interdependence, some groups of countries have been considering the benefits of
coordinating monetary and/or fiscal policies.

There are two primary decisions that need to be made in developing coordinated
policies. The first is establishing optimal institutional arrangements. The second involves
Specifying the policy rules that the policy maker in each country will use to respond to shocks
that affect the countries.

This chapter considers the optimal monetary policy arrangement among interdependent
economies. The model employed is a two country, two currency sluggish cash flow model
with fixed and flexible exchange ratesl. Money is valued in this economy because households
must use cash to purchase consumption goods and firms must use cash to pay their workers. I
assume countries coordinate policies in order yield the highest level of welfare for all agents. I
take this approach because there are several groups of countries that are attempting to
coordinate their policies. Also, this model establishes a benchmark for models of non-

cooperative behavior.

 

' The sluggish cash flow models have been popularized by Lucas(1990), Fuerst (1992,1994) and Christiano and
Eichenbaum (1995).

48

Iii}

tic

tht

Ill‘i

[he

CXL‘

at.
S

11

49

The questions this chapter provides answers to are: In an open economy setting, what
are the effects of monetary innovations? What is the role of the monetary authorities? Finally,
what is the best institutional arrangement for currency exchange--a flexible exchange rate
regime or a fixed exchange rate regime?

To anticipate the results, brief answers to the questions posed above are: monetary
innovations do have real effects. The role of the monetary authority is to smooth interest rates.
Lastly, if the monetary authority is unconstrained in both the fixed and flexible exchange rate
regimes, the monetary authority can attain the Pareto optimal allocations. However, if the
money growth rate is constrained to be positive on average, then the fixed exchange rate
regime is best.

The rest of the paper proceeds as follows. Section I sets up the model used
throughout. Section II proves the existence of a competitive equilibrium with fixed and
flexible exchange rates and discusses the qualitative features of the model. Section [E derives
the optimal monetary policies for the fixed and flexible exchange rate regimes. Section IV
investigates which policy is best, a constant money growth rate rule or an interest rate target, if
the monetary authority is constrained to keep the average money growth rate positive. Also in
Section IV comparisons are made between the fixed exchange rate regime and the flexible

exchange rate regime. Section V concludes.

Section 1; The Model

There are two infinitely-lived countries populated with many infinitely-lived identical.

agents. There are three types of agents in this model: households, firms, and financial

50

intermediaries. There also exists governments that collect taxes from (pay transfers to) the
households in the economy, and monetary authorities that inject (withdraw) cash into (from)
the financial intermediaries. Since there are numerous agents all of which behave
competitively, I will restrict my attention to a representative agent of each type in each

country.

Section 1.1 The Representative Household

The representative household in each country consists of three members: a worker, a
shopper, and a saver. Each member performs distinctive tasks. The shopper purchases the
two consumption goods produced in this economy. Consumption good one is produced solely
in country one and consumption good two is produced only in country two. The saver's role is
to deposit the funds allocated to savings into the financial intermediaries. The worker in
country i allocates time to the production of good i (i =1,2). Households have preferences
defined over consumption and leisure. The representative household’s lifetime utility function
is given by

u=Eozils‘(U<c't,c2t) +V(T-Lt»},
where CE, is consumption of good j by a household in country i at time t (i,j=1,2), T is the
household's time endowment2 and Lit is work effort by the worker in country i at time t, B is
the discount factor (Be(0,1)). It is assumed that U(.,.) is continuous, increasing and concave in
both arguments, and V(.) is assumed to be continuous, increasing and concave. When the
competitive equilibrium is shown to exist and when deriving the optimal monetary policies, the

following utility function is employed:

 

2 It is assumed that T >2 so that the Pareto optimal level of employment is feasible.

E?

(‘1
It?
L‘UI

Silt)

l‘t‘l‘.

Writ
demy-
Curler

Shim”:

51

U=Eozil3t(log(clit)+108102n)+(T‘Lit))}.
where the expectations are over the realization of world wide shocks. This specification is
used for two reasons. The first is that this utility function, along with the production function,
allows for analytic solutions. The second is, given the closed form solutions, the general
equilibrium effects of different shocks are easily understood and the optimal monetary policy
rule that attains the highest welfare has a clear economic interpretation. The shocks in the
model are all iid in nature and are discussed in greater detail below.

Since the timing of the decisions is important in this model, I will be very careful
about describing the behavior of the agents and timing of their decisions. (The timing of the
decisions and the realization of the shocks are listed chronologically on page 53.) The
representative household in country i (i=1,2) begins each period holding only country i's
currency and none of country j's (jati). At the start of each period, before the technology
shocks and the money shocks are known, the household divides its currency holdings (Mn)
between funds allocated to savings (Ni!) and funds allocated to consumption purchases (Mi,-
Nit). Once made, this savings/consumption decision can not be altered.

After the savings decision is made the household separates. The worker offers her
services in the labor market (Lit) (i =1,2). The shopper uses the funds allocated for
consumption purchases to buy consumption goods one and two. It is assumed that in order for
the shopper to purchase the consumption good produced in country i, he must be using the
currency of country i (i=1,2).’ This framework, due to Lucas (1982), creates a transactions
demand for foreign currency. Thus, a shopper in country one (two) takes D1, (D2,) units of
currency to the foreign exchange market and buys foreign exchange at a price Z,‘1 (L). The .

shopper for the representative household in country one (two) uses these funds to purchase

52

consumption good two (one). The remaining funds allocated to consumption can be used to
purchase consumption good one (two). The cash-in—advance constraints for the household in
country one, therefore, are given by

M',—N,,—D,,2P‘,c',, and chaplain,
where Pi is the price of the consumption good. Similarly for a household in country two, the
cash-in-advance constraints are given by:

1912,—N2,.l)2,21>2,c22t and D,,2(1/Z,)P‘,e'2,.
The saver in country one (two) takes the N1l (N21) dollars allocated to savings and goes to the
foreign exchange market. There he uses Q21t (012,) units of currency to buy foreign exchange
at a price Z"1 (L). The L '1Q21,(Z‘ let) units of foreign exchange are deposited in the
representative financial intermediary in the foreign country. The remaining funds are then
available to be deposited in the representative financial intermediary in the domestic country.
This set up implies the cash constraint facing the saver in country one (two) is given by

N112 02¢an (Nltz 02a+0'a).
The gross nominal return for a dollar deposited in the financial intermediary in country one
(two) is given by 1+R‘, (1 +18.)

Note that in this model there are two reasons for a household to obtain foreign
exchange: to purchase consumption goods--a transactions demand--and to deposit funds into the
foreign country's financial intermediaryua financial demand. At the end of the period, the
deposits by a household in country one (two) placed in the representative financial

intermediary in country two (one) plus interest earned on the deposits are exchanged back into

country one's (two's) currency at the end of period exchange rate given by 2, (1/ 2, ). Also,

any excess currency from the household one's (two’s) cash-in-advance constraint for foreign

53

1. Households decide how much to allocate to goods consumption and to savings.

STATE OF THE WORLD IS REVEALED

2. The saver allocates savings to the financial intermediaries in both countries. The Shopper

allocates its funds to consumption goods one and two.

3. Firms borrow funds, hire labor and produce the consumption goods.

4. The shopper purchases the consumption goods.

5. Firms repay their loans.

6. Households reunite and pool their resources. These resources include the return on

savings, the residuals from the cash-in—advance constraints on consumption goods, wage

income, profits from the domestic firms and intermediaries, and the tax/transfer payment.

54

produced goods is exchanged back into country one's (two's) currency at the end of period
exchange rate 2, (1/2,).

One of the salient features of this model is that even though the amount allocated to
savings can not be altered, the portion of the household's savings placed in the financial
intermediaries in countries one and two is at the discretion of the household and the placement
decision is made with full contemporaneous information. I assume there is some degree of
separability between the financial market and the goods market. That is, for a given level of
risk, one can imagine that households will allocate their savings to the accounts that offer the
highest return. Therefore, in this model I allow households to trade assets as new information
concerning the returns on these assets becomes available. However, it is doubtful that
households are willing to liquidate assets and transfer resources from the financial sector to the
goods sector whenever laundry detergent goes on sale. Therefore, it is assumed that
households cannot alter their portfolio decision that was made at the outset. In this model, the
households allocate funds to the account that offers the highest return given the riskiness of the
asset. Since the deposits are made after the state of the world is revealed, there is no risk and
the households seek the highest return possible.

Thus far, there has been no need to delineate between the fixed exchange rate model
and the flexible exchange rate model. The differences between models arise in how the
exchange rate is determined. In the fixed exchange rate model the exchange rate is set at the
beginning of the each period before the state of the world is revealed. Once determined, the

monetary authorities are committed to exchange currency at the beginning of the period and at

the end of the period at this predetermined rate. This implies that Zt = 2, . Since the

55
households begin each period with the same level of wealth and the shocks are iid across both

countries, the logical choice for the fixed exchange rate is 2,: 2, =Ml,/ M2,. In the flexible

exchange rate model, the exchange rate is the price that equates the demand and supply for
foreign currency. In this model, the foreign exchange market opens at the beginning and at the
end of the period and the households' demands and supplies of foreign currency at this time
determines the exchange rate.

The representative household in country i owns the goods producing firm and the
financial intermediary in the country i (i=1,2). Also, the representative household pays
(receives) a tax (transfer) from the government. This tax/transfer scheme is a form of a social
insurance that insures the households against the idiosyncratic shocks. The tax/transfer scheme
keeps wealth constant over time. In a no growth economy with iid shocks, this type of policy
would be preferred by households since expected utility would be higher for constant wealth
than for variable wealth. In addition the expected value of the tax/transfer is zero.

At the end of the period the representative household pools its resources, consumes it
consumption goods, and enjoys its leisure. The pooled resources become the basis for next
period's wealth. For the representative household in country one the pooled resources are
given by

Mlt+1 =(M't-P‘.c‘1t-zt P1281.) +(Q'1. R't-QZ..+Q"'..<2. 12,)(1 +R21>>+

(W‘,L,,+n",+n“,+t‘,M‘.).
The first set of terms is the unspent cash from goods market transactions. The second set of
terms is the return from deposits in the financial intermediaries. The final set of terms is the

profits from the firm and the financial intermediary plus (minus) transfers (taxes).

56

Similarly, for the representative household in country two next period's wealth is given
by

M2... 1 =(M21- pica—(112 ,)1>, ‘c'al + (022.18.012.12. I2.)+Q'a<1 +11.»

+(w2,1.2,+n‘2,+r1’2,+t2,M2,).
Recall in the fixed exchange rate regime A: Z, =Mlt/ M2,, whereas in the flexible exchange
rate regime the end of the period exchange rate is not guaranteed to be equal to the beginning
of the period exchange rate.

I am only concerned with stationary rational expectational equilibria. Therefore all
growing variables must be detrended. The only growing variables in this model are the money
stocks of each country. Lower case letters denote the detrended variables. The only exception
is that the detrended beginning of the period exchange rate is denoted by e(s) and the end of
the period exchange rate is denoted e(s) . The detrended transition equation for the household
in country one is given by
m" =(m'e<s> p2(s>c21(s> -p'<s)c‘1<s> +q'1<s>R‘<s>- q21(s)+q21(s)(l +R2>1 e(s) /e(s))

+ w'(s)L,(s)+n“+r1“+t‘)/(1+x'(s)), 2.1
where primes denote next period's values. The transition equation for the representative
household in country two is given by
m” =(m2-(1/e(S))p‘(s)cla(s)-pz(8)cza(8)) +q221s>R2<s)- q'a(s)+q‘2<s)(1+R‘) e(s)/ e(s)

+w2(s)1.,(s)+n”+n‘2+t2)/(l +x2(s)). 2.2

Given the continuity and concavity of the utility function and the compactness of the

constraint set, the household's problem can be cast in terms of a dynamic program. The

programming problem for the household in country one is given by

57

Itm‘)=max..a,mimax..t,,{U(c‘1(s).c21<s»+V(T-L.(s»+1sltm")}<l><ds)
where the maximization is subject to

m‘-n‘<h<s>2p‘(s>c‘l(s),

d1(s)2e(s)p’<s>c21(s>.

n‘zq‘11s)+q21(s>.
The transition equation for ml' is given by eq 2.1. The first order conditions of the

representative household in country one are given as follows

12‘,(s)<r>(ds) =lx3,(s)cb(ds) 2.3.a
k21(s)=l'1(s) 2.3.h
U1(c'1(s).c21(s»=p'<s){BJ'(m">/<1 +x‘(s»+>~'.(s>} 2.3.c
11216161816»=e<s>p21s>iir<m19<1 +x‘1s» +1216» 2.3.d
V'(T-L1(S))=BJ'(ml')Wl(S)/(1+xl(S)) 2.3.e
11{J'(m")/(l +x‘(s))}lz‘(s)=13l 2.3.f
1311'(m")/(1+x‘(s»}l(1+R2>( e(s) /e(s))-1] =x’11s) 2.3.g
m‘-n‘a,(s)2p‘(s)e'1(s) with equality if 111(s) > 0 2.3.h
d1(s)2 e(s)p2(s)c21(s) with equality if 12,(s) > 0 2.3.1
n'zq‘,(s) + q21(s) with equality if 71.31(s) > 0 2.3. j

where 7111(S), A21(s), and 7131(s) are the multipliers for the cash-in-advance constraint for good

one, the cash-in-advance constraint for good two, and the cash-in-advance constraint on the

savings allocation decisions respectively. The envelope condition is given by:
l'lm")=IiU<c'11s).c21(s))/p‘(s>}<l>(ds). 2.3.1.

Similarly, the representative household in country two's maximization problem is given

58

J(m2) =maxato,mlmax..t.q1U(c22<s>.c22<s» +V(T'L2(S))} + bltm")}¢<ds>
where the maximization is subject to

mz-n242(s>2p2(s)cza(s).

d2(S)2 e(s>"p‘<s>c‘s<s).

112-2922(5) + (112(5)-
The transition equation for m2' is given by eq. 2.2. The first order conditions of the

representative household in country two are given as follows

1A12(s)<l>(ds) =lx32(s)<r>(ds) 2.4.a
4‘26) =422(s) 2.4.b
111162618219) =e(s)"p'(s)ilsl'(m2'>/(1 +x21s» +1216» 2.4.c
11216261626» =p’<s>{1u'(m2')/(1 +x21s» +1226» 244
V'(T-Ia)=BJ'(m2')w2(S)/(l+x2(S)) 2.4.e
[3{J'(m2’)/(1+x2(s))}(l +R2(s)e(s)/ e(s) - 1) =132 2.4.1‘
BiJ'(m2')/(1+x2(8))}[(1+R’)l=7»32(S) 2.4.g
mz-nz- d2(s)2p2(s)c22(s) with equality if 7122(3) > 0 2.4.h
d2(s)2 e(s)“p‘(s)e‘2(s) with equality if 1‘2(s) > 0 2.4.1
n22q22(s)+q12(s) with equality if 132(s) > 0 2.4. j

where 712(5), 122(s), and 732(3) are the multipliers for the cash-in-advance constraint for good

one, the cash-in-advance constraint for good two, and the cash-in-advance constraint on savings

allocation decisions respectively. The envelope condition is given by
J'(m2')=l{U(c‘2(s),e22(s))/p2(s)}<1>(ds). 2.4.k

These equations represent the optimality conditions of the representative households.

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59

Section 1.2 The Representative Firms and the Representative Financial Intermediaries

The Firms

The representative firm operating in country one receives p1(s) for each unit of output
sold. The representative firm has the production technology given by 0(S)H1(s)°‘(s) where H1(S)
is the amount of labor employed by the firm at time t, 0(s)e® where G) is a continuous mapping
from the abstract state space into the real line. Similarly, (x(s)8A where A is a continuous
mapping from the abstract state space into (1/2,1). The wage rate is given by wl(s). Since the
representative firm starts the period without any money balances, it must finance its wage bill
by borrowing funds from the domestic financial intermediary. Its borrowings are restricted by
the amount of loanable funds held at the domestic financial intermediary3. Total deposits at the
intermediary are given by: q11(s)+e(s)q12(s)+xl(s). The first two terms are deposits by the
households in country one and two respectively. The third term is the monetary injection that
occurs through the financial intermediary. Since the representative firm must borrow to hire
labor, the wage bill and hence employment at the firm is restricted by
q'1(s>+e(s)q‘a(s>+x'(s>zw‘(s>H1(s).
Therefore, the firm's problem is given by

11“=maxH{p‘(s)0(s)H,(s)°““’-w‘(s)H,(s)(1 +R‘) subject to

q'.(s)+e<s>q‘a(s) +x‘(s)2w’(s>Hi(s).

The representative firm in country two operates in a similar fashion. The production

technology for the representative firm is given by: §(S)H(s)2'(”) where §(s)e®, and y(s)eA. The

 

3 Financial intermediaries could be allowed to exchange deposits. Allowing for this would not change the results.

60

representative firm operating in country two obtains funds from the representative financial
intermediary in country two. The firm's problem in country two is given by:
n”=maxH{p2(s)0(s)H2(s)*‘S’-w2(s)li2(s)(1 +R2)} subject to

922(S)+(1/e(8))qzl(5)+X2(S)2W2(S)H2(S)-

The Fingcioi Intermediaries

The representative financial intermediary in country one receives deposits from the
households in country one and country two and promises to pay them a gross nominal return of
(1 +Rl) for each unit of currency deposited. Also, as aforementioned, the representative
financial intermediary in country one is the sole recipient of country one's monetary injection.
As long as the interest rate is non-negative, the intermediary will loan out all its funds to the
firm. Profits for the financial intermediary in country one are given by

n“ =(q'11s) +e<s>c1'2(s) +x'(s»<1 +R')-(q‘1(s)+e<s>q'2(s»(1+R‘>.

The first term is the return from lending all the funds in the intermediary to the firms and the
second term is the repayment of the principal plus interest to the representative households.
Clearly, this can be simplified so that profits are given by

n"=x'(s)(1+R‘).

Similar reasoning implies profits for the representative financial intermediary in country two is
given by:

11I2 =x2(s)(l +112).

61

Section 1.3 The Monem and Fiscal Authorities

Each period country one’s (two’s) monetary authority injects cash into the
representative financial intermediary in country one (two) of the amount x1(s) (x2(s)). In
addition to the injections that occur through the financial intermediary, in the fixed exchange
rate model, the monetary authorities also accommodate each household's demand for foreign
exchange at the beginning and at the end of the period. In the flexible exchange rate model,
however, the monetary authorities do not intervene in the foreign exchange market. In the
section where the competitive equilibrium is derived and the qualitative features of the model
are discussed, the monetary injections are assumed to be iid and xi(s)eX where X is a
continuous mapping from the abstract state space into the positive reals. In the section of the
paper where the optimal monetary policies are derived, the monetary injections are a function
of the state of the world at time t. That is, the monetary authorities increase (decrease) the
money supplies after the households have made their savings decision and after the technology
shocks are realized. This assumption is intended to capture the ease with which the monetary
authorities can react to shocks in the economy.

