Prof. Bryan Caplan

Econ 918

Spring, 1998

Week 2: Theories of Money Supply

  1. The Monetary Base
    1. There are numerous measures of "the" money supply; the least controversial and the most fundamental is known as the monetary base.
      1. In a fiat regime, the monetary base is currency, coins, and deposits with the Fed.
      2. Under a commodity standard, the monetary base is the (non-industrial?) metallic stock.
    2. A simple test for base money: base money is net wealth; non-base money is not. If I hold $1 in currency and the price level declines, my wealth is greater, and no one else's is smaller. In contrast, if a price level decline merely increases the holder's wealth but reduces someone else's wealth by an equal amount, the item held is not base money.
      1. Ex: Under the gold standard, a fall in the price level enriched the holders of Federal Reserve notes, but increased the Fed's debts to the public by the same amount (since the Fed pledges to redeem a fixed quantity of gold per dollar).
      2. Why does going off the gold standard turn currency into net wealth?
      3. In modern fiat monetary systems, the monetary base is normally the only thing under the complete control of the central bank/government. (In practice, responsibilities are divided between agencies; e.g., in the U.S., both the Fed and the Treasury play a role, although the Fed is clearly dominant).
      4. In consequence, if you are just looking at the market for base money, it probably makes sense to draw the money supply curve as a vertical line.
  2. Broader Measures of the Money Supply + Money Substitutes
    1. Other - broader - measures of the money supply often receive attention, e.g. M1, M2, M3, etc.
    2. At the same time, there are many items that are nowhere counted as money (e.g. credit cards), that still seem to be very close substitutes for money.
      1. If you wanted to somehow include credit cards in a monetary aggregate, how would you do it?
    3. These two facts give rise to pointless disputes about what is/is not money. What does it matter to an agent if e.g. a mutual fund is money, or is merely a close substitute for money?
    4. The tendency to classify some items as money is closely connected to "required reserves" laws, which e.g. require banks to hold base money reserves of 2% against savings accounts. But this is really no different than e.g. imposing a requirement that mutual funds hold at least 2% of their fund's value in the form of base money.
  3. Endogeneity of Broader Money Supply Measures
    1. Suppose you are interested in the behavior of a monetary aggregate that is at least somewhat broader than the monetary base. While the government has some control over this aggregate, the quantity of money broadly measured will fluctuate even if the government does nothing. In other words, the quantity of money broadly measured is "endogenous."
    2. Implication #1: While the supply curve for the monetary base can be drawn as a vertical line, the supply curve for broader monetary aggregates might not be vertical (or it might be a function of other variables not shown on the 2-D graph).
    3. Implication #2: It is possible that in spite of an observed correlation between money supply movements and e.g. output movements, that the government does not deserve credit/blame.
    4. There are basically 2 kinds of quite different theories of money supply endogeneity, with very different implications.
      1. Interaction of interest rates and "money multiplier."
      2. Interaction of income and "money multiplier."
    5. Different theories also ascribe quite different consequences to the same co-movements; the same sort of endogeneity may be credited with dampening or amplifying fluctuations - or may have no impact on fluctations at all!
  4. King and Plosser Made Easy, I: The Model
    1. Early stages of RBC had no explanation for observed real-monetary correlation. K-P argue that this can be handled by thinking of monetary services as a intermediate good that is complementary with real economic activity. The resulting model provides an interesting and fairly unique example of money supply endogeneity.
    2. The model (we’ll just look at K-P’s simplified version): 2 productive sectors, 1 intermediate good, 1 final good.
      1. Goods industry: output is either consumed or used as input for future production.
      2. Financial industry: output is intermediate good - transactions services. Transactions services economize on time and other resources needed to exchange goods.
    3. , where k is the amount of capital, n is the amount of labor, and d is transactions services. Production is CRS, all inputs have standard properties, and the shocks to the production technology both have expected values of 1.
      1. Labor, capital, and transaction services’ prices given by w, q, and r .
    4. Firms swap 1 unit of claim for 1 unit of expected output at price v, so firms max: . CRS technology yields flat supply curve for shares at v*.
    5. Government issues stock of (0-interest) nominal currency, C, with goods-price 1/P.
    6. Financial services are produced using only labor, and with CRS: d=hn, so r =wh. Banks pass their return along to depositors, minus service fee. (So banks are more like mutual funds). Stock of deposits is assumed to be proportional to flow of transactions services; banks hold the legal minimum of currency. Therefore, , where B is nominal bank reserves, q is the legal reserve ratio, and g is the constant of proportionality between deposits and transactions services.
    7. Representative agent has standard OF: , where x indicates consumption, and
    indicates leisure (total time minus labor supply). But the agent works with a "shopping time" constraint, so he picks the quantity of transactions services d, and real currency c to minimize total transactions costs wn+r d+R/(1+R)*c (quantity of shopping time*value of time plus quantity of financial services*price of f.s. plus "rental price" (interest foregone) of currency*quantity of currency held).
  5. King and Plosser Made Easy, II: The Results
    1. Transactions cost minimization reveals:
      1. Demand for both (real) currency and financial services is directly proportional to output.
      2. Real currency demand decreases as the nominal interest rate rises, and increases as the price of financial services and the opportunity cost of time rise.
      3. Demand for financial services rises as the nominal interest rate rises, and falls as the price of financial services and the opportunity cost of time rise
        1. (Question: Why doesn’t demand for financial services increase when time becomes more valuable?)
    2. Price level depends positively on: high-powered money (currency + bank reserves) and nominal interest rates; it depends negatively on output, price of financial services and labor, and real bank reserves. (Increase in real reserve demand holding high-powered money constant reduces price level).
    3. Therefore: Real activity (including real deposit services and real deposits) is neutral wrt base money changes. Since K-P assume that banks are always exactly at the legal minimum RR, fluctuations in deposits have to be the result of variations in the public’s currency/deposit ratio. (Does this make sense? Couldn’t K-P have gotten more plausible results if they allowed for excess reserves?)
    4. K-P on the money-output relation: First, a correlation between output and broad money is predicted by the model, so it’s not surprising. Second, a correlation between output and base money is not predicted, but not impossible either depending on the central bank’s feed-back rule.
    5. Observations: The endogeneity emphasized by K-P is quite different from almost anyone else's. Consider the case where there are no reserve requirements. K-P assume that then banks will hold no base money; but there will still be a determinate price level so that the real supply of currency equals the public's real demand for currency. In this case:
      1. The supply of deposits only affects money demand and prices via the financial services fee.
      2. The real supply of deposits r d depends entirely on the real economy.
      3. The nominal supply of deposits Pr d will positively covary with real activity unless P is strongly counter-cyclical.
      4. If the nominal supply of deposits positively covaries with real activity, then (since the nominal supply of currency is fixed), the "money multiplier" increases when real output increases.
    6. (Looking ahead) Note the massive contrast between the endogeneity emphasized by K-P and the endogeneity discussed in the free-banking literature.
      1. The free bankers assume that the public holds no base money, and the banks hold all of it; K-P assume that the public holds all base money, and the banks hold none of it.
      2. The free bankers argue that the money multiplier contractss in response to an increase in nominal income; K-P assume that the MM expands in response.
      3. While the free bankers emphasize the macro-stabilization properties of their preferred system, K-P actually argue that there isn't any problem of macrostabilization to begin with!
      4. In K-P, what happens when demand for both notes and deposits rises? What if there were price rigidity?
  6. Fiscal Theories of (Base) Money Supply: The Role of Seigniorage
    1. Governments can raise revenue just by printing up new base money. This is called "seigniorage" or "the inflation tax."
    2. This suggests a very simple model of money supply determination: Governments maximize seigniorage; they pick the money supply growth rate to get at the peak of the Laffer curve for inflation tax revenue. While this is a clean and simple theory, it is hard to see its application in modern, industrial countries - though it explains a lot about LDC’s and many historical instances.
    3. Why isn't seigniorage at its maximum in all countries?
    4. Models like K-P emphasize the endogeneity of the "money-multiplier." A very different perspective is to view the monetary base as itself endogenous - though in a very different sense. Not endogenous from the point of view of the government as a whole, but endogenous from the point of view of a single agency - namely, the monetary authority. This suggests a theory of money supply growth driven by the need for some (not maximum) seigniorage.
    5. Sargent and Wallace’s "unpleasant monetarist arithmetic": if you hold future expenditure and taxation decisions constant, AND rule out explosive debt growth, then only a narrow set of monetary policies are feasible (from that one agency’s perspective) because the central bank prints money to make up the difference.
    6. Suppose the Fed chooses a fixed money growth rule - then its choices are even more tightly constrained.
    7. If there is significant sensitivity of money demand to the nominal interest rate (and thereby to expected future inflation), then S-W point out that it may not even be possible to temporarily reduce inflation with monetary policy!
  7. The Microanalytics of Optimal Seigniorage (from Mankiw)
    1. Government has to satisfy a present-value budget constraint (which is equivalent to ruling out explosive debt).
    2. Expenditure is exogenous; money demand is just a linear function of output (note: this assumes away the most obvious deadweight cost of inflation stemming from the increase in nominal interest rates).
    3. Government has two revenue sources: seigniorage, and an output tax. Both taxes have deadweight losses; the government picks the mix of taxes that minimizes deadweight losses. (Note: a non-altruistic government might want to do this. Why?)

