Nouriel Roubini and David Backus

Lectures in Macroeconomics

Chapter 6. Money and Inflation

Today we're going to look at the determination of nominal variables, specifically the price level, its rate of change the inflation rate, and the nominal interest rate. The idea is that inflation is associated with high rates of money growth. This theory, you'll see shortly, exhibits a strong separation between real and nominal variables, since we have already described how real variables are determined with no mention of the price level or inflation rate. This is a hallmark of Classical theory. We'll see shortly that the Keynesian theory does not have this feature, and economists differ about whether it is an embarrassment, a strength, or both.

The Quantity Theory of Money
Open Market Operations
Interest Rates and Inflation
Evidence
Application: Friedman's Money Growth Rule
Application: Big Inflations
Summary
Further Reading
Further Web Links and Readings
Variable Definitions

The Quantity Theory of Money

Now suppose we do the same thing with money. This is unrealistically simple (remember, we're doing theory now!) but suppose the government were to replace every dollar with two new dollars, marked so we can tell the difference between old and new dollars. Then you'd expect, I think, that prices in terms of new dollars would be twice as high. In short, changes in the money supply executed in this way will be associated with proportionate changes in prices, with no effect on output or employment.

Of course the world is more complicated than this, and monetary policy consists of more than just currency exchanges, but some of the same reasoning applies more generally (or may apply, we'll look at some data shortly). The so-called quantity theory of money is the result of two ideas: that money is not fundamental (pieces of paper don't change the effectiveness of GM's manufacturing processes or marketing strategies), and that its usefulness is in executing transactions. Let's start with the latter. Suppose we think of Y as all the transactions in the economy and PY is the dollar value of all these transactions (sales revenue). Then we need M dollars of money to make all these transactions each period, or

M = P Y.

Note that this equation has the stock-split property: if we double M then we double PY. We can make this more specific by associating transactions Y with real GDP, PY with nominal GDP, and P with the GDP deflator.

A slight generalization is that money can be used several times each period for transactions, as it goes from one person to another. That is,

M V = P Y,

where V is the velocity of money, the number of times each period a unit of money is in a transaction. The assumption of the quantity theory, which dates back at least three hundred years (a long time in economics), is that velocity is approximately constant. This equation maintains the stock-split property, that increases in M are associated with proportionate increases in PY.

In principle the increase in PY could be in P, Y, or both. Later we'll consider a theory in which Y changes are possible (the Keynesian theory). But for now let's say that Y is not affected by M. This is the assumption that fundamentals like Y are not influenced by M, just as a firm's value is not influenced by a stock split. The theory behind this in our case is that Y has been determined by the production function and the labor market. That leaves only one thing to adjust when M changes: the price level P. In short, changes in the stock of money lead, in this theory, to proportionate changes in prices.

The same theory can be reinterpreted in terms of the inflation rate, the rate of growth of the price level. To see this, we need to covert the quantity theory relation to growth rates. We take the quantity equation at two different dates and divide, getting

(M_t /M_t-1) (V_t /V_t-1) = (P_t /P_t-1) (Y_t /Y_t-1 ).

For reasons similar to our growth accounting relations in Chapter 4, this leads to (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 variables (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

If money growth does not influence output, then higher money growth leads to higher inflation. Period. This prediction is overly strong, as we'll see, but the simplicity has some value of its own, including making it easy to remember. As Milton Friedman put it: "Inflation is always and everywhere a monetary phenomena." It's only after you think about that sentence for a while that you realize it's not as informative as it first sounds.

Open Market Operations

P_t (G_t-T_t) = dM_t = M_t - M_t-1

which says each dollar of deficit is financed by printing dM new dollar bills. Literally, the government pays its bills with currency. This is how Yugoslavia, for example, got such a high inflation rate: the costs of fighting the war were paid for, in large part, with cash, which by now is nearly worthless.

The other way the government gets currency into the economy is by changing the composition of its balance sheet. The government's balance sheet might be represented, in highly streamlined form, as (approximate numbers for 1992, billions of dollars):
 

Now suppose the government (generally the central bank) wants to increase the quantity of currency in the economy by 10 billion dollars. It does this by buying 10 billion of bonds from someone in the private sector, and paying for them in cash. This changes the balance sheet accordingly. This is referred to as an open market purchase of government securities, for obvious reasons, and is the method of choice in most developed countries. The institutional details sometimes looks quite different (the US, for example, has a highly developed "money'' market for short term securities, and we never actually see cash changing hands), but this is still basically what is going on underneath it all.

