EDIT
 Compressing Reality

# Corporate Taxes

## Consumption Taxes

Because all income is either spent or saved, a consumption tax is equivalent to a flat tax that allows you to deduct savings. Presumably, consumption taxes are less costly to file, but given that we currently only spend 0.01% of GDP on tax-filing "title": "The Cost of Tax Compliance", it seems unlikely that this particular benefit will be that important of a factor.

Therefore, any study that finds consumption taxes are preferable to income taxes is equivalent to finding that

1. Savings should be deductible from income taxes,
2. and/or flat taxes are preferable to progressive taxes (as consumption taxes tend to be flatter than income taxes).

More generally, the economic consensus that consumption taxes are preferable to income taxes "title": "Beyond the Pro-Consumption Tax Consensus" is equivalent to (1) and/or (2).

The question becomes, then, which is true? Are both true? We’re going to examine (1) now and then (2) later.

## Lower Taxes Increase Savings

### Nonbehavioral Changes

Suppose we currently had a 20% tax break, but that the government was considering allowing a deduction for savings. Ignoring any behavioral changes, consider two scenarios

If everyone currently saved 10% of their income, then this would result in an increase in savings by 0.2% of total income.

If, on the other hand, half the population saved 20% of their income while half saved none, we find that 0.4% more of total income will be saved.

In both examples, the overall savings rate was 10%, but the tax cuts had twice as large an effect in the second. From this we can see that the distribution of savings-behavior matters a great deal in determining how effective consumption taxes and savings deductions are at boosting national savings.

Let $f(i,s)$ be the number of people with incomes $i$ and savings-rates $s$, and let $T$ be the current (flat) tax rate. Then, we can compute the overall savings increase from a tax cut with $$\int_0^1 \int_0^\infty T \cdot s^2 \cdot i \cdot f(i,s) di ds$$ simplifying yields $$T \cdot \int_0^1 s^2 \cdot \int_0^\infty i \cdot f(i,s) di ds$$

If we let $g(s)$ represent the total amount of money earned by people with savings rate $s$, this becomes $$\int_0^1 s^2 \cdot g(s) ds$$

In this way, if we assume everyone has a savings rate of 5% and that the tax rate is about 30%, we can expect exempting savings from taxation to increase savings by 0.075% of income while reducing tax revenue by about 1.5%. Hence, we’ll be giving up \$20 in tax revenue for every$1 in savings, and while admittedly those \$20 do go to the people, this doesn’t seem like a very effective way to increase the savings rate. Let’s consider the other extreme: that 5% of the income-earners (weighted by income) saves all their income while the other 95% save none of it. In this case, we can expect to increase the savings by 1.5% of income for the same cost in revenue, giving us a 1-to-1 tradeoff between revenue and savings. Recall, that shifting$1 from consumption to savings is morally equivalent to raising long-term laborer consumption by between \$1.14 and \$2.84. This is an extremely effective policy change.

So, empirically, where are we at? Well, recall from our discussion of corporate tax rates these stats:

 Group Savings Rate "title": "Wealth Inequality in the United States Since 1913: Evidence From Capitalized Income Tax Data" Avg Income "title": "Where the 1 Percent Fit in the Hierarchy of Income" % of Income Top 1% 37% $1,310,000 21.6% 90-99% 14%$167,000 24.8% Bottom 90% 0% \$36,000 53.6%

While there is obviously additional variance within these groups, accounting for the variance between them will give us a lower bound on allowing the deduction of savings. From this, we can compute that (given a 30% flat tax) allowing savings to be deducted should still decrease revenue by 1.5% of personal income but it should also increase savings by 1.03%.

This is the strongest argument I’ve seen for less progressive income taxes. If you want to get distracted by politicized jargon, this is the “trickle down effect.” This obviously has implications for tax progressivity, and, in my opinion, these implications are quite interesting. While that’s far afield from this post, we’ll talk about it in the next one.

Given that our lower bound on the benefits of saving a dollar is 1.9 utils with 60% of that being an externality. This implies that our 1.5% decrease in revenue causes at least a 1.17% increase in labor income - not to mention the benefits to the investors themselves.

## Flat Taxes

I know I said we’d address (2) later, but I’d like to mention it briefly now.

Given that people’s utility functions are approximately logarithmic with respect to income [todo: link], we can mathematically show that a flat tax will have minimal effect on people’s labor choices, and this matches the low elasticities of labor supply found empirically [todo: cite].

However, if we introduce “effective welfare” via either real welfare or progressive taxation, then this logarithmic model implies that people will work fewer hours as taxes go up. Therefore, a logarithmic modeling of people’s utilities implies that welfare and progressive taxation will both cause people to work fewer hours, while a flat tax won’t [show].

Indeed, empirical work finds that guaranteed welfare (which progressive taxation operationally is) reduces average hours worked "title": "Negative income tax".

All in all, then, it seems clear that flat taxes will promote greater economic activity than progressive taxes, which gives an additional reason for economists to prefer them. The cost, of course, is a less equitable distribution of resources.