He writes:
> After reading all of Mr. Vienneau's posts, I had given up hope
>of seeing him complete a correct mathematical exposition of his
>thoughts. His most recent post at least convinced me that he can
>(given enough time to work on his algebra!) provide a correct
>mathematical exposition.
If my last post is correct, my mathematics has been correct all
along aside from my emendations. Given Mr. Witte's attacks on my
"cravenness" in refusing to acknowledge the "mistakes" he found in
my posts, he ought to admit he was wrong. If he now understands
the mathematics, failure to do so in this context exhibits a want
of character.
>For your benefit, what he is trying to do is
>revisit the Cambridge controversies of the 1960's.
Here Mark demonstrates the Markov property - no memory. Some time
ago in this thread, I wrote
RV> The Cambridge Capital Controversy was a complex and multifaceted
RV> affair. Two important Neoclassical summaries are Christopher Bliss'
RV> book "Capital Theory and the Distribution of Income (1975) and Frank
RV> Hahn's paper "The Neo-Ricardians" (Cambridge Journal of Economics, V.
RV> 6, No. 4, 1982). Although Bliss and Hahn are not in total agreement,
RV> they both argue that disaggregated Neoclassical theory is sound and
RV> does not need an equation equating the demand and supply of "capital."
Mr. Witte's references throughout his post are well-worth examining.
>At best he has a
>passing understanding of a minor part of the capital theory
>literature. For the interested reader, what Mr. Vienneau is trying to
>express can be found more clearly deliniated in the following books.
>
>1) Harcourt, Geoff (1972) Some Cambridge Controversies on the Theory of
>Capital. Cambridge: Cambridge University Press.
>
>2) Pasinetti, Luigi (1977) Lectures on the Theory of Production. London:
>MacMillan Press.
>
> This controversy is now viewed in the literature as a very
>tired debate. Far from being a spike in the heart of neo-classical
>theory, it is considered a topic in the history of economic thought.
>The questions raised by the instigators of this debate have been
>answered by many and are nicely summarized in the standard text by
>Burmeister. (Burmeister, Edwin (1980) Capital Theory and Dynamics.
>Cambridge: Cambridge University Press).
Mr. Witte here tries to write out a whole body of literature. Calling
these ideas a "tired debate" is rhetoric in the bad sense - contentless.
And that is the view of only some literature. I have not been arguing
that disaggregated neo-classical theory is mistaken, but that it does
not support the aggregation apparently typical of Lucas' school of
macroeconomics. This conclusion is generally agreed on to a greater
or lesser extent in the literature. So Mr. Witte's comment about a
"spike in the heart of neo-classical theory" is irrelevant to my
use of the CCC here.
American historians will be astonished to learn they have enough
historical perspective to adequately treat the Vietnam war. I have
prepared for this idea of relegating the CCC to the history of
thought. Recall that Mr. Witte recommended a R.G.D. Allen book
of 1967 - the same era as the CCC. Does he remember writing:
MW> I would not suggest that logic spoils with age just as I would not
MW> suggest that anything new is worthless.
The problem with claiming the questions raised by the CCC have been
answered is that Neoclassicals do not have one common opinion on the
answers, as will be apparent below.
...
>> The point of this exercise is to show that disaggregated
>>Neoclassical models with heterogeneous capital goods do not support
>>the claim that the interest rate is equal to the marginal product of
>>"capital." I consider this argument to be on all fours since it is
>>well-established in the literature.
>
> In his posts, Mr. Vienneau has displayed failures of
>mathematics, economic reasoning, and now here, a failure of logic. It
>is easy to construct a neoclassical model with heterogeneous capital
>goods which does support the claim that the interest rate is equal to
>the marginal product of capital [See Samuelson, Paul A. (1962)
>"Parable and Realism in Capital Theory: The Surrogate Production
>Function" Review of Economic Studies, 29, pp. 193-206]. The school of
>thought to which Mr. Vienneau claims to attach himself argues that
>such cases are uninteresting. You cannot, as he asserts, show that
>all disaggregated neoclassical models do not support the claim.
>Furthermore, it is a poor research agenda which attempts to prove a
>negative.
I nowhere referred to "all disaggregated neoclassical models." In fact,
I wrote
RV> Equation 36 states that capital per head is the additive inverse of
RV> the slope of the tangent to the factor price frontier at the selected
RV> (r, w) point. But I have already shown that capital per head is the
RV> inverse of the slope of a particular secant passing through that
RV> point. In general, these slopes will differ. So the interest rate is
RV> *not* the marginal product of capital.
Note the use of the phrase "in general." Furthermore, I first referred
to that Samuelson paper, and explained its results. The marginal
product of a value measure of capital is the interest rate iff labor
values prevail. Would Mr. Witte accept that long term equilibrium
prices are labor values - no transformation necessary? If not, why
cite Samuelson?
Formerly, I have explictly cited Paul Davidson's new textbook as an
attractive alternative positive approach to macroeconomics. That
approach is not necessarily Neo-Ricardian.
> In the main body of his post (which I have not repeated in an
>effort to save band width), Mr. Vienneau shows that a general
>neoclassical model will produce different rates of return (defined as
>the own rates of return). This is the gist of the Frank Hahn paper
>that he enjoys citing so much. It is much less than he promised, and
>it misses entirely the point of the debate.
I would say the (debated) point of the Hahn paper is that the
Neo-Ricardian model is a special case of Neoclassical economics. I
brought up this divergence of own rates in Neoclassical models to
clarify my remarks in this interchange:
RV> I do have problems with the claim that in Neoclassical
RV> models, the rate of return is the same in all lines of
RV> production, abstracting from risk. For the sake of
RV> argument, we can assume that endowments just happen
RV> to be such that all own rates of interest are equal for
RV> all produced means of production actually produced.
>
MW> This is straight out of Ricardo's "falling rate of profit." Lines of
MW> production in the neo-classical model which pay a higher rate of
MW> return will attract resouces from other areas until the zero economic
MW> profit condition holds everywhere. The neo-classical model is an
MW> allocative general equilibrium model with mobile factors so that
MW> endowments don't really come into it.
Does Mr. Witte get Neoclassical economics correct here? I do agree this
is an aside to my main point.
>The question is whether or
>not, under reasonable conditions, we can define an aggregate measure
>of capital, whose marginal product equals the interest rate. Fans of
>neo-classical models are pleased to note that Burmeister (op. cit.)
>did this some 15 years ago, as I will now summarize for you.
This is not the same approach as the cited Samuelson paper.
> Suppose we believe that we live in a world in which steady
>state consumption (and utility) is lowered with increases in the
>interest rate. i.e. The higher is the interest rate, the more
>consumption we put aside for future generations and the less happy we
>are in the meantime!
No a priori reason exists to believe this is true. One of the main
points of the CCC was to show that previous rationales for this
sort of reasoning were mistaken.
>Given this (quite reasonable) assumption, we can
>derive a necessary and sufficient condition that our model economy
>needs to satisfy for this to be true. This is the condition given in
>Burmeister (1980) Theorem 4.3. An economy where this condition holds
>is called a "regular economy".
I might as well summarize this condition, since Mr. Witte doesn't.
Compare steady state pure circulating capital economies with the same
technological possibilities, but different interest rates. The
aggregate value of capital goods will differ because the prices of
given capital goods will vary with the interest rate (price Wicksell
effects) and because the appropriate composition of capital goods
will also vary (real Wicksell effects). The condition is that the
real Wicksell effect is negative, i.e. the change in composition
of capital goods with the rate of interest, when evaluated at the
original set of prices, will lower the value of capital with a rise
in the rate of interest.
I do not fully understand the index that allows aggregate production
functions, given this condition. It is not the value of capital goods.
>In such an economy it is possible to
>derive an index K and a function F(K) such that across steady state
>(for which read neoclassical supply and demand) equilibria the
>function F(K) has all the properties of the aggregate production
>function that Mr. Vienneau hates so much. In particular, the marginal
>product of the index K is equal to the rate of interest (profit). This
>is Theorem 4.4 in Burmeister (1980 op. cit.).
It's hard to believe that Burmeister thinks this result settles the
CCC. In his entry on "Wicksell Effects" in the _New Palgrave_,
Burmeister writes:
"The value of capital, however, is not an appropriate measure of the
'aggregate capital stock' as a factor of production except under
extremely restrictive conditions...This possibility - that (16)
[negative real Wicksell effects - RV] does not hold everywhere -
is perhaps the most interesting conclusion to emerge from the
Cambridge controversies...Imposing some set of conclusions on the
technology T() should be sufficient to assure that the real
Wicksell effect is always negative. Such conditions would be of
interest - especially if they could be empirically tested - since
they would validate the qualitative conclusions derived from the
one-good models often used in macroeconomics without any
theoretical justification for ignoring aggregation problems...
Unfortunately, no set of such sufficient conditions is known, but
the literature on capital aggregation suggests that they would
impose severe restrictions on the technology."
What can one say about a model where conditions on the data
(technology) cannot even be specified to justify its use, but it is
thought that such conditions would be "severe restrictions"?
I think this emphasis on aggregation might be misplaced. Consider an
extremely simple economy in a stationary state in which only one
consumption good is produced. Capital consists of a single good
functioning as pure circulating capital. Labor and the capital good
can produce either more of the capital good or the consumption good.
Net output, labor services, and capital services can each be measured
in their own technical unit with no aggregation problems. Variations
in the interest rate will be associated with continuous variations in
the wage and the price of the capital good. So one can differentiate
net output per head with respect to the value of capital. Yet the
interest rate need not be the marginal product of value capital here.
Why is Burmeister's index a more appropriate measure here? Why is a
similar index not needed for labor?
> Since models can be specified in a variety of ways, a very few
>following the path of the Neo-Ricardians (like Mr. Vienneau), most
>following the path of the modern neoclassical literature, the choice
>between these approaches cannot rely on existence alone.
Mathematics is mathematics, whichever side of the pond one may be on.
In this thread I have explicitly not relied on a Neo-Ricardian
interpretation.
>The choice
>of which route to take must be based on which specification seems more
>palatable ex ante and which one provides more predictive power. Is the
>rate of profit in the ice cream sector really of no interest to
>someone considering investing in the lawnmower sector?
This difference in profit rates among sectors is a characteristic of
the Neoclassical model of intertemporal equilibrium as in, say, Debreu
(1959). If Mr. Witte rejects this conclusion, he should reject
Neoclassical economics and accept Classical economics where all
rates of profit tend to equality in competitive conditions. This was
a major aspect of the argument in:
G. Dumenil and D. Levy, "The Classicals and the Neoclassicals: A
Rejoinder to Frank Hahn," _Cambridge Journal of Economics_, 1985.
>Do the
>empirical specifications of the models Mr. Vienneau prefers better
>fit the data? The evidence I have seen indicates that the answer to
>both questions is no. Thus it is no surprise that the field of
>economics has chosen the path it has.
I previously cited Franklin Fisher's simulation results to show why
the empirical success of aggregate production functions of the Cobb
Douglas form, at least, are no evidence that the conditions needed
to justify the use of aggregate production functions obtain.
> Mr. Vienneau (harkening back to a bit of work which had some
>following at Cambridge in the 1960's) has shown why care must be taken
>in the use of the aggregate production function in macroeconomic
>modeling. He hasn't provided an alternative model that can be used
>for macroeconomic questions. Burmeister shows explicitly the extra
>assumption needed for the aggregate production function approach to be
>valid, and then we are back to judging models based on their
>predictive power. The standard neoclassical macro model has been shown
>to yield useful predictions in a variety of circumstances and so would
>seem (to me at any rate) to be worth pursuing.
Notice that Mr. Witte has changed his tune. It's no longer the case
that the equality of rates of return in different lines of production
and profit maximizing justify aggregate measures of capital. It is not
the case that his simple story about why the prices of capital
services are the value of their marginal products applies equally to
disaggregated and aggregated measures equally.
We are agreed that the interest rate is the marginal product of capital
only in special circumstances.
> To sum up let's quote Frank Hahn whom Mr. Vienneau seems to
>count has his great ally in this debate.
[Amusing but irrelevant Hahn quote attacking the Neo-Ricardians deleted]
I'm quite aware of Frank Hahn is not a Neo-Ricardian. My point was always
rigorous Neoclassical general equilibrium theory does not support Mr.
Witte's original contentions. What does Frank Hahn have to say in the
quoted article that's relevant?
