Part Two: The source of hyperinflation: rational behavior by a lax government
Summary:
– There is a theoretical inflation threshold that maximizes government revenue. However, the inflation rates observed during episodes of hyperinflation are much higher than this optimal rate.
– The time lag in adjusting real monetary balances allows the state to increase its revenues (in real terms) by constantly increasing the amount of money it issues. This is the mechanism at work in the episodes of hyperinflation described by Cagan.
– In this context, hyperinflation lasts as long as the government is unwilling to reduce its spending: it will then increase the amount of money in circulation, thereby forcing itself to increase this amount even further in the future due to the decline in the purchasing power of the resulting money supply.
Introductory note: this article is the second part of a contribution intended to explain the hyperinflationary mechanism presented by Cagan in his article, which is often used as a reference on this subject, and follows on from a first part that has already been published.
In the previous article, we characterized the demand function used by Cagan to explain hyperinflation. This function takes into account only the main relevant variable: expected inflation. In this context, the creation of money by the government mechanically leads to inflation.
Why, then, does a government persist in creating money [1]? The answer may seem simple at first glance: the government is in difficulty, can no longer borrow on the markets, is unwilling or unable to reduce its spending, and therefore finances itself through money creation.
However, we have seen that in a hyperinflationary context, every time the government issues money, economic agents rush to get rid of it, thereby creating inflation. The additional money created by the government for its financial needs therefore paradoxically leads to an increase in its overall financial needs (via inflation), especially when the inflation anticipated by economic agents is high [2].
Is it therefore pointless for a government to finance itself through money creation if we refer to this model? Not really, firstly (1) because the reasoning is only valid when inflation is already at a high level, and secondly (2) because of the simplification made regarding the adjustment period for real cash balances.
We will first develop the first point through the concept of the Seigniorage Laffer curve (1), before focusing on the consequences of the existence of a delay in the adjustment of agents’ real cash balances for the monetary financing of the state (2).
- (1) The Laffer curve of seigniorage, or the existence of a limit level of inflation that maximizes government revenue in the context of monetary financing.
To understand the principle of the seigniorage Laffer curve, let us first recall the principle of the Laffer curve.
The Laffer curve
The principle of the Laffer curve (named after the American economist and publicist Arthur Laffer) is part of fiscal policy and answers the following question: what is the maximum level of taxation theoretically possible in an economy?
The bell-shaped curve illustrates the concave relationship between the level of taxes in an economy and the tax base on which these taxes are levied. In the rising part of the curve, the higher the tax rate, the higher the total level of tax (S = tax rate * tax base). However, at a certain level, increasing the tax rate will decrease the total tax. The reason for this is that the tax base is itself linked to the tax rate: the more the tax rate increases, the more the country’s consumption and production will theoretically decrease, and therefore the more the total wealth of the economy will decrease [3].
This explains why the increase in tax revenue following an increase in the tax rate is less and less significant in the first part of the curve. The downward sloping part of the curve therefore corresponds to a situation in which the increase in the tax rate has such a significant depressive effect on the economy (and therefore on the tax base) that this increase results in a decrease in the total level of taxes.
The extension to the Laffer curve of seigniorage
The principle of the Laffer curve of seigniorage is the same. Note that this is a concept of medium/long-term equilibrium at work here: the question is what happens if a new equilibrium inflation rate is chosen (assuming that the government determines the inflation target).
Here, inflation П plays the role of the tax rate, and real cash balances M/P play the role of the tax base. This relationship results from the mathematical expression of seigniorage [4]:
S = ΔM/P = (Δ M / M ) * (M / P) =gm(M/P) = П (M/P) [5]
M/P corresponds to the level of real cash holdings. This formalization also allows us to understand why seigniorage revenues are called « inflation tax. »
How can the government increase its seigniorage revenue? By increasing the money supply, seigniorage revenue will only increase if the additional revenue from inflation exceeds the decline in the tax base resulting from the increase in inflation (M/P).
Empirical studies tend to show that the relationship between real money demand and inflation is concave (as Cagan does), i.e., for low levels of inflation, the decrease in real cash demand resulting from the increase in inflation is relatively small, while it will be greater in the case of high levels of inflation. It is this concave relationship that means that, at low levels of inflation, an increase in the level of inflation will increase seigniorage revenues, whereas above a certain threshold, the decrease in the tax base will be such that seigniorage revenues will be lower than before. We therefore find the relationship presented above via the Laffer curve .
According to this analysis, revenues from money creation are maximized at a certain level of inflation (A here). In most countries, however, it is very rare to find studies that cite monthly inflation rates exceeding 15% (equivalent to an annual rate exceeding 400%). This is surprising when we know that inflation rates in episodes of hyperinflation exceed 50% per month. Why, then, would a government deliberately increase the level of inflation if it knows that its revenues will be lower as a result?
