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Matt Rognlie on negative interest rates

What Lower Bound? Monetary Policy with Negative Interest Rates (Job Market Paper)

Abstract:  Policymakers and academics have long maintained that nominal interest rates face a zero lower bound (ZLB), which can only be breached through major institutional changes like the elimination or taxation of paper currency.  Recently, several central banks have set interest rates as low as -0.75% without any such changes, suggesting that, in practice, money demand remains finite even at negative nominal rates. I study optimal monetary policy in this new environment, exploring the central tradeoff: negative rates help stabilize aggregate demand, but at the cost of an inefficient subsidy to paper currency. Near 0%, the first side of this tradeoff dominates, and negative rates are generically optimal whenever output averages below its efficient level. In a benchmark scenario, breaking the ZLB with negative rates is sufficient to undo most welfare losses relative to the first best. More generally, the gains from negative rates depend inversely on the level and elasticity of currency demand. Credible commitment by the central bank is essential to implementing optimal policy, which backloads the most negative rates. My results imply that the option to set negative nominal rates lowers the optimal long-run inflation target, and that abolishing paper currency is only optimal when currency demand is highly elastic.

The paper is here, and it contains many new analytical points.  As you would expect from Matt, it is also extremely well-written.  Here are previous MR posts related to Matt Rognlie.

Here Eric Lonergan criticizes Swiss negative interest rates.  On the blog of Miles Kimball, you will find many arguments for negative nominal interest rates, and also the abolition of currency, another topic covered by Matt in his paper.

By the way, here is the latest on Swiss bond rates, negative even at ten years out.

Matt Rognlie on Piketty, net capital returns, and housing

Brookings emails me:

Capital income is not growing unboundedly at the expense of labor, and further accumulation of capital in fact most likely means a fall in capital’s share of total income – refuting one of the main theories of economist Thomas Piketty’s popular book Capital in the 21st Century — according to a paper presented today at the Spring 2015 Conference on the Brookings Papers on Economic Activity (BPEA).

Existing studies that show an increase in capital’s share of income miss the growing role of depreciation in short-lived capital, in items such as software, says MIT’s Matthew Rognlie in “Deciphering the Fall and Rise in the Net Capital Share.”  Rognlie subtracts depreciation in seven large developed economies (the US, Japan, Germany, France, the UK, Italy, and Canada) to get net capital income, and finds that the only long-term rise in capital’s share of income is in housing. Capital income elsewhere in the economy has grown moderately, but it is only recovering from a large fall that lasted from 1948 through the 1970s.

Piketty’s Capital argues that the role of capital in the economy, after falling during the Depression and two world wars, is set to recover to the high levels of the 19th and early 20th centuries. According to Piketty, wealth will accumulate amid slowing economic growth to push up the capital-to-GDP ratio in the economy, which will then cause an increase in capital’s share of income — and growing inequality.

In contrast, Rognlie finds that a rising capital-to-GDP ratio is most likely to result in a fall in capital’s share of income, since the net rate of return on capital will fall by an even larger proportion than the capital-to-GDP ratio rises. Outside of housing, postwar changes in the value of the capital stock have not led to parallel changes in capital’s share of income. In fact, the value of the capital stock relative to private income reached its highs in the late 1970s and early 1980s, when capital’s share of income was near a low.

Rognlie shows that the share of net income generated by housing has risen in all seven large developed economies since data became available. “Housing’s central role in the long-term behavior of the aggregate net capital share has… not been emphasized elsewhere…Observers concerned about the distribution of income should keep an eye on housing costs,” he writes.

Brad DeLong offers comment.

Here Jim Tankersley has a superb profile of Rognlie and the story behind his comment, MR plays a role too.  Recommended.

More Matt Rognlie on Piketty — the most important point

Matt has what is probably the single best, focused technical critique of Piketty.  Here are his concluding remarks:

Compared to the grand scope of Piketty (2014), the objective of this note has been quite narrow: to systematically explore the relevant evidence on diminishing returns to capital. Technical and uninspiring as this question may be, it is an essential step in knowing whether the prediction of rising capital income and inequality through accumulation—a prediction that gives Capital in the Twenty-First Century its title—will really come to pass. And given the evidence here that Piketty (2014) understates the role of diminishing returns, some skepticism is certainly in order.

