Basic Lecture Notes for Hall and Taylor, Chapter 5:
Intro to U.S. Money and Fiscal Policies

Maintained by: Leigh Tesfatsion
Last Updated: 29 September 1996

PLEASE NOTE: These basic lecture notes on HT Chapter 5 are required for Econ 302. If possible, students should read these notes prior to attending class lectures on HT chapter 5. A more advanced detailed version of these notes is also available on this web site; the advanced notes are recommended but not required.

Basic References:
HT Chapter 2, Pages 54-55;
HT Chapter 5, Pages 132-4;

A. Overview

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 HT. The discussion by HT in Chapter 5 concerning the effects of monetary and fiscal policy in the long run will be deferred until after the HT model has been more fully developed in subsequent chapters.

B. The Definition of Money and the Monetary Base

Since February 1980, one of the main measures of aggregate money used by the Federal Reserve System (or Fed for short) is so-called transactions money (M1), defined as follows:

Currency issued by the Fed (U.S. dollar bills and coins) in public circulation, plus travelers' checks held by the public, plus demand deposits (non-interest bearing checkable deposit accounts) held by the public, plus interest-bearing checkable deposit accounts held by the public.
The financial assets in M1 are readily available to households and firms for transactions purposes.

The Fed also uses successively broader measures of money that include financial assets that are less and less like the readily available financial assets in M1. For example, M2 includes everything in M1 plus additional financial assets such as time deposits that generally can only be withdrawn without penalty after some specified maturity date. Following HT, we will focus attention on the narrowest money measure, M1.

In somewhat simplified form, M1 can be represented as the sum of currency (U.S. dollar bills and coins) in public circulation, denoted by CU, plus checkable deposit accounts held by the public, denoted by DEP. The algebraic expression for M1 is then

(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 private bank reserves, denoted by RES:

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

More precisely, RES consists of currency held by private banks in their vaults (hence not in circulation) plus deposit accounts 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 reflects the decisions of private citizens concerning how they want to hold their money, whether as currency in their pockets or as deposit accounts in banks. Thus, CU/DEP is not under direct government control.

The Fed attempts to exert control over M1 either by changes in Mb or by changes in the money multiplier. The Fed can change Mb through "open market operations" -- that is, through the purchase or sale of dollar-denominated government bonds to U.S. citizens or to citizens of ROW.

For example, a sale by the Fed of a U.S. Treasury bill to a U.S. citizen in exchange for dollars means that there is a contraction in the amount of currency in circulation, hence a contraction in Mb. Alternatively, if the private citizen pays by a check drawn on a deposit account at a U.S. bank, the honoring of this withdrawal forces the bank to draw down its reserves. It follows that Mb decreases in this case as well.

The Fed can also change Mb by changing the rate of return (the "discount rate") that the Fed charges banks who wish to borrow reserves from the Fed. Finally, the Fed can directly attempt to change the money multiplier by changing reserve requirements.

Unfortunately for the Fed, the relation (3) between Mb and M1 is not always stable over time. For example, during the Great Depression, private citizens were subject to bank panics that caused them to suddenly withdraw their funds from the banking system, resulting in a sharp increase in CU/DEP. Also, banks held reserves in excess of the required minimum amount because they were reluctant to make loans, resulting in an increase in RES/DEP. Consequently, the control of the Fed over M1 is by no means absolute.

For simplicity, following HT, 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.

C. The Government Budget Constraint

The government budget constraint (also called the government budget identity) is an accounting identity that shows how the government finances its expenditures in any given period of time. HT present a simplified form of this budget constraint in which government can only finance its expenditures by the following three means: (a) collecting income tax revenues; (b) issuing new money; or (c) selling new bond issue to (borrowing from) the U.S. private sector or ROW.

It will be useful to express this budget constraint in algebraic form. Recall that, for any period T, G(T) denotes government expenditure on goods and services, t denotes the income tax rate, F(T) denotes government transfer payments, N(T) denotes government interest payments on the outstanding government debt, and P(T) denotes the GDP implicit price deflator. Letting DM(T) and DB(T) denoting the change in money and bonds during period T, the budget constraint for period T then takes the form:

(4)  P(T)[G(T)+F(T)+N(T)]  =    tP(T)Y(T)    +   DM(T)   +    DB(T)  .

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

Often (4) is written in the following equivalent form that focuses attention on the financing of the government deficit:

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

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

REMARK: In HT equation (2-5), page 55, the right side should be divided by P since the left side is measured in real terms.

D. Monetary and Fiscal Policy Options for Government

The money supply M is referred to as a monetary policy instrument. Government expenditure 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. But what does "monetary policy" and "fiscal policy" mean? These government policy options are explained below.

Monetary Policy  =  Changes in DM(T) undertaken by the Fed by
                    means of open-market operations in period T
                    (selling government bonds to, or purchasing
                    government bonds from, the U.S. private
                    sector or ROW)

(6) P(T)[G(T)+F(T)+N(T)]  =  tP(T)Y(T)     +     DM(T)    +    DB(T)

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

An example of a monetary policy would be an increased Fed sale of government bonds to private banks in each period T from 0 bonds to 2 bonds, 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 a decrease in DMb(T), hence in DM(T); for the reserves RES held by private banks are now decreased in each period T by the $2,000 that private banks now pay to government in exchange for bonds. This decrease in DM(T) is offset by an increase in DB(T) by $2,000 in each period T because the number of government bonds held by the private sector in each period T now increases by 2, and each bond is worth $1000.

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

(7)  P(T)[G(T)+F(T)+N(T)]  =   tP(T)Y(T)  +    DM(T)    +     DB(T)

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

Perhaps an easier way to remember the meaning of fiscal policy is to note that a fiscal policy changes the size of the government deficit without changing the rate of money issue.

"Printing Press" Financing of Expenditures

              =  Using changes in DM(T) alone to finance
                 government expenditures.

(8)  P(T)[G(T)+F(T)+N(T)]  =  tP(T)Y(T)   +   DM(T)    +    DB(T)

         Change in            No change       Change       No change
       G(T)+F(T)+N(T)           in t         in DM(T)      in DB(T)

An example of printing press financing would be if the government decided to finance some expenditure by means of a check drawn on a deposit account that is obtained at the Fed in exchange for a government bond sold to the Fed. Recall that the bond supply B(T) only measures the nominal value of bonds held by the U.S. private sector or by ROW in period T; it does not include bonds held by the Fed (an agency of the government). Thus, DB(T) 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 government bonds to the Fed in exchange for a deposit account. As will be clarified later, this leads to "too many dollars chasing too few goods," a potentially inflationary situation.

E. 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 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: Bonds B with a Fixed One-Period Nominal Interest Rate R^N

  Nominal value of bond holdings 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 Deposit 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).

F. The Demand for Money

For simplicity, HT 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).

HT 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 (5-4)]:

   #Money Demand Relation#:

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

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

As we will see in subsequent chapters, relation (13) is essentially the HT 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).

G. The Supply of Money

Following HT, 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    .