The fiscal authorities in this economy collect taxes from (give transfers to) the
households. The tax transfer scheme keeps the households' wealth constant for all time
periods. Without this transfer scheme the households' wealth would vary over time.
Households prefer this policy since the variability in wealth absent this scheme would yield
lower expected lifetime utility. The governments in this economy maintain a “balanced”

budget each period; that is, taxes collected from households in one country are equal to the

62

transfers paid out to the households in the other country. Thus, the tax collections by country
i’s government are handed over to country j’s government and distributed as transfers to the
households. As aforementioned, this tax transfer scheme provides a form of social insurance
that insures the households against the idiosyncratic shocks. Thus the governments provide a

. . . 4
servrce--a form Of income maintenance.

Section II. Egoilibrium

Now that all the actors in the economy have been described the next step is to prove
the existence of a competitive equilibrium and describe the qualitative aspects of the models.
In this section, I will search for a competitive equilibrium where all constraints bind. The
qualitative features of the fixed and flexible exchange rate economies are then analyzed. I

begin by defining the competitive equilibrium for these models.

Definition: A oompetitive eguilibriom is a sequence of prices and allocations and constants, ni,
and J '(mi), such that, given these prices, allocations, and constants

(i) the households' problems are solved,

(ii) the firms' problems are solved,

(iii) the financial intermediaries' problems are solved,

(iv) arbitrage conditions on deposits are satisfied; that is,

(1+R1)=(1+R2) for the fixed exchange rate model

(1 +R‘)(e(s)/ e(s) ) =(1 +18) for the flexible exchange rate model,

 

4 Examples of governments giving lump sum transfers is not uncommon. This transfer scheme is similar to
coinsurance proposed by Ingram (1959) and others. In addition, the European Union has in several of its plans to
coordinate policies have discussed Similar coordinated fiscal policies as well.

63

(v) the joint government budget constraint balances, and
(vi) all markets clear.
There are six markets in the fixed exchange rate economy. The market clearing
conditions are given by:
012(S)+cll(s) =9(S)L1(S)°'"’,
921(8)+cza(S)=C(S)la(S)"”.

L1(8) =Hi(S) i=1,2

The flexible exchange rate model imposes two additional market clearing conditions that arise
because the foreign exchange market opens at the beginning of the period and again at the end
of the period. The market clearing conditions for foreign exchange are given by:
ld11s>+q211s>l=lda(s>+q'2(s)le(s>. and
[d2(S)-P1(S)Clz(8)+qlz(S)(1+Rl)l=[d1(S)-P2(S)021(S)+qzt(8)(1+R2)l e(s) .
Under the assumption of initial equal wealth distribution, iid shocks and the tax/transfer
scheme the equilibrium will be a symmetric equilibrium. Existence of a unique competitive
equilibrium for the fixed and flexible exchange rate regimes are proved separately in the

following two subsections.

[1.] Competitive Equilibrium in the Fixed Exchange Rate Regime

Proposition 2.1: Assume the exchange rate is fixed. In the class of equilibria where all the

constraints bind, there exists a unique competitive equilibrium.

64

mpg; See Appendix 2.1.
Given the symmetry of the model, it is shown in the appendix that the optimal savings
decisions for the households in both countries are identical. Given this result the allocations
are as follows
Consumption allocations: c1j(s)=[0(S)L1(s)“(s)]/2 c2j(s)=[C(s)IQ(s)Y(s)]/2 j= 1,2
Labor supply: L1(S)=B(a(S)/(a(8)+Y(S)))2(2n+xl+x2)/((1-n)(1+X‘)),
14(8) =B<y<s>l<a<s> +1<s>»2<2n +x‘ +x2)/((1-n)(1 +18»,
prices: p'<s>=(1-n>/9(s>Ll(s>“‘”,
pits)=(1-n>/c(s)14(sy“’.
w‘(s) =(1 +x‘(s))(l-n)/213, 1: 1,2
(1 +R‘)=(1 +112) =Hats)+t(s»<1-n)l/<2n+x'(s> +x’(s».
deposits: q‘1(s>=q‘a<s>=12a1s>n+a<s>x‘(s>-y<s)x’<s>l/12(a<s>+vts)>l
q’ds)=q221s)=1211s>n+y<s>x’<s)«x(s>x‘(s>l/12(a<s>+v(s»l
taxes: 1‘6) = 1 +x‘(s>—<a<s>/<a(s) +1<s>>><2n+x'<s) +x’(s»-
(n+x‘(s»(<a(s>+1<s>><1~n>l<2n+x‘(s)+x21s>>-(1~a<s»(1-n)
12(S)=1 +x21s>-<y(s)/<a(s) +1<s>>><2n+x‘(s) +x2<s»-

(n+x’(s»((a(s>+t(s))(1-n>/<2n+x'(s)+x’~’(s»-<1-1(s>)(1-n>.

Note first that the interest rate is primarily determined by three factors: how productive
the firms are (as measured by the marginal productivity shocks 01(5) and 7(5)), the amount of
currency circulating in the goods market, (l-n), and the amount of loanable funds in country
one and country two (2n+x1(s)+x2(s)). The intuition behind this result is simple: the interest

rate is determined by the supply and the demand for loanable funds.

65

In the fixed exchange rate model, monetary injections in one country that are different
than what households' anticipate will have spillover effects in the other country. This result is

stated more formally in the following proposition.

Proposition 2.2. Monetary injections that are larger (less) than anticipated will cause interest

rates in both countries to fall (rise), and cause output and employment in both countries to rise

(fall).

Proof: The interest rate results follows from differentiating the interest rate with respect to xi(s)
(i=1,2). Similarly differentiating the equilibrium labor supply with respect to xi(s) (i = 1 ,2)

gives the result that monetary innovations increase work effort.

Monetary injections that are larger than anticipated will lower the interest rates in both
countries because they increase the supply of loanable funds. For instance, consider an
unanticipated increase in country one’s money supply. The increase in loanable funds shifts
the supply of funds rightward, lowering the interest rates in country one. The interest rate in
country two is initially higher than the interest rate in country one. However, since country
two’s interest rate is higher depositors will want to deposit more funds into the representative
financial intermediary in country two. Deposits increase (decrease) in country two’s (one’s)
financial intermediary until the rates of return are equated across countries. As a result, the
increase in loanable funds decreases the interest rates in both countries. In response to the

lower interest rates, firms will be able to hire more labor and output will increase.

66

Note also that larger than anticipated marginal productivity shocks will increase the
interest rates. If the marginal productivity shocks are above (below) their mean values, firms
will demand more (fewer) loanable funds and thus exert upward (downward) pressure on
interest rates. Consider a marginal productivity shock in country one that is larger than
anticipated. This shock increases the representative firm’s demand for loanable funds. This
effect increases the interest rates in country one. Since interest rates are higher in country one,
depositors will allocate more funds to country one’s financial intermediary and fewer funds to
country two’s financial intermediary. Therefore, the supply of loanable funds will increase in
country one’s representative financial intermediary and fall in country two’s representative
financial intermediary. The net effect is interest rates are higher than normal in both countries

with country one receiving a higher percentage of the available loanable funds.

[1.2 Compotigive Equilibrium in the Flexible Exchange Rate Regime

Proposition 2.3: Assume the exchange rate is flexible in the class of equilibria where all the

constraints bind, there exists a unique competitive equilibrium.

Proof: See Appendix 2.2.

 

It is shown in the appendix that the optimal savings decision for the households in both
countries is identical. This implies the allocations and prices are given by:
Consumption: c‘j(s)=[e(s)L,(s)°“”]/2 c2j(s)=16(s)1.,(s)*‘"]/2 j=1,2

Labor supply: L1(S)=ZB[n+xl(S)l/I(1+xl(S))(1-n)l,

67

[e(S)=215[n+x2(S)l/I(l +x2(S))(1-n)l,
Prices: p‘(s>=(1-n)/le(s)Li(s)““’l.

p’ts)=(1-n>/lc(s>La<sy“’l,

(1 +R')=a<s><1-n>/<n+x‘(s»,

(1 +112) =1<s>(1-n>/(n+x’(s».

e(s)=1, and

e(s) =[7(S)(n+X‘(S))l/la(8)(n+x2(S))l.

Taxes: 1 =0

The qualitative features of this model are given in the following proposition.
Proposiiion 2.4: Monetary injections of country one's (two's) currency that are greater than
anticipated lower the interest rate in country one (two) and increase output in country one

(two), there is no impact on interest rates and output in country two (one).

Proof: Follows immediately from differentiating the equilibrium conditions.

 

Note the nominal interest rate in country one (two) depends only on the discount factor
and the money growth rate in country one (two). That is, the interest rate in country i is
independent of the money growth rate in country j (i at j). This is similar to the result in
Helpman and Razin (1981). There too the monetary growth rates in country j only affect the

interest rate in country j. In their model, unanticipated monetary Shocks have real effects

68

because it changes the value of real debt. In this paper unanticipated monetary shocks have
real effects due to the portfolio rigidity.

Therefore, because the interest rate in one country is unaffected by the money growth
rate in the other country in the flexible exchange rate model, monetary innovations in one
country do not have any real effects in the other country.The intuition behind this result is as
follows: Consider again an unanticipated monetary injection by the monetary authority in
country one, given the households' preferences, the representative household in country one
will take the same amount of funds to the foreign exchange market as the representative
household in country two. This implies the beginning of the period exchange rate will be
unity. Then for a larger than anticipated monetary injection in country one, interest rates will
fall. This alone would cause agents to deposit fewer funds in country one‘s financial
intermediaries and more into country two's financial intermediaries. However, in this model
the end of the period exchange rate adjusts to equate the return per dollar of savings across
countries. Therefore, there is no incentive to alter the household’s a priori deposit decision.
Because of this, the supply of loanable funds will not increase in country two and employment
in country two can not expand. Only country one absorbs the monetary innovation.

In the flexible exchange rate model monetary innovations only have real effects in the
country where the innovation originated, whereas in the fixed exchange rate economy monetary
innovations in one country have real effects in both countries. Intuitively, it would seem that
the optimal monetary policy would involve coordination of the monetary authorities’ activities
in the fixed exchange rate economy while in the flexible exchange rate economy no

coordination is necessary. The next two sections verify this.

69

Section III. thimal Monetary Policy

In this section of the chapter, I search for the optimal monetary policy under the fixed
and flexible exchange rate regimes. The optimal monetary policy for each regime is derived in
two steps. First the social planner's problem is solved. Second it is shown that the social
planner's problem can be supported by a competitive equilibrium. It is shown that in order to
attain the Pareto optimal allocations, the monetary authority must react to the realization of the
technology shocks and “undo” the rigidities that prevent the Pareto optimal allocations from
being attained. There are two rigidities that the monetary authority needs to eliminate. The
first is due to the cash-in-advance constraints, the second rigidity is due to the portfolio
decision.

In both exchange rate regimes, the optimal monetary policy derived below is an
interest rate peg. That is, the monetary authority reacts to shocks to keep the gross nominal
interest rate at a fixed level-—unity. Also, it is verified below that the optimal monetary policy
in the fixed exchange rate regime does in fact require a coordinated policy. This is not the case
for the model with flexible exchange rates. With flexible exchange rates, the optimal monetary
policy requires that the monetary authority in country i should respond only to shocks in
country i (i = 1 ,2).

The first step in deriving the optimal monetary policy is to solve the social planner’s
problem. The social planner's problem is the same in both regimes. The planner's problem is
to maximize the utility of each country's representative household given the resource

constraints. The only constraints facing the social planner is that consumption allocations are

70

feasible and that the time allotted to work effort is feasible. The solution to the problem
includes the following efficiency conditions:
V'(T-L1(s))/U1(cli(s),czi(s))=01(s)0(s)L1(s)°‘(sH i=l,2 2.5.a
V'(Fitch/Uncle).816»=11s>¢<s>1a<sy‘”" i=1.2 2.5.b

The optimal monetary policy must be consistent with efficiency conditions 2.5.a,b.

11.1 An Optimal Monetary Policy for the Fixed Exchange Rate Regime

Comparing equation 2.5.a to the household's optimal decision rules, it is easy to verify
that by combining equations 2.3.c, 2.3.c, 2.4.c, and 2.4.e and the first order conditions of the
firm in country one that the combination of these equations is identical to the social planner's
problem if and only if 211(s)=0 (112(s)=0) and the gross nominal interest rate is equal to unity.

Similarly, equation 2.5.b is identical to the decentralized competitive outcome if 121(5) =0
(122(s)=0) and the nominal interest rate in country two is equal to unity. The Aij(s)'s equaling
zero imply that the cash-in-advance constraints are non-binding or are " just " binding for all
states of the world; that is, households are satiated with cash balances. At this interest rate,
the representative financial intermediary would still be willing to loan out all of their funds.

Before an optimal policy is derived, there are two technical details that must be
addressed. First the restriction on the marginal productivity shocks ensures that the Pareto
optimal work effort is feasible. Recall that 01(5) and y(s) are restricted to be in the range

(1/2,1). Given the logarithmic specification of the utility function and the social planner's

71

efficiency conditions 2.5.a,b, the Pareto optimal work effort for country one (two) is given by
201(5) (27(5)). Therefore, the Pareto optimal work effort will always be feasible.

The second issue that needs to be addressed is the existence of multiple equilibria.
This is easy to discern since the agents are satiated with cash balances in equilibrium. If M
units of cash balances satiate the household then for any a > 0 M +8 units of cash balances also
satiates the representative household. Also, because the nominal interest rate is unity the
borrowing constraint does not bind or just binds. It is not possible to assume the cash-in-
advance constraints and the borrowing constraints "just" bind since this would lead to an
overidentified system. Thus the following solution strategy is pursued: I assume that the cash-
in-advance constraints are non binding and the borrowing constraint "just" binds. Given this
solution strategy the competitive equilibria are derived below. I show that the monetary
authorities will inject (withdraw) funds into (from) the financial intermediary if the marginal

productivity shocks are larger (less) than anticipated. This leads to the following proposition.

Proposigion 2.5; In the fixed exchange rate economy, there exists a competitive equilibrium in

which the monetary authorities can attain the Pareto optimal allocations.

P_ro_of; The proof is by construction. First recall from the social planner's problem that the
optimal labor supply for the household in country one (two) is 201(5) (2y(s)). The rest of the
proof proceeds as follows. The prices and allocations of the consumption goods are derived for
both representative households. Then it is shown that the households expect the money supply
to be contracted at a rate equal to the inverse of household's discount rate. The optimal

portfolio decisions are then obtained; that is, the optimal qij(s)'s (i,j=1,2) are solved for. Then

72

the deposits for the representative households can be obtained. Finally, the monetary policy
rule is derived that ensures these Pareto optimal allocations are achieved.

Recall that if the Pareto optimal allocations are to be achieved, a necessary condition is
that the cash—in-advance constraints do not bind. Rearranging 2.3.c and 2.4.e and using the
market clearing condition for good one, the price for good one is (for now) given by

P1(S)=[J'2(1)(1 +X1(S))+J'1(1)(1 +X2(S))1/e(8)l[l31' 1(1)J'2(1)9(S)L1(S)°‘(s)l'l-
Similarly, by combining equations 2.3.d, 2.4.d, and the market clearing conditions for good
two, the price for good two is given by

92(S)=[J'2(1)(1+xl(S))+J'1(1)(l+X2(S))1/e(8)l[1/e(8)151'1(1)J'2(1)C(S)la'“’l'l.
These prices imply that consumption allocations are given by

c'1(s>=A(s>e(s)L1(s>“‘”.

eats)=(1-A(s))e(s)Li(s)““’.

c’ns)=A<s)c(s)Ia(sy‘”.

c2210 =(1-A<s)>c(s)la(s>*“’,
where A(s)=[J',(l)(1 +x2(s))][J'2(1)(1+xl(s))+J'1(1)(1+x2(s))1/e(s)]'1.
These consumption allocations and prices can be substituted into the envelope condition to
yield

1=l(0/(1+x'(s)))<l>(ds) i=1,2. 2.6.a,b
These conditions can be interpreted as stochastic versions of the optimal monetary policy rule
given by Friedman (1969)5.

Next, to find the optimal qij(s)'s, recall that the representative firms in country one and

country two first order conditions for profit maximization are given by

 

5 Roughly defined, these equations say that the expected value of the money supply growth should equal the inverse
of the household's discount factor.

tit

50!

Ne:
{Us
USei

&d\ g

The

Rm

Mic

73

ats)p'<s>e(s)Li<s>“‘”=w‘(s>L1(s> and x(s)p2(s)q<s>la(s)*“’=w21s>Lz<s>
respectively. Substitute the "just" binding borrowing constraint, the price of goods prices, the
fixed exchange rate e(5)= l, and the fact that n=qu(s)+q2j(s) (j = 1,2), into the first order
conditions. Then
q',(s>=12a(s)n +u(s)X'(S)-y(8)x2(5)l[201(8) +1<s>>1". i=1.2
q’,-(s)=12v(s)n-a<s>x‘(s) +Y(S)x2(S)l[2(0t(S) +1<s>>l". i=1.2.
The nominal wage rate is given by
w‘(s)=(1 +x‘(s))/[1il',-(1)], j=1,2.
Next J’(1) is solved for. To do so I use the wages, the qij(s)'s, the equilibrium labor supply
decision and substitute these into the just binding borrowing constraints to yield
2q‘,(s)+x‘(s)=2ot(s)(1 +x‘(s))/1il',(l), and
2.122(3) +x2(S) =27(S)(1 +x2(S))/BJ'2(1)-
Solving for B/(1+xi(s)) in the above equations and substituting into 2.6.a,b yields
13(1)=1120<s>+a<s>>l<2n+x‘<s>+x2(s»1a>(ds).
Next to solve for the optimal ni's. Recall 1/2 is the lower bound on the distribution of the
01(s)'s and y(s)'5. Next define x to be the smallest monetary growth rate. These values are
used to pin down the deposit decision. Substitute for fiJ’(m)/(1+x1(s)) (i=1,2) in the cash-in-
advance constraint assuming the constraint just binds for the extreme values of the shocks.
The ni's are then given by
n‘=(1-x)/(l +x).
Rearranging the borrowing constraint and solving for the xi(s)'s yields the optimal monetary
policy rule given by

X1(S)=X2(S)=[BJ'(1)n-Y(S)-a(8)l/IY(S)+a(S)-fiJ'(1)l. 2.7

74

Since the x'(s)'s and the J'(1)'s are the same prices and consumption allocations can be
simplified to
c',-(s)=e(s>L1(s>°‘“’ I2 c2,<s>=Q(s)Ia(s>*‘"’/2 i=1.2.
p'(s)=2<1 +x‘(s»/llsJ'(1>e<lei(s)°“”l.
p’(s)=2(1 +x2(s>)/lw'(0c<s>Lz(sy“’l.

This completes the proof.

Note the money supply rule given by 2.7 is increasing in the (1(5) and 7(5) shocks.
This should not be too surprising since Proposition 2.2 showed that employment is an
increasing function of positive monetary innovations and from the social planner’s problem it
was shown that the Pareto optimal work effort is increasing in the marginal productivity
shocks. Note also that the monetary rules are the same for both countries. This should not be
too surprising either, since Proposition 2.2 also showed that unanticipated monetary injections
have the same effect on interest rates irrespective of the country from which they originated.
Finally, note that the monetary policy rule is independent of the 0(5) and C(5) shocks. This is
because the optimal labor supply is independent of these shocks. With a more general
specification of the utility function the monetary rule would likely depend on these shocks.
However, closed form solutions could not be obtained if the utility function was of the more
general form of the constant relative risk aversion class. In the next section the optimal

monetary policy for the flexible exchange rate regime is derived.

