Part 1: Focus on the currency demand function proposed by Cagan
Summary:
– During periods of hyperinflation described by Cagan, the main variable explaining changes in real money holdings is expected inflation, with other variables being negligible.
– When the government increases the money supply to finance its spending, economic agents respond by adjusting their real cash holdings: everyone gets rid of their excess money by buying physical goods to store their wealth, which leads to inflation. In the case of stable equilibria, the only way for the government to reduce inflation is to reduce its monetary financing.
– By theorizing this behavior and considering inflation expectations to be adaptive, Cagan shows in his work that the demand for money can be considered stable even in a period as unstable as hyperinflation.
Introductory note: Hyperinflation is a phenomenon that attracts little interest in current debates. However, it is often worth remembering that the monetary orthodoxy advocated by the Bundesbank (a culture partly inherited by the ECB when it was created) is due to the traumatic memory of the hyperinflation episode in the Weimar Republic in the 1920s, which some believe contributed to the rise of the National Socialist Party, with the consequences that everyone is familiar with. Today, Germany continues to advocate monetary orthodoxy with a line that could be summarized as « the state budget is one thing, monetary policy is another, » while others are calling for the ECB to directly monetize the debt of our financially troubled states. After all, what is the danger? A little inflation or hyperinflation? Where is the line between the two? Under what conditions can hyperinflationary dynamics be triggered?
This article, in two parts, reviews the major contributions to the literature on this subject from a purely theoretical perspective.
Philippe Cagan’s article « The monetary dynamic of hyperinflation, « published in 1956 in a collection of papers on the quantity theory of money edited by Milton Friedman , « Studies in the quantity theory of money, « has since become a standard reference on the subject. Still cited in some current papers, Cagan laid the foundations for the behavior of money demand in a hyperinflationary environment. Better still, he showed that, in a context as unstable as an episode of hyperinflation (where prices can rise by more than 1,000% each month in some cases!), money demand could nevertheless remain very stable. In the debate between Keynesians and neoclassical economists on the stability of money demand [1], Cagan’s contribution is therefore in line with the arguments of the « quantitativists, » showing that the hypothesis of stable money demand supported by the latter could not be contradicted by the presence of hyperinflationary episodes.
To understand the dynamics of hyperinflation, we will first take a long look at the money demand function proposed by Cagan. In a second part, which will be the subject of a future article, we will use this tool to show how a hyperinflationary dynamic can be triggered.
Hyperinflation: some statistical characteristics.
Cagan defines hyperinflation in his article as « a period during which inflation exceeds 50% per month. » In his study, Cagan examines several experiences of hyperinflation (Austria, Germany, Greece, Hungary, Poland, Russia). In all these cases, every month, prices and the quantity of fiat money increased at astronomical rates (19,800% monthly inflation on average for Hungary over one year, for example!).
The main characteristic observed, however, is that real money holdings tend to decline (i.e., prices rise faster than the amount of money in circulation).
In his article, Cagan proposes a money demand function that can explain the behavior of real money holdings during episodes of hyperinflation.
General information on the money demand function
A money demand function can take several forms, depending on the country and the economic context. Cagan mentions the following variables: wealth (1), income (2), and the expected return on other forms of wealth compared to the return on money (3).
1-With regard to wealth, the concept is easy to understand: when an individual’s wealth [2] increases, they will generally consume more and therefore be inclined to hold more money, given that money is the ultimate liquid payment instrument.
2-Similarly, when an individual’s income increases, it is reasonable to assume that they will hold a larger amount of money.
3-The third variable is the most important in the context of this study. It is the difference between the expected return on other forms of wealth and the expected return on money (in other words, the opportunity cost of money).
Let’s start with the return on money. What does this correspond to?
– For banknotes and coins, this return is clearly 0: no one gains or loses anything in nominal terms by holding money in the form of coins or banknotes.
– For demand deposits, the return is negative if the individual pays for the associated banking services (which is the case for most of us in France), and positive if the individual has a demand deposit account that pays sufficient interest (which is what online banks currently offer).
So what are the other ways of holding wealth?
– We can hold our wealth in the form of bonds or shares: the expected return will then be higher than that associated with holding banknotes or coins in general, but with additional risk (credit, market, liquidity, etc.).
We can also hold our wealth in the form of physical assets. In his contribution, Cagan refers to « durable consumer goods, » which can be considered analogous. It is this latter form that is important here.What is the expected return on a « durable consumer good »? It corresponds to the anticipated increase in the price of these goods [3], i.e., the anticipated inflation on these goods. It is therefore clear that, in a period of prolonged inflation affecting consumer goods, it is preferable to hold wealth in the form of goods rather than currency, since the former has a zero real return while the latter has a negative real return (which is all the greater when inflation is high).
In other words, inflation makes the return on real cash holdings even more negative when the real return on consumer goods is zero [4]. We can therefore see the dynamics of hyperinflation taking shape: the more agents anticipate a high inflation rate, the less they will want to hold cash.
