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The Size of Firms and the Nature of Innovation

Big firms do things differently

Published onJun 02, 2023
The Size of Firms and the Nature of Innovation
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We are used to thinking about income inequality between individuals, but inequality between firms is vastly larger. In the US, the richest 1% of individuals earned about 20% of all income in 2018.1  In contrast, the top 1% of US firms by sales earned about 80% of all sales in 2018. The economy is populated by a few “superfirms” and multitude of small- to medium-size businesses. And this disparity is getting more extreme over time.2 Does this huge disparity in firm size matter for innovation and technological progress? Do big firms differ in the type of R&D they do, and if so, why?

The academic literature about the empirical link between firm size and innovation is an old one, dating back to the 1960s at least,3 and we do not have space to do it full justice here. Instead, in this post we’ll focus on work using a variety of approaches to document that there are important differences in how innovation varies across firm sizes. In a followup post, we’ll examine some explanations for why.

One quick point before digging in: when economists talk about firm size, they typically refer to its total sales or (more rarely) its employment count. Defined in this way, firm size is often used as an imperfect proxy for the number of business units of a firm (i.e. the number of product lines it has).

Fact 1: Firm size and R&D rise proportionally

The first important fact about firm heterogeneity and innovation is that corporate R&D expenditures scale up proportionately with their sales. In other words, when sales double, money spent on R&D doubles too. This doesn’t have to be the case: for example, it has been shown that other inputs in production such as labor4 and capital5 do not scale proportionately with firm sales (less than proportionately for labor, more than proportionately for capital).

This proportional relationship has been shown time and again, at least for firms above a certain size who do at least some R&D.6 To illustrate this point, the figure below shows the relationship between firm sales and R&D expenses among publicly traded firms who report doing some R&D. The data is from Compustat (a database of publicly listed firms) and each dot represents 750 firm-by-year observations. In this graph, we control for year and fine sector (SIC4) so that the variation we isolate is across firms, within a year and within a sector.7 The slope is strikingly close to 1 on a log-log plot, meaning that the typical publicly listed firm increases its R&D expenditures by 10% when its size increases by 10%.

Firm R&D expenditures by firm sales (log plot)

Notes: Graph generated by Arnaud Dyèvre, with data on US publicly listed firms from Compustat. The sample of firms only include firms who report some R&D expenditures in a year. Sales and R&D are deflated using the Bureau of Labor Statistics CPI.

This finding was first observed in the 1960s and has been reproduced across many studies since. In the figure below, from a seminal 1982 study by Bound, Cummins, Griliches, Hall and Jaffe, the authors have plotted log R&D expenditures of a panel of 2,600 manufacturing firms, as a function of their log sales, in 1976. The same proportional relationship is observed.

Firm R&D expenditures by firm sales (log plot). Data from Bound, Cummins, Griliches, Hall and Jaffe (1982)

The 1-to-1 proportionality of R&D to sales may lead one to conclude that the immense heterogeneity in firm sizes does not matter for the aggregate level of innovation. After all, if R&D scales proportionately with firm size, then an economy consisting of 10 firms with $1 billion in sales each will spend as much on R&D as an economy consisting of one firm with $10 billion in sales. But as we’ll see, this conclusion would be erroneous.

Fact 2: Larger firms get fewer inventions per R&D dollar

A variety of different lines of evidence show that firms get fewer inventions per R&D dollar as they grow.

Let’s start with patents  (we’ll talk about non-patent evidence in a minute). The 1982 study by Bound, Cummins, Griliches, Hall and Jaffe mentioned earlier found that firms with larger R&D programs get fewer patents per dollar of R&D. Their result is summarized in Figure 3 (panel A) below; it shows an exponential decrease in the number of patents per R&D dollar as one moves up the size of firm’s log R&D expenditure. In a more recent and more comprehensive exploration of this relationship, Akcigit & Kerr (2018) use the universe of firms in the US matched to patents to document that patents per employee also decrease exponentially as a function of log employment (panel B). The relationships shown in the figures are very similar and suggest that bigger firms are getting fewer patents per productive unit—employment or R&D dollar. 

Left: Patents per dollar of R&D as a function of total R&D expenditures (x-scale in log). From Bound, Cummins, Griliches, Hall & Jaffe (1982).

Right: Patents per employees as a function of total employee count (x-scale in log). From Akcigit & Kerr (2018).

Patents are not synonymous with invention though. It could, for example, be that as firms grow larger they create just as many inventions per R&D dollar, but they become less likely to use patents to protect their work. But in fact, the opposite seems to be true. Mezzanotti and Simcoe (2022) report on the Business R&D and Innovation survey, which was conducted between 2008 and 2015 by the US Census Bureau and the National Science Foundation. This survey asked more than 40,000 US firms, from a nationally representative sample, about their use of intellectual property. They find larger firms are much more likely to rate patents as important. For example, 69% of firms with more than $1bn in annual sales rate patents as somewhat or very important, compared to just 24% of firms with annual sales below $10mn. This relationship also holds when you compare responses across firms belonging to the same sector, in the same year. In other words, if we had a perfect measure of innovation that is not affected by selection like patenting is, we would find an even stronger negative relationship between firm size and patent per R&D dollar or per employee. Small firms have more patents per employee or R&D dollar, in spite of being less likely to file patents than big firms.