Interest Rates and Inflation

i_t = r_t + p_t^e.

The question is what our theory tells us about the relation to be between inflation and nominal interest rates. The theory that fits in with our stock-split analogy (fundamentals do not change, and r is a fundamental) is that the real interest rate r is determined by investment and saving without regard for money and inflation. That's apparently what we assumed in our presentation of this aspect of the Classical theory, since there was no mention of money when we determined the real interest rate and output. For a given real interest rate, what happens to the nominal interest rate if inflation rises? Clearly the nominal interest rate rises by the same amount. Thus an increase in inflation (really, expected inflation since it's the future that matters) leads to higher nominal interest rates.

Evidence

Here's how the theory does in practice. The first prediction can be expressed two ways: velocity is approximately constant or (this follows from the quantity equation) the price level mimics the money stock adjusted for output growth. In logarithms,

log P_t = log M_t - log Y_t + log V_t.

By assumption V is constant, so if M is growing faster than Y we should see a comparable rise in the price level. Do we? I've graphed these variables in Figure 1, with M defined as the broad money stock, M2 (which includes, as we've noted, time and saving deposits as well as checking accounts). (Y here is real GDP and P is the implicit GDP deflator.) I think you'll agree that the relation is pretty good---maybe as good as you'll ever see in economics (we have aspirations, but this isn't physics). To a first approximation, it seems that the assumption of constant velocity isn't too bad. Most of the increase in the price level over the past thirty years has been associated with a comparable increase in the broad stock of money. There are, however, some wiggles in velocity over the short term (up to three years, say) that we may want to look more closely at.

How well does this work in the short run? You can see in Figure 1 that there are some "wiggles" that reflect fluctuations in velocity. What does that do to our prediction? If we graph annual growth rates we know (recall our GDP graphs) that these short-run movements will show up more clearly. In terms of the theory, the prediction is

(P_t -P_t-1)/P_t-1 = (M_t -M_t-1)/M_t-1 - (Y_t -Y_t-1 )/Y_t-1

or:

p = m - y

since velocity is assumed to be constant. These variables are graphed in Figure 2, where we see that the connection between money growth and inflation is much looser for these short-run movements. In this sense, the theory is a much better prediction of long-run tendencies than short-run fluctuations.

Our second prediction concerns interest rates. In the theory we saw that the real interest rate was determined by saving and investment schedules. In principle these curves, and hence the real rate of interest, can move around over time---for example, as government deficits vary. The nominal interest rate will move around for a second reason: because expected rates of inflation vary. With the exception of the Korean War, inflation was less than four percent until the late 60s. It rose during the Vietnam War, peaked above 10 percent in 1975, declined slightly, and peaked again at about ten percent in 1980. The question for the moment is whether this pattern is reflected in interest rates. In Figure 3 I've graphed the one-year treasury rate and the rate of inflation (computed from the GDP deflator). Here, too, the relation isn't bad: we tend to see high rates of interest in those periods when inflation is highest, and vice versa. As a rough approximation, at least, nominal interest rates reflect rates of inflation. There are still, though, some significant short-run deviations. Note in particular that real rates, measured as the difference between the two curves, were higher in the late 1980s than elsewhere in the entire postwar period.

Thus the classical quantity theory seems to provide a reasonably good guide to long-run trends in inflation and interest rates. In the short-run, though, something more complicated seems to be going on. That's our objective for the Keynesian theory to come: to get a better understanding of these short-term fluctuations.

Application: Friedman's Money Growth Rule

Over the years Friedman provided many arguments for constant money growth rates. Here are a few of them (stated as hypotheses to think about, not self-evident truths):

• This policy should have good long-run properties (low inflation).
• It might be better than actual policy over the last forty years, since it would probably eliminate some of the big mistakes (like the high inflation rates of the 1970s).
• Discretionary short-run policy management leads, in practice, to shortsightedness and bad long-run policy decisions. Eg, suppose the Fed continually increases the money stock to avoid recessions. The result is higher inflation, not demonstrably better output performance.
• Monetary policy is a string, you can pull on it but you can't push. In other words, you can use it to start a recession, but not to stop one.

