Advanced Lecture Notes for Hall and Taylor, Chapter 5

Course Instructor: Professor Leigh Tesfatsion
Last Updated: 3 February 1996

HT5: Intro to U.S. Monetary and Fiscal Policy

Basic References: Hall and Taylor, Chapter 2, Pages 54-55;
                  Hall and Taylor, Chapter 5, Pages 132-4;

     These notes attempt to clarify the meaning of monetary and
fiscal policy within the context of U.S. institutions and to
explain the standard modelling for money demand adopted by Hall
and Taylor.  The discussion by Hall and Taylor in Chapter 5
concerning the effects of monetary and fiscal policy in the long
run will be deferred until after the Hall and Taylor model has
been more fully developed in subsequent chapters.

#A. The Definition of Money#

     Since February 1980, the narrowest aggregate measure of
money used by the Federal Reserve System (the central banking
system of the U.S., usually called the "Fed") is so-called
"transactions money" M1, defined as follows:

 M1  =  Coins, dollar bills, traveler's checks, demand deposits
        at commercial banks, and other checkable deposits at
        commercial banks and thrift institutions such as NOW
        (negotiable orders of withdrawal) accounts and ATS
        (automatic transfer service) accounts.

The U.S. also uses various broader measures of money (M2, M3, L)
that include successively more illiquid financial assets, i.e.,
financial assets such as time deposits that are not as readily
accessible to households and firms for transactions purposes.
Following Hall and Taylor, however, we will focus attention on M1.

     In somewhat simplified algebraic form, M1 can be represented
as the sum of currency (CU) plus checkable deposits (DEP):

(1)   M1  =  CU   +   DEP    =  [ ------  +  1]  x  DEP  .

On the other hand, the liabilities of the Fed that are usable as
money are called the "monetary base," or "high powered money,"
and are denoted below by Mb.  Roughly speaking, these liabilities
consist of currency CU plus bank reserves (RES):

                                  CU        RES
(2)   Mb   =   CU + RES   =   [  -----  +  ----- ]  x  DEP .
                                  DEP       DEP

Bank reserves RES consist of currency held by private banks
in their vaults plus deposits held by private banks at the Fed.

     Solving (2) for DEP, and substituting into (1), gives the
following relation between Mb and transactions money M1:

                  [ CU/DEP  +   1  ]
(3)      M1  =   --------------------   x   Mb  .
                  [CU/DEP + RES/DEP]

The ratio M1/Mb is known as the #money multiplier#.  In a
fractional reserve banking system such as the U.S., the
reserve-deposit ratio RES/DEP is bounded below by a required
minimum ratio of reserves to deposits.  On the other hand, the
currency-deposit ratio CU/DEP is a behavioral characteristic of
private agents that is not under direct government control.

     The Fed attempts to exert control over M1 either by changes
in Mb (through "open market operations" in which bonds are
exchanged for currency) or by changes in the money multiplier
(through changes in reserve requirements or through changes in
the discount rate that the Fed charges banks who wish to borrow
reserves from the Fed.)  The relation (3) between Mb and M1 is
not always stable over time, however, particularly in difficult
periods (e.g., the Great Depression) when private agents are
subject to "bank panics" that causes them to suddenly withdraw
their funds from the banking system, and when banks hold
reserves in excess of the required minimum amount because they
are reluctant to make loans.  Consequently, the control of the
Fed over M1 is by no means absolute.

     For simplicity, following Hall and Taylor, it will be
assumed below that the Fed #does# have the power to exert
absolute control over the money supply M1, hereafter simply
denoted by M.

#B. The Government Budget Identity#

     The #government budget identity# (or #government budget
constraint#) simpy states that the government must finance all
of its expenditures in any given period of time either by
collecting tax revenues, or by issuing new money, or by
borrowing through the sale of new bond issue either to the
domestic private sector or to ROW.  Assuming all tax revenues
are collected through an income tax t, and using the symbol
definitions introduced in Hall and Taylor, Chapters 1-4, this
budget identity can be expressed in nominal form as:

(4)  P[G + F + N]    =     tPY        +    DM      +     DB  ,

 Nominal Government    Nominal Income   New Money     New Bond
    Expenditures        Tax Revenues     Issue         Issue

where DM and DB denote time rates of change in the nominal money
supply M and the nominal bond suppy B, respectively.  Often (4)
is written in the following equivalent form that focuses
attention on the financing of the government deficit:

                                DM                  DB
(5)  [G+F+N]  -  tY     =     ------       +       ----  .
                                 P                   P

   Government Deficit     New Money Issue      New Bond Issue
    (in real terms)       (in real terms)      (in real terms)

REMARK: In equation (2-5) of Hall and Taylor, page 55, the right
side terms should be divided by P.

