Diminishing Returns and the Zero Lower Bound — Both Piketty and Rognlie Forget about the Money

Root Bug
Root Bug
Apr 8, 2015 · 11 min read

Matthew Rognlie’s analysis of Thomas Piketty’s predictions of increasing inequality is to the point on both (1) the role of housing and (2) the poor substitutability of capital for labor. But it suffers from a neoclassical blindness to the existence of money and the role of the risk-free interest rate in determining the costs of (financial) capital for real investments.

The returns on capital can only diminish if the interest rate and hence discount rates for real investments fall further. Currently, this cannot happen, because of the zero lower bound (ZLB) of interest rates, which acts as a “minimum wage of capital”. Eliminating the ZLB and implementing a land value tax (LVT) simultaneously would be a superiorly competitive strategy and solve a majority of our economic concerns.

Otherwise the “oversupply of capital” — essentially an oversupply of labor — will just drive the economy into a more severe depression. The unemployment, deflation pressures, and public deficits we are currently seeing in Western economies are the results of the ZLB and the low substitutability that Rognlie emphasizes.

If there is one thing we should’ve learned from The Financial Crisis, it is the dangers of making real world predictions based on economic models that omit the monetary and financial system — and the basics of finance. Apparently we haven’t.

Not only housing, but all real estate — which is unequally distributed

Matthew Rognlie’s criticism of Piketty’s “r>g theory” and the prediction of constantly rising inequality has received a lot of attention, and his work is admirably thorough.

However, Rognlie is not the only one, nor the first, to notice that most of Piketty’s “increase in the amount of capital” is actually rise in the value of land (see e.g: Stiglitz, Karl Smith, Galbraith).

Many like to conclude from Rognlie’s analysis that “since the housing ownership is much more evenly spread than productive capital, it may be less worrying for inequality.” (It maybe partly because of this framing that Rognlie’s critique receives so much attention.) However, this is not the case. Homeownership is one of the biggest unearned polarizers of both income and wealth differences: the higher and more reliable your income, the bigger and cheaper a mortgage you can get.

Also, the issue of rising land values does not only apply to housing but to centrally located real estate in general. This includes office buildings in central business districts. Overall, the limited resource of land (location) is very unequally distributed. (In fact, the distribution of land ownership was one of the first cases to which Vilfredo Pareto applied his famous 80–20 principle.)

Others have, more appropriately, drawn the conclusion that what we really need is not a wealth tax but a land value tax. (see e.g. Noah Smith, Tim Worstall)

Restrictive zoning and “NIMBYing” are of course one factor maintaining accommodation deficits and hence unnecessarily high rents and housing prices. Zoning and construction regulation could be slackened in many places. But removing city planning altogether won’t solve the land issue, as accessible locations will still be limited. As a bottleneck resource, they will continue to capture a big portion of productivity gains.

Also, some city planning is very useful and valuable, as all land use has externalities (positive and negative) on the value of adjacent land. Zoning makes these predictable, mitigating windfall gains and losses. The absence of planning would also result in less efficient infrastructure and transit systems, further reducing the availability of locations with good accessibility.

High depreciation rates = low capital intensity of technologies -> low substitutability

Unlike some Chicago economists liked to believe, capital is not some generic “putty clay” that can be applied productively in different quantities at will. The opportunities to increase capital intensity in production are significantly limited by available technologies. If we assume that all capital assets can be produced with labor (i.e. we omit land and natural resources), capital intensity essentially means how much beforehand on average all the work required for producing the end product needs to be done.

As The Economist paraphrases Rognlie’s point on the changing nature of capital:

“Modern forms of capital, such as software, depreciate faster in value than equipment did in the past: a giant metal press might have a working life of decades while a new piece of database-management software will be obsolete in a few years at most.”

This higher rate of depreciation essentially means that new technologies are less capital intensive than earlier ones — even if they increased labor productivity significantly. In other words, even if they allow a more valuable output with the same amount of labor, they don’t need so much work to be done in advance. Of course, robots that make, repair, and program themselves could eventually turn this trend on its head, but for now, Rognlie’s arguments for a low substitutability of capital for labor are well grounded. Piketty mistook the rise in land values for a rise in capital intensity.

