Inflation and price indices
andrea.parisi | Published: 25 Sep 2024, 9:42 a.m.
Inflation has been in the headlines over the past few years: the steady rise of prices has become an ubiquitous concern, affecting businesses, investors, and everyday consumers. In simple terms, inflation is a sustained increase in the general price level of goods and services in an economy over time. It is often measured as an annual percentage change in the Consumer Price Index (CPI), which tracks the prices of a basket of common goods and services.
In its original meaning, inflation referred to the practice of debasing gold and silver coins by including non-precious materials. The term comes from the Latin word "inflatio", which literally means "increase" or "expansion". In the past, rulers would create new money by substituting circulating currency with coins that had a reduced content of precious metal, often replaced by more common metals like copper or zinc. By doing so, they could produce more coins using the same amount of precious metal. For example, if 10% of the gold in circulating coins was substituted with another material, there would be enough gold to increase the number of circulating coins by 11%. This allowed the issuer of the coins (the holder of the right to mint) to create free money for their own purposes. The resulting increase in the total monetary mass always led to price increases, which is why today we term the latter "inflation". However, inflation has further consequences: when the amount of circulating money increases, those who receive it first will benefit, as they can spend it before the effects of the price increase spread throughout the economy. This is known as the Cantillon effect, named after the French economist Richard Cantillon, who first described it.
Si l’augmentation de l’argent effectif vient des mines d’or ou d’argent qui se trouvent dans un État, le propriétaire de ces mines, les entrepreneurs, les fondeurs, les affineurs, et généralement tous ceux qui y travaillent, ne manqueront pas d’augmenter leurs dépenses à proportion de leurs gains. Ils consommeront dans leurs ménages plus de viande et plus de vin ou de bière, qu’ils ne faisaient, ils s’accoutumeront à porter de meilleurs habits, de plus beau linge, à avoir des maisons plus ornées, et d’autres commodités plus recherchées. Par conséquent ils donneront de l’emploi à plusieurs artisans qui n’avaient pas auparavant tant d’ouvrages, et qui par la même raison augmenteront aussi leur dépense ; toute cette augmentation de dépense en viande, en vin, en laine, etc. diminue nécessairement la part des autres habitants de l’État qui ne participent pas d’abord aux richesses des mines en question. Les altercations du marché, ou la demande pour la viande, le vin, la laine, etc. étant plus forte qu’à l’ordinaire, ne manquera pas d’en hausser les prix. Ces hauts prix détermineront les fermiers à employer d’avantage de terre pour les produire en une autre année : ces mêmes fermiers profiteront de cette augmentation de prix, et augmenteront la dépense de leur famille, comme les autres. Ceux donc, qui souffriront de cette cherté, et de l’augmentation de consommation, seront d’abord les propriétaires des terres, pendant le terme de leurs baux, puis leurs domestiques, et tous les ouvriers ou gens à gages fixes qui en entretiennent leur famille.
This simple logical argument, according to which individuals furthest from the source of new money creation will be disproportionately affected, has been known for over 200 years. It implies that those on fixed incomes will bear the brunt of inflationary pressures. Despite its longevity, this idea is rarely discussed in economics. The argument takes on even greater significance in the context of modern fiat currency systems.
Modern money, disentangled by gold, is easier to inflate. The monetary mass has been steadily increasing over the past 100 years. Meanwhile, global productivity has surged, with significant gains in goods production. This increase in output has largely offset the price increases that would have been expected from the growth in monetary mass. As a result, the focus of "inflation" has shifted from the expansion of money supply, to the increase of prices. The stated goal is to keep prices stable for the benefit of the public, but this approach has come at the cost of depriving individuals of the price reductions that technological progress would have otherwise provided. Prior to the abandonment of the gold standard, price declines were common; today, they are less so.