But rejection of this specific mechanism does not constitute rejection of all Piketty (2014)’s themes. Inequality of labor income, for instance, is a very different issue—one that remains valid and important. Capital itself remains an important topic of study. Among large developed economies, the remarkably consistent trend toward rising capital values and income is undeniable. As Sections 3.3 and 3.4 establish, this trend is a story of rising capital prices and the ever greater cost of housing—not the secular accumulation emphasized in Capital — but it has distributional consequences all the same. Policymakers would do well to keep this in mind.

The full piece is here (pdf), excellent and on target throughout.

To be perfectly frank on this one, Matt here is completely correct and Piketty has not produced any effective response to this point, either within the book or without.  The internal response “I still think we need to worry about inequality therefore I side with Piketty” simply represents a misunderstanding of Matt’s argument.  Piketty’s mechanism of accumulation, as laid out in his book, is simply the wrong mechanism for understanding growing inequality, both theoretically and empirically.  And it is a shame that the Giles critique from the FT has attracted so much attention because it has distracted everyone from the more serious problems with the argument of the book.

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.

Matt Rognlie on secular stagnation

In the comments of Askblog, Matt writes:

…the “secular stagnation” hypothesis is in dire need of some cogent back-of-the-envelope estimates, and I don’t think it holds up very well. A long-term fall in the average real interest rate from, say, 2% to -1%, would be absolutely extraordinary. It would imply massive increases in the valuation of long-lived, inelastically supplied assets like land, and massive increases in the quantity of long-lived, elastically supplied capital like structures.

Just to illustrate how extreme the implications can be, consider the following (sloppy) calculation. The BEA’s average depreciation rate for private structures is currently about 2.5%. A decline in the real interest rate from 2% to -1% implies a decline in user cost r+delta from 4.5% to 1.5%, of a factor of three. If the demand for structures is unit elastic (as economists, unjustifiably from an empirical standpoint, tend to assume with Cobb-Douglas functional forms), this would imply a threefold increase in the steady-state quantity. Since structures are already 175% of GDP, this would imply an additional increase of 350% of GDP, more than doubling the overall private capital stock and nearly doubling national net worth. The transition to this level would require such an extraordinary, prolonged investment boom that we would not face slack demand for many, many years.

(There are many things wrong with this calculation, but even an effect a fraction of this size serves my point, especially when you keep in mind that land values would be skyrocketing as well. The bottom line is that proponents of secular stagnation have not yet contended with some of the basic numbers.)

There is more here.  That is via David Beckworth.

I am still waiting for a model of secular stagnation that rationalizes both a negative real interest rate and positive investment, which indeed we are observing in most countries circa 2014.  That means, by the way, I don’t quite agree with Matt’s sentence “The transition to this level would require such an extraordinary, prolonged investment boom that we would not face slack demand for many, many years.”  There are some “reasoning from a price change” issues floating around in the background here.  Is it the productivity of just new capital that has fallen to bring the natural interest rate to negative one?  Or the rate of return on old capital too, in which case the value of the extant capital stock is not given by the calculation in question?  Tough stuff, but you know where the burden of proof lies.  Can this all fit together with the fact that nominal gdp is now well above its pre-crash peak?  And that we are seeing positive net investment?  In any case I agree with Matt’s broader point that the implied magnitudes here don’t seem to fit the facts or even to come close.

Speaking of Piketty (or did I mean to write “speaking of Scott Sumner?”), Scott has a question:

…here’s what confuses me.  Some of the reviews seem to imply that Piketty argues that real rate of return on capital represents the rate at which the wealth of the upper classes grow.  Is that right?  If so, what is the basis of that argument?  I don’t think anyone seriously expects the grandchildren of a Bill Gates or a Warren Buffett to be 10 times as wealthy as they are.