75

Section HI.2: timal Mone Polic in the Flexible Exchan e Rate Re ime

The solution strategy in this subsection is similar to the solution strategy in the
previous subsection. The solution to the social planner's problem is given by 2.5 .a,b. Again
comparing these conditions to the representative households' conditions for optimality and the
first order conditions for the firms, it is easy to verify that the representative household's
efficiency condition is the same as the social planner's first order conditions if and only if
Aij(s)=0 (i,j=1,2) and (1 +Ri)=1 (i=1,2). Therefore, the optimal monetary policy is one that
keeps the interest rates at unity in both countries. Again, optimality implies the cash-in-
advance constraints should be non-binding or "just" binding. This implies the same type of
multiplicity problem as in the previous subsection. In order to deal with the multiplicity of
equilibria in this case, it is assumed that the cash-in-advance constraint for consumption good
one (two) purchased by the representative household in country one (two) does not bind.
However, the cash-in-advance constraint for consumption good one (two) purchased by the
representative household in country two (one) "just" binds. That is, households will take just
enough money to the foreign exchange market so that the marginal value of a dollar used for
the purchase of the foreign produced good is zero. In addition, after the foreign produced
good is purchased the household has no foreign currency left over. Also, as in the previous
section, it is assumed that the borrowing constraint just binds. This solution strategy leads to

the following proposition.

76

Proposition 2.6: In the flexible exchange rate economy, there exists a competitive equilibrium

in which the monetary authority can attain the Pareto optimal allocations.

ML: The proof is again by construction. Recall from the social planner's problem that the
optimal labor supply for the representative household in country one (two) is 201(5) (27(5)).
Given these values the rest of the proof proceeds as follows. The prices of the consumption
goods are derived. Then the amount allocated to the purchase of foreign exchange to purchase
foreign produced consumption goods is derived. Then the beginning and the end of period
exchange rates are solved for. Finally the optimal money supply rules are derived.

Recall from eq. 2.5.a,b that the multipliers on the cash-in-advance constraints are equal
to zero. Using this fact and the market clearing conditions on consumption goods implies
prices and allocations are given by

P1(S) =11 '2(1)(1 +X1(S)) +1 ' 1(1)(1 +X2(S))(1/C(S))l[l31 ' 1(1)] '2(1)9(S)L1(S)“‘s)l'l-
021s) =11'2<1>(1 +x‘<s» +J' 1100 +x2(S))(1/e(8))1[1/e(S)BJ' 111>J'2<1)c(s>la(sy“’l"
c‘its)=A<s>9<s>L1(s)““’,
c‘a(s)=(1-A(s))9(s)L1(s)“"’.
ciitsl=A<s>cts>La<s>lS£
cats) =(1-A(s>)c(s>la<sy“’,
where A(s)=[J'1(l)(1+x2(s))][J'2(l)(1+x1(s))+J'1(l)(l+x2(5))1/e(s)]'1.
These values imply
d1(S) =(1 +x'(s»/1131' 1(1)(1/e(S))l.
e(s) =(1 +x2(s))(1/e(s))/Il31'a(1)l.

77

Using the arbitrage condition e(s)/é(s)(1+Rl)=(1+R2) and the market clearing condition for
end of the period exchange rate, implies that q12(s) =e(5)q21(5). Then the beginning and the
end of period exchange rates are given by
e(s) =10 +x‘(s»J' 1(1)1/0'2(1)0 +x2(S)l, and
6(5) =e(s)'l.
The consumption allocations and goods prices, therefore, can be simplified to
c‘,(s)=[0(s)L,“‘"]/2, i=1,2
c’.<s)=lt(s)ta*“’l/2 i=1.2
p‘ts)=20 +x'(s»/0r10>e(s)Ll(s>°‘“’). and
112(5) =20 +x’(s»/0ra0tensor").
Wages are given by
w'(s)=(1+x‘(s))/(1il',(l)), and
was) =0 Ham/(13190».
Substituting the values for the pi(s)'s and the ciJ-(5)'5 into the envelope condition again yield the
stochastic version of the Friedman rule, that is
l =l(h/(1+x‘(s)))d>(ds) i=1,2.
Given these wages and prices and the relationship of the qij(s)'s, the just binding
borrowing constraint can be rearranged and substituted into the above equations to yield:
J'1(1)=l[201(s)/(n+x‘(s))]<D(ds), and
J'2(1)=l[27(S)/(n+x2(S))l¢(dS).
Recalling that unity is the upper bound on the distribution of the 01(s)'s and 7(5)'s, and x be the
smallest monetary growth rate. The ni's are then given by

n‘=(l—x)/(1+x).

78

The optimal monetary policy rule is obtained from rearranging the just binding borrowing

constraint from the firms' first order condition to yield
xl(s)=[201(s)-nBJ'1(1)]/[[3J'1(1)-201(s)], and 2.8.a
x2(S)=[27(S)-nBJ'2(1)]/[BJ'2(1)-27(S)l- 2.8.0

This completes the proof.

Unlike the fixed exchange rate rule where the policies need to be coordinated to attain
the Pareto optimal allocations, the monetary policies in this model are independent of each
other. In particular, the money supply rule is simple: the monetary authority in country one
(two) should alter country one's (two's) money supply in response to the marginal productivity
shocks in country one (two). The money supply is increasing in the marginal productivity
shocks. This is so because the Pareto optimal labor supply is increasing in the marginal
productivity shocks, and recall from Proposition 2.4 that the equilibrium labor supply is
increasing in larger than anticipated monetary injections. Thus for larger than anticipated
marginal productivity shocks the monetary authority will increase the money supply in order to
increase employment to the Pareto optimal level. The results in the previous sub-section and
this sub-section are similar in some respects to the Mundell-Flemming model in that
coordination of policies is needed for fixed exchange rates regimes whereas for flexible
exchange rates the monetary authority in country i can tend to shocks in country i (i=1,2)

alone.

79

Section IV; Policies in a Constrained Environment

It was shown that in both the fixed and the flexible exchange rate regimes, the
monetary authority can attain the Pareto optimal allocations. This requires that the money
supplies should on average be contracted at a rate along the lines suggested by Friedman
(1969). In the last section both exchange rate regimes--the fixed and the flexible exchange rate-
-are equally good since the monetary authority can in both regimes attain the Pareto optimal
allocations.

This section considers what is the best monetary policy, an interest rate peg or a
constant growth rate rule, when the money growth rate is constrained to be positive on
average. This may be the case if a certain amount of revenue must be raised by seigniorage to
finance a portion of government spending. The choice of monetary policies is investigated
under the fixed and flexible exchange rate regimes. Also, when the money growth rate is
constrained to be non-negative on average the Pareto optimal allocations cannot be attained and
the allocations in the fixed exchange rate and flexible exchange rate regimes will likely have
different welfare properties. Because of this, comparisons can be made between the two
regimes.

Two welfare measures are used to compare the alternative policies. The first measure
is calculated by finding the expected per-period utility of the representative household under
the growth rate rule and the interest rate rule. Whichever policy yields the higher expected
utility will be preferred. The second method used is defined as the percent increase in

consumption required so that the expected level of utility level in the competitive equilibrium

80

where the money growth is constrained to be positive on average is equal to the expected
utility level in the Pareto optimal environment. That is in the following equation Ac is solved
for

E{u(c',(s) + Ac,c2i(s) + Ac) +V(T-L,)} = E{u(c”’°,,c2"°,) +V(T—L"°)}.

The welfare loss is given by Add

With these two welfare measures not only can comparisons be made between the two
policies but also across regimes. That is, given the choice of a fixed exchange rate regime or a
flexible exchange rate regime, which regime would agents prefer? It is shown below that in
both regimes the interest rate rule is preferred to the constant money growth rate rule. Given
that the interest rate peg is preferred, it is easy to verify that the fixed exchange rate economy
is preferred.

Considered below are six different monetary growth rates and interest rate targets that
corresponds to each money growth rate rule. The interest rate target is an interest rate that
would prevail in a non-stochastic environment. That is, if the monetary growth rate rule is to
increase the money supply by x percent, then the interest rate target keeps the interest rate
pegged at (1 +R)=(1 + i )/B. This interest rate rule would keep the average growth rate of the
money supply at x percent. The constant growth rates looked at are growth rates of 3, 5, 10,
20, 30, and 40 percent.

To keep things simple, I assume the marginal productivity shocks can take on two
values. That is, 01(5) and 7(5) can take on the value of .65 or .75 with equal probability. If the
shocks are independent, then there is a 25 percent chance that 01(5) and 7(5) equal .75, a 25
percent chance that 01(5) and 7(5) equal .65, and a 50 percent chance that one of the marginal -

productivity shocks equals .65 and the other marginal productivity shock equals .75.

81

Table 2.1 contains the results of the simulations for the fixed exchange rate model.
The first line in each row labeled "x" percent refers to the constant money growth rate of
"x" % , and interest rate is the interest rate that corresponds to that money growth rule. Note
that for a given growth rate, the expected utility is higher and the welfare loss is lower for the
interest rate target. The fourth column is the loss ratio, which is the ratio of the two welfare
losses for a particular growth rate. The closer the numbers in the column are to zero the more
preferred the interest rate rule is, if the ratio is equal to one the rules yield the same welfare
loss, and if this ratio is greater than one the growth rate rule is preferred. Notice in all
simulations the loss ratio is less than one. This implies the interest rate peg is preferred. The
intuition to why the interest rate peg is the preferred policy is simple: with larger than
anticipated marginal productivity shocks the representative firm's demand for loanable funds
will be higher. This will put upward pressure on interest rates. The interest rate target
accommodates these shocks by increasing the money supply in response to the marginal
productivity shocks. That is, the interest rate peg is a procyclical policy that accommodates
the demand for loanable funds. Because of the portfolio rigidity, this increase in the money
supply increases employment, bringing the economy closer to the Pareto optimal level of
employment. In particular, the money supply rule is given by

x'(s) =x21s> =19<<a<s> +1(s»/2>0-n>-n0 + E )1/0 + i ).

This policy is clearly procyclical. The monetary authority, by pursuing an interest rate peg,
responds to the average marginal productivity shocks. For larger than anticipated marginal
productivity shocks, the monetary authority increases the money supply and increases

employment. Because of the portfolio rigidity, the increase in loanable funds allows for

82

employment to increase. The findings here are similar to that of Poole (1970) that if shocks
mainly affect money demand then the best policy is to target interest rates.

Table 2.2 shows the simulations for the flexible exchange rate economy. Since the
money growth rate in country i affects only the interest rate and employment in country i,
there will be a separate policy rule for each country. The results are similar but more dramatic
than those in Table 2.1. That is, the interest rate target is much better than the constant money
growth rate rule. Again the interest rate target is procyclical. The monetary growth rules that
attain the interest rate target are given by

X'(S)=Ba(S)I(l-n)-n(1 + x >110 + a )1".

x2(S) =B7(S)I(1-n)-n(1 + i )l[(1 + i )1'1
Similar to the fixed exchange rate model, the procyclical policy in country i keeps the economy
closer to the Pareto optimal level of work effort than the money growth rate rule would.

Given that the interest rate rule is preferred to the constant money growth rate rule, the
results of the model are compared across regimes. That is, which regime leads to the highest
level of expected utility? In this model the answer is clear. Since the Pareto optimal
allocations are the same for both regimes and the welfare loss is lower in the fixed exchange
rate regime, it is preferred. To make the flexible exchange rate regime equivalent to the fixed
exchange rate regime expected consumption of both goods would need to increase by .08
percent if the money growth rate was to be 3 percent on average to as low as .05 percent if the
average money growth rate is 40 percent. The intuition why the fixed exchange rate regime is
preferred is as follows. Recall that the equilibrium employment level is below the Pareto
optimal level when the money growth is constrained to be positive. Consider the case where.

01(5)= .75 and 7(5):.65 and the average money growth rate is 3 percent. In the fixed exchange

83

rate regime, the monetary authorities respond to the “average” marginal productivity shock.
In this case with 01(s)= .75 and 7(5):.65 and the average money growth rate being 3 percent,
the interest rate rule implies the money growth rate is 3 percent in response to these shocks.
The 01(5), 7(5), and money shocks affect the labor supply and labor demand curve. I will
restrict my attention to analyzing the outcome in country one in both regime56. First the high
01(5) shock shifts the labor demand curve rightward. The money growth rate being equal to its
expected value implies the labor supply curve does not shift. The shift in labor demand curve
causes the real wage and employment to increase. Now consider the same shocks in the
flexible exchange rate model. The demand curve for labor shifts to the same position.
However, in country one the money growth rate is 5.88 percent. This causes the labor supply
curve to shift back more than in the fixed exchange rate model. Therefore, employment is
higher in the fixed exchange rate model. Therefore, equilibrium employment is closer to the
Pareto optimal level. Because of this, the fixed exchange rate economy yields a lower welfare

loss and higher expected utility than the flexible exchange rate economy.

Section V: Conclusion

 

This paper investigated the optimal monetary policy in a two country liquidity effects
model. It was shown that the optimal monetary policy was an interest rate peg that keeps the

nominal interest rate at unity. Moreover, it was shown that the monetary authority is capable

 

5 It is easy to verify that the level of employment in country two will not be closer to the Pareto optimal level.
However, the expected gain in utility from the increase in output exceeds the expected loss in utility from the lower
output in the other country.

84

of attaining the Pareto optimal allocations irrespective of the monetary regime--a fixed
exchange rate regime or a flexible exchange rate regime. Then for the case where monetary
growth rates are constrained to be positive on average, it was shown that an interest rate target
is preferred to a constant money growth rate rule. Also, in this case it was shown that the
fixed exchange rate regime is better than the flexible exchange rate regime.

For policy advice this paper gives clear guidelines for countries attempting to
coordinate their policies: A fixed exchange rate regime where the monetary authority targets
interest rates is preferred. There are, however, a few caveats. First to arrive at closed form
solutions a very restrictive utility function had to be used. Second since the monetary
authority must respond to the portfolio rigidity, it must be true that the monetary authority is
able to quickly gather information about the shocks. Further work should address these issues
as well as investigate the optimal policies in a non-cooperative atmosphere as well as the

optimal policies for countries that do not have identical wealth distributions.

85

TABLE 2.1: WELFARE UNDER FIXED EXCHANGE RATE REGIME

 

 

 

 

 

 

 

 

MONEY EXPECTED WELFARE LOSS RATIO
GROWTH UTILITY LOSS

3 PERCENT 3.2555 1.448 % .9223
INTEREST RATE 3.2567 1.346 %

5 PERCENT 3.2466 2.105% .947
INTEREST RATE 3.2480 1.993 %

10 PERCENT 3.2181 4.141% .973
INTEREST RATE 3.2195 4.054%

20 PERCENT 3.1413 9.60% .988
INTEREST RATE 3.1427 9.49%

30 PERCENT 3 .0470 16.16 % .993
INTEREST RATE 3.0484 16.05%

40 PERCENT 2.9425 23.45 % .995
INTEREST RATE 2.9438 23.33%

 

 

 

 

p=.95,0=g=2

 

86

TABLE 2.2 WELFARE UNDER FLEXIBLE EXCHANGE RATE REGIME

 

 

 

 

 

 

 

MONEY EXPECTED WELFARE LOSS RATIO
GROWTH UTILITY LOSS

3 PERCENT 3.2537 1.584% .860
INTEREST RATE 3.2566 1.362 %

5 PERCENT 3.2447 2.240% .90215
INTEREST RATE 3.2474 2.070 %

10 PERCENT 3.2156 4.299% .950
INTEREST RATE 3.2193 4.083%

20 PERCENT 3.1395 9.278 % .978
INTERESTRATE 3.1424 9.139%

30 PERCENT 3.0452 16.299 % .988
INTEREST RATE 3.0480 16.095%

40 PERCENT 2.9407 23.585 % .991
INTEREST RATE 2.9434 23.385 %

 

 

 

 

p=.95,o=g=2

 

 

87

Appendix 2.1: Proof of Proposition 1:

m The proof will be by construction. By assuming the cash-in-advance constraints bind it
will be shown that there exist unique ni for the representative household in country i, i= 1,2.
Given the identical wealth distribution, 1 will make a guess that the optimal saving's decision is
the same for households in countries one and two. Then the rest of the variables will be solved
for. Then I will go back and confirm the initial guess.

First using the equations 2.3.b,2.3.c,2.3.d,e=1, and the binding cash-in advance
constraint yields d‘(s)=(1-n)/2. Similarly, for the household in country two combining eq.
2.4.b,2.4.c,2.4.d, e= 1, and the binding cash-in advance constraint yields

d2(s)=(1-n)/2.

This implies the consumption allocations are
c11(s)=c12(s)=0(s)L1(s)°‘(s)/2 and
c210)=c22<s>=.(s)1a(s>':‘S’/2.

Prices then are given by
p'<s)=(1-n>/(e<s>L1(s)““’). and
132(5)=(1-n)/(C(S)I-/2(S)Y(S))-

Wages are w'(s)=(1+x'(s))(l—n)/(2p)
w2(s) =(1 +x2(s))(1-n)/(20).

Interest rates are given by (1+Rl)=01(s)(1-n)/(q11(s)+q12(s)+xl(s))
0 +R2)=7(S)(1-n)/((1/<121(S) +q221s)+x2(s>>.

Using e=1 and the no arbitrage condition on deposits the optimal qij(s)'s are given by

q‘i(s>=q'a(s)=12a(s)n+u(sht‘(s)-1(s)x2(s)l/12(a(s)+1(s»l. and

88

(121(5)=(122(S) =121<s>no<s>x‘(s>+i(s)x2(s)l/12(a(s) +i(s))1.
Interest rates are given by
(1 +R‘)=(1 +R2)=[(0t(s)+7(5))(l-n)]/[2n+x1(s) +x2(S)].
Then equilibrium labor supply can be gotten from the firm's first order conditions.
For a household in country one the equilibrium labor supply is given by
L1(S) = [Ow/(01(8) +7(S)ll3(2n +X1(S)+X2(S))2[(1-n)(1 + X1(S))l'l
For a household in country two the equilibrium labor supply is given by
L20) = [V(S)/(a~(8) +11s)113(2n+x‘(s> +x’(s»2l0-n>0 +x’<s»l
From eq. 2.3.a, eq. 2.3.c, eq. 2.3.f, and the envelope condition we have
1 =I.(13/0 +X1(S)))[0L(S)(I'nl'dl(s)+ed2(S)/(qll(s)+Cq12(5)+XI(S))I‘D(dS)
Substituting for the optimal d1(5) and symmetry implies the equation can be written as
1 =I.0/0 +x'(s»)la<s>(1-n)/<2q'1<s)+x'<s»l¢<ds)
Then substitute for q11(s). This yields
1 =l,(6/(1 +x'(s)))[(a(s) +7(5))(1-n)]/[2n + x'(s) +x2(s)]<l>(ds) 2.9
Clearly eq. 2.9 is decreasing in 11. If n=1 then the right hand side of eq. 2.9 is exactly zero.
Also, if n=0 then the right hand side of eq. 2.9 exceeds unity by assumption one. By
continuity of 11 there exists a unique fixed point n‘e(0, 1) satisfying eq. 2.9. Similarly, for a
household in country two eq 2.1,2.4.c,2.4.f, and the symmetry of the deposits and substituting
for d2(s) yields
1 =l,(B/(1 +xl(s)))[(o.(s) +7(5))(1-n)]/[2n + x1(s) +x2(s)]d>(ds) 2.10
The right-hand-side of eq. 2.10 is strictly decreasing in n, and if n=1 then the right-
hand-side equals zero. If n=0 then the right-hand-side exceeds one by assumption one. By _

continuity of 11 there exists a fixed point ne(0, 1) satisfying eq. 2.10. Note that eq. 2.10 is

89

identical to eq. 2.9. Next substittute these equibrium values back into household's reource
constraint and solve for and solve for the t '5 so that wealth remains unchanged. This yields
t‘(s) =1 +x‘(s)-(a(s)/(a(s) +7(5)))(2n +x1(s)+x2(s))-
<n+x‘<s»((a(s>+7(s»0-n)/<2n+x‘<s)+x2<s>>-04<s>>0-n)
30) = 1 +x2(s)-0(s)/(a(s> +7(5)))(211+X1(S)+X2(S))-

(n+x2<s»((a(s)+1<s>>0-n)/(2n+x‘<s>+x’<s»-0-v<s»0-n).

