Elasticity of substitution — a short refresher

16 Jun, 2014 at 16:05 | Posted in Economics | Comments Off on Elasticity of substitution — a short refresher

Thomas Piketty argues in Capital in the Twenty-First Century that capital’s share of income will probably continue to rise in the future. In the neoclassical production and growth models that he refers to, as capital goes on accumulating, diminishing returns on capital isn’t strong enough to stop net capital incomes from expanding. In model terms, this means that the elasticity of substitution between capital and labor is greater than one. Since the reasoning may not be totally transparent to all interested, this short video may be of some assistance …

What — really — is ‘effective demand’?

16 Jun, 2014 at 11:25 | Posted in Economics | 1 Comment

J__Jespersen_683346aEconomists of all shades have generally misunderstood the theoretical structure of Keynes’s The General Theory. Quite often this is a result of misunderstanding the concept of ‘effective demand’ — one of the key theoretical innovations of The General Theory.

Jesper Jespersen untangles the concept and shows how Keynes, by taking uncertainty seriously, contributed to forming an analytical alternative to the prevailing neoclassical general equilibrium framework:

Effective demand is one of the distinctive analytical concepts that Keynes developed in The General Theory. Demand and demand management have thereby come to represent one of the distinct trademarks of Keynesian macroeconomic theory and policy. It is not without reason that the central position of this concept has left the impression that Keynes’s macroeconomic model predominantly consists of theories for determining demand, while the supply side is neglected. From here it is a short step within a superficial interpretation to conclude that Keynes (and post-Keynesians) had ended up in a theoretical dead end, where macroeconomic development is exclusively determined by demand factors …

It is the behaviour of profit-seeking firms acting under the ontological condition of uncertainty that is at the centre of post-Keynesian concept of effective demand. It is entrepreneurs’ expectations with regard to demand and supply factor that determine their plans for output as a whole and by that the effective demand for labour.

Therefore, it was somewhat unfortunate that Keynes called his new analytical concept ‘effective demand’, which may have contributed to misleading generations of open minded macroeconomists to concluding that it was exclusively realized demand for consumer and investment goods that drives the macroeconomic development. Hereby a gateway for the IS/LM-model interpretation of effective demand was opened, where demand creates its own supply.

tmp10C1_thumb1On the contrary, it is the interaction between the sum of the individual firms’ sales expectations (aggregate demand) and their estimated production costs (aggregate supply) that together with a number of institutional conditions (bank credit, labour market organization, global competition and technology) determine the business sector decisions on output as a whole and employment …

The supply side in the goods market is an aggregate presentation of firms’ cost functions considered as a whole. It shows a relation between what Keynes called ‘supply price’, i.e. the sales proceeds that, given the production function and cost structures, is needed to ‘just make it worth the while of the entrepreneurs to give that employment’ (Keynes, 1936: 24). This means that behind the supply curve there is a combination of variable costs plus an expected profit at different levels of employment. At each level firms try to maximise their profit, if they succeed there is no (further) incentive for firms to change production or employment.

These assumptions entail that the aggregate supply function (what Keynes called the Z-curve) is upward sloping and represents the proceeds that has to be expected by the industry as a whole to make a certain employment ‘worth undertaken’ … In fact, this aggregate supply function looks like it was taken directly from a standard, neoclassical textbook, where decreasing marginal productivity of labour within the representative firm is assumed; the main difference is that Keynes is dealing with the aggregate sum of heterogeneous firms i.e. the industry as a whole.

The other equally important part of effective demand is aggregate demand function, which is the value of the sales that firms as a whole expect at different levels of macro-activity measured by employment (as a whole) …

Firms make a kind of survey-based expectation with regard to the most likely development in sales and proceeds in the nearer future. This expectation of aggregate demand (as a whole) is a useful point of departure for the individual firms when they have to form their specific expectation of future proceeds. This sales expectation will therefore centre around the future macroeconomic demand (and on the intensity of international competition).

Accordingly, Keynes’s macro-theory has a microeconomic foundation of firms trying to maximise profit, but differs from neoclassical theory by introducing uncertainty related to the future, which makes an explicit introduction of aggregate demand relevant i.e. the expected sales proceeds by business as a whole.

