Can We Believe Anything About Markups?

The existential challenge of heterogenous production functions

Markups are the difference between price and marginal cost. The existence of markup (assuming linear pricing) shows that there is misallocation. There are people who are willing to pay more than it costs to produce the good who are never able to buy it. This misallocation could be due either to fixed costs to enter, or from firms having market power and getting excess profits, but in either case it would increase efficiency to equate marginal cost and price.

There are two ways which you can have misallocation. You can have a markup for the industry as a whole. You can also have variation in markups within a given industry. The latter implies that, within a given industry, you could reallocate inputs and raise output, holding the level of technology is constant. Hsieh and Klenow (2009) model this as individual firms facing a tax on their inputs (whether labor or capital), which drives a “wedge” between their optimal usage and what is actually done. (It’s called a wedge because deadweight loss will be a triangle). Holding the total input to an industry constant, they show that you could raise output between 30 and 60 percent in China and India by reducing misallocation to the level of the United States.

The key assumption here is that the firms within an industry share a “technology”. This is not literally a technology, but simply that they share the same optimal ratios of input. Carrillo, Donaldson, Pomeranz, and Singhal (2023) completely overturns the received wisdom on firm-level misallocation, and calls into question everything which economists are doing on the matter. While there is misallocation on the level of industries, there is essentially no misallocation between firms. They do this by introducing a new method to estimate misallocation without needing to assume a shared production function, which they’re able to do because they have much better identification than anyone.

Normally, economists need to estimate the production function for the industry as a whole. However, the production function can change from year to year, and is jointly determined by supply and demand. We don’t know, when a firm changes its inputs, whether it was its demand that changed, or its productivity. If we assume that they share a productive technology, then we can have a linear regression (taken in logs) and use instrumental variables to tease out unobserved supply and demand shocks. The standard method (used in De Loecker-Eeckhout-Unger (2020)) is to use investment into a fixed input, under the assumption that it’s a function of productivity in prior periods, and that productivity is following a random walk. This doesn’t work unless you assume that they all share the same production function to estimate. There has been some work, such as Boehm and Oberfield (2020), which separates out clusters within an industry when they have very different bundles of inputs, but this will miss when firms have different methods using the same inputs.

CDPS use a quirk of Ecuadorian infrastructure procurement to isolate the demand shocks. For projects below a certain size, projects are awarded at random. These are sizable shocks, which don’t occur super frequently (such that we can identify the impact of any given shock). With this in hand, CDPS are able to use the standard ratio estimator of markups for the behavior of each firm. When firms get a contract, they increase their sales output by more than they increase what they pay their inputs, with an industry-wide markup of 1.15. However, all firms, regardless of the ratio of inputs that they use, share the same markup and change their behavior in the same way. Thus, there is essentially no misallocation across firms, with a gain of perhaps 1% possible from reallocating inputs from firm to firm.

I should note that I don’t necessarily believe their figure for the efficiency of the industry as a whole. The markup is fundamentally a residual, so if we’re not measuring something (like the profit to the owner) then we’re gonna consistently overestimate the markup. What I absolutely do believe is the result regarding the dispersion of markups, which requires only the assumption that we’re mismeasuring the residual in similar ways across firms.

When they estimate the dispersion of markups between firms using the conventional methods that assume the same production function, they arrive at losses from misallocation somewhere between 4 and 54 times greater than what they found. Yes, times. Not a percentage, times. If there are such widespread differences in production functions, even within seemingly narrowly defined industries like construction, how can we possibly think that economy wide measures of markups and misallocation mean anything!

I have no doubt that firms are charging markups. I simply have to doubt our ability to measure them.