Friedman's points are a combination of theory, fact, and pessimism regarding government, little of which is inarguable. But I think all of these issues are important. It's still an open question how well (or poorly) such a policy would do, but it's had an effect on actual policy. I think that after the experience of the 1970s, when policy repeatedly failed to eliminate either inflation or business cycles, policymakers are less ambitious now about managing the economy in the short-term. Greenspan, for example, does not adhere to a rigid money growth rate rule, but he uses monetary growth rates as guides to the long-run inflation content of his policies. At the same time, he is willing to make large policy changes in response to special conditions, something clearly opposed by Friedman. In the wake of the 1987 stock market crash Greenspan, in conjunction with other central bankers, engineered a sharp increase in funds and a sharp drop in interest rates to cushion the fall. There was some worry at the time that this would eventually lead to higher inflation, and inflation did rise somewhat over the next 3-4 years, but I think most observers view it as an astute move that may have prevented financial and economic disaster.

There's also some discussion recently about whether monetary policy should be more expansionary. The argument in favor is that this might help us get out of a recession when we are stuck in one; we'll see how next week. Friedman's counterargument might be that (i) it won't do it ("string") and (ii) it will lead to inflation over the longer run. The Fed currently has members with both views, plus the entire spectrum in between. And since you never know what would have happened if you had followed some other policy, there's lots of room for differences of opinion.

My feeling is that, like much of what Friedman says, there's a useful point here but he's pushed it too far. I'd guess that a constant growth rate rule, for average growth rates over two to five years, would be a pretty good long-run policy. That leaves room for short term deviations, without letting them get out of hand: so when the economy is headed towards a recession, the Fed will expand the money supply and reduce interest rates; while it will do the reverse if the economy is growing too fast and there are signals of inflationary pressures in the economy. This would probably eliminate most of the excesses of the last thirty years. As an economist at the Bank of Canada put it: "Our goal is to avoid disasters, like the inflation of the 1970s. Anything else is a bonus."

Application: Big Inflations

But why? If the relation between money growth and inflation is so clear, why don't these countries simply print less money? If only it were so easy! The real problem most of these countries had was a large fiscal deficit. Let's think how that influences monetary policy. If a government is running a deficit, then it must issue iou's of some sort to pay for it. Roughly, speaking, it may issue money (dollar bills or their local equivalent) or interest-bearing debt (treasury bills and notes) denoted with the variable B. Mathematically we can express this as

P_t (G_t - T_t) = dM_t + dB_t,

or, in real terms:

G_t - T_t = dM_t / P_t + dB_t / P_t

where the two terms on the right are issues of new money (dM) and new interest-bearing debt (dB), respectively. This is an example of a government budget constraint: it 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, typically, is that a political impasse makes it nearly impossible to reduce the budget deficit. Given the government's budget constraint, it must then issue debt. Now for US debt there is apparently no shortage of ready buyers, but the same can't be said for Argentina or Russia. If they can't issue debt and they can't reduce the deficit, the only alternative left is to print money: in short, when they can't pay their bills any other way, they pay them 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 government, by printing money, acquires real goods and services, seignorage is is effectively a tax imposed by the government on private agents. Such a seignorage tax is also called the inflation tax. The reason is the following. From the definition of seignorage:

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)

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

To understand the relation between money creation, budget deficits and seignorage see, for example, the data for Brazil in Figure 4, Figure 5 and Figure 6. Through 1993 it appeared that Brazil was committing the cardinal sin of inflation stabilization: they are trying to reduce the inflation rate by controlling money, but without solving their underlying budget problems. Experience indicates that this approach is bound to fail.

The thing I like about this analysis is that it gives a strange twist to Friedman's quote: inflation might be a monetary phenomenon, but the money is a reflection of bad fiscal policy, not monetary policy. We might say instead: "Inflation is always and everywhere a fiscal phenomenon."

To understand better why inflation is a fiscal phenomenon, note again that a government with a budget deficit can finance it either by printing money (that leads to seignorage or the inflation tax) or by issuing public debt:

(G-T) = dM/P + dB/P = p (M/P) + dB/P

Note also that countries such as Argentina, Bolivia, Brazil and Israel had very high inflation rates in the 1980s. Now, if inflation was purely a monetary phenomenon caused in the first place by an exogenous excessive rate of growth of money, these countries could have reduced inflation quite fast by printing less money and reducing the growth rate of the money supply. Instead, all these countries had a really hard time in reducing their inflation rates. So, if inflation was due to an exogenous high growth rate of money, why didn't these countries print less money ? The main problem is that these countries had large structural budget deficits and printed money to finance it. In this sense, the excessive growth rate of money that led to seignorage and caused inflation was not exogenous but rather endogenous and caused itself by the need of these governments to finance their budget deficits.

