## Saturday, July 09, 2005

### Some Simple Fiscal Arithmetic

I keep hearing that because tax revenues are rising it proves that cutting taxes raises revenues (e.g. from the Washington Times, "The numbers are an eye-popping vindication of the Laffer curve...").  Let’s deal with this claim because it’s a case of correlation being interpreted as causation to prove a preconceived notion.

For the purposes of illustration, assume an economy that naturally cycles from boom to trough to boom to trough, etc., independent of the level of taxes or government spending.  This biases the model against rising revenues when taxes are cut.  If revenues rise anyway, it can't be from the cut in taxes.  Let the economy follow the pattern 80 – 90 – 100 – 110 – 120 -110 – 100 – 90 – 80 – 90 – 100 – 110 – 120 –  110 - etc. in a never ending pattern.

Let’s start with a tax rate of 30% and begin in a trough.  Then tax revenues are currently (.30)(80) = 24.  In an attempt to stimulate the economy (even though it doesn’t actually do so in this economy, it doesn't matter why taxes are cut, it can be for political reasons as well) cut taxes to 25%.  Revenues at the trough are now 20 so initially, right after the tax cut, the deficit will widen since revenues fall from 24 to 20.

But what happens to revenues is subsequent periods?  As the economy recovers independent of the tax cut, revenues begin rising.  In the next period, when output is 90, revenues will be (.25)(90) = 22.50.  In the period after that, revenues are (.25)(100) = 25.  Note that revenues have risen relative to the value of 24 under the old tax rate at the trough.  It is at this point you might begin to see stories in the news, as now, about how the tax cut caused so much stimulus that revenues increased.  In subsequent periods, revenues increase further to 27.50 then 30 confirming this effect for those unwilling to look past simple correlations for the evidence they seek.

Just because revenues rise after a tax cut does not mean that the tax cut caused the increase in revenues.  To make such a determination requires separating changes in output into changes due to the tax cut and changes due to other factors.  This is not an easy thing to do, but when attempts are made to do this properly, the evidence for tax cuts bringing about increased revenues is difficult to find.

Don't be fooled by the rhetoric surrounding simple correlations.  It is intended to support a particular preconceived point of view.  But because it is nothing more than a simple correlation, it is not evidence that the point of view has any validity.

Posted by on Saturday, July 9, 2005 at 07:52 PM in Budget Deficit, Economics, Taxes | Permalink  TrackBack (3)  Comments (10)