Saturday, September 6, 2014

Explaining the "other things equal" clause to Nick Rowe

At Worthwhile Canadian Initiative, Nick Rowe writes:
"Those of us who teach Intro Economics know we have to spend some time carefully explaining the "other things equal" clause, and why it matters. Because the students won't get it unless we explain it. We tend to take it for granted that the silent "other things equal" clause is understood, but it might not be understood by all."
Other things being equal, there's been a raging debate in philosophy of science over the past couple of decades regarding the legitimacy of "CP-laws" -- that is to say "laws" hedged by a ceteris paribus clause. The 'other things equal' clause may be headed in the same direction of a Santa Claus, something we let children believe in that we know doesn't exist. 

Anyway, there's a hilarious exchange in the 19th century between William Thornton and John Cairnes where they each respectively denounce and uphold and uphold and denounce seemingly "contrary" principles that are in fact simply different statements of the same principle. The secret to the debacle is the kakeidoscopic versatility of their respective ceteris paribus clauses. 

Just yesterday, I posted "Ceteris paribus, Dr. Jekyll tans his own Hyde" at Ecological Headstand. It's scheduled to publish on EconoSpeak next Tuesday as the penultimate installment in the supply-creates-its-own-demon series. But rather than send readers clicking all over the place, I'll just paste it again below:

"In too many cases one is unsure of exactly what restraints are being imposed and by what authority the exercise is legitimated. Fittingly, the history of ceteris paribus is a history of studied ambiguity." – Joseph Persky
Let us not worry about too many cases. Let's focus on the paradigmatic case. Persky identified Alfred Marshall's role in "spreading the word" of ceteris paribus:
"It is very likely that Alfred Marshall picked up his use of ceteris paribus from Cairnes. Although he doesn't cite Cairnes in his methodological discussions of the phrase, Marshall does use the following quotation from Cairnes in a discussion of the wages-fund theory: 'the rate of wages, other things being equal, varies inversely with the supply of labour.' 
"Whatever its origins, the fact remains that Marshall was the one to popularize ceteris paribus."
The phrase was actually "other things being the same," which appears eleven times in Cairnes's Some Leading Principles of Political Economy: Newly Expounded. Notice that Marshall cited Cairnes "in a discussion of the wages-fund theory." More specifically, Marshall was criticizing Cairnes's attempt to "resuscitate" the wages-fund theory, in which Cairnes avoided the old pitfalls "only by explaining away so much which is characteristic of the doctrine." Apparently, though, Marshall must not have noticed that it was precisely the infernal ambiguity of the ceteris paribus device that enabled Cairnes to explain away the pitfalls in the doctrine. Marshall went on to promote the use of the ceteris paribus "pound" in static analysis.

Persky's article mentions the methodological critique of ceteris paribus by twentieth century philosophers of science and cites Daniel Hausman's introduction to those arguments. A subsequent ceteris paribus "industry" has blossomed in philosophy in which "hardly a year passes without the appearance of at least a few articles on this topic in major journals." Although it would be an exaggeration to call it a consensus, there are cogent arguments "that extant attempts to save ceteris paribus laws from vacuity are massive failures." In a recent article, T. V. Carey has proposed Galileo's method of successive approximation as a "partial solution to the ceteris paribus problem."

While the philosophers are busy resolving the methodological difficulties raised by ceteris paribus, I would like to turn my attention to the political consequences of this magical clause. Cairnes's attempt to revive the wages-fund doctrine was a response to William Thornton's apparently decisive repudiation of it in On Labour Its Wrongful Claims and Rightful Dues; Its Actual Present and Possible Future. The wages-fund doctrine had lent pseudo-scientific legitimation to fierce partisan polemics against trade unionism.

Cairnes's response encompassed both defense and attack. It is in his defense of the wages-fund doctrine that the passage cited by Marshall appears. In a later chapter on trades unionism, Cairnes attacked a statement by Thornton to the effect that "the quantity of industrial work to be done is… 'at any give time a fixed quantity.'" Cairnes objected to this assumption vehemently:
"...I must make bold to say that, within the range of economic reasoning, no more profound fallacy finds a place than is contained in this inference; nor, I must add, is there one more pregnant with practical consequences of a pernicious kind."
The review of Thornton's book in The Edinburgh Review for July 1869 took a more good-natured and humorous view of Thornton's gaffe:
"That the rate of wages is governed, as Adam Smith and his followers have conceived, by the proportion between the capital disposable for the payment of labour and the number of the recipients of that capital, is a notion that Mr. Thornton scouts with contempt, and he consigns the chimerical 'wages-fund' to the lowest limbo of unrealities. Yet, while attacking the name, we find him occasionally, under the pressure of facts, using language which virtually admits the thing, as when he says, 'that at any given time the whole quantity of work to be done is a fixed quantity, and the uttermost which employers can afford to pay for having it done is a fixed amount'; and in other places his language recognises the inevitable fact that employment must be limited by the amount of capital which at the time being sets it in motion, that amount being the thing to which Smith, McCulloch, Fawcett, and other writers have assigned the offensive name."
Thornton erred in "virtually admitting" the chimerical notion that he "scouts with contempt." Cairnes compounded error by not noticing that the "profound, pernicious fallacy" he bitterly denounced on page 251 of his book was none other than a restatement of the wages-fund doctrine he had stoutly defended back on page 174.

