05 May 2014

The Importance of Capital in Economic Theory

This is my EconLib article this month. I told the editor that this isn’t my personal favorite piece, and it’s not my “best” piece in some objective sense. But if I had to pick a single article (word for word) to represent my contribution to professional economics, it would be this one. It summarizes some of the “news you can use” from all the work I did in grad school.

Two excerpts below, but I’m going to insist that you guys click the link and read the whole thing. If you hang out at this blog, trust me, you are going to need this background because I am going to hit this topic a lot in May what with the Piketty stuff going down (coincidentally) at the same time I wrote this article for EconLib.

Although the example in the previous section seems simple enough, its lesson is relevant even for today’s PhD economists. Relying on simplified mathematical models, they have been taught that in a competitive market economy, the real interest rate equals the “marginal product of capital,” just as surely as the real wage rate equals the “marginal product of labor.”

The logic here is straightforward: If a firm hires a worker for an additional hour, its output will increase by a certain amount. If the labor market is competitive, the firm must pay the worker a wage corresponding to the market value of this increment in the firm’s physical output.

By the same token—as modern economists typically reason—if the firm hires an extra unit of capital, then physical output will increase, and so the firm must pay the owners of this capital an interest payment corresponding to the market value of this increment in physical output.

However, this typical logic confuses physical capital goods with financial capital. If a firm hires a specific capital good for a unit of time, the payment is the rental price of the capital good.

and

Framed in terms of macroeconomic aggregates, the Keynesians do seem to have a strong case against the RBC theorists and other free-market economists who think the economy should be “left alone to sort things out” during a recession. If we use a model that represents the capital stock by a single number (call it “K”), then it’s hard to see why a boom period should lead to a “hangover” recessionary period. Yet if we adopt a richer model that includes the complexities of the heterogeneous capital structure, we can see that the “excesses” of a boom period really can have long-term negative effects. In this framework, it makes sense that after an asset bubble bursts, we would see unusually high unemployment and other “idle” resources, while the economy “recalculates,” to use Arnold Kling’s metaphor.

23 Responses to “The Importance of Capital in Economic Theory”

1. Tel says:

For example, if the forklifts that the independent company rents out to the warehouse could be sold on the open market for \$1 million, then their owners would enjoy a 10-percent return each year on their invested capital. But if the forklifts could be sold for \$2 million, then the \$100,000 payments—due to the “marginal product” of the forklifts—would correspond to only a 5-percent interest rate.

Let’s suppose we knew that any business could easily borrow money at 6%, then we could also presume that a business paying \$100,000 every year for rental could choose to pay up to \$1.66 million for capital and still come out the same (ignoring maintenance contracts, tax, depreciation, etc). So it is undeniable that there is a strong link between the return on assets and interest rates. Any firm deliberately choosing to rent rather than buy when interest payments are lower than rental payments would be losing money.

However, suppose that the market price of the land is \$1 million. Therefore, if the owner continues to hold the land (rather than selling it outright) and merely rents it out, the landlord is implicitly investing \$1 million of his financial capital in the piece of real estate, on which he is earning a 10-percent return. If very safe, long-term bonds were yielding 12 percent, the owner might seriously consider selling his real estate and switching his (financial) capital into the bonds, where it would earn a higher return.

Exactly… someone holding an under-performing asset is tempted to buy bonds instead, or move the capital elsewhere. At the same time, someone paying unreasonably high rents is tempted to borrow the money and buy the asset for themselves. Thus the link between returns on capital assets and interest rates remains strong.

However, I’ll point out that with the example of selling the land, you have an asset in the land that will remain delivering a constant income for a very long time… if you buy 5 year bonds you get a known return (let’s say better than the return on the land) for 5 years, but after that maybe bond rates have dropped and the next 5 years don’t look so good any more. If bond rates do drop, most likely that implies that land prices tend to go up (i.e. the same lever that links asset prices to interest rates also works in reverse, so falling interest rates tend to inflate asset prices). For this reason, selling your land might still be a bad idea even if it does seem to be an under-performing asset because you can also sell your land next year, or the year after, or 10 years after so you need to judge not just present day interest rates, but your expectation of all future interest rates.