"The Sraffian picture of Neoclassical theory is this. At any moment
in time we can observe something physical called the stock of capital
(K) as well as the amount of labour (L). There is a concave production
function
Y = F( K, L )
where Y is output. In a neoclassical equilibrium all inputs are used
and must be paid their marginal products. The latter are known once
(K, L) are known. Hence the rate of profit of capital, the real wage
and the distribution of income are all known once F(), K and L are
known. The concavity of F further implies that the rate of return on
capital is non-increasing (generally decreasing) in K. This construction,
to be called the parable, Sraffians claim to be not logically
watertight except in the single good economy. In this they are
generally correct...
There is no doubt that in neoclassical economics as in macroeconomics
simple models are used in order to obtain definite answers and that
these models will not survive logical scrutiny. Whether they can be
useful nonetheless is a hard question which I cannot answer. But just
as the multiplier collapses when fixed prices are not assumed so does
the neoclassical parable claim that of two economies in Sraffian
equilibrium, the one with the higher rate of interest (profit) will
have the lower 'capital' labour ratio. Nor can one argue that the
economy with the higher interest rate will have lower consumption per
head. All of this is simply a reiteration of the proposition that
there is no valid aggregation of wheat and barley into something
called capital. But unless one wishes to claim that agregation is
essential if a theory is to be called neoclassical, so that Arrow-
Debreu for instance are not neoclassical, none of this has any
bearing on the main issue of this lecture. Sraffa performed a
service in showing how neoclassical arguments can be used to show
neoclassical aggregation parables to be in logical difficulties.
But that cannot help with a critique of marginal theory.
Notice that it is Mr. Witte' view, not mine, that Neoclassical theory
is aggregated.
Opinions may differ on which research programs are progressive and
which are degenerating. Scholars in a field should at least be taught
about the existence of contemporary research programs with significant
followings. Better, they should be taught about the achievements and
defects of competing research programs so they can make up their own
scores. How well does the teaching of economics meet this ideal?
Robert Vienneau
I have been following this debate with interest (as an
ex-Cambridge undergrad) and am glad to see that our protaginists are finally
beginning to understand one another and converge to something that may be
considered standard economic thought. It still seems, however, that Mr.
Vienneau has a little way to go and, although I'm sure it won't, I hope this
post helps him a little more or, at least, encourages him to put forward a
constructive way of looking at the macroeconomy to replace the one he seems to
detest so much. I have studied the Cambridge Controversies (I would argue
probably more so than you) and I really believe, as do most neo-classical
economists that the whole thing was a red herring. Of course, using an
aggregate for the stock of capital relies on certain conditions (c.f.
Burmeister's regular economy) but, again, the fact that models using it have
helped explain many macro issues is an obvious reason for continuing with the
approach. The approach still leaves some puzzles to explain and that is why
many macroeconomists are now working on models with heterogeneous capital
goods. (Also they are now in a position to do so since computing power has
advanced so much). Perhaps Mr. Vienneau could tell us his approach to solving
macro-problems (or is he one of those micro-economists who thinks that
worrying about things that affect everyone, i.e. the macroeconomy, is
pointless).
>He writes:
>
>> After reading all of Mr. Vienneau's posts, I had given up hope
>>of seeing him complete a correct mathematical exposition of his
>>thoughts. His most recent post at least convinced me that he can
>>(given enough time to work on his algebra!) provide a correct
>>mathematical exposition.
>
>If my last post is correct, my mathematics has been correct all
>along aside from my emendations. Given Mr. Witte's attacks on my
>"cravenness" in refusing to acknowledge the "mistakes" he found in
>my posts, he ought to admit he was wrong. If he now understands
>the mathematics, failure to do so in this context exhibits a want
>of character.
>
I'm afraid that this is the type of logical non sequitur that
Mr. Vienneau is famous for making. I would say, given how bad some of the
maths was earlier in the debate, it is refreshing to see him finally getting
his maths right. Now at least my fellow readers can finally follow what's
going on.
>>For your benefit, what he is trying to do is
>>revisit the Cambridge controversies of the 1960's.
>
>Here Mark demonstrates the Markov property - no memory. Some time
>ago in this thread, I wrote
>
>RV> The Cambridge Capital Controversy was a complex and multifaceted
>RV> affair. Two important Neoclassical summaries are Christopher Bliss'
>RV> book "Capital Theory and the Distribution of Income (1975) and Frank
>RV> Hahn's paper "The Neo-Ricardians" (Cambridge Journal of Economics, V.
>RV> 6, No. 4, 1982). Although Bliss and Hahn are not in total agreement,
>RV> they both argue that disaggregated Neoclassical theory is sound and
>RV> does not need an equation equating the demand and supply of "capital."
>
"A complex and multifaceted affair"? How, then, could Hahn
dismiss it all in just one short article?
Again disaggregated neo-classical theory may not support the
aggregation typical of ALL respected macroeconomics; the results achieved
using such models do!
>American historians will be astonished to learn they have enough
>historical perspective to adequately treat the Vietnam war. I have
>prepared for this idea of relegating the CCC to the history of
>thought. Recall that Mr. Witte recommended a R.G.D. Allen book
>of 1967 - the same era as the CCC. Does he remember writing:
>
>MW> I would not suggest that logic spoils with age just as I would not
>MW> suggest that anything new is worthless.
>
Personally I think that, with regards to economics
"It's all in Marshall"!
Read again Mr. Vienneau's paragraph above Mr. Witte's quote. I guess this was
just a slip that he had corrected later on in the post. Samuelson's paper does
NOT show that the marginal product of a value measure of capital equals the
interest IFF labour values prevail, he showed that they did IF labour values
prevail. There is a huge difference between those two statements that all our
fellow readers should be aware of. I'm sure Samuelson is cited here as an
example of how disaggregated and aggregated neoclassical theory CAN be in
agreement.
>Formerly, I have explictly cited Paul Davidson's new textbook as an
>attractive alternative positive approach to macroeconomics. That
>approach is not necessarily Neo-Ricardian.
>
I should read this (as probably should interested readers) as it might provide
me with what Mr. Vienneau has singularly failed to do - an alternative model!
>> In the main body of his post (which I have not repeated in an
>>effort to save band width), Mr. Vienneau shows that a general
>>neoclassical model will produce different rates of return (defined as
>>the own rates of return). This is the gist of the Frank Hahn paper
>>that he enjoys citing so much. It is much less than he promised, and
>>it misses entirely the point of the debate.
>
>I would say the (debated) point of the Hahn paper is that the
>Neo-Ricardian model is a special case of Neoclassical economics. I
>brought up this divergence of own rates in Neoclassical models to
>clarify my remarks in this interchange:
>
>RV> I do have problems with the claim that in Neoclassical
>RV> models, the rate of return is the same in all lines of
>RV> production, abstracting from risk. For the sake of
>RV> argument, we can assume that endowments just happen
>RV> to be such that all own rates of interest are equal for
>RV> all produced means of production actually produced.
>>
>MW> This is straight out of Ricardo's "falling rate of profit." Lines of
>MW> production in the neo-classical model which pay a higher rate of
>MW> return will attract resouces from other areas until the zero economic
>MW> profit condition holds everywhere. The neo-classical model is an
>MW> allocative general equilibrium model with mobile factors so that
>MW> endowments don't really come into it.
>
>Does Mr. Witte get Neoclassical economics correct here? I do agree this
>is an aside to my main point.
Unfortunately, as someone who knows and respects Mr. Witte, I have to believe
that he slips up here. The Ricardo argument is correct (inasmuch as that is
what Ricardo believed) but the whole point of neoclassical economics is that
endowments DO matter. I have talked to Mr. Witte about this and I am sure that
he is now in agreement.
>
>>The question is whether or
>>not, under reasonable conditions, we can define an aggregate measure
>>of capital, whose marginal product equals the interest rate. Fans of
>>neo-classical models are pleased to note that Burmeister (op. cit.)
>>did this some 15 years ago, as I will now summarize for you.
>
>This is not the same approach as the cited Samuelson paper.
>
Yes, readers, this is not the same approach as in the Samuelson paper! It was
good of Mr. Vienneau to point this out.
>> Suppose we believe that we live in a world in which steady
>>state consumption (and utility) is lowered with increases in the
>>interest rate. i.e. The higher is the interest rate, the more
>>consumption we put aside for future generations and the less happy we
>>are in the meantime!
>
>No a priori reason exists to believe this is true. One of the main
>points of the CCC was to show that previous rationales for this
>sort of reasoning were mistaken.
>
Mr. Vienneau is right again. This is an ASSUMPTION and like
all assumptions is not based on prior reasoning but on what we think is useful
for the model at hand. To quote Solow before using the aggregate production
function for the first time,
"All theory is based on assumptions ; that is what makes it theory!"
Incidentally, the Nobel committee, unlike Mr. Vienneau, cannot be too worried
about aggregation as that is what Solow received his Nobel Prize for.
>>Given this (quite reasonable) assumption, we can
>>derive a necessary and sufficient condition that our model economy
>>needs to satisfy for this to be true. This is the condition given in
>>Burmeister (1980) Theorem 4.3. An economy where this condition holds
>>is called a "regular economy".
>
>I might as well summarize this condition, since Mr. Witte doesn't.
>
>Compare steady state pure circulating capital economies with the same
>technological possibilities, but different interest rates. The
>aggregate value of capital goods will differ because the prices of
>given capital goods will vary with the interest rate (price Wicksell
>effects) and because the appropriate composition of capital goods
>will also vary (real Wicksell effects). The condition is that the
>real Wicksell effect is negative, i.e. the change in composition
>of capital goods with the rate of interest, when evaluated at the
>original set of prices, will lower the value of capital with a rise
>in the rate of interest.
>
>I do not fully understand the index that allows aggregate production
>functions, given this condition. It is not the value of capital goods.
>
Correct. But it shows that using "aggregate capital" may not
be such a bad "parable" after all. Again, models should be judged on
predictions - not assumptions!
... that macro models require assumptions made at a higher level than micor
models - no surprise for any student of economics here! "Severe restrictions"
are fine : When predicting the arc taken by a fired cannonball, Napoleon's
artillery were assuming that there was no air. (If that is not a "severe
restriction" what is?) Still, his guns did destroy a few cities!
>I think this emphasis on aggregation might be misplaced. Consider an
>extremely simple economy in a stationary state in which only one
>consumption good is produced. Capital consists of a single good
>functioning as pure circulating capital. Labor and the capital good
>can produce either more of the capital good or the consumption good.
>Net output, labor services, and capital services can each be measured
>in their own technical unit with no aggregation problems. Variations
>in the interest rate will be associated with continuous variations in
>the wage and the price of the capital good. So one can differentiate
>net output per head with respect to the value of capital. Yet the
>interest rate need not be the marginal product of value capital here.
>Why is Burmeister's index a more appropriate measure here? Why is a
>similar index not needed for labor?
>
Here, Mr. Vienneau is wrong. In such a simple economy, the
rate of interest does equal the marginal product of capital. Read any
intermediate or above macro textbook to see this case discussed ad nausiam.
Again, that is not the point. The point is, surely, the
"empirical success of aggregate production functions".
>> Mr. Vienneau (harkening back to a bit of work which had some
>>following at Cambridge in the 1960's) has shown why care must be taken
>>in the use of the aggregate production function in macroeconomic
>>modeling. He hasn't provided an alternative model that can be used
>>for macroeconomic questions. Burmeister shows explicitly the extra
>>assumption needed for the aggregate production function approach to be
>>valid, and then we are back to judging models based on their
>>predictive power. The standard neoclassical macro model has been shown
>>to yield useful predictions in a variety of circumstances and so would
>>seem (to me at any rate) to be worth pursuing.
>
>Notice that Mr. Witte has changed his tune. It's no longer the case
>that the equality of rates of return in different lines of production
>and profit maximizing justify aggregate measures of capital. It is not
>the case that his simple story about why the prices of capital
>services are the value of their marginal products applies equally to
>disaggregated and aggregated measures equally.
>
Yes, if that was Mr. Vienneau's point (and it had been difficult to answer
that question prior to his most recent post) then the argument is over. But
then, as Mr. Vienneau himself pointed out, it had been since Debreu!
>We are agreed that the interest rate is the marginal product of capital
>only in special circumstances.
>
>> To sum up let's quote Frank Hahn whom Mr. Vienneau seems to
>>count has his great ally in this debate.
>
>[Amusing but irrelevant Hahn quote attacking the Neo-Ricardians deleted]
>
Highly ammusing but relevant in the sense that Mr. Vienneau had done exactly
what Hahn was atacking : He had criticised the standard approach to
macroeconomics without proposing any alternative that could successfully
explain the macroeconomic time series that we observe.