How is it possible that both Thornton and Cairnes could commit the identical errors while taking diametrically opposite positions on the question of the wages-fund? The answer lies in the ineluctable vagueness and ambiguity of the ceteris paribus clause. In the hall of mirrors where "other things remain the same," what "other things" are included in or excluded from the ceteris paribus pound is tacit as is exactly how they are "the same."

Adding intrigue to irony, Persky credited William Petty with introducing the term ceteris paribus into economic discourse. It is also quite possible the Petty wrote the earliest version of Thornton's "fixed quantity of work to be done." Except in Petty's version it was "a certain proportion of work to be done," not a fixed quantity. There is a world of difference between a fixed quantity and a certain proportion. No doubt part of the shape-shifting magic of ceteris paribus arises from its equivocation on whether it is quantities or proportions or both that are being the same.

Maybe ceteris vertigus (other things being dizzy) would be a better name.


Nick Rowe said...

Sandwichman: When medics do a test of a new drug, they get 100 people and toss a coin to decide who gets the new drug and who gets a placebo. And they toss a coin because they know that other things matter too, but they aren't at all sure what those other things are. All they know (or all they think they know) is that the toss of the coin itself is not one of those other things, and will be uncorrelated with those other things.

And people who drive cars know that pressing down the gas pedal causes the car to go faster, other things equal, but they don't always know what all of those other things are. (And the cruise control doesn't know whether the car is going uphill or into a headwind or on a gravel road.) But they can still use that knowledge about the effect of gas pedal on speed to drive at roughly the speed limit. Just like the Bank of Canada can use its knowledge to keep inflation at roughly 2%.

Sandwichman said...


Yes, I'm glad you brought that up. I know about drug testing. My housemate is an Assistant Professor in the Department of Anesthesiology, Pharmacology & Therapeutics at UBC.They use double-blind experiments with a control group to test drugs. They don't use the term ceteris paribus in some thought experiment from which they generalize. Designing a drug test is very complicated and there is a lot of controversy about whether a particular result was valid, centering around the composition of control groups

I'm also glad you mentioned driving cars. Nancy Cartwright uses the analogy of a "nomological machine" to probe the constraints that have to exist for ceteris paribus laws to not be vacuous. Because they originate from these nomological machines:

"C-P laws are both local and fragile: they hold just where and when the relevant machine is working correctly. The successful identification and use of such laws cannot be achieved by uncontextual general principles alone, but requires messy contextual knowledge..."

So, yes, a case can be made for the local and contextualized use of ceteris paribus. That doesn't make it appropriate for generalized all-purpose application. said...

The terminology of ceteris paribus is a bit murky indeed. Discussion of nomological anything is not helpful for econ because this refers to physical laws, and while physical laws show up in parts of economics, they are not that relevant in other parts, despite the borrowing by economists of some of the math involved.

Both "other things equal" and "other things the same" are potentially confusing if one looks to closely at them. Unfortunately probably a longer description is needed to really nail this sucker down. So, "other things unchanged except for how they would have changed with this thing changing, but allowing for the impact on them of this thing changing." said...

Ooops. Messed it up. Try "Other things unchanged except for how they would have changed without this thing changing and allowing for the impact on them in the future of this changing." Something like that, although even this can be debated. After all, when a change in price causes expectations to change so while we normally say demand curves slope downwards, ceteris paribus, but if we take into account the induced change in expectations we can get a completely different outcome, if an increase in price causes a change to an expectation of future price increases, we can see people buying more of something when its price rises.

Peter Dorman said...

Greetings, S-man (and Barkley and Nick R). The CP condition should be considered as a condition like any other. We believe x holds subject to the following conditions, and so on.

What this means is that CP needs to be assessed and not merely enunciated. In particular, it’s important to ask whether there are any logical interconnections between the factors allowed to vary (or their outcomes) and the factors on whose non-varyingness the analysis is conditional.

Example: applying more pressure to the gas pedal will cause the car to accelerate, CP. You have to add this condition because it might be the case that the car, at this very moment, begins to go steeply uphill, which would slow it down. Suppose the gradient of the road is the only other factor that could affect the car’s speed. (This is obviously wrong, but we’re just musing.) Then the relevant question is whether there is any reason to suppose that changes in pressure on the gas pedal themselves affect the likelihood of the CP condition holding. No, so CP works here.

Now here’s another example, familiar to labor economists. Suppose I say that raising workers’ wages will lower a firm’s profits, CP, with one of the factors assumed to not vary being workers’ productivity. What’s the assessment of CP here? It turns out there are multiple reasons why a wage change would cause productivity to change, like selection and motivation effects. Thus the onus would be on anyone invoking CP conditionality to identify the specific circumstances under which productivity would not change. In other words, CP can logically be invoked only where this narrower set of circumstances is in place.

I haven’t read the philosophers on this one, and I wonder whether my thinking is in line with theirs. This is the approach I use in teaching economics, however.

Sandwichman said...

"What this means is that CP needs to be assessed and not merely enunciated."

Yes, Peter, that seems to me close to what Nancy Cartwright is saying. I wonder, though, if one actually identifies and assesses all of the known disturbing factors, what is then left of the c-p claim? Isn't it then superfluous?

What got me started down this path was not the philosophy of science literature but J.M. Clark's 1927 essay on "The Relation between Statics and Dynamics," which accords well with Marshall's 1898 article, "Distribution and Exchange." Both of them are saying the ceteris paribus clause and it's putative laws