Results for “piketty”
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More Matt Rognlie on Piketty

From the comments:

Krugman correctly highlights the importance of the elasticity of substitution between capital and labor, but like everyone else (including, apparently, Piketty himself) he misses a subtle but absolutely crucial point.

When economists discuss this elasticity, they generally do so in the context of a gross production function (*not* net of depreciation). In this setting, the elasticity of substitution gives the relationship between the capital-output ratio K/Y and the user cost of capital, which is r+delta, the sum of the relevant real rate of return and the depreciation rate. For instance, if this elasticity is 1.5 and r+delta decreases by a factor of 2, then (moving along the demand curve) K/Y will increase by a factor of 2^(1.5) = 2.8.

Piketty, on the other hand, uses only net concepts, as they are relevant for understanding net income. When he talks about the critical importance of an elasticity of substitution greater than one, he means an elasticity of substitution in the *net* production function. This is a very different concept. In particular, this elasticity gives us the relationship between the capital-output ratio K/Y and the real rate of return r, rather than the full user cost r+delta. This elasticity is lower, by a fraction of r/(r+delta), than the relevant elasticity in the gross production function.

This is no mere quibble. For the US capital stock, the average depreciation rate is a little above delta=5%. Suppose that we take Piketty’s starting point of r=5%. Then r/(r+delta) = 1/2, and the net production function elasticities that matter to Piketty’s argument are only 1/2 of the corresponding elasticities for the gross production function!

Piketty notes in his book that Cobb-Douglas, with an elasticity of one, is the usual benchmark – and then he tries to argue that the actual elasticity is somewhat higher than this benchmark. But the benchmark elasticity of one, as generally understood, is a benchmark for the elasticity in the gross production function – translating into Piketty’s units instead, that’s only 0.5, making Piketty’s proposed >1 elasticity a much more dramatic departure from the benchmark. (Keep in mind that a Cobb-Douglas *net* production function would be a very strange choice of functional form – implying, for instance, that no matter how much capital is used, its gross marginal product is always higher than the depreciation rate. I’ve never seen anyone use it, for good reason.)

Indeed, with this point in mind, the sources cited in support of high elasticities do not necessarily support Piketty’s argument. For instance, in their closely related forthcoming QJE paper, Piketty and Zucman cite Karabarbounis and Neiman (2014) as an example of a paper with an elasticity above 1. But K&N estimate an elasticity in standard units, and their baseline estimate is 1.25! In Piketty’s units, this is just 0.625.

And this:

What does this all mean for the Piketty’s central points – that total capital income rK/Y will increase, and that r-g will grow? His model imposes a constant, exogenous net savings rate ‘s’, which brings him to the “second fundamental law of capitalism”, which is that asymptotically K/Y = s/g. The worry is that as g decreases due to demographics and (possibly) slower per capita growth, this will lead to a very large increase in K/Y. But, of course, this only means an increase in net capital income rK/Y if Piketty’s elasticity of substitution is above 1, or if equivalently the usual elasticity of substitution is above 2. This is already a very high value, and frankly one to be treated with skepticism.

Meanwhile, it is even harder to get growth in r-g, which most readers take to be Piketty’s central point. Suppose that in recent decades, r has been roughly 5% while g has been 2.5%, and suppose that g will ultimately fall to around 1%. In Piketty’s framework, this implies an increase in steady-state K/Y of 2.5. If there is an elasticity of 1 (in Piketty’s units), this implies a decrease in r from 5% to 2%, and thus a *decrease* in the gap r-g from 2.5% to 1%. The point is that with this unit demand elasticity and the exogenous net savings assumption, it is the ratio r/g rather than the difference r-g that is constant, which means that a decline in g leads to a proportionate decline in r-g. (Note that Krugman’s review is ambiguous about this distinction.)

What would we need to obtain even a tiny increase in r-g in this setting – say, of half a percentage point? We would need r to fall from 5% to only 4% while g fell from 2.5% to 1%, increasing r-g from 2.5% to 3%. But given the 2.5-fold increase in K/Y, a decline in r by a factor of only 1/5th implies an elasticity of substitution (in Piketty’s sense) of nearly 4. This implies an elasticity of substitution in the *usual* gross production function sense of nearly 8, not plausible by any stretch of the imagination.

