• Sergio Focardi

Inflation: it's not what you think it is

In some posts and articles I have argued that in a complex evolutionary economy the concepts of inflation and growth are vague concepts that risk supporting decisions that are more harmful than useful. Inflation and growth are concepts widely used at the academic level, at the journalistic level, in current discourse and in political discourse. In all these areas it is thought that they are obvious and well-defined concepts, currently used by authoritative people. Arguing the opposite may seem like a form of intellectual hubris, a desire to go against the tide for no real reason.


Well, that's not the case. The main reason is that modern advanced economies are complex evolutionary systems that change much more rapidly than in the past. The classic concept of inflation does not represent well economic systems in which products and services change rapidly. The changes are given by technology but also by the symbolism associated with products and services. Today there is an entire advertising and public relations industry that rapidly develops and changes the image of products and services.


In this post I would like to illustrate the problems related to the concept and measure of inflation in very simple and intuitive terms. I will use the data relative to the USA in the period 1950-2020 because these data can be easily verified on the Federal Reserve Economic Data (FRED) website. However, similar considerations apply to European nations.


The classic concept of inflation

Let's start with some considerations with which, I believe, it is easy to agree. According to official data found on the FRED website, in the period 1950-2020 inflation in the US caused the consumer prices of goods and services to rise ninefold. In the current view, inflation means rising prices of goods and services. It looks like a simple and intuitive concept. If all prices would change by the same percentage it actually would be a sound concept. But it is not, because prices change differently, some go up others go down, quantities change, and products and services themselves change.


What does it mean that prices in 2020 are nine times higher than in 1950? There is clearly a serious problem of comparison. Many products and services available today did not exist in 2020, and most of the products and services that existed in the 1950s are substantially different today. On the other hand, products and services available in 1950 no longer exist today. To give some examples, personal computing, cell phones, jet planes, microwave ovens, high-definition television did not exist in the 1950s. Cars, trains, medical care, household appliances, clothes, sports shoes had very different characteristics. We must conclude that it is:


impossible to directly compare the prices of product and services in 2020 with those in 1950.


This is the first point that must be highlighted: over long periods it is not possible to define the concept of inflation as a change of the prices of products and services because products and services change completely in the period considered. There is no observable that represents the change in the prices of goods and services simply because products and services change. We can build weighted averages of prices with various criteria but no direct comparison is possible between sets of products and services so profoundly different.


Since the concept of inflation is so strongly rooted in both economic thought and that of the general public, let's see what possible solutions could be adopted. Recall that the classic concept of inflation is about raising prices. We could calculate the amount of money needed to maintain a certain social level. For example, we could calculate the amount of money needed to maintain the same social level in 1950 and 2020 and define as inflation the percentage change in this amount. But this would be a social concept of inflation, different from the notion of inflation as an increase in the price level. We will return to this point later in this post.


To assess the increase in the price level over long periods, the first idea that comes to mind is to consider not the entire spectrum of products and services that appeared on the market at some time between 1950 and 2020 but only a subset of products and services that have remained truly unchanged throughout the period. One possible narrative could be the following: Inflation is a general feature of the economy. It is not possible to evaluate the increase in prices on all products but we can limit ourselves to analyzing the change of prices of products and services that remained unchanged. But in the 70 years from 1950 to 2020, no reasonable set of products and services, which we can consider representative of the economy, has remained unchanged. Over long periods there is no possibility of direct comparison.


Alternatively, one might think that inflation could be calculated only over short periods and possibly extended to longer periods by a process of mathematical integration. Suppose to break the long period, in our case 70 years, into subperiods of much shorter length, for example in 70 periods of one year each. But this method does not solve the problem of calculating inflation as a change in prices because qualitative changes of products and services as well as the addition of new products and services also exist at the level of subperiods. If we want to make a rigorous calculation there is no method that allows us to calculate the price index of a set of products and services that evolve rapidly. If a product does not exist at the beginning of the period but exists at the end of the period or, vice versa, ceases to exist during the period, it is impossible to calculate how much its price has changed.