Also, Piketty seems to imagine that capital can always be accumulated by saving up more money. However, in a closed economy, net savings are limited by profitable real investment opportunities. Rognlie is on the right track in that, theoretically, an increased desire to save should result in the yields of capital falling. According to supply and demand, a factor or resource in abundant supply should fall in market price. This was already pointed out by Banko Milanovic of the World Bank in his 2013 paper:

“But, the reader will ask, if the capital/output ratio increases so much, would not the marginal return to capital diminish? Would not r go down? This is obviously a soft point of Piketty’s machinery.” (Milanovic 2013, p. 9)

“Will the reader be convinced by the argument that the elasticity of substitution between capital and labor is likely to remain high, and that an increase in capital will not drive r down?” (Milanovic 2013, p. 10)

Unfortunately, high substitutability of capital for labor is not the only factor that can maintain high returns on capital. Tragically, the economics discipline is so segregated that capital theorists don’t understand macro — and neither capital theorists nor macroeconomists (want to) understand money.

“Capital” has two different meanings

Before explaining the role of money and the risk-free interest, it might be useful to avoid a possible source of confusion in terminology.

In economics, “capital” usually refers to real assets that allow easier production or provide some other real benefits in the future. In addition to physical production goods (machines, buildings, tools etc.), this includes e.g. technologies and new product designs created by R&D investments. This was also the meaning used above when discussing “capital intensity”.

In finance and accounting, on the other hand, “capital” refers to “financial capital”, which is any property or security that can generate income in the future for its holder. In addition to the ownership of real capital assets (directly or indirectly through shares in companies or funds), this includes all forms of credit (including money), immaterial property rights, and other kinds of privileges that can be owned and traded (e.g. taxi badges and patents).

Joseph Stiglitz recently emphasized in his INET talk the distinction between productivity-increasing “capital” and “wealth”, which also includes capitalized rents from monopolies and privileges. Piketty uses capital synonymously with “wealth”.

In the case of a company, real capital assets appear on the “assets” side of the balance sheet (together with any credit and IPRs the company might hold), while “capital” in the financial sense refers to the “liabilities” side of the balance sheet: The capital structure of the company determines how the risks of the company’s assets and business are allocated between shareholders and creditors.

Rognlie importantly points out that the market value of a company’s shares can diverge significantly from the book value of its assets. (Rognlie 2014 p. 15) This is not only the result of those product designs, human capital, or other immaterial assets that a company cannot capitalize into its balance sheet for accounting reasons, but also any monopoly rents or competitive advantages established through a strong brand or customer relations.

This distinction between “real capital assets” and “financial capital” is even more important for what we mean by “the cost/price of capital”. Rognlie writes about “capital” in the first sense, and by the “real price of capital” (Rognlie 2014, e.g. p. 2–3) he means the production or acquisition cost of the assets in question. So to him, a rise in land value is a “rise in the real price of capital”.

However, when we talk about the “cost of capital” in finance, we mean an investor’s profit requirement for an investment or company in question. For credit finance, this is the interest rate. The cost of equity is the return that would make an investor deem the investment “profitable”, i.e. worth making. This depends on the interest rate on deposits and the perceived risks involved, as will be explained. For an investment decision, it is common to calculate the Weighted Average Cost of Capital (WACC) from credit and equity costs and use this as a discount rate for expected cash flows.

The interest rate determines the returns on producible capital

Rognlie’s analysis is based on an economic model without a monetary system — which is quite a typical neoclassical approach. This assumes that all savings are automatically turned into real capital investments. Increased saving hence increases the supply of production goods and automatically lowers their net yields.

Reality differs from this in that we have a monetary system, which allows individuals to also save as credit on others and lets companies and other people to spend or invest on credit (i.e. by going into debt). However, new money does not emerge by saving. All monetary savings are someone else’s debt and one person’s income is another’s expense or real investment. The monetary system is a zero-sum game.

Moreover, the return yielded by risk-free credit — bank deposits — determines the costs of equity: the profit required of real capital investments.

As long as the risk-free interest rate follows the natural rate of interest — the rate at which overall desires to save are approximately in balance with profitable real investment opportunities — the outcome is pretty much the same as in a model omitting money. However, if the interest rate fails to keep the macroeconomy in balance, the story is very different.

Diminishing returns on capital — or a worse depression? The interest rate decides

Let’s assume we have a closed economy or an externally balanced open one, i.e. one with a balanced current account. If the overall desires to save exceed the available profitable investment opportunities (and there is no fiscal stimulus), this essentially means that not everyone gets to earn and save as much as they would like to. In practice, this means involuntary unemployment and underemployment. In the absence of wage regulations and excessively generous social security, this results in lowering pressures on nominal wages, and hence also prices, i.e. deflation pressures.

