# M. Jed’s Post on Demographics and Tax Collection

In a recent post, I noted that the growth rate in real tax collections per capita is higher when a Democrat is President than when a Republican is President. I’ve had several other posts in which I noted that collections do not seem to be negative correlated with tax rates, but do seem to be correlated with proxies for enforcement. M. Jed, an Angry Bear reader and frequent poster in the comments section, believes that demographic changes may be what really drives changes in tax revenue growth. What follows is his analysis. (My response will appear in the comment section.)

My thanks to M. Jed for doing this work.

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Using data from 1950 to 2005 from these four government sources , I ran a regression using ln(Real GDP) as the dependent variable. The explanatory variables were (a) ln(top marginal tax rate), (b) [ln(top marginal tax rate]^2, (c) ln(total people aged 45-54), and (d) ln(prior year’s Real GDP) – i.e., lagged dependent variable. GDP was chosen as the dependent variable to test whether reductions in tax rates, when controlled for demographics, induced higher output. I used natural logs on the time-series data because I would expect it to have an exponential shape to it (growing at a fairly steady percentage year after year, rather than at a linear rate). The independent variables were chosen to control for demographics and at the same time control for the time-series nature of Real GDP (over long period of times both population and GDP would be expected to rise) and to examine whether cutting tax rates had an impact on increased output. This demographic age cohort was selected because it is consistently the highest paid over the time frame examined, and I assume over large population samples pay correlates with output. The use of the squared term of the top marginal tax rates was chosen because Laffer hypothesized a curve (think Ax – Bx^2). Lagged terms are often added to time-series data because of the informational content in the prior period (think about what other information you would use to predict tomorrow’s temperature if you already know today’s temperature and could use that as one of your factors). The time period was selected based on data availability and to try to approximate the same time series of cactus’ above-referenced post.

The regression fit was 99.7% as measured by the adj. R squared, though time series data typically has high fits because of the sequential nature of the data (as with daily temperature forecasts). The coefficients on (a) and (d) were positive and statistically significant, the coefficient on (b) was negative and statistically significant and the coefficient on (c) was positive but just barely missed the significance threshold.

So what does all this mean? Well, the regressions produce a formula to predict the dependent variable (in this case Real GDP). Because the regression formula is in the form of a quadratic (y= K + Ax + Bx^2), where x equals the top marginal tax rate, and because (a) and (b) have opposite signs, we can find the value of x for which GDP is maximized. This regression predicts that the GDP maximizing top marginal tax rate is 37.1%.

Additionally, and to verify my results, I also regressed total real tax receipts against the same independent variables. I also regressed the same dependent variables in one case using only (a) and (b) and in another using only (a) – (c). And for both dependent variables I also ran regressions using 5-year moving averages of the same data to smooth out the impacts of business cycles. In all of the regressions the signs on the coefficients remained the same. In using tax receipts, the marginal tax terms did not quite reach the significance threshold for the one-year data and four dependent variables, but did for the five-year data. For all of the other regressions the coefficients were significant. The fit was no less than 88% for all twelve regressions. The twelve predicted top marginal tax rates ranged from 33.7% – 39.6%, with an average and median of 36.2% with the GDP variable producing optimal tax rates about 0.5% lower than the average and Receipts variable producing optimal tax rates about 0.5% higher than the average.

So in conclusion, my analysis indicates that indeed a Laffer Curve seems to exist, that at today’s tax rates and demographics, we are probably just slightly above the optimum top marginal tax rate. Assuming the primary objective of tax policy is to maximize either GDP or tax receipts, we should probably not return the top marginal tax rate return to 39.6% and definitely not above that, but that said, there exists little statistical evidence for deeper cuts in the top marginal rate. And finally my analysis suggests that using single variable correlations, as cactus tends to prefer, can produce slightly misleading results.

My spreadsheets are available to anyone who wants them – please contact me at “m period jed at hotmail period com.” Many thanks to cactus for encouraging and advising portions of this post.