Do New Keynesians need to assume (much) labour hoarding?

We know that measured productivity falls in a recession (relative to trend).

Real Business Cycle theorists say that this is because a negative productivity shock is what caused the recession.

Keynesians say that a negative aggregate demand shock is what caused the recession, and labour hoarding (firms don't like to lay off workers even if they don't need all of them to produce the goods they can sell) is what causes measured productivity to fall.

But New Keynesians assume firms are monopolistically competitive. As every first year economics student knows, monopolistically competitive firms in zero-profit long run equilibrium produce where their Average Total Cost curve slopes down. If the ATC curve slopes down, total factor productivity will fall if output falls (and rise if output rises).

So New Keynesians don't need to assume labour hoarding to explain why productivity is procyclical.

But do the numbers add up right? Is this effect big enough to explain all the cyclical variation in productivity? Maybe not. Maybe they need to assume some labour hoarding too.

I don't know if any of this is new.

New Keynesians assumed monopolistic competition for lots of reasons, but explaining why productivity is procyclical wasn't one of them. So if it can also explain why productivity is procyclical, that is an independent confirmation of New Keynesian macroeconomics. They weren't "discovering" empirical gold by digging where they already knew the gold was buried (pdf).

In zero-profit long run equilibrium, an individual firm's demand curve must be tangent to its ATC curve. (Price must equal ATC for zero profits, and if the two curves crossed the firm wouldn't be maximising profits, because it could make positive profits by moving to a point where P > ATC.)

If the demand curve is tangent to the ATC curve, those two curves must have the same slope (and same elasticity) at the tangency point. Since a monopolistically competitive firm's demand curve has a negative slope (by definition), its ATC curve must have the same negative slope.

We know that Marginal Revenue = (1-1/E)P, where E = elasticity of demand. And we know that profit-maximising firms produce where MR=Marginal Cost. Simple algebra tells us that P=[1/(1-1/E)]MC. If E=4, then P=(4/3)MC, so firms would set prices as a 33% markup over marginal costs to maximise profits. That's probably in the right ballpark empirically, IIRC.

If the elasticity of an individual firm's demand curve is 4, then the elasticity of its ATC curve is also roughly 4, in the neighbourhood of the long run equilibrium point.

If the elasticity of its ATC curve is 4, that means a 4% drop in output would cause a 1% fall in total factor productivity, and a 3% drop in inputs (approximately). If employment of all inputs dropped by the same proportion, a recession in which real GDP fell by 4% (relative to trend) would see a 3% fall in employment of labour (relative to trend).

Hmmm. That difference between 4% and 3% is big enough to matter (proportionately), but not big enough to explain Okun's Law. Because Okun's Law says that the percentage decline in output is typically two or three times as big as the percentage decline in employment. So even if we stretched Okun's Law to say it's only two times as big, that would mean a 4% decline in output should cause only a 2% decline in employment, rather than the 3% decline in employment my back-of-the-envelope calculation comes up with.

So I'm only halfway there to explaining Okun's Law without assuming labour hoarding.

Maybe labour hoarding is the other half?

Or maybe my calculation isn't quite right. What about hours per worker? If the decline in employment came about 50% through hours per worker declining, and 50% through number of workers declining, then I'm all the way there, without needing to assume any labour hoarding.

Or maybe something else?

Comments

[Giovanni]

Nick,

Good on you for citing Axel Leijonhufvud's brilliant "Life Among the Econ", probably the single most instructive thing I read during my grad student days. Someone really should do an updated version incorporating recent developments. ("The contempt of the New Macro for the Old is palpable. Should they encounter an Old Macro, New Macros will immediately form a circle and chant 'ad hoc, ad hoc, ad hoc' until the Old Macro skulks away in shame.)

[Nick Rowe]

Giovanni: Yep. I was thinking about where I had got that "discovering" gold metaphor from, and then realised it was Axel.

[rsj]

You have mix effects as well. I.e. suppose that the production of durable goods requires less labor than the production of services. In the recession, if demands for durable goods falls more than demand for services, output will fall more than employment without labor hoarding.

[Nick Rowe]

rsj: yep. Good point. I wonder how big that effect would be empirically.

[Giovanni]

Nick,

Is the number of firms exogenous in your analysis? I'm thinking that in most real-world monopolistically competitive markets at least part of any cyclical decline in industry demand would be absorbed through firms going out of business. To the extent this occurred it would reduce economies-of-scale effects on productivity, with remaining demand distributed among a smaller number of producers.