This completes the proof.

90

Appendix 2.2: Proof of Proposition 2.3:

Proof: The proof will be by construction. I will assume that the constraints hold with equality.
I will solve for all the equilibrium prices and allocations and Show that these values are
consistent with positive multipliers on all constraints. Since each household starts each period
with the same level of wealth and they have identical preferences, the savings decision ni will
be the same for both countries. The optimal savings decision will be derived at the final stages
of the proof. For now, I will take the his as given and solve for the remaining variables.
To derive the consumption allocations 3b—d and the binding cash-in-advance

constraints can be combined to yield

d'(s)=[(l-n)/2e(s)].
Similarly, equations 4.b-d and the binding cash-in-advance constraints for the household in
country two can be combined to yield

d2(s)=[(1-n)e(s)/2].
The optimal value for d2(s), the cash-in-advance constraints, and the market clearing condition
for good one can be combined to find the equilibrium price for good one. This price is given
by

p'<s) =10-n)0 +e<s>>le<s)L°‘“’1.
The consumption allocations can be obtained be rearranging the cash-in-advance equations
from the household in country one and the household in country two. This leads to

c‘1(s)= 11/0 +e(S))19(S)Li°"”,

c'2(s>=1e(s>/0 +e<s>>19<s>Li“‘”.

91

Similarly, the prices and the consumption allocation for good two can be gotten by the same
process. Combining eq. 2.3.c-d, 2.4.e—d, the cash-in-advance constraints for good two, and
the market clearing conditions for good two yields the following price for good two and
consumption allocations given by

02(S)=I(1-n)(l +e<s>“)l/2c(s>la*“’.

c22(s>=1e(s)"/0 +e<s>“>1¢<s)Ia*‘". and

cite) =10/0 +e<s)")lc(s)1a*“’.
Next substitute these consumption values for good one (two) for household one (two) along
with the corresponding prices into the envelope condition eq. 2.3.k (2.4.k). to yield

Jl'(1)=2/(1-n) (J2'(1)=2/(1-n))).
Thus the derivative of the value function is the same for both countries.

Equations 2.3.c and 2.4.e and substituting for wi(s)Li(s) (i= 1,2) from the firms
borrowing constraint can be rearranged to obtain the household's optimal labor supply
decision. The labor supplies for countries one and two are given by

L.(s)=2131q‘1(s)+q'a<s>+x‘(s)l/l0 +x‘(s»0-n)l, and
L;(s)=20[q21(s)+q22(s)+x2(s)]/[(l +x2(8))(1-n)l-
Now in order to derive expressions for the interest rates in country one and country two,
substitute for prices and for wi(s)Li(5) from the borrowing constraint into the firm's problem
and rearranging. Doing this for both countries yields
0 +R‘)=1a<s)0-n>0 +e(s»/(q'1<s) +q‘a(s) +x'(s»l. and
0 +122) =h<s>0-n)0 ”(syn/(0211s)+<12<s>+x2<s>11
The nominal wages are then given by substituting the optimal labor supply decision and the -

interest rate into the firms' first order conditions to yield

92

w'(s)=(l +x‘(s))(1-n)/2li, and

w2(s) =(1 +x2(s))(1-n)/2[3.
Next use eq. 2.3.f and 2.4. g no-arbitrage conditions on bank deposits to solve for the exchange
rates and interest rates. That is in equilibrium the exchange rate adjusted interest rate are
equated. Rearranging eq. 2.3.g and eq. 2.4.f yields

(1 +R')(e(s)/ e(s))=(1 +18). 2.11
To solve for the exchange rates e(s) and 6(5) . I use the market clearing conditions for the
exchange rates which are

e(s>1d‘(s>+q21(s)l=1d”<s>+q‘2<s)l, and

e(s) [q]2(s)(l +R')] =[q21(s)(l +R2)]. 2.12.a,b
Next substitute (1 +VR1) from eq. 2.11 into eq. 2.12.b which yields

e(s)qzi(s) =q‘2(s). 2. 13
Then substitute eq. 2.8 and the equilibrium values for the di(s)'s into eq. 2.12.a and
rearranging yields

e(s) = 1 .
Given this value for e(s), q12(5)=q21(s)s(0,n) and eq. 2.11 implies that 6(5) is defined to be

61s) =v(s>(n+x‘(s»/la(s)(n+x’<s»l.
Consumption allocations are given by

c1j(s)=0(s)L1(s) ““72, j = 1,2

021(S)=C(S)L2(S) “81/2 i=1.2
Equilibrium labor supplies are given by

t,(s)=2p(n+x')/(1+x‘(s))(1—n), and

IQ(5)=2I5(n+x2)/(l +x2(s))(l-n).

93

Prices are given by

p‘(s>=0-n)/e(s>Li(s)“‘8’,

p’ts)=0-n>/cs>1a(s)*“’,

w‘<s)=0 +x'(s»0-n»/20.

w’ts) =0 +x21s»0-n»/211,

(1 +111) =o(s)(l—n)/(n+x‘(s)),

0 +112) =Y(S)(1'n)/(D+X2(S))s

e(s)= 1,

e(s) =h(s>(n+x‘(s»l/la<s><n+x’<s»l

t‘ =1:2=O
To determine the optimal ni's, substitute into eq. 2.3.a (2.4.a) and 2.3.h (2.4.b) for 211(5),
7131(5), 9112(5), and 132(s)and rearranging yields

1 =I.0/(1+x‘(s»>la<s>0-n)/(n +x'<s))1<1><ds>,
for a household in country one and,

1 =L0/0 +x2(s)>)h(s)0-n)/(n+x’(s»ld>(ds).
for a household in country two. These functional equations are strictly decreasing 11. They
exceed unity when n equals zero, and equal zero when n equals unity. By continuity of 11 there
exists a unique fixed point. Since x1(5) and x2(s) are drawn from the same distribution as are
ot(s) and 7(5), the n's that solve these functional equations are identical.

This completes the proof.

Chapter 3: Real Effects from Unanticipated Changes in the Money Supply in a Model with
Inven ories d redit Goods: Friedman 1968 Revisited

In his 1968 American Economic Association Presidential Address, Milton
Friedman argued that only unanticipated, not anticipated, increases in the supply of money
could lead to increases in output and employment. More specifically, the unanticipated
increase in the supply of money would cause the labor supply curve to shift rightward due
to misperceptions of the real wage by workers. This would lead to a reduction in real
wages and increases in employment and output. Friedman argued these effects would last
anywhere from two to 10 years due to some type of market frictions. Rigorous models
establishing these "Friedman effects" were constructed by Lucas (1972, 1975), and Barro
(1977). Though these models could capture the initial effects of an unanticipated increase
in the money supply process, the were less successful in accounting for the dynamic
behavior outlined by Friedman. In addition, these models relied on agent’s misperceptions
of variables that were readily available to them. Because of their inability to capture
business cycle dynamics and because they rely on misperceptions of available data, these
models are no longer considered as appropriate models of capturing the effects of monetary
innovations.

More recently, there has been renewed interest in the effects of monetary
innovations on interest rates and real activity. Indeed, this resurgence has come about due
to recent developments in theoretical models and to the advances made in time series
econometrics. Empirical papers by Christiano and Eichenbaum (1992a), Bernanke and
Blinder (1990), and Sims (1991) find empirical evidence consistent with the conventional

wisdom concerning unanticipated increases in the money supply and real variables. That

94

95

is, larger than anticipated increases in the money supply lower the interest rate and
increase real activity.

Theoretically, Fuerst (1992) showed that, by incorporating Lucas’ (1990) liquidity
effects framework into a production economy, monetary innovations could have real effects
that are consistent with conventional wisdom. Christiano (1991) showed that when the
Fuerst model was calibrated to be consistent the United States economy, the expected
inflation effect dominates the liquidity effect and interest rates rise rather than fall in
response to larger than anticipated monetary injections.

Christiano and Eichenbaum (1992b) are able to modify the model so that larger
than anticipated monetary injections cause interest rates to fall and output to rise. They
accomplish this by assuming investment decisions are made before the state of the world is
revealed and by allowing contemporaneous wage income to be used for consumption
purchases. Though the contemporaneous response of interest rates and output are
consistent with the empirical evidence cited above, the dynamic properties of the model are
not.

This paper modifies the work of Christiano and Eichenbaum (1992b) and Fuerst
(1992). In doing so, the economy reacts to monetary shocks in a manner similar to what
Friedman described. Before describing that model, I will discuss the Christiano and
Eichenbaum (1992b) model and a similar model that includes inventories alone. The
problem in Christiano and Eichenbaum’s model is that output and consumption fall
precipitously in the periods following the unanticipated monetary injection before gradually
returning to their steady state levels. This property of the model is clearly not consistent
with the empirical evidence cited above. The basic liquidity effects model of Christiano

and Eichenbaum is described in Section I. Also, the dynamic response of the variables in

96

the model to a one standard deviation Shock to the money supply is discussed. In Section
II, inventories are added to the model. The reason inventories are added is simple:
realism. On average, the total stock of inventories is roughly 90 percent of output (see
Christiano (1988), Kydland and Prescott (1994), or Cooley and HanSen (1995)'). In
addition, inventory investment is the most volatile component of GDPZ. Because of these
facts alone, inventory accumulation should be considered a potential factor in making
these stylized models more consistent with the empirical evidence of business cycle
fluctuations. Another reason to model inventories is that the volatility of inventory
investment may aid in propagating idiosyncratic shocks, such as monetary shocks. That is,
suppose that inventories assist in producing output, and suppose output increases in
response to a monetary shock. If inventories accumulate in response to this shock, it is
possible that this will cause output to remain above its steady state value for several
periods. Inventories, therefore, may make the real effects of a monetary innovation persist
longer.

It is shown that including inventories does not improve the model. In fact the
contemporaneous behavior of consumption and the interest rate, as well as the dynamic
behavior of these variables to a one standard deviation shock to the money supply process
are not consistent with the empirical evidence

Section HI attempts to rectify this problem by including credit goods. This
modification vastly improves the model. In fact, the response of the variables seems to be
consistent with Friedman’s (1968) view of the effects of monetary innovations. However,

there are two potential problems that arise with this model. The first problem is the

 

' Christiano's (1988) figure for inventories comes from the Survey of Current Business Table 1.2.
2 Romer (1995) states that inventory accumulation’s average share of the fall in GDP in recessions relative to
normal growth is 30.7 percent

97

contemporaneous response of the interest rate and consumption may be in the wrong
direction. The second problem is that this model implies that consumption lags the cycle,
whereas, the data tell us consumption leads the cycle in United States. This second
problem may not be too problematic. The data indicate that consumption leads the
business cycle and is positively correlated with money growth. Most economists are in
agreement on these facts. However, the response of consumption to unanticipated
increases in the money supply process is less understood. In order to quantify how
consumption responds to unanticipated increases in the money supply process one needs to
take a stand on the money supply process. The profession is not in agreement about how
this can be done empirically. Different identifying assumptions about the money supply

process may lead to different results (Gordon and Leeper 1992). Section IV concludes.

Section I: The Basic hristiano d Eichenbaum Model

In the basic Christiano and Eichenbaum model there are three types of agents:
households, firms, and financial intermediaries. Each agent of each type is assumed to be
identical. Therefore, the actions of a representative agent of each type can be studied. The
household consists of three members. Each member carries out distinct tasks. The first
member, the saver, is responsible for depositing the current period’s savings allocation
(N0 into the financial intermediary. The second member, the shopper uses the remaining
funds (Mt-Ni) to purchase consumption goods. The third member, the worker, offers
services in the labor market to the goods producing firm in exchange for wage
compensation (W 1L1). When the agents perform these tasks is discussed more fully below. 7

(The timing of agent's decisions is listed on page 98.)

98

Timing:

l. Households decide how much to allocate to goods consumption and to savings.
STATE OF THE WORLD IS REVEALED

2. Savings are deposited in the financial intermediary.

3. Firms borrow funds, hire labor and produce the consumption goods.

4. The shopper purchases the consumption goods. Firms purchase capital.

5. Firms repay their loans.

6. Households reunite and pool their resources. These resources include the return on
savings, the residuals from the cash-in-advance constraints on consumption goods,
wage income, and profits from the firms and intermediaries.

99

The main difference in these liquidity effects models from the standard real business cycle
models is the timing of the agents' decisions. The household starts the period holding Ml
units of currency. Before the state of the world is known, the household allocates N, units
of currency to the saver. The remaining Mt - Nl units of currency plus contemporaneous
labor receipts (W 1L1) can be used to purchase the consumption good3. Once the household
chooses N, it is prohibited from realigning its portfolio.

The household receives utility from consuming the consumption good and from
leisure. In particular, the household’s per period utility is given by

U(c,,l-L,)=7In(c,)+(l-7)ln(l-L,), 3.1

where c, is consumption at time t, L, is labor at time t. The time endowment is normalized
to unity so that H... is leisure at time t. The household’s lifetime expected utility is given

by

u=EoZp‘U(c,,l-L,), 3.1’

t=0
where is the [3 discount factor and Be(0,1).

After the savings decision is made, the household separates and the state of the
world is revealed. Recall that decisions made before the state of the world is revealed can
not be changed. Thus the amount allocated to savings can not be realigned. This portfolio
rigidity is what allows for the realizations of the money supply process that differ from

what was expected to have real effects.

 

3 It is assumed that the current period's wage receipts are given directly to the shopper so that the shopper can
use these receipts for goods purchases.

100

As stated above, the saver deposits funds into the financial intermediary. The
shopper uses the remaining funds plus labor income to finance consumption purchases.
The worker offers his services in the labor market.

The representative financial intermediary accepts deposits from the household (N7)
and receives cash injections from the monetary authority (X,). By assumption, the
representative goods producing firm needs to obtain funds in order to finance its wage bill.
As long as the gross nominal interest rate exceeds unity, the representative intermediary
will loan out all of its funds to the firm. At the end of the period, the profits of the
representative financial intermediary are paid to the representative household as dividends.

The representative firm hires labor each period and purchases capital in order to
maximize profits. As stated above in order to hire workers, firms must borrow from the
financial intermediary. Firms own their own capital stock. The additions to the capital
stock, thus investment, are decided on before the state of the world is known. Production
is carried out using the neoclassical production firnction

F(K,,H,)=K,°‘(exp(ut)H,)"“ 3.2
Profits for the firm are given by
ITt =P,{F(K,,H,) -KHi +(1—6)K,}-W,H,(1+R,)3 W,Ht S Nt +X,. 3.3
The goods producing firm chooses labor and capital 50 to maximize the discounted value of
its dividend payments to the representative household. Since the representative household
owns the firm, dividend payments are paid to the household at the end of each period.

The only stochastic variable in this framework is the money supply process.
Following Christiano (1991) and Christiano and Eichenbaum (1992b), I assume the money ‘

supply process follows a first order autoregressive process given by

101

Xl =(1-p)X+ pX,_l +8t ,
where a, ~N(0,.014)4.

Given the above set-up, the household’s problem can be written in terms of its
dynamic program. Since I am only concerned with stationary rational expectational
equilibria, all growing variables must be detrended. Since technology is labor augmenting,
all real variables will be growing at the rate exp(tt). To make the time t real variables
stationary they must be detrended by the exp(ut). Similarly, all nominal variables will be
growing along with the changes in the money supply. The nominal variables dated at time t
must be detrended by the time t money supply. In the dynamic programming problem, the
usual convention of denoting detrended variables with lower case letters and dropping time
subscripts, and using primes to denote next period’s values is employed below. The

dynamic program for the household is given by

J(m,k,k) = maxndo’ml’k. I maxcflL’H’k. b {U(c,l - L) + 111(m' , k' , k' )F(s,ds)},
subject to m - n + wL 2 pc,
11 + x 2 b, and
DZWH,
and the transition equation is given by
m'=[m + nR - pc + wL + (1 + R)x + p(exp(-ua)lr°‘r1"°‘ - k'+(l — 5)k) - wH - bR] / (1 + x),

and k is the aggregate capital stock, and F (5, ds) is the distribution function.
After renorrnalizing by the time t money supply, the first order conditions
from this programming problem can be rearranged to yield the following efficiency

conditions

 

4 This is the empirical estimate in Christiano and Eichenbaum (1992b).

102

U,(c ,1-1. ) w
t t _______l 3.5.a
UL(ct91'Lt) PI

 

Uc(Ct,1-Lt) B Uc(ct+1’l-Lt-H)

 

 

 

 

E = E 1+R 3.5.b
.11 P. } ...{(1 +x.> P... < .)
E {BUc(Ct+l’l - LHI)1:
H P,,,(1+x,) ‘
3.5.c
B2 Uc(ct+2’l-Lt+2) a H:
E1410 +X P Pt(eXP('l~l°~)akt+i L141 +(1—9»
t+l) ”2
W —1
(l +R,) {j} (1-a)exp(-ua)ktaLtl-a 3.5.d
1

Equation 3.5.a is the household’s leisure-labor decision. The household equates
the marginal rates of substitution between leisure and consumption to the real wage.
Equation 3.5.b is the household’s portfolio choice decision. The household chooses how
much to allot to savings and to consumption at time t based on the information at the
beginning of time t.

The optimal capital accumulation equation is given by eq. 3.5.c. This decision is
also based on information available at the beginning of time t. This assumption is intended
to capture the fact that investment is a long range plan that is not likely to be reversed for
small deviations from the expected state of the world. This efficiency condition can be
interpreted as follows: if the firm decides to increase the capital stock by one unit, this
will have the effect of lowering the end of period profits by Pt dollars. Because of this, the
household will have fewer cash balances available for consumption in the next period.
That is, they will, in expectations, buy l/PHI fewer consumption goods . This causes the
household to suffer discounted disutility given by 0Uc(q+1, l-EH). Therefore, the time t

cost of increasing the capital stock by one unit is given by the left-hand side of eq. 3.5.c.