I really don't think that that is Mr. Witte's view. It is clearly Frank Hahn's
view that the "aggregation parables" of Solow wer "neoclassical" but then this
is all semantics. Most economists today would just go about there business of
trying to explain the world without worrying what label they were operating
under. Is Mr. Witte a "New Classical"? I know him very well (or at least
better than Mr. Vienneau who claims this) and I have no idea!
>Opinions may differ on which research programs are progressive and
>which are degenerating. Scholars in a field should at least be taught
>about the existence of contemporary research programs with significant
>followings. Better, they should be taught about the achievements and
>defects of competing research programs so they can make up their own
>scores. How well does the teaching of economics meet this ideal?
>
> Robert Vienneau
>
Yes. Provided that these "contemporary research programmes with
significant followings" do indeed have "significant followings" and have
something constructive to say about the world rather than the destructive
comments of Mr. Vienneau (and similar people).
Just my tuppence worth.
--
**************************************************************************
* Maybe the time has gone, the faces I recall. *
* But things in this life change very slowly if they ever change at all. *
* No use in asking why, it just turned out that way. *
Stephen Millard has lots of interesting things to say, but I cannot
answer all his dodges. I'm really taking too much time on this. I do
think Stephen has seriously amended the position Mark Witte was
arguing.
Can I count the Post Keynesian theory of distribution as a
contribution of "Harcourt's school?" If so, doesn't having explicitly
pointed out by the late 50s the possibility of stagflation count as a
progressive contribution?
Can Stephen summarize Wynne Godley's approach to macroeconomics? (I'm
not claiming to be able to.)
Does Solow's rate of return characterize technical possibilities open
to an economy? Is it a tautology devoid of all explanatory power?
Anyway, I thought I had a telling point, or at least a question I'd
like to see an answer to:
RV>I think this emphasis on aggregation might be misplaced. Consider an
RV>extremely simple economy in a stationary state in which only one
RV>consumption good is produced. Capital consists of a single good
RV>functioning as pure circulating capital. Labor and the capital good
RV>can produce either more of the capital good or the consumption good.
RV>Net output, labor services, and capital services can each be measured
RV>in their own technical unit with no aggregation problems. Variations
RV>in the interest rate will be associated with continuous variations in
RV>the wage and the price of the capital good. So one can differentiate
RV>net output per head with respect to the value of capital. Yet the
RV>interest rate need not be the marginal product of value capital here.
RV>Why is Burmeister's index a more appropriate measure here? Why is a
RV>similar index not needed for labor?
But Stephen says the premises of my questions are wrong:
SM> Here, Mr. Vienneau is wrong. In such a simple economy, the
SM>rate of interest does equal the marginal product of capital. Read any
SM>intermediate or above macro textbook to see this case discussed ad
SM>nausiam.
So more tedious math. Sector 1 produces tons steel, sector 2 bushels
corn. Usual production functions:
1 = f1 ( a01, a11 ) (1)
1 = f2 ( a02, a12 ) (2)
Spot and forward prices for markets clearing at the beginning of the
year are:
p0 = price of a person-year
p1(1) = price of a ton steel available at year's start
p2(1) = price of a bushel corn available at year's start
p1(2) = price of a ton steel available at year's end
p2(2) = price of a bushel corn available at year's end.
Profit-maximizing leads to marginal productivity conditions:
p0 = p1(2) d f1/d a01 = p2(2) d f2/d a 02 (3)
p1(1) = p1(2) d f1/d a11 = p2(2) d f2/d a12 (4)
No pure economic profit exists:
p1(2) = a01 p0 + a11 p1(1) (5)
p2(2) = a02 p0 + a12 p1(1) (6)
Assuming quantity endowments happen to be those along a balanced
growth path, relative prices, wages w, and interest rate r are
constant. Assume wages are paid at the end of the year:
p0 = w/(1 + r) (7)
Now here I find I made a slip in the mathematics that my debating
partners accepted (although I mentally corrected it so my conclusions
were ok). The steel own interest rate is:
1 + r = p1(1)/p1(2), (8)
where my notation reflects that all own rates are equal. Thus,
p1( 1 ) = (1 + r) p1( 2 ) (9)
Let corn at year's start be the numeraire and p be the constant spot
price of steel. We have:
p1( 1 ) = p (10)
p1(2) = p/(1 + r) (11)
The corn own rate of interest is:
1 + r = p2(1)/p2(2). (12)
Since year's start corn is numeraire, I have:
p2(1) = 1 (13)
p2(2) = 1/(1 + r) (14)
The marginal productivity equations become:
w = p d f1/d a01 = d f2/d a 02 (15)
p (1 + r) = p d f1/d a11 = d f2/d a12 (16)
These are the marginal productivity conditions Mark Witte mistakenly
asserted, in a less than virtuoso performance, depended on an unstated
assumption of a Leontief technique.
The equations asserting costs are just covered become the Sraffian
system, as we all unconsciously assumed before:
a11 p (1 + r) + a01 w = p (17)
a12 p (1 + r) + a02 w = 1 (18)
At this point, I've outlined the simple 2-good long run equilibrium
model that, given r, determines the six unknowns a01, a02, a11, a12, w
and p. The price of a *ton* of steel is equal to the value of the
marginal product of (a physical quantity of) steel, but there's no
equation relating the interest rate to the marginal product of the
*value* of capital.
Relying on my previous exposition, the factor price frontier for a
given technique is:
w = [1 - a11 (1+r)]/[(a01 a12 - a11 a02)(1+r) + a02] (19)
This is generally not a straight line. So going by my previous
arguments about tangents and secants, the marginal product of the
value of capital, dy/dk, is generally not equal to the interest rate.
So with that out of the way, anybody want to answer my question? Why
is Burmeister's capital index appropriate here where net output
(assuming a stationary state), capital, and labor can all be measured
in their own technical units? Is there more to what's going on here
than aggregation problems?
I'm depressed about my above slip, but I'm still inclined to insist
that Mark Witte acknowledge his "corrections" of my previous
exposition of this model were mistaken. After all, his flames seemed
to fall on the following scale of politeness, in my opinion:
Human beings
Robert Vienneau
Major participants in the Cambridge Capital Controversy
Mark Witte
Some bystander comments on the Cambridge school, e.g. Harry
Johnson and Terence Hutchison. (Tied with Internet flames
in less serious fora)
My favorite bit of polemic in the CCC is the Solow article following
the much-referenced Samuelson paper. His preface explaining what's
going on stated merely that since apparently nobody read these
prefaces with understanding, he was going to start right in with the
mathematics. Stephen, what's yours?
Robert Vienneau
------------------------------------------------------------
And, more important, the construction of an appropriate
'index of aggregate capital' such as K may be impossible
because the index involves unobservable economic variables.
-- Edwin Burmeister
------------------------------------------------------------
The danger of lapsing into empty formalism and depriving the
theory of clear-cut results was of course recognized by several
suppy and demand theorists and considered a fundamental
weakness. In view of it some of them were prepared to dispense
with the alleged generality of neoclassical theory and return
to some version of traditional neoclassical analysis. After the
recent debate in capital theory this involved ruling out reswitching
and other 'perverse', i.e. non-conventional, phenomena in terms of
sufficiently bold assumptions about available techniques. It
comes as no surprise that given these assumptions the central
neoclassical postulate of the inverse relation between the
capital-labour ratio and the rate of profit should re-emerge as
'one of the most powerful theorems in economic theory' (Sato, 1974,
p. 355). However, in order to be clear about this move it deserves
to be stressed that it was motivated, as one author expressly
admits, by the fact that 'regular economies' have 'desirable
properties' (Burmeister, 1980, p. 124).
-- Heinz Kurz
------------------------------------------------------------
I'm a fairly quick study and just had to get out my old GE notes.
Mr. Vienneau's references were of little help since Northwestern's library
has a policy that beyond the top 30 journals in a subject, they are price
sensitive. However, I had studied the Burmeister book a bit and it's very
clear.
>He writes:
>
>> After reading all of Mr. Vienneau's posts, I had given up hope
>>of seeing him complete a correct mathematical exposition of his
>>thoughts. His most recent post at least convinced me that he can
>>(given enough time to work on his algebra!) provide a correct
>>mathematical exposition.
>
>If my last post is correct, my mathematics has been correct all
>along aside from my emendations. Given Mr. Witte's attacks on my
>"cravenness" in refusing to acknowledge the "mistakes" he found in
>my posts, he ought to admit he was wrong. If he now understands
>the mathematics, failure to do so in this context exhibits a want
>of character.
I'm sorry that you feel that I did not give you sufficient credit. I know what
you mean about questioning the character of net posters. I once called a guy
to account for a model in which he differentiates a Leontief production
function. Not only was this error never acknowledged, but he has consistently
suggested that my criticism was that his point rested on the use of the
Leontief technology. I've always assumed this was due to his lack of knowledge
about differentiability, rather than a cynical attempt to misrepresent my
arguments. I've had my doubts though about whether I've been too trusting.
You've given me pause to question my character. I was trying to be kind and
passed up shots at some of the other odd things you always have in your posts.
That's patronizing, and it does a disservice to your sincere desire to learn
more about neoclassical macroeconomic theory. I will make up for this
insensitivity. In your previous posting:
>RV> The problem with locating *the* rate of interest in a
>RV> model of intertemporal equilibrium is that there's no
>RV> room for money. All time is collapsed to a single point,
>RV> and the future is foreseen. An institution of
>RV> money does not make much sense in this context.
Interesting. You're suggesting that money's role is somehow to moderate the
effects of uncertainty. Your unmoved by the characeterization of money as a
medium of exchange, store of value and unit of account?
>RV> So far no mention has been made of interest rates. This is
>RV> because interest rates are a derivative phenomenon, of little
>RV> importance in themselves. But to understand capital theory,
>RV> they must be investigated.
Again, interesting on its face. The point of modelling is to explain a range
of economic phenomena. For example, development economics has found the
neo-classical approach to be very useful in explaining the variation in
interest rates across countries as a function of differences in their
capital-labor ratios.
>
>>For your benefit, what he is trying to do is
>>revisit the Cambridge controversies of the 1960's.
>
>Here Mark demonstrates the Markov property - no memory. Some time
>ago in this thread, I wrote
>
>RV> The Cambridge Capital Controversy was a complex and multifaceted
>RV> affair. Two important Neoclassical summaries are Christopher Bliss'
>RV> book "Capital Theory and the Distribution of Income (1975) and Frank
>RV> Hahn's paper "The Neo-Ricardians" (Cambridge Journal of Economics, V.
>RV> 6, No. 4, 1982). Although Bliss and Hahn are not in total agreement,
>RV> they both argue that disaggregated Neoclassical theory is sound and
>RV> does not need an equation equating the demand and supply of "capital."
Hmm, how did this tread get started? As I recall, you attacked someone who
suggested that the marginal product of capital was related to the level of
interest rates (hence the title of this thread). You made claim about how
this assertion was preposterous since neo-classical economists knew it to be
false but went ahead, pretending it to be true. You made some statement about
this being the reason for your choosing not to be a professional economist.
While Hahn admits that the stated formulation is correct, he does not argue
that it is interesting. You may remember the following from Hahn about this
school of thought which he calls a "Great Charade."
"Everyone agrees that the modelling of institutions by neoclassical economics
is too sparse. No one considers that we have a satisfactory accouint of
expections formations. No one believes that any actual economy can be studied
free of initial conditions ("history"). Now think of a single contribution of
Harcourt's group to a single one of these issues. Or put it the other way
round: think of a question you would like to ask of an actual economyu which
can be asnswered by means of Sraffa prices? Or if that is too much to ask:
what is the operational content of neo-Ricardian theory? What observation
will falsify it or at least make it doubtful? What observation will falsify
it or at least make it doubtful? Is it enough to say that "the profit rate"
is not observed and that there is almost universal joint production and
absence of constant returns? And if not, what issue intellectual or otherwise
is solved by what must then be taken as accounting identities?"
I know you find this amusing but irrelevant. It is amusing, but it's
precisely relevent.
If your point (always an elusive beast) was to suggest that models purporting
to aggregate heterogeneous capital are of no value, you must surely
acknowledge that you are wrong. Hahn is emphatically arguing that this
approach is the only one of value because it allows us to address interesting
economic issues, like "Are rising interest rates inflationary?"
Hahn is making the point that the way standard macro
handles this issue is a much better way to proceed than anything you are
advocating.
Do I really need to defend Lucas again? You'd better call Sweden before a
Nobel Prize is awarded.
You began venting your spleen with just the point that neoclassical theory
is wrong and everyone knows this but pretends otherwise.
