Saturday, March 1, 2014

Did Keynes have a Theory of Aggregate Supply?

My old classmate Nick Rowe has a new post on Chapter 3 of The General Theory.  In Nick's words,
Start with three equations.
1. The production function: Y=F(L). Output (Y) is a function of employment (L). 
2. A "classical" labour demand curve: W/P=MPL(L). The real wage (W/P) equals the Marginal Product of Labour, which is a decreasing function of employment. This is Keynes' "first classical postulate", which he agreed with. 
3. A "classical" labour supply curve: W/P=MRS(L,Y). The real wage equals the Marginal Rate of Substitution between labour (or leisure) and output (or consumption). This is Keynes' "second classical postulate", which he disagreed with (except at "full employment"). 
From 1 and 2, plus some tedious math, we can derive what Keynes calls "the aggregate supply function": PY/W = S(L). It shows the value of output, measured in wage units, as a function of employment. It is substantively identical to the Short Run Aggregate Supply Curve in intermediate macro textbooks that assume sticky nominal wages: Y=H(P/W), which uses the exact same equations 1 and 2, but presents the same solution differently. 
From 1 and 3, plus some tedious math, we can derive a second "aggregate supply function", that is not in the General Theory: PY/W = Z(L). It is substantively identical to the short run aggregate supply curve implicit in New Keynesian models, which assume sticky P and perfectly flexible W, so the economy is always on the labour supply curve and always on the production function.
From 1 and 2 and 3, plus some tedious math, we can solve for Y, L, and W/P, and derive a third aggregate supply function: Y=Y*. This is the textbook Long Run Aggregate Supply curve. It is identical to the solution we could get if we solved for the levels of Y, L, and W/P that satisfied both the first and second "aggregate supply functions".
Nick's first supply curve is the only supply curve in The General Theory. All else is due to misinterpretations by later economists who tried to make sense of what Keynes really meant (ineffectively in my view).  We don't need sticky prices (supply curve number 2) and we don't need to reintroduce the second classical postulate through the back door (supply curve number 3).  That is 1950s MIT talking and it led us down the wrong path.

In Chapter 4 of The General Theory, Keynes suggests that we measure output in wage units. Here is Nick again on that point...
Keynes' weird habit of measuring output in wage units had an unfortunate result: because [it implies that]  doubling the real wage, for a given level of output and real income, would exactly double output demanded. 
That is simply false. There is no unique concept of output in a multi-good economy. Contrary to Nick's assertion, there is nothing 'weird' at all about the measurement of GDP in wage units. It is a clever device that allows us to measure real GDP and to concentrate on the determinants of aggregate economic activity.

And Nick claims later in his post that
There is absolutely nothing new on the supply-side in chapter 3 of the General Theory.
Not so. Although there is no 'theory' of aggregate supply that would satisfy a micro economist, that is not the same as Nick's claim that there is nothing new. What is new is the assertion that Keynes will drop the classical second postulate. In other words: throw away the labor supply curve. Making sense of that statement is what my own work is all about.

Back to Nick...
It is the demand-side that is new. It is the idea that the demand for goods is a function of the quantity of labour that households are actually ableto sell. If households are rationed in the labour market, that will spillover and affect their demand in the output market. Because the amount of labour they are actually able to sell, and hence the income they will earn from wages plus non-wages, depends on demand. Which means that demand depends upon demand. Demand depends on itself. That was new, and interesting."
I agree that the consumption function, the idea that "demand depends on itself",  was a central element of the theory of The General Theory. But is there a Keynesian consumption function in the data? I don't think so. At least, not in the form that Keynes postulated in the GT.

Attempts to reconcile short run cross section evidence and long run time series evidence on the value of the multiplier led to permanent income theory and the Ricardian equivalence debate. That debate is what we are all so heated up over right now. If the GT is nothing but the Keynesian multiplier, and if that theory is wrong, then what is the Wannabe Keynesian left with?
The Wannabe Keynesian is left with the theory of supply; a denial of the classical second postulate. My work builds a cohesive microeconomic foundation to the economics of Keynes' theory of aggregate supply. That foundation denies Say's law, (the proposition that supply creates its own demand) and it allows us to us refocus the debate on where it belongs. What is the best way to restore effective demand?


  1. Roger: "Nick's first supply curve is the only supply curve in The General Theory."

    Agreed. In the sense that Keynes both had that supply curve in the GT, and said that the economy was always *on* that supply curve.

    The second and third supply curves are implicitly there in the GT, but Keynes said that the economy would be *off* those supply curves, except at "full employment". (They are there in the GT in the sense that Keynes uses them to define "full employment".)

    We really need to be careful how we use the word "supply".

    In my opinion, "supply" (or "quantity supplied") does *not* mean the quantity sellers actually produce and sell. It means the quantity sellers *would like to* produce and sell, if they could find willing buyers. If we don't use the word the way I use it, we can *never* talk about "excess supply". There is excess supply of labour in the GT (except at full employment), because households cannot sell as much labour as they want to sell. The economy is *off* the labour supply curve. It is off my second and third supply curves. Which does not mean those second and third supply curves don't exist.