103

The benefit is given by the right-hand side of eq. 3.5.c and is interpreted as follows. The

addition to the capital stock at time t increases profits at time t+1

(P,,1(exp(-ua)k?,lL‘fff - (l — 5)). These profits will be paid back to the household at the
end oft+1, and therefore be available for consumption at time t+2 yielding discounted
marginal utility BzUc(c,+2,1-L,+2/Pt+2. Along the optimal path, the household equates
these costs and benefits. Equation 3.5.d is the firm’s optimal labor demand decision.
Note, labor demand is a decreasing function of the nominal interest rate.

These four equations, the cash-in—advance constraint for the consumption good, the
borrowing constraint, and the market clearing conditions yield a system of seven equations

and seven unknowns. The market clearing conditions are given by

exp(-—p.or)kf‘L1,")l =ct + km —(1 —25)kt , 3.6.a
Ht=L1, 3.6.b
mt=ml+19 3.6.c

where eq. 3.6.a is the aggregate resource constraint, eq. 3.6.b is the market clearing
condition for the labor market and 3.6.c is money market equilibrium. The consistency
condition on the capital stock implies k=k. Therefore, given these conditions, solutions to
the seven unknowns (Pt, (1+Rt) W,, N,, C,, L ,, K“) can be sought and their dynamic
paths can be traced out.

Since this system of equations is non-linear, an approximation technique must be
employed to trace out the dynamic path of the variables. The method used here is the same
employed by Christiano (1991). The solution strategy involves four steps. These steps
are: (1) choose values for the free parameters, (2) find the steady state values for the non- ’
stochastic system, (3) linearize the system around the steady state, and (4) use the method

of undetermined coefficients to solve for the unknowns.

104

The parameter values used here are as follows: B=(1.03)’25, 11:.0041, p=.32, and
x= .012 (these numbers are all taken from Christiano and Eichenbaum (1992b)). In
addition, 7 is chosen so that the time allocated to work is consistent with the average time
spent at work for the average individual; that is, percent of time at work is .2195. This
implies 7= .24. Next, 01 is chosen so that the labor share of output in this model is
consistent average labor share of output for the United States. This implies 012.3. Finally,
Christiano (1991) finds that the average consumption-output ratio and capital-output ratio is
.73 and 10.59 respectively. Using these values, the depreciation rate is obtained from the
resource constraint. This yields 6:.023.

The dynamic responses of the variables are shown in Figures 3.1-3.5. The figures
show the percent deviations from the steady state of the nominal interest rate, output,
consumption, employment and the real wage, and work effort to a one standard deviation
shock to the money supply process. Figure 3.1 depicts the percent change in the interest
rate to the monetary shock. Note the interest rate initially falls then begins to rise in
subsequent periods. (The intuition for the response of these variables to the shock is
discussed in detail below.) Figure 3.2 shows how output responds to an unanticipated
increase in the money supply. In response to the shock, output rises above its steady state
level. In fact it remains above its steady state level for several periods after the shock.
Consumption’s deviation from its steady state level is depicted in Figure 3.3.
Consumption increases in the period of the shock but then falls drastically in subsequent
periods. The percent change in employment is depicted in Figure 3.4. Employment rises

with the shock and remains slightly above its steady state value for six periods.

 

5 This number is also taken from Christiano and Eichenbaum (1992b).

105

Note that the contemporaneous movements of the variables seem to be consistent
with conventional wisdom. The dynamics of the model, however, are not. In particular,
consumption (shown in Figure 3.3) falls after the shock and then gradually returns to its
steady state value. Since prices rise, consumers buy fewer consumption goods. The
additional output then must go into investment. The reason for this is simple: The rise in
prices implies consumption (a cash good) will be more expensive than investment (a credit
good)6. Therefore, consumption falls and investment increases. The data reported by
Cooley and Hansen (1995) imply that consumption is positively correlated with monetary
aggregates. So given a persistent innovation in the money supply process that causes the
money supply growth rate to be above its steady state level of growth for several periods,
then it should also be the case that consumption should be above its steady state level too.
It clearly is not.

Returning to Figure 3.1, the nominal interest rate remains below the steady state
value in the period following the shock then rises as the expected inflation rises.
Empirically, Christiano and Eichenbaum (1992a) present evidence that the nominal interest
rate remains below the steady state value for as many as 16 quarters following the shock.

In this model, the real wage rises initially, falls drastically in the period after the
shock, and then gradually returns to the steady state. The reason for this initial rise in real
wages is as follows. Consider the demand and supply for labor drawn in real wage space.
Assume that the model is in steady state when hit by a monetary shock. The monetary
innovation reduces interest rates. This implies the labor demand curve shifts to the right.

The labor supply curve shifts to the left because consumption increases above its steady

 

6 I am using the term credit good in the same manner as Lucas and Stokey (1983), Cooley and Hansen (1995),
and Carlstrom and Fuerst (1995) use it. Credit goods are goods that are not subject to a cash-in-advance
constraints.

106

state value (this follows from equation 3.5.a). The direction of the shifts of both of these
curves implies the real wage must increase. Since the rightward shift in labor demand
exceeds the leftward shift in labor supply, employment increases in the period of the
shock. In the following period, the nominal interest rate increases but still remains below
its steady state value. This implies the labor demand curve in the period immediately
following the shock is to the right of the steady state labor demand curve. Since
consumption is still above its steady state value, the labor supply schedule in this period
must lie to the left of the steady state labor supply schedule. Taken together, this implies
that the real wage must still be above its steady state level. In the second period after the
shock, the nominal interest rate exceeds its steady state level. This in turn implies that the
labor demand schedule in this period lies everywhere to the left of the steady state labor
demand schedule. Likewise since consumption falls, the labor supply schedule must lie to
the right of the steady state labor supply curve. As a result, it can be inferred from these
shifts that not only does the real wage fall in the third period after the shock, it is also true
that the real wage in this period is below the steady state real wage. In subsequent periods
the nominal interest rate gradually falls back to the steady state level. As the interest rate
falls, the labor demand schedule gradually shifts back to its steady state position. The real
wage in this model is procyclical. However, it is procyclical for entirely different reasons
than in the standard RBC model. In the standard RBC model the real wage is procyclical
because technology shocks make the firm more productive increasing its demand for labor.
In this model the real wage is procyclical due to the money supply's effect on interest rates
and prices.

The major shortcoming of this model is its inability to replicate the dynamic

behavior of output, consumption, interest rates, and real wages. The model, however, is

107

consistent with the contemporaneous response of variables to a money shock. Christiano
and Eichenbaum (1992b) rectify this problem by making it costly for households to adjust
their portfolios for several periods after the shock. This costly portfolio adjustment
assumption helps make the model more consistent with the empirical evidence. Instead of
taking this approach, I investigate the implications of the dynamic behavior of the variables
if the real side of the economy is modeled more explicitly. In particular, in the next

section, inventories are added to the model.

Section II. The Christiano and Eichenbaum Model with Inventories

This section incorporates inventories into the model investigated in Section 1.
Recall the two reasons for adding inventories to the model: the first is that the stock of
inventories at a point in time is non-negligibIe--roughly 90 percent of output. Also, recall
that if inventories accumulate in response to a monetary innovation, then it may be possible
that the real effects of a monetary innovation will persist for several periods. ( The timing
of the model is discussed on page 108.)

In this section, I assume inventory decisions are made after the state of the world
is revealed. Moreover, I assume the inventory purchases are not subject to a cash-in-
advance constraint. I assume, as in Christiano (1988) and Kydland and Prescott (1994)

that inventories assist in the production of output. The production function specification is

108

Timing:

1. Households decide how much to allocate to goods consumption and to savings.

STATE OF THE WORLD IS REVEALED

2. Savings are deposited in the financial intermediary.

3. Firms borrow funds, hire labor and produce the consumption goods.

4. The shopper purchases the consumption goods. Firms acquire capital and inventories.

5. Firms repay their loans.

6. Households reunite and pool their resources. These resources include the return on
savings, the residuals from the cash-in—advance constraints on consumption goods,
wage income, and profits from the firms and intermediaries.

109

as in Kydland and Prescott (1994) given by

l -l

F1K.,H.,s.)=l0- v)(I‘<:‘(exp(ut)H.)‘-“)7 + 115.7 1".
where S. are inventories at time t, and the capital stock in this section (K) is net of

inventories .

Removing the growth trend from the production function yields

1 l

statics.) =10 -v)(exp<-au)12?H."°‘)i mom/wits? 1".
Also as in Kydland and Prescott, I assume that in the growth economy inventories do not
depreciate and the ratio of inventories to output is .907. The parameters 01, v and w are free
parameters. The parameter v is chosen to be 38. This value implies that inventories are
complements to capital and labor in producing output. The parameters 01 and w are chosen
so that the capital-output ratio and the inventory-output ratio in this model is the same as
the average capital-output ratio and the inventory-output ratio over the cycle for the United
States economy. The values for 01 and \y that achieve this are .363 and .0062,
respectively. Except for the expression for goods market clearing and an additional
efficiency condition for inventory accumulation, the model is same as in Section I. The
efficiency conditions are

U,(c,,1-L,) _&

 

 

 

3.6.a
UL(c,,1-L,) Pl
.. —L ,
El-1{UC(Ct,1 Ll)}: Et,1{ B Uc(cl'fl’1 l-H)(1+Rt) 3.6.b
Pt (1+Xt) P141

 

7 The aggregate capital stock is then adjusted so that the sum of inventories and capital is equal to 10.59 as in
Section 1. Experiments with inventory to output ratios of .25 ranging to 1.5 had little affect on the qualitative
aspects of the model.

8 Sensitivity analysis was done by letting v=1.5 and v=4.5. These changes do not qualitatively change the
results. In fact, they hardly affect the quantitative results.

110

BUc(ct+191' L1H)

 

 

 

 

E :
“'{ P...0+x.) }
2 3.6.c
B Uc (ct-+2 91' LHZ) "
E P f k L + 1—5
“{(I'I'XHI) PH2 t( l( t: 1981) ( ))
Et{BUc(ct+l’l-Lt+])}:
Pt+l(l+xt)
2 3.6.d
B Uc(ct+291'Lt+2) A _
E'{(1+x,,,) 11.. P.1(f.0<..L..s.)+0 11))
W —l
(1+Rt)=(FE—) (f,(lr,,L,,s,)) 3.6.c.
1

Equation 3.6.d is the efficiency condition for optimal inventory accumulation.

The resource constraint is given by

l l

statics.)=l(1-v)(exp(<zu)12?H."°‘)i moth/00.71: =

ct + 12,,1—(1-8)1tt +st+1 +ust
The cash—in-advance constraint on consumption goods and the borrowing constraints are as
in Section I.

To examine the dynamics of the model the same solution strategy is employed as in
Section I. The responses of the interest rate, consumption, the real wage, and work effort
to a one standard deviation shock to the money supply are reported shown in Figures 3.6-
3.10. Note that the interest rate rises in response to a larger than anticipated monetary
injection. The reason for this is simple: the real rate of interest increases. The real rate of
interest is the amount of consumption goods the household is willing to give up this period

in exchange for an expected increase in consumption next period; that is,

111

BU¢(c,+1,l-Lt+1)/ Uc(c,,1-L,) . The increase in the real rate of interest occurs due to the
drop in consumption this period and the expected increase in consumption next period.
Given that the combination of this effect and the rise in expected inflation dominate the
non-Fisherian effect, the nominal interest rate increases. Thus, not even the
contemporaneous response of the interest rate is consistent with the time series evidence.
Before I try to amend this model, I will first investigate how the other variables behave in
response to the monetary shock.

The real wage in this model falls in response to the monetary shock. This occurs
because the increase in the interest rate shifts the labor demand curve to the left. Labor
supply shifts out because of the contemporaneous drop in consumption. Both of these
shifts cause the real wage to fall. Since equilibrium work effort goes up, it must be the
case the rightward shift of the labor supply curve exceeds the shift in labor demand. Since
work effort increases in the period of the shock, output must rise. Notice also that
consumption falls, and investment in capital goods does not change. This implies
inventory investment must rise by a higher percent than the increase in output. In fact,
inventory investment increases by over 40 percent. In the period after the shock, the
nominal interest rate rises again due to the real interest rate being above its steady state
level and due to the expected inflation effect. The increase in the nominal rate causes the
labor demand curve to shift even further back than in the initial period. Labor supply
shifts further to the left because consumption again falls. Because the shift in labor
demand exceeds the shift in labor supply, employment falls. In subsequent periods, the
interest rate falls shifting the labor demand curve back toward its steady state position.
Also, the fact that consumption is slowly rising causes the labor supply curve to shift

gradually back to it steady state position. The shiftings of these curves cause the real wage

112

to gradually return to its steady state level, and for employment to increase until it returns
to its steady state level.

Clearly, the addition of inventories does not improve the dynamic behavior of the
model. In fact, it makes the model worse. In the next section, I will add a credit good to

the model to try to remedy the deficiencies cited above.

Section III. Inventories and Credit Goods: Friedman (1968)

In this section of the paper, credit goods are added to the modelg. I add credit
goods for two reasons. First credit goods account for significant percent of consumption
purchases (see Cooley and Hansen (1995)). Second it is possible that in response to a
monetary shock consumption of the credit good and inventory investment both increase.
This could cause total consumption to increase and the addition to inventories may make
the effects of the monetary shock more persistent.

Adding credit goods changes the model in four ways. First, the utility function
needs to be modified to incorporate credit goods. Second, an additional efficiency
condition is added. Third the aggregate resource constraint needs to be modified. The
budget constraint gets modified to incorporate credit goods. Everything else in the model
is the same as in Section II.

The timing of the model is slightly different than the models in Sections 1 and II.

In this case after the savings decision is made and goods are produced, both consumption.

 

9 Again, these are credit goods as defined in Lucas and Stokey (1983). The best way to think of these credit
goods is that they are like purchasing goods on a credit card where no interest is owed if you pay-in-full at the
end of the period.

113

goods are purchased. The cash goods are paid for at the time of purchase. The credit
goods, on the other hand, are paid for at the end of the period when the household pools
its resources. The timing of the agents' actions are given on page 115.

The new utility function is given by

U(c,,,c2,,l - L,) =7lln(c,,) + 721n(c2,)+(l-71— 72)ln(l- L,) , 3.7

where cit is consumption of good i at time t (i=1,2 where on is the cash good and on is the
credit goodm), L, is labor supplied at time t, the time endowment is normalized to unity so

that l-Lt is leisure at time t. The household’s lifetime expected utility is given by

u =E020‘U(c,,,c,,,1-L,), 3.7:

1 =0
where 09(0,1).

The efficiency conditions are given by

Uc1(clt’02t31- Lt) _ EAL

 

 

 

 

 

3.8.a
UL(Clt,C2t,I-Lt) Pt
UC l-L UC is 9.,I'L_,
E1_]{ 1(CllacZI9 1)}: Et_1{ B “0171,qu ‘1)(1+Rt) 381)
Pt (1+Xt) Pt+1
BUc](Clt+l’c21+lsl' L711)
El-l{ :
3.8.c
[32 UC](clt+22C21+2al'I-IH2) A
E P f k ,L ,s + 1—5
1-1{(1+XH1) Pt+2 t( 1( 1 t t) ( ))

 

‘0 I assume that credit goods account for 7.5 percent of total expenditures on consmnption goods. This value
implies that in steady state the average propensity to save is roughly .05 which is consistent with time series
average in Baier 1990.

114

BU°1(clt+hczt+l’l ' L1H) _

 

 

 

 

E,{
Pl+l(l+xt)
3.8.d
2 UC (C +270 +291-L+) “
13.11;: ‘ " P" '2 P.1(f.(k..L..s.)+0—u»
( 1+1) t+2
Uc2(clt9c2t’1-Lt)}= Et{ [3 UCI(CIt+lac2t+l:]'Lt+l)(1+Rt)} 3..8€
Pt (1+X,) PM
—I
W ,.
(1+R,)=(P—‘] (f2(k,,L,,s,) 3.8.f.
t

The dynamics of this model are depicted in Figures 3. 10-3. 15. Not much has changed
from Section II in regard to the initial response of the variables. Notice, however, that the
nominal interest rate falls in the period after the shock. The nominal interest rate falls
because the of the expected price deflation“. Because the nominal rate falls, the labor
demand curve shifts to the right. The labor supply curve shifts to the left due to the
increase in consumption”. Since equilibrium work effort increases, the shift in labor
demand is greater than the shift in labor supply. In the following period, the nominal
interest rate remains below its steady state level due to prices again falling (consumption in
this period barely changes). Since the nominal interest is below the steady state level, the
labor demand curve will be everywhere to the right of the steady state level, but to the left
of the labor demand curve in the previous period. The labor supply curve does not move
much from the previous period because consumption is essentially unchanged. The shift in

labor demand exceeds the shift in labor supply since employment is above its steady state

 

” Prices will still be above their steady state level, but the drop in prices is enough to lower the nominal
interest rates.

‘2 Because consumption in this period is above the steady state level of consumption the labor supply curve will
lie everywhere to the right of the steady state labor supply curve.

115

Timin :

1. Households decide how much to allocate to purchase cash goods and to savings.

STATE OF THE WORLD IS REVEALED

2. Savings are deposited in the financial intermediary.

3. Firms borrow funds, hire labor and produce the consumption goods.

3‘

The shopper purchases the consumption goods. The cash goods are purchased using
cash. The credit goods obtained and the household pays for these goods at the end
of the period when the household reunites and pools its resources.

LII

. Firms repay their loans.

F"

Households reunite and pool their resources. These resources include the return on
savings, the residuals from the cash-in-advance constraints on consumption goods,
wage income, andprofits from the firms and intermediaries.

116

level. In subsequent periods, the nominal interest rate rises and consumption falls, the
former falling moves the labor demand curve back to it original position, and the latter
decreasing causes the labor supply to shift back to it original position.

An interpretation of this model is that a monetary injection that exceeds
household’s anticipated values affects the economy in a way that was described by
Friedman (1968). That is, an unanticipated increase in the money supply initially affects
goods prices more than nominal wages. In response, the real wage falls. Employment
increases because the higher prices reduce consumption which causes the labor supply
curve to shift to the right. After the initial impact of the shock, the effects are propagated
over time due to the increase in inventories and the price deflation. In addition in this
model, the interest rate falls below its steady state level for several periods following the
shock. This persistence effect on interest rates in response to an unanticipated increase in
the money supply process is also unique to this model”. Also, this model predicts the real

wage is procyclical after the initial monetary shock.

Section IV: Conclusion

In a general equilibrium model, this paper produces a response of output and
employment to a monetary innovation that is consistent with the story outlined by
Friedman (1968). What is more, the effects are persistent. That is, output and
employment remain above their steady state levels for several period’s following the Shock.
In the period following the shock, the nominal interest falls below its steady state level and
remains below its steady state level for four quarters. In addition to getting persistent

effects on output, employment and the interest rate, the model also predicts the real wage

 

'3 Christiano and Eichenbaum are able to get persistence by making it costly for agents to adjust their portfolio.
There is no such adjustment cost incorporated in this model.

117

will be procyclical and inventory investment will be the most volatile of all variables
examined. The main shortcoming of the model is that consumption lags the business cycle

rather than leading the cycle as the data suggests it does.