• Tel says:

I probably should follow up to say that in a modern economy, the interest rate that you can get by buying bonds as an investor is massively lower than the interest rate that any firm can borrow at.

Thus, a large gap appears, which allows considerably more wiggle room than what I have suggested above.

2. Gene Callahan says:

“For example, if the forklifts that the independent company rents out to the warehouse could be sold on the open market for \$1 million, then their owners would enjoy a 10-percent return each year on their invested capital. But if the forklifts could be sold for \$2 million, then the \$100,000 payments—due to the “marginal product” of the forklifts—would correspond to only a 5-percent interest rate.”

Well, yes, but if “the” market interest rate is 7.5%, and the fork lifts don’t go for \$1.5 million, then we are not in equilibrium. This is why Lachmann is right, and you are wrong, on own rates of interest.

• Major_Freedom says:

We wouldn’t be in equilibrium even if the fork lifts did fetch \$1.5 million.

3. Bob Murphy says:

Guys, look at what’s going on here:

(1) People say the marginal physical product of capital has something directly to do with determining the real interest rate.

(2) Critics show that no, we can have a high or a low real rate of interest, consistent with any physical marginal product of capital you want.

(3) You then assume we know on other grounds what the rate of interest is, and use that to contradict the critics.

If you guys pulled this kind of move with an area where we *agreed* on the underlying economics, the mistake would be hilarious.

• Tel says:

Look, no one (not even Gene, I think) is saying that marginal return (measured in dollars per annum) is exactly the same thing as interest rates (measured in percent per annum, hence a completely different unit).

My point is that there tends to be a three way relationship between:
• the interest rates that an investor can borrow at;
• asset prices;
• and asset returns.

Those three can’t move independently to each other without opening up arbitrage opportunities. As for which of the three moves in any given situation, it could be any of them.

4. Matt M (-Dude Where's My Freedom) says:

Bob,

I’m very confused by all of this and I’m not even sure what specific question to ask. The master builder analogy makes sense. I guess maybe I need to learn more about Piketty’s book, but as of now I’m not even sure what the argument is over. What conclusions does he reach that you are disputing? I’m assuming he’s more nuanced than “the current recession was caused by corporate greed” but I haven’t read his book or paid much attention to it really.

• Bob Murphy says:

Matt M I’ll be posting tons on this for a few weeks, so just hang on… I realize this must be confusing, since even people with PhDs are scoffing like I’m making simple mistakes.

5. Sean says:

OK, but isn’t the market price of the forklifts going to be affected by their utility to the warehouse firm, They won’t become worth \$2m if they can only generate surplus of \$100k per year. Is that right?

• Tel says:

If the firm can easily borrow money at a low rate, e.g. 1% interest, then why not just buy the forklifts? The interest payments are still lower than what the forklifts are earning, so you still make a profit.

• Sean says:

Right but doesn’t that then raise demand and the price goes up to a new steady-state?

6. Transformer says:

Bob,

Clarifying question: Bill Woolsey yesterday expressed a view quite close to mine

“I think the Austrian answer is that the reason for the existence of interest is time preference. Productivity of capital is neither necessary or sufficient.

I think this is true, though it is important to emphasize that the productivity of capital (technologies that make round about methods more productive) impacts the exact level of interest.”

I assume you agree with the first part. What about the second ?

7. Kevin Donoghue says:

“Even economist Piketty’s bestselling book explicitly devoted to capital still relies on a very simplistic conception of capital as a single aggregate.”

I know lots of people are making claims like this. (This alliance between Post-Keynesians, Sraffians and Austrians is a strange thing to behold.) But readers of the book will notice something odd. Piketty isn’t saying what they were told he would be saying. To take one example from a great many, see page 49:

“To be clear, although my concept of capital excludes human capital (which cannot be exchanged on any market in nonslave societies), it is not limited to “physical” capital (land, buildings, infrastructure, and other material goods). I include “immaterial” capital such as patents and other intellectual property, which are counted either as nonfinancial assets (if individuals hold patents directly) or as financial assets (when an individual owns shares of a corporation that holds patents, as is more commonly the case). More broadly, many forms of immaterial capital are taken into account by way of the stock market capitalization of corporations.”

