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If #2 is true, then government lacks scale-economy. In which case we should consider more seriously that authority should devolve to local autonomy over time.

That last link is broken.

[Fixed! Sorry - SG]

Just sticking with #1 for the moment, the thing that bothers me is that we need to look not at gross transfers but at net transfers.

To take a simple example, the following two tax/transfer systems are identical (they are both just different ways of administering the same negative income tax):

A The government collects 50% of everyone's income in taxes, and gives everyone a transfer of 50% of average income.

B The government taxes all income above the average at a 50% tax rate. It gives a transfer to all those with below average income equal to 50% of the difference between their income and the average.

But the gross taxes (and gross transfer payments) will be bigger with A than B. If my mental math is right (don't trust me) the size of government will be twice as big in B than A. I think I would prefer some sort of average net marginal tax rate as my measure of the size of government as a redistributive agent.

But this is really an aside from the main point of your post, Stephen. I see it as your arguing that there is no particular reason to think that the relative price of government-provided goods should either rise or fall over time. Seems a reasonable benchmark.

I should have written: "will be twice as big in A than B"

Nick, the difference between A and B depends on the distribution of incomes. In A, transfers/taxes are 50% of total income. In B, it can be anything between 0% and 50%. Consider the case where everyone but two people earn average income. One of these two earns a dollar more than average, the other a dollar less. Taxes and transfers are one dollar. Or even more extreme, everyone earns average income, and no transfers occur.

Hmm, I'm getting a strong feeling of deja lu:

In case you don't want to follow the link, I wrote a very similar post to yours (you were more polite about it) in response to very similar comments from Coyne a couple of years ago. Maybe you can make him see the light where I clearly failed :)

Andrew: I think you are right. And I was right when I said "don't trust me" on my math ;).

So the measured size of government in A will not be twice as big as in B. But it will be bigger. Right? Even though the after-tax-and-transfer distribution of income is exactly the same?

Several observations on Coyne's view, in declining order of obviousness:

1. A not-insignificant share of GDP growth is due to population growth, so obviously government spending should remain a constant percentage of GDP in this respect.

2. It is natural that as people become wealthier they increase their consumption of all sorts of things. It would be bizarre if this led them only to consume more private goods, rather than public goods as well. It doesn't strike me as being an unreasonable default assumption that increased demand for various goods would be distributed out evenly between the two sectors, again suggesting that government spending should remain a constant percentage of GDP. Furthermore, it seems to me not unreasonable that increased spending should be skewed toward public goods, given the nature of the big-ticket items government provides: health care, education, and above all insurance. Insurance is a big one -- richer people want more of it. As society gets richer, people in general want more of it, and because of the weakness of private markets, turn to the state (I'm thinking here of implicit as well as explicit insurance, such as consumer protection and so forth. State pensions are also typically an insurance product.) On top of that, post-secondary education has become an important leisure activity. Health care is too obvious to merit discussion.

3. There is the argument about the significance of externalities, which I think has something to it. Take, for instance, the value of a new refrigerator to a Chinese worker, and compare it to the negative environmental externality associated with its manufacture. Because he's poor, the choice is a no-brainer, he takes the fridge. But as society becomes wealthier, the welfare gains associated with increased consumption of private goods (e.g. household electronics) diminishes. As a result, the externality starts to look a lot bigger by comparison. The worker becomes willing to sacrifice more income in order to eliminate it. Or the congestion externality from private vehicles starts to look more serious, so you see demands for public transit. I've spent a lot of time in Taiwan over the past 20 years, and you can see quite easily how a massive increase in demand for public goods (particularly transit, parks, and environmental cleanup) is a natural consequence of increased affluence.

All consumption is subject to diminishing (welfare) returns. However, because goods that are subject to collective action problems are precisely the ones that are not well supplied by the market, relative satiation is higher in the category of private goods. As a result, it would seem that the natural tendency should be for people to want the percentage of growth channeled into the public sector to increase over time. (Of course, whatever inability there may be on the part of the public sector to deliver the goods that people want may generate some negative feedback.)

P.S. Thanks for the nice reviews (op cit).

Our pleasure. As to point 1, Andrew's preferred measure is real, per capita spending, so population growth and inflation are accounted for, but not real per capital income growth.

Great to see you commenting here Joseph!

Unless the long run average propensity to save rises with income (it doesn't seem to much) then by definition the average income elasticity of demand for goods is one.