\ “WW-=1 i i i 1
Interest Rate /
. /
l
-02 ‘1 ,I —
‘1
l l l
5 10 15 20
time
Fig 3.2: Change in Output
I I l
0.1 A —
l \\
0.05 .4
l \
output / \
0 ‘r 'r i Ni”um-IN“? ‘r : e s
_0.0- L l I
5 10 15
time

0.l

118

I

/

Fig 3.1: Change in Interest Rate

 

 

 

I
a .
I

 

 

 

 

 

 

 

 

 

20

119

Fig 3.3:Change in Employment

 

 

 

 

 

 

0'2 I I I
0.15 It "
I I
I '1
l
l
I ‘1
0.1 j 11 _
l 1
Employment I 1‘
I l
0.05 l k _
f
O 1 ! MM , .
l l I
5 10 15 20
time

Fig 3.4: Change in Consumption

I I l
/\
0.1 . / \

 

 

-y‘.‘

f‘o-d’JI— v . . § i r i
i

0

Consumption /
l l

-01 1/
l 1 l l 1

time

 

 

 

120

 

Fig 3.5: Change in Output
I F l I I l I
0.1
l
l
l
0<

output

,,.,.o—--.-.<>-mm.p-o --------- 6 ------- .4)
1 f/
l
l
\ /
-0.l

 

 

 

 

 

l l l I l 1
2 4 6 s 10 12 14
time
Fig 3.6:Change in Interest Rate
l l I I I I I
0.2 -—l
0 l _
Interest Rate
0< ‘ “WW-Wt
_0,1 1 l l I 1 l l
2 4 6 s 10 12
time

 

 

121

Fig 3.7: Change in Employment

 

 

 

 

 

 

 

 

 

I I I T I l I
i
0.1 \ _.
‘1
0< \ ”we :5 e e e
Employment i
1, -
20.2 L
l l l l l l J
2 4 6 8 10 12 14
time
Fig 3.8: Change in Consumption
I I I H l I I
0.04 _
0.02 "
ohm-me --------- e --------- e --------- now-“'9 ..... enm—e—«mew-«ti
Consumption
.00 _
~(yo l l l l l l l l
2 4 6 8 10 12 14

122

Fig 3.9: Change in Inventories

 

40 I I I I I I r
'I
20 . / ‘ J
i
I I
Inventories / \
04f» ------- o --------- o» --------- o --------- d “ gm.» --------- o --------- o --------- o ---------- o -------- 4}

—2O

 

 

 

123

Fig 3.10: Change in Output

0'04 I I I I I I

 

0.02 I

 

 

 

Output /
’ “new.
00- ----- o -------- o -------- o -------- a “Om-=0
-007 l l 1 I 1 1 I
2 4 6 8 10 12 14

Fig 3.11: Change in Interest Rate

 

 

I I I I T I '
0.2 . _.
/I
0.1 . l \ —
Interest Rate ‘\
04L -------- O -------- 0 """" 9 """" AflW‘wv—
9":—

 

 

 

_07 I I I I I I I

 

124

Fig 3.12: Change in Investment

 

 

 

 

 

 

 

 

0'02 I I I I I I I
0.01 _
investment /
04 fl*w'M""’W}
.001 I I I I I I
2 4 6 8 10 12 14
time
Fig 3.13: Change in Employment
I I T I I I I
0.06 _
I
I
I
0.04 _.
Employment
0.02 _
I
I RX
“new... __
0<p-.-+----o--—o~-~— "6 “'1’
_0,07 I I I I I I I
2 4 6 8 IO 12 I4

125

Fig 3.14: Change in Consumption

 

 

 

 

 

0'2 I 1 I 1 I I I
0.1 - _
I
v ...... 9 ........ 9 ....... ¢ ........ !/ N.h¢h.+‘—"4>
Consumption /
/
—0. —
I I l I I I I
2 4 6 8 10 12 14
time
Fig 3.15: Change in Inventories
I F gr I I I I
40 .

/ I _
1 \

20 . /
Inventories ,1

04M

pf.”
MM

 

 

IQ
—
1—
_
—
.—
~—
—

 

In a series of papers, Christiano and Eichenbaum (l992a,b) and Christiano,
Eichenbaum and Evans (l994a,b) (hereafter CEE) use VAR models to search empirically for
the existence of liquidity effects. Briefly summarizing their results, under their identification
scheme, they find liquidity effects do exist and can last for several periods. In this chapter, the
identification scheme employed by CEE is discussed and the VAR models are reestimated using
quarterly data from 1959. 1-1993.4. In order to choose among the competing models, impulse
response functions are constructed and the models are judged on the criterion outlined in
Eichenbaum (1995). In addition, an alternative detrending procedure is employed and the
models are reestimated. The impulse response functions from these models are also evaluated
according to Eichenbaum’s criterion. If the impulse response functions of these models are
qualitatively similar using different detrending techniques and the models do not have
“incredible” predictions, then more faith can be placed in CEE's empirical results.

In Section 1.1, Eichenbaum’s method for evaluating just identified VAR models is
reviewed. The models of CEE are also reestimated and evaluated according to Eichenbaum’s
criterion. In Section 1.2, the variables are made stationary by differencing the data rather than
passing the data through the Hodrick-Prescott filter as CEE did. In addition to these models
being evaluated according to Eichenbaum’s criterion, the impulse response functions of these
models are compared and contrasted with the impulse response functions of the HP filtered
models.

Section II examines other shocks in the CEE specification. The impulse response

functions are compared to what theory would predict about these different types of shocks. In

126

127

addition, the impulse response functions are compared and contrasted with related empirical
papers.

Section III concludes.

W

In order to verify or refute an empirical model or the claims of a theoretical model, the
models must pass a battery of tests. It is not unusual to require that a theoretical model be
consistent with the data on all dimensions, also it is typically required that the empirical results
come from a system of economic or reduced form equations that arise from some “well-
specified” theoretical model. The problem with the former is that a theoretical model is a
simplified version of reality and therefore is likely to be misspecified in some way or another.
The problem with the latter is that it is possible to work backward from any empirical results to
some theoretical model. More to the point, there is an identification problem associated with
most empirical models and the identifying assumptions that are required to "disentangle" the
different shocks are seldom innocuous. The problem of blending theory and econometrics is not
particular to macroeconomics. However, it seems to be more evident in this branch of the
science. Given this, Eichenbaum (1995) addresses this problem and suggests guidelines for
theorists and macroeconometricians to follow. For the macrotheorist, Eichenbaum cites Lucas
(1980) as the basis for evaluating models. That is, suppose it is known how certain economic
variables react to a certain type of shock, then, at a minimum, the responses of the variables to
a shock in the theorists' abstract economy should look like the responses of the variables in the
real economy to the same type of shock. The more a model can answer simple questions
correctly the more faith that can be placed in the model’s ability to answer more difficult

questions. To apply this type of test to an artificially constructed economy, theorists need to

128

know how the economy responds to certain types of shocks. Additionally , the theorists
require some type of metric to compare the results of their models to how the actual economy
responds to the same type of stimulus. To quantify how the economy responds to "simple"
shocks is one of the jobs of the econometrician.

In attempting to gauge qualitatively and quantitatively the effects of different types of
shocks, Eichenbaum states the econometrician must first decide which variables to include in
her model. That is, using Eichenbaum’s example, if the researcher wants to investigate how the
economy responds to increases in the money supply caused by actions taken by the monetary
authority, higher order monetary aggregates (say M1 or M2) may be inappropriate. These
higher order aggregates, Eichenbaum argues, may be inappropriate because they also capture
changes in the money supply due to actions taken by financial institutions and demand side
factors. Narrower monetary aggregates, such as the monetary base or nonborrowed reserves,
are likely to be less contaminated.

In addition to the choosing the “right” variables to include, Eichenbaum states that if
different models, employing different identifying restrictions, yield similar answers to a
particular question then some guidance is given for the construction of theoretical models. The
theorist's model should be consistent with this " robust" empirical finding. Therefore, one way
to aid the macrotheorist is for the macroeconometricain to conduct sensitivity analysis by
employing different identifying restrictions and see how sensitive the results are to different
econometric models.

Another check of the model Eichenbaum suggests is for the econometrician to ask: are
the responses of the variables to innovations “incredible”? For example, suppose a shock,
causes output to rise for several periods and the model predicts that the unemployment rate also

increases. This model is discarded because of its incredible predictionnsince in reality

129

unemployment is countercyclical not procyclical.

Given Eichenbaum’s guidelines for setting up econometric models and determining the
plausibility of the model’s predictions, I reexamine the models studied in CEE using the
guidelines given above. Before the CEE models are estimated and examined, I will briefly
summarize the results of similar work by Christiano and Eichenbaum (1992a,b). The purpose
of their study is to quantify the effects on interest rates of an unanticipated increase in the
money supply. Christiano and Eichenbaum use a four variable VAR model. The data are
quarterly observations from 1960.1 to 1993.4. The variables used are the federal funds rate,
the natural logarithm of gross domestic product (GDP), the natural logarithm of the GDP
deflator (price), and the natural logarithm of a monetary aggregate (M). Among the monetary
aggregates experimented with were the natural logarithm of the monetary base (Mbase) and the
natural logarithm of nonborrowed reserves (NBRC). They argue that these monetary
aggregates seem to be the most appropriate in attempting to quantify the effects of unanticipated
increases in the money supply since these aggregates are not as “contaminated” by other supply
and demand disturbances as higher order monetary aggregates. Christiano and Eichenbaum’s
identification scheme employs the assumption that unanticipated changes in the monetary policy
rule are some orthogonalized component of the of the monetary aggregate. That is, they use
the Wold causal ordering to identify unanticipated money supply shocks. For example, the
following Wold causal {M, Fedfim, GDP, Prices} implies the monetary authority’s feedback
rule does not include contemporaneous values of the federal funds rate, the price level, or
GDP, whereas an ordering {Fedfun, Price, M, GDP} implies that the monetary authority’s
feedback rule includes the contemporaneous values of the federal funds rate and the price level
but it does not respond to the contemporaneous value of GDP. Christiano and Eichenbaum use

four lags of the variables to remove the serial correlation from the residuals.

130

In order to make the system stationary, Christiano and Eichenbaum pass the data
through the HP filter before estimating their model. In addition to this stationary inducing
transformation, they also report the results of their model when the variables are made
stationary by removing a piecewise-linear trend, and when the variables are made stationary by
diffferencing the data until they are stationary. Christiano and Eichenbaum find that their
results are qualitatively similar for the different stationary inducing transformations. Using the
ordering {Mbase, Fedfun, GDP, Price} they find that an unanticipated increase in the money
supply process leads to a contemporaneous rise in the federal funds rate. The federal funds
rate remains “high” for several periods following the shock. Therefore, when unanticipated
changes in the monetary base are used as the unexpected component of the money supply
process the liquidity effect is not present in the data. That is, unanticipated increases in the
money supply process increase the federal funds rate rather than lowering it.

Christiano and Eichenbaum argue that orthogonalized components of the monetary base
may not be the appropriate variable to use as the unexpected component of monetary policy.
Their reason for this is as follows: liquidity effects are believed to arise through the purchase
of securities by the Federal Open Market Committee (FOMC). The decisions of the FOMC
are made largely independent of the amount of borrowed reserves. Therefore, the appropriate
measure of unanticipated policy should not include the transactions carried out at the discount
window. Because of this, Christiano and Eichenbaum argue that the unanticipated component
of nonborrowed reserves is a better measure of unexpected changes in monetary policy.

Using the ordering {NBRC, Fedfun, GDP, Price}, they find that the interest rate
remains below its pre-shock level for 16 quarters. Thus, Christiano and Eichenbaum show that
by choosing a narrower definition of money (NBRC) unanticipated increases in the money

supply process lower interest rates. In addition to these findings, Christiano and Eichenbaum

131

investigate a different type of unexpected change in the monetary authority’s policy. Following
Sims (1991) and Bernanke and Blinder (1990), they argue that innovations in the federal funds
rate may be an appropriate measure of unexpected monetary policy actions. This is true if the
monetary authority has been pursuing an interest rate target. Empirically, they find that an
unexpected increase in the federal funds rate is accompanied by a reduction in nonborrowed
reserves and a drop in output. A reasonable interpretation is as follows. In order to raise
interest rates, the FOMC sells bonds in the open market, thereby reducing nonborrowed
reserves and the supply of loanable funds. In response to the reduction in loanable funds,
interest rates rise. Output falls in response to the higher interest rates.

CEE (1994 a,b) build on the work of Christiano and Eichenbaum. They expand the list
of variables in the VAR model to include the log of commodity pieces (PCOM), the
unemployment rate (UNEM) and the log of total reserves (TR). CEE work exclusively with
data that has been detrended by passing the data through the HP filter. Figures 4.1 - 4.7 show
the actual series plotted against the HP—trend. To denote a HP detrended series X a “C” will
be placed in front of that series so it will read CX and a T will be placed in front of the variable
to denote the HP-trend. The data used are quarterly data from 1959.1-1993.4. Figures 4.8 and
4.9 show the detrended federal funds rate plotted against detrended nonborrowed reserves
(Figure 4.8) and plotted against the detrended monetary base (Figure 4.9) along with the
contemporaneous correlations. Note that the federal funds rate is negatively correlated with
nonborrowed reserves and nearly uncorrelated with the monetary base. Also, the cyclical
component of nonborrowed reserves is much more volatile than the cyclical component of the
monetary base.

Eichenbaum’s guidelines suggest that the variables the researcher chooses should

generate the shocks that the researcher wants to investigate. Here interest lies in unexpected

132

monetary policy shocks. Given the narrow definitions of money and the interest rate used,
CEE’s choice of variables seems reasonable. Another point made by Eichenbaum is that the
responses of variables to shocks should not be incredible. A few potentially incredible
responses are worth discussing. First, unanticipated increases in nonborrowed reserves should
not lead to a reduction in total reserves. It seems unlikely that as a result of financial
institutions receiving more funds than expected from the monetary authority, they would end up
holding fewer funds. Also, suppose in response to an unanticipated increase in the money
supply the unemployment rate and output increases. Given Okun’s Law this prediction seems
“incredible". Finally, suppose in response to an unanticipated increase in the money supply,
interest rates fall, output increases and prices fall. This price deflation is not inconsistent with
some theoretical models. For this response to be plausible the interest rate must affect the
supply side more than the demand side. Thus, a temporary price deflation would not be
"incredible". However, most economists believe money is neutral in the long run. Therefore,
it should be the case that after a period of time prices would rise. A model that did not predict
this would also be discarded.

CEE achieve identification by the Wold causal ordering. This identification scheme
leaves open the question: Which ordering is correct“? Before proceeding, 1 will describe why
commodity prices were included in the model. CEE’s reasoning for the inclusion of the
commodity prices is as follows. CEE assert the Federal Reserve has likely reacted to
movements in commodity prices. In particular, CEE claim the Federal Reserve has responded

to changes in the price of crude oil. As a result of including commodity prices in the Federal

 

1 CEE only report results when unanticipated increases in the money supply lower the federal funds rate.

It should be noted that this result is not robust to all specifications. Typically, if the federal funds rate is
placed before the monetary aggregate an unanticipated increase in the money supply process causes interest
rate to increase. CEE discard these models based on the “incredible” responses of other variables in the
system.

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Reserve’s reaction function, the “price puzzle” (as labeled by Sims (1991)) vanishes. That is,
Sims (1991) found that in response to monetary policy innovations prices responded in a
manner that was counterintuitive. Sims also found that in response to unanticipated increases in
the federal funds rate, output fell for several periods and prices rose for several periods. One
would expect prices to fall in response to a shock that causes a sustained reduction in output.
This finding was peculiar enough that Sims labeled this fining as the “price puzzle”.

To illustrate how the price puzzle disappears with the inclusion of commodity prices,
consider the a six variable VAR without commodity prices. One of CEE's orderings excluded
commodity prices. The ordering of the variables CEE used is as follows {CGDP, CPRICE,
CNBRC, CFEDFUN, CTR, CUNEM}. The unanticipated component of the money supply
process is the orthogonalized component of nonborrowed reserves. The response of the
variables to a one standard deviation shock to the money supply process is depicted in Figure
4.10 row 3. First, notice that in response to the monetary innovation the federal funds rate
falls by 33 basis points and total reserves increase. Both of these responses are significantly
different from zero. In response to the increase in nonborrowed reserves, there is a price
deflation that lasts two and a half years. This response, however, is not significantly different
from zero. It seems that prices should rise in response to an increase in the money supply. The
point estimates, however, indicate prices will fall for several periods. The response of prices in
this model to a monetary innovation is not consistent with conventional wisdom.

Next consider the dynamic response of variables in a seven variable VAR model
employed by CEE that includes commodity prices. The ordering of the variables is {CGDP,
CPRICE, CPCOM, CNBRC, CFEDFUN, CTR, CUNEM}. Figure 4.11 row 4 depicts. the
response of the variables to an unanticipated increase in the money supply process. The

response of the variables given this ordering seems more plausible. In particular, an

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unanticipated increase in the money supply still lowers the federal funds rate (by 18 basis
points). The point estimates of output show that output increases in response to the monetary
innovation. However, these point estimates are not significantly different from zero. Prices
rise in the period after the shock, but these responses are not significant. The unemployment
rate, however, increases for two periods before falling. This seems peculiar especially since
the point estimates of output indicate output is rising. I think this prediction of output and
unemployment moving in the same direction is peculiar enough to discard the model on the
grounds that it gives incredible predictions. The rest of this sub-section experiments with
different orderings to seek plausible models of the effects of unanticipated increases in the
money supply.

For brevity, I investigate three other orderings used by CEE. I first place CNBRC
first so that the ordering is given by {CNBRC, CGDP, CPRICE, CPCOM, CFEDFUN, CTR,
CUNEM}. This ordering implies that the contemporaneous values of all variables are excluded
from the monetary authority’s feedback rule and the unanticipated increases in the money
supply affect all variables in the current period. Figure 4.12 row 3 depicts the response of the
variables in the system to an innovation in the money supply process. In this case, the federal
funds rate falls by nearly 27 basis points in the period of the innovation. The response shows
that interest rates will remain significantly below their pre-shock level for three quarters.
Output falls while the unemployment rate increases. The response of prices is not significant.
Is this plausible? Consider an lS-LM model with a Lucas AS curve. Suppose there was an
unanticipated increase in the money supply process. If prices do not immediately adjust to keep
real money balances unchanged, interest rates will fall, shifting out the LM curve. The .
aggregate demand shifts to the right because of the shift in the LM curve. Thus, output

increases and, in time, prices rise. This version of the IS-LM model is not consistent with the

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impulse response functions discussed above. Consider the prototype monetized RBC model.
An unanticipated increase in the money supply acts as a tax on labor income so workers supply
fewer hours and employment and output fall. In the monetized business cycle model, prices
increase for two reasons. The first is because the increase in the money supply puts upward
pressure on prices. The second is due to the reduction in output. Interest rates, in this model,
also increase. Now consider the limited participation models of Lucas (1990) and

Fuerst( 1992). In these models, unanticipated increases in the money supply lower interest
rates. Output and employment increase. Therefore, the empirical results of this model are not
consistent with any of the standard models that are “well equipped” to discuss the affects of
monetary policy shocks.

