Ch. 19: The Demand for Money

Goals:  1. To examine the factors that affect the demand for money.
           2. To explore how the economic theories of the demand for  money evolved in response to economic data and ideology.
          
 

1. Early Theories of Money Demand

    ---Quantity Theory of Money

        Proposed by Irving Fisher in 1911.
          Derives from the attempt to establish a link between the quantity of money and the amount of spending in the economy.
          Assumes the all money is used for transactions.
          Link : Division of total spending (= PxY, where P is the price level, Y is the real output, and PxY is the nominal GDP) by the quantity of money (= M) yields the measure of "Income Velocity of Money"

 
(example:  If PxY = 40 and M = 5, then V = 8)
          Equation of Exchange :   M x V = P x Y
          It follows from the definition of the velocity and, thus, holds every period, i.e. is an identity.
          How can we go from an identity to a theory?
          By attempting to predict changes in the involved variables between periods.  If, for example, M increases by 5%, what will happen to V, P and Y?

          Quantity Theory: This theory assumes that a) velocity is (nearly) constant [due to the fact that the theorists considered that the main determinants of velocity are institutional variables such as the frequency and synchronicity of payments, the speed of trasportation/mail, etc.]; b) the real output Y is at or near full employment most of the time. Based on these assumptions:

This means that changes in the quantity of money M will result in equal changes of the price level P, i.e. inflation.

          Quantity Theory of Money Demand: The above described quantity theory of the economy is in fact a theory of money demand since all the quantity of money in the economy is willingly held by somebody. It can thus be written as:

In other words, the money demand is affected only by income, since the factor of proportionality (1/V) is constant.

     ---Cambridge Approach

         Created by Economists at Cambridge University in England who took a different approach than quantity theorists. They started by asking the question: Why do people demand money?  Their answer was:
          As a medium of exchange  and as a store of value.  Then they explored these reasons further.
          Money as a medium of exchange:  Since to carry out more exchanges a household must have more income and needs to hold more money, it follows that Income (i.e. P x Y ) is the main determinant of money demanded for exchanges.
          Money as a store of value: The value stored in assets, money among them, is a household's wealth. Thus wealth is the main determinant of the demand for money as a store of value.  But wealth is difficult to measure.  Cambridge economists theorized that wealthier people were making higher incomes as well.  Thus they assumed that income can be used as a proxy for wealth since it seems that income is proportional to wealth. Thus they used:
          ASSUMPTION (1):  Wealth is proportional to income
            (note:  This is an assumption of convenience and can be relaxed!)
        Therefore Cambridge economists concluded that the overall demand for money is proportional to income, i.e.
                     
where the factor of proportionality k is constant by assumption (1)  [but will not be constant if (1) is relaxed].

     ---Velocity Constancy

        Both of the above theories treat velocity as constant but for different reasons.  The quantity theory claims that velocity cannot change as long as the technology of payments and the economy's institutions remain unchanged.  The Cambridge approach claim that velocity can change only if assumption (1) does not hold.
          Data show that in actuality velocity  falls during recessions!  A good theory must be able to account for this fact.

     ---Keynes' Liquidity Preference Theory

        J. M. Keynes, in his 1936 book: The General Theory of Employment, Interest and Money, provides a more detailed and advanced theory of money demand. His departure point was the Cambridge approach which, after relaxing assumption (1) he adjusted so that allowed the introduction of interest rates as a major determinant of the money demand.  The presence of interest rates can easily explain the behavior of the velocity during recessions.
        Keynes identifies 3 motives for demanding money:
            1. Transactions Motive:  Money demanded for transactions is proportional to income (as in quantity theory)
            2. Precautionary  Motive:  Money demanded for precaution is proportional to income
            3. Speculation Motive: Money demanded for speculation/investment will depend on expected return.
        Speculation: Consider an investor with 2 choices:
                            A. Invest in bonds with return:  RET^e
                            B. Invest in cash with return: 0%
        When will the investor choose alternative B, i.e. when will she demand to hold money for speculation?
        Apparently when  RET^e< 0.
        When is  RET^e negative?
        When the prices of bonds are expected to fall enough so that the capital loss will overwhelm the current yield.
        When are bond prices expected to fall?
        When investors think that current interest rates are too low (as compared to some normal value) and are expected to rise.
         It follows that when interest rates are low investors will hold more cash to avoid capital losses and negative returns, while when interest rates are high they hold more bonds to reap the expected capital gains. In other words, interest rates affect the quantity of money that is demanded inversely.
       
