we want a broad tax base in general—doubling the size of a tax quadruples its social cost, so it’s better to have lots of small taxes rather than a few big taxes
But why not do taxes that don't have social costs? Taxes on land and land-like assets; taxes that internalize externalities (e.g. carbon taxes); taxes on zero-sum games (e.g. higher education); taxes where the dead-weight loss is intended (e.g. cigarettes).
These are good options when available. You should start by setting all the Pigouvian taxes at optimal levels then go from there. Having not thought about it very much, taxes on unimproved value of land seem good but can't fund something like a modern government without major distortions, so you'll end up with lots of other stuff in your basket.
I don't think any taxes have zero social costs. Maybe you're imagining that they have a net zero cost, i.e. where costs born by some people are offset by gains enjoyed by others?
It's maybe off-topic, but I'm concerned by the accounting realities attendant to some of the taxes you mentioned, and similar ones, e.g. carbon taxes and cigarette taxes. It doesn't seem likely that either would or are actually internalizing externalities in practice. Cigarette taxes are often 'earmarked' or allocated to entirely unrelated goods or services, e.g. schools, and that can be disastrous when smokers actually respond to higher taxes by buying fewer (legal, i.e. taxed) cigarettes. Similarly, it doesn't seem like the costs of 'carbon' are actually internalized by the tax itself if the tax revenues themselves aren't directly used to offset those costs by, e.g. capturing carbon, reimbursing losses incurred because of 'carbon', or, more sensibly, saving to offset the expected future costs.
"Social cost" in economics usually refers to the sum of private costs (wikipedia), such that a transfer from one person to another would have no social cost.
"Internalizing an externality" usually means making the private costs better reflect the social costs (so it's not relevant what is done with the tax revenue).
Sure, and there are good reasons for that technical terminology.
But it's weird to claim that any transfer between people, especially one that's coerced, has "no social cost". That's perhaps an unreasonable objection, particularly in this context.
Is there another term then for something generally 'beyond' 'internalizing an externality'? It just doesn't seem likely to be effective to simply impose private costs equal in magnitude to other 'social' costs and then claim victory. Maybe I'm just conflating the economic concept with a kind of accounting-like generalization of the 'match expenses to revenue' principle.
In practice, it seems counter-productive to ignore how specific tax revenues are allocated. It certainly seems most natural to me to allocate those revenues to offset the relevant 'social costs' that inspired the taxes originally.
doubling the size of a tax quadruples its social cost
Could you explain that in more detail? Why is that?
If this is true, wouldn't we have to worry about correlation between types of tax? Taxing A at 1 and B at 1 has social cost 2 if they're totally independent and social cost 4 if they're actually the same thing.
It also bothered me. I think we should interpret "lots of small taxes" as "taxing wide range of trades and activities", rather than literally having lots of different kinds of taxes. For example it seems clearly better to have one income tax for the whole population than inventing separate taxes for various groups of people (and probably missing some).
We still need to worry about correlations - obviously taxing one thing will affect other markets.
I think the reverse is true as well - many "same" taxes include diversity already. Taxing "consumption" is actually many millions of different things (with some correlation, but not 100%). Likewise "income" or even "regular income" is taxing any of many many choices of income.
To be clear, this is the low-order approximation around 0; as explained in Paul's link (sibling to this) the effect away from zero involves the shape of the supply and demand curves through the relevant region of prices (and the stated claim holds when they're linear).
doubling the size of a tax quadruples its social cost, so it’s better to have lots of small taxes rather than a few big taxes
I doubt that's the case. Compliance costs scale roughly linearly with the number of different taxes.
Compliance costs with filing taxes in the US were roughly ~200 billion in 2018 for a tax revenue of ~3300 billion.
The solution you propose also sounds really complicated when people have to optimize the timing of when they make capital gains with times when the risk-free rate is low.
The solution you propose also sounds really complicated when people have to optimize the timing of when they make capital gains with times when the risk-free rate is low.
When you sell assets you deduct the amount you paid for them. The proposal is to multiply that basis by the total amount of risk-free interest that would have accumulated over the intervening period, which can be calculated by looking up a single number in a table. I agree that using the risk-free rate when you sell would be insane.
(From the perspective of tax optimization, I think this is much simpler than the status quo. From the perspective of tax accounting, this mechanism takes the place of the distinction between long-term and short-term capital gains, and is radically simpler than that.)
taxing excess returns seems like it’s almost a free lunch: it reduces an investor’s losses as well as their gains, so they can just lever up their investments to offset the effect of taxes.
