The purpose of this post is to walk through the math that Dr. Joseph Haslag and Abhi Sivasailam used in their case study, “Previous Estimates Overstate ‘Fair Tax’ Rates, Harms,” in an effort to be completely transparent.

First, they estimated the average family size in Missouri:

average family size = (size of Missouri population) ÷ (number of resident filers)

= 5,778,901.81 ÷ 2,626,773.55 = 2.2

Next, they estimated the size of the average rebate value, using the federal poverty threshold approximation associated with a family of 2.2, which is $15,393:

average rebate value = federal poverty threshold approximation × sales tax rate proposed in HJR 36

= $15,393 × 0.0511 = $786.58

Then, they estimate the cost of the rebate system, which is equal to the amount of rebates awarded:

(average rebate value) × (number of families qualified for the rebate) = (cost of rebate system)

$786.58 × 2,626,773.55 = $2,066,167,540

Lastly, they compute τ, the revenue-neutral tax rate:

τ = (government revenue + cost of rebate program) ÷ (aggregate personal consumption)

τ = ($7,117,761,408 + $2,066,167,540) ÷ $158,531,333,333 = 0.0579313171 = 5.793 %

where government revenue equals the sum of individual income, corporate income, and sales taxes.

We see that the size of the tax base, β, decreases if the amount of exemptions increase. This indicates that the sales tax needs to be assessed on a broad base in order to for the rate to remain low. By decreasing the number of exemptions that exist in the status quo, Missouri can establish a sales tax rate that’s lower than other estimates have suggested.

In their case study, Haslag and Sivasailam explain that expanding the list of services that are taxed would not result in a dramatic increase in the cost of living. In a previous post to this blog, Sivasailam elaborated on this concept:

[I]t’s important to understand that a change in the tax code implies a change in incentives. People and firms alike respond to these changing incentives in many ways, including altering their supply and demand of goods and services. With that in mind, the claim that the prices on all goods and services would increase by the tax rate is misleading.