This is where the central bank would normally lower interest rates to balance the economy. However, currently many Western economies are stuck at the zero lower bound of interest rates. At this point the result is not increased investment and lower returns on capital but more unemployment — or a need for the government to accumulate more and more debt, fiscal stimulus to keep the economy running .

Regardless of how much the “supply of saving” (i.e. people’s desire to save) increases, this does not lower the returns on capital unless the interest rate can fall to the natural rate where net desires for monetary savings are eliminated and hence aggregate and supply and demand for labor are balanced.

Quantative easing is mainly an inefficient placebo medicine based on the outdated quantity theory of money. It does not lower discounting rates notably nor reduce people’s desires to save.

Many economists and commentators have noted the possibility that even the long-term natural (or equilibrium) rate of interest might have fallen significantly below zero (see e.g. Summers, Blanchrd et al, Avent, Buiter).

What we would really need to do is to eliminate cash (in order to allow negative nominal interest rates) or to adopt a higher target inflation rate to allow more room to cut real interest rates.

The Remedy: a land value tax + removing the zero lower bound

On the other hand, if the real interest rate did fall to e.g. -5 %, we would see our real estate bubbles explode to unprecedented proportions. As land does not erode (Rognlie 2014, p. 13), is limited in supply, and has few direct substitutes, in valuing it we are essentially discounting an infinite cash flow — a perpetuity. When the discount rate approaches the expected growth rate of the cash flow, the net present value approaches infinity.* While the ratio of producible capital to income is determined largely by the capital intensity of available technologies, the capitalized value of monopoly resources is strongly dependent on the market interest rate.

However, in the current situation, this effect is much more an opportunity than a threat. The biggest obstacle to implementing a proper land value tax (LVT) is that imposing it suddenly would make real estate prices crash, resulting in a massive, unjust wealth transfer in the real estate market. A mere glance at the situation shows that the dilemmas associated with both LVT and removing the zero lower bound solve each other. We can compensate for the lower costs of capital by raising the LVT rate at the same time with removing the ZLB.

With no lower bound on interest rates, Piketty’s r (the average return on capital) can even drop negative. Good bye r>g dilemma and never-ending accumulation of patrimonial wealth.**

Western countries have a unique opportunity to make a shift towards a more equal and prosperous economy. More over, the move would be extremely competitive for any first mover: A lower interest rate would devalue an area’s currency lowering labor costs, and both LVT and negative interest rates government debt would allow reducing harmful taxes on trade (income tax, VAT, corporate taxes), vastly increasing any area’s competitiveness over productive, risk-bearing real investments.

It remains to be seen, which economy first realizes the potential in this superior strategy.

Also Rognlie’s point about the importance of growing income differences between types of labor is very relevant. To counter this, we need to maximize mobility between professions by removing artificial rigidities and privileges, ensuring access to education, as well as maximizing competition over employees.

The details for implementing this strategy and an analysis of its full impacts can be found in the book Fixing the Root Bug, available digitally and in print.

Tuure Parkkinen

The writer is an author, institutional entrepreneur, and economic engineer-philosopher. He has developed the Root Bug hypothesis that identifies the main flaws in our current economic system and provides fresh solutions for a fair, sustainable, and growth-independent economic system that facilitates all desired growth. Follow the Root Bug on Facebook and Twitter, and subscribe to the YouTube channel and the newsletter (in the right-hand column).

*The valuation formula for a growing perpetuity is V = P0/(r-dP), where P0 is the first year’s expected cash flow, dP is the annual growth rate of the cash flow, and r is the discount rate employed, including risk premiums. In reality, the value won’t turn infinite, as increased volatility raises risk premiums. Instead, real estate prices become extremely speculative with negative real interest rates — in the absence of proper land value taxation.

**If we additionally mitigate risks of long-term unemployment and ensure that people have the realistic alternative to work less in the mid-term (if they so desire), we can make supply meet demand on the individual level regardless of aggregate demand. Then g (the economic growth rate) can be whatever people really want it to be. Economic growth becomes a matter of personal preference, while we can allow productivity to grow (unnecessary work to be destroyed) as much as technology allows.

Rognlie, Matthew, 2014, “A note on Piketty and diminishing returns to capital”, retrieved 29.3.2015, http://www.mit.edu/~mrognlie/piketty_diminishing_returns.pdf

Milanovic, Branko, 2013, “The return of ‘patrimonial capital’: review of Thomas Piketty’s Capital in the 21st Century”, World Bank, retrieved 9.4.2014, http://mpra.ub.uni-muenchen.de/52384/1/MPRA_paper_52384.pdf

Other references under the respective hyperlinks.

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