1. So we would expect to see G/GDP rising with income if government goods were mostly luxuries (income elasticity greater than one) and private goods mostly necessities (income elasticity less than one).

2. Also, if technical improvement were lower in government goods (so their relative prices were rising over time) AND IF they were price inelastic (so a rise in price increases total revenue) we would expect to see G/GDP rising over time. But if they were price elastic, we would expect to see G/GDP falling over time.

It's not obvious to me that those assumptions make sense generally. Sure, there are examples of government goods that fit those assumptions. But there are examples of private goods that fit those examples too.

That leaves me with a constant G/GDP ratio as the default position.

Perhaps the bigger story is the share of manufacturing in GDP relative to services, going back to Stephen's point. It's manufactured goods that have seen the big fall in relative prices, relative to services, and the declining share of GDP (along with agriculture). Government mostly does services, and transfer payments.

While it may be possible for the utility of government to fall, or rise, over time, I see no reason why either of these would necessarily be the case, nor why if it should fall, it could not at some other time rise. In times of peace and plenty it may fall, just as in times of scarcity and war it may rise, but more or less I would expect a stable proportion.

Some thoughtful points. Some, I hope, thoughtful replies:
1. You say that public spending will (and should) naturally rise in line with output, inter alia, because governments will (and should?) redistribute income to those falling below some constant fraction of average incomes. But even if we accept that assumption, spending for such overtly redistributive purposes is only a small part of overall government spending, and can hardly, on its own, justify a percent-of-GDP standard. And if the assumption is relaxed, that proportion may well fall as incomes rise. If the minimum income is defined instead in market basket terms, there is no necessary reason why it must rise in line with average incomes, and therefore with rising incomes the proportion of the population falling below that constant (absolute) line should be expected to fall.
I’m aware that “absolute” standards of deprivation have an element of relativeness to them — what might have been considered a decent standard of living 50 years ago would be appalling today — but it is also true that relative standards have an element of absoluteness: part of the intuitive appeal of “half the median income” as a standard of poverty is our awareness that half-the-median is still uncomfortably close to subsistence. But the further incomes rise above subsistence, the smaller the fraction of average incomes we may wish to set as a floor. When the average wage is a million (constant) dollars, as one day it will be, I submit the decent minimum will not be set at $500,000. At any rate, it is not a given, which is what percent-of-GDP implies. It’s a choice.
2. You say that productivity increases are impossible in the public sector, at least when it comes to services, because they are so labour intensive, and yet they must increase wages to keep pace with the private sector. Ergo, overall spending must rise in line with incomes. But what drives increases in private-sector service wages (Baumol’s disease aside)? Rising productivity. If it is possible to raise productivity in the private sector service sector, through outsourcing and the like, why is it not possible to do the same in the public sector?
Indeed, one would expect productivity to increase in one particular respect: economies of scale. As population rises, fixed costs are spread over a larger base. Does the public sector have significant fixed costs? You bet. Ontario does not spend as much per capita as PEI, not because Ontario delivers less in the way of services, but because it is so much larger. And yet average incomes are much lower in PEI, which supposedly should mean much lower levels of public spending.
3. Joe Heath argues that, as societies grow richer, they become more interested in the kinds of things that governments can do, such as internalizing externalities. (Which is an argument, in the congestion example he cites, for congestion pricing, not public transit.) But other kinds of public spending tend to fall with prosperity. As an economy grows above trend, for example, we should expect to see unemployment rates fall, especially long-term unemployment, leading to reductions in welfare and associated costs.
Some factors, in other words, would tend to pull spending above the constant real per capita baseline. Others would tend to pull it below. I’m calling it a wash.

Andrew: Since I got involved in this, I may as well respond.