My excellent Conversation with Thomas Piketty

Lots of disagreement in this episode, though always polite.  Here is the transcript, video, and audio.  Here is part of the summary:

He joined Tyler to discuss just how egalitarian France actually is, the beginning of the end of aristocratic society, where he places himself within French intellectual history, why he’s skeptical of data from before the late 18th century, how public education drives economic development, why Georgism isn’t sufficient to address wealth inequality, the relationship between wealth and cultural capital, his proposal for a minimum inheritance, why he turned down the Legion of Honor, why France should give reparations to Haiti despite the logistical difficulties of doing so, his vision for European federalism, why more immigration won’t be a panacea for inequality, his thoughts on Michel Houellebecq’s Submission, and more.

Here is one excerpt:

COWEN: If I visit every major country in Europe, what I observe is the highest living standard is arguably in Switzerland — Norway and Luxembourg aside. Switzerland has one of the smallest governments, and they attempt relatively little redistribution. What is your understanding of Switzerland? What if someone said, “Well, Europe should try to be more like Switzerland. They’re doing great.” Why is that wrong?

PIKETTY: Oh, Switzerland. It’s a very small country, so it’s about the size. . . . Actually, it’s smaller than Île-de-France, which is a Paris region. Now, if you were to make a separate country out of Île-de-France, GDP per capita, I think, would actually be higher than Switzerland. Of course, you can take a wealthy region in your country and say, “Okay, I don’t want to share anything with the rest of the country. I’m going to keep my tax revenue for me. I’m going to be a tax haven based on bank secrecy.” That’s going to make you 10 percent or 20 percent richer. I’m not saying —

COWEN: It’s been a long time since Switzerland relied on bank secrecy, right? Following 9/11, that Swiss advantage largely went away.

PIKETTY: Oh, that’s wrong. Oh, you’re wrong on this.

We talk about Matt Rognlie and Greg Clark as well.  Recommended, this was fun for me to reread.

Sunday assorted links

1. The culture that is Singapore golf club script theft punishment.

2. Very good thread on some Matt Rognlie results, paper here.  The whole “market power lowering the returns to labor” bit really doesn’t seem to be holding up.

3. The Viewer (recommended videos, affiliated with The Browser).

4. ABBA outfits, and their story as a tax dodge.

5. What’s wrong with social science and how to fix it.

Is this why budget deficits might prove sustainable?

By Adrien Auclert, Hannes Malmberg, Frederic Martenet, and Matthew Rognlie:

We use a shift-share approach to quantify the general equilibrium effects of population aging on wealth accumulation, real interest rates, and capital flows. Combining population projections with household survey data from the US and 24 other countries,we project the evolution of wealth-to-GDP ratios by changing the age distribution,holding life-cycle asset and income profiles constant. We find that this compositional effect of aging is large and heterogeneous across countries, ranging from 85 percent-age points in Japan to 310 percentage points in India over the rest of the twenty-first century. In a general equilibrium overlapping generations model, our shift-share provides a very good approximation to the evolution of the wealth-to-GDP ratio due to demographic change when interest rates remain constant. In an integrated world economy, aging generates large global imbalances in the twenty-first century, pushing net foreign asset positions to levels several times larger than those observed until today.

Via Steven Bogden.  This is very likely an important piece.

Stansbury and Summers on the declining bargaining power of labor

In one of the best papers of the year, Anna Stansbury and Larry Summers present what is to me the best non-“Great Stagnation” story of what has gone wrong, and I have read many such accounts.  Here is their abstract:

Rising profitability and market valuations of US businesses, sluggish wage growth and a declining labor share of income, and reduced unemployment and inflation, have defined the macroeconomic environment of the last generation. This paper offers a unified explanation for these phenomena based on reduced worker power. Using individual, industry, and state-level data, we demonstrate that measures of reduced worker power are associated with lower wage levels, higher profit shares, and reductions in measures of the NAIRU. We argue that the declining worker power hypothesis is more compelling as an explanation for observed changes than increases in firms’ market power, both because it can simultaneously explain a falling labor share and a reduced NAIRU, and because it is more directly supported by the data.