>
>American historians will be astonished to learn they have enough
>historical perspective to adequately treat the Vietnam war. I have
>prepared for this idea of relegating the CCC to the history of
>thought. Recall that Mr. Witte recommended a R.G.D. Allen book
>of 1967 - the same era as the CCC. Does he remember writing:
Huh? A number of the historians here do work on the Vietnam war. I brought
up the Allen book because you where raising a stink about modern's making
this stupid mistake about r=MKP. Allen's book is frequently referenced in top
journals even now, the CCC stuff rarely is. Hence the term "tired debate."
Do you believe that no issue is ever settled and that the field can never move
on?
>
>MW> I would not suggest that logic spoils with age just as I would not
>MW> suggest that anything new is worthless.
>
>The problem with claiming the questions raised by the CCC have been
>answered is that Neoclassicals do not have one common opinion on the
>answers, as will be apparent below.
>
>...
>>> The point of this exercise is to show that disaggregated
>>>Neoclassical models with heterogeneous capital goods do not support
>>>the claim that the interest rate is equal to the marginal product of
>>>"capital." I consider this argument to be on all fours since it is
>>>well-established in the literature.
>>
>> In his posts, Mr. Vienneau has displayed failures of
>>mathematics, economic reasoning, and now here, a failure of logic. It
>>is easy to construct a neoclassical model with heterogeneous capital
>>goods which does support the claim that the interest rate is equal to
>>the marginal product of capital [See Samuelson, Paul A. (1962)
>>"Parable and Realism in Capital Theory: The Surrogate Production
>>Function" Review of Economic Studies, 29, pp. 193-206]. The school of
>>thought to which Mr. Vienneau claims to attach himself argues that
>>such cases are uninteresting. You cannot, as he asserts, show that
>>all disaggregated neoclassical models do not support the claim.
>>Furthermore, it is a poor research agenda which attempts to prove a
>>negative.
>
>I nowhere referred to "all disaggregated neoclassical models." In fact,
I think this is just the tirade you used to start this branch of the thread.
Moreover, let me quote from the fifth line of your previous post.
"The point of this exercise is to show that disaggregated Neoclassical
models with heterogeneous capital goods do not support the claim that
the interest rate is equal to the marginal product of "capital.""
So you are wasting our time to point out that *some* don't? And you have
reason to believe that these models tell us something useful about the world?
>I wrote
>
>RV> Equation 36 states that capital per head is the additive inverse of
>RV> the slope of the tangent to the factor price frontier at the selected
>RV> (r, w) point. But I have already shown that capital per head is the
>RV> inverse of the slope of a particular secant passing through that
>RV> point. In general, these slopes will differ. So the interest rate is
>RV> *not* the marginal product of capital.
>
>Note the use of the phrase "in general." Furthermore, I first referred
>to that Samuelson paper, and explained its results. The marginal
>product of a value measure of capital is the interest rate iff labor
>values prevail. Would Mr. Witte accept that long term equilibrium
>prices are labor values - no transformation necessary? If not, why
>cite Samuelson?
I brought up the Samuelson reference since it was one you had cited earlier
and which was a simple example of a model where the interest rate and the
marginal product of capital were equal. Samuelson's model is just one easy
specification, there are others with more relaxed assumptions.
>
>Formerly, I have explictly cited Paul Davidson's new textbook as an
>attractive alternative positive approach to macroeconomics. That
>approach is not necessarily Neo-Ricardian.
And his specifications have strong empirical implementations?
>
>> In the main body of his post (which I have not repeated in an
>>effort to save band width), Mr. Vienneau shows that a general
>>neoclassical model will produce different rates of return (defined as
>>the own rates of return). This is the gist of the Frank Hahn paper
>>that he enjoys citing so much. It is much less than he promised, and
>>it misses entirely the point of the debate.
>
>I would say the (debated) point of the Hahn paper is that the
>Neo-Ricardian model is a special case of Neoclassical economics. I
>brought up this divergence of own rates in Neoclassical models to
>clarify my remarks in this interchange:
>
>RV> I do have problems with the claim that in Neoclassical
>RV> models, the rate of return is the same in all lines of
>RV> production, abstracting from risk. For the sake of
>RV> argument, we can assume that endowments just happen
>RV> to be such that all own rates of interest are equal for
>RV> all produced means of production actually produced.
>>
>MW> This is straight out of Ricardo's "falling rate of profit." Lines of
>MW> production in the neo-classical model which pay a higher rate of
>MW> return will attract resouces from other areas until the zero economic
>MW> profit condition holds everywhere. The neo-classical model is an
>MW> allocative general equilibrium model with mobile factors so that
>MW> endowments don't really come into it.
>
>Does Mr. Witte get Neoclassical economics correct here? I do agree this
>is an aside to my main point.
It seems like a simple putty-clay specification.
>
>>The question is whether or
>>not, under reasonable conditions, we can define an aggregate measure
>>of capital, whose marginal product equals the interest rate. Fans of
>>neo-classical models are pleased to note that Burmeister (op. cit.)
>>did this some 15 years ago, as I will now summarize for you.
>
>This is not the same approach as the cited Samuelson paper.
True, there are many possible approaches which give the result which you
objected to in starting your branch on this tread.
>
>> Suppose we believe that we live in a world in which steady
>>state consumption (and utility) is lowered with increases in the
>>interest rate. i.e. The higher is the interest rate, the more
>>consumption we put aside for future generations and the less happy we
>>are in the meantime!
>
>No a priori reason exists to believe this is true. One of the main
>points of the CCC was to show that previous rationales for this
>sort of reasoning were mistaken.
And they have an approach with more empirical muscle?
The point of the CCC was pure negativism with no empirically falsifiable
hypotheses. It allowed a clique of economists to publish a few articles and
made neoclassical economists take more care in stating the conditions under
which aggregation is possible. However, I can't believe that even the most
dogmatic of the CCC people believed we lived in anything but a (possibly
non-market clearing) neo-classical world.
>
>>Given this (quite reasonable) assumption, we can
>>derive a necessary and sufficient condition that our model economy
>>needs to satisfy for this to be true. This is the condition given in
>>Burmeister (1980) Theorem 4.3. An economy where this condition holds
>>is called a "regular economy".
>
>I might as well summarize this condition, since Mr. Witte doesn't.
>
>Compare steady state pure circulating capital economies with the same
>technological possibilities, but different interest rates. The
>aggregate value of capital goods will differ because the prices of
>given capital goods will vary with the interest rate (price Wicksell
>effects) and because the appropriate composition of capital goods
>will also vary (real Wicksell effects). The condition is that the
>real Wicksell effect is negative, i.e. the change in composition
>of capital goods with the rate of interest, when evaluated at the
>original set of prices, will lower the value of capital with a rise
>in the rate of interest.
>
I'm glad you find something which with to agree. The regular economy
condition is less strong than this one. This condition enables one to use a
value aggregate of capital. In a regular economy we can use Burmeister's index
for capital. Again this is just a "parable", the point is that in a regular
economy standard neoclassical results (such as the inverse correlation between
rates of return and the capital:labour ratio) hold. I hope you go to look at
chapter 5 from Burmeister which explains that many of the feasible CCC
equilibria are even less interesting in a dynamic economy.
>I do not fully understand the index that allows aggregate production
>functions, given this condition. It is not the value of capital goods.
>
>>In such an economy it is possible to
>>derive an index K and a function F(K) such that across steady state
>>(for which read neoclassical supply and demand) equilibria the
>>function F(K) has all the properties of the aggregate production
>>function that Mr. Vienneau hates so much. In particular, the marginal
>>product of the index K is equal to the rate of interest (profit). This
>>is Theorem 4.4 in Burmeister (1980 op. cit.).
>
>It's hard to believe that Burmeister thinks this result settles the
>CCC.
The controversy is settled. Cambridge (England) won! In order to aggregate
you need to make further assumptions (viz. regular economy) - big wows! If
the model generates dynamics which match aggregate data, then these further
assumptions are not a problem.
I think we are back to your original post here, the one that so amazed and
annoyed me in the first place. You are saying that in one one sector model,
the marginal product of capital and the interest rate are unequal? Is this a
long run equilibrium model?
>
>> Since models can be specified in a variety of ways, a very few
>>following the path of the Neo-Ricardians (like Mr. Vienneau), most
>>following the path of the modern neoclassical literature, the choice
>>between these approaches cannot rely on existence alone.
>
>Mathematics is mathematics, whichever side of the pond one may be on.
>In this thread I have explicitly not relied on a Neo-Ricardian
>interpretation.
Ah, mathematics. If A and B are not disjoint, then proof of B is not a
proof that A is not true. That one specification works, it is not a reason to
avoid another valid specification which is more empirically useful.
>
>>The choice
>>of which route to take must be based on which specification seems more
>>palatable ex ante and which one provides more predictive power. Is the
>>rate of profit in the ice cream sector really of no interest to
>>someone considering investing in the lawnmower sector?
>
>This difference in profit rates among sectors is a characteristic of
>the Neoclassical model of intertemporal equilibrium as in, say, Debreu
>(1959). If Mr. Witte rejects this conclusion, he should reject
>Neoclassical economics and accept Classical economics where all
>rates of profit tend to equality in competitive conditions. This was
>a major aspect of the argument in:
>
> G. Dumenil and D. Levy, "The Classicals and the Neoclassicals: A
> Rejoinder to Frank Hahn," _Cambridge Journal of Economics_, 1985.
>
>>Do the
>>empirical specifications of the models Mr. Vienneau prefers better
>>fit the data? The evidence I have seen indicates that the answer to
>>both questions is no. Thus it is no surprise that the field of
>>economics has chosen the path it has.
>
>I previously cited Franklin Fisher's simulation results to show why
>the empirical success of aggregate production functions of the Cobb
>Douglas form, at least, are no evidence that the conditions needed
>to justify the use of aggregate production functions obtain.
You are saying that flexible formulations are bad? Flexibility is good in
that it shows that the specification is not driving the results.
>
>> Mr. Vienneau (harkening back to a bit of work which had some
>>following at Cambridge in the 1960's) has shown why care must be taken
>>in the use of the aggregate production function in macroeconomic
>>modeling. He hasn't provided an alternative model that can be used
>>for macroeconomic questions. Burmeister shows explicitly the extra
>>assumption needed for the aggregate production function approach to be
>>valid, and then we are back to judging models based on their
>>predictive power. The standard neoclassical macro model has been shown
>>to yield useful predictions in a variety of circumstances and so would
>>seem (to me at any rate) to be worth pursuing.
>
>Notice that Mr. Witte has changed his tune. It's no longer the case
My point from the beginning (I lack the flexibility of Robert Vienneau) is
that under valid conditions, arbitrage will bring the return on capital to the
underlying interest rate. This approach to modelling has been shown to be
very useful for understanding the world. This is my tune.
>that the equality of rates of return in different lines of production
>and profit maximizing justify aggregate measures of capital. It is not
>the case that his simple story about why the prices of capital
>services are the value of their marginal products applies equally to
>disaggregated and aggregated measures equally.
>
>We are agreed that the interest rate is the marginal product of capital
>only in special circumstances.
The reason this specification has come to dominate is that its "special
conditions" seem to match those we observe in the real world.
>
>> To sum up let's quote Frank Hahn whom Mr. Vienneau seems to
>>count has his great ally in this debate.
>
>[Amusing but irrelevant Hahn quote attacking the Neo-Ricardians deleted]
It's back! Care to reply to it's irrelevant critiques?
Whew, moving targets are hard to hit. Neoclassical economists do many things
because they can.
>Opinions may differ on which research programs are progressive and
>which are degenerating. Scholars in a field should at least be taught
>about the existence of contemporary research programs with significant
>followings. Better, they should be taught about the achievements and
>defects of competing research programs so they can make up their own
>scores. How well does the teaching of economics meet this ideal?
>
> Robert Vienneau
>
In the competitive market place of ideas, specifications which do well at
explaining the data or have other pleasing intuitive appeal get published.
Sterile formulations get a polite nod and are left to appear irregularly
in obscure journals, particularly those edited by friends of the writer.
To quote Mark Blaug from his book, "The Cambridge revolution: Success or
Failure",
"Anyone who has been attentive to the recent resurgence of the
neo-classical research programme in regional analysis, urban economics,
applied welfare economics, cost-benefit analysis, the economics of education,
labour economics, the economics of time, the economics of search and
information, the economics of crime, the economics of fertility, the economics
of marriage, the economics of private property rights -- the list is really
endless -- can hardly doubt that there is life yet in the concepts of
maximisaton, equilibrium, substitution and all other tricks of the trade of
mainstream economics. Cambridge UK, however it tries, cannot get along
without these ideas and in that lies the overwhelming superiority of the
neo-classical tradition in economic thought."