3. Much as I'm a fan of road pricing, it's weirdly dogmatic to say that the congestion externality provides an argument for road pricing but not public transit. You can put a tax on the transportation modality that generates the negative externality, or you can put a subsidy on a different modality that is a close substitute (mass transit), yet does not generate the externality. Both are just ways of aligning private and social cost. (Thinking back to the fridge: you can put a tax on CFCs, or you can subsidize HFCs; both come to pretty much the same thing, insofar as they change relative prices.) Since the two policies are consistent and promote the same objective there is no need to choose between them. The question is just which is more efficient under which circumstances. Road pricing works on highways and (sometimes) city cores, elsewhere the transaction costs are prohibitive. So you get demand for public transit. (Btw, Taipei had a private mass transit system for a long time. Organizing a competitive mass transit system has it own peculiar difficulties, which it why people there were so eager to embrace public transit.) As for your conjecture that unemployment rates should decline over time, I simply don't follow your reasoning.
2. The claim is not that productivity increases are impossible in the public sector (although there is a real question about whether the national accounts measure productivity increases in the public sector correctly). The claim is just that productivity increases in the service sector tend to lag behind increases in manufacturing (and agriculture). What drives the Baumol argument is the claim that increases in private service-sector wages are not based on productivity gains in the private service-sector, but (largely) on productivity gains in the private manufacturing-sector. In other words, even if productivity in the service sector was completely stagnant, wages would still rise over time. As a result, if government provides more in the way of services than it does in the way of manufactured goods, government spending would increase as a percentage of GDP (for exactly the same reason that the cost of repairing a refrigerator has risen, over time, relative to the cost of buying a refrigerator). Even if government got more productive in providing services, it would have to be at a rate that outstripped productivity gains in the manufacturing sector (e.g. the economies of scale would have to be greater than those realized elsewhere). This is highly unlikely for a variety of reasons.
1. A lot of the expensive programs, particular insurance programs, are based on an income-substitution principle -- people are essentially insuring that they will receive some fraction of their income during times at which they are out of the labour-market. This is obviously true of EI, CPP, workers' comp, and there are elements of it in welfare. Naturally what people are going to want to insure is a just that, a fraction of their income, so as incomes rises so will the "cost" of these programs (so will the amount that people spend, privately, on life insurance). People also seem to want to spend at least a constant fraction of their income on health care, with technological innovation subsequently guaranteeing that this will be an increasing fraction. Same goes for education. These are the big-ticket items.

So I guess I'm not seeing how this is a wash. When you say "some factors would tend to pull spending below the constant real per capita baseline." It's true that if the broader public were to completely change the way it thought about welfare and stop thinking that real benefits should rise over time, then you would have one example. I find that hypothetical rather unlikely though, mainly because of the number of welfare recipients who are single mothers with children. In the first place, this gives the welfare system insurance-like characteristics (for many women, it serves as divorce, or, male-abandonment insurance). In the second place, it means that is serves a (barebones) equal-opportunity function with respect to children, where it is relative income that counts. One can say that this is a choice, not a given, but this entire discussion is about the preferences people have, and the responsiveness of government to those preferences. The important point is that government grows as a result of first-order choices made by individuals, not second-order choices about the size of government. Finally, it should be noted that the negative incentive effects of welfare payments on labour-market participation are a function of the lower-end wage rate, so as economic growth increases the latter, the primary argument against raising welfare entitlements is diminished.

"You can put a tax on the transportation modality that generates the negative externality, or you can put a subsidy on a different modality that is a close substitute (mass transit), yet does not generate the externality. Both are just ways of aligning private and social cost. (Thinking back to the fridge: you can put a tax on CFCs, or you can subsidize HFCs; both come to pretty much the same thing, insofar as they change relative prices.)"

They only have the same effects if you assume the demand for transport (or CFC+HFC fridges) is perfectly inelastic (which doesn't seem plausible to me). Otherwise it's better to tax the externality than subsidise a competitor (transactions costs aside). You will get too much transport (or fridges) otherwise.

Plus, subsidies need to be financed by taxes, which usually have deadweight costs. Taxes on negative externalities have negative deadweight costs (you fix the externality, plus you can reduce the distortions from other taxes needed to finance other stuff the government does).

For some reason, I missed the fact that Andrew had posted. Thanks for stopping by, and for taking the time to comment.

1) Those are valid points, but as you say, the choice here is political. But it's an easy example of a case where we'd expect GDP shares to stay constant.

2) But what drives increases in private-sector service wages (Baumol’s disease aside)? Rising productivity. If it is possible to raise productivity in the private sector service sector, through outsourcing and the like, why is it not possible to do the same in the public sector?

This isn't quite correct. Wages rise with average national productivity: this is why Chinese manufacturing workers are paid only a small fraction of Canadian manufacturing workers, even if output-per-worker is comparable. The wages of hairdressers haven't gone up because they are more productive; they've gone up because if they didn't, they'd find another job. Hairdressers are still in business because it's a service whose demand increases with income, so they stay profitable by increasing their prices (relative to manufactured goods). To the extent that government sector services have the same cost structure, they too have to keep raising the price of what it provides - in the form of taxes.