- (2) The time lag in adjusting monetary balances: the source of the potentially unlimited nature of inflation tax revenues
We have previously described the money demand function used by Cagan. This function made an important assumption in order to make the statistical study feasible: it was assumed that the desired real cash balances were equal to the actual real cash balances, in other words that the adjustment period for real cash balances was zero [6].
However, this assumption is very simplistic. It is even invalid, since it is precisely the presence of a cash adjustment period that is at the root of hyperinflation dynamics. The government can actually take advantage of this adjustment period: when it increases the amount of money in circulation more than it has in the past, cash balances do not adjust immediately but with a certain delay, so it is as if the tax rate had increased without the tax base having decreased. By implementing a policy whereby the government continually increases the amount of money in circulation, it takes advantage of the adjustment period for cash reserves each time, so that the inflationary tax generates increasing revenues.
This would not be the case if economic agents anticipated this mechanism. What Cagan says on this subject is is that individuals’ persistent confidence in the future value of money (one might think of a certain inertia in individuals’ habits and beliefs) maintains this adjustment period and therefore does not cause an extreme flight from this currency (even if, for Cagan, this period shortens as the episode of hyperinflation lasts).
The key to ending episodes of hyperinflation as described by Cagan lies in the hands of the government concerned.
The episodes of hyperinflation described by Cagan do not correspond to self-generating processes where the spiral is uncontrollable [7]. In this context, the key to ending episodes of hyperinflation lies in the hands of the state concerned: all it needs to do is reduce its monetary financing.
Before this dynamic kicks in, we might also ask why the state resorts to this method of financing (see Box 1 for a historical example). It is often the simplest solution when the state becomes insolvent. State insolvency can be described as a situation in which the state collects the maximum possible taxes through income tax (maximum of the Laffer curve) and inflation tax (maximum of the seigniorage Laffer curve). In this context, taking advantage of the adjustment period for cash reserves in order to increase its revenues is one of the simplest solutions for the state if it wants to maintain its level of spending.
It should also be noted that in a hyperinflationary context, the collection of standard taxes (income tax, profit tax, etc.) is often best abandoned altogether, as collection delays make the real revenue from these taxes very low.
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Box 1 In past episodes, political problems have always been associated with the onset of hyperinflation. This was the case in Zimbabwe not long ago, where lax and discretionary policies by the government and its central bank led to serious financial losses, and where the government wanted to maintain its level of spending constant for political reasons. The hyperinflationary spiral (231 million percent per year in 2008) came to an end when the government agreed to allow foreign currencies to be used as a means of payment, leading to de facto dollarization of the economy. Often, the credibility of a currency is destroyed following episodes of hyperinflation, so that the country issues a new currency or moves towards dollarization of its economy, as happened in Zimbabwe. |
CONCLUSION: the key points of Cagan’s reasoning
In light of Cagan’s explanations, when a state finances its debt through money creation, hyperinflation can potentially occur under several conditions:
– the inflation rate exceeds the inflation rate that maximizes seigniorage
– the state has no other financing options or is unwilling to use them
– the government does not seek to significantly reduce its level of spending.
For the hyperinflationary equilibrium to be stable, economic agents must have a certain degree of confidence in the government’s ability to change its behavior. Otherwise, changes in the money supply would be unlikely to alter the existing dynamics.
Notes:
[1] For simplicity’s sake, we say directly that « the government creates money, » rather than saying that the government asks its central bank to print money and then transfer the funds directly to it.
[2] Due to the logarithmic form of the chosen function (which can be justified by the different reactions of agents depending on whether the yield gap is small or very large).
[3] The underlying assumption here is that the public sector produces less wealth with this tax than the private sector would have done without it.
[4] It should be noted that seigniorage as measured here corresponds to the amount of monetary financing by the government in real terms, so it corresponds, all other things being equal, to the increase in real monetary cash in circulation in the economy at a given moment.
[5] Under the usual assumptions, we can assume without altering the reasoning that the rate of monetary growth is equal to the rate of inflation. Note that Phelps (1973) considers it more logical to regard the nominal interest rate as the tax rate on real cash holdings (which does not change our analysis here, as the latter is the sum of a real interest rate assumed to be fixed and inflation).
[6] See Cagan (1956) for more details on this methodological point.
[7] Recall that the idea of a self-generating process is as follows: price increases lead to a proportionally greater decline in real cash balances, which in turn takes the form of inflation greater than the initial inflation. According to Cagan, this instability has never occurred in practice.
