Bryan Caplan  

Semi-Rivalry and Fiscal Externalities

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Free Markets to the Rescue... When Government Cries Wolf...
Suppose a country has a progressive tax system.  If everyone equally consumes government benefits, isn't everyone with below-median income automatically a net fiscal burden - i.e., a person who withdraws taxes more from the Treasury than he contributes?

Naive analysts usually assume that the answer has to be "yes."  More sophisticated analysts recognize, however, that some government services are "non-rival."  Once these goods exist, the marginal cost of allowing one more person to consume them is zero.  National defense is a standard example: If we had a baby boom, no one would say, "We'll need more nuclear weapons to protect these kids."  Regardless of your views on foreign policy, the cost of defending (N+1) people is no greater than the cost of defending N people. 

The higher the share of non-rivalrous goods in the budget, the easier it is for low-income taxpayers to carry (or more than carry) their own weight.  Before you compare individuals' tax payments to their consumption of government services, you should subtract out all spending on non-rivalrous goods.  For example, if 20% of government spending goes to non-rivalrous goods, you should compare individuals' tax payments to .8*average government spending.

On reflection, though, this analysis is still woefully naive.  In the real world, goods are not either 0% rival or 100% rival.  There's a continuum.  Some goods are close to the 0% pole, others to the 100% pole.  But most goods are semi-rival - somewhere in the middle.

Consider roads.  Most roads are virtually empty in the middle of the night.  The marginal cost of driving at 2 AM is only a slight amount of wear-and-tear on the asphalt.  During rush hour, however, the marginal social cost of driving skyrockets.  When you drive a 5 PM, you aren't just slightly damaging the pavement; you're slightly inconveniencing thousands of other motorists.  During mildly congested hours, the marginal cost is somewhere in between.  Instead of classifying roads as either "non-rival" or "rival," then, you should admit that they're semi-rival, then try to accurately place them on the continuum.

In principle, switching from binary classifications ("rival" or "non-rival") to continuous classifications (degree of "semi-rivalry") could make our estimates of fiscal externalities more or less optimistic.  In practice, however, the effect is strongly optimistic. 

Why?  Because when empirical researchers use a binary standard, they usually treat "rival" as the rule, and "non-rival" as the exception.  Only goods close to the 0% rival pole - especially national defense, interest on the national debt, and R&D -  go into the "non-rival" category.  Everything else gets tossed into the rival category.  If 20% of spending goes in the non-rival category, this approach implies that spending is 80% rival overall.

With a continuous standard, reclassification has almost no effect on the classic non-rival goods.  Fine, maybe they're 1% rival rather than 0%.  But reclassification has a huge effect on the so-called "rival" goods.  When you break them down, you could easily find that one-fourth are 25% rival, one-fourth are 50% rival, one-fourth are 75% rival, and one-fourth are 99% rival.  Switching to continuous classification therefore brings overall rivalrousness from (.2*0+.8*1)=80% down to (.2*.01+.2*.25+.2*.5+.2*.75+.2*.99)=50%.  Quite a shift!

But doesn't this prove far too much?  If most government services are semi-rival, doesn't the same hold for private goods?  Of course.  Look around.  In many (most?) businesses, the marginal cost of serving one more customer is trivial.  But there's no reason to run from this symmetry.  In the private sector, people who buy bargain tickets do not "burden" customers who pay full fare.  In fact, due to semi-rivalry, people who buy bargain tickets benefit full-fare customers by making a wider variety of flights profitable.  The same can easily hold in the public sector as well.


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COMMENTS (17 to date)
Dilettante writes:

In the 7th paragraph you list "interest on the national debt" among the non-rivalrous goods or services. Why should it be considered a good or a service at all? If a store I buy at pays interest because it borrowed money to run it's business, that's no service to me. Their service is the goods they sell me, customer support they provide etc.

david writes:

Because governments have a unique characteristic that no private business can provide, that is, a lifespan exceeding generations combined with a creditworthiness backed with armed men.

So when governments take on more long-term debt, credit risk for society as a whole falls; this is reflected in a change in the riskfree interest rate. In a capitalist society, nobody can exclude you from the riskfree rate, so it's a non-rival good.