From my first reply to you, I have asked intuitively why you reject
the basic neo-classical specification. Even in my last post, I asked whether
you truly believed that investment in the ice-cream producing sector was not
affected by the rate of return in the lawn mower producing sector. As always,
my question was ignored.
I guess the basic question from this long running feud is whether you
think the class of models you seem to hold so dear do a better job of
describing the world. Well do you...?
These have been crossing in the mail, so I'm preparing a longish
response to an unanswered Mark Witte post that will answer some of his
questions. I do not see any reason to be embarassed about trying to
get the logic of an argument correct.
And Mark, I was generally interested in some of Stephen's answers to
my questions. Also, my last two good model had circulating capital,
not fixed. Even if it had fixed capital, there could be a very special
point where the price of steel is positive, but it is not produced,
i.e. the precise boundary between the two regimes. Of course, fixed
capital would change my math.
Some longish quotes, therefore tedious typing:
This is not the first exposition of stagflation in Post Keynesian
theory, but here's J. Robinson in Chapter 2 of _Essays in the Theory
of Economic Growth_ (1962):
"A Bastard Golden Age
We must now consider another type of limit upon
the rate of accumulation. Inflationary pressure,
bringing financial checks into operation, may
arise when there is no scarcity of labour -
indeed a great mass of non-employment - if the
real wage-rate refuses to be depressed below a
particular level. A higher rate of accumulation
means a lower real-wage rate. When the desired
rate of accumulation is greater than the rate
which is associated with the minimum acceptable
real wage, the desire must be checked. A situation
in which the rate of accumulation is greater than
the rate which is being held in check by the threat
of rising money wages due to a rise in prices (as
opposed to a rising money wages due to a scarcity
of labour) may be described as a bastard golden
age.
The rate of accumulation may be less or greater than
the rate of growth of population, so that non-employment
is increasing or diminishing...
A bastard golden age sets in at a fairly high level of
real wages when organized labour has the power to
oppose any fall in the real-wage rate. Any attempt to
increase the rate of accumulation, unless it is
accompanied by a sufficient reduction in consumption
out of profits, is then frustrated by an inflationary
rise in money-wage rates. In such a situation, the
rate of accumulation is limited by the 'inflation
barrier'."
Now for some Hahn quotes from "The neo-Ricardians." I agree with
Stephen Millard that Pasinetti has the better of the argument with
Solow over the rate of return. But I'm not so sure about Hahn:
"Hence, the defined rate of return (minus one)
measures the marginal rate at which consumption
at date 0 can be transformed into consumption at
date one. Putting it this way does not add anything
to what we already know from the theorem. Professor
Pasinetti however, is wrong to think it a tautology,
because (a) there would be no sense in the claim that
the rates of return in terms of numeraire are *determined*
by marginal productivity (marginal transformation rates).
To know the latter, we must know where on the
feasible set we are; (b) the fundamental theorem is not
in conflict with special classical saving hypothesis;
(c) strictly the latter is embodied in preferences and we
need to know these to get rates of return."
And the basis for my math is totally unoriginal:
"When the neoclassical economist arrives on the island, he
is told all the alternative ways known to islanders in which
each good can be produced by means of goods and labour. This
information is summed up by
1 = fj( a1j, a2j, a0j ), j = 1, 2 (10)
So there are constant returns to scale and no joint production.
Each function fj( ) shows all the combination of inputs capable
of producing one unit of output good j...
But we have now reached the first of our conclusions. It will be
agreed that you cannot get more neoclassical than differentiable
fj( ) and it will have been recognized that fji is the marginal
product of i in the production of j. In (14) and (15) *every*
possible marginal product has been used. It follows that if you
ask the neoclassical economist: but what 'determines' r? he
cannot find yet another marginal productivity to do it for him.
He is in *exactly* the same boat as the Sraffians, i.e. he needs
one more equation which cannot be derived from the production
relations which he has given. Moreover, notice the meaninglessness
of a sentence like: 'the marginal product of labour determines the
real wage'. You need to solve all nine equations to find either
labour's marginal product or the real wage. This was patiently
explained by Robertson (1931) and it is rather odd that neo-Ricardians
continue to assert that in neoclassical theory the rate of profit or
anything else is 'determined' by marginal productivity.
The reason I do not comment line by line on your corrections, Mark, is
I consider them complete nonsense. I do not see any point to get a
purchase on. In my first fixed capital model, I thought you were
confused about how the technique was chosen and objected to infinitely
long lasting capital goods. So I gave a circulating capital model in
which I explicitly showed how the technique was selected. Here you
were confused by the ability to measure the capital good in a single
technical unit, even though it differed from the consumption good. So
I posted a model with two capital goods in which this confusion was
not possible.
I think Stephen is confused by the concept of the "rental rate."
I realize that my use of factor price frontiers is not something in
the toolkit of every Neoclassical economist, but I expect Stephen to
be able to explain that they apply to both Leontief and continuous
microeconomic production functions. Furthermore, I'd like to see
somebody demonstrate that the interest rate is not equal to the
marginal product of the value of capital (excepting special cases)
without using factor price frontiers, only the equivalent marginal
productivity formulation.
Would somebody else like to attempt to explain the simple two good
case with one circulating capital good, one consumption good to Mark
and Stephen? Or at least endorse my mathematics?
As a consolation to the one making the math mistake, Ian Steedman
had to correct James Tobin's inability to get it right.
Robert Vienneau
"I came in praise of Witte, not to criticise him"!
Gentle reader,
A studious reader of this news group will be now have noticed
two different vintages of Mark Witte. On the one hand, there is the
macroeconomist, who by working through models and "tired old literature"
seeks to understand the economy as a whole. On the other hand we have Mark
Witte the microeconomist who believes that equilibrium occurs where supply
equals demand, the marginal products of each individual bit of capital are
equal to their own individual rental costs and these are different from each
other. Like wine, where one can like red or white (though I prefer red
("rusty tops?" rather than "French lagers") - Mr. Vienneau : Which is your
preference?), both "vintages" are correct and, as far as I know, have not
moved in their beliefs during this debate. "What is this tale supposed to
teach us?" Nothing much! I was just paraphrasing everybody's favourite
Samuelson paper! ;-)
I do not think that I have at all ammended the position
of Mark Witte who I believe has always been sceptical about the
usefulness of such anti-Neoclassical logic and who was, justifiably,
unhappy about the mathematical skills demonstrated in the earlier posts of
Mr. Vienneau. Also, I'm not sure what Mr. Vienneau means by dodges. It sounds
perjorative, but surely not. I can't imagine anyone writing, "So-and-so is
wrong, and of course, I could prove this, but I haven't the time." It would
seem that writers on the net would be bound by the rule of any sensible
debate: If you can't comment, don't.
>Can I count the Post Keynesian theory of distribution as a
>contribution of "Harcourt's school?" If so, doesn't having explicitly
>pointed out by the late 50s the possibility of stagflation count as a
>progressive contribution?
>
Did they point out the possibility of stagflation? I'm sure that interested
readers would like to know the reference. The neoclassical synthesis
of the fifties and sixties did ignore the supply side and hence ruled out the
stagflation which was a distinct possibility of the fully laid out
neoclassical macro model. Perhaps, the Post-Keynesian theory of inflation
(viz. "real wage resistance") had better predictive power (if you don't believe
that the high inflation in the seventies was caused by the Fed printing
dollars to finance Vietnam - I'll leave that one to historians!)
>Can Stephen summarize Wynne Godley's approach to macroeconomics? (I'm
>not claiming to be able to.)
>
If Mr. Vienneau (and other readers) are interested I might try in a later
post. Unfortunately, my copy of his macro textbook is currently in Portsmouth,
England whereas I am in Chicago. However, that will alter by Thursday and so
I'll be able to get back to that in a week or so.
>Does Solow's rate of return characterize technical possibilities open
>to an economy? Is it a tautology devoid of all explanatory power?
>
>
I think Mr. Vienneau knows the answer to that one. Yes, it is a tautology but
has little bearing on the rate of interest as implied by the time preference
of consumers. That is the one which, in a general equilibrium one good world,
will equal the Marginal Product of Capital as all our intermediate macro
textbooks tell us.
>Anyway, I thought I had a telling point, or at least a question I'd
>like to see an answer to:
>
>RV>I think this emphasis on aggregation might be misplaced. Consider an
>RV>extremely simple economy in a stationary state in which only one
>RV>consumption good is produced. Capital consists of a single good
>RV>functioning as pure circulating capital. Labor and the capital good
>RV>can produce either more of the capital good or the consumption good.
>RV>Net output, labor services, and capital services can each be measured
>RV>in their own technical unit with no aggregation problems. Variations
>RV>in the interest rate will be associated with continuous variations in
>RV>the wage and the price of the capital good. So one can differentiate
>RV>net output per head with respect to the value of capital. Yet the
>RV>interest rate need not be the marginal product of value capital here.
>RV>Why is Burmeister's index a more appropriate measure here? Why is a
>RV>similar index not needed for labor?
>
>So more tedious math. Sector 1 produces tons steel, sector 2 bushels
>corn. Usual production functions:
>
> 1 = f1 ( a01, a11 ) (1)
>
> 1 = f2 ( a02, a12 ) (2)
>
>Spot and forward prices for markets clearing at the beginning of the
>year are:
>
> p0 = price of a person-year
> p1(1) = price of a ton steel available at year's start
> p2(1) = price of a bushel corn available at year's start
> p1(2) = price of a ton steel available at year's end
> p2(2) = price of a bushel corn available at year's end.
>
These make no sense. If we are in a stationary state then prices will be
constant. Why not call p0/p2 w and p1/p2 p with the obvious implication
that corn is the numeraire? Also define r as the rental rate of steel i.e.
what a firm has to pay to rent one ton of steel for one year to use in
production. Then the first order conditions for the firms will imply that
w = f11(l1,s1) = f21(l2,s2)
and r = f12(l1,s1) = f22(l2,s2)
using obvious notation. Here f12 is the marginal product of steel in the
production of steel and f22 is the marginal product of steel in the
production of corn. Thus, I have, as promised, restored the standard
neoclassical result in the economy that Mr. Vienneau described. In his
description of the model which followed, Mr. Vienneau derived results that
are just not correct for an economy in steady state (where again prices
are constant over time). This, unfortunate display of poor maths leads me
to suggest that Mr. Vienneau always check his maths before posting.
>
>
>I'm depressed about my above slip, but I'm still inclined to insist
>that Mark Witte acknowledge his "corrections" of my previous
>exposition of this model were mistaken.
> After all, his flames seemed to fall on the following scale of politeness,
> in my opinion:
>
> Human beings
> Robert Vienneau
> Major participants in the Cambridge Capital Controversy
> Mark Witte
> Some bystander comments on the Cambridge school, e.g. Harry
> Johnson and Terence Hutchison. (Tied with Internet flames
> in less serious fora)
>
I always think of the House of Commons as the model of politeness.
To quote a typical exchange,
"As the honourable member for Portsmouth South pointed out using
woefully ignorant reasoning ..... "
Where would British MPs rate on your politeness scale, Mr. Vienneau?
Readers, it seems Mr. Vienneau has been hurt by his treatment in this
debate. Thinking of flames which remind me of heat. I vaguely recall a quote
from some U.S. President (one of the ones that wasn't assassinated, I think)
about heat and kitchens. But what do I know, I'm just some English guy.
>
>My favorite bit of polemic in the CCC is the Solow article following
>the much-referenced Samuelson paper. His preface explaining what's
>going on stated merely that since apparently nobody read these
>prefaces with understanding, he was going to start right in with the
>mathematics. Stephen, what's yours?
>
I would say, probably the same one. My interpretation of it was slightly
different though. I thought he was complaining that the participants in the
debate never speak to each other. (Unlike in this one!)
We are at least agreed on something!
> Robert Vienneau
Steve Millard
--
* Maybe the time has gone, the faces I recall. *
* But things in this life change very slowly if they ever change at all. *
* No use in asking why, it just turned out that way. *
* So meet me at midnight, baby, inside the sad cafe. *
There's no inconsistency. This debate was settled a long time ago and I mock
you for thinking it is still of interest.
>How does Stephen
>Millard respond to my pointing out this inconsistency? By a
>historically informed quip about Marshall. Is this accurately
>characterized as a dodge? I don't think it central so I do not chase
>after it other than to note his debating style. It does not surprise
>me that Mark and Stephen's style is informed by the House of Commons.
>(Even in insults, I would like to be called Robert. Although if
>Stephen could indulge in the most nasty form of address possible in
>the Commons, I'd be amused to see how he can add more honorifics to my
>last name.)
For people who are new to this tread, this is not of the more coherent things
Robert Vienneau has written. Given this, I would understand why anyone might
put this header in his or her kill file.
