Revenue maximizing IIT rate is 100 for all but top tax brackets

A user asked:

I had a question about Tax Brain. I’d like to see what tax rate maximizes revenue in each bracket under a certain set of behavioral assumptions. However, when I try to do this for any bracket below the top bracket, the maximum rate seems to be 100%, which seems odd to me. I was wondering if there was a bug in the program or if I am not doing something correctly.

For example, https://www.compute.studio/PSLmodels/Tax-Brain/42835/

Here is my thinking on this question so far:

  1. It does not surprise me that the revenue maximizing rate is 100 for lower brackets. The rates at which these lower brackets are taxed are inframarginal for many taxpayers, and the inframarginal revenue could well make up for the behavioral changes of the subset of taxpayers who are affected at the margin.

  2. In the Tax-Brain simulation, which sets Rate 6 to 0.99, we see many taxpayers with overall tax cuts, which is counter-intuitive. I believe what is happening is that some taxpayers who are facing rate 6 on the margin are reducing their income in response to the rate hike, and the reduction in income continues beyond the lower bound of the affected bracket, in some cases leading to a lower overall tax liability. Following the empirical literature, Behavioral-Responses applies the ETI response at the margin to the taxpayer’s entire income. We could change this – at the cost of computational intensity and some code complexity – but then we would be divorcing ourselves from the ETI estimates from the literature. I hope there is a solution I am missing.

I’d very much appreciate others’ thoughts on these issues.

@matthjensen, I’m not sure I understand point number one.

Two papers of interest here would be Giertz (2009) and Creedy and Gemmell.

@jdebacker, thanks very much for the paper references. These look helpful and I will read them closely.

To clarify point 1:

My point was just that the people facing rate 7 would be unaffected behaviorally by the rate 6 cut, and the increased revenue from people facing rate 7 could swamp any behavioral effect from people facing rate 6.

See a stylized example below.

Consider a world with two taxpayers and two rates/brackets.

Tax Law (Pre-Reform)
Bracket 1 is from 0 - $50 and the corresponding rate 1 is 0%
Bracket 2 is from $51 - $100 and the corresponding rate 2 is 50%.

Taxpayer Characteristics (Pre-Reform)
Taxpayer 1 makes $25 / year
Taxpayer 2 makes $100 / year

Tax Liabilities (Pre-Reform)
Taxpayer 1 owes $0
Taxpayer 2 owes $25
Total revenue: $25

Now we implement a reform where rate 1 goes to 100%.

As a result, Taxpayer 1 stops working, but Taxpayer 2’s behavior is unaffected. The rate change was inframarginal.

Tax Law (Post-Reform)
Bracket 1 is from 0 - $50 and the corresponding rate 1 is 100%
Bracket 2 is from $51 - $100 and the corresponding rate 2 is 50%.

Taxpayer Characteristics (Post-Reform)
Taxpayer 1 makes $0 / year
Taxpayer 2 makes $100 / year

Tax Liabilities (Post-Reform)
Taxpayer 1 owes $0
Taxpayer 2 owes $75
Total revenue: $75

So another way to put it is just that I wasn’t surprised that the revenue maximizing rate for brackets below the top one might be 100% (if only search up to 100%).

@matthjensen, Got it. Thanks for the explanation.

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