Cagan: Money and HyperinflationIn post-WWI Germany ... and other episodes of hyperinflation• The demand for real balances was stable• The higher the opportunity cost of holding money, the less

money people chose to hold• The hyperinflation was not self-generating

In self-generating inflation, a small rise in prices causes a flight from money:

High inflation Higher expected inflation Higher inflation

• The rates of money creation and inflation exceeded the real-revenue maximizing rate• Weak, desperate government relied on an inflation tax ... but

couldn’t even get the tax rate right

Cagan’s Model• The demand for real balances depends on

• Real wealth• Real income• The opportunity cost of holding money—the “interest rate”

• When inflation (C)is high and variable– real wealth and income don’t vary nearly as much as inflation and

can be ignored– the opportunity cost of holding real balances is the expected rate

of inflation (E)ln(M/P)d = - γ – α E or (M/P)d = e- γ – α E

• Adaptive expectations: Expected inflation increases to extent actual inflation exceeds what was expected

dE/dt = β(C – E)

Cagan’s Model: Critical Features

• Expected inflation is a weighted average of past inflation– Inflation in more recent months weighted more heavily than inflation

in less recent months• The elasticity of real balance demand with respect to expected

inflation increases with expected inflation[d(M/P)/(M/P)]/[dE/E] = -αE

• If money growth is independent of inflation, inflation is self-generating when αβ > 1.

δC/C = - β/[1 - αβ]If inflation is not self-generated, it must be driven by money inflation

• An “inflation tax” is levied on real balances: – Steady state tax revenue is R = C x (M/P)– Steady state tax revenue is maximized when C = 1/α

Parameter Estimates for Germany, August 1922 – November 1923

• Ignoring outliers toward end of the German hyperinflationα = 5.46 β = .15

• Toward end of the hyperinflation period, people held real balances in excess of what the model predicts People anticipated currency reform and stabilization

Cagan Conclusions• Money demand (the demand for real balances) is stable

even in the face of hyperinflation– Parameters α and β are estimated with confidence– Money is “scarce” in times of hyperinflation—real

balances become vanishingly small• Inflation is not self-generated

As Milton Friedman would have it, “Inflation is always and everywhere a monetary phenomenon.”

• Weak, desperate government inflates too rapidly for its own good– Initial increases in money inflation rates yield high real tax

revenues because of lags in real balance adjustments– But such high rates of inflation tax cannot be sustained

Sargent (1982): The Ends of Big Inflations

Drivers of big inflations: “printing money for your friends”Austria, 1919 – 1922• ... expansion of central bank notes stemmed mainly from the bank’s

policy of discounting treasury bills. .. [but] also from it’s practice of making loans and discounts to private agents at nominal interest rates of between 6 and 9% per annum.

Hungary, 1919 – 1924• The government of Hungary ran substantial budget deficits...financed

by borrowing from the State Note Institute...An additional cause in the increase in liabilities of the institute was the increasing volume of loans that it made to private agents.

Germany, 1919 – 1923• During 1923 (actually beginning summer 1922), the Reichsbank

began discounting large volumes of commercial bills...at nominal rates of interest far below the rate of inflation, amounting virtually to government transfer payments to the recipients.

Sargent (1982): Rat-X and The Ends of Big Inflations• Firms and workers strike inflationary bargains in light of expectations

of high inflation.• They expect high rates of inflation because ... current and prospective

monetary and fiscal policies warrant these expectations.• The current rate of inflation and people’s expectations of future rates

may well seem to respond slowly to isolated actions of restrictive monetary and fiscal policies that are viewed as temporary.Thus inflation only seems to have a momentum of its own. It is actually the long-term government policy of persistently running large deficits and creating money at high rates which imparts the momentum to the inflation rate.

• ... eradicating inflation would require far more than a few temporary restrictive fiscal and monetary actions.

• It would require a change in the policy regime: there must be an abrupt change in the continuing government policy, or strategy, for setting deficits now and in the future that is sufficiently binding to be widely believed.

Germany: From 1923 Hyperinflation to 1924 Stabilization • Rentenmark issued by Rentenbank – 1 trillion Mark = 1 Rentenmark– Quantity of Rentenmark limited by law respected by Rentenbank– Maximum Rentenmark available to government limited by law

• Budget swung to balance– Taxes raised– Gov’t workers/Railroad workers discharged/those over-65 retired– Postal workforce reduced/Reichsbank workforce reduced

• Dawes Plan implemented (Chas Dawes: VP ‘25, Nobel Prize)– Reparations restructured– Reichsbank put under Allied supervision: Parker Gilbert, Agent

–Stabilization loan obtained• Stabilization crisis: sharp but short-lived

Sarah CrownInflation and Currency Depreciation in

Germany, 1920-1923: A Dynamic Model of Prices and the Exchange Rate

Giuseppe Tullio – a professor of monetary economics at the University of Brescia,

Italy

Brief Survey/Problems of the Literature• The Quantity Theory of Money

– Bresciani-Turroni (1937)– Cagan (1956)– Graham (1930)– Jacobs (1975, 1976)– Khan (1975, 1977a, 1977b, 1980)

• Exchange Rate– Frenkel (1976)

• Rational Expectations– Sargent and Wallace (1973)– Sargent (1977)

Tullio’s “Correct” Model• Domestic and foreign currency substitution in the demand for

real money balances• A dynamic mechanism allowing short-run deviation of the

exchange rate from PPP• A feedback from prices to money

Dynamic ModelTABLE 1A DYNAMIC MODEL OF EXCHANGE RATE CHANGES AND INFLATION

1. The Exchange RateD ln S = (1) where the partial equilibrium level of the exchange rate, (Ŝ) is Ŝ = (1a)and bu is the demand for real cash balances:bȗ = (1b)2. PricesDln p = (2)AndD = ƛ (d ln p - ) (2a)3. Supply of nominal cash balances (3)where y is potential output:Ӯ = (4)