Other empirical studies of innovations have relied on different measures of innovative output and have reached a similar conclusion. In a creative 2006 study of the financial service industry, Josh Lerner uses news articles from the Wall Street Journal to identify new products and services introduced by financial institutions. For example, if a story about a new security or the first online banking platform is written in the WSJ, Lerner counts it as an innovation and attribute it to a bank in the Compustat database. Consistent with papers using patent data, he finds that innovation intensity scales less than proportionately with firm size. (Note that Lerner measures size as the log of assets here rather than log sales, due to the nature of the industry studied.)

You can also look for the introduction of innovations in other places. In 1982, the US Small Business Administration created a database of new products, processes or services in 100 technology, engineering or trade journals, and linked these inventions to firms. In their 1987 paper using this data, Acs & Audretsch also find that larger firms have fewer innovations per employees and fewer innovations per dollar of sales than small firms. (Though they emphasize that this isn’t universal; in some industries, large firms produce more innovations per dollar than small firms - but this isn’t typical)

Finally, Argente et al. (2023) use product-scanner data in the consumer goods sector over 2006-2015 to obtain details on every product sold in a large sample of grocery, drug, and general-merchandise stores, including the associated firm that markets the product. Here, they identify innovation as the introduction of a new product; as the figure below illustrates, bigger firms consistently introduce fewer new products, relative to the number of products they already sell (gray line below).

From Argente et al. (2023)

Of course, not all new products are equally innovative. To deal with this issue, Argente and coauthors use data on the attributes of each product. Since they know the price and sales of each product, they can run statistical models to estimate a dollar value consumers put on different product attributes. They can then “quality adjust” new product introductions by the introduction of products that include new attributes, where attributes are given more weight if associated with higher prices (or sales). This more sophisticated approach yields the same result: when you adjust for quality, you still find that larger firms are less innovative (relative to their size) than small ones.

(Incidentally, Argente and coauthors also use text similarity algorithms to link firm patents to consumer products, and find larger firms tend to have more patents per consumer product, not less. That’s further evidence that the decline in patents per productive unit as firms grow larger probably reflects a decline in invention, not merely less reliance on patents.)

Fact 3: Larger firms produce more incremental innovations

Finally, when large and established firms actually do innovation resulting in observable products and services, it is more likely to be directed toward improving existing products rather than creating new ones. A few pieces of evidence point to this.

First, relying on another survey of firms, Akcigit & Kerr (2018) find a strong negative association between firm size and the share of R&D dedicated to business areas where the firm has no existing revenues. The bigger a firm is, the more it tries to improve its existing products.

Patent evidence also points to larger firms engaging in more incremental innovation. For example, Akcigit and Kerr (2018) also find that larger firms are more likely to cite their own patents, which is an indication that they are hewing close to the intellectual landscape they have previously explored. For example, among firms that filed a single patent in 1995, 9% of citations to recent patents went to the firm’s own patents. Among firms that filed 2-5 patents, the share rises to 17%. Among firms filing more than 100 patents in 1995, nearly a third of citations to recent patents went to the firm’s own patents! While bigger firms will tend to cite their own work more often simply because their own patents occupy a larger share of the total citable material, Akcigit and Kerr show this effect isn’t big enough to drive the results.

You have to be cautious leaning too heavily on patent citations as a signal of knowledge flows though (though I think the fact that this analysis predates the year 2000 is one reason to be more confident), but Argente et al. (2023) obtain similar results using different approaches, at least for the consumer products sector. Rather than look at the extent to which a firm cites its own patents, they look at how similar or different is the text of a patent to the text of the firm’s prior patents. If a firm’s patent uses a lot of the same language as its earlier patents, that’s another signal that its innovation is more incremental and less radical. By this measure, they find larger firms are less likely to have novel patents.

From Argente et al. (2023)

Lastly, Argente and coauthors can also use their data on actual products sold to go beyond patents. If we reinspect their figure from earlier in this article, which plotted the rate of new product introduction versus the size of firms, we see further evidence that large firms introduce more incremental innovations. While the rate of new products falls by roughly 50% from the smallest to the largest firms, the rate of quality-adjusted new products falls by more than 80%, indicating new products are less likely to introduce new valuable product attributes among large firms.

Bigger Isn’t Better?

Taken together, we have something of a puzzle. It appears that larger firms get fewer innovations per dollar of R&D and that those innovations tend to be more incremental and less impactful. That isn't necessarily a problem, and we would caution against leaping to conclusions based on this descriptive correlational data. Still, together these three facts present a puzzle: given the apparent decline in the productivity of their R&D, why do large firms keep investing in R&D at the same rate as small firms?

We’ll look at some theories in a follow up post.

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Cited in the Above

Measuring knowledge spillovers: the trouble with patent citations


Articles Cited

Kwon, Spencer Yongwook, Ma, Yueran, and Zimmermann, Kaspar. 2023. 100 Years of Rising Corporate Concentration. SAFE WP No. 359. http://dx.doi.org/10.2139/ssrn.3936799

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Acs, Zoltan J. and David B. Audretsch. 1987. Innovation, Market Structure, and Firm Size. The Review of Economics and Statistics vol. 69 (4): pp. 567–74. https://doi.org/10.2307/1935950

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