Ghost of Christmas Past writes:

Of course, while gov't spending on infrastructure produces partly rivalrous goods, nearly all gov't spending on subsidizing the consumption of ordinary goods and services by the poor goes for rivalrous goods (food, housing, medical services, educational services, etc.-- all rivalrous). Even when rivalrous services are produced using part-rivalrous plant (e.g., policing/rivalrous utilizing prisons with high fixed cost/part-rivalrous), if you integrate over time you discove that the "non-rivalrous" portion really is pretty rivalrous, because though capital investments are lumpy they are still driven by demand.

As for discount air tickets, that analogy probably appeals to you because air travel is the quintessential example of a very-high-fixed-cost industry with low marginal costs and ultra-rapid inventory spoilage. Even if the last ticket sold for some flight goes for less than than its proportional share of fixed costs, the price at least defrays part of those costs.

Relatively few goods spoil so rapidly or have such skewed fixed/variable cost ratios. Government "services" to the poor don't have a spoilage problem and don't use much fixed plant. Both the administrative portion of the spending (bureaucracy) and the delegated portion (subsidized poor people spending taxpayers' money) goes for rivalrous goods. That means the harm to taxpayers of adding extra poor people is not submarginal nor even some kind of sawtooth function where the first pauper costs a million, then the next 500 cost very little (so the average declines rapidly for a while), then the 501st costs another million, etc.. No, the cost of subsidizing paupers just scales linearly with the number of poor people.

(Redistribution programs also harm taxpayers by forcing them to "bid against themselves." Taxpayers pay more for many goods because government redistribution confiscates taxpayers' savings to fund rival bidders for current consumption goods. For example, government subsidies to impecunious house buyers (FHA, Fannie, Freddie) drive up the prices taxpayers pay for houses. Much of the additional price ends up in the pockets of "percentage takers" like real estate salesmen, loan brokers, etc. Section 8 subsidies drive up apartment rents. SNAP subsidies (food stamps) increase the price of food to workers; etc, etc.)

People who consume government subsidies don't make anything useful "more available" to taxpayers. Government "redistribution services" are not provided competitively and voluntarily like "airline services." Redistribution has negative value to taxpayers, and is tolerable only when lack of redistribution has even more negative expected value (e.g., from the crime which desperate poor people would otherwise commit). Redistribution is a kind of bribe to poor people to stay in their neighborhoodsr and watch TV or stay drunk or distract themselves with meaningless rivalries over local dope-dealing spots rather than foray into richer peoples' neighborhoods to steal for subsistence.* Anything that adds to the total cost of redistribution is unequivocally bad for taxpayers.

*Of course I have given you the pure theory of redistribution. In practice much redistribution is driven by "public choice" considerations, also called "vote buying" or simply "corruption." Politicians forcibly redistribute from taxpayers to potential supporters to aggrandize themselves even when smaller amounts of redistribution would suffice to pacify the underclass.

David Friedman writes:

1. Why do you put this in terms of percent non-rivalrous instead of talking about the shape of the marginal cost curve for providing government services--cost as a function of number of people the services are provided to?

2. It isn't clear that marginal cost of national defense wrt population is zero. Arguably, the more people and wealth in a country the more the benefit of conquering it, hence the more has to be spent to defend it. You might consider that if your position were correct, small countries would either spend enormously more per capita than large countries or routinely get conquered.

david writes:

But the top countries with highest military expenditure as a percentage of GDP are precisely small countries with malleable borders. In order: Eritea, Saudi Arabia, Oman, UAE, Israel, Chad, Jordan, Iraq, Georgia.

Only then does the US turn up on the tables, and then it is followed by such luminaries as Kuwait, Angola, Armenia, Lebanon, Syria. These are all countries where recent territorial challenges continue to occupy the political consciousness.

I.V. writes:

So countries, cities and companies should merge with other countries, cities and companies to get the fixed costs down? No, the size of population or number of employees makes the government more complex, corrupt and inefficient and the interst groups stronger. There is an optimal size depending on many factors.

Matt H writes:

So when the Richwine thing came out, I made a spread sheet. If you only count education, social security and medicare spending. The average person gets about $600k in government benefits over a life time. In order to pay that much in taxes they need to earn over 70k a year and work 44 years (21-65). The tax system is progressive, the fact that illegal infiltrators won't pay their way is trivial, because few natives can.