House prices — still out of line

15 Jun, 2014 at 12:35 | Posted in Economics | Comments Off on House prices — still out of line

chart2_

Piketty interview (SR P1)

15 Jun, 2014 at 11:13 | Posted in Economics | Comments Off on Piketty interview (SR P1)

 
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Click here and then scroll down the page to “Engelsk version”.

What we ought to discuss (instead of depreciation rates)

14 Jun, 2014 at 21:24 | Posted in Economics | 2 Comments

 

Piketty and the neoclassical heart of darkness

13 Jun, 2014 at 20:32 | Posted in Economics | 2 Comments

If you have an apple and I have an apple and we exchange these apples then you and I will each have one apple.

But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas.

George Bernard Shaw

I came to think about this dictum when today reading yet another Piketty critique — this time by Matthew Rognlie (on which Brad DeLong has some interesting thoughts). As I see it the gist of the critique is that neoclassical economists — force-fed on growth models taking for granted constant returns to scale and diminishing marginal returns in each factor — can’t really accept, or even comprehend, Piketty’s argument that  the rates of return on capital will not diminish.

In Paul Romer’s Endogenous Technological Change (1990) knowledge is made the most important driving force of growth. Knowledge (ideas) are presented as the locomotive of growth — but as Allyn Young, Piero Sraffa and others had shown already in the 1920s, knowledge is also something that has to do with increasing returns to scale and therefore not really compatible with neoclassical economics with its emphasis on constant returns to scale.

Increasing returns generated by non-rivalry between ideas is simply not compatible with pure competition and the simplistic invisible hand dogma. That is probably also the reason why neoclassical economists have been so reluctant to embrace the theory wholeheartedly.

msg-new-way-of-thinking

Neoclassical economics has tried to save itself by more or less substituting human capital for knowledge/ideas. But knowledge or ideas should not be confused with human capital. Although some have problems with the distinction between ideas and human capital in modern endogenous growth theory, this passage gives a succinct and accessible account of the difference:

Of the three statevariables that we endogenize, ideas have been the hardest to bring into the applied general equilibrium structure. The difficulty arises because of the defining characteristic of an idea, that it is a pure nonrival good. A given idea is not scarce in the same way that land or capital or other objects are scarce; instead, an idea can be used by any number of people simultaneously without congestion or depletion.

Because they are nonrival goods, ideas force two distinct changes in our thinking about growth, changes that are sometimes conflated but are logically distinct. Ideas introduce scale effects. They also change the feasible and optimal economic institutions. The institutional implications have attracted more attention but the scale effects are more important for understanding the big sweep of human history.

The distinction between rival and nonrival goods is easy to blur at the aggregate level but inescapable in any microeconomic setting. Picture, for example, a house that is under construction. The land on which it sits, capital in the form of a measuring tape, and the human capital of the carpenter are all rival goods. They can be used to build this house but not simultaneously any other. Contrast this with the Pythagorean Theorem, which the carpenter uses implicitly by constructing a triangle with sides in the proportions of 3, 4 and 5. This idea is nonrival. Every carpenter in the world can use it at the same time to create a right angle.

Of course, human capital and ideas are tightly linked in production and use. Just as capital produces output and forgone output can be used to produce capital, human capital produces ideas and ideas are used in the educational process to produce human capital. Yet ideas and human capital are fundamentally distinct. At the micro level, human capital in our triangle example literally consists of new connections between neurons in a carpenter’s head, a rival good. The 3-4-5 triangle is the nonrival idea. At the macro level, one cannot state the assertion that skill-biased technical change is increasing the demand for education without distinguishing between ideas and human capital.

Paul Krugman also has some interesting thoughts on the history of that dangerous idea — increasing returns: 

I have worked and written on a lot of topics. It is, however, the idea of increasing returns that has been the most important theme in my work. And it is my work in helping to clarify the role that increasing returns plays in economics that is the main excuse I have for my existence. The idea of increasing returns is, of course, a very old one, going back at least to Adam Smith. Nonetheless, until the 1980s economics was heavily dominated by what we may call the Ricardian Simplification: the assumption of constant returns and perfect competition …

The world isn’t really characterized by constant returns, and it was essential to go beyond the Ricardian Simplification, if only to be able to say to the policymakers that we had explored that terrain and found little of use.

