Tuesday, December 1, 2015

Revenue Estimates, Part 2

Another month of tax revenues released by the State of Kansas, another month of arguments on Twitter.  Beyond amusement at the arguments, is there a reason I post on this type of thing? Yes-it's because the arguments present are common to other data problems, specifically in people misunderstanding, misstating, and misleading. 

I've posted on this before, but the short of it is this: Kansas governor Sam Brownback reduced tax rates in an attempt to grow the economy, tax revenues declined (predictably), and the government has struggled to create a workable budget and satisfy the budgetary demands of schools and other government functions.  More recently, the initial Fiscal Year 2016 revenues were missing estimates, forcing a lower revision of the estimates in November 2015 (less money for government functions).  This of course intensified the political argument over the tax cuts. 

The argument between policy wonks really comes down to two political dimensions: size of government and economic effect of tax cuts.  Here are the general positions I've seen:

  • Modified Laffers: We can cut the short term tax rate spurring economic growth, and within a couple of years, tax collections (read: potential size of government) will be greater under new lower rates than it would under lower rates (government stays the same or increases).
  • Pure Laffers: We can cut the short term tax rate, and the size of government to what we believe is a reasonable level.  This will spur economic growth, and thus an increase in tax revenues.  In turn we can again reduce the rate in the future, spurring more economic growth.
  • Keynsians: Reducing the tax rate won't necessarily improve the economy, especially when combined with short-term reduction of government spending.  This reduction could lead to a death-spiral, in which government is continually underfunded, spending is reduced.
  • General Cynics:  (ok, I only know one person like this): Tax cuts will not create growth or increase spending, but we should cut taxes anyways because teachers and other government employees make too much money (read: the government is too big).
Anyways, that lays out the landscape, let's look at the arguments, largely the misconceptions and what is true.  I'll cover three main issues: actual revenue amounts, accuracy of estimates, and the long-term revenue growth.


One of the arguments made this year is that tax revenues are actually up. This is true, but only for the last Fiscal Year (2015).  Revenues are down for Fiscal Years since 2012.  In fact, in FY 2015 the State took in less than it did in 2012 by more than $400 Million, or 7.6%.  Since 2008 (last year prior to recession) revenues have only increased 2% in total, while averaging 5.6% annually over the past 40 years (will get to this later).

FYI, FY 2016 revenues will not exceed 2008 either, with the current revenue estimate at 6.1 billion dollars.


One of the criticisms leveled at the administration is that they are continually missing revenue estimates, so the estimates must be bad.  I looked into this, and found that by normal statistical methods (mean absolute deviation, mean squared error), the last three years have been very accurate.  In general, from 1976-2012, estimators missed by an absolute average of 5.2%, whereas the last three years, they have missed by 1.1%, 4.9%, and 1.1%.

Great?  Actually this is big problem.  If we look at the past 25 years, the estimates are hedged low during non-recession years (actuals always end up higher, creating slack).  That slack can be used as a buffer in recession years. The problem: the last three years are the first time since 1988 that a revenue estimate has been missed in a non-recession year.  The chart below demonstrates that variance.  If there is no slack in non-recession budgets, a recession in the next few years could create a massive budgetary problem.


One of the questions I see a lot is the about the longer term trends.  Specifically, how much have revenues grown recently?  For this I looked at the last 40 years, 1976-2015.   The numbers have increased quite a bit, mostly for explainable reasons, here are the most explainable:
  • Population Growth: More people = more government spending.  Kansas populations has increased since 1976 from about 2.3 million to 2.9 million.
  • Inflation: In common terms things get more expensive over time, so government has to spend more on salaries, benefits, and goods in order to prove the same level of service.  Though, it's not clear that CPI is a clear estimator of inflation's impact on government expenditures.
  • Role of Government: Government provides  more in terms of services than it has in prior periods of American History.
This is another place where metrics get tricky.  
  • If we look at raw numbers, revenues have increased by over 800% since 1976.  But this is a compound growth problem so that doesn't mean 800%/40 years  = 20% growth a year.
  • Using a correct compound growth calculation, the growth is actually 5.6% a year.*
  • Compensating for population growth, the actual growth rate is 4.9% annually.  By way of comparison CPI (which may or may not be a good measure of inflation in this case) grew by 3.7% annually over this time period.
Quick point of reference, the correct equation for compound annualized growth rate is below. I know that this is an area that many people struggle with mathematically, but it is important to realize the equation becomes exponential because you are effectively "growing prior growth":

I'll likely do more in the future to parse out government expansion versus inflationary increases, but this gives you an idea for now.  It appears revenue has grown 4.9% annually while inflation has grown 3.7%.  1ish% annual increase in size of government?  Maybe.  But there are a lot of other factors that could play into that number.   A couple of charts to inform the discussion.


A few points we can take away from this:
  • The tax cuts, as could be expected, had an immediate negative impact on tax revenues.
  • Tax revenue projections have been good from a statistical perspective, but bad from the positions that:
    • This is not a recession.
    • This is a negative miss.
    • This may mean that not enough slack exists to deal with future recessions.
  • Historically, per capita revenues have grown at approximately 4.9% a year, over a period that averaged 3.7% CPI growth.

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