The next ordering experimented with places unemployment first. That is, the ordering
{CUNEM, CGDP, CPCOM, CPRICE, CNBRC, CFEDFUN, CTR}. This implies that the
money rule responds to the contemporaneous values of the unemployment rate, output, and
prices. Also, innovations in the money supply process only affect the contemporaneous values
of total reserves and interest rates. The results of this experiment are depicted in Figure 4.13
row 5. Using this ordering, an unanticipated increase in the money supply significantly lowers
the interest rate for two quarters. Initially interest rates fall by 15 basis points and remain
below their pre-shock level in the subsequent period. Thus the liquidity effect lasts roughly two
quarters. In periods following the innovation, the point estimates show that the unemployment
rate falls and output increases. More importantly, this ordering yields results that are
consistent with the limited participation models and with IS-LM/AS-AD models. However, the
point estimates of the unemployment rate, output and prices are not significant.

The last ordering investigated puts the federal funds rate before nonborrowed reserves.

The ordering used with this specification is {CGDP, CPRICE, CCOM, CFEDFUN, CNBRC,

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CTR, CUNEM}. The impulse response functions using this ordering are depicted in Figure
4.14 row 5. With this identification scheme, unanticipated increases in the money supply cause
output and prices to rise in the period after the shock. Again it is the case that these responses
are not significant. Interest rates fall by almost seven basis points. However, in the period of
the shock the unemployment rate increases. This increase is significantly different from zero.
Also the point estimates show that the unemployment rate will increase for three quarters after
the shock. The fact that output and the unemployment rate move in the same direction for
several periods casts doubt on the plausibility of this model.

In sum, when orthogonalized components of nonborrowed reserves are considered as
the unanticipated component of monetary policy, the ordering that is “most” consistent with
existing theoretical models of unanticipated increases in the money supply is {CUNEM,
CGDP, CCOM, CPRICE, CNBRC, CFEDFUN, CTR}. The point estimates of this model are
consistent with a version of the IS-LM/AS-AD model and with limited participation models.
Other specifications investigated were discarded due to implausible implications of the models.

The next set of experiments conducted by CEE investigates the effects of unanticipated
changes in the federal funds rate. They pursue this strategy because Bernanke (1990),
McCallum (1983), and Sims (1991) have argued that for the majority of the post World War 11
period the Federal Reserve has been targeting the federal funds rate. Therefore, CEE claim
that unanticipated changes in the federal funds rate are good candidates for innovations in
monetary policy. CEE use the federal funds rate as the interest rate in their model because the
Federal Reserve has more control over this interest rate than most other interest rates where
other actors affect the demand and supply curves.

I consider three different orderings of the seven variable VAR. In all cases the

orthogonalized component of federal funds rate is the unexpected component of monetary

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policy. Most treatments in intermediate macroeconomics textbooks state that an unanticipated
increases in interest rates due to contractionary monetary policy cause output and prices to fall
and the unemployment rate to increase. The limited participation models also predict that
output would fall and unemployment would rise in response to an unanticipated monetary
contraction that leads to higher interest rates. Monetized RBC models predict that an
unanticipated increase in the interest rate is due to increases in the money supply. Employment
and output fall in response to the increase in the money supply that drives up interest rates.

The first ordering considered is {CGDP, CPRICE, CCOM, CFEDFUN, CNBRC,
CTR, CUNEM}. The dynamic responses of the variables to an unanticipated increase in the
federal funds rate are reported in Figures 4.15 row 4. Note that the unemployment rate falls
initially before rising in subsequent periods. Output falls and the reduction in output is not
significant. In fact, none of the point estimates, with the exception of the federal funds rate, are
significant. Notice that prices rise in response to a monetary contraction. This is not consistent
with either the IS-LM/AD-AS model or the limited participation models. Because of this, I
discard this model because of its incredible predictions.

The next ordering places the monetary policy rule first. The dynamic response of the
variables to an innovation in the federal funds rate is depicted in Figures 4.16 row 1. Using the
ordering {CFEDFUN, CGDP, CPRICE, CCOM, CNBRC, CTR, CUNEM}, it is easy to see
that the impulse response functions are implausible. That is, the model predicts that
nonborrowed reserves fall and total reserves increase. If the unanticipated increase in interest
rates is caused by the FOMC selling bonds to financial institutions then it seems reasonable to
expect to see both nonborrowed reserves and total reserves falling. Note, that this model .
predicts total reserves and nonborrowed reserves move in opposite directions. This could

conceivably occur if the Fed held discount rate constant the federal funds rate increased. If this

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occurred then the level of borrowings may increase so that total reserves increased and
nonborrowed reserves fell. However, the unemployment rate and output move in the same
direction. This finding is not consistent with any of the theoretical models of monetary
innovations discussed above.

The next ordering investigated is given by {CUNEM, CGDP, CPRICE, CCOM,
CFEDFUN, CNBRC, CTR}. Figure 4.17 row 5 depicts the impulse responses of an
innovation to the federal funds rate. The point estimates show that the unemployment rate
increases, output falls and nonborrowed reserves fall. However, total reserves rise in response
to an unanticipated increase in the interest rate. As stated above, this could conceivably happen

if the discount rate does not change and the federal funds rate increased by a great deal.

5' II'CEEIIII °IE'Efi S . D

CEE make the data in their VAR models stationarity by passing the data through the
HP filter. In this section, a different stationary inducing transformation is employed. More
specifically, the data is differenced until it is integrated of order zero. Using these transformed
series, the VAR models in the previous section are re-estimated and the impulse response
functions are evaluated using Eichenbaum’s criteria. Unit root tests were done on all variables.
The results are reported in Appendix 4.1. Using the Augmented Dickey Fuller tests, it is

shown that the data are 1(1) with the only exception being prices which are [(2).

Before the VAR models are estimated it is instructive to look at HP filtered series
plotted against the difference data. Figures 4.18—4.25 depict the difference data (denoted with a
D) and the HP filtered data (denoted as before with a C). Also, the correlation coefficients for
each series is given. Notice in all cases that the HP filtered data and the difference data are

positively correlated. The correlation coefficients range from as high as .31 for the federal

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funds rate and as low as .11 for prices.

As before, the first set of orderings in the VAR specification is used to examine the
effects of unanticipated changes in the monetary policy when the unanticipated change is
defined to be the orthogonalized component of non-borrowed reserves. Again five lags of each
variable are used to remove the serial correlation from the residuals. The first ordering is
{DGDP, D2PRICE, DCOM, DNBRC, DFEDFUN, DTR, DUNEM}. This ordering implies
the money supply rule depends on the contemporaneous values of the change in GDP, the
change in inflation, and the change in commodity prices. In addition, unanticipated changes in
the money supply will not affect these variables in the current period. Figure 4.26 depicts the
response of the variables to a one standard deviation shock to DNBRC. In this case, the
federal funds rate falls by 23 basis points and total reserves increase. The change in output and
inflation increase with a lag, but these point estimates are not significant. Thus the behavior of
the variables to a shock to DNBRC is similar to the model with HP filtered data. As in the
VAR model with HP filtered data, the unemployment rate increases. Again, this finding seems
peculiar especially since point estimates indicate that GDP increases.

The next ordering experimented with is {DNBRC, DGDP, D2PRICE, DFEDFUN,
DTR, DUNEM}. Using this ordering unanticipated increases in the money supply (innovations
to DNBRC) will affect all variables contemporaneously. In this case the interest rate falls by
29 basis points (compared to 27 basis points in the model with HP filtered data), the
unemployment rate increases and output falls (as in the model with HP filtered data). This
finding seems implausible. Certainly the three theoretical models discussed above do not yield
this prediction. Therefore, I discard this model due to its incredible predictions. The impulse
response functions for this specification are depicted in Figure 4.27.

The ordering that was most “successful” concerning the effects of unanticipated

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increases in the money supply with HP filtered data is also the most consistent with differenced
data. The dynamic response to an unanticipated monetary shock is depicted in Figure 4.28. An
innovation to DNBRC with the ordering {DUNEM, DGPD, D2PRICE, DCON, DNBRC,
DFEDFUN, DTR} causes the federal funds rate to fall by 20 basis points. In the period
following the shock, the unemployment rate falls, output, inflation and commodity prices
increase. Thus, the responses of the variables in the model with difference stationary data
looks qualitatively similar to the responses with HP filtered data. However, only the point
estimates of the federal funds rate are significant.

The last ordering I investigated puts the change in the Federal funds rate before the
change in nonborrowed reserves. With the ordering, the federal funds rate falls by almost 12
basis points in the period following the shock. This point estimate is not significantly different
from zero. Output, inflation and commodity prices all rise, as does the unemployment rate.
These point estimates are also not significant. Therefore, given the point estimates of the
responses of the change in output, the change in the unemployment rate behaves in a manner
that is “incredible”. This ordering using difference stationary data is also qualitatively similar
to HP filtered data. In fact, all the results are very similar to the HP filtered results. These
results are depicted in Figure 4.29.

Instead of the orthogonalized component of the change in nonborrowed reserves being
interpreted as an unanticipated change is monetary policy, the orthogonalized component of the
change in the federal funds rule is now considered the unanticipated change in monetary policy.
The same orderings will be investigated as when orthogonalized components of the HP filtered
federal funds rate were considered as unanticipated monetary policy actions.

The first ordering is {DGDP, D2PRICE, DPCOM, DFEDFUN, DNBRC, DTR,

DUNEM}. The response of the variables in the system to a one standard deviation increase in

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the change in the federal funds rate is depicted in Figure 4.30. As in the model with the HP
filtered data, the unemployment rate and nonborrowed reserves initially fall. Since output
proceeds the federal funds rate it will not respond to contemporaneous shocks to the federal
funds rate. In the period following the shock, output falls and continues to fall in subsequent
periods. These point estimates are not significant. The point estimates also show that total
reserves initially rise before falling. The findings in this model are not at all consistent with
conventional wisdom. That is, if the Federal Reserve wanted to raise interest rates we would
expect them to sell bonds thus decreasing total reserves. With this ordering, the exact opposite
happensntotal reserves increase.

If the federal funds rate is placed first, the ordering is {DFEDFUN, DGDP, D2PRICE,
DPCOM, DNBRC, DTR, DUNEM}. Then the response of the variables to an unanticipated
change in the federal funds rate is quantitatively similar to the case when HP filter was used.
As with the model with HP filter data, output and employment respond in a manner that is
“incredible”. That is, output increases and unemployment falls. The impulse response
functions are depicted in Figure 4.31.

Finally when DNBRC is placed before the change in the federal funds rate and the
ordering is given by {DGDP, D2PRICE, DPCOM, DNBRC, DFEDFUN, DTR, DUNEM}.
An innovation to the change in the federal funds rate results in responses that are not all
consistent with conventional wisdom. In particular, GDP increases, unemployment falls, non-
borrowed reserves and total reserves increase and inflation increases. This response is depicted

in Figure 4.32.

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CEE only report the responses of the variables in their VAR model to what they claim
are monetary policy innovations. If their identification scheme is correct then their findings
indicate that unanticipated increases in the money supply lower interest rates and may increase
output. But how do we know if their identification scheme is correct? One way to check their
model is to see how the variables respond to other types of shocks in the system. In particular
for the HP detrended data, I focus on three additional shocks. They are shocks to the cyclical
component of GDP, the unemployment rate, and total reserves. For the differenced data, I
investigate additional shocks as well. If the responses of these variables are credible then CEE
may have identified monetary policy innovations. The idea employed here is to apply Lucas’
criteria for judging a model. Can the model provide adequate answers to simple questions, that
is, are the responses of variables to other shocks in the model credible? If so, then more weight
can be placed on the model’s ability to answer more difficult questions (how does the economy
respond to monetary innovations).

As stated above, 1 consider the effects of innovations to the cyclical component of
GDP, the unemployment rate, and total reserves for the HP filtered data. Because the effects on
the variables differ depending on the method used to detrend the variables, the remainder of
this section proceeds as follows. In Section 11.1, the HP filtered data is analyzed. In Section
11.2 the difference stationary is analyzed. In these subsections, 1 first discuss the effects of these
shocks in terms of what theory would predict, then I compare the prediction to the impulse

response functions for the different shocks. Section 11.3 concludes.

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Seetlonll

Detrending the data using the HP—filter allegedly removes the estimated long-run trend
from the variables. What remains after the detrending are the estimated cyclical components of
the data. Therefore, the shocks to CGDP, CUNEM, and CTR should be thought of as
transitory shocks to GDP, the unemployment rate, and total reserves respectively. Given that
these shocks are transitory, how would the variables in the system respond to each of these
shocks? 1 will discuss each in turn.

Suppose there is a transitory shock that temporally raises GDP for some time, say, a
positive technology shock. This positive technology shock would increase the marginal product
of labor causing the labor demand curve to shift outward. This would cause an increase in
employment, and most likely a reduction in the unemployment rate. If this shock were
persistent then firms would increase investment since the marginal product of capital would
also be higher. Since the shock is temporary, household’s consumption should not change too
much. The increase in the supply of output and the increase in the demand for goods due to an
increase in investment will have an ambiguous effect on the interest rate. If the increase in the
supply of goods is greater (less) than the increase in the demand for goods the real interest rate
will fall (rise) (see Barro (1994) p. 231-234). If the real interest rate increases it is likely that
banks will lend out more funds. The increase in loans implies banks are drawing down their
excess reserves. In sum, a positive technology shock to GDP should decrease the
unemployment rate, interest rates should rise and total reserves should fall as banks are more
willing to loan funds out due to the higher real interest rate. However, this is not the only Story
for these responses. Another plausible story is that there was an aggregate demand shock and

there is some nominal rigidity in the model so that the aggregate supply curve is upward

144

sloping. Given the identification scheme, there is no way to delineate between a transitory
supply shocks and aggregate demand shocks.

Figure 4.11 row 1 depicts the response of the variables to an innovation to CGDP when
CGDP is placed first in the ordering. Note the unemployment rate, the interest rate and
nonborrowed reserves all fall. The point estimates indicate that total reserves fall. However,
this point estimate is not significantly different from zero. Figure 4.12 row 2 depicts the results
to an innovation in the cyclical component of GDP when the ordering is given by {CNBRC,
CGDP, CPRICE, CCOM, CFEDFUN, CTR, CUNEM}. In this case, the unemployment rate
falls, the interest rate increases and the point estimates are significantly different from zero.
Total reserves initially rise before falling. The point estimate of the cyclical component of total
reserves, however, is not significantly different from zero. Neither of the point estimates for
CPRICE' and CCOM is significant.

When the ordering is given by {CUNEM, CGDP, CPRICE, CCOM, CNBRC,
CFEDFUN, CTR}, an innovation to the cyclical component of GDP, only the response of
CGPD is significantly different from zero. The point estimate of the CFEDFUN shows that the
cyclical component of the federal funds rate will be above its pre—shock level for two years.
These responses are depicted in Figure 4.13 row 2.

Figure 4.14 row 1 shows the responses of the variables when the ordering is given by
{CGDP, CPRICE, CCOM, CFEDFUN, CNBRC, CTR, CUNEM}. These impulses indicate
that CUNEM falls. In addition to the fall in CUNEM, CCOM and CFEDFUN increase. The
point estimates of these variables are significantly different from zero. CCOM may increase as
the increase in demand for investment goods increases the prices of these goods. Also, the
interest rate will increase if firms attempt to borrow more funds to purchase investment goods.

Figure 4.15 row 2 and Figure 4.16 row 2 depicts the response of the variables to a

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shock to CGDP when the ordering is given by {CFEDFUN, CGDP, CPRICE, CCOM,
CNBRC, CTR, CUNEM} and { CUNEM, CGDP, CPRICE, CCOM, CFEDFUN, CNBRC,
CTR}, respectively. In both cases, the responses of the variables are consistent with a positive
transitory technology shock or a shock to aggregate demand.

The next shock investigated is a shock to the cyclical component of the unemployment
rate. Theoretically, a transitory shock to the unemployment rate should affect variables much
like a negative technology shock. That is a shock that increases the unemployment rate should
lower output and put downward pressure on interest rates and prices. According to row 7 in
Figures 4.11, 4.12, 4.14, and 4.15, none of the responses to a shock to CUNEM are
significantly different from zero. Thus, these orderings provide little insight. However, it is
possible that a shock to the unemployment rate has completely different effects. Consider a
shock to labor force participation where more people decide to look for work, but there is no
increase in the number of people who find jobs. For example, an increase in individuals
looking for work in the summer because school is no longer in sessionz. In this case the effects
from this type of shock may be small. When CUNEM is placed first in the ordering as is the
case in Figures 4.13 and 4.16, an innovation to CUNEM decreases output, commodity prices
and interest rates. These variables are all significantly different from zero. These results seem
plausible. A possible story behind these responses is in response to a shock to the
unemployment rate that causes output to fall, firms will produce less and demand fewer inputs.
This will lower the demand for inputs and lower prices. In addition, firms will demand fewer
loanable funds and the interest rate will fall. If the Fed increases the money supply in response
to the negative shock, nonborrowed reserves and total reserves will increase and interest rates

will fall even farther.

 

2 1 thank Robert Rasche for making me aware of this point.

146 .

The last shock I investigate is a shock to total reserves. One possible story is that in the
absence of any actions by the monetary authority total reserves would increase if banks decide
to make fewer loans at all interest rates. That is, if the reserve to deposit ratio increases. If
the reserve to deposit ratio increased, total reserves initially would increase. The money
supply would eventually fall since an increase in the banks desire to lend funds would decrease
the money multiplier. This would have the effect of driving up the real rate of interest. The
increased interest rates would lower consumption and investment. Also as a result of the higher
interest rates, output would fall and the unemployment rate would also increase. Prices would
fall in response to the shocks. As time passes, output would increase and the unemployment
rate would fall. Looking at Figures 4.11, 4.12, 4.14, 4.15 row 6 and Figures 4.13 and 4.17
row 7, the response of these variables to an innovation in total reserves is consistent with this
story.

In sum, these orderings are consistent with the conventional wisdom about how the
economy responds to transitory shocks to GDP, the unemployment rate, and total reserves.
When unemployment is placed first in the ordering, a transitory shock to the unemployment
rate leads to responses that are significantly different from zero. Recall in Section I, this
ordering yielded the most credible results. However, even if this is the correct ordering, the
liquidity effect is smallest in this case (interest rates fall by only 8 basis points) and the effects

on output and the unemployment rate are not significantly different from zero.

In this section, I investigate the total effect on the seven variables to different shocks in

the system. These responses are depicted in Figures 4.32 to 4.40. As in the last section, the

147

responses of the variables are compared to what different theoretical models would predict.
Also, given the advances in time series econometrics, estimating small scale VAR models and
reporting the results of the impulse response functions to transitory and permanent shocks has
been somewhat of a growth industry. Because of this, there is a growing body of literature that
documents how economic variables respond to different permanent and transitory shocks. The
impulse response functions of the sum of the effects in the difference stationary version of the
CEE model can be compared and contrasted with this literature as well. In particular, are the
responses of the variables to shocks to output and shocks to the unemployment rate in this
model similar to the findings by other authors who have investigated these types of shocks? In
addition to comparing the impulse response functions to other researcher's studies, I draw
comparisons between the responses in the CEE model to what theoretical models predict.
Finally, I reexamine the shocks CEE called monetary policy shocks to see if the long-run
responses of the variables are credible.

