Investment & growth: some problems

A while back, Dietrich Vollrath wrote a famous post called "You can't reform your way to rapid growth." We should add to this: you can't invest your way to rapid growth either. The government's "number one mission" of boosting economic growth is therefore a challenging one.

To see the issue, consider an aggregate production function:

Y = TK^aL^b

where Y is output; K is capital; L is labour; T is total factor productivity or, if you prefer, technology; a is the elasticity of output with respect to capital; and b the elasticity of output with respect to labour.

This implies that growth in labour productivity is equal to the growth in capital stock per worker multiplied by a (the elasticity of output with respect to capital) plus growth in technology.

So, how big is a? Or, in other words, how much extra output do we get if we increase the capital stock?

The answer is: not much.

One common approach here - well, more of a first pass really - is to assume perfect competition and constant returns. If so, it can be shown that a is equal to capital's share of income. Which is not much. Last year, corporate profits were 21.7% of GDP. If we allow for some of the income of the self-employed also being capital income, then a is around 0.3.

Which implies that a 10% increase in the capital stock, all else equal, will give us a 3% rise in output.

But 10% of the capital stock is a huge sum. The ONS estimates that the net capital stock excluding housing is £3.5 trillion. So a 10% rise in it is equivalent to 15% of GDP. It would take many years (and much else!) to achieve that.

If this sounds modest, remember that investment doesn't merely to add to output. It can reduce it. When Lidl invests in a new store, it reduces Tesco's sales, for example. And investment in wind turbines is intended to reduce the output of gas-fired power stations.

We've lots of evidence from different times and places that the elasticity of output with respect to capital is indeed small. In his famous paper which kickstarted this approach to thinking about economic growth Robert Solow estimated (pdf) that only one-eighth of the increase in US GDP per worker between 1900 and 1949 was due to increases in the capital stock. The rest, he said, was due to technical progress. In Fully Grown, Dietrich Vollrath estimated that from 1950 to 2000 a rise in the US's physical capital stock per person accounted for only 0.64 percentage points of the 2.2 per cent annual rise in real GDP per capita. Nick Crafts has estimated (pdf) that less than one-third of growth in advanced economies between 1913 and 1973 was due to a bigger capital stock. And Gavan Conlon and colleagues have estimated (pdf) that a fall in capital growth accounted for less than half of the slowdown in the UK's hourly productivity growth between 2001-07 and 2014-19.

Now, we shouldn't be fixated on precise numbers here. Aggregate production functions and measures of both the capital stock and depreciation have massive theoretical and practical problems: Solow himself said that such measures "will really drive a purist mad." But the picture here is clear: it takes a lot of capital spending to deliver only moderate increases in GDP.

Intuition, I suspect, confirms this. Imagine if the capital stock were, say, twice as large as it is. How much higher would productivity be?

Almost certainly not twice as high. Having twice as much office space won't make us twice as productive. Having twice as many lorries won't allow drivers to make twice as many deliveries in a week. Having more trains will get you to work in a less frazzled state, but not so much so as to double your productivity. More software would not necessarily eliminate bugs but would perhaps have more features which we just rarely use. And so on.

Let's put this another way. If the elasticity of output with respect to capital were large, then we might presume that capital investment was very profitable. But if this were the case, then we would already be seeing lots of it. Which we are not. Granted, this is partly because economic instability and a lack of finance have held back capital spending. But you have to argue that these are very powerful constraints indeed to solve this basic paradox.

Instead, elasticity optimists have a better potential response. It's that investment does not raise output merely by increasing the amount of kit we have. It's that new capital goods embody better technologies, so investment raises total factor productivity.

Yes, but by how much? The newest lorry, or latest version of any software package, isn't very much better than five-year old ones.

But what about investment in brand-new industries? Here, we run into two problems. One is brute maths. New industries, by definition, are small and so even if they expand tremendously their macroeconomic impact is small; an industry that accounts for 1% of GDP and trebles over ten years will add only 0.2 percentage points a year to GDP growth - and less insofar as it detracts demand from older businesses. The other is that new techs are often initially unreliable (do a Google image search for London Bridge) and it's hard to find workers and managers who understand them. That constrains both their expansion and efficiency. For these reasons, Nick Crafts has said (pdf) that "the early years of a general purpose technology will see little or no impact on aggregate productivity growth." Between 1760 and 1830, UK GDP per head grew by only 0.2% a year even in the face of technical changes that transformed lives.