In practice, approximations are made. The current approximations consist in considering short periods, a month, a quarter, a maximum of one year, and in choosing a basket of products and services that can be considered constant in these short periods. Inflation is calculated as a change in the price of the basket of goods over the period considered, for example, one year, using one of the indices that have been proposed (Laspeyres, Paasche, Fisher). The inflation thus calculated is extended to the entire economy.


For example, using the Paasche index, the price of the basket is calculated at the beginning of the period and at the end of the periodor leaving the quantities produced unchanged; the index is the ratio between the price of the basket at the end of the period and that at the beginning of the period. Typically this ratio is multiplied by one hundred to express it as a percentage.


Let's review the approximations implied in this method. First, price changes resulting from any qualitative changes of products in the basket generally contribute to the calculation of inflation. Corrective methodologies have been proposed, such as the hedonic method which replaces a product with a series ofcharacteristics. These methods, however, have limited applicability. If the prices of products or services rise due to qualitative improvements, improvements are ignored and the relative price increases contribute to inflation.


In addition, at each period the composition of the basket might change. Changing the composition of the basket typically implies a qualitative change in the basket. However, changes in the composition of the basket do not affect inflation, which is calculated at each period regardless of previous periods.


Finally, changes in the price of products and services excluded from the basket, typically luxury products or high-innovation products, have no effect on the calculation of inflation. However, inflation calculated on the basket is automatically applied to these products and services characterized by a high level of both technological and/or symbolic innovation.


Until now we have assumed that if the products remain qualitatively unchanged it is possible to create an index of the price change. However, even the calculation of the index that represents the change of the prices of the basket in a period is problematic because prices, in general, move in different directions. It is well known that there is no unique way of creating a price index. In fact, to create an index you have to weigh every percentage change but the weights are arbitrary. The indices of Laspeyres, Paasche or Fisher are the most used but in reality there are infinite indices.


Therefore, it is illusory to think that inflation generally and rigorously represents the change in the prices of an economy's products and services. This number, the general change in prices, does not exist. Inflation represents the change, period by period, in the prices of a subset of fairly stable products and services. The basket is, in general, a subset representing the consumption of medium- or low-income households. The placing on the market of new products outside the basket, with the consequent enlargement of all the products that can be purchased, is not taken into account in the calculation of inflation. On the contrary, most price changes resulting from qualitative changes within the basket are calculated as inflation.


From the point of view of households, inflation is perceived as a reduction in the purchasing power of money because the same amount of money allows to buy smaller quantities of products and services. Households, however, also perceive as inflation the widening spectrum of products and services available. If a family realizes that with the same income it loses social position, they inevitably think that there is inflation. The reality is different. Much of what is perceived as inflation is insufficient wage growth in the face of an ever-expanding supply of products and services.


To sum up:


Over long periods, change of the price level is not a well-founded concept.


Products and services are constantly changing and no concept of index of price change and therefore of inflation can be defined.


The concept of inflation applies over short periods where it expresses the price index of a basket of goods and services that excludes many highly innovative products.


To calculate inflation over long periods, inflation rates are multiplied in each period. For example, if in three consecutive years the annual inflation rate was 2%, 3%, and 4%, the three-year inflation rate is: 1.02x1.03x1.04-1=9.26%. This composition does not necessarily refer to an unchanged basket of goods and services. Every year the composition of the basket can change.


The fundamental problem of the current calculation of inflation is as follows:


Inflation is systematically overestimated because it does not take into account changes in the quality of products and services.


On the other hand, households also perceive the loss of social position due to the unfavourable evolution of the wage-profit ratio over medium-long periods. Households perceive their loss of purchasing power given constant wages as inflation. But the reality is different: in the last thirty years labor incomes, wages, have not followed the evolution of the economy.


How can the concept of inflation evolve?

In the classical sense, inflation is defined as a change in the price of a good or service that remains unchanged over time. But, as we have seen, this situation is far from modern economic reality in which products and services change rapidly. Inflation is a theoretical term that represents the index of the change in prices of a basket of goods and services over a limited period. Inflation is an operationally defined variable whose numerical value depends on operational choices: choice of basket, choice of method of indexation of the basket, any corrections such as hedonic methods.


How can we assess inflation over long periods, considering that products change qualitatively, new products are introduced and old products disappear from the market? Are we to say that inflation is an arbitrary concept? Can we say that prices in 2020 are not comparable with those of 1950 and therefore are arbitrary?