Unless I’m missing something, the formal apparatus in Piketty’s book simply is not capable of generating the results he touts. There are two very simple issues that break it quantitatively – first, the distinction between elasticities of substitution in the gross and net production functions; and second, the fact that as g falls, an extraordinarily high elasticity of substitution is necessary to prevent r from falling along with it and actually compressing the arithmetic gap between r and g. Perhaps there are modifications to the framework that can redeem it, but as it currently stands I’m baffled.

I believe Matt is correct.  I would simply note that diminishing returns to capital — relative to other factors of production — are likely to hold in the long run.  See also these earlier MR comments by Rognlie and Harless.  And here are Piketty’s lecture notes.

Krugman’s review of Piketty

You will find it here.  Excerpt:

Just about all economic models tell us that if g falls—which it has since 1970, a decline that is likely to continue due to slower growth in the working-age population and slower technological progress—r will fall too. But Piketty asserts that r will fall less than g. This doesn’t have to be true. However, if it’s sufficiently easy to replace workers with machines—if, to use the technical jargon, the elasticity of substitution between capital and labor is greater than one—slow growth, and the resulting rise in the ratio of capital to income, will indeed widen the gap between r and g. And Piketty argues that this is what the historical record shows will happen.

Krugman calls the book “awesome,” but here are his critical remarks:

I don’t think Capital in the Twenty-First Century adequately answers the most telling criticism of the executive power hypothesis: the concentration of very high incomes in finance, where performance actually can, after a fashion, be evaluated. I didn’t mention hedge fund managers idly: such people are paid based on their ability to attract clients and achieve investment returns. You can question the social value of modern finance, but the Gordon Gekkos out there are clearly good at something, and their rise can’t be attributed solely to power relations, although I guess you could argue that willingness to engage in morally dubious wheeling and dealing, like willingness to flout pay norms, is encouraged by low marginal tax rates.

My own review is still due out in about a week’s time.

Colombian sentences to ponder

His close colleague, fellow senator Iván Cepeda, says Petro’s ideas transcend traditional left-right boundaries. “He has been inspired by many sources . . . he has a solid Marxist foundation but has also read a lot of French post-structuralism and other political traditions. He is also a serious economist . . . who has read thinkers like Naomi Klein and is in dialogue with [French economist Thomas] Piketty”.

And this:

If Petro wins in Colombia and if, as recent polls suggest, former Brazilian president Luiz Inácio Lula da Silva pulls off what would be a momentous comeback victory in October, the seven most populous nations in Latin America — Brazil, Mexico, Colombia, Argentina, Peru, Venezuela and Chile — will all be under leftwing rule.

Here is more from the FT.

Sunday assorted links

1. “In 2018, there were 20,933 calls to San Francisco’s government complaining about human feces.

2. Does urbanization contribute to depression?

3. China polygenic scores comparison of the day.

4. Informal norms for surfing property rights, a’la Schelling.

5. A Chinese liberal reviews Thomas Piketty.

6. Can you undo your vaccine?

7. Abhijit Banerjee, chef.  And his new cookbook is here.

What I’ve been reading

1. Anne Enright, The Green Road.  Could Enright be the least heralded, English-language novelist in the United States today?  I also was a big fan of her last book Actress.  Her short pieces are wonderful as well.  Having won a Booker, she is hardly obscure, and yet I have never had anyone tell me that I absolutely must read Anne Enright?  Even after the very recent burst of interest in Irish writers…I will read more of her!

2. Patrick Leigh Fermor, The Traveller’s Tree: A Journey Through the Caribbean Islands.  My favorite Fermor book, the best sections were on Trinidad and Haiti, but you might have known I would think that.

3. Nadia Durbach, Bodily Matters: The Anti-Vaccination Movement in England, 1853-1907.  Back then vaccines were quite often dangerous: “Victorian public vaccinators used a lancet (a surgical instrument) to cut lines into the flesh in a scored pattern.  This was usually done in at least four different places on the arm.  Vaccine matter, also called lymph, would then be smeared into the cuts…[often] vaccinators required infants to return eight days after the procedure to allow lymph to be harvested from their blisters, or “vesicles.”  This matter was then inserted directly into the arms of waiting infants…After 1871, a fine of up to 20 shillings could be imposed on parents who refused to allow lymph to be taken from their children for use in public vaccination.”  Oddly, or perhaps not, the arguments against vaccines haven’t changed much since that time.