With inflation now referring to the increase in price levels, its measurement is a task more complicated than tracking the growth in monetary mass. One surprising aspect of "modern" inflation (at least from my perspective, given my scientific background) is that its measurement is delegated to national statistics institutes. Without questioning their professional capabilities, the fact that inflation can only be measured by official institutes makes these measurements as unscientific as they can be. Although private institutes around the world provide estimates of inflation, these never enter official calculations. In other words, national statistics institutes act like authoritative "prophets", whose results are taken at face value without scrutiny. This is antithetical to the principles of science. Furthermore, there is not a single measurement of inflation, but rather multiple measurements depending on the objective, and these are all commonly referred to as "inflation" despite measuring different things.
We can try to gain insight into this set of measurements by looking at how price increases are tracked. We introduced the nominal GDP in our previous article. The nominal GDP corresponds to the total value of goods produced during a time period $T$. Typically, this corresponds to one year, and we will assume that from now on. The nominal GDP can be expressed as: \begin{equation} \begin{array}{lcl} \textsf{nominal GDP} & = & \sum_{j \in K} N_j P_j\\ & = & N P \end{array} \end{equation}
where $P_j$ and $N_j$ are the price and number of units of item $j$, $K$ is the set of all available items, and $N$ is the total number of items and $P$ is the average price of an item, defined as: \begin{equation*} P = \frac{1}{N} \sum_{j \in K} N_j P_j \end{equation*}
Now suppose we wish to compare the GDP of two different years, trying to answer the question of whether production has increased. When prices from year to year change, it becomes difficult to make a meaningful comparison. Suppose the kind and amount of items remain the same, but prices increase. In this case, P will increase, and thus the nominal GDP will also increase. However, this increase in GDP does not reflect an actual increase in production, but rather an increase in prices. To remove the effect of price inflation, the nominal GDP is divided by the rate of price increase: the resulting real GDP should provide a better way to compare productivity and economic performance across different years.
If $r$ is the rate of price increase and $P'$ the average price of goods in the second of the two years, then \begin{equation} \label{CPI-base} P' = r P \end{equation}
and the real GDP is calculated as: \begin{equation} \label{real-GDP} \textsf{real GDP} = \frac{\textsf{nominal GDP}}{r} \end{equation}
The rate of price increase $r$ plays a crucial role in these calculations. As discussed earlier above, the evaluation of this number is delegated to the national institutes of statistics. Additionally, while one might think that measuring the increase in prices is a unique business, in reality the definition of $r$ has morphed into a plethora of estimates, each with a specific focus. Thus, the factor $1/r$ appearing in equation \eqref{real-GDP} is called the GDP deflator, but measuring $r$ in \eqref{CPI-base} has morphed into measuring the Consumer Price Index and a number of similar measures which do not actually measure $r$, but some connected quantity.
All methods have in common the methodology that is used for the estimate which, even now, is an active area of research. Currently, several methods are used, each with its own issues: a look at the Wikipedia page listing the most popular methods is illustrative.
Generally speaking, to evaluate $r$ we need to estimate the change in prices over a given time period, taking into account how many items are being exchanged on the market. In formula, this would be given by: \begin{equation} r = \frac{P'}{P} = \frac{\sum_{j \in K} N_j P'_j}{\sum_{j \in K} N_j P_j} \end{equation}
where $K$ is the set of items on the market. However, in practice, we typically do not have access to information about all different kinds of goods exchanged on the market. Owing to this limitation, the value of $r$ is evaluated as: \begin{equation} r \simeq \frac{\sum_{j \in K'} w_j P'_j}{\sum_{j \in K'} w_j P_j} \end{equation}
where $K'$ represents a "meaningful" subset of the global set of goods $K$, and $w_j$ are weights that measure the relative importance of good $j$ exchanged on the market with respect to the full set of goods in $K$. Setting $w_j = 1\ \forall j$ one gets: \begin{equation} r \simeq \frac{\sum_{j \in K'} P'_j}{\sum_{j \in K'} P_j} \end{equation}
The above formula gives the Dutot price index. While setting $w_j = 1$ may not be justified, in most cases there are no detailed information to evaluate the correct weight for each good. However, it may be possible to gather aggregate information through surveys or other means. For example, using expenditure data from surveys, it is possible to build a "basket" of goods that reflects typical consumer spending patterns. This basket can then be used to evaluate the average change in value of each good within the basket. If an arithmetic mean is used, the index is called the Carli index; if a geometric mean is used, then it is called the Jevons index. The resulting averaged value is an estimate of the relative price change for the given typology of goods. The next step is to collect all typologies of goods and perform a weighted average, where the weights are based on the relative importance of each good within the basket. Summing up, the rate $r$ is evaluated as: \begin{equation} r \simeq \sum_{\lambda \in \Lambda'} w_{\lambda} r_{\lambda} \end{equation}
where $\Lambda'$ is a subset of typologies of goods available on the market, and $w_{\lambda}$ are the weights assigned to each typology. The values $r_{\lambda}$ are evaluated using an average of prices collected using either an arithmetic or geometric mean: \begin{equation} r_{\lambda} = \left \{ \begin{array}{l l} \sum_{k \in \lambda} \frac{p'_k}{p_k} & \textsf{Carli}\\ \left( \prod_{k \in \lambda} \frac{p'_k}{p_k} \right)^{1/|\lambda|} & \textsf{Jevson} \end{array} \right . \end{equation}
The methodology described is not unique and can vary between countries. Additionally, even when weights are estimated using survey data, there is no universal rule for determining the basket of goods to be included in the index. An interesting example is the inclusion or exclusion, depending on the country, of housing costs and rents from the consumer price index. When the cost of buying a new house is excluded from the calculation of the CPI, it might reflect the effective short term costs encountered by the average household, but it will not take into account the fact the the current generation entering the job market is unable to afford buying a house, whereas their grand-parents were able to buy one with an average salary. Even more these costs may change more than the CPI.
The basket of goods is often updated over time, with new items being added or old ones removed depending on changes in consumer spending patterns or other factors. However, there is no coded and well defined scientifically driven mechanism that drives these changes: proof of this is the fact that the national institutes of statistics in each country operate differently and make different choices. This can lead to inconsistencies and challenges in comparing inflation rates across different periods or countries.
The discrepancy between the "original" meaning of inflation and the "modern" meaning of inflation has become more evident in recent years as many economists have acknowledged that their Consumer Price Index does not takes into account the effects of substitutions. As the price of a good goes up, a consumer might decide to buy an equivalent less expensive product. This substitution is not captured by the estimates of the institutes of statistics if the index monitors the changes in price of the same goods without taking into account this effect. Now, this may seem a logical observation, and an index that takes into account the effect of substitution would certainly provide a better picture of the true cost of living. The problem however is that once again we are moving away from the original definition of $r$ and of inflation, towards something akin to "cost of living" or, even worst, "survival". The fact that individuals must switch to lower quality products is a loss of standard of living. Unfortunately this distinction and careful handling of mathematical equations seems not correctly undertaken in economic theory. Even if the difference between taking into account or not substitution might be small, the yearly differences are compounded, leading to long term large discrepancies. The transition through these different approaches has led to moving from economic policies that could increase standard of living (if inflation is measured as the increase in monetary mass), to policies that at least try to maintain standard of living (when inflation is measured without taking into account substitution), to economic policies that essentially maintain survival (when substitution is further taken into account).
Most importantly, the focus on the "modern" meaning of inflation has shifted the common thinking from a view of technological advance providing abundance to people, to a view of technological advance providing a simpler life at same prices. The expansion of monetary mass has moved the gains that people would have otherwise achieved, towards those who are closer to money creation, as Cantillon understood two hundred years ago. The fact that wealth distribution has become more skewed as discussed here is the result of this expansion of the monetary mass.