Recently there have been several papers investigating the effects of permanent and
transitory shocks on real and nominal variables. A few noteworthy contributions whose results
I make comparisons to are: King, Plosser, Stock and Watson (1991) (hereafter KPSW), Gali
(1992), and Crowder, Hoffman, and Rasche (1996) (hereafter CHR). In KPSW they identify
the permanent shocks in a six variable VECM model that includes nominal variables. The
permanent shocks are a balanced growth shock (a technology shock), an inflation shock, and a
real interest rate shock. They find that a technology shock permanently increases output,
whereas, a permanent shock to inflation has no permanent effect on output. Gali (1992) uses a
structural VAR model and imposes a priori restrictions on the economic relationships among
the four variables in the system. Gali finds that a technology shock increases output by .71

percent initially and 1.1 percent after 20 quarters. Also, the nominal money stock increases in

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response to the shock, however, the point estimates are not significant. Prices fall initially but
then return to their pre-shock level. Also in Gali's model, nominal interest rates hardly move
in response to technology shocks. CHR (1996) is a hybrid of the KPSW and Gali models.
They do not impose any a priori restrictions on the model. Instead, they test for cointegrating
relationships among the variables and use these relationships to help determine the economics
of the model. In response to a supply shock, CHR find that output increases permanently.
Real balances and the nominal money supply (M1) also end up permanently higher. Prices,
however, end up permanently lower. The nominal interest remains significantly below its pre—
shock level for roughly 30 periods.

Given these results, how do "technology" shocks in the difference stationary model
compare to these other results. There are two candidates for technology shocks in the seven
variable difference stationary model. These are shocks to DGDP and DUNEM. 1 will first
discuss the effects of shock to DGDP. The effects of shocks to DGDP are depicted in figures
4.33 row 1, 4.34 row 2, 4.35 row 2, 4.36 row 1, 4.37 row 1, 4.38 row 2, 4.39 row 2 and
4.40 row 1. The results of these models are qualitatively similar so 1 will restrict my
discussions to the impulse responses in Figure 4.33 row 1. An innovation to DGDP results in
output being permanently higher. In response to this shock the unemployment rate falls,
inflation increases, nominal interest rates rise and nonborrowed reserves fall. Are these
findings consistent with the other empirical work cited above? In short, no.

With exception of output, all the variables that are common across models move in
opposite directions. In particular, the interest rate in this model increases. In CHR, the
interest rate falls and in Gali the interest rate falls slightly. In CHR inflation falls initially.) In
this model, inflation increases but the point estimates are not significant. Do these

contradictions imply that the CEE identification scheme is incorrect? Not entirely. There is no

149

way to explain away the differences in the models; however, there is a plausible theoretical
explanation underlying these impulse functions. In response to a permanent technology shock,
suppose that individuals increase their consumption because the shock is believed to be
permanent and investment increases because the marginal product of capital is higher. As a
result, the real interest rate ends up higher. Because the interest rate is higher, the opportunity
cost of holding money increases banks and accordingly hold fewer reserves, so total reserves
and nonborrowed reserves will fall.

Alternatively, a shock that permanently increases the unemployment rate could be
considered a shock that increases the natural rate of unemployment. Such a shock is depicted
in Figures 4.33 row 7, 4.34 row 7, 4.35 row 2, 4.36 row 7, 4.37 row 7, 4.38 row 7, 4.39 row
1 and 4.40 row 2. Since the impulse response functions are qualitatively similar I will restrict
my attention to Figure 4.35 row 1. In this case, an innovation to the unemployment rate causes
the point estimate of the unemployment rate to be higher six years after the shock. Output
remains below its pre-shock level for six years after the shock.

The next shock I consider is an inflation shock. The responses of the variables in the
CEE model can be roughly compared to the impulse responses in what CHR term an
inflationary expectations shock. The sum of the effects of the variables to an inflationary shock
is depicted in Figures 4.33-4.40, in the row that is labeled with D2PRICE. Note, in response
to an inflation shock output temporarily increases, the unemployment rate falls, interest rate
rises, nonborrowed reserves and total reserves fall. These findings are roughly consistent with
CHR. 1n CHR, an inflationary expectations shock temporarily increases output and nominal
interest rates. The inflationary expectations shock also lowers the money supply. Thus, CHR
reason that in response to an increase in inflationary expectations the Federal Reserve contracts

the money supply and as a result the nominal interest rates will rise. If however, the increase

1111

163

sht‘

51.1

150

in the nominal interest rate is lower than the increase in the expected rate of inflation, then the
real interest rate has fallen and output may increase. Thus, the sum of responses to an inflation
shock in CEE model is consistent with the findings in CHR.

The next shock investigated is a shock to commodity prices. The corresponding long—
run responses of the variables to a shock to commodity prices are depicted in the row labeled
DCOM in Figures 4.33-4.40. A shock to PCOM lowers GDP and the unemployment rate for
six years. These point estimates are significantly different from zero. In addition, the federal
funds rate rises and total reserves and nonborrowed reserves fall. Also, inflation increases but
this response is not significant at any horizon. A plausible explanation for these impulses is a
negative supply shock due to an increase in oil prices. This shock could lower output. The
unemployment rate would increase. The decrease in supply and the higher oil prices would
increase inflation. The higher inflation would increase the federal funds rate and in response to
the higher opportunity cost of holding money banks would hold fewer reserves. This explains
the drop in total reserves and nonborrowed reserves. Thus, an innovation to commodity prices
is consistent with an adverse supply shock3.

Finally, I look at the sum of effects on the variables that CEE call monetary policy
shocks. In Figures 4.33-4.40 the row labeled NBRC shows the long-run effects on the
variables to innovation in DNBRC. That is, these figures show what happens to the levels of
the variables to different innovations. Note these responses are consistent with conventional
wisdom: An increase in the money supply will lower interest rates in the short run, output will
increase and prices will rise. In the long run, there will be no effects on any of the real
variables. However, the long-run effect on the variables due to an innovation in the Federal

funds rate is quite implausible. That is, output and the unemployment rate are "permanently"

 

3 An example of this would be an increase in the price of oil.

151

affected by monetary policy shocks. One would expect that monetary policy shocks would
only have transitory real effects. Because there are permanent real effects, I do not believe that
the shocks to the federal funds rate in the difference stationary version of the CEE data can be
considered a monetary policy innovation. Rather it is a shock that permanently effects output

and the unemployment rate, such as a shock to the real interest rate that is discussed in KPSW.

This chapter investigated the empirical work of CEE (1994 a,b) and subjected their
model to the criteria outlined in Eichenbaum (1995). It was shown that the model produces the
most credible results when the unemployment rate is placed first in the ordering. In this instance,
unanticipated increases in the money supply caused by monetary policy initially decrease the
interest rate. Because CEE only report "monetary policy" shocks it is hard to gauge how credible
their results are. Because of this, I investigated other shocks in the system. It was shown that the
impulse response functions of the variables to shocks to the cyclical component of GDP, the
unemployment rate, and total reserves are credible. Thus, using HP filtered data, an ordering that
places the unemployment rate first may provide insights about the effects of unanticipated

monetary policy shocks.

Instead of passing the data through the HP filter, I also consider differencing the data
until the data are 1(0). In this case, the initial response of the variables is qualitatively similar to
the HP filtered model. However, some of the long-run responses are not credible. In particular,
an innovation to the federal funds rate has an effect on output and the unemployment rate that is
significant even six years after the shock. We would not expect a transitory monetary policy
shock to have such long-run effects. Also, the long-run responses of the variables are not

consistent with the findings reported in Crowder, Hoffman, and Rasche (1996) or Gali (I992).

152

Because of this, I am skeptical that the Wold causal ordering with difference stationary data can
identify monetary policy shocks.

Finally, neither of these transformations schemes are innocuous. Cogley and Nason
(1995) and Amsler (1996) argue that passing the data through the HP filter may add a cyclical
component to the data. Therefore, the results using the HP filtered data may not tell us anything
about the true cyclical component. Also, univariate "detrending" may introduce specification
error if some of the data are nonstationary but cointegrated.

Differencing the data to make it stationary may also lead to improper inferences. By
differencing the data to make it stationary, the researcher may be ignoring long-run relationships
that are present in the data. Thus, the researcher may be throwing out information. In fact, a test
for cointegrating relationships among the seven variables GDP, inflation, commodity prices,
nonborrowed reserves, the federal funds rate, total reserves, and the unemployment rate, using
Johansen's maximum likelihood test, finds four cointegrating relationships at the 5 percent
significance level. A study that incorporates these cointegrating relationships may be more
successful in identifying monetary policy shocks and if the model can identify a money supply
rule, this formulation may be able to answer the more difficult question: what is the effect on

other variables when the money supply rule changes?

153

Figure 4.1: GDP

 

 

 

7.4

 

 

 

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20

154

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155

Figure 4.3: Nonborrowed Reserves

11.0

 

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156

Figure 4.4: Monetary Base

 

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157

Figure 4.5: Total Reserves

 

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158

Figure 4.6: Price Level

 

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160

Figure 4.8: Detrended Federal Funds Rate and Nonborrowed Reserves

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161

Figure 4.9: Detrended Federal Funds Rate and Monetary Base

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Appendix 4.1

Augmented Dickey Fuller Unit Root Tests

 

 

 

 

 

 

 

 

 

in Levels

Variables in Logs unless AR=4 No Trend AR=4 Trend
otherwise noted

GDP -1.307 -2.307
Inflation (DPRICE) -1.918 -1.667
Nonborrowed Reserves 1.737 —O.678
Total Reserves -2. 198 -2.060
Federal Funds Rate * 1.984 —O.662
Unemployment Rate* -2.203 -2.337
Commodity Prices -O.132 -2.196

 

 

 

* The Variable is in levels
“Significant at the 5 percent level.

Augmented Dickey Fuller Unit Root Tests

in Differences

 

 

 

 

 

 

 

 

 

Variables in Logs unless AR=4 No Trend AR=4 Trend
otherwise noted

GDP -4.697* -4.904*
Inflation (DPRICE) -5.421* -5.568*
Nonborrowed Reserves -3.767* -4.337*
Total Reserves 4068* -4.ll6*
Federal Funds Rate * -3.032* -3.629*
Unemployment Rate* -4.908* -4.887*
Commodity Prices -5.783* -5.781*

 

 

 

* The Variable is in levels
**Significant at the 5 percent level.

 

 

References

210

References

Amsler, Christine, 1996, Are HP filtered data stationary?, working paper Michigan State
University.

Baier, Scott L.,1990, The consumption function, Master's Thesis, Bowling Green State
University.

Barro, Robert J., 1977, Unanticipated money growth and unemployment in the United States,
American Economic Review, p. 101-115.

Barro, Robert J., 1994, Macroeconomics, Fourth Edition, John Wiley and Sons.

Bernanke, Benjamin, and A. Blinder, 1990, The federal funds rate and the channels of
monetary transmission, Working Paper 3487, National Bureau of Economic Research.

Cagan, Phillip. 1969, The lag in monetary policy as implied by the time pattern of monetary
effects on interest rates,” American Economics Review Papers and Proceedings, p.
277-284.

Carlstrom, Charles T., and T. Fuerst, 1995, Interest rate rules vs. money growth rules: A
welfare comparison in a cash-in-advance economy, Federal Reserve Bank of Cleveland
working paper 9504.

Christiano, Lawrence. J . , 1988, Why does inventory investment fluctuate so much?, Journal of
Monetary Economics, 21, 247-280.

Christiano, Lawrence. J., 1991, Modeling the liquidity effect of a money shock, Federal Reserve
Bank of Minneapolis Quarterly Review, Winter.

Christiano, Lawrence J. and M. Eichenbaum, 1992a, Identification of the liquidity effect of a
monetary policy shock, Working Paper 3920, National Bureau of Economic Research.

Christiano, Lawrence J. and M. Eichenbaum, 1992b, Liquidity effects and the monetary
transmission mechanism, American Economic Review Papers and Proceedings p.346-
353.

Christiano, Lawrence J . and M. Eichenbatun, 1995, Liquidity effects, monetary policy and
the business cycle. Journal of Money Credit and Banking, p. 1113-1136.

 

211

Christiano, Lawrence J ., M. Eichenbaum and CL Evans. 1994a, Identification and the effects
of monetary policy shocks, Federal Reserve Bank of Chicago Working Paper (WP-94-
7).

Christiano, Lawrence .J, M. Eichenbaum, and CL. Evans, 1994b, The effects of monetary
policy shocks: evidence from the flow of funds, Federal Reserve Bank of Chicago
Working Paper (WP-94-2).

Cogley T., and J.M. Nason, 1995, Effects of the Hodrick—Prescott filter on trend and
difference stationary time series: implications for business cycle research. Journal of
Economic Dynamics and Control, vol. 19 255—278.

Cooley, Thomas F. and G. D. Hansen, 1989, The inflation tax in a real business cycle model,
American Economic Review 79:733-748.

Cooley, Thomas F. and G. D. Hansen, 1995, Money in the Business Cycle, in W
W, edited by Thomas F. Cooley. Princeton University Press.

Crowder, William J ., D. L. Hoffman, and R. H. Rasche, 1996, Identification in cointegrated
systems in equilibrium and dynamic analysis, manuscript.

Doan, Thomas A., 1995, RATS User's Manual, version 4, Estima.

Eichengreen, Barry, 1993, European monetary unification, Journal of Economic Literature,
September, p.1321-1357.

Eichenbaum, Martin J ., 1995, Some comments on the role of econometrics in economic theory,
Economic Journal, p. 1609-1621.

Eichenbaum, M., and C. Evans, 1992, Some empirical evidence on the effects of monetary
policy shocks on exchange rates, manuscript Federal Reserve Bank of Chicago.

Evans Charles L. and F. Santos, 1993, Monetary policy shocks and productivity measures in
the G-7 countries, Federal Reserve Bank of Chicago Working Paper (W P-93-12).

Friedman, Milton, 1968, The Role of Monetary Policy, American Economic Review, p. 1-17.

Friedman, Milton, 1969 The optimal quantity of money. in The optimum quantity of money
and other essays, Chicago press, 1-50.

Friedman, Milton, 1975, Factors affecting the level of interest rates, in Currentlsmin.

WWW edited by Thomas M. Hvrilesky and John T. Boorrnan.
AHM Publishing Corporation.

Fuerst, Timothy S., 1992, Liquidity loanable funds and real activity. Journal of Monetary
Economics 29, 3-24.

212

Fuerst, Timothy S. , 1994, Optimal monetary policy in a cash-in—advance economy, Economic
Inquiry, p. 582-596.

Gali, Jordi, 1992, How well does the IS-LM model fit the postwar US. data, Quarterly Journal of
Economics, May.

Gordon, David B. and E. M. Leeper, 1994, The dynamic impacts of monetary policy: An
exercise in tentative identification, Journal of Political Economy, 102 p. 1228-1247.

Greenwood, Jeremy, and G. Huffman, A dynamic equilibrium model of inflation and
employment, Journal of Monetary Economics 19, p. 203-228.

Hamilton, James D, 1994, W3 Princeton University Press.

Helpman, Elhanan, 1981 , An exploration in the theory of exchange rate regimes, Journal of
Political Economy, 90, 865-890.

Helpman, Elhanan and A. Razin, 1981, Dynamics of a floating exchange rate regime, Journal
of Political Economy, 89, 728-754.

Hoffman Dennis L. and Rasche. RH, 1991, Long-run income and interest elasticities of
money demand in the United States, Review of Economics and Statistics, 78, p. 665-
674.

Hoffrnan Dennis L. and Rasche. RH, 1991, Money demand in the US. and Japan: Analysis
of stability and the importance of transitory and permanent shocks, Michigan State
University Working Paper no. 9010.

Ingram, James, 1959, State and regional payments mechanisms, Quarterly Journal of
Economics, p. 619-632.

King, Robert G., C.I. Plosser, J .H. Stock, M.W. Watson, 1991, Stochastic trends and
economic fluctuations, American Economic Review, vol. 81 no. 4

Kydland, Finn E., 1989, The role of money in a business cycle model, Institute for Empirical
Economics, Discussion paper 23.

Kydland, Finn E., and E. Prescott, 1994, The workweek of capital and its implications, Journal
of Monetary Economics 21, 343-360.

Lastrapes, W.D. and Selgin, G., 1994, The liquidity effect: Identification short-run interest
rate dynamics using long-run restrictions. mimeo University of Georgia.

Leeper, Eric M. and D. B. Gordon, 1992, In search of the liquidity effect, Journal of Monetary
Economics, 29, p. 341-369.

 

213

Lucas, Robert E., Jr., 1972, Expectations and the neutrality of money, Journal of Economic
Theory, 4, p. 103-124.

Lucas, Robert E., Jr. , 1975, An equilibrium model of the business cycle, Journal of Political
Economy, 83, p. 1113-1144.

Lucas, Robert E., Jr. , 1980, Methods and problems in business cycle theory, Journal of Money
Credit and Banking, 12, p. 696-715.

Lucas, Robert E., Jr. , 1982, Interest rates and currency prices in a two-country world, Journal of
Monetary Economics 10, 335-359.

Lucas, Robert E. Jr., 1990, Liquidity and interest rates, Journal of Economic Theory 50, 237-
264.

Lucas, Robert E., Jr., and N. Stokey, 1983, Optimal fiscal and monetary policy in an economy
without capital, Journal of Monetary Economics, 12, p. 55-93.

Lucas, Robert E., Jr. , and N. Stokey, 1987, Money and interest in a cash-in-advance economy,
Econometrica, 55, p. 491-513.

McCallum, Benjamin, 1983, A reconsideration of Sims evidence concerning monetarism,
Economic Letters, 13, p. 167-171.

Melvin, Michael. 1983. The vanishing liquidity effect of money on interest rates, Economic
Inquiry vol. XXI no.2 p. 188-202.

Mishkin, Frederick S. 1981. Monetary policy and long-terrn interest rates: An efficient
market approach, Journal of Monetary Economics, p. 29—55.

Mishkin, Frederick S. 1981. Monetary policy and short-terrn interest rates: An efficient
market- rational expectations approach, Journal of Finance p. 63-72.

Pagan, A. R. and J. C. Robertson. 1995. Structural models of the liquidity effect, Australian
National University working Paper no.283.

Poole, William, 1970, Optimal choice of monetary instruments in a simple stochastic macro
model, Quarterly Journal of Economics, 84, 197-216.

Rasche, Robert H. , 1993. Monetary aggregates, monetary policy and economic activity,
Federal Reserve St. Louis.

Reichenstein, William. 1987. The impact of money on short -run interest rates, Economic
Inquiry vol.XXV no. 1 p. 67-82.

Romer, David, 1996, AdvancedMacrgemmnn‘cs, McGraw Hill

214

Sargent. Thomas A., and N. Wallace, 1982, The real bills doctrine versus the quantity theory: A
reconsideration, Journal of Political Economy, 90, p. 1212-1236.

Sims, C. A., 1992. Interpreting the macroeconomic time series facts: the effects of monetary
policy, European Economic Review.

Strongin, Steve, 1992, Identification of monetary policy disturbances: explaining the liquidity
puzzle, manuscript, Federal Reserve Bank of Chicago.

Watson, Mark, 1995, Vector Autoregressions and Cointegration, in the Handbook of
Econometrics, vol. 4.

Wooldridge, Jeffrey M., 1994, Notes on simultaneous equation models. mimeo Michigan State
University.

Wooldridge, Jeffrey M., 1994, Notes on instrumental variable estimation. mimeo Michigan
State University.

 

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