4. Andrew G. Farrand, The Algerian Dream: Youth and the Quest for Dignity.  There should be more books like this!  Imagine a whole book directed at…not getting someone tenure, but rather helping you understand what it is actually like to be in Algeria.  Sadly I have never been, but this is the next best thing.  As I say repeatedly, there should be more country-specific books, simply flat out “about that country” in an explanatory sense.  As for Algeria, talk about a nation in decline…

Eswar S. Prasad, The Future of Money: How the Digital Revolution is Transforming Currencies and Finance is a useful overview of its source material.

Anna Della Subin, Accidental Gods: On Men Unwittingly Turned Divine, starts with the question of how Emperor Haile Selassie became a god to Rastafarians in Jamaica, and then broadens the question accordingly, moving on to General Douglas MacArthur, Annie Besant, and much more.  I expect we will be hearing more from this author.  At the very least she knows stuff that other people do not.

You can learn the policy views of Thomas Piketty if you read his Time for Socialism: Dispatches from a World on Fire, 2016-2021.  Oddly, or perhaps not, his socialism doesn’t seem to involve government spending any more than fifty percent of gdp, which would be a comedown for many European nations.

Kathleen Harward and Gabriella Sulbarán, The Shared Dog, for young children, teaching the economics of property rights through the tale of a dog.  From BrandyPie Books.

David Splinter responds to Saez and Zucman

When estimating income inequality with tax data, accounting for missing income presents many challenges. Researchers have adopted different approaches to address these challenges. Saez and Zucman (2020) discuss differences between the national income distributions of Piketty, Saez, and Zucman (PSZ, 2018) and Auten and Splinter (AS, 2019a). Saez and Zucman also make updates to their estimates for retirement income, partially responding to one of the concerns raised in AS. In this reply, I explain that SZ only partly correct this problem and do not address other issues raised by AS. For the allocation of underreported income—the most consequential difference between AS and PSZ—I show that the AS approach conforms with special audit studies in five ways, while the PSZ approach is inconsistent with them. I also provide historical background on the two projects, respond to technical points raised, and discuss estimates of tax progressivity.

Here is the link to the paper.

On audiobooks

From my email, from Robert Kwasny:

I imagine you listen to audio books rarely but, still, I wonder if you have any new thoughts on this topic.

Few thoughts of my own:

1. Shakespeare audiobooks are excellent. Much better than watching blu-rays. Unlike on real stage, Prospero (voiced by Ian McKellan in one production) can actually whisper softly to Miranda without worrying about people in the back rows. Stage directions are already included in the dialogue.

2. Pop psychology and self-help are terrible. Once cannot easily skip or skim the boring parts.

3. History books written by academics (e.g. The Sleepwalkers) are tough unless one already knows the necessary context. Otherwise it’s easy to get lost in the thicket of background facts. That’s probably true for all dense books. For example, Piketty’s books are available on Audible but I didn’t even bother sampling them. It’s just a wrong format.

4. I’ve had great experience with books written by authors with journalistic experience. Robert Caro’s works are excellent in audio form. William Manchester’s Churchill biography is good as well. Lawrence of Arabia by Scott Anderson too. Good audiobooks can’t be just one fact after another, they need to tell a story.

5. If the book’s author does the narration it’s usually bad. Voice acting is hard.

Unfortunately I don’t know of any book created specifically for audio. Where are biographies of Bob Dylan with songs included? Or books on rhetoric with audio of great speeches included? Audiobooks (and ebooks for that matter) don’t seem to be a new medium, at least so far. 10 years ago I would have not predicted that.

I have no new thoughts on audiobooks!  Though for my next book (which is co-authored), I was asked to read at least part of the AudioBook.  I will thus develop additional thoughts over time.

