So You Want To Estimate Markups

A practical guide

Let’s imagine that you are a student at a large research university in America who wishes to know how distorted the economy is. That is, how far away is output from the social optimum, given a certain set of technologies? You might also want to know, has the market power of big corporations increased or decreased? Are companies earning excessive profits? In order to know this, you need to know how large markups are in the economy. This essay will cover how to estimate these markups using publicly available data, with an eye toward making it intuitive and simple for the novice. But first, some terms.

A “markup” is simply the difference between marginal cost – the cost it takes to produce one additional unit of a good – and the price which it is sold at. This markup can exist for several reason. It could be a sign of the firm having market power, and pricing in order to extract profits. (If you recall, a monopoly causes social loss because it has to restrict the quantity in order to increase the price. This will be important later on). It could also be because there were fixed cost, and in order to make back the cost there has to be a markup. (Explaining why there are markups actually does require a bit more work, but you can see my discussion of the Dixit-Stiglitz framework here). In any event, greater markups indicate more distortions, and an inefficient allocation of resources across firms. (There should be some rule against having a third parenthetical interruption, but this result needn’t hold with non-linear pricing. This was previously on the blog, so I’m unabashedly shilling for it). So how would we go about estimating the markup?

We could simply divide output by price. If there were no fixed costs, this would indeed indicate the markup, but this is obviously incredibly unrealistic. We could also try and estimate consumer demand for the product, which is the approach taken by Berry, Levinsohn, and Pakes (1995) and its many children. This approach is *extremely hard*, and takes quite detailed data on consumer demand (prices, quantities, characteristics, consumer attributes), as well as needing to just assume the way in which firms engage in competition. The data requirements have restricted it to very specific industries, like automobiles in the case of BLP, or the ready-to-eat cereal industry, as in the case of Aviv Nevo (2001). I also don’t really know much about it, so instead we’re going to cover the thing which I do know something about, which is the production approach to estimating markups.

The production approach to welfare estimation is to take the ratio of the elasticity of output with respect to its share of expenditures, given some production function. The production function is simply the optimal combination of variable and non-variable components, and some unobserved productivity. If you are familiar with the Solow model, variable and non-variable correspond roughly to labor and capital, so output Y is a function f(L, K), though labor is not just the employees of a company but also includes materials and energy and so on. This data is relatively simple to obtain, and it is even easier to obtain data on revenue, which can be a proxy for output.

We will, of course, need to estimate the production function. I’m not entirely sure I believe this, but the argument is that capital is less flexible than labor, so it is fixed by the productivity draw of the period before. This actually allows us to estimate a production function for each year of data, using last year’s draw as an instrument.

One of the most important papers using this method is De Loecker, Eeckhout, and Unger “The Rise of Market Power and the Macroeconomic Implications” (2020). They want to know if market power, or the ability for firms to extract excess profits by reducing their quantity supplied, has increased in America. They argue that it has, although this is driven entirely by a few superstar firms that have been wildly profitable. The implication is that there is more misallocation in the US economy since 1980, and that rectifying this is more of a “free lunch” than it would be if it were simply due to firms having larger fixed costs and smaller variable costs.

Except, uh, forget about all that. There’s one very big problem – DLEU don’t use the measure of output, but of revenue. This is a really big deal. Remember how I mentioned how one of the reasons we would care about markups is because firms could increase their profits by reducing their quantities? In order for the revenue to give you a meaningful estimate of markups, you have to say that firms are price takers. In other words, you have to rule out any ability of the firms to affect their own price. If they can affect their own price, the ratio estimator contains no information about the actual markup.

The logic behind this is in the well-titled “Some Unpleasant Markup Arithmetic”, by Bond, Hashemi, Kaplan, and Zoch. Suppose that there is a firm which purchases inputs in a perfectly competitive market at some price it cannot affect. It faces an inverse demand curve, so price is a function of demand. (E.g. 1–x). The elasticity of revenue with respect to the input X is determined both by the slope (the elasticity) of the inverse demand curve and the output elasticity of the input, rather than just the output elasticity alone. Specifically, the elasticity with respect to revenue is 1 plus the elasticity as a function of price and quantity, times the elasticity with respect to quantity and the input. We are faced with a cost minimization problem; the answer to this is to markup the price by 1 over 1 plus the elasticity with respect to price and quantity. This is the same as the elasticity of revenue, so if we use that to estimate the markup, we end up with 1 – no markup, price equal to marginal cost!

Again, the whole point of markups – the whole reason that they happen, the whole reason they are bad – is that the firm can influence the price that people pay for the good by changing the quantity which is produced! So if the ratio estimator is only informative when people pay exactly the markup, which misses the whole point. You must use the quantities, not revenue.

There are other difficulties, of course. In order for us to recover the markup, the variable component needs to be actually variable, and the invarying part actually not varying. If firms face some cost to adjust their inputs, then the markup will be partly determined by the cost of changing their input, which cannot be directly observed. We also need for the productivity draw to follow a random walk, which may not happen if the firm is not a price taker.

So is there anything which can be recovered? De Ridder, Grassi, and Morzenti have an excellent paper “The Hitchhiker’s Guide to Markup Estimation” on what it’s still useful for. You may not be able to find the level of markups, but you can say something about trends in markups (if the industry has a constant production function from year to year) and about the dispersion of markups between firms. Dispersion of markups requires that different firms face different demand elasticities, and it is possible for each individual firm’s markup (as estimated with revenue) to covary with the true markup, even while the average markup does not.

De Ridder, Grassi, and Morzenti have access to complete data on firms in France from 2009 and 2019, which is rather like being able to check your answers against the answer key. The dispersion and trends predicted by the production method are extremely accurate. This might be enough to rescue De Loecker et al. – even though we don’t know how big markups are at any given time, we can plausibly argue that they have gotten either larger or smaller over time.

I have some scattered thoughts. It is possible that these excess profits are a good thing, insofar as it might be the result, or perhaps a cause, of greater innovation. In a roundabout way, this is really just concerned with mismeasured inputs into research and development. If we ever miss a source of spending – and this source of spending grows over time – then we will persistently misestimate profits.