> Mark Witte, apparently a New Classical Macroeconomist, discovers the
> Cambridge Capital Controversies. He cannot be expected to have
> absorbed all the literature he cites in just a couple of days. Whether
> he goes on to study this controversy, or is content with his hasty and
> muddled dismissal is up to him.


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:


> The problem with locating *the* rate of interest in a
> model of intertemporal equilibrium is that there's no
> room for money. All time is collapsed to a single point,
> and the future is foreseen. An institution of
> 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 characterization of money as a
medium of exchange, store of value and unit of account?


> So far no mention has been made of interest rates.  This is
> because interest rates are a derivative phenomenon, of little
> importance in themselves. But to understand capital theory,
> 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
>> revist the Cambridge controversies of the 1960's.


> Here Mark demonstrates the Markov property - no memory. Some time
> ago in this thread, I wrote
> 
>    The Cambridge Capital Controversy was a complex and multifaceted
>    affair. Two important Neoclassical summaries are Christopher Bliss'
>    book "Capital Theory and the Distribution of Income" (1975) and Frank
>    Hahn's paper "The Neo-Ricardians" (Cambridge Journal of Economics, V.
>    6, No. 4, 1982). Although Bliss and Hahn are not in total agreement,
>    they both argue that disaggregated Neoclassical theory is sound and
>    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 account of
expectations 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 answered 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? 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 relevant.
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.


> 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
> disaggregated neo-classical theroy  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.


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
joournals 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?



>     "I would not suggest that logic spoils with age just as I would not
>     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 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
> 
>    "Equation 36 states that capital per head is the additive inverse of
>    the slope of the tangent to the factor price frontier at the selected
>    (r, w) point. But I have already shown that capital per head is the
>    inverse of the slope of a particular secant passing through that
>    point. In general, these slopes will differ.  So the interest rate is
>    *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 explicitly 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 woud 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:
> 
>>> I do have problems with the claim that in Neoclassical
>>> models, the rate of return is the same in all lines of
>>> production, abstracting from risk. For the sake of
>>> argument, we can assume that endowments just happen
>>> to be such that all own rates of interest are equal for
>>> all produced means of production actually produced.
> 

>> This is straight out of Ricardo's "falling rate of profit." Lines of
>> production in the neo-classical model which pay a higher rate of
>> return will attract resources from other areas until the zero economic
>> profit condition holds everywhere. The neo-classical model is an
>> allocative general equilibrium model with mobile factors so that
>> 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 that 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 live 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.


>  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?


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?


> 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.


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?


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...?