>
>These have been crossing in the mail, so I'm preparing a longish
>response to an unanswered Mark Witte post that will answer some of his
>questions. I do not see any reason to be embarassed about trying to
>get the logic of an argument correct.
>
>And Mark, I was generally interested in some of Stephen's answers to
>my questions. Also, my last two good model had circulating capital,
>not fixed. Even if it had fixed capital, there could be a very special
>point where the price of steel is positive, but it is not produced,
>i.e. the precise boundary between the two regimes. Of course, fixed
>capital would change my math.
Robert Vienneau, you've posted four models. Two of them may have been correct
but were uninteresting. The other two (the first and last) were just silly
and wrong. It's good that you did not repost your last model, why dig the
hole any deeper?
>
>Some longish quotes, therefore tedious typing:
>
>This is not the first exposition of stagflation in Post Keynesian
>theory, but here's J. Robinson in Chapter 2 of _Essays in the Theory
>of Economic Growth_ (1962):
>
>
[SNIP]
When losing a debate, it's good to change the subject. This long string of
posts was concerning whether models which equated the marginal product of
capital with the interest rate have any value. So why is Robert Vienneau
going off in this tangent about hyperinflation? Perhaps it is less painful
than admitting he's been wasting a lot of time on something silly.
[As have I by replying and anyone who bothered to read all this stuff.]
>
>The reason I do not comment line by line on your corrections, Mark, is
>I consider them complete nonsense. I do not see any point to get a
>purchase on.
I see, you are right but you can't say why. There's a socialist newspaper
salesman who frequents a corner near here who uses similar logic.
>In my first fixed capital model, I thought you were
>confused about how the technique was chosen and objected to infinitely
>long lasting capital goods. So I gave a circulating capital model in
>which I explicitly showed how the technique was selected. Here you
>were confused by the ability to measure the capital good in a single
>technical unit, even though it differed from the consumption good. So
>I posted a model with two capital goods in which this confusion was
>not possible.
Well, the errors you made on the first and last models where more basic and
the confusion was probably more on your end.
How about a compromise. Suppose that I were to conceed that all your models
were breathtakingly original and correct. Even if this were so, why are they
in any way interesting? How do the special cases they represent tell us
anything about the world in which we live? How do their predictions dominate
those of the standard neo-classical model?
[This line of questioning has been raised in my every reply to Mr. Vienneau
but he seems to react to it the way a Vampire reacts to a cross.]
>
>I think Stephen is confused by the concept of the "rental rate."
>
>I realize that my use of factor price frontiers is not something in
>the toolkit of every Neoclassical economist, but I expect Stephen to
>be able to explain that they apply to both Leontief and continuous
>microeconomic production functions.
I'd like Stephen to wash my car. How does this apply to the issue of why the
specification you love so dearly is better than the one which is used by
mainstream economics?
Furthermore, I'd like to see
>somebody demonstrate that the interest rate is not equal to the
>marginal product of the value of capital (excepting special cases)
>without using factor price frontiers, only the equivalent marginal
>productivity formulation.
You would like someone to re-type those passages out of Burmeister's book
again?
>
>Would somebody else like to attempt to explain the simple two good
>case with one circulating capital good, one consumption good to Mark
>and Stephen? Or at least endorse my mathematics?
Your cry for help is noted.
>
>As a consolation to the one making the math mistake, Ian Steedman
>had to correct James Tobin's inability to get it right.
>
> Robert Vienneau
Again, why do you think that models which satisfy the condition that the
interest rate not equal the marginal product of capital are in any way
interesting for describing our world? This is the critique raised by Hahn,
Burmeister, Stephen, me, and any number of other people. This is a critique
utterly dodged by you in each of your posts.
It is amazing to see Robert Vienneau accuse Steve Millard (or anyone)
of engaging in "dodges."
>I'm really taking too much time on this. I do
>think Stephen has seriously amended the position Mark Witte was
>arguing.
>
I don't think so. My point from the beginning is that it's perfectly
reasonable to model the economy with an arbitrage condition that leads to the
marginal product of capital being equal to the interest rate. Robert Vienneau
began this branch of this thread by claiming the opposite.
>
>Can I count the Post Keynesian theory of distribution as a
>contribution of "Harcourt's school?" If so, doesn't having explicitly
>pointed out by the late 50s the possibility of stagflation count as a
>progressive contribution?
>
>Can Stephen summarize Wynne Godley's approach to macroeconomics? (I'm
>not claiming to be able to.)
>
>Does Solow's rate of return characterize technical possibilities open
>to an economy? Is it a tautology devoid of all explanatory power?
And Robert Vienneau accuses Steve of dodging?
>
>
>Anyway, I thought I had a telling point, or at least a question I'd
>like to see an answer to:
>
>RV>I think this emphasis on aggregation might be misplaced. Consider an
>RV>extremely simple economy in a stationary state in which only one
^^^^^^^^^^ ^^^^^
>RV>consumption good is produced. Capital consists of a single good
>RV>functioning as pure circulating capital. Labor and the capital good
>RV>can produce either more of the capital good or the consumption good.
>RV>Net output, labor services, and capital services can each be measured
>RV>in their own technical unit with no aggregation problems. Variations
>RV>in the interest rate will be associated with continuous variations in
>RV>the wage and the price of the capital good. So one can differentiate
>RV>net output per head with respect to the value of capital. Yet the
>RV>interest rate need not be the marginal product of value capital here.
>RV>Why is Burmeister's index a more appropriate measure here? Why is a
>RV>similar index not needed for labor?
>
>But Stephen says the premises of my questions are wrong:
>
>SM> Here, Mr. Vienneau is wrong. In such a simple economy, the
>SM>rate of interest does equal the marginal product of capital. Read any
>SM>intermediate or above macro textbook to see this case discussed ad
>SM>nausiam.
>
>So more tedious math. Sector 1 produces tons steel, sector 2 bushels
>corn. Usual production functions:
>
> 1 = f1 ( a01, a11 ) (1)
>
> 1 = f2 ( a02, a12 ) (2)
>
Once again, Robert Vienneau is presenting a perfectly silly model. He claims
that it is a stationary state long run equilibrium model, but it is clearly no
such thing. If it's a steady state, why would any steel be produced? There's
no depreciation so any steel produced would increase output and capital
intensity.
[SNIP]
> These are the marginal productivity conditions Mark Witte mistakenly
> asserted, in a less than virtuoso performance, depended on an unstated
> assumption of a Leontief technique.
A virtuoso performance is Pavarotti singing "Nessun Dorma." A less than
virtuoso performance is Alphafa singing "I Love You Truly." Catching Robert
Vienneau's elementary math error was closer to the latter than the former.
The fact that you can't understand that the way you specified that model was
clearly Leontief is laughable.
>
>The equations asserting costs are just covered become the Sraffian
>system, as we all unconsciously assumed before:
>
> a11 p (1 + r) + a01 w = p (17)
>
> a12 p (1 + r) + a02 w = 1 (18)
>
>At this point, I've outlined the simple 2-good long run equilibrium
>model that, given r, determines the six unknowns a01, a02, a11, a12, w
>and p. The price of a *ton* of steel is equal to the value of the
>marginal product of (a physical quantity of) steel, but there's no
>equation relating the interest rate to the marginal product of the
>*value* of capital.
>
>Relying on my previous exposition, the factor price frontier for a
>given technique is:
>
> w = [1 - a11 (1+r)]/[(a01 a12 - a11 a02)(1+r) + a02] (19)
>
>This is generally not a straight line. So going by my previous
>arguments about tangents and secants, the marginal product of the
>value of capital, dy/dk, is generally not equal to the interest rate.
>
>So with that out of the way, anybody want to answer my question? Why
>is Burmeister's capital index appropriate here where net output
>(assuming a stationary state), capital, and labor can all be measured
>in their own technical units? Is there more to what's going on here
>than aggregation problems?
>
>
>I'm depressed about my above slip, but I'm still inclined to insist
>that Mark Witte acknowledge his "corrections" of my previous
>exposition of this model were mistaken.
I have posted corrections to your previous posts. If you disagreed with my
posts, correct my errors on a copied post. The way you post a new and
different model each time I raise an objection hardly indicates confidence you
your part.
I would be delighted to see you repost your original model and have a tutorial
on what Leontief means.
>After all, his flames seemed
>to fall on the following scale of politeness, in my opinion:
>
> Human beings
> Robert Vienneau
> Major participants in the Cambridge Capital Controversy
> Mark Witte
> Some bystander comments on the Cambridge school, e.g. Harry
> Johnson and Terence Hutchison. (Tied with Internet flames
> in less serious fora)
>
This doesn't make any sense to me. Your whole persistence in flogging this
long settled bit of trivia doesn't make much sense either.
The basic question which you have dodged in every post you have made is why
you prefer the specification you do to the valid and very useful one employed
by modern neo-classical economists?
>
>My favorite bit of polemic in the CCC is the Solow article following
>the much-referenced Samuelson paper. His preface explaining what's
>going on stated merely that since apparently nobody read these
>prefaces with understanding, he was going to start right in with the
>mathematics. Stephen, what's yours?
You claim you don't have time to respond to all of Steve's "dodges" but you
have time to post all this crap?
Here's a nice "polemic" from Burmeister's book.
"Under assumptions that make the question meaningful, the necessary
and sufficient condition for consumption efficiency in an
infinite-time-horizon problem -- the Cass condition that the consumption price
sequence does not grow too fast -- is exactly the same as for the
one-capital-good case.
Perhaps the primary conclusion to be drawn is that economic theory is
able to provide useful results even when the existence of heterogeneous goods
makes the task more difficult. All too often, though, these complications are
worsened by posing irrelevant questions rather than examining only hte
feasible dynamic options stressed here."
>
> Robert Vienneau
>------------------------------------------------------------
Let n = the number of times I've replied to you.
For the n'th time, what does your prefered specification explain about the
world that neo-classical model does not? For that matter, what do your models
say about the world at all?
The Marshall quip a dodge? I thought a dodge was what Al Bundy drives. No, the
point about not being interested in papers written in the 60s is that economic
thought has progressed since then as has, although this is not relevant in
this particular case, society. (Papers about trade under a fixed exchange
rate, capital flow controlled system just wouldn't cut it any more!). The
debates of the 1960s were settled in the 1960's. Burmeister and Hahn have both
told us that they are red herrings and that we shouldn't be worried about
using neoclassical theory (provided that when we aggregate we realise that
this involves additional assumptions). The way the debate was carried out and
the logic used to solve the arguments is timeless, viz. we are having an
extremely similar debate and using basically identical logic (save for a few
mathematical errors!). It is interesting to note debating style (perhaps
people could start a new thread on this one if they were so inclined). The
English style (as epitomised by the Commons) is much more sarcastic
than the American style (as epitomised by Congress). What is interesting is
that Mark Witte should have developed such an English style. Comments Mark?
Now to business. In my (neoclassical) world the households own the capital
(which I'm sure is the steel of Robert's model unless I am very confused).
They rent this steel to the producers of both sectors at the price of r per
unit of capital per period. That is what I mean by the "rental rate", Robert.
When steel is produced the consumers buy it. This, of course, means foregone
consumption so this begs the question, "Why would they do that?" The answer is
that by renting out their holdings of capital they can obtain an income which
they can use to buy corn (the consumption good of Robert's model). As a mental
exercise, let's consider what happens when I forego 1 unit of corn today. As
corn is the numeraire and the relative price of steel is p (Note that we are
taking these as given - p is determined in equilibrium). So given my one unit
of foregone corn, I can buy 1/p units of steel. This will earn me r/p "rental
income" next period. (We are in a stationary state remember. Robert forgot
this.) Thus, we can think of r/p as the "rate of interest" in
this model (i.e. the amount of "next period" consumption we can get by
foregoing one unit of consumption this period). As I showed in my last post
the first order (profit maximising) conditions for the firm (which would be
the same ones that Robert would get in a steady state) imply that
f12(l1,s1)/p = f22(l2,s2) = r/p
i.e. The Marginal Product of Capital (Steel) in each sector expressed in terms
of units of steel is equal to r/p the "rate of interest". Now, out of
equilibrium (which in this non-stochastic world is the steady state) these
equations wouldn't hold (Robert's version of them is correct) but then we're
arguing about equilibrium so this is not an issue. One more thing for
neoclassical fans. Suppose consumers were using a discount factor of beta and
we had 100% depreciation. Then we would have the following (familiar) equation
r/p = 1/beta
(Robert perhaps you would like to work through this one?)