      Output Tax

      Inflation Tax


      Deadweight Loss

    5. Government minimizes sum of deadweight costs, s.t. the lifetime balanced-budget constraint.
    6. Implications are standard: government uses both taxes; use of both taxes increases as expenditures increase; deadweight burdens of taxation are equalized at the margins. This includes the intertemporal margin - so a government following this model will smooth taxes over time.
    7. Empirical results work: nominal interest rates and inflation positively related to T/Y.
    8. Other explanations of the data? Would a generic "big government" theory explain the same facts?
  8. Two Centuries of British Seigniorage (from Barro)
    1. Interesting period to consider, for several reasons:
      1. Long-term adherence to commodity standard (with 2 temporary suspensions).
      2. Numerous wars generating temporary expenditures.
      3. Largely unregulated markets and interest rates.
    2. Results:
      1. Positive correlation between government spending and wars.
      2. During gold standard periods, money uncorrelated with spending; inflation is (slightly) positively correlated.
      3. During suspension periods, money growth strongly correlated with spending; inflation (more strongly) positively correlated.
      4. Barro doesn't find the price level to be stationary, which is surprising since other studies of the gold standard conclude this.
    3. Unable to distinguish between a deficit/interest and a purchase/interest link statistically.
    4. However, there were two interesting natural experiments when deficits increased but purchases did not; these were not associated with large interest rate increases.
      1. Slave compensation payments
      2. "Budget crisis" of 1909