Note, however, that these countries could have in principle avoided the high inflation if they had cut their budget deficits (thus reducing the need for seignorage revenues) and/or if they had financed their budget deficits by issuing bonds rather than by printing money. This leads to the further question: why weren't the deficits reduced and/or why weren't the deficits financed by issuing bonds?

Budget deficits are often very hard to reduce for political and structural reasons: cutting deficits implies reducing government spending and/or increasing taxes and both policies are politically unpopular. Also, in countries with inefficient tax collection systems and where there is a lot of tax evasion, it is hard in the short-run to reform the tax system so as to increase (non-seignorage) revenues. Conversely, increasing seignorage revenues is much easier as it implies printing new money, an executive action rather than a legislative action as in the case of traditional taxes. Of course, seignorage is as much of a tax as regular taxes but it is politically more hidden (at least at low levels of inflation) as the effect of higher money growth leads to higher inflation only slowly over time.

For what concerns the possibility of (non-inflationary) bond financing rather than (inflationary) monetary financing of the deficits, there are several obstacles to such a policy option in many developing countries. First, bond markets are not very well developed (and in some cases altogether absent) in many countries. Second, citizens are concerned about buying nominal long-term bonds issued by the domestic government because an unexpected increase in inflation by the government would lead to a fall in the real value of these bonds (that is equal to a wealth tax on the public holdings of such bonds). Third, bonds indexed to inflation and/or short-term bonds that pay returns close to current market rates are still subject to default risk if the government decide to renege on its obligations. Fourth, the ability to borrow abroad and/or issue bonds denominated in foreign currency in international capital markets may also be limited by the default risk of the country. Fifth, even when some bond borrowing may be available either domestically or abroad, governments may not be willing to issue such bonds. In fact, bond financing is more expensive than monetary financing (seignorage) since governments do not pay interest on their monetary liabilities while they have to pay interest (high ones if inflation is high) on their borrowing. Sixth, borrowing by issuing debt means that the stock of debt goes up every year by the amount of the the flow of debt financing: B_t+1 = B_t + dB_t. This growth of debt may be very costly and not be sustainable in the long-run. In fact, if the public debt grows a lot (relative to GDP), at some point private agents might become unwilling to buy new debt (or even roll-over old debt that comes to maturity) as high debt increases the probability that the government might at some point default on its debt obligations. So, if such a panic occurs and the private sector refuses to buy new debt and/or renew the old one, a government with a structural budget deficit will eventually be forced to start printing money and thus create inflation. Therefore, in face of a structural deficit, trying to reduce inflation today by issuing bonds rather than printing money will just lead to higher debt in the future that will eventually force the government to monetize the deficit (when the debt constraint is hit) and thus will cause inflation in the future. Again, inflation is a fiscal phenomenon and there is no escape from it if the underlying deficit problem is not solved: attempts to reduce current inflation by issuing bonds only implies that future inflation will be higher when the ability to issue debt is exhausted and the government is forced to switch to a monetary financing of the deficit.

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

Finally, note that for someone operating an international business, the thing to remember is that "big inflations'' are relatively common. So what do you do if you're hit with one? You'll probably find that the most important thing you can do is streamline your cash management. If you can reduce the payment terms from (say) 60 days to 30 days, you increase your "real'' revenue substantially. You may also find that big inflations leads to policy changes, like price controls, that make your life more complicated. Finally, you may find that your financial statements, and incentive programs based on them, are highly misleading, since they measure performance in terms of the local currency, whose value is changing rapidly. For a US subsidiary, high inflation triggers a change in the rules for translating financial entries into dollars for tax and reporting purposes (hyperinflation is defined, for this purpose, as 100 percent over 3 years).

Summary

1. The Classical theory exhibits complete separation between real variables and inflation. There is, by construction, no effect of money growth on real output or the real rate of interest.
2. In the Classical theory, inflation is driven by money growth (the quantity theory) and nominal interest rates by inflation (the Fisher relation).
3. In the data, the theory's predictions look better for long-run trends than for short-run fluctuations.
4. Extremely high rates of inflation are generally associated with high rates of money growth, often the result of financing large fiscal deficits by printing money. In this sense, there's no simple distinction between monetary and fiscal policy.

Further Reading

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 controversies on NAIRU and the New Economy.

Variable Definitions

Copyright: Nouriel Roubini and David Backus, Stern School of Business, New York University, 1998.