• Tel says:

To be clear, although my concept of capital excludes human capital (which cannot be exchanged on any market in nonslave societies),

He has just defined every student loan as slave dealing, and since governments in many Western nations actively support student loans, he must have a rather low opinion of politicians.

8. Philippe says:

Bob,

“Framed in terms of macroeconomic aggregates, the Keynesians do seem to have a strong case against the RBC theorists and other free-market economists who think the economy should be “left alone to sort things out” during a recession. If we use a model that represents the capital stock by a single number (call it “K”), then it’s hard to see why a boom period should lead to a “hangover” recessionary period.”

This is misleading. It is Neoclassical economists that represent the capital stock by a single number. i.e. Chicago School economists and the like. So-called ‘New Keynesians’ are basically neoclassicals. It was Cambridge Keynesians who attacked this approach and showed it to be flawed. And the Cambridge argument was that the basic foundations of marginalist economics are incoherent.

• Major_Freedom says:

Keynes used K to describe capital in the General Theory, while paying lip service to capital of “specific types” without actually integrating it into is theory of markets or policy prescriptions.

The single aggregate “K” is orthodox Keynesianism.

You are mistaken.

• Philippe says:

“The aggregation problem

In neoclassical economics, a production function is often assumed, for example, Q = A. f(K,L) where Q is output, A is factor representing technology, K is the sum of the value of capital goods, and L is the labor input…

This vision produces a core proposition in textbook neoclassical economics, i.e., that the income earned by each “factor of production” (essentially, labor and “capital”) is equal to its marginal product. Thus, with perfect product and input markets, the wage (divided by the price of the product) is alleged to equal the marginal physical product of labor. More importantly for the discussion here, the rate of profit (sometimes confused with the rate of interest, i.e., the cost of borrowing funds) is supposed to equal the marginal physical product of capital…

Piero Sraffa and Joan Robinson, whose work set off the Cambridge controversy, pointed out that there was an inherent measurement problem in applying this model of income distribution to capital. Capitalist income (total profit or property income) is defined as the rate of profit multiplied by the amount of capital, but the measurement of the “amount of capital” involves adding up quite incomparable physical objects – adding the number of trucks to the number of lasers, for example. That is, just as one cannot add heterogeneous “apples and oranges,” we cannot simply add up simple units of “capital.” As Robinson argued, there is no such thing as “leets,” an inherent element of each capital good that can be added up independent of the prices of those goods.

http://en.wikipedia.org/wiki/Cambridge_capital_controversy#The_aggregation_problem

• Tel says:

There’s an inherent measurement problem in attempting to apply any sort of economic calculus to such concepts as “aggregate supply” and “aggregate demand” as well. This gets even worse when looking at a time series.

The economy of 1980 is composed of different activity to the economy of today, so no aggregate is comparable, other than in approximate terms.

• Bob Murphy says:

Philippe,

I understand what you’re saying. Note that here and here I explained that there were heterodox economists in the Keynesian tradition who also rejected the idea that r=MPK.

In the EconLib article, I am commenting on current policy controversies. And there, it is correct to say that the popular Keynesians–like Krugman, DeLong, and Karl Smith–have been the ones adopting a “potential GDP hasn’t fallen so we need stimulus” approach, whereas the free-market guys have been saying “whoa, the economy is really complicated, let’s think about this first.”

• Philippe says:

But this issue of aggregating capital doesn’t have anything to do with being “free market” or not. Real Business Cycle theory does it! So do all other forms of “free market” neoclassical economics (Chicago school, etc).

• Bob Murphy says:

Right Philippe. I am telling free-market economists who currently aggregate capital in their models, that they should stop doing that because their diagnosis and prescription regarding recessions will make much more sense with a disaggregated capital structure.

9. Keshav Srinivasan says:

Bob, I don’t know enough about economics to know what is and isn’t relevant to the debate, but Gene said in his comment “This is why Lachmann is right, and you are wrong, on own rates of interest.” So I searched on his blog and found these two posts:
gene-callahan.blogspot.com/2013/02/sraffa-and-own-rates.html
gene-callahan.blogspot.com/2013/02/lachmann-on-sraffa.html

Are these two posts challenges to the view you articulate in the EconLib article, or are they about a completely different issue? If they are relevant, how would you refute them?