There are doubtlessly ways to increase productivity in the public sector, but it's hard to see how they can account for much more than the occasional level shift, and not a continual rate of growth.

And I suppose there are some fixed costs to providing govt services, but I don't think that the dynamics work in favour of your argument. If you have fixed costs plus variable costs that grow at a fixed rate, the growth rate of the total will increase as time goes on, and at the limit, the rate of growth of total costs will be the rate of growth of the variable costs.

Tough to use share of GDP accounting without knowing the government spending ROI (the right would consider future taxpayer earnings and the left would consider longevity or some quality-of-living metric). For now we just assume all government spending has the rate equal to private sector GDP growth or to interest rates or grading historic investments. If an isolated city of 15000 has no hospital, share of GDP is a horrible method to account the return of government spending for more than one hospital construction. The first hospital gets you a return probably higher than the eqivalent tax-cuts or debt runup. But the second may be very marginal and the third hospital may wind up costing the town even if free.
The alternative I suggest is just to use all the assumptions (basically a partial externality accounting) made by various non Right-Wing organizations. So if CDI says Japan foreign aid is may below Denmark; I'd rather just go with the blind assumption foreign aid is good than using private sector GDP growth rates is a measure of what to spend on public (if USA investment banks make record profits it shouldn't be a signal to build sewers unless they are to function as banker jails). German Watch ranks us 56 of 57 for environment policy, so I'd just go with the assumption fighting AGW is good and enact carbon taxes based on our global ranking rather than upon private sector GDP growth. Our daycare is 20th among OECD. To max counter-cyclical effect you enact it in recession (encouragement to work), to max $$ you fund it in overheated economy (increasing pool of available workers/taxpayers when wages are high).
Another key factor is time asymmetry. Even if you want to keep public spending at some ratio to private, you'd want to base daycare spending on what you expect 30 years down the road (when kiddies with higher pay and lower criminality), not what insurance companies are earning now. I guess I figured out Northern Europe was doing stuff right and now I just use them as a model for the larger economies to try to emulate. In a flu epidemic, you don't scale down federal flu funding just because the insurance industry goes bankrupt.
The share-of-the-pie argument is convenient because we have little accounting of public rates of return and all too much accounting for stock option private profit timeframes. Don't forget to subtract federal debt from GDP figure. You can ruin your version of the measure by running up retarded debt levels and keeping the ratio same as under surplus. If you want a 50-50 ratio for a small town your accounting suggests 10 prisons and 10 (really big) McDonalds is superior to one prison and 10 McDonalds.
Demographics is another coarse measure. Surpluses during boom prime years is the natural way to fund boomer health. Shrinking hospital revenues just when boomers retire and get cripply seems silly.

"2. It is natural that as people become wealthier they increase their consumption of all sorts of things. It would be bizarre if this led them only to consume more private goods, rather than public goods as well."

Luxury goods and private healthcare pretty much ensure more income equals more private spending. Though you could adjust a Luxury Tax to force some ratio and you could enact a comparitive pay-through-your-teeth cutting-in-line-tax to move up the public sector surgery wait list assuming the revenues were directed in a way that saves a gross amount of costs/lives (If an oil exec wants to pay $1M to jump up heart surgery line and the funds go to giving the Calgary hospital gelFAST and creating a roomy flu waiting room and nurses the choice is obvious).

Andrew, a psychology study a few years back figured people get a lot more happiness from their first $10000 in income. So a PPP target to shoot for. There are other priorities but these types of income supplements already exist in oil kingdoms for analysis. Canada already catches mothers with welfare. But misses those who want to retrain or re-educate in this globalized world and misses those who are more proficient volunteers than labourers (how many Einsteins didn't/don't have rich relatives and would've thunk if GAI?). I spent about 5000 employed hours unable to save $5000 over years. Many priorities but a near-term target would be to subsidize anyone who wants to increase their skill set or attempt a small business in addition to automatic mom welfare. There is a study from Quebec that suggests 40% of daycare prograames costs are paid in immediate income tax revenue growth; is a subsidy to work.

Nick: agreed. The key words in my sentence are "pretty much the same". The key words in your sentence are "transaction costs aside".

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