Is the slowdown in economic activity observed in developed countries over the past 30 years the result of a real shortage of new ideas or a measurement error? Current growth indicators underestimate economic activity, but do not explain its decline.

A somewhat pessimistic view of the economy is to think that the slowdown in activity that we are seeing in most developed countries is real and lasting, in particular because new ideas are increasingly difficult to find. Robert Gordon thus defends the idea that the age of great inventions is behind us, and that this slowdown is both inevitable and irreversible. To give some figures and put the current situation into perspective, the reader can refer to the work of Bergeaud, Cette and Lecat (2016) who propose an assessment of the growth of the GDP and productivity since the XIX^{e} century in several countries. Thus, since 1890, the GDP per French capita has grown by an average of 2.1% each year, but only by 1.2% since 1980, 1% since 1990 and 0.7% since 2000.

### Feedback on measuring economic growth

In opposition to this view, several commentators have pointed out the possibility that this measured growth is currently underestimated, notably relying on the Solow paradox: technology is omnipresent, but seems to have no effect on national statistics. Two arguments suggest that the current slowdown in growth may be a statistical artifact. First, the measurement of economic growth was designed to measure changes in market activity, and thus does not fully capture changes in well-being by omitting important dimensions such as increases in lifespan or domestic production. For example, many recent innovations involve activities outside the market sphere, such as time spent on social media or time saved by shopping online. While these activities may increase well-being, they have never been included in the calculation of economic growth.

The second source of measurement error is of a different nature, since it is not a question of definition, but a practical difficulty. To understand it, it is useful to look back at how national statistical institutes assess growth. The first step is to calculate “nominal output”, i.e. to add up the monetary value of goods and services sold. However, because of inflation – a general increase in the price level – a euro spent today does not correspond to the same purchasing power as it did thirty years ago. This means that it is necessary to subtract the inflation rate from nominal output growth to obtain real output growth. Therefore, an overestimation of inflation by 1% translates into an underestimation of measured real output growth by 1%. Since nominal output is relatively easy to measure, the crux of the problem lies in how inflation is estimated. Inflation is supposed to measure the change in the purchasing power corresponding to a given unit of money. So, if the price of the same model of a car increased by exactly 3% between 2017 and 2018, we can say that the inflation on this car is 3%. However, in practice, car manufacturers evolve their models by adding different options from one year to the next, thus improving its quality. To assess inflation, it is then necessary to subtract from the observed price change the part that is due to this improvement in quality, which turns out to be a very delicate step in practice. This problem linked to the modification of products by the same manufacturer and its impact on growth was identified in the mid-1990s by the Boskin Commission and led to the estimate that American growth was thus missing around 1.1 percentage points in 1996.

### Do we really know how to measure innovation?

But what happens when the producer of the product itself is replaced by another? For example, when a restaurant replaces its neighboring competitor because it offers menus that consumers prefer? In practice, when a product or service disappears without being replaced by a new version from the same producer, national statistical institutes use a method called “imputation”. In concrete terms, this involves attributing to this product or service the average price change observed among similar products or services that have not disappeared, before replacing it with another. Assessing the measurement error linked to this mechanism is the subject of a recent study that we conducted with our colleagues Timo Boppart, Peter Klenow and Huiyu Li. The source of error that we identified comes from the fact that imputation assumes that the average price change of the surviving products is a good approximation of the price change of the product that disappeared. Now the work of Joseph Schumpeter, among others, has shown that the phenomena of destructive creation – the replacement of companies by others that are more productive and innovative – occur precisely because the new producer offers a good that is cheaper, once the price is adjusted for quality.

Using a theoretical model, we propose a simple formula to assess the measurement bias resulting from this dynamic of destructive product creation. This formula also has the advantage of being able to be estimated using only the data of the market share of entering establishments compared to surviving establishments, i.e. establishments that already existed last year and that did not exit. The intuition is as follows: when two products have the same quality, the producer who sells them at the lowest price will have a higher market share and, symmetrically, a producer whose quality-adjusted prices are lower will capture a higher market share than the others. Following this logic, the market share of surviving establishments decreases as soon as their quality-adjusted price increases relative to those produced by entering establishments. The imputation method usually used by national statistics institutes makes the implicit assumption that the market share of surviving establishments is stable over time. A decrease in this market share is therefore a sign that inflation is overestimated – since the fall in prices brought about by new entrants is not taken into account – and therefore that growth is underestimated.

We therefore estimate this bias on data from US establishments between 1983 and 2013. The results are presented as time series in Figure 1 below. The green curve corresponds to total growth, defined as the sum of growth measured by the Bureau of Labor Statistics (BLS) and published annually under the name “Multifactor Productivity”, and of the missed growth due to the bias we have just described. The blue curve also presents our estimates of this “missing” growth.

### Estimates of invisible growth

We then make several observations. First, the magnitude of the missed growth linked to the measurement bias described above is of the order of 0.6 percentage points per year over the thirty years considered. This corresponds to approximately a quarter of total growth. Second, we do not observe any particular trend in the share of total growth that would be missed. This result is important because it offers an initial response to the hypothesis that the slowdown observed since the mid-2000s in the United States would be due to a measurement error. Our results suggest instead that growth is significantly underestimated, but that this has always been the case, at least for three decades. Finally, we repeat the same exercise in different sectors in order to determine the main source of the measurement error linked to creative destruction. It is then interesting to note that the manufacturing industry contributes only very modestly to the 0.6 percentage point that we estimate. On the contrary, the sectors playing a predominant role are those experiencing high business turnover rates: hotels and restaurants, commerce and health.

These results are valid for the United States, but what about other countries? We replicated this study in France with our colleague Simon Bunel (Aghion et al., 2018) and estimate a bias of 0.5 points since 1994, slightly lower but in the same order of magnitude as in the United States. Interestingly, in France too, this measurement bias does not seem to explain the observed slowdown in productivity.

### A more optimistic view of growth and income trends

A natural question at this point is whether this measurement bias has an impact on the economy, particularly given that there seems to be no discernible trend in the magnitude of the missing growth. Yet knowing real growth precisely is useful for answering many questions. For example, existing studies use measured inflation to calculate children’s real income relative to their parents’. Chetty et al. (2017) document that 50% of children born in 1984 had higher incomes than their parents at age 30. If we take into account the missing growth, children’s real incomes would increase by about 17% relative to their parents’, significantly increasing the proportion of those who are more successful than their parents. Thus, to the extent that inflation is overestimated due to imputed values, a larger proportion of children appear to be economically better off than their parents. This improvement in economic well-being may shed a somewhat more positive light on current conditions, despite the gloom of slower productivity growth. On the other hand, a more negative consequence of this measurement bias is that inequalities, for example geographical, could be more pronounced than we think: indeed, as documented by Aghion et al. (2018) for France, the richest departments (measured in GDP per capita) are also those for which growth would be most significantly underestimated.