So far, we studied the determinants of real variables: Y, C, S. I, r, W/P, N (See Chapter 5).

We should now consider the determination of nominal variables: the price level P, the nominal wage W, the inflation rate, the nominal interest rate i.

Basic idea: the price level (and the nominal wage rate) depend on the level of the money supply. The rate of inflation depends on the rate of growth of the money supply.

In the classical theory, money is a veil that does not affect real variables. It affects only nominal variables.

**The Quantity Theory of Money**

Example of the neutrality of money: the government replaces every dollar with two new dollars. Effect: the prices of all goods in terms of new dollars would be twice as high.

Quantity theory of money and prices:

1. Money is not fundamental for real variables.

2. The usefulness of money is in executing transactions.

Suppose:

Y = All transactions in the economy in a period of time

PY = Value of all transactions (sales revenues)

So, we need M dollars to make all these transactions each period:

M = PY

So, if we double M, we double PY.

Reinterpret:

Y = Real GDP

P = GDP deflator index

PY = Nominal GDP

Slight generalization: money can be used several times each period for transactions, as it goes from one person to the other:

MV = PY

or: V = PY/M

where V is the velocity of money, the number of times each period a unit of money is in a transaction.

Assumption of the quantity theory: V is constant so that changes in M are associated with proportional changes in PY.

In principle, the increase in PY could be in P or Y or both.

For now assume that Y (real output) is not affected by M. This means that a fundamental real variable such as Y is not affected by money since it is determined by the production function and labor market equilibrium (as seen in the Classical Theory).

Then, only P (the price level) can change when M changes.

Implication: changes in the stock of money lead to proportional changes in the price level.

The same theory can be reinterpreted in terms of the inflation rate. Take, the quantity equation at two dates and divide, to get:

(M_{t} / M_{t-1}) (V_{t} / V_{t-1})
= (P_{t} / P_{t-1}) (Y_{t} / Y_{t-1})

This leads (approximately):

(M_{t} - M_{t-1})/M_{t-1} + (V_{t}
- V_{t-1})/V_{t-1} = (P_{t} - P_{t-1})/P_{t-1}+
(Y_{t} - Y_{t-1})/Y_{t-1}

or: **m + v = p + y**

where lower case characters represent the rate of growth of upper case characters (i.e. m is the rate of growth of money M).

If velocity is constant, we get approximately, the growth rate of money equals the growth rate of prices (inflation) plus the growth rate of output:

(M_{t} - M_{t-1})/M_{t-1} = (P_{t}
- P_{t-1})/P_{t-1}+ (Y_{t} - Y_{t-1})/Y_{t-1}

or : **m = p + y**

Implication: if higher money growth does not affect output, higher money growth leads to higher inflation.

**Open Market Operations**

How do governments increase the money supply ?

One way is to print money to finance budget deficits:

P_{t}(G_{t}-T_{t}) = dM_{t}
= M_{t} - M_{t-1}

i.e. each dollar of deficit is financed by dM_{t}
new dollar bills.

Other way to change the money supply: changes in the composition of the balance sheet of the government:

Government Debt | 4,000 |

Bonds | 3,800 |

Currency | 200 |

Suppose the government (generally the central bank) wants to increase the quantity of currency in the economy by 20 billion $.

It does this by buying 20b of bonds from someone in the private sector, and paying for them in cash.

This is an *open market purchase of government securities*
that increases the money supply:

Government Debt | 4,000 |

Bonds | 3,780 |

Currency | 220 |

Effect of open market operations performed by the Fed on short-term interest rates.

**Interest Rates and Inflation**

The real interest rate (r) is the difference between the
nominal interest rate (i) and the expected inflation rate (p^{e}):

r = i- p^{e}

or : i = r + p^{e}

The real interest rate is determined by savings and investment (see chapter 5) with no relation to money and inflation.

So, for given real interest rate, the nominal interest
is determined by the inflation rate: higher p^{e} leads to higher
i.

**Evidence on the monetary theory**

The complete separation between real and nominal variables is overly strong in the short-run run, but it is a good approximation of the long run effects of money.

**First prediction**: velocity is constant or the price
level follows the money stock adjusted for the level of output. In logarithms:

log P_{t} = log M_{ t} - log Y_{ t}
+ log V_{ t}

i.e. if the money supply grows faster than output, we should see a comparable increase in the price level. See Figure 1: the match is quite good but note that there are ‘wiggles’ in velocity.

If we graphs annual growth rates, we should get that:

(P_{t} - P_{t-1})/P_{t-1} = (M_{t}
- M_{t-1})/M_{t-1} - (Y_{t} - Y_{t-1})/Y_{t-1}

since velocity is assumed to be constant.

Figure 2: the link between money growth and inflation is much looser for short run movements. So the theory is a much better prediction of long run trends than short run fluctuations.

**Second prediction**: higher inflation leads to higher
nominal interest rates. (Caveat: i can move also because of changes in
r).

Figure 3: movements in i match movements in p. Caveat: 1980s.

Conclusion: the classical theory provides a reasonable approximation for long run trends in inflation and interest rates.