In fact, there are two other reasons why increased capital spending won't increase growth very much.
One is that many investments won't yield the expected gains. This has little to do with the state making bad decisions. It's simply because of what Keynes called "the dark forces of time and ignorance which envelope our future". Nobody can reliably foretell which projects will pay off and whch won't and so some investment spending will inevitably be wasted. Indeed, because decisions are driven by sentiment ("animal spirits") Salman Arif and Charles Lee have found that increases in capital spending lead to lower, not higher, macroeconomic growth in the short-run.

There's a second problem. Devoting more of our national income to investment requires that we devote less to private or public consumption. That would entail uncomfortable changes in our standard of living. It would also require hundreds of thousands of people to change jobs, away from consumer sectors and towards producing capital goods; where else can the builders, turbine and solar panel installers come from? That would take many years simply because people are slow to move and retrain. There's little sign that the government is ready to face such changes in our economic priorities.

Obviously, none of this is to decry increased investment. It will raise growth - just not by much.

Instead, what I'm saying is that raising long-term trend GDP growth significantly is damnably hard, and it cannot be achieved by a single magic bullet or reliance upon a few new industries. Instead, what's needed is a broad spectrum approach using many policies. Not least of these is to adopt the Obama doctrine: "don't do stupid shit" such as preventing growth by planning controls, trade barriers or political instability. On this, Labour has at least made a start. But it is the start of a long and difficult journey.

Comments

[Paddy Carter]

I am not disputing your main message, but I was thinking that some of these considerations (some investments put other firms out of business, others fail) must already be included in whatever the aggregate K=>Y relationship seems to be.

A couple of things that might interest you. As you know, the separation of K and T has always been more of a matter of methodological convenience, not a description of how things really work. When I was doing my econ education I was told models of capital-embodied technical change were too fiddly and unsatisfactory for various reasons, but it looks to me like more recent work has cracked it. The idea that K can change T opens up the possibility of a larger impact of investment on growth - see the first paper here for instance:
https://www.kellogg.northwestern.edu/faculty/jones-ben/htm/research.htm

and some recent work has started thinking about the economy as a production network, and asking whether investments in some parts of that network might have large spillovers, this one for example:

https://www.richmondfed.org/-/media/RichmondFedOrg/publications/research/working_papers/2024/wp24-02.pdf

[rsm]

What if my main mission is to get government to just let me sleep outside on commons again, not growth, which just makes me depressed because more growth inevitably means more enclosure and less freedom not to participate in markets?

[TickyW]

Investment expenditure definitely adds to value added. If investment expenditure in a period is domestically sourced then aggregate user cost won't change and so national income must grow by I. There is no reason to suppose that raised investment expenditure will reduce consumption expenditure.

[Paulc156]

@TickyW...all things equal more income diverted into investment requires less income spent elsewhere.

[LTR]

"We should add to this: you can't invest your way to rapid growth either..."

Adding this would however be incorrect, since China has been investing itself to profound growth since 1977. No other country has come near the investment level or the growth since then. And, a sense of the quality of growth that is evident comes from looking at the world-leading research productivity in China.

The Chinese accomplishment has come with prominent Western economists continually arguing that the Chinese economy is in dire shape.

https://fred.stlouisfed.org/graph/?g=1pOZz

August 4, 2014

Real per capita Gross Domestic Product for China and United Kingdom, 1977-2023

(Indexed to 1977)

[TickyW]

@Paulc156

You make a good point but if the capex were funded from retained profits would not national income rise by I?

[TickyW]

@paulc156

If Y - C = S then increasing I increases S. This comes about either through an increase in Y or a decrease in C.

My understanding of Keynes suggests that increasing I increases both Y and S.

[Blissex]

«The government's "number one mission" of boosting economic growth»

For whom? The usual purpose of generic terms is to obfuscate propaganda. But for example the governments of the past 40 years have achieved high growth for the living standards of finance and property rentiers (entirely redistributed from the lower classes), a huge success.

«consider an aggregate production function»

Any consideration that begins with the fantasy of an "aggregate production function" seems to me to be silly or propaganda. Just skip it.

«Solow estimated (pdf) that only one-eighth of the increase in US GDP per worker between 1900 and 1949 was due to increases in the capital stock. The rest, he said, was due to technical progress. [... etc. ...]»

Now that is more interesting. But is still highly misleading: most of the increase in productivity has been due to the enormous "consumer surplus" of coal and oil, which for very cheap provide enormous amounts of work. Oil fields are the most productive capial ever "invented".