[Nick Rowe]

Giovanni: Yes, it (implicitly) is exogenous. Good point.

[Giovanni]

Doesn't this creat a theoretical problem? In the initial situation all firms are operating at the tangency of their ATC and their firm-specific demand curve: this is the zero-profit condition in market equilibrium. Now the recession hits and all demand curves (but not ATCs) shift to the left. In this new situation no firm can be covering cost: every firm-specific demand curve now lies everywhere below the corresponding ATC. Something's got to give, in the form of firms exiting the industry. This must continue until the firm-specific demand facing every surviving firm has shifted back to its original position and the initial zero-profit tangency is restored.

[Steve Roth]

Nick, I would very very much like to hear your thoughts on the body of thinking here:

http://effectivedemand.typepad.com/

[Nick Rowe]

Giovanni: yes, but:

There's the micro short run, in which the number of firms does not adjust to long run equilibrium where P=ATC.

And there's the macro short run, in which prices are sticky, and don't adjust to long run equilibrium where AD shocks have no real effects.

Let's assume we are in the short run in both micro and macro senses.

[Nick Rowe]

Steve: A few weeks back I skimmed his post where he laid out his theory. It didn't seem promising as an investment of my time, relative to the 1001 other things I could and should be reading. One can never tell, of course, without having read it thoroughly, but that's the same uncertainty problem we face with any investment decision, so we have to make the best decision we can about when to stop investing and throwing good time after bad. It looked like it would take me a few hours to try to figure out what he's saying, another few hours to do a blog post on it, then more hours still arguing, probably passionately and unproductively, in the comments. Not worth the candle, in expected value terms.

If someone who knew economics and whose intuition I trusted told me it's worth reading, I would possibly do so.

Now I expect he's going to come on here and telly me I really REALLY MUST read it.

(Has he read an intro text? ;-) )

[Steve Roth]

Nick: He certainly seems to understand the essentials and quite a bit more, including some amount of economics history. But unfortunately I can't be the person to recommend the hours of work. That's why I was trying to foist it off on you!

[W. Peden]

Mancur Olson, in "The Rise and Decline of Nations", says that if prices & wages are sticky and stickiest in cartelized sectors, then those sectors with least sticky prices & wages (what he calls the "flexprice" sectors) will bear the brunt of a period of macroeconomic adjustment and will have an influx of resources, so e.g. contra Herbert Hoover, during a recession the rate of profit in the apple-selling sector will be unusually low relative to the average.

If higher productivity sectors, like skilled manufacturing and finance, can most easily cartelize and rent-seek from the government, then the Olsonian business cycle theory implies a transfer of resources from high-productivity sectors with the stickiest prices to low-productivity sectors with more flexible prices. This is different from a straightforward monopolistic competition explanation, because it's precisely the fact that some sectors ARE competitive that causes the transfer of resources.

So disaggregating somewhat allows one to predict at least some degree of procyclical productivity AND it's not ad hoc because it's derived from a MUCH broader New Institutional macroeconomic and microeconomic theory.

[Nick Rowe]

W Peden: good point. Agreed that's not ad hoc. And (I think) the effect on measured total productivity will be magnified by the change in relative prices, because the prices in the flex-price sector will fall, so even if the two sectors had the same productivity, the measured *value* of total output per unit of inputs will appear to fall, because we get relative output increasing in those sectors where relative prices are falling.

That's just one of the problems of using an aggregate like economy-wide total factor productivity where you are aggregating across goods as well as across inputs, so you need relative prices to add apples and oranges, and land and labour, so you are no longer talking about a purely "engineering" relationship. It's a god-awful mix of engineering plus accounting.

[W. Peden]

Does this partly explain the "UK puzzle", which is that UK employment has fallen far less than one would expect given the fall in RGDP? (Recent revisions to RGDP data suggest that this puzzle is less serious than one would suggest, because RGDP figures understated output.)

The major bailout of the high productivity UK financial sector prevented the extreme fall in the cost of financial intermediation that would have resulted had banks like RBS gone bust. There was also substantial help for particular industrial sectors e.g. car manufacturing, almost all of which have to be high value-added industries to survive the high value of the pound. On the other hand, the UK has a generally flexible labour market and plenty of sectors (like tourism, business services and media) that would operate as a flexprice sector.

Olson's chapter on stagflation and business cycles is very interesting, if only because it's an example of someone drawing on Clower, Lucas and Public Choice Theory, all to arrive at something that's some hybrid of a New Keynesian model and "The Calculus of Consent". (It's not a mathematically formalised model, though.) I like the idea, because I like the basic premise of New Keynesian models (i.e. finding the microeconomic foundations of how expected demand shocks can affect real output) and generally dislike the superficial nature of explanations like sticky wages or menu costs.