Paul Ralley writes:

Matt H - are you ignoring tax incidence in the $70k figure? Plus sales tax, duty, import duty, tariffs etc. (doesn't income tax only account for c. 20% of government revenue?) I accept your general point re $70k, but think that its a significantly lower figure.

Emily writes:

The proportion of taxpayers who will be net taxpayers is not known just by knowing that everyone consumes the same benefits and there's a progressive tax code, even without non-rivalrous goods. The proportion of taxpayers who are net taxpayers depends on the progressiveness of the tax code and the distribution of income. You can create a system where all but one person is a net tax recipient (if the income distribution is sufficiently right-tailed/the tax system sufficiently progressive) or where all but one person is a net taxpayer (if the income distribution is sufficiently not right-tailed/the tax system is progressive but not that progressive.)

Andrew writes:

@david,
The top five countries with respect to military spending per capita are the United States, China, the United Kingdom, France, and Russia.

Finch writes:

> National defense is a standard example: If we
> had a baby boom, no one would say, "We'll need
> more nuclear weapons to protect these kids."
> Regardless of your views on foreign policy,
> the cost of defending (N+1) people is no
> greater than the cost of defending N people.

This has always been a deeply flawed example.

First of all, whether or not you ideologically would prefer defense spending not scale with population, it very clearly does. So empirically, the idea that defense is non-rival is false.

Second, it doesn't even make theoretical sense. I bought a safe for my wife's jewelery and our important documents. I did no such thing for my paperclip jar. The more valuable something is, the more you pay to protect it, given a particular level of threat and a particular level of risk aversion. There are at least three factors there that determine spend: value, threat, and risk aversion, not just two. And this is completely ignoring vote buying, waste, and corruption, which ought move with population. I know you don't want these things, but they certainly exist.

To David Friedman's point, it's not obvious how this spending moves with other factors. Notably, it might move more with the size of the economy than with population. You trade a little more, you need a little more Navy. You have a larger population, you need a little more National Guard. All else equal.

A lot of people argue defense is non-rival when they really mean that they think the threat is less than most people think, or that they are willing to run higher risk of catastrophic events than most people. This is what the "of course defense is non-rival - I don't even want it!" argument comes down to.

Finch writes:

I might add that Bryan often uses value-laden terms like "naive" to describe arguments and evidence he disagrees with. In this case, he goes out and calls the thinkers themselves "Naive analysts."

Rhetorical techniques like this don't generally help your case. In fact, they may make you less credible because name-calling suggests you are arguing with your heart and not your head.

Tom West writes:

Redistribution has negative value to taxpayers, and is tolerable only when lack of redistribution has even more negative expected value

Strongly incorrect, as the existence of private charity shows.

Government enforced redistribution simply allows those who value such to get the most out of their contribution. (I'll leave moral aspects aside.)

Tony N writes:

Perhaps it’s an error to think in terms of marginal cost in the first place. Indeed, for non-rivalrous goods the added marginal cost of an additional consumer is zero, but adding a cost is not the same as not reducing a cost.

While it’s true that a population increase of 100K would not require the acquisition of additional nukes, such an increase would represent the opportunity to reduce the per capita cost of maintaining the current arsenal, with each additional tax payer picking up his portion of the tab.

The fact that one is not imposing an additional burden does not mean one is pulling his own weight.

Lawrence H. White writes:

David Friedman's second point channels an argument that Earl Thompson made in the JPE.

Jeff writes:

This post assumes a static mix of rival and non-rivalrous goods provided via public expenditure. Adding large numbers of immigrants to the voter registration roles may change that mix, yes? And probably not much to either of our likings, I fear.

MingoV writes:

Caplan's argument, using a private sector example, forces businesses to sort customers by income. Businesses then must calculate charges so that customers with above median income cover all the fixed costs plus the variable costs for that 50% of customers. Businesses then charge only the marginal costs to customers with below median income. When fixed costs are high, the above median income customers incur much greater costs than the below median income customers. Caplan considers this to be fair, despite every customer getting exactly the same product or service. The fairness escapes me. It's just another argument for highly progressive taxation.

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