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): CU (1) M1 = CU + DEP = [ ------ + 1] x DEP . 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 below. #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 B(T) --------------------------------------------------------------- #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 . M ----------------------------------------------------------------- #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) = ---------------------------- . H(T) ---------------------------------------------------------------- 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 where P(T+1) - P(T) (11) INF(T,T+1) = ---------------- . P(T) 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 (5-4)]: #Money Demand Relation#: M^D (13) ----- = kY^e - hR^N^e . P real money depends positively and negatively on the demand by on expected real expected nominal interest firms and income rate on bonds households 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 .