# Taxes and (After Tax) Income

I gotta say… posting columns of data in blogger is a pain in the butt. I now understand why nobody tends to do it. I tried for a while to upload the stuff as pictures but failed. So I’m entering the data by hand… forgive any uneven formatting.

Ignoring costs completely, how much benefit do we get from lower taxes? From a really cool Congressional Budget Office study on tax rates and incomes we use the following data: Total Effective Federal Tax Rates, all quintiles (Table 1A, line 15),
Average Pre- Federal Tax Income, all quintiles (Table 1C, line 30), Average After- Federal Tax Income, all quintiles (Table 1C, line 44) from 1979 to 2003.

The table below shows how the average pre-tax and after-tax income growth rate for various periods correlate with taxes.

Period…pre-tax inc growth…av after tax income growth
t to t+1…………………-0.04…………………………0.01
t to t+2…………………-0.17………………………….-0.08
t to t+3…………………-0.27…………………………-0.16
t to t+4…………………-0.19…………………………-0.05
t to t+5…………………-0.06…………………………0.11
t to t+6…………………-0.09…………………………0.09
t to t+7…………………-0.01…………………………0.19
t to t+8…………………0.06…………………………0.28
t to t+9…………………0.16…………………………0.39
t to t+10…………………0.05…………………………0.37

The table can be read as follows… the average pre-tax income growth rate from one year to the next has a negative 3.6% correlation that year’s taxes. Thus, according to the table, over the first few years, the higher the tax rate, the lower one’s pre- and after-tax income. But, lower taxes are associated with lower income growth, both pre- and after-tax, over longer periods of time. For example, the average after tax income growth rate over a five year period is higher when taxes are higher; the same is true of the average after tax income growth rate over a six, seven, eight, nine and ten year span.

Thus, over the long haul, it would seem that we are better off with taxes at the high rather than the low end of the sample we observed over the 1979 to 2003 period. Assuming I haven’t made a mistake and/or this is not an artifact of the data, what is probably going on is that the government is actually providing services that over the long run boost people’s incomes by more than it costs them in taxes. These services include education, public health, maintaining the Northern defenses that keep out the bloodthirsty Canadian hordes, and infrastructure. When taxes are lowered, either these functions are performed at lesser levels, or government borrowing crowds out private investment.

But perhaps taxes don’t have an immediate effect upon income. The table below compares taxes to their effects beginning in the following year, as opposed to their effect the same year.

Period…pre-tax inc growth…av after tax income growth
t+1 to t+2…………………-0.23………………………………-0.16
t+1 to t+3…………………-0.30………………………………-0.20
t+1 to t+4…………………-0.23………………………………-0.11
t+1 to t+5…………………-0.08………………………………0.06
t+1 to t+6…………………-0.06………………………………0.05
t+1 to t+7……………………0.00………………………………0.15
t+1 to t+8……………………0.13………………………………0.31
t+1 to t+9……………………0.21………………………………0.41
t+1 to t+10…………………0.26………………………………0.42

Results are similar to, but stronger than the results in the earlier table. In the short run, lower taxes put more money in our pocket, but in the long run, we are made worse off.

For those interested in something slightly more statistically rigorous… let’s see whether taxes actually have an effect, or are merely correlated with growth. Summary statistics for an ordinary least squares regression using the average after tax income growth rate from period t to t+1 as the dependent variable, and as dependent variables the average after tax income growth rate from period t to t+1, the tax rate from the previous year, and the average tax rate over the previous 5 years:

Observations:……………19

…………………………………………Coefficients……P-value
Intercept………………………………-10.96…………0.04
pre tax inc growth, t to t+1………0.94……………0.00
tax rate, previous year……………-0.14………..….0.59
av tax rate, prev 5 years…………..0.66…………..0.07

Thus… as pre tax income rises, after tax income rises, and the result is statistically significant. However, while the previous year’s tax rate is negatively correlated with a given year’s after-tax income, this result is not statistically significant unless one is in the habit of using an alpha of 60% or more! On the other hand, as the average tax rate over the previous five years rises, after tax income rises, and this result is statistically significant at the 10 percent level.

Looking at the effect of taxes over longer periods:

Observations: 14

…………………… … …Coefficients……P-value
Intercept……………………………………-20.13…………0.01
pre tax inc growth, t to t+… … 0.90……………0.00
tax rate, previous year……………-0.28…………0.30
av tax rate, prev 10 years…………1.22…………0.01

Using the average tax rate over the previous ten years instead of over the previous five produces similar, albeit stronger results – the average tax rate for the previous ten years has a positive coefficient, and is significant even at the 1% level.

Thus… unless the data is flawed or otherwise aberrant, or there is an error in this analysis somewhere, it would seem that we are better off with slight increases in the tax rate than the slight decreases in the tax rate GW has chosen to usher in. This is clearly not a result that GW or his cheerleaders would expect. (Nor, I would guess, one they would pay any attention to should they become aware of it.)

Postscript 1. My spreadsheets are available upon request.
Postscript 2. Anyone have any idea where I can get this data for a longer time period? It would be nice to know if these results hold over longer periods of time.