Formalization of the money demand function chosen by Cagan
According to Cagan, anticipated inflation also appears to be « the only variable that fluctuates widely enough to account for drastic changes in real cash holdings. » Based on these observations, he proposes a money demand function that can explain episodes of hyperinflation. The money demand function presented by Cagan therefore has the expected inflation rate as its main variable, with the other variables being ignored in order to explain the behavior of money demand during periods of hyperinflation. He therefore takes the function:
Log(M/P) = constant – α (anticipated inflation)
Where (M/P) represents actual cash holdings and α is therefore the semi-elasticity of money demand to expected inflation, a positive coefficient since when expected inflation increases, the demand for money decreases if reality is consistent with the theory explained above (it can be shown that the elasticity of money demand to expected inflation can be measured by α * expected inflation).
An important simplification is made here: Cagan assumes that the adjustment time between desired cash holdings and actual cash holdings is zero, and therefore that the level of desired cash holdings is equal to the level of actual cash holdings. This assumption is essential for the conductability of his statistical study, but is relaxed in the rest of his study for the theoretical explanations that we will discuss later.
Other essential assumptions and statistical results:
A second equation is important here: the one that determines expected inflation. There is no concrete measure of the latter for the period in question [5], so how can it be modeled? By assuming [6] that inflation expectations are adaptive, i.e., that they are revised at a given time t, based on the difference between the actual inflation rate and the expected inflation rate, and after solving differential equations, Cagan directly expresses expected inflation as a function of actual inflation, i.e., known variables. More precisely, he considers expected inflation as a weighted average of current and past inflation rates, with exponential smoothing so that recent inflation has a much greater weight than past inflation in determining expected inflation.
The statistical results he obtains, highly significant regression coefficients with correlation coefficients very close to 1, lead him to conclude that variations in expected inflation can explain variations in real cash holdings in a hyperinflationary context [7]. The stability of these coefficients therefore supports the hypothesis of stable money demand, much touted by quantity theorists, even in periods of instability such as episodes of hyperinflation.
The lesson from this analysis is that the money supply plays a key role.
The process it describes can therefore be interpreted as a dynamic process in which the trajectory of prices over time is determined by the quantity of money in circulation and by an (exponentially) weighted average of past variations in that quantity of money. The key element underpinning this interpretation is the mechanics of money demand relied upon by quantity theorists, which can be simplified in this analysis as follows: when the quantity of money increases, economic agents adjust their level of real cash holdings to bring it back to the desired level; by attempting to get rid of their excess nominal cash holdings by purchasing goods and services, they drive up the price level [8].
Thus, it is past and current changes in the money supply that will cause episodes of hyperinflation. Except in the case of a self-generating process (a special case that Cagan describes theoretically in his essay) [9], hyperinflation can only end with slower growth in the money supply, which will impact expected inflation and thus have the opposite effect on the demand for money, resulting in a smaller increase in the price level.
If the analysis therefore suggests that episodes of hyperinflation can be explained by excessive growth in the money supply, the question that remains to be addressed is why governments increase the amount of money in circulation. Is it suicide? Not really.
Continued in Part 2 s (coming soon).
Notes:
[1] The term « stability of money demand » refers to the fact that the parameters of the money demand function are stable: they do not vary significantly over time (all other things being equal). The debate on the stability of money demand was the subject of much discussion in thesecond half ofthe 20th century. The debate is indeed difficult to settle: if a money demand function proves to be statistically unstable (a Chow test on the parameters is sufficient, for example, to prove this instability), some may still argue that this statistical instability stems from the fact that certain variables are omitted or poorly measured (measuring innovations such as credit cards is very difficult), or from the fact that the explained variable (money) is poorly defined (the choice of aggregate being subjective in nature). Even if, as Friedman says, « there is little if any difference between asserting that the demand for money is highly unstable and asserting that it is a perfectly stable function of an indefinitely large number of variables. »
[2] We are still talking about individuals here, and never about businesses. The concept of money is different for the latter in that it is an input in its own right (in concrete terms, a business’s working capital requirement can be considered an essential factor of production; by its very nature, a business sees its cash inflows follow its outflows). However, the analysis remains unchanged insofar as, according to Friedman, a company’s money demand function can be considered to depend on the same variables as an individual’s money demand function, such that the two functions can be conflated (see Friedman 1956).
[3] Of course, this excludes the rate of depreciation of this asset, which can be assumed to be constant without altering the reasoning proposed here.
[4] We are, of course, considering inflation on consumer goods here.
[5] Today, anticipated inflation can be measured through surveys, or, for example, by taking into account the difference between the yields on inflation-indexed bonds and the yields on bonds with the same characteristics but not indexed to inflation (even if this measure is not perfect).
[6] Again, this is a simplifying assumption, which therefore limits the scope of his study, as he discusses in his essay
[7] The purpose of this article is not to comment on the statistical methods used here, which of course have certain limitations in view of the advances made over the past half-century in econometric science (the stationarity of variables is an obvious limitation of these results, for example).
[8] The reasoning seems simplistic, but in reality it is not far from the reality of the hyperinflationary episodes described by Cagan: in this context, the returns on bonds and other assets were negligible in the face of inflation (price instability leading in any case to a very strong aversion to debt contracts), so the choice of goods proved to be the most logical choice (hence the function chosen). Prices were rising so fast that anyone receiving money rushed to spend it, both to cover their needs and to acquire goods as a store of value, the latter being much safer and more profitable than money. In a normal context, a money demand function naturally takes into account assets as another potential store of value.
[9] The idea of a self-generating process is as follows: rising prices lead to a proportionally greater decline in real cash holdings, which in turn takes the form of higher inflation than before, and so on. According to Cagan, this instability has never occurred in practice.