If one admits increasing returns into one’s economic model, two other consequences follow. First, increasing returns are intimately bound up with the possibility of multiple equilibria. There can be multiple equilibria in constant-returns models, too, but they are rarely either plausible or interesting. By contrast, it is very easy to be persuaded of both the relevance and importance of multiple equilibria due to increasing returns … Second, once there are interesting multiple equilibria, you need a story about how the economy picks one. The natural stories involve dynamics — the cumulation of initial advantages that may be accidents of history …

All of this is fairly obvious, and indeed the history of thought in economics is littered with manifestos on the need to take into account increasing returns, multiple equilibria, dynamics, and the role of history … Nonetheless, it wasn’t until the 1980s that increasing returns really got into the mainstream of economics. I wasn’t the only one in the movement: Paul Romer, in particular, wrote several papers I wish I had written … applying increasing returns to economic growth …

Paul Krugman Incidents from my career

In one way one might say that increasing returns is the darkness of the neoclassical heart. And this is something most mainstream neoclassical economists don’t really want to talk about. They prefer to look the other way and pretend that increasing returns are possible to seamlessly incorporate into the received paradigm.

A couple of years ago yours truly wrote a review of David Warsh’s great book on growth theory – Knowledge and the wealth of nations – for an economics journal. The editor accepted it for publication – but only if I was willing to lift out the parts where I highlighted Warsh’s discussion of increasing returns to scale and the efforts neoclassical economics over the decades had put into trying to willfully “forget” this disturbing anomaly. Moral: some dogmas are not to be questioned – at least not if you want to be published!

How to become a big-shot economist

13 Jun, 2014 at 18:33 | Posted in Economics | Comments Off on How to become a big-shot economist

 

For my daughter Tora, who has just made her first year at Stockhom School of Economics.

Rites

12 Jun, 2014 at 19:25 | Posted in Varia | Comments Off on Rites

 

Ack Värmeland, du sköna (Jussi Björling)

12 Jun, 2014 at 15:25 | Posted in Varia | Comments Off on Ack Värmeland, du sköna (Jussi Björling)

 

Neoclassical synthesis — is that really in Keynes?

12 Jun, 2014 at 11:44 | Posted in Economics | 1 Comment

cateA new second edition of An Encyclopedia of Keynesian Economics is out, featuring accessible, informative and provocative contributions by leading Keynesian scholars working in the tradition of Keynes. For those interested in the debate on Keynes and the Keynesian Revolution it is a must.

[Oh, and yes, yours truly is one of the contributors – as are e. g. David Colander, Sheila Dow, Geoff Harcourt, Donald Moggridge, Paul Samuelson, Robert Solow and Warren Samuels.]

Many of the entries are still highly interesting reads. One of my favourites is Edward McKenna’s and Diane Zannoni’s Neoclassical Synthesis — which sums up with the following words:

Finally it should be noted that the neoclassical economists’ adoption of classical theory of supply tied Keynesian thought to a theory wholly at variance with that advanced by Keynes himself, in Chapter 3 of General Theory. Had the neoclassicals not done this, it is unlikely that they would have neglected the issue of price formation. And, given the nature of Keynes’s theory, it is certain that the issue of income distribution would have assumed far greater prominence than it has in the neoclassical synthesis.

Comparing McKenna’s and Zonnoni’s view with Krugman’s

the doctrine, made famous by Paul Samuelson but actually there in Keynes too, that macroeconomic policy is needed for full employment but once you have that a relatively free-market policy works

or DeLong’s

the *fons et origo of what Stiglitz regards as a major intellectual error – was none other than John Maynard Keynes himself

yours truly, on this issue, definitely sides with McKenna/Zannoni and Stiglitz.

What ought to be on every macroeconomist’s reading list

11 Jun, 2014 at 13:38 | Posted in Economics | 2 Comments

What is the problem we wish to solve when we try to construct a rational economic order? … If we possess all the relevant information, if we can start out from a given system of preferences, and if we command complete knowledge of available means, the problem which remains is purely one of logic …

The-Use-of-Knowledge-in-Society_800x600-05_2014-172x230This, however, is emphatically not the economic problem which society faces … The peculiar character of the problem of a rational economic order is determined precisely by the fact that the knowledge of the circumstances of which we must make use never exists in concentrated or integrated form but solely as the dispersed bits of incomplete and frequently contradictory knowledge which all the separate individuals possess. The economic problem of society is … a problem of the utilization of knowledge which is not given to anyone in its totality.