    "There is no unique concept of output in a multi-good economy. Contrary to Nick's assertion, there is nothing 'weird' at all about the measurement of GDP in wage units. It is a clever device that allows us to measure real GDP and to concentrate on the determinants of aggregate economic activity."

    As a "clever device", to avoid aggregation problems, it fails. Because we cannot aggregate workers any more easily than we can aggregate output, or capital goods. The wages and labour of a brain surgeon and a bartender are very different. We can't add them together into something we call "L" in an aggregate production function. There is no "standard unit" of labour or wages.

    If Keynes contribution was simply to say that the economy was *off* the labour supply curve when the economy was at less than full employment, I would say that is zero contribution. It is almost a definition of what we mean by "less than full employment".

    I say that Keynes' big contribution was in developing a better theory of aggregate demand, to explain why the economy would be off at least two of those three supply curves (and maybe off all three supply curves). And his key insight was that demand depends on itself, in a world where firms and or households cannot sell as much output and/or labour as they want to sell.

    And I think that New Keynesians have swept that key insight under the rug. They just assume (that people expect the economy will eventually return to) full employment, even though there is absolutely nothing internal to the NK model to make that a rational expectation. That is what Keynes would be rolling in his grave about. The marginal propensity to consume out of permanent income is (roughly) one. The permanent income multiplier is (roughly) infinite. There is absolutely nothing in NK models that says that it is rational to expect permanent income to equal full employment permanent income, and that all other expectations are irrational. And Taylor Rules do not help NK models escape this result. NK economists just assume it away. They are as bad as "classical" economists who just assumed (an automatic tendency towards) full employment.

    NK models are models of monetary exchange economies without money. That's why they have this result. Keynes understood that the only thing preventing this result was some sort of "real balance effect" (not necessarily a Pigou effect). NK models lack real balances, and so lack any sort of real balance effect.

    One of my old posts developing this idea:

    1. "As a "clever device", to avoid aggregation problems...[measurement of GDP in wage units] fails"

      I happened to be thinking about this topic, for other reasons, and I'm going to object. First of all, while it "fails" in the sense that it doesn't entirely overcome aggregation problems, it's surely an improvement: a brain surgeon is more like a bartender than a smartphone is like a hamburger; labor is more homogeneous than output. And in Keynes' time, when there was less human capital around than there is today, and less "human land" (less superstar effects, for example), the homogeneous labor assumption was perhaps not all that unreasonable (that is, you could reasonably exclude from your analysis the jobs that involved a lot of human capital). Obviously today it's not very useful for empirical work, but conceptually I can still think of a brain surgeon as earning some premium over the raw cost of labor, whereas I can't even imagine what to say about how one should compare smartphones and hamburgers (not to mention massages, depositions, months of shelter, etc). I know there are utilitarian methods that attempt to make these comparisons (after all, we do have price indices and "real" output statistics), but I find them quite unsatisfying (one reason I'm attracted to Scott Sumner's focus on nominal output) and still find that, even with all its difficulties, converting things into labor units can shed light on the situation.

    2. Nick and Andy

      Here is JM's take on the objection of non-homogenous labor from Ch 4.

      "In dealing with the theory of employment I propose, therefore, to make use of only two fundamental units of quantity, namely, quantities of money-value and quantities of employment. The first of these is strictly homogeneous, and the second can be made so. For, in so far as different grades and kinds of labour and salaried assistance enjoy a more or less fixed relative remuneration, the quantity of employment can be sufficiently defined for our purpose by taking an hour’s employment of ordinary labour as our unit and weighting an hour’s employment of special labour in proportion to its remuneration; i.e. an hour of special labour remunerated at double ordinary rates will count as two units. We shall call the unit in which the quantity of employment is measured the labour-unit; and the money-wage of a labour-unit we shall call the wage-unit.[5] Thus, if E is the wages (and salaries) bill, W the wage-unit, and N the quantity of employment, E = N.W."

      I like the use of wage units as opposed to a price index because it removes the need for detrending. I will say more about this in a future post.

    3. Thanks for your comments Nick

      And here is a clickable link to your post.


    4. Hi

      Roger Farmer

      This is what I was looking for from last week. Great work done. :)

      Short Run Aggregate Supply

  2. If the GT is nothing but the Keynesian multiplier, and if that theory is wrong, then what is the Wannabe Keynesian left with? The Wannabe Keynesian is left with the theory of supply; a denial of the classical second postulate.

    Also chapter 12 (though that might lead to confusing a Wannabe Keynesian with a post-Keynesian), and chapter 2 (though that might lead to confusing a Wannabe Keynesian with Paul Krugman).

  3. what ever math people try to use to come up with a supply function there will be basic assumptions, and if those assumptions are false then the theory is false.........