#C. Monetary and Fiscal Policy Options for Government#

     The money supply M is referred to as a "monetary policy
instrument" of government, and government expenditures G on
goods and services, the income tax rate t, government transfer
payments F, and government interest payments N on the outstanding
government debt are all referred to as "fiscal policy instruments"
of government.  But what does "monetary policy" and "fiscal
policy" mean?  These government policy options are explained

#Monetary Policy#  =  Changes in DM undertaken by the Fed by
                    means of open-market operations (selling
                    government bonds to, or purchasing
                    government bonds from, private banks and
                    the private nonfinancial sector).

(6)   P[G+F+N]    =      tPY     +     DM    +    DB

     No change        No change     Changes in DM offset by
     in G+F+N           in t             changes in DB
                                    (open market operations)

An example of a monetary policy would be an increased Fed
purchase of government bonds from private banks from 0 bonds
purchased per month to 2 bonds purchased per month at $1000 per
bond.  Recalling equation (2), and the fact that we are taking
the money multiplier to be a given stable value, this results in
an increase in DMb (and hence in DM) because the reserves RES
held by private banks are now increased by $2,000 per month.
This increase in DM is offset by a decrease in DB of $2,000 per
month because the number of government bonds held by the private
sector each month, each worth $1000, has decreased by 2.

#Fiscal Policy# = Bond-financed changes in the level G of
                government expenditure and/or in the income tax
                rate t, with an #unchanged# rate of new money
                issue DM.

(7)  P[G+F+N]    =     tPY    +    DM     +     DB

             Change in          No change      Possible
          G,F,N, and/or t         in DM      change in DB

#"Printing Press" Financing of Expenditures#  =  Using changes
              in DM alone to finance government expenditures.

(8)  P[G+F+N]      =      tPY     +      DM      +      DB

      Change           No change        Change       No change
     in G+F+N            in t           in DM          in DB

An example of printing press financing would be if the
government decided to finance its expenditures by means of
checks drawn on a deposit account obtained at the Fed in
exchange for government bonds sold to the Fed.  Recall that the
bond supply B only measures bonds held by the U.S. private
sector or by ROW but not by the Fed (an agency of the
government), so that DB is unaffected when government purchases
or sells government bonds to the Fed.  In effect, then, the
government creates currency out of thin air when it sells its
bonds to the Fed in exchange for a deposit account.  As will
later be clarified, this leads to "too many dollars chasing too
few goods," a potentially inflationary situation.

#D. Rates of Return and Interest Rates#

     An "asset" is anything of durable value.  "Real assets" are
assets in physical form, and "financial assets" are ownership
claims against real assets, either directly (e.g., stock share
certificates) or indirectly (e.g., purchasing power in the form
of money holdings, or claims to future income streams that
originate from real assets).

     A "nominal rate of return" R^N is a money rate of return
that can be earned by holding either a financial asset (e.g.,
pesos, stock shares, Treasury bills, corporate bonds, government
bonds,...) or a real asset (land, equipment,...) over a stated
period of time.  Formally, the #nominal rate of return# on any
asset A over a period of time from T to T+1 is defined as follows:

(9)  R^N(T,T+1)   =

    [Money Value of A at T+1] + D(T,T+1) - [Money Value of A at T]
                      Money Value of A at T

where D(T,T+1) denotes the money value of any gains or losses (services,
dividends, rents, profits, depreciation, etc.) obtained from holding the
asset from T to T+1.

     A nominal rate of return that an agent borrowing a quantity
of money agrees to pay to the lender of the money is referred to
as a #nominal interest rate#.