On other matters, I was very impressed by Robert's quote from Joan Robinson. I
have read this essay (though it was many years ago) and so should have
remembered it. Kudos to Robert! However, as I said in my last post stagflation
is very possible in a neoclassical world as well! As to the rate of return
argument, yes Hahn is correct here (as he invariably is!) but see Burmeister's
book Chapter 5 for why it is the case that for this concept to be
meaningfully defined we must be living in a "regular economy". Factor price
frontiers are not something in the toolkit of every neoclassical economist.
Perhaps they should be? I think that most macroeconomists are just not
interested in the implied trade off between wages and profits. Profits go to
small shareholders (people like you and me who work for wages) and pension and
investment funds. These are held by the same people who like you and me work
for wages. In other words, in a modern society, capitalists and labourers are
typically the same people so the macroeconomic assumption that all profits are
distributed to consumers in the form of dividends is not way off the mark.
I've probably set myself up for a whole new debate here but I'm sure that
Robert will understand that I was only suggesting a possible reason for the
lack of interest in a wage-profit frontier.
To close, I think that the protaginists in this debate are coming much closer
together than they would care to admit. I hope that the whole thing has been
educational for all of our readers and I am looking forward to my holiday in
England where I will be visiting (among others) the place where this all
started back before I was even born!
Stephen Millard
Maybe responses to this unanswered Mark Witte post are pointless at
this point, but...
MW>Hmm, how did this thread get started? As I recall, you
MW>attacked someone who suggested that the marginal product of
MW>capital was related to the level of interest rates (hence the
MW>title of this thread). You made claim about how this
MW>assertion was preposterous since neo-classical economists
MW>knew it to be false but went ahead, pretending it to be true.
MW>You made some statement about this being the reason for your
MW>choosing not to be a professional economist.
If I were a professional, I would find that many would dismiss my
interests out of hand and argue that the schools in which I'm
interested do not exist. Out of curiousity, does Northwestern's limit
to the 30 top journals in economics include either the _Journal of
Post Keynesian Economics_ or the _Journal of Economic Issues_? Can
somebody tell me whether these or the _Cambridge Journal of Economics_
are available at the U. of Chicago?
MW>While Hahn admits that the stated formulation is correct, he
MW>does not argue that it is interesting. You may remember the
MW>following from Hahn about this school of thought which he
MW>calls a "Great Charade."
I'm amazed at Hahn's suggestion that the dependence on intial
conditions of the solution path to a clockwork model sets the model in
history. Really?
MW>Hahn is making the point that the way standard macro handles
MW>this issue is a much better way to proceed than anything you
MW>are advocating.
I do not read Hahn as necessarily defending macro, as opposed to G.E.
I do not see that I've really advocated much of anything yet in this
thread. I have given a couple of references. I do not see anything
wrong with a theoretical argument about the consistency of different
aspects of an approach to modeling.
(And, by the way, I could have picked other problems. One I cannot
explain is that the aggregate behavior of utility maximization on the
part of many individuals *generally* cannot be represented by the
utility maximization of a representative individual. See Kirman's
article in the _Journal of Economic Perspectives_ in the last 2 or 3
years. The other problem with Lucas' work that leaps to my mind is a
reliance on ergodicity. The alternative to rational expectations is
not systematic error, but learning problems in nonergodic processes. I
think Lucas has commented on ergodicity.)
MW>The controversy is settled. Cambridge (England) won! In
MW>order to aggregate you need to make further assumptions
MW>(viz. regular economy) - big wows! If the model generates
MW>dynamics which match aggregate data, then these further
MW>assumptions are not a problem.
Cambridge, England won the battle, but lost the war. Has mainstream
practice been affected at all? Do they even perceive that Cambridge
offered an alternative? (See below.) Does the mainstream see their
research program as increasingly ad hoc and degenerative?
Furthermore, what are legimate and illegimate uses of aggregate
production functions? For legimate uses, I might be willing to include
simplifications when explaining a model whose emphases lie elsewhere
and demonstrating the consistency of a theory with assumptions of
"regularity." For example, once upon a time in sci.econ, I explained
the golden rule of growth in an aggregate setting, when that setting
is not necessary. I also once demonstrated that the Pasinetti paradox
is consistent with regularity.
An illegimate use is the teaching of economics such that students are
conveyed the impression that regularity follows from maximizing
behavior and the "reasonable" assumptions often imposed in G.E. to
ensure existence. Mark seems to have offered something like this
impression in his natural language comments about the technicalities.
I suspect many economists convey this impression to beginners.
I also think - and I expect Mark to be amazed and annoyed - that the
use of aggregate production functions in empirical work is rarely
justified. One might be able to accept it as an illustration of a
model with greater expansion elsewhere, perhaps, but that's about all.
Now for my claim that Mark has an imprecise understanding of what's
needed for aggregation to support the Neoclassical parable:
MW>My point from the beginning (I lack the flexibility of Robert
MW>Vienneau) is that under valid conditions, arbitrage will bring the
MW>return on capital to the underlying interest rate. This approach
MW>to modelling has been shown to be very useful for understanding
MW>the world. This is my tune...
MW>...From my first reply to you, I have asked intuitively
MW>why you reject the basic neo-classical specification. Even in
MW>my last post, I asked whether you truly believed that
MW>investment in the ice-cream producing sector was not
MW>affected by the rate of return in the lawn mower producing
MW>sector. As always, my question was ignored.
Assume the economy is competitive in the sense that there is free
entry and exit, and finance is free to flow where it will. I accept
this as a fruitful model of a competitive economy. I think this is a
*Classical* criterion, not a Neoclassical idea. I do not see that I am
here assuming that agents take prices as given.
Furthermore, ignoring important difficulties, assume the expectations
on which investments are made are actually realized. Then I expect the
rate of profit in different sectors to be equal. I am less sure that
the rate of profit should be modeled as equal to the money rate of
interest, not above it. This assumption would confine a whole
structure of financial institutions and intermediaries to the short
run. But, for purposes of discussion and simplicity, I have almost
always assumed so.
My claim is that this story does *not* justify the Neoclassical
parable (except under special conditions). The Sraffian system shows
the realization of this story. Yet it is perfectly compatible with a
failure of the Neoclassical parable.
I am perfectly aware that financial analysts talk about "the cost of
capital" as being the risk-free rate of interest, generally taken to
be the rate of interest on government bonds. And I accept this story
(minus my proviso) will make the cost of capital equal to the rate of
interest. I fail to see what this has to do with the claim that the
marginal product of value capital equals the rate of interest, as that
claim is taken in rigorous theory.
MW>And they have an approach with more empirical muscle? The
MW>point of the CCC was pure negativism with no empirically
MW>falsifiable hypotheses. It allowed a clique of economists
MW>to publish a few articles and made neoclassical economists
MW>take more care in stating the conditions under which
MW>aggregation is possible. However, I can't believe that even
MW>the most dogmatic of the CCC people believed we lived in
MW>anything but a (possibly non-market clearing) neo-classical
MW>world.
Ignoring the tone, I still couldn't disagree more. I do not think
Kalecki, Kaldor, Robinson, or Sraffa thought Neoclassical theory could
cast much, if any light, on real world capitalist economies. By
Neoclassical theory, in this context, I mean either General
Equilibrium theory, as in Walras or Debreu, and aggregate
macroeconomics as expounded by Mark. The relationships of the above
Cambridge-school economists to Marshall is more problematic.
I assume Mark's reference to non-market clearing is to the claim that
Keynesian economics is a special case of Neoclassical macroeconomics
in which some prices are sticky or rigid or the auctineer is discarded
(usually with no theory replacing him whatsoever?). This makes
Keynesianism a special case of macro, which recall is a special case
of G.E. I think leading Post Keynesians would reject this
characterization of Keynes as a special case of a special case
entirely.
Let me expand by noting three possible readings of Sraffa's book, a
cryptic but key text in this discussion.
1. As part of a Neoclassical G.E. model within which one can
investigate the consistency and coherence of various ideas. This is
all I have been doing in this thread.
2. As a rediscovery of a Classical logic. Sraffian prices are
Classical 'natural prices' or Marxian 'prices of production'. I don't
know that it's more relevant here or above, but notice the similarity
between the subtitle of the first volume of Marx's _Capital_, "A
Critique of Political Economy," and Sraffa's subtitle "Prelude to a
Critique of Economic Theory."
3. As an exposition of a price system consistent with Keynes _General
Theory_. Quantity flows are determined by investment decisions prior
to prices, not mutually determined. Say's law need not not hold.
Readings 2 and 3 offer a route forward, although it still needs to be
more articulated. Sraffians have spent a lot of time arguing with
Neoclassicals in the context of the internal critique suggested by 1,
revolutionizing the history of economic thought as suggested by 2, and
arguing with Marxists also as suggested by 2.
I also understand those who think Sraffa represents the culmination of
certain traditions and the way forward lies elsewhere. Geoff Hodgson
and Philip Mirowski represent two economists who I find interesting
along these lines. Nor is it the case that I think economists outside
of Post Keynesianism are worthless. I do think Neoclassical
macroeconomics, apparently as advocated by Mark Witte, is not a
fruitful path.
MW> I guess the basic question from this long running
MW>feud is whether you think the class of models you seem
MW>to hold so dear do a better job of describing the world.
MW>Well do you...?
As you can see, I have barely mentioned the approaches I find
worthwhile. The models you think I hold so dear, Neoclassical G.E.
interpretations of certain mathematics, I think have next to no
empirical implications.
The approaches I like seem worthwhile to me on intuitive grounds. They
leave room open for history to enter in. They are not a-institutional.
They do not depict firms as passively adjusted to consumer maximizers
who ultimately determine the economy. They allow investment decisions
to create the environment in which it is determined whether the
expectations underlying them are realized. They have room for
dynamics. They depict the economy as having multiple centers of
power. They even allow for an element of class struggle in the
determination of income.
Of course, these approaches could stand greater articulation.
(And, Mark, I am not impressed with the paragraphs following the
paragraphs you quoted from Hahn and Blaug.)
I'm not sure if Stephen will be physically able to participate
shortly. If I were in England, I'd think I'd prefer sampling pints of
ales and bitters at the neighberhood pub, but what do I know? I'm just
some guy from the U.S.A.
SM>The way the debate was carried out and
SM>the logic used to solve the arguments is timeless, viz. we are having an
SM.extremely similar debate and using basically identical logic (save for a
SM>few mathematical errors!).
I certainly would not say the presence of mathematical errors
distinguishes our discussion from the CCC.
I want to think more about Stephen's mathematics. I'll confine myself
to one short note:
SM>The Marginal Product of Capital (Steel) in each sector expressed
SM>in terms of units of steel is equal to r/p the "rate of interest".
I, of course, still deny the marginal product of a numeraire unit of
capital (a bushel corn unit of steel) is necessarily equal to the rate
of interest. But I do not think I am denying anything Stephen is
asserting.
SM>On other matters, I was very impressed by Robert's quote from Joan
SM>Robinson...However, as I said in my last post stagflation
SM>is very possible in a neoclassical world as well!
I judge research traditions more dialectically. A tradition gets less
credit for showing their model conforms to a phenomenon after the
event than for pointing out its possibility beforehand when all other
traditions are denying it. Furthermore, consider this claim. Once upon
a time, Neoclassical economists thought that an increase in capital
intensity with a decline in interest rates was a logical consequence
of profit maximizing and substitution behavior. (I do not claim to
know the necessary history to justify that statement.) After the CCC,
Neoclassical economists introduced ad-hoc adjustments to retain this
belief. If so, this adjustment is characteristic of a degenerating
research program.
SM>...Factor price frontiers are not something in the toolkit of
SM>every neoclassical economist. Perhaps they should be? I think
SM>that most macroeconomists are just not interested in the
SM>implied trade off between wages and profits. Profits go to
SM>small shareholders (people like you and me who work for wages)
SM>and pension and investment funds. These are held by the same
SM>people who like you and me work for wages. In other words, in a
SM>modern society, capitalists and labourers are typically the same
SM>people so the macroeconomic assumption that all profits are
SM>distributed to consumers in the form of dividends is not way off
SM>the mark. I've probably set myself up for a whole new debate here
SM>but I'm sure that Robert will understand that I was only suggesting
SM>a possible reason for the lack of interest in a wage-profit frontier.
Instead of arguing about the truth value of these statements, do you
want we to argue that mainstream economics reflects a certain
apologetic political vision?
Robert Vienneau
---------------------------------------------------
"An *aggregate production function* is designed to
represent many complex microrelations of production
in simple terms. The quest for simplicity is most
certainly laudable. It should be noted, however, that in
contributions to aggregation theory we learn that the
conditions for consistent aggregation of micro relations
of production to a macro relation are excessively
restrictive, such that the aggregation conditions can
safely be assumed to be never realised in reality; as
Franklin Fisher pointed out long ago, the conditions for
any such derivation are 'far too stringent to be believable'...