There is a good deal of critical thinking about how different macroeconomic trends fit together, and a willingness to consider disconfirming evidence, so I do recommend you read through this one.

I have five main worries about the argument:

1. Rather than labor losing bargaining power, I think of the key development as “management measuring the marginal product of labor more precisely.”  Admittedly that does lower the bargaining power of the majority of workers, given the 20/80 rule, or whatever you think the proper proportions are (Stansbury and Summers themselves presumably are underpaid, but in general wage dispersion has been going up in high-skilled sectors).

A minority of highly productive workers have much more bargaining power than they did before, which doesn’t quite fit the “lower bargaining power per se” hypothesis.  And under my interpretation, easier unionization may not be much of a solution, since the problem here is the actual reality of who produces what.  Consistent with my view, labor’s share is not really down if you consider the super-talented labor/owners/capitalists who start their own companies.  That is a return to labor as well.

2. It is a noted advantage of the Stansbury and Summers approach that is explains the now-lower natural rate of unemployment.  The puzzle, I think, is to explain both lower NAIRU and the slower labor market matching observed over the post-2009 labor market recovery.  Their hypothesis seems to predict a higher degree of worker desperation, and thus quicker matches, than what we actually observed.

If you think, as I do, that employers are now better aware of the diversity of worker quality, and that only ex post do they learn that quality, employers will be more careful upfront, which probably does slow down matching speeds, thus fitting the data better.

3. If you play down market power, and postulate a fall in the share of labor, you might expect investment to be robust, but measured investment clocks in as mediocre.  The authors discuss this point at length on pp.45-46 and offer multiple rebuttals, but I suppose I still think the first-order effect here ought to be stronger than what we (seem to) observe.

4. If corporate profits are so high, how is this consistent with the persistently low demand postulated by Summers’s “secular stagnation” hypothesis?  The paper does consider this question very directly on p.56, but I genuinely (just as a matter of grammar) do not understand the answer the authors are suggesting.  Here goes:

A fair question about the labor rents hypothesis regards what it says about the secular stagnation hypothesis that one of us has put forward (Summers 2013). We believe that the shift towards more corporate income,that occurs as labor rents decline,operates to raise saving and reduce demand. The impact on investment of reduced labor power seems to us ambiguous, with lower labor costs on the one hand encouraging expanded output and on the other encouraging more labor-intensive production, as discussed in Section V.So,decreases in labor power may operate to promote the reductions in demand and rising gap between private saving and investment that are defining features of secular stagnation.

I suppose I had thought of low rates of profit as a (though not the?) defining feature of secular stagnation, but again I may not have understood this passage correctly.

5. Matt Rognlie found that the decline in labor’s share went to housing and land ownership, not capital.

In any case, here is a whole paper full of economics, go and enjoy it.

Has the Labor Share Declined? Maybe, maybe not.

In a 2017 post Asher Schechter correctly noted:

Of the various ills that currently plague the American economy, one that has economists particularly worried is the decline in the labor share—that is, the part of national income that’s allocated to wages.

Lots of theories have been proposed to explain the decline in labor share including automation, globalization and increased markups. In a big if true paper, Koh, Santaeulalia-Llopis and Zheng argue that all of these theories are wrong because there has been no decline in labor share once we take into account that the BEA changed how intellectual property was treated in the national accounts.

The lack of attention to measurement can severely misguide economic theory. We demonstrated that the change in the accounting treatment of IPP—from expensed to capitalized—gradually implemented by the BEA since 1999 is the sole driver of the decline of the accounting LS. Furthermore, our examination of the accounting assumptions behind the capitalization of IPP—mainly that all IPP investment rents are attributed to capital—indicates that less arbitrary and extreme assumptions on the factor distribution of IPP rents yield a trendless accounting LS. In other words, the LS decline is an artifact of the change in the accounting treatment of IPP in national accounts, and this is at odds with current macroeconomic theory that considers the accounting decline as an economic phenomenon at face value.

