# A Note on the Required Tax Rate in a National Retail Sales Tax: Preliminary Estimates for 2005-2014

**Summary**

Earlier this week, President Bush said that replacing the income tax with a national retail sales tax was an idea worth considering. This note updates earlier estimates of the required tax rate in a NRST [National Retail Sales Tax] (reported in Gale (1999)).

The main finding is that to replace the income tax on a revenue-neutral basis over the next 10 years would require a sales tax rate of more than **26 percent**. To replace all federal taxes on a revenue-neutral basis over the next 10 years would require a sales tax rate of about **60 percent**.

This estimate is predicated on several assumptions: (a) the intended statutory sales tax base would be a very broad measure of consumption; (b) about 20 percent of that base would be eroded due to avoidance, evasion, or legislative action (i.e., loopholes), and (c) the NRST would have a demogrant equal to the poverty threshold for each family times the sales tax rate.

Note also that the rates quoted are tax-exclusive tax rates: that is, they represent the rate at which items would be “marked up at the cash register.” For example, if an item costs $100 before sales tax, and a $25 sales tax is added, the tax-exclusive tax rate is 25/100 = 25 percent. The same rate can also be quoted as a tax-inclusive rate of 20 percent, where the tax-inclusive tax rate is defined as the tax ($25) divided by the total cost to the consumer ($125). ^{1}

Thus, to replace the income tax would require a 21 percent tax-inclusive rate and to replace all federal taxes would require about a 38 percent tax-inclusive rate.

**Calculations**

All of the analysis, details, and justifications presented here follow Gale (1999). The required tax-exclusive tax rate in an NRST can be written as

t = R/(C-X-aT+D)

where R is the revenue to be replaced, C is the actual tax base, X is the amount of consumption covered by the demogrant, T is federal transfers, a is the share of federal transfers that are currently untaxed, and D is the deficit. ^{2}

I calculate this figure using 2003 data and then scale the figure by the ratio of taxes as a share of GDP in 2005-2014 divided by taxes as a share of GDP in 2003 to develop revenue-neutral figures for the decade. ^{3}

The basic parameters are as follows:

C = (C* – SST)*(1-b)

C* = expenditures on the statutory consumption tax base, gross of state sales taxes = $7,413 billion in 2003.

SST = state sales taxes = $344 billion in 2003. State sales taxes are deducted from the base because they do not represent consumption.

b = the combined rate of avoidance, evasion, and legislative “adjustment” to the base = 0.20. This is a conservative estimate relative to everything that is known about how actual tax systems operate.

X = $1,812 billion. This is the amount of consumption that would be effectively face no sales tax.

a = 0.75, taken from Gale (1999), representing the fact that most transfers are not taxed.

T = $1,070 billion

D = $368 billion

R = $776 billion for the income tax

R = $1,877 billion for all federal taxes

C, X, T and D are calculated in the same way as in Gale (1999). All data are taken from the aggregate National Income and Product Accounts for 2003. With these figures, the tax rate to replace the income tax in 2003 is 22.8 percent and the tax rate to replace all federal taxes is 55 percent.

Recall, however, that revenues in 2003 were at long-term lows. The income tax only raised 7.3 percent of GDP in revenue, and total revenues were only 16.5 percent. To obtain an estimate of the revenue neutral tax rate over the next 10 years, we multiply the tax rate needed to replace the income tax by 8.6/7.3, the ratio of income tax revenues as a share of GDP in the 2005-14 baseline to income tax revenues as a share of GDP in 2003, and multiply the tax rate needed to replace all federal taxes by 18.2/16.5.

This yields a required tax rate of 26.8 percent to replace the income tax and 60.7 percent to replace all income taxes. These are tax-exclusive rates. The equivalent tax-inclusive rates are 21 percent and 37.8 percent, respectively.

**Reference**

William G. Gale. 1999. “The Required Tax Rate in a National Retail Sales Tax” National Tax Journal. Vol. LII. No. 3. September. 443-457.

^{1}The terminology tax-exclusive and tax-inclusive comes from whether the tax payment itself is included in the denominator. Income taxes are typically quoted in tax-inclusive forms.

^{2}Some sales tax advocates put G, government purchases, in the denominator as well, on the grounds that their sales tax includes government purchases in the base. This results from a conceptual mistake and a logical mistake. The conceptual mistake arises because even if government taxes its own net purchases, it can not raise net revenue from that activity, since it just has to pay more for its own purchases—that is, its spending goes up by as much as its revenue does. The logical mistake that they made in calculating the required tax rate is that when they calculated the amount of money the federal government could collect from a sales tax, they assumed that the pre-sales tax price of a good would be the same as the current price. But when they calculated how much government would have to spend to keep programs at the same real level under a sales tax, they assumed that the pre-sales tax price of goods would fall. This is obviously inconsistent. Making either consistent set of assumptions — that prices are constant in both cases or prices fall in both cases — results in the equation above. See Gale (1999).

^{3} In order to calculate consumption and hence the tax base, data on a historical year is needed; 2003 is the most recent year for which complete data are available.

*I thank Barry Bosworth, Len Burman and Peter Orszag for comments, and Matt Hall and Melody Keung for assistance.*