#Example 1#:  Bond B with Fixed One-Period Nominal Interest Rate R^N

  Nominal value of B at T:  B(T)
  Nominal value of principal plus interest at T+1:

                 B(T)   +   B(T) x R^N

  #Nominal Interest Rate# on B from T to T+1:

             B(T)  +  [B(T) x R^N]  -   B(T)
             -------------------------------     =    R^N


#Example 2#: Money in the form of currency or
           non-interest-bearing checking accounts

  Nominal market value of money holdings at time T = M
  Nominal market value of money holdings at time T+1 = M
  #Nominal rate of return# on a unit of money held from T to T+1:

                     M    -     M
                    ---------------    =   0   .


#Example 3#: Housing (with explicit or implicit rental payments)

  Nominal market value of house at T:  H(T)
  Nominal market value of house at T+1 plus rent from T to T+1:

                   H(T+1) +  r(T,T+1)

  #Nominal rate of return# to house ownership from T to T+1:

                            H(T+1) + r(T,T+1) - H(T)
          R^N(T,T+1)  =   ----------------------------     .


     For many purposes, we are often interested in nominal rates
of return corrected for changes in prices. In macroeconomics the
#real rate of return# associated with an asset A from T to T+1 is
defined to be its nominal rate of return over this period #minus#
the rate of inflation over this period, where the inflation rate
is calculated in terms of some given price index P:

(10)    R(T,T+1)      =       R^N(T,T+1)       -       INF(T,T+1)

      real rate of           nominal rate             inflation rate
      return from           of return from             from T to T+1
       T to T+1                T to T+1


                             P(T+1)  -  P(T)
(11)        INF(T,T+1)   =   ----------------   .

Note in particular, using Example 2, that the #real# rate of
return on holding money (in the form of currency or non-interest
bearing checking accounts) is given by the negative of the
inflation rate.  That is, money earns a negative rate of return
when the inflation rate is positive (prices are going up) and a
positive rate of return when the inflation rate is negative
(prices are going down).

#E.  The Demand for Money#

    For simplicity, Hall and Taylor assume that the economy they
are attempting to model has only two financial assets: money M
and bonds B.  Money is assumed to pay no interest and hence has
a zero nominal rate of return (see Example 2, above).  Bonds are
assumed to pay a nonzero nominal interest rate R^N(T,T+1) from T
to T+1 for each possible T (see Example 1, above).

     Hall and Taylor note three important empirical observations
about money demand:

   (a) All other things equal, the demand for money is
       #negatively# related to the #nominal# interest rate
       on bonds, because this nominal interest rate is the
       "opportunity cost" of holding money instead of holding
       bonds.  In algebraic terms:

(12)      R^N(T,T+1)      =    R(T,T+1)         +        INF(T,T+1)

         opportunity           real rate  of         loss in purchasing
         cost of holding       return which          power of the money
         money from T          could be earned       held from T to T+1
         to T+1                instead by holding
                               bonds from T
                               to T+1

   (b) All other things equal, the demand for money is #greater#
       when income is #higher# and #lower# when income is
       #lower#.  Money is needed to carry out transactions,
       which vary in proportion to income.

   (c) All other things equal, the demand for money is #higher#
       when the general price level is #higher# and #lower# when
       the general price level is #lower#.  More dollars are
       needed to pay for goods when the general price level goes up.

Letting k and h denote given positive constants, an algebraic
relation that captures all three empirical observations on money
demand behavior is as follows [compare Hall and Taylor, equation

     #Money Demand Relation#:

(13)   -----    =           kY^e         -         hR^N^e      .

     real money      depends positively     and negatively on the
     demand by       on expected real       expected nominal interest
     firms and       income                 rate on bonds

     As we will see in subsequent chapters, relation (13) is
essentially the Hall and Taylor model for money demand with one
exception:  For analytical simplicity, Hall and Taylor assume
that money demand depends on the #real# interest rate rather
than on the #nominal# interest rate.  For the moment we will
retain the conceptually more accurate formulation (13).

#F. The Supply of Money#

     Following Hall and Taylor, it will be assumed that the Fed
simply sets the supply of money M^S to some given target level M.

     #Money Supply Relation#:

(14)      M^S   =    M    .