Tuesday assorted links

1. Further evidence for the importance of female role models: “We find that, among high-ability female students, being assigned a female professor leads to substantial increases in the probability of working in a STEM occupation and the probability of receiving a STEM master’s degree.”

2. Which Conversations with Tyler guest is your intellectual doppelgänger?  A fun test you can take.

3. “According to the researchers, consumers notice no difference when a quarter of the milk butter in a cake is replaced with larva fat. However, they report an unusual taste when it gets to fifty-fifty and say they would not want to buy the cake.”  Link here.

4. Krugman reviews Piketty (NYT).

5. Kevin Drum’s simple theory of DT’s optimism about the coronavirus.  And the economics of mandated sick pay.  And “Detroit to restore water service to unpaid homes to allow people to wash their hands to avoid coronavirus.

Thursday assorted links

1. NYT covers minimum wage and suicide debate.

2. “According to Novokmet, Piketty & Zucman, the UK’s “per adult national income (€ PPP)” was just ahead of Russia’s in 1980” — No further comment from me.

3. Balding on Huawei.

4. “Media Trades is a simple, free tool that addresses this problem by allowing people from the left and right to trade media content.

5. Guitar made out of 106 iPhones.

Claims about real rates of return

With recourse to archival, printed primary, and secondary sources, this paper reconstructs global real interest rates on an annual basis going back to the 14th century, covering 78% of advanced economy GDP over time. I show that across successive monetary and fiscal regimes, and a variety of asset classes, real interest rates have not been “stable”, and that since the major monetary upheavals of the late middle ages, a trend decline between 0.6-1.8bps p.a. has prevailed. A consistent increase in real negative-yielding rates in advanced economies over the same horizon is identified, despite important temporary reversals such as the 17th Century Crisis. Against their long-term context, currently depressed sovereign real rates are in fact converging “back to historical trend” – a trend that makes narratives about a “secular stagnation” environment entirely misleading, and suggests that – irrespective of particular monetary and fiscal responses – real rates could soon enter permanently negative territory. I also posit that the return data here reflects a substantial share of “nonhuman wealth” over time: the resulting R-G series derived from this data show a downward trend over the same timeframe: suggestions about the “virtual stability” of capital returns, and the policy implications advanced by Piketty (2014) are in consequence equally unsubstantiated by the historical record.

That is from a new paper by Paul Schmelzing, via the excellent Kevin Lewis.

Consistency about elasticities, revisited

From Ross Rheingans-Yoo, the content is all his, I will not do a double indent:

  • If marginal wealth is taxed an additional 0.5%/yr at the high end, then fewer people will amass and invest that much wealth—some will instead disperse it among a wider number of family members, donate it to charitable or political causes, or spend it on expensive consumption. (Saez and Zucman, in their potential-revenue analyses, assume that this effect is quite small, and that the wealthy will mostly accept lower returns on wealth.)
  • Similarly, if the marginal opportunities to invest became worse by 0.5%/yr, fewer people would chose to invest, by the same token. Additionally,the effects should be the same size, as it’s the same decision-makers facing the same incentives!
  • But if pushing on the price (read: rate of return) has little effect on the quantity of investment, then pushing on the quantity of investment should have a large​ effect on the price! (Unless we’re at some magic kink in the supply curve for unspecified reasons…)
  • So a small amount of additional capital competing for investment opportunities should quickly reduce the competitive rate of return.

What’s the practical upshot? Well, if the authors’ assumptions about revenues are right, then Piketty’s r>gr>g “wealth spiral” can’t proceed unchecked, since capital simply can’t accumulate without competition quickly reducing the average rate of return back below gg.

What is the incidence of the corporate income tax?

Emmanuel Saez and Gabriel Zucman seem to think the correct answer is to assume that there is no substitution away from capital or from the corporate sector:

This paper proposes a new way to do distributional tax incidence better connected with tax theory. It is crucial to distinguish current distributional analysis from tax reform distributional analysis. Current distributional analysis shows the current tax burden by income groups and should assign taxes on each economic factor without including behavioral responses: taxes on labor should fall on labor earners, taxes on capital on the corresponding asset owners, and taxes on consumption on consumers. This allows to distribute both pre-tax and post-tax current incomes and measure the economically relevant tax wedges on each factor without having to specify behavioral responses. Tax reform distributional analysis shows the impact of a tax reform and should describe the effect on pre-tax incomes, post-tax incomes, and taxes paid by income group separately and factoring in potential behavioral responses. Various scenarios can be considered given the uncertainty in behavioral responses. We illustrate our methodology using a simple neo-classical model of labor and capital taxation.