**Application: Friedman’s Money Growth Rule**

Mainstream view: monetary policy should be used to fine tune the economy, to help smooth the recurrent ups and down of the business cycle.

Milton Friedman view: the Fed should follow a policy consistent with a constant rate of growth of the money supply.

Arguments for Friedman’s view:

1. This policy would have good long run effects (low inflation).

2. It would be better than actual fine-tuning policies since it would avoid some big mistakes (the high inflation rates of the 1970s).

3. Discretionary short-run policy management leads to shortsightedness and bad long-run policy decisions.

4. You can use monetary policy to start a recession, but not stop one.

Today, Greenspan and the Fed do not follow a policy of targeting a rigid money growth rule. The Fed tries instead to target a short term interest rate (the Federal Funds rate).Actual US monetary policy is more flexible and discretionary than advocated by Friedman.

**Application: Big Inflations**

High inflation rates in the 1980s in countries such as Argentina, Bolivia, Mexico, Brazil and Israel.

If this is due to high money growth, why don’t countries print less money ?

The main problem was that these countries had a large fiscal deficit and printed money to finance it.

If a government has a fiscal deficit, it can finance it either by printing money and/or by issuing public debt:

P_{t}(G_{t} - T_{t}) = dM_{t}
+ dB_{t }= (M_{t} - M_{t-1}) + (B_{t }-
B_{t-1})

or:

(G_{t} - T_{t}) = (dM_{t} /P_{t})
+ (dB_{t}/P_{t})

This tells us that what the government doesn't pay for with tax revenues, it must finance by issuing debt of some sort.

So why do these countries increase the money supply? The problem is that a political impasse makes it nearly impossible to reduce the deficit. Given the government's budget constraint, it must then issue debt.

If they can't issue debt and they can't reduce the deficit, the only alternative left is to print money: in short, they pay their bills with money, which is easy enough to print. The effect of this, of course, is that these countries experience extremely high rates of inflation.

Note that whenever a central bank prints "fresh money" it can obtain goods and services in exchange for these new pieces of paper. The amount of goods and services that the government obtains by printing money in a given period is called "seignorage". In real terms, this quantity of goods and service is given by the following expression:

Seignorage_{t} = dM_{t}/P_{t}
= New bills printed during the period / Price level during the period.

The monetary aggregate that the central banks control directly is the "monetary base", consisting of currency in the hands of the public and reserves of the commercial banks deposited in the central bank. Thus, when we refer to a central bank as "printing more money", we mean increasing the monetary base.

Note that since the governement, by printing money, acquires real goods and services, seigniorage is is effectively a tax imposed by the governement on private agents. Such a seigniorage tax is also called the inflation tax. The reason is the following. From the definition of seigniorage:

Seignorage_{t} = dM_{t} / P_{t}
= (dM_{t} /M_{t} ) (M_{t}/P_{t})

Since the rate of growth of money (dM/M=m) is equal to inflation (p) (assuming, for simplicity, that the rate of growth of output y is zero), we get:

Seignorage_{t} = p_{t} (M_{t}/P_{t})
= Inflation Tax

In other terms the inflation tax is equal to the inflation rate times the real money balances held by private agents.

The inflation tax must be equal the tax rate on the asset
that is taxed times the tax base. In the case of the inflation tax, the
tax base are the real money balances while the tax rate at which they are
taxed is the inflation rate. In other terms, if I hold for one period an
amount of real balances equal to M_{t}/P_{t}, the real
value of such balances (their purchasing power in terms of goods) will
be reduced by an amount equal to p_{t} (M_{t} /P_{t})
after one period.

The reduction in the real value of my monetary balances caused by inflation is exactly the inflation tax, the amount of real resources that the government extracts from me by printing new money and generating inflation.

For the relation between money creation, budget deficits and seigniorage see the data for Brazil in Figure 4, Figure 5 and Figure 6.

Causes of inflation and high money growth:

1. The budget deficit is hard to reduce for political and structural reasons.

2. Credit and bond markets are not very well developed and therefore bond financing of deficits is hard.

3. Bond financing is more expensive than monetary financing (seigniorage) since you don’t pay interest on money.

So, if you can’t reduce the deficit and you can’t issue debt, the only alternative s to print money to finance the deficit.

Consequence: high rates of growth of money and high inflation.

Implication: **High inflation is always a** **fiscal
problem**. In fact the nominal budget deficit is:

P_{t}(G_{t} - T_{t}) = dM_{t}
+ dB_{t }= p_{t}M_{t} + dB_{t }=

= Seigniorage (inflation tax) + Debt Financing

While the near proximate cause of high inflation is always
**monetary** as inflation is associated with high rates of growth of
money, the true structual cause of persistent high inflation is a **fiscal**
deficit that is not eliminated with cuts in spending and/or increases in
(non-seigniorage) taxes.

How to cope with inflation when you are in an international firm operating in a high inflation country ?

1. Streamline cash management (invest in indexed assets).

2. Reduce payment terms periods.

3. Delay your nominal payments.

4. Measure financial performance in terms of dollars.

5. Hedge your currency risk.

**Further Web Links and Readings**

For more Web readings on this chapter's topics look at the home pages on Macro Analysis and Macro Data sources and the controversy on NAIRU.