          Keynes' overall demand for nominal and real money (or real money balances) can be described as:
                   

            Implication for velocity:  Inverting Keynes' demand for real money balances and substituting in the definition of velocity yields:
                   

          It can easily be seen that as i increases, the denominator falls and the fraction increases.  Consequently, higher interest rates lead to higher velocity and inversely.  The procyclicality of velocity is explained by the procyclicality of the interest rates.

 2. Modern Theories of Money Demand

        ----Baumol-Tobin Theory of Transaction Demand for Money

         Further exploration of the demand of money for transactions reveals that it also depend s upon interest rates!
          Insight: Households and businesses can invest part of their transaction balances in interesting bearing assets (bonds) for the periods that they do not use them and make additional interest income. But such investment will be subject to costs (brokerage fees and time/shoe-leather costs).  Thus there will be an optimal decision to be made at the point where MC =MB.
          Results:  The higher the interest rate, the larger the amount decision makers put into interest bearing assets, the smaller the amount of money they hold!
                        The higher the investment cost, the less the amount put into bonds, the higher the money held.
                        The higher the income the larger the amount of money held.
            Thus:  (M^d/P) = f (i, Y, b)

        ----Demand for Speculation (Tobin's Risk-Return Analysis)
          Tobin theorized that money is demanded as one of the assets to be included in investors' portfolio. As such it competes with the other assets most of which have positive expected returns. 
          What will motivate individuals to hold money when its return is the negative of the expected inflation?
          Tobin claimed that money has no risk and risk-averse investors will hold money as part of their portfolio diversification strategy.
          This argument is problematic since there are other risk-free assets (e.g. T-Bills) with positive expected returns. These assets dominate money.  Therefore Tobin's analysis is a theory of portfolio choice, not a theory of money demand for speculation.

      ----Friedman's Restatement of the Classical Theory
          Milton Friedman started by recognizing that money can be treated as an asset and, thus, the demand for money can be treated as the demand for a financial asset.
          Unlike Keynes and the Keynesian economists who postulate that the expected return on money is zero  (or the negative of expected inflation if it is different than zero), Friedman claims that money has a positive return r_m, that consists of interest paid on the included deposits, the implicit value of bank services, and the transaction convenience of money.
          Friedman also replaced wealth (an asset demand determinant) with his concept of permanent income Y_p, defined as the household's long-run average income.  Actual income may be above or below its long-run average.
          Friedman stated that the other assets competing with money in the households' portfolios were:  Bonds (r_b), Equities (r_e), and Commodities (p^e).  Ignoring risk and liquidity considerations, the demand for money will depend on permanent income (as a replacement for wealth) and relative expected returns of the competing assets compared to money:
               

         The last three terms of the equation are the relative expected returns.
          Friedman argued that as interest rate (i.e. returns) increase, banks can charge higher loan rates.  Since loans become more profitable, banks will want to attract more funds to loan out by attracting more deposits. To do so they will increase the (possibly implicit) rate they pay on money r_m. Consequently, the return differentials r_b-r_m, r_e-r_m, p^e-r_m, do not change substantially and, thus, they do not have much of an impact on the demand for money.  Hence the demand can be simplified to:
               

            This expression is very close to the expression derived by the classical theory, hence a restatement.
            The velocity issue:
                Using the inverse of Friedman's function and the definition of velocity yields:
                   

                Since permanent income is fairly constant (as a long-run average), velocity will respond directly to changes in income.  Income decreases during recessions and increases during expansions, resulting in procyclical behavior for velocity.

            ---- Evaluation of Theories
              Empirical work shows that interest rates affect the money demand significantly, unlike Friedman's predictions.  Therefore drawing a negatively sloping demand for money is appropriate.

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