...Sometimes this use is defended on the grounds that
these functions fit the data fairly well and their estimated
marginal products approximate closely the observed
'factor prices', the wage rate and the profit rate (which is
a highly dubious claim). However, this must not be interpreted
as rendering some *empirical* credibility to the aggregate
production function. As Fisher (1971) has pointed out some
time ago the seemingly good fit is simply an artefact of the
constancy of the profit (and thus the wage) share. Hence there
is neither theoretical nor empirical support for the aggregate
production functions used in many New Growth Models.
-- Heinz D. Kurz and Neri Salvadori
---------------------------------------------------
After much pretense about the "degenerate" nature of neoclassical theory and
its logical inconsistencies, Mr. Vienneau objects to neoclassical theory
because it does not conduct all its analysis through the prism of his
ideology.
In article <950309023...@p1.utica.kaman.com>,
Rob Vienneau <r...@utica.kaman.com> wrote:
>SM = Stephen Millard, MW = Mark Witte
>
MW>Hmm, how did this thread get started? As I recall, you
MW>attacked someone who suggested that the marginal product of
MW>capital was related to the level of interest rates (hence the
MW>title of this thread). You made claim about how this
MW>assertion was preposterous since neo-classical economists
MW>knew it to be false but went ahead, pretending it to be true.
MW>You made some statement about this being the reason for your
MW>choosing not to be a professional economist.
>
>If I were a professional, I would find that many would dismiss my
>interests out of hand and argue that the schools in which I'm
>interested do not exist.
You call this a reply? Or an apology?
>
MW>While Hahn admits that the stated formulation is correct, he
MW>does not argue that it is interesting. You may remember the
MW>following from Hahn about this school of thought which he
MW>calls a "Great Charade."
>
>I'm amazed at Hahn's suggestion that the dependence on intial
>conditions of the solution path to a clockwork model sets the model in
>history. Really?
That wasn't Hahn's point. This wasn't even close to anything he was talking
about.
>
MW>Hahn is making the point that the way standard macro handles
MW>this issue is a much better way to proceed than anything you
MW>are advocating.
>
>I do not read Hahn as necessarily defending macro, as opposed to G.E.
>I do not see that I've really advocated much of anything yet in this
>thread. I have given a couple of references. I do not see anything
>wrong with a theoretical argument about the consistency of different
>aspects of an approach to modeling.
And given the choice of valid theoretical frameworks, you would have
the field avoid the approach which has empirical applicability?
I can't say that you've really advocated much of anything either.
>
>(And, by the way, I could have picked other problems. One I cannot
>explain is that the aggregate behavior of utility maximization on the
>part of many individuals *generally* cannot be represented by the
>utility maximization of a representative individual. See Kirman's
>article in the _Journal of Economic Perspectives_ in the last 2 or 3
>years. The other problem with Lucas' work that leaps to my mind is a
>reliance on ergodicity. The alternative to rational expectations is
>not systematic error, but learning problems in nonergodic processes. I
>think Lucas has commented on ergodicity.)
>
MW>The controversy is settled. Cambridge (England) won! In
MW>order to aggregate you need to make further assumptions
MW>(viz. regular economy) - big wows! If the model generates
MW>dynamics which match aggregate data, then these further
MW>assumptions are not a problem.
>
>Cambridge, England won the battle, but lost the war. Has mainstream
>practice been affected at all? Do they even perceive that Cambridge
>offered an alternative? (See below.) Does the mainstream see their
>research program as increasingly ad hoc and degenerative?
I have repeatedly asked you for an implementable alternative and you have
repeatedly failed to provide one. Your criticisms are ad hoc and the
literature you have advocated hasn't gone anywhere in the last twenty years,
which sounds like the definition of degenerative to me.
>
>Furthermore, what are legimate and illegimate uses of aggregate
>production functions? For legimate uses, I might be willing to include
>simplifications when explaining a model whose emphases lie elsewhere
>and demonstrating the consistency of a theory with assumptions of
>"regularity." For example, once upon a time in sci.econ, I explained
>the golden rule of growth in an aggregate setting, when that setting
>is not necessary. I also once demonstrated that the Pasinetti paradox
>is consistent with regularity.
>
>An illegimate use is the teaching of economics such that students are
>conveyed the impression that regularity follows from maximizing
>behavior and the "reasonable" assumptions often imposed in G.E. to
>ensure existence. Mark seems to have offered something like this
>impression in his natural language comments about the technicalities.
>I suspect many economists convey this impression to beginners.
>
Clearly no one would claim that _assumptions_ are a result of maximizing
behaviour. Generally, there is little interest in examining the equilibrium of
models, for which no equilibrium exists. I suppose from this perspective
assumptions needed to ensure existence may be called "reasonable."
>I also think - and I expect Mark to be amazed and annoyed - that the
>use of aggregate production functions in empirical work is rarely
>justified. One might be able to accept it as an illustration of a
>model with greater expansion elsewhere, perhaps, but that's about all.
>
You can expect me to be annoyed that you continue to making sweeping
condemnations of standard approaches in economics without reason, support or
useful alternatives.
All models have "special conditions." This is what makes them models. It is
the choice of useful models which makes for good research.
>The Sraffian system shows
>the realization of this story. Yet it is perfectly compatible with a
>failure of the Neoclassical parable.
>
>I am perfectly aware that financial analysts talk about "the cost of
>capital" as being the risk-free rate of interest, generally taken to
>be the rate of interest on government bonds. And I accept this story
>(minus my proviso) will make the cost of capital equal to the rate of
>interest. I fail to see what this has to do with the claim that the
>marginal product of value capital equals the rate of interest, as that
>claim is taken in rigorous theory.
You have accused Steve Millard of engaging in "dodges." Then you raise this
stuff? I fail to see what this has to do with the claim that the marginal
product of capital equals the rate of interest as well.
>
MW>And they have an approach with more empirical muscle? The
MW>point of the CCC was pure negativism with no empirically
MW>falsifiable hypotheses. It allowed a clique of economists
MW>to publish a few articles and made neoclassical economists
MW>take more care in stating the conditions under which
MW>aggregation is possible. However, I can't believe that even
MW>the most dogmatic of the CCC people believed we lived in
MW>anything but a (possibly non-market clearing) neo-classical
MW>world.
>
>Ignoring the tone, I still couldn't disagree more.
Oh, the tone, the tone!
>I do not think
>Kalecki, Kaldor, Robinson, or Sraffa thought Neoclassical theory could
>cast much, if any light, on real world capitalist economies. By
>Neoclassical theory, in this context, I mean either General
>Equilibrium theory, as in Walras or Debreu, and aggregate
>macroeconomics as expounded by Mark. The relationships of the above
>Cambridge-school economists to Marshall is more problematic.
>
[Attempt to enlist support from Keynesians by imagining a slight on my part
against their paradigm deleted.]
>
>Let me expand by noting three possible readings of Sraffa's book, a
>cryptic but key text in this discussion.
>
>1. As part of a Neoclassical G.E. model within which one can
>investigate the consistency and coherence of various ideas. This is
>all I have been doing in this thread.
I would hope that most books in economics could be characterized in this
manner.
This was certainly not the stance you took to start this branch of the
thread. You began with an attack on the honesty of practioners of
neo-classical economics.
>
>2. As a rediscovery of a Classical logic. Sraffian prices are
>Classical 'natural prices' or Marxian 'prices of production'. I don't
>know that it's more relevant here or above, but notice the similarity
>between the subtitle of the first volume of Marx's _Capital_, "A
>Critique of Political Economy," and Sraffa's subtitle "Prelude to a
>Critique of Economic Theory."
I don't know if it's more relevant than the similarities between Baywatch and
Models, Inc.
>
>3. As an exposition of a price system consistent with Keynes _General
>Theory_. Quantity flows are determined by investment decisions prior
>to prices, not mutually determined. Say's law need not not hold.
>
>Readings 2 and 3 offer a route forward, although it still needs to be
>more articulated. Sraffians have spent a lot of time arguing with
>Neoclassicals in the context of the internal critique suggested by 1,
>revolutionizing the history of economic thought as suggested by 2, and
>arguing with Marxists also as suggested by 2.
>
>I also understand those who think Sraffa represents the culmination of
>certain traditions and the way forward lies elsewhere. Geoff Hodgson
>and Philip Mirowski represent two economists who I find interesting
>along these lines. Nor is it the case that I think economists outside
>of Post Keynesianism are worthless. I do think Neoclassical
>macroeconomics, apparently as advocated by Mark Witte, is not a
>fruitful path.
Neoclassical macro seems a fruitful path for understanding interesting issues
in growth and our real world economy. However, neoclassical macro seems to be
a fruitless path for you to indulge your political and ideological priors.
>
MW> I guess the basic question from this long running
MW>feud is whether you think the class of models you seem
MW>to hold so dear do a better job of describing the world.
MW>Well do you, punk?
>
>As you can see, I have barely mentioned the approaches I find
>worthwhile. The models you think I hold so dear, Neoclassical G.E.
>interpretations of certain mathematics, I think have next to no
>empirical implications.
These where the models you attempted to put forward to support your attack on
modern neo-classical theory. Why bring these models up to criticize models
which are subject to empirical verification? Why waste our time with models
even you don't believe?
>The approaches I like seem worthwhile to me on intuitive grounds. They
>leave room open for history to enter in. They are not a-institutional.
>They do not depict firms as passively adjusted to consumer maximizers
>who ultimately determine the economy. They allow investment decisions
>to create the environment in which it is determined whether the
>expectations underlying them are realized. They have room for
>dynamics. They depict the economy as having multiple centers of
>power. They even allow for an element of class struggle in the
>determination of income.
That's nice.
Who will break the news to Gary Becker, Robert Fogel, Doug North, Ronald Coase
and Joel Mokyr that their analysis ignores history and institutions.
(No letters please from U of C people along the lines: "Ah a quiz. Let's see.
Who doesn't belong on this list?")
Who will tell all the I.O. economists that firms have no role in determining
the economic environment?
>
>Of course, these approaches could stand greater articulation.
>
Really?
>(And, Mark, I am not impressed with the paragraphs following the
>paragraphs you quoted from Hahn and Blaug.)
>
Actually, I was hoping that their devastating critque of your ideas would
suppress you.
>
>I'm not sure if Stephen will be physically able to participate
>shortly. If I were in England, I'd think I'd prefer sampling pints of
>ales and bitters at the neighberhood pub, but what do I know? I'm just
>some guy from the U.S.A.
>
[Questions for Steve Millard deleted. I'm sure Steve will be "physically able
to participate" in the debate assuming Sraffarian goons have not been sent to
dispatch him.]
>
>Instead of arguing about the truth value of these statements, do you
>want we to argue that mainstream economics reflects a certain
>apologetic political vision?
>
> Robert Vienneau
>
Yes. I'd prefer that you had stated your belief that neo-classcial analysis is
mistaken because it does not pay due attention to the role of class struggle
in the economy. I would not have tried to argue with your beliefs. (Thus
saving us both a lot of time.) Instead, you pretended that your dismissal of
neoclassical macro analysis had some basis in reason. In fact, you could only
offer the complaint that the assumptions which ensure that capital can be
aggregated are "restrictive" (if an assumption isn't restrictive you shouldn't
make it) and "unrealistic" (hence the term model).
In doing so, you recalled the Cambridge Capital Controversies, in which people
with a similar ideology to yours, tried the same tactic. This despite the fact
that they recognized the need to make "strong" assumptions when modelling.
(You may recall the Joan Robinson quote: "A map on the scale of 1:1 isn't very
useful.") Hahn has consistently pointed out their intellectual dishonesty in
this matter.
This is not to say that assumptions are sacrosanct. You mention the debate
over rational expectations and representative agents. These issues are given
serious consideration because researchers have proposed alternative, testable
models with different assumptions. They may supplant the current assumptions
if they display greater predictive and analytical power.
Alas, by your own admission in this post, you have no alternative to the models
used by neoclassical macroeconomists that can address the multitude of topics
which have been fruitfully studied by this methodology. Our choice then is to
ignore these questions, because we cannot advance your political agenda while
adressing them, or to continue trying to understand the world in which we live
with the tools at hand, until and unless better ones come along. The choice is
clear. That is why the debate is dead.
Mark Witte
" In a subject where there is no agreed procedure for knocking out errors,
doctrines have a long life." [In this instance, about 25 years.]
Joan Robinson
Marx, Marshall and Keynes (1955)