Doing the math on gross receipts taxes
(Note: The post below later became background paper on the economics of gross receipts taxes. The math’s in the appendix at the end.)
Lots of lawmakers like gross receipts taxes (GRTs). The reason is simple: they raise a ton of money with low rates. And while that’s usually a good thing, a quirk in the way GRTs are structured makes them an inherently lousy way to raise revenue.
Here’s how they work. GRTs tax everything sold by businesses. They tax final goods, intermediate goods, raw materials, everything. That means things with lots of production stages get taxed over and over—something economists call “tax pyramiding”—while things with short production chains don’t.
It’s easy to see the problem. Products end up with totally different effective tax rates. High-tax industries vertically integrate to cut tax burdens. And this tax-induced madness distorts investment patterns toward tax-favored industries, magnifying their economic harm over time.
Makes sense, right? I’ve seen this argument dozens of times, as far back as U.S. Treasury studies on “turnover” taxes from the ‘30s.
But what I never see is anybody who does the math. It’s pretty simple, so why not?
So for the two people still reading at this point, here’s my version of the math, courtesy of my office whiteboard last week:
I. Effects on Firm Structure in a Two-Firm Industry
Consider an industry with two firms that produce a final product in two stages: manufacturing and retail. The manufacturing company ("upstream" firm) assembles the product, and the retail company ("downstream" firm) sells it to retail consumers. To keep things simple, assume the upstream firm sells all its output to the downstream firm, and both companies are competitive price takers (think contestable markets).
If the companies operate independently, the profit of upstream firm is given by:
,where R is the upstream company’s revenue, t is the gross receipts tax rate, and C is the upstream company’s total cost of production. Similarly, the profit of the downstream firm is given by:
,where R, t and C are defined as above. Because the costs of the downstream firm consist of both purchases from the upstream firm and its internal costs of production for labor and capital, 
can be decomposed into the sum of 
, where
is the cost of purchases of intermediate goods from the upstream firm and K equals the downstream firm’s internal production costs. In this case, the total tax burden faced by the two unmerged firms is equal to
.Under these conditions, when does it make sense for the two companies to vertically integrate?
Note that in the absence of taxes, companies will organize in the best possible way. If taxes cause them to organize differently, they will generally be less efficient firms. That is, if companies merge for tax reasons they will have a higher total cost of production than they’d otherwise have.
Imagine the two firms in the above example vertically integrated into a single company. The profit of the merged firm is given by
,where e is the increased total cost of production due to the merged firm being organized inefficiently. In practice, this inefficiency probably varies with output, but to keep things simple it’s assumed to be a fixed production cost. The tax burden of the merged firm is then
,which is less than the total tax burden of the unmerged firms by an amount equal to 
. As a result, the total profit of the merged and unmerged firms will differ by an amount equal to
.That means under a gross receipts tax, industries will vertically integrate only if the tax benefits of doing so—that is, 
—outweigh the efficiency losses from merging companies that are better left separate. More formally
if e >
, firms remain unmerged;
if e <
, firms will merge;
if e =
, firms are indifferent between merging and remaining separate.
II. Effects on Effective Tax Rates Across Industries
In addition to encouraging inefficient vertical integration, gross receipts taxes also lead to disparate effective tax rates across industries, distorting investment patterns in the economy over time.
To see why, imagine two industries: one where it is highly inefficient to vertically integrate, and one where the efficiency costs of integration are small. That is, imagine an industry that won’t integrate A such that e > 
, and another industry that will integrate B such that e = 0. Under a gross receipts tax, industry A will remain unmerged, while industry B will vertically integrate for tax reasons.
In this case, the effective tax rate faced by industry A is given by
.By comparison, the effective tax rate faced by industry B is given by
The effective tax rates faced by industries A and B differ by only one term in both the numerator an denominator: 
. Because it’s assumed that 0 < 
< 1, the addition of a constant equal to 
to both the numerator and denominator increases the value of 
. As a result, > 
, which means industries A and B face different effective tax rates, for no good reason other than a poorly designed tax.
That’s a bad thing, because it means gross receipts taxes will distort investment patterns in the economy over time, away from industry A and toward B. And that makes everybody poorer, making them an inherently lousy tax.
I leave it as an exercise for the reader to empirically test the impact of GRTs on vertical integration using value added data from the Survey of Manufacturers. Let me know if it works.
Posted by Andrew on Wednesday August 16, 2006 | Feedback?
