How Antitrust Regulators Could Use the ‘Perpetual Inventory Method’ to Value R&D

Rohan Shah —  22 February 2021

The slew of recent antitrust cases in the digital, tech, and pharmaceutical industries has brought significant attention to the investments many firms in these industries make in “intangibles,” such as software and research and development (R&D).

Intangibles are recognized to have an important effect on a company’s (and the economy’s) performance. For example, Jonathan Haskel and Stian Westlake (2017) highlight the increasingly large investments companies have been making in things like programming in-house software, organizational structures, and, yes, a firm’s stock of knowledge obtained through R&D. They also note the considerable difficulties associated with valuing both those investments and the outcomes (such as new operational procedures, a new piece of software, or a new patent) of those investments.

This difficulty in valuing intangibles has gone somewhat under the radar until relatively recently. There has been progress in valuing them at the aggregate level (see Ellen R. McGrattan and Edward C. Prescott (2008)) and in examining their effects at the level of individual sectors (see McGrattan (2020)). It remains difficult, however, to ascertain the value of the entire stock of intangibles held by an individual firm.

There is a method to estimate the value of one component of a firm’s stock of intangibles. Specifically, the “stock of knowledge obtained through research and development” is likely to form a large proportion of most firms’ intangibles. Treating R&D as a “stock” might not be the most common way to frame the subject, but it does have an intuitive appeal.

What a firm knows (i.e., its intellectual property) is an input to its production process, just like physical capital. The most direct way for firms to acquire knowledge is to conduct R&D, which adds to its “stock of knowledge,” as represented by its accumulated stock of R&D. In this way, a firm’s accumulated investment in R&D then becomes a stock of R&D that it can use in production of whatever goods and services it wants. Thankfully, there is a relatively straightforward (albeit imperfect) method to measure a firm’s stock of R&D that relies on information obtained from a company’s accounts, along with a few relatively benign assumptions.

This method (set out by Bronwyn Hall (1990, 1993)) uses a firm’s annual expenditures on R&D (a separate line item in most company accounts) in the “perpetual inventory” method to calculate a firm’s stock of R&D in any particular year. This perpetual inventory method is commonly used to estimate a firm’s stock of physical capital, so applying it to obtain an estimate of a firm’s stock of knowledge—i.e., their stock of R&D—should not be controversial.

All this method requires to obtain a firm’s stock of R&D for this year is knowledge of a firm’s R&D stock and its investment in R&D (i.e., its R&D expenditures) last year. This year’s R&D stock is then the sum of those R&D expenditures and its undepreciated R&D stock that is carried forward into this year.

As some R&D expenditure datasets include, for example, wages paid to scientists and research workers, this is not exactly the same as calculating a firm’s physical capital stock, which would only use a firm’s expenditures on physical capital. But given that paying people to perform R&D also adds to a firm’s stock of R&D through the increased knowledge and expertise of their employees, it seems reasonable to include this in a firm’s stock of R&D.

As mentioned previously, this method requires making certain assumptions. In particular, it is necessary to assume a rate of depreciation of the stock of R&D each period. Hall suggests a depreciation of 15% per year (compared to the roughly 7% per year for physical capital), and estimates presented by Hall, along with Wendy Li (2018), suggest that, in some industries, the figure can be as high as 50%, albeit with a wide range across industries.

The other assumption required for this method is an estimate of the firm’s initial level of stock. To see why such an assumption is necessary, suppose that you have data on a firm’s R&D expenditure running from 1990-2016. This means that you can calculate a firm’s stock of R&D for each year once you have their R&D stock in the previous year via the formula above.

When calculating the firm’s R&D stock for 2016, you need to know what their R&D stock was in 2015, while to calculate their R&D stock for 2015 you need to know their R&D stock in 2014, and so on backward until you reach the first year for which you have data: in this, case 1990.

However, working out the firm’s R&D stock in 1990 requires data on the firm’s R&D stock in 1989. The dataset does not contain any information about 1989, nor the firm’s actual stock of R&D in 1990. Hence, it is necessary to make an assumption regarding the firm’s stock of R&D in 1990.

There are several different assumptions one can make regarding this “starting value.” You could assume it is just a very small number. Or you can assume, as per Hall, that it is the firm’s R&D expenditure in 1990 divided by the sum of the R&D depreciation and average growth rates (the latter being taken as 8% per year by Hall). Note that, given the high depreciation rates for the stock of R&D, it turns out that the exact starting value does not matter significantly (particularly in years toward the end of the dataset) if you have a sufficiently long data series. At a 15% depreciation rate, more than 50% of the initial value disappears after five years.

Although there are other methods to measure a firm’s stock of R&D, these tend to provide less information or rely on stronger assumptions than the approach described above does. For example, sometimes a firm’s stock of R&D is measured using a simple count of the number of patents they hold. However, this approach does not take into account the “value” of a patent. Since, by definition, each patent is unique (with differing number of years to run, levels of quality, ability to be challenged or worked around, and so on), it is unlikely to be appropriate to use an “average value of patents sold recently” to value it. At least with the perpetual inventory method described above, a monetary value for a firm’s stock of R&D can be obtained.

The perpetual inventory method also provides a way to calculate market shares of R&D in R&D-intensive industries, which can be used alongside current measures. This would be akin to looking at capacity shares in some manufacturing industries. Of course, using market shares in R&D industries can be fraught with issues, such as whether it is appropriate to use a backward-looking measure to assess competitive constraints in a forward-looking industry. This is why any investigation into such industries should also look, for example, at a firm’s research pipeline.

Naturally, this only provides for the valuation of the R&D stock and says nothing about valuing other intangibles that are likely to play an important role in a much wider range of industries. Nonetheless, this method could provide another means for competition authorities to assess the current and historical state of R&D stocks in industries in which R&D plays an important part. It would be interesting to see what firms’ shares of R&D stocks look like, for example, in the pharmaceutical and tech industries.