This character of the fundamental problem has, I am afraid, been obscured rather than illuminated by many of the recent refinements of economic theory … Many of the current disputes with regard to both economic theory and economic policy have their common origin in a misconception about the nature of the economic problem of society. This misconception in turn is due to an erroneous transfer to social phenomena of the habits of thought we have developed in dealing with the phenomena of nature …

To assume all the knowledge to be given to a single mind in the same manner in which we assume it to be given to us as the explaining economists is to assume the problem away and to disregard everything that is important and significant in the real world.

Compare this relevant and realist wisdom with the rational expectations hypothesis (REH) used by almost all mainstream macroeconomists today. REH presupposes – basically for reasons of consistency – that agents have complete knowledge of all of the relevant probability distribution functions. And when trying to incorporate learning in these models – trying to take the heat of some of the criticism launched against it up to date – it is always a very restricted kind of learning that is considered. A learning where truly unanticipated, surprising, new things never take place, but only rather mechanical updatings – increasing the precision of already existing information sets – of existing probability functions.

Nothing really new happens in these ergodic models, where the statistical representation of learning and information is nothing more than a caricature of what takes place in the real world target system. This follows from taking for granted that people’s decisions can be portrayed as based on an existing probability distribution, which by definition implies the knowledge of every possible event (otherwise it is in a strict mathematical-statistically sense not really a probability distribution) that can be thought of taking place.

But in the real world it is – as shown again and again by behavioural and experimental economics – common to mistake a conditional distribution for a probability distribution. Mistakes that are impossible to make in the kinds of economic analysis – built on the rational expectations hypothesis – that Levine is such an adamant propagator for. On average rational expectations agents are always correct. But truly new information will not only reduce the estimation error but actually change the entire estimation and hence possibly the decisions made. To be truly new, information has to be unexpected. If not, it would simply be inferred from the already existing information set.

In rational expectations models new information is typically presented as something only reducing the variance of the parameter estimated. But if new information means truly new information it actually could increase our uncertainty and variance (information set (A, B) => (A, B, C)).

Truly new information give birth to new probabilities, revised plans and decisions – something the rational expectations hypothesis cannot account for with its finite sampling representation of incomplete information.

In the world of rational expectations, learning is like being better and better at reciting the complete works of Shakespeare by heart – or at hitting bull’s eye when playing dart. It presupposes that we have a complete list of the possible states of the world and that by definition mistakes are non-systematic (which, strictly seen, follows from the assumption of “subjective” probability distributions being equal to the “objective” probability distribution). This is a rather uninteresting and trivial kind of learning. It is a closed world learning, synonymous to improving one’s adaptation to a world which is fundamentally unchanging. But in real, open world situations, learning is more often about adapting and trying to cope with genuinely new phenomena.

The rational expectations hypothesis presumes consistent behaviour, where expectations do not display any persistent errors. In the world of rational expectations we are always, on average, hitting the bull’s eye. In the more realistic, open systems view, there is always the possibility (danger) of making mistakes that may turn out to be systematic. It is because of this, presumably, that we put so much emphasis on learning in our modern knowledge societies.

As Hayek wrote:

When it comes to the point where [equilibrium analysis] misleads some of our leading thinkers into believing that the situation which it describes has direct relevance to the solution of practical problems, it is high time that we remember that it does not deal with the social process at all and that it is no more than a useful preliminary to the study of the main problem.

Added: Just in case you’re contemplating commenting on this post and think that Hayek is all bad — read this!

Rethinking Economics Conference in London June 28-29

10 Jun, 2014 at 19:57 | Posted in Economics | 1 Comment

rethink london
 
You find more on the conference here

Brothers in Arms

10 Jun, 2014 at 18:27 | Posted in Varia | Comments Off on Brothers in Arms

 

Piketty and reasonable estimates of depreciation rates (wonkish)

10 Jun, 2014 at 10:22 | Posted in Economics | Comments Off on Piketty and reasonable estimates of depreciation rates (wonkish)

Thomas Piketty emails:

“We do provide long run series on capital depreciation in the “Capital is back” paper with Gabriel [Zucman] (see http://piketty.pse.ens.fr/capitalisback, appendix country tables US.8, JP.8, etc.). The series are imperfect and incomplete, but they show that in pretty much every country capital depreciation has risen from 5-8% of GDP in the 19th century and early 20th century to 10-13% of GDP in the late 20th and early 21st centuries, i.e. from about 1%[/year] of capital stock to about 2%[/year].