Labor share appears to have declined globally. Have most countries changed their accounting practices? Quite possibly, but more investigation is needed. Many of the theories are also quite plausible which perhaps explains the reluctance of theorists to give up on the “fact”. The Koh et al. paper has been circulating for a few years but most seem to brush it off. Autor, Dorn, Katz, Patterson and Van Reenen, for example, say:

Although there is controversy over the degree to which the fall in the labor share of GDP is due to measurement issues such as the treatment of capital depreciation (Bridgman, 2014), housing (Rognlie, 2015), self-employment and proprietor’s income (Elsby, Hobjin, and Sahin, 2013; Gollin, 2002) and intangible capital (Koh, Santaeulalia-Lopis and Zheng, 2016), there is a general consensus that the fall is real and significant.

Wait and see is probably rational at this stage. If the paper makes it through peer-review at the JPE, it will be more difficult to ignore.

It is arresting how many facts are in fact open to question. Maybe.

Hat tip: David Andalfatto somewhere on twitter.

Piketty, Housing, and Capital Share

Gianni La Cava has a very interesting article (based on a longer paper) on what accounts for the rising share of capital in the income accounts:

A key observation in Thomas Piketty’s Capital in the Twenty-First Century (Piketty 2014) is that the share of aggregate income accruing to capital in the US has been rising steadily in recent decades. The growing disparity between the income going to wage earners and capital owners has led to calls for government intervention. But for such interventions to be effective, it is important to ask who the capital owners are.

Recent research has shown that the long-run rise in the net capital income share is mainly due to the housing sector (e.g. Rognlie 2015, Torrini 2016 – see Figure 1). This phenomenon is not specific to the US but has been evident in almost every advanced economy. This suggests that it is not entrepreneurs and venture capitalists that are taking an increasing share of the economy, but land owners.

…The decomposition of the national accounts by type of housing indicates that the secular rise is mainly due to a rising share of imputed rent going to owner-occupiers. The owner-occupier share of aggregate income has risen from just under 2% in 1950 to close to 5% in 2014 (top panel of Figure 2). The share of income going to landlords (i.e. market rent) has also doubled in the post-war era. But, in aggregate, the effect of imputed rent is larger simply because there are nearly twice as many home owners as renters in the US economy. A similar phenomenon is observed in the personal consumption expenditure data (bottom panel of Figure 2). In other words, today’s landed gentry are predominantly home owners, not private landlords.

…The geographic decomposition reveals that the long-run rise in the housing capital income share is fully concentrated in states that face housing supply constraints. To see this, I divide the states into ‘elastic’ and ‘inelastic’ groups based on whether the state is above or below the median housing supply elasticity index (as measured by Saiz 2010). This index captures both geographical and regulatory constraints on home building across different US regions. For 50 years, the share of total housing capital income going to the supply-elastic states has been unchanged at about 3% of GDP (Figure 3). In contrast, the share going to the supply-inelastic states has risen from around 5% in the 1960s to 7% of GDP more recently. Notably, these divergent trends in housing capital income are not due to a few ‘outlier’ states where housing supply is particularly constrained, such as New York or California – instead, there is a clear negative correlation between the long-run growth in housing capital income and the extent to which housing supply is constrained across all states (Figure 4).

Negative interest rates are looking worse

And eurozone banks down 41% since ECB introduced negative interest rates, notes

That is from @RobinWigg.  The Japanese market has not responded positively either.

Of course negative interest rates, while intended as a form of stimulus, or currency depreciation, are also a tax on financial intermediation.  Negative interest rates, even if you agree with them in principle, are also a sign that more straightforward measures are politically impossible.

Here is Landon Thomas Jr. on negative rates in Sweden (NYT): “…many investors saw the rate cut as smacking of desperation and the latest sign that global central bankers are moving toward a round of competitive devaluations — also known as currency wars — as a way to stimulate their economies.”

Miles Kimball has written much in favor of negative rates, Izabella Kaminska against, if you wish to survey further opinions.  Here is Matt Rognlie.

I don’t see negative rates as the main problem today, but it’s getting harder to see them as a potential remedy.  They’re a sign that economies are trying to solve their core problems on the cheap.

Addendum: Here is Neil Irwin at NYT.

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