No Western fiscal authority I have heard of thinks of tax incidence in these terms.

There is an argument that you first write down the “no-response” burden in order to arrive at the actual estimated burden, as the authors seem to note.  That is not an argument for coming up with a “no adjustment” estimate and marketing it to The New York Times (and others?) as correct and based on normal assumptions, without first adjusting for incentives and capital responses and shifts in the ultimate tax burden.  Would we have known about these underlying assumptions — which lie behind their subsequent calculation of wealth inequality — at all, if not for the tireless work of Phil Magness and Wojtek Kopczuk on Twitter?

Returning to the paper, it has some quite weak sentences, such as: “But it [no adjustment] also has the advantage of not being dependent on assumptions on behavioral responses.”

You might as well argue that assuming zero price elasticity of demand “has the advantage of not being dependent on assumptions on behavioral responses.”  In reality, one is assuming about the least plausible behavioral response possible.

Here is some background material from Wojtek Kopczuk, which works through how the proffered inequality measures and corporate tax assumptions are related.  And from Steven Hamilton.  Here is also the recent David Splinter summary analysis on tax progressivity.  Wojtek notes in his Twitter thread:

The bottom line: corporate tax should be felt by other forms of capital. That’s the standard assumption. CBO makes it, Auten-Splinter make it, Piketty-Saez-Zucman make it. Who does not? Saez-Zucman (2019) do not.

Here is the semantic innovation from the Saez-Zucman paper:

We think it is more useful to say that cutting corporate taxes could increase workers’ wages rather than say
that the tax burden on workers would fall.

Say both!  Here are two well-known and also generally accepted AER papers suggesting that the corporate income tax places a burden on real wages.

Michael Smart agrees with me on the new Saez-Zucman piece:

Zucman has now kindly posted an early working paper to support the SZ assumption. I do not find this WP convincing. We’re simply told that the “natural description” of tax incidence is its legal incidence, i.e. 100% shareholder incidence of CIT.

I find this episode appalling, and I hope The New York Times is properly upset at having been “had.”


Saturday assorted links

1. Human corpses keep moving for a year after death.

2. Scarce labor and low interest rates.  By Benzell and Brynjolfsson.

3. My Stubborn Attachments philosophy podcast, Elucidations, with Matt Teichman.

4. Are we living in the most influential time ever?

5. Average is Over: “These synthetic husbands have an average income that is about 58% higher than the actual unmarried men that are currently available to unmarried women.

6. Thomas Piketty slides based on his forthcoming book; the word “Mormon” does not appear.

Increases in Inequality Have Been Overestimated

Stephen Rose of the Urban Institute (not exactly a right-wing or libertarian think tank) compares recent studies measuring changes in inequality and finds that although inequality has increased the Piketty and Saez (2003) results, which generated a tremendous amount of discussion and research, are very likely over-stated.

The results from at least four studies were compared for three measures of income change: change in median incomes, share of growth captured by the top 10 percent, and the changing income share of  the top 1 percent. In all cases, Piketty and Saez (2003) were the outlier, showing the most increased inequality. And in all three measures of income change , Piketty, Saez, and Zucman (2018) found much less growth in income inequality than Piketty and Saez (2003).

This brief does a meta-analysis of different findings to estimate a “consensus” level of change…I find that instead of stagnating, real median incomes grew by just over 40 percent (1 percent a year) from  1979 to 2014;  the top 10 percent of the income ladder captured 45 percent of income growth from 1979 to  2014; and the share of the top 1 percent grew 3.5 percentage points.

All studies find that income inequality rose after 1979, but common perceptions that all income gain went to the top 10 percent and middle class incomes stagnated (or even declined) are wrong.

Russ Roberts also has several good videos showing how the numbers can be cut in various ways.