DepreciationOf course there are huge variations across industries and across assets, and depreciation rates could be a lot higher in some sectors. Same thing for capital intensity.

The problem with taking away the housing sector (a particularly capital-intensive sector) from the aggregate capital stock is that once you start to do that it’s not clear where to stop (e.g., energy is another capital intensive sector). So we prefer to start from an aggregate macro perspective (including housing). Here it is clear that 10% or 5% depreciation rates do not make sense.”

No, James Hamilton, it is not the case that the fact that “rates of 10-20%[/year] are quite common for most forms of producers’ machinery and equipment” means that 10%/year is a reasonable depreciation rate for the economy as a whole–and especially not for Piketty’s concept of wealth, which is much broader than simply produced means of production.

No, Per Krusell and Anthony Smith, the fact that “we conducted a quick survey among macroeconomists at the London School of Economics, where Tony and I happen to be right now, and the average answer was 7%[/year” for “the” depreciation rate does not mean that you have any business using a 10%/year economy-wide depreciation rate in trying to assess how the net savings share would respond to increases in Piketty’s wealth-to-annual-net-income ratio.

Who are these London School of Economics economists who think that 7%/year is a reasonable depreciation rate for a wealth concept that attains a pre-World War I level of 7 times a year’s net national income? I cannot imagine any of the LSE economists signing on to the claim that back before WWI capital consumption in northwest European economies was equal to 50% of net income–that depreciation was a third of gross economic product…

Brad DeLong

Some of the critics of Piketty obviously think that the issue is theoretical and that somehow he has misspecified the standard growth model. Now, Piketty doesn’t really talk that much about the standard (Solow) growth model in the book, but let’s do a back of the envelope analysis based on that model and say we have that diehard neoclassical model (assuming the production function is homogeneous of degree one and unlimited substitutability) such as the standard Cobb-Douglas production function (with A a given productivity parameter, and k  the ratio of capital stock to labor, K/L) y = Akα , with a constant investment λ out of output y and a constant depreciation rate δ of the “capital per worker” k, where the rate of accumulation of k, Δk = λyδk, equals Δk = λAkαδk. In steady state (*) we have λAk*α = δk*, giving λ/δ = k*/y* and k* = (λA/δ)1/(1-α)Putting this value of k* into the production function, gives us the steady state output per worker level y* = Ak*α= A1/(1-α)(λ/δ))α/(1-α)Assuming we have an exogenous Harrod-neutral technological progress that increases y with a growth rate g (assuming a zero labour growth rate and with y and k a fortiori now being refined as y/A and k/A respectively, giving the production function as y = kα) we get dk/dt = λy – (g + δ)k, which in the Cobb-Douglas case gives dk/dt = λkα– (g + δ)k, with steady state value k* = (λ/(g + δ))1/(1-αand capital-output ratio k*/y* = k*/k*α = λ/(g + δ). If using Piketty’s preferred model with output and capital given net of depreciation, we have to change the final expression into k*/y* = k*/k*α = λ/(g + λδ). Now what Piketty predicts is that g will fall and that this will increase the capital-output ratio. Let’s say we have δ = 0.03, λ = 0.1 and g = 0.03 initially. This gives a capital-output ratio of around 3. If g falls to 0.01 it rises to around 7.7. We reach analogous results if we use a basic CES production function with an elasticity of substitution σ > 1. With σ = 1.5, the capital share rises from 0.2 to 0.36 if the wealth-income ratio goes from 2.5 to 5, which according to Piketty is what actually has happened in rich countries during the last forty years.

Being able to show that you can get the Piketty results using one or another of the available standard neoclassical growth models is of course — from a realist point of view — of limited value. As usual — the really interesting thing is how in accord with reality are the assumptions you make and the numerical values you put into the model specification.

Divenire

9 Jun, 2014 at 19:39 | Posted in Varia | Comments Off on Divenire

 

I’m probably not the only blogger/researcher that likes to listen to music while writing/working. Zbigniew Preisner, Philip Glass, Miles Davis, Arvo Pärt and Jan Garbarek are longtime favorites. Ludovico Einaudi is a rather new acquaintance.

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