At last night’s GOP debate, Senator Marco Rubio accused Ted Cruz of sneaking a value-added tax (VAT) into his tax reform plan.

RUBIO: Here is the one thing I'm not going to do. I'm not going to have something that Ted described in his tax plan. It's called the value-added tax. And it's a tax you find in many [countries] in Europe.

…

CRUZ: Well, Marco has been floating this attack for a few weeks now, but the problem is, the business flat tax in my proposal is not a VAT. A VAT is imposed as a sales tax when you buy a good.

Rubio is right. Cruz’s business flat tax is a subtraction-method VAT. Businesses play a flat 16-percent tax rate on the difference between sales price and the cost of inputs purchased from other businesses—i.e., value-added. If all businesses are subject to the tax, the business flat tax will add up to 16 percent of the final price of goods purchased by consumers.

How does it work? Consider a loaf of bread. Say the farmer sells the wheat to a miller for 25 cents. Assuming the farmer has no deductible expenses, the initial tax would be 4 cents (16 percent of her 25 cents of income). The miller grinds the wheat and sells flour to a baker for a dollar. His value added is 75 cents, which is subject to 12 cents of business flat tax. The baker sells the loaf of bread for $2 and remits another 16 cents of tax on her $1 of value-added. The total tax adds up to 32 cents, or 16 percent of the final sale price.

The real world is more complicated of course, but this simple example shows how subtracting non-labor costs from sales produces a tax at each stage of production that will add up to 16 percent of final sales (assuming perfect compliance).

The VAT is different from state sales taxes because it is included in the price of the good rather than added at the cash register. That’s one reason why some conservatives object to it—Rubio cited Ronald Reagan. And why Cruz may be so defensive.

It also means that the equivalent sales tax rate would be a bit higher than the VAT rate. The net-of-tax price of that loaf of bread is $1.68 ($2 minus 32 cents). Thus, a 32 cent tax is 19 percent of the net-of-tax price.

A VAT is also harder to evade than a sales tax. When retailers fail to remit sales tax, the tax authority loses all the revenue, but with a VAT retailers are responsible for only part of the tax liability.

Cruz’s VAT is different from the European version in the way it’s administered and in scope.

Most countries use a credit-invoice VAT where firms are responsible for tax on the entire sale price, but claim a credit for taxes already paid by their suppliers. If all their suppliers remit the VAT, then the credits completely offset the tax owed on purchased inputs. And the ultimate tax liability is the same as under the subtraction-method. The credit method is considered an improvement since it is self-enforcing: Purchasers will demand tax invoices from their suppliers so they can claim the credits.

Most countries also exempt many items—such as food and medicine—while the Cruz business flat tax has a very broad base. For a given tax rate, a broader base translates into higher revenue and better compliance.  But it also makes the tax more regressive since taxes on necessities hit lower-income households especially hard.

It’s also important to point out—as Cruz did in the debate—that his plan also repeals the payroll and corporate income tax. While his VAT imposes a 16 percent tax on labor compensation, that is only slightly higher than the combined employer and employee payroll tax rate for workers with earnings below the Social Security earnings maximum.

Interestingly, Senator Cruz’s business flat tax differs from what most tax wonks call a flat tax, which is a subtraction-method VAT with the labor portion remitted directly by wage earners. Professors Robert Hall and Alvin Rabushka developed the concept in the 1980s. Their flat tax is more progressive since the wage tax includes a generous exemption. A still more progressive variant, which the late David Bradford called the X-tax, includes progressive rates rather than a single-rate flat rate.

They are all variations on the same theme. But they are all VATs.