# Tax the Rich

Dylan Matthews has a typically excellent explainer about taxing the rich. Just click the link.

I have one thought. Matthews is soft on capital income.

Matthews wrote

Saez and Diamond also argued that capital income — income from things like capital gains, corporate profits, dividends, etc. — should be taxed, which broke with previous models of optimal tax theory. (Our current capital gains top rate is 23.8 percent.) Those models had suggested the proper tax rate on capital income was zero, on the grounds that it discouraged savings: If you spend money on an investment, your profits are taxed, but if you spend money on food or a house or what have you, you don’t get hit with a capital tax — so a capital tax’s presence pushes you to spend more and save less.

This is a roughly correct description of the previous models, but it isn’t exact. In fact, the mathematical result is that as time goes to infinity the tax rate on capital income should go to zero. There is no justification for arguing that this means the rate should be zero in 2019 or 3019. The infinite jump from t goes to infinity to now is simply a dishonest rhetorical trick.

Another problem is that the academic literature on capital income taxation is not sound. The classic paper by Judd is simply mathematically incorrect. Yet it is still regularly cited. The key assumption which Judd made which makes his conclusion a mistake (a mistake like 2+2=5 not a mistake like taking a crazy assumption seriously) is that the state runs a balanced budget. Given Judd’s assumptions, the correct math shows a positive tax rate on capital income for all time.

It is interesting that a math boo boo could be so influential. One might almost guess that ideology and self interest are involved.

If the state is allowed to run deficits or surpluses, then the optimal policy involves building up a huge sovereign wealth fund so high that all desired spending is financed by the socialist profits on state owned means of production (this is just what the math says). At that point, the optimal tax on capital income is zero, because there is no reason not to tax. In particular if one wishes to tax capital income because one cares about inequality, the math suggests no compromise at all. In the simplest model it is optimal to tax capitalists until the richest capitalist has the national average income. With more reasonable assumptions, an egalitarian who also cares about efficiency would end up taxing the rich until they become poorer than average.

An egalitarian would accept that the tax on capital income eventually go to zero when the recipients of capital income are as poor as the average person or poorer. A class warrior who wanted the rich to starve but didn’t want to deprive workers of capital to work will would tax the rich till they starved.

A critique of the standard anti capital income taxation program should conclude “it is not until capital income ceases to go to the rich and goes to the relatively poor can we inscribe on our banner from each capitalist zero taxes and to each capitalist the full market income”

In contrast, if some have high labor income, it is best to let them end up with above average income. As is often argued, the equality efficiency tradeoff is different for capital income taxation, but it is different because less is optimally conceeded to the rich in the name of efficiency. Nothing or less than nothing should be conceded.

This is a simple mathematical result based on standard assumptions.

Also the standard model assumes dynamic effiency. Matthews is very smart, but he accepts the assumption that we should encourage saving. This is an implication of the Ramsey Cass Koopmans model, which might or might not have anything to do with reality. It is possible to decide if a higher steady state ratio of capital to effective labor implies higher or lower welfare.

It has been argued that the standard case for more capital is valid if r>g where r is the expected return on capital (including the expected value of risky returns) and g is the trend rate of gdp growth. In fact, it is valid only if rf > g where rf is the safe rate of interest which has almost always been less than g. This isn’t a fringe claim. It is Public Debt and Low Interest Rates Olivier Blanchard — another Frenchman, January 2019.

He would have cited AngryBear if he had known about this post.

In fact, the math says we can benefit from lower saving. This means a higher debt to gdp ratio would be better if it crowds out saving. I have co-authors now, so I shouldn’t type more.

The mathematical is political.

Isn’t our current problem that we have too much capital? ROI hasn’t been rising in general.

@kaleberg Yes indeed. That is the last bit of the post about Blanchard and dynamic inefficiency.

But it is also separately true that if we didn’t have too much capital, a reasonable way to manage things would be to tax capital income and invest the proceeds in a sovereign wealth fund.

I am asserting that the idea that, even if it goes mostly to rich people and we would like to tax it, we shouldn’t tax capital income because that reduces saving is wrong in many different ways.

It isn’t the implication of standard models in which we can’t possibly have too much capital and also those models don’t fit the data which suggest that we do have too much capital.

Basically, the argument against taxing capital income has no intellectual merits whatsoever. It isn’t the alleged result in the literature (which is about what should happen as time goes to infinity not about now). A key paper in the literature is just wrong (this is known and I’m not the one who proved it). And finally, the standard assumption in the literature is inconsistent with the available data.

So it fails in different ways. Multiple arguments against the conclusion are valid arguments.

On the other hand, there is no other hand.

The math is true when we have consistent overlap and productivity is increasing. (The math being debt can continue)

It is so true, in fact, we can replace G with Shoe, and prove the ability of shoe stores to maintain increasing debt, as long as productivity increased faster.

What have you done to stipulate that G is the proper variable in your starting model? If I can replace G with Shoe, and prove similar results, what is accomplished? I can make the model discrete, it still works.

@matt Young. I may not have been clear enough, but you should have understood that you don’t understand.

Your parenthetical statement “(the math being debt can continue)” is not OK discussion. You should have written “(*if* ‘the math’ is the claim that debt can continue)”. Instead, you claimed the authority to tell me what I meant. You are wrong about what I wrote. Your interpretation is inconsistent with the text (my post). The math is absolutely not simply the claim that debt can continue.

The math is the assertion that, in the standard model, higher debt causes a Pareto improvement if rf

RW,

There is no chance you could possibly write anything clear enough to make Matt Young understand.

And that is not due to your writing.

So, not looking at this as a modeling problem. Do we have too much capital? Or have we changed the economy via policy such that investing capital in ways that create more capital. That is, the economy is more rent seeking than production seeking.

We’ve had massive consolidation. No real capital increasing happening there, just consolidation of existing capital. We’ve had off shoring, no real capital producing activity there, just licensing, royalties via contracting with foreign companies for production. We have tax reduction turned into stock boosting.

To argue we have too much capital suggests that an economy is a function independent of human intent, ideals and thus not a human construct.

This nation as a capital owner has done what since the moon shot to improve it’s capital activity and thus growth? With 76% of our capital being intangible which is the legal and education system you only have to look at our current government conduct to understand we don’t have too much capital. We have been destroying our primary capital (burning through it) while consolidating the tangible capital resulting in inert tangible capital.

I showed years ago here at AB that the top 1%’s income was doubling faster than the economy could grow.

The math models may say we have too much capital, but I think reality is saying something different.

Daniel. “productive capital” has been decaying since the 20’s. I think the problem is, you have to understand the difference, that what you call “productive” capital crested in 1923 and hit the point where its future productivity was going to decline and the rise of rentier finance in the 80’s. We have been bleeding “productive capital” since the mid-20’s. The post-war era provided a different model of growth that wasn’t based on pure capital flows. But productive capital basically didn’t grow nearly as fast as during the 1879-1923 period even then. “Offshoring” has kept many companies in business who would have been forced off the field, which has created a over capacity in consumer products, which has contributed to the general deflation since 1984. Throwing stuff at people has worked to pacify the “people” into decadent behavior, a weird political “liberal/conservative” they call it that simply has run its course. Underneath this overcapacity is the dollar standard, which if would collapse, would signal the end of the global system started in the 1970’s and create one hell of tide rushing out.

So yeah, we have to much capital. It causes rentier’s to look for easy fixes and low taxes create the inefficiency. Low government investment causes low investment demand to push down new investment privately..

We don’t have too much capital, we have the wrong sort of capital because we don’t tax pollution and resource extraction enough.