    Keynes concept of effective demand which he points out in chapter 3 simply assumes that as the number of employees increases then the increased income for entrepreneur expected for each added employee decreases, for many reasons which he asserts multiple times in the GT

    and for many of the same reasons the amount the entrepreneur NEEDS to make (Keynes supply curve) does not decrease the same as the demand curve does, in fact it may increase

    so eventually they intersect and that determines the effective demand

    if someone comes up with a fancy equation for the supply curve taking into account lets say only certain factors, or using more modern theories that don't fit reality, then the basic assumptions may in fact be false and the supply curve is not useful for understanding reality

    I believe Keynes terms and explanations in chapter 3 work best for my understanding

  4. Daniel,
    You give the basic idea of effective demand. Yet, since Keynes, economists have seen effective demand and aggregate demand as the same thing. This is an error. Effective demand is the limit upon aggregate demand, in the sense that entrepreneurs will not see more profit beyond the effective demand limit, and so will curb production and output. Thus effective demand defines the natural level of GDP.
    I measure effective demand as a function of labor share in relation to the % utilization of labor and capital. The measure matched every top of the business cycle since the 60's when data for capacity utilization began. The measure currently points to a natural level of real GDP between $16 and $16.1 trillion. This is well below CBO projections. This will be the first time that the economy will fall short of what economists consider full employment... just what Keynes warned about in chap 3 of GT.
    Roger asks, What is the best way to restore effective demand? My answer is to raise labor share back up. It is at an all time low since WWII. But it is not an easy thing to do.

  5. What Edward said. Thirty years of upward redistribution, and off-the-charts concentrations of income and wealth, are starving and strangling the economy. Demand is not creating its own demand.

    If this surmise is right -- that the problem is essentially monetary, insufficient velocity -- then it doesn't matter (to address Evan Soltas) whether it is solved by empowering unions or just transferring the labor share directly. The latter seems at least somewhat more likely to occur in any reasonable time frame.

    1. Daniel, ed and Steve
      Yes: labor's share is correlated with economic activity and I agree that if employment were to increase, so would labor's share. Is the problem monetary? Very broadly yes; it is a problem in the asset markets and I believe the solution also lies in the asset markets.

  6. In one sense, Nick Rowe's statement about the aggregate supply side in The General Theory of Employment, Interest, and Money is correct - it's nothing really all that new. After all, despite his disagreements with the so-called "Classical School", J.M. Keynes himself still remained highly influenced by Alfred Marshall throughout much of his life - not just in terms of thought, but even in terms of the style of presentation. (If one reads Industrial Fluctuations or The Theory of Unemployment by A.C. Pigou and compares that to A Tract on Monetary Reform or A Treatise on Money by J.M. Keynes, and then compare it with the Principles of Economics by Alfred Marshall, one could easily spot the family resemblance.)

    However, to say that the aggregate supply side of The General Theory appears only in Chapter 3 isn't the complete story - in fact, J.M. Keynes himself writes in a footnote on Page 25 that there is an employment function which is "closely related" to the aggregate supply function. The footnote points to Chapter 20, which is called "The Employment Function". Chapter 20 is found in Book V of The General Theory.

    Other references to Chapter 20 (and more generally, Book V) can be found on Page(s) 7-8, 12-13, 89, 119, 201-202, 208-209, 230, 232, 243, 246, and 253. Why is Book V important? Because it is there that Keynes deals with the target set up in The Theory of Unemployment by A.C. Pigou, on his own colleague's own terms, and successfully bests Professor Pigou. For some secondary source references, please see the following links - all pieces are written by the same author, but all of them are very good nonetheless:

    Also, don't forget to consult Chapters 8 to 10 in Part II of The Theory of Unemployment by A.C. Pigou and Chapters 19 to 21 in Book V of The General Theory of Employment, Interest, and Money by J.M. Keynes for proper inspection!

  7. "It is the idea that unemployment has an inherent tendency to return to some special natural rate that is a property of the available technology for finding jobs. It is a fact of nature, a bit like the gravitational constant in celestial mechanics."

    This is what gives me so much angst about he state of the economy.

    1. We have a bunch of fed and comfortable people who are not being put to work. Meaning WE ARE ALREADY BUYING THEIR LABOR, instead of getting goods and services for it, we get nothing. They just sit at home.

    2. We have technology at out finger tips to put all them to work AND:

    a) let them have more $ than they have now.
    b) reduce the money we spend on them thru welfare.

    RF, what am I missing? Why are economists so unwilling to price excess labor ASSUMING THEY ARE ALREADY FED AND COMFY?

    It's one thing to talk about labor markets in absence of $750B in welfare, but once WE HAVE THE WELFARE which exists because 30M+ are not worth ROI at the current wage and regulatory rates... what fool doesn't price their labor admitting we have $750B to lever them into taking a job?

    Who doesn't use the $10K taxpayers pay to the non-worker to push the worker to do something profitable for their neighbor?

    THE TECHNOLOGY EXISTS. Millions of search and bids happen in milliseconds. Smart agents can be deployed doing amazing filtering. Workers and Jobs and Employers can be rated on hundreds of nuances, and yet with all this technology, the economists profession is sitting around with some formulas and dbeates that have nothing to do with reality.

    We are going to adopt direct weekly wage subsidies, and have weekly clearing and feedback on both sides of the low end labor market.

    That is the PINNACLE of animal spirits for both buyer and seller, innovator, and consumer.

    What does it take to get Economists to put forward GI/CYB open source software as their preferred solution?


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