Can the Private Sector Support What the Public Sector Claims To? (Part II)

Tuesday, September 11, AD 2012

This is the second part in a three-part series.  Part I can be found here.  Part III can be found here.


Crowding out on its own can never make a case for the privatization of social services.  Even with government crowd out, the total amount of money raised for a particular cause is higher with government involvement (or equal in the case of total crowd out).  For instance, if a cause is funded entirely by the private sector, say at $100, and the government steps in with a $50 subsidy.  Supposing the crowd out rate is 60%, the private donations drop by $30 because of the $50 government “donation.”  However, the total gift to the charity is now $120 (the government’s $50 plus the private sector’s $70), which is higher than the purely private $100.

However, this doesn’t take into account the efficiency contrast between the private and public sector.  Here is where my model begins to take shape.  For starters, suppose that the government operates with a 30/70 split and the private sector operates with a 70/30 split and a modest crowd out rate of 60%.  Let’s follow that tax dollar collect by the government.  Suppose that the government collects and budgets $1 in taxes for a social cause.  The amount of money actually going to the cause, after the deduction for administrative expenses, is $0.30.  However, that tax dollar also causes a crowd out of 60%, or $0.60 in private giving.  No, in fairness, the private giving also has its administrative expenses, so the actual causes experiences only 70% of the $0.60 in decreased funding, which amounts to $0.42.  The end result is that the extra $0.30 injected by the government is more than counteracted by a drop in $0.42.  Thus, the government involvement actually causes a drop in funding for the actual cause.

One is free to play with the numbers, of course.  We were conservative in our estimates of private giving efficiencies and crowd out rate.  If we continue to hold the private efficiency rate at 70/30, it turns out that the crowd out rate can drop to around 43% before we hit the break even point.  This is a comfortably low number by all accounts in the literature.  Yet even this assumes a modest 70/30 private giving efficiency.  If we adjust this to the median, which is closer to 90/10 (10% administrative costs), we find that the crowd out rate can fall as low as 33% before we hit the break even point.  What this tells us is that for more than half the charities, there is a substantial decrease in actual available funds when the government raises taxes to subsidize the programs.  Were such a reality to be understood and made public, it would cause a fiscal scandal greater than any experience by the few immoral and manipulative bad apples in the world of private charitable organizations.

Now, we should admit that this is based on a definition of “crowd out” that can be unclear in the literature.  Many authors use the term without defining whether the crowd out percentage is a function of the taxed dollar ($1) or the final injection after administrative costs are factored out ($0.30).  We assumed the later because in the two mathematical models (Krause and Andreoni) we were able to follow actual variables, and it was the taxed dollar that resulted in the crowd out.  However, is a subsequent paper, Andreoni himself seems to be leaning towards the later definition.  If that is true, the situation changes*.  It turns out that total available post-administrative funds is increased by government involvement in all cases (and only breaks even if private giving is perfectly efficient and crowd out is 100%), but the increase is such a small percentage of the total taxes collected (between 10% and 13% using the same efficiency and crowd our assumptions), that the expenditures become difficult to defend from any reasonable moral perspective.  Such a reality, even in this case, would cause a public scandal if it were explained to the average voter.

If their are economists among us who can clarify this definition with a solid reference, I would be more than grateful to hear an answer.  I have at least ten papers from economics journals on my desk, none of which are specific enough on the definition of crowd out to decide this point.


 * In the case that crowd out is defined as a function of the money spent on the actual cause by the government rather than the taxed dollar, the mathematical exercise is a bit more complicated.Out of the dollar collected via taxation, only $0.30 of it is going to make it through the bureaucratic structures of the government.  When the $0.30 is injected into the cause, it results it a decrease of $0.18 (60% of of $0.30) of private giving due to crowd out.  Of course, this is a decrease in $0.18 of giving, not of actual money to the cause.  In fairness, even the private charity has its administrative costs.  Thus, the decrease is private funding is only 70% of the $0.18, or $0.126.  Nevertheless, the total difference made by the government $1 is the $0.30 decreased by the crowded out $0.126, which comes to $0.174.  Therefore, it is a mistake to think that he government gets even its 30% of the dollar for the social cause.  The net gain experienced by the cause is only 12.6%.  Think about this on a larger scale.  In order for the government to make a $1,000,000 difference in a cause, it must collect $5.75 million in tax money.

One is free to play with the numbers to see the impact of combining efficiency and crowd out rates.  Our experiment was based on a conservative 70% private giving efficiency and a modest 60% crowd out.  If we assume the median private giving efficiency of 90% and Andreoni’s 70% crowd out rate, the net government difference on the tax dollar falls to 11.1%.  So to raise that $1,000,000, the government would have to collect over $9 million in taxes.

Notice that the cause is still “technically” better off.  Even in the more extreme case, the cause still gets its additional $1,000,000 in funding.  In fact, this will always be the case.  While the combined rate falls as private efficiency and crowd out rise, even with a private efficiency of 100% and a crowd out of 100%, the government simply replaces every dollar in the social cause.  Yet the replacement come at quite a cost to the taxpayer.  If a private charitable organization were to operate on these dismal percentages, it would make the front page of the New York Times in the most scandalous of manners.

 Read Part III here.