Cagan: Money and Hyperinflation
In 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 hyperinflation
α = 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 longterm 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 Crown
Inflation 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 Model
TABLE 1
A DYNAMIC MODEL OF EXCHANGE RATE CHANGES AND INFLATION
1.
The Exchange Rate
D ln S = ɑ1 ln(Ŝ 𝑆)
where the partial equilibrium level of the exchange rate, (Ŝ) is Ŝ = 𝐵𝑈 (𝑏ȗ 𝑝𝑢𝑠 )
and bu is the demand for real cash balances:
bȗ = ƴ𝑒 −𝛽1𝜋 𝑒 𝑒 −𝛽2𝐷𝑙𝑛𝑝 𝑒 −𝛽3𝐷𝑙𝑛𝑆 ƴ𝛽4
(1b)
2.
Prices
Dln p = ɑ2 ln 𝐵𝑈 𝑝 𝑏ȗ + ɗ1 ln (𝑦 ӯ)
And
D𝜋 𝑒 = ƛ (d ln p - 𝜋 𝑒 )
3. Supply of nominal cash balances
𝐷2 ln 𝐵𝑈 = ɑ3 ln(𝑦 𝑝)/𝐵𝑈) + ɑ4 𝐷𝑙𝑛((𝑦 𝑝)/𝐵𝑈) + ɗ2 ln(ӯ 𝑦) + 𝑐𝑜
where y is potential output:
Ӯ = 𝑦𝑜 𝑒 ɗ4𝑡
(1)
(1a)
(2)
(2a)
(3)
(4)