10. theyenguy says:

Liberalism featured the sovereignty of Banker Regime of democratic nation states, which provided policies of investment choice and schemes of credit in fiat money, producing seigniorage in Equity ETFs, and Credit ETFs, where the investor was the centerpiece of economic activity. Not only did Dividend Excluding Financial Investment, DTN, but also Nation Investment, EFA, and Small Cap Nation Investment, SCZ, figured prominently in the age of credit, through debt trade investing, seen in H&E Equipment Services, HEES, United Rental, URI, and AER, and currency carry trade investing, seen in Eurozone Small Cap Dividends, DFE, and presented in their combined Yahoo Finance Chart.

An inquiring mind asks what is the cost of a forklift from either one of the two aforementioned companies? This is a question implicit your article The Importance of Capital in Economic Theory.

Since the GFC, through money manager capitalism, we have had investors strongly buying the Small Cap Pure Growth companies, H&E Equipment Services, HEES, and United Rental, URI, the two providers of forklifts, which began trading lower in April 2014 on the failure of credit. These companies represent short selling opportunities.

These providers of forklifts are toxic assets in the sense that they both have a Debt To Equity Ratio and a LT Debt To Equity Ratio that cannot be repaid, which suggests that the forklift providers are zombie companies.

The price of forklifts to businesses is the cost of a business loan, that is interest, secured by inventory and other assets that can be claimed and sold; it is in this economy, that is the May 2014 economy, zero.

These lynchpin companies became liabilities not assets to society, when they were transformed by Global ZIRP and became Frankensteins of the Creature from Jekyll Island. Once investors start aggressively disinvesting and derisking out of these lynchpin investments and other debt leveraged and currency carry trade leveraged investments, the much feared economic deflation, will commence; and what was in the age of credit, inflationism, becomes in the age of debt servitude, destructionism.

With the soon coming death of fiat money, defined as Aggregate Credit, AGG, and Major World Currencies, DBV, and Emerging Market Currencies, CEW, the new money, that being diktat money, defined as the mandates of regional leaders to establish regional security, stability, and sustainability, will serve as the wheels for the economy.

With the failure of credit, seen in China, YAO, ECNS, CHIX, Russia, RSX, ERUS, Emerging Europe, ESR, the US Small Caps, IWM, IWC, Credit Providers, MA, V, DFS, AXP, and Commodities, DBC, trading lower, authoritarianism is the new paradigm, which features the age of debt servitude, where the God ordained sovereignty of the Beast Regime of regional governance and totalitarian collectivism, seen in Revelation 13:1-4, which provides economic life experience in policies of diktat and schemes of debt servitude in diktat money, and which establish seigniorage in Regional Fascism, and which establishes the debt serf as the centerpiece of economic activity.

It is out of the European Debt Crisis, that is out of tossing waves of sovereign, banking, and corporate insolvency of the Club Med Nations, specifically Portugal, Italy, Greece, and Spain, that the New Monster is rising to replace the Creature from Jekyll Island. It is not the Interventionist of creditism, corporatism and globalism; rather the Regional Animal, with the form of a leopard, having feet like those of a bear and a mouth like that of a lion; and thus operates by stealth, roots outs it enemies and devours its prey by crushing, ripping and tearing them apart.

And as seen in Revelation 13:5-10, there is a Regional Leader waiting in the wings of Europe’s stage, who will soon step into the limelight, and through cunning and shrewdness, will rise to power through regional framework agreements, to rule the Eurozone, with the help of a Regional Monetary High Priest, seen in Revelation 13:11-18. The word, will and way of the Sovereign will replace all traditional constitution, national and historic law. And that of the Seignior will establish seigniorage, that is moneyness, for all residents of the EU. The mandates of fascist leaders will coin diktat money which will establish economic value and grease the wheels of economic activity.

In the age of credit the economy, there were two economic goods, consumable output and leisure, demanded by households. Now in the new economy, that is the age of debt servitude, there is increasingly one economic good, consumable output demanded by regional fascist leaders.