Another factor which pays for the lunch is the increase in demand and decrease in supply of risk-free capital. Demand increases in order to fund the excess margin needed for all that leverage. On the supply side, people should keep a somewhat smaller chunk of their funds in risk-free assets, as they leverage up the risky side of their portfolios. The overall effect should be an increase in risk-free capital costs, i.e. the real risk-free interest rate.
I'd have to do the math, but my guess is that the change in real risk-free rate would (to first order) match the gains from the tax, and pay for the lunch. That said, I love this idea of (properly structured) capital gains taxes as a substitute for a sovereign wealth fund.
Also, my current understanding is that risk compensation is definitely not the large majority of investment returns. The last chapter of Cochrane's Asset Pricing text has a great discussion of the topic. The main conclusion is that explaining returns via risk exposure requires unrealistically high levels of risk aversion - like, one or two orders of magnitude above the risk aversion levels implied by other activities.
Also, my current understanding is that risk compensation is definitely not the large majority of investment returns. The last chapter of Cochrane's Asset Pricing text has a great discussion of the topic. The main conclusion is that explaining returns via risk exposure requires unrealistically high levels of risk aversion - like, one or two orders of magnitude above the risk aversion levels implied by other activities.
What's the competing explanation?
Haven't looked at the historical numbers, but in recent times it seems like (i) with log utility and a naive model of "future=past," optimal leverage is around 2x, (ii) most investors are much more risk averse than log utility (even for casino risk). So it seems like things basically add up here for most of the market. Was the situation an order of magnitude different in the past?
Cochrane mainly talks about this in the context of the equity premium. His main answer is "we don't know why there's an equity premium, we've tried the obvious risk-aversion models and they don't make sense."
The key issue is not just "most investors are much more risk averse than log utility", but how much more risk averse exactly. Cochrane tries to back out the curvature of the utility function (measured as , where c is consumption) based on observed market parameters, and he shows that needs to be around 50. For sense of scale, log utility would imply , and in the range of 1 to 5 is typical in theoretical models - that's the sort of risk aversion you'd expect to see e.g. in a casino. would imply some bizarre things - for example, assuming real consumption growth of around 1% annually with 1% std dev, the risk free rate should be around 40%. (Cochrane has a bunch more discussion of weird things implied by very high risk aversion, and looks at some variations of the basic model as well. I don't know it well enough to expound on the details.)
Personally, I suspect that the "true" answer to the problem is some combination of:
... but I haven't gotten around to building and solving models for these yet; my interest is more on the market microstructure end of things.
With regard to distortions one need to look at supply (and possibly demand) elasticities. It is possible that a small tax could produce a larger welfare loss than that of a large tax.
It might also be good to look at where the tax is initially falling -- have not thought this out yet but is there a multiplier effect potential here?
Another view might also be that of costs -- why is the cost of governance any more distortionary than the presence of costs anywhere else in the input markets? Maybe the approach here should be to look at potential real economic profits in the input cost prices (which would include cost of government) and make those incremental costs the distortionary element.
Can you explain more why the tax rate on the risk-free-rate portion of investment income should be 0? A positive rate here implements a proxy wealth tax (without raising the reporting problems of a direct wealth tax), and a nonzero wealth tax might be part of an optimal tax policy (e.g., for the lots-of-small-taxes argument, if no other reason).
(I'm not sure that this is right, and am mostly asking this question from a stance of exploratory uncertainty.)
This is basically the argument in my second bullet. You can make what you will of that argument, I think I still believe it---taxing savings just seems strictly worse than a similarly-progressive tax on income.
(I also don't much like a wealth tax for the same reason.)
Ah, that makes sense.
Separately, I'm not entirely convinced by that second bullet point -- it seems like a non-omniscient state planner in a non-stationary environment would benefit from being able to determine the desired level of redistribution after the wealthy have accrued their income as wealth, rather than needing to get it right as they earned it.
(I'm assuming away the confiscatory impulse here, naturally; in practice, the political economy of confiscation causes serious issues for deferred decisions about distribution like this.)
How should a state tax investment income if it wants to maximize its citizens’ welfare? This sounds like a simple question but I find it surprisingly hard to think about. Here are some of the positions I’ve moved through over the last few years:
My current best guess is that we should tax capital gains at the same rate as ordinary income, but only tax returns above the risk-free rate. (So if I buy short-term government bonds, I owe no taxes, and if I make less than that then I get a deductible loss.) I think this is likely to be better than either the status quo or most of the alternatives I’ve heard seriously discussed.
But given that my views have gone through this many revisions, my all-things-considered view is more like “This is really complicated, who knows.” I hope this post h helped move you in that direction.