[W. Peden]

For 'premise' read 'research programme'.

[oops]

Are you sure about your "We know that measured productivity falls in a recession (relative to trend)" claim? Isn't the correlation between productivity and growth basically nil, as per McGrattan/Prescott?

[Nick Rowe]

W Peden: the UK Puzzle was sort of at the back of my mind when I wrote this. But I'm really too unsure about what's been going on in the UK to say anything useful about it.

oops: I'm not familiar with McGrattan/Prescott. I'm not really sure about anything. And productivity is hard to measure. But some version of Okun's Law has been around for some time now (we got worried whether Okun's Law had broken down in the US in the recent recession, but then they revised the GDP data). But we aren't talking about a correlation between the *level* of productivity and the *growth rate* of GDP. We are talking about the level of productivity (relative to trend) and the level of GDP (relative to trend).

[W. Peden]

Nick Rowe,

"But I'm really too unsure about what's been going on in the UK to say anything useful about it."

Then you're in the same position of expertise as the Office of National Statistics!

[Kathleen]

@oops: In 2010 did some research in this area when I was exploring the differences between Canadian and US labour productivity trends. Using data from International Labour Statistics from the US Dept. of Labour, like McGrattan/Prescott I found that the correlation between GDP Growth and Labour Productivity growth changed significantly sometime around 1995. This was in stark contrast to Canada which was still exhibiting falling productivity during recessions. Interestingly Canada's labour productivity turned higher around 2009 just as Canadian GDP tanked.

[Kathleen]

sorry... meant to say that the correlation between US GDP growth and US Labour productivity changed somewhere around 1995.

Susan Houseman et al have some interesting theories on how offshore outsourcing may be behind this change. I think it has alot to do with the adoption of office based technologies and "do more with less" management techniques (of which offshore outsourcing is one).

[rsj]

There is some data here:

"In search of Keynesian Labor Demand"

http://econweb.umd.edu/~davis/eventpapers/BilsTesting.pdf

"We find evidence in support of Keynesian labor demand over a constant-markup
version of flexible-price labor demand. First and foremost, we estimate that price markups
decline considerably for durables relative to nondurables in expansions. This result is robust
to measuring cyclicality of marginal cost under alternative measures of labor’s price and
under a broad range of assumed short-run substitutabilities of capital and labor. Because of
countercyclical markups for durables, the cyclical movements in marginal cost predicted by
industry durability, Engel-curve elasticity, and capital share are only modestly passed through
to cyclical movements in price. In that regard, the evidence is consistent with a Calvo model
calibrated to the frequency observed in the micro data, or even less frequent.

But not all the evidence aligns with sticky prices. Procyclical marginal cost, driven by
producing a luxury or producing with a highly capital-intensive technology, does not generate
a markup decline. And higher frequency of price change produces neither more cyclical
prices nor price markups, beyond the extremely procyclical pricing of energy goods. The
observed cyclical wedges between labor’s marginal product and price might be better
explained by intended pricing by firms, principally countercyclical markups for durables,
rather than unintended markup movements that are the byproduct of price stickiness. "

[JW Mason]

A version of rsj's mix effects is Joan RObinson's disguised unemployment.

In a recession, some unemployed people will engage in activity that looks like work, and gets taken as work by the statistical agencies. Robinson's example was selling pencils on the street.

I think there is a more general version of this, which recognizes that in normal times labor markets are not in equilibrium. More productive enterprises are always bidding away workers from less productive ones. With lower demand this slows or halts, and a higher proportion of workers stay in jobs that are less productive. (I'm not 100% sure this works if you think it through more systematically than I have.)

Then of course there's the channel from demand to technical productivity, presumably via investment, the < a href="http://en.wikipedia.org/wiki/Verdoorn's_law">Kaldor-Verdoorn Law. Productivity doesn't just change in response to random "shocks," it may change in response to demand-induced fluctuations in output.

[Jacques René Giguère]

1) In times of recession, it is ( was ) common to lay off the supposedly easily repleceable blue-collars ( and anyway who care if they starve, they're just workers...) and keep the supposedly precious white-collar ( and they're our own class, it just can't be done...). So measured productivity will fall and labor hoarding will be observed.
2) Tradeable presumably use more capital. Samuelson core is empty and leave room for downward price adjustment. It would be intersting to check with capital intensive non-traadable services such as hotels.