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Friday, April 15, 2005

More on taxes

Went to the Stat Abstract and grabbed the number of personal returns filed, the percentage investigated, and a few other variables, for the last 14 years. I also went over to the BLS and grabbed current-dollar GDP figures. The sample is not large enough for an academic paper, but might be large enough to see if anything is going on. In essence I wanted to relate the number of returns filed to national income, whether there was a recession in that year (or the year prior) and the percentage of returns that were audited in that year.

First off, here's a picture of tax returns filed over the past fourteen years:

Taking the data and cranking them through STATA here's what we get:

. newey lnreturns lngdp recession examined,lag(1)

Regression with Newey-West standard errors
maximum lag: 1

Number of obs = 14
F( 3, 10) = 95.92
Prob > F = 0.0000

| Newey-West
lnreturns | Coef. Std. Err. t P>|t|
recession | -.0025529 .0057722 -0.44 0.668
examined | -.0328769 .0068858 -4.77 0.001
lngdp | .2191607 .0158496 13.83 0.000
_cons | 9.750075 .1455673 66.98 0.000

What does it all mean? The dependent variable is the natural log of returns filed, and thus the coefficients can be interpreted as percentage changes in returns filed for a one unit change in the explanatory variable.

Four years in the sample corresponded with recessions (1990/1991 and 2000/2001) and therefore in those years the variable recession takes a value of one, and in the other years it has a value of zero. The parameter estimate indicates that in a recession year the government receives .2% fewer returns than in other years. However, the t-statistic is very small indicating that the parameter cannot be differentiated from zero with any great level of confidence.

For every percentage of returns investigated (audited) the federal government receives approximately 3% fewer returns. This is an interesting result, but doesn't tell us whether the reduced number of returns is from tax avoidance or work avoidance. Tax avoidance would occur if people were pushed into the informal or underground economy to work, were paid wages, but did not pay income tax. Work avoidance might occur if an individual decided not to work, and hence not to file, if the odds of an audit are higher. We need more/different data to answer which effect dominates.

The higher is GDP the more returns are filed, as would be expected. A one percent increase in GDP will lead to a .21% increase in the number of returns filed. This is fairly substantial if the federal government can egender a 4% annual growth rate, income returns filed will increase approximately 1% - and arguably the amount of taxes paid to the government will increase simultaneously.

What got me started on this random adventure was thinking about the hub-bub Tax Freedom Day generates (see graph below) and whether the further into the year we "work for" the government would influence the number of returns filed. Calculating the number of days between January 1 and the Tax Freedom Day estimated by the Tax Foundation, I get the following:

. newey lnreturns lngdp recession examined days,lag(1)

Regression with Newey-West standard errors
maximum lag: 1

Number of obs = 14
F( 4, 9) = 749.38
Prob > F = 0.0000

| Newey-West
lnreturns | Coef. Std. Err. t P>|t|
lngdp | .2302764 .0135985 16.93 0.000
recession | .0001959 .0045782 0.04 0.967
examined | -.0252728 .0050667 -4.99 0.001
days | -.0012674 .0001802 -7.03 0.000
_cons | 9.785191 .1330965 73.52 0.000

Nothing much changes except we get an interesting coefficient on DAYS. Every day Tax Freedom Day is pushed back reduces the number of returns by .1%. Again, it is not clear if this is tax avoidance or work avoidance. However, there does seem to be a tradeoff betweeen economic growth (which generally is correlated with lower tax burdens and less regulation) and the number of returns examined and the overall burden of the tax system.

What hasn't been addressed is whether the overal tax dollars remitted to the federal government increase or decrease in the same pattern as the number of returns. If I get some time I might scare up the data.

Again, this naive analysis is only suggestive that there might be a relationship between the burden of the tax system (as reflected in DAYS) and the overall number of tax returns filed.

For the uninitiated, this type of problem falls in the area known as Public Choice.

GDP is probably proxying for increases in the labor force as well as picking up a measure of the return to income - the more people working, the more people filing returns, c. par. It would be more interesting to put both the number of people in the labor force and income in the regression.

NB: The predicted value for the parameter on labor force should be less than one, because of joint filers, so it's not going to measure cheaters very cleanly.

BRH (I think I know who you are :-),

I'll go grab the U.S. labor force and include it - you are right that the positive parameter estimate on GDP is reflecting a few different influences on the number of returns filed. Hopefully, the bias from the omitted variables is not enough to change signs (which is really my concern, although the original post talked about predicted effects). I think I can find dollars per filed return, which might be a more interesting dependent variable - using returns filed as a stochastic regressor (although $/return on the left side would still bother me)
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