Wrigley, "Energy and the english industrial revolution (2013):
"Noting that one steam horse power was estimated as providing the power equivalent of 21 manual labourers, he suggested that in France ca 1840 steam engines were performing the work of 1.2 million labourers but that by the mid-1880s the rapid expansion in the use of steam engines meant that this figure had risen to 98 million labourers, ‘two-and-a-half slaves for each inhabitant of France’ [19, III, p. 74]."

[Blissex]

«some recent work has started thinking about the economy as a production network»

Amazing news from America!

In other parts of the world that kind of work is not so recent. :-)

[rsm]

"entirely redistributed from the lower classes"

Why not incorporate the "alchemy of banking" in your model, which allows indefinitely-expanded balance sheets (backstopped by the Fed) to create money-like instruments that make up the bulk of assets on the balance sheets of the rich?

[Paddy Carter]

«some recent work has started thinking about the economy as a production network»

I wrote that badly. What I should have written is that they have recently figured out how to write down formal mathematical models of production networks within a general equilibrium setting, and as a result are starting to reach conclusions that others, not tied to formality, might already have reached. (and many some new conclusions)

[LTR]

https://www.nytimes.com/2024/07/17/business/britain-labour-industrial-policy-economy.html

July 17, 2024

To Revitalize Britain’s Economy, a Plan for a Stronger Government Role
The Labour Party’s economic agenda, like many other programs around the world, puts political leaders more firmly in charge of industrial policy.
By Patricia Cohen

The last time a freshly minted Labour government unabashedly campaigned on an ambitious national industrial policy to revive the British economy was 50 years ago, and the results were generally viewed as disastrous.

The 1974 program of subsidies, state ownership and power sharing among business, unions and government resulted in strikes that paralyzed the nation. And the government’s goal of picking industrial winners turned into a policy of backing losers like the automaker British Leyland and British Steel Corporation.

The current Labour Party has clearly jettisoned that ’70s era legacy. Keir Starmer’s new government, which is scheduled to formally lay out its economic agenda when Parliament opens on Wednesday, is nonetheless embracing the idea that the government must play a key role in driving Britain’s stagnant economy.

Policies that put political leaders more firmly in charge of the economy have taken hold all over the world. India, Brazil, Malaysia and many European capitals have all signed on...

[Blissex]

"the government’s goal of picking industrial winners turned into a policy of backing losers like"

The finance and property sectors!

The article by Patricia Cohen repeats (like our blogger here does) the thatcherite propaganda that the governments of the past 40 years have not done "industrial policy" where instead they have spent (or lent forever at 0%) hundreds of billions, and since 2008 literally trillions, to boost the finance and property "industries", guaranteeing the jobs and bonuses of their executives with super-generous subsidies and money-no-object bailouts.

The amount of public funds that New Labour and Conservatives+LibDems have spend on industrial policy for the finance and property "industries" have been much bigger and over a much longer period than any spending on "British Leyland and British Steel Corporation". Just one case:

http://www.coppolacomment.com/2018/01/the-carillion-whitewash.html$
«RBS was deeply insolvent. Rescuing it cost the U.K. Government £45bn, and RBS has lost a further £58bn since. Nearly ten years after the crisis, it is still in majority public ownership.»

[Jan Wiklund]

But who the hell is concerned about GDP anyway?

Most research, for example see Richard Layard, confirms that people are not interested in having more, per se, what we are interested in is not having less than the next guy. A more egalitarian society would make us more happy than a fast-growing economy.

Probably for more than one reason – more focus on growth requires heavy restructuring, insecurity and loss of habitat. We will need to say farewell to friends and family – which definitively makes us more unhappy.

Why not focus on getting rid of waste (for example ridiculously high CEO rewards, consultants fees and contractor profits)? Perhaps that would give room for some raises for those on the lower 70 % of the income scale?

[rsm]

"Rescuing it cost the U.K. Government £45bn"

When you have a standing unlimited dollar swap line with the Fed, does any UK taxpayer ever have to pay for any of it?

"Why not focus on getting rid of waste (for example ridiculously high CEO rewards, consultants fees and contractor profits)? Perhaps that would give room for some raises for those on the lower 70 % of the income scale?"

What if politically, you will always run into Trumps who will more than undo anything you try to set in place, so to avoid the endless cycles why not use the power of central banks' being able to lend forever at 0% to fund a high basic income?