Let's fix some concepts. In the presence of qualitative changes, inflation becomes the relationship between the growth of the market price of a product or service and the theoretical growth of the price corresponding to the qualitative improvement of the product or service in question. We call this second concept generalized inflation. In the absence of qualitative changes generalized inflation coincides with classical inflation.


Conceptually there is a big difference between the two notions of inflation. Consider only one product, for example, wheat. Suppose that the price of one kilogram of grain at time t is Pt while it is P(t+1) at the next time. In the classical sense, inflation is simply the percentage change (P(t+1)-Pt)/Pt. For example, if the price goes from 2 euros to 2.5 euros we have an inflation of i = 0.5 / 2.5 = 20%.


If wheat were to change in quality,we would have to say that the price at tempor t+1 is the product of a qualitative increase 1+q multiplied by inflation (1+i):: P(t+1)=Pt(1+q)(1+i). For example, if we had a price increase due to the qualitative element of 10% and an inflation of 10% the percentage change in price should be (1+0.1)(1+0.1)-1=21%. In this case inflation is the residue after the theoretical price change due to the qualitative improvement.

Calculating the correct price increase due to a qualitative improvement is equivalent to calculating the theoretical price of goods and services. However, there is no theoretical price of goods and services, there is only a market price. Financial assets have a theoretical price equal to the discounted sum of future cash flow expectations. But this concept is not applicable to real products and services.


It could be argued that the theoretical price of a product or service is proportional to the amount of labor required to produce it. Recall that in aggregate the only cost is labor. This reasoning, however, risks becoming circular. In fact, work is not homogeneous and there is no theoretical price of labor. And in any case, automation has increasingly released the quality and quantity of products and the quantity and quality of the work necessary to produce them. We cannot calculate the theoretical value of products and services based on the theoretical price of labor.


To arrive at a theory of inflation in the presence of innovation and qualitative changes, it is necessary to adopt a more general and more abstract vision. As we saw in the previous section, inflation in the classical sense is calculated as a weighted average of the inflation of each product of a narrow basket of goods. This is because it is easy to calculate the percentage change in the price of a product that exists throughout the period under review. But we do not have an individual measure of the qualitative change of a product or service.


To arrive at a reasonable concept of generalized inflation, we begin by observing that products and services exhibit different levels of complexity and are subject to qualitative changes of different magnitudes. For the moment we are using these expressions vaguely but what we want to say is quite clear. Pasta is a less complex product than mobile phones. Clothes, on the other hand, have a very high level of innovation due to pressure from fashion and the fashion public relations industry. Intuitively, products that are not very complex, both technologically and symbolically, have a low level of innovation and their price changes can be assimilated to inflation in the classical sense. On the other hand, it can be imagined that highly complex products are subject to strong qualitative changes. It is very difficult to clarify whether such price changes are justified or not.


But how do we divide products and services into two categories of low and high innovation? Hidalgo and Haussman introduced complexity indices, both economic complexity indices -ECI- and product complexity indices -PCI. Figure 1, shows the PCI for the year 2019




Figure 1. Product Complexity Index year 2019 according to Hidalgo and Haussmann. There is a clear separation between products with high complexity and those with medium-low complexity.


So let us consider in general two variables q and i that represent inflation and quality. In the article The qualitative theory of green growth we have described a methodology for estimating variables i,q. We consider the set of all products and use the PCI – Product Complexity Index – introduced by Hidalgo and Haussman. We divide the products into two groups, the low PCI products and the high PCI products. We stipulate that inflation is zero on high-innovation products and that it is calculated using traditional methods for low-PCI products. If there is no inflation in the classical sense, price changes are due only to qualitative changes. In the opposite case, the qualitative changes are zero.


The variable q thus introduced is an indirect measure of quality. The basic idea is that for highly innovative products, the price change is entirely justified by the change in quality and innovation. Generalized inflation is a lower number than classical inflation. Economic growth is therefore higher.


It is possible to describe a more abstract view of inflation in the context of economic growth. In this view, the observable nominal GDP is formed by the product of three variables:

GDP=QuantityxQualityxInflation.


The description of the theory of qualitative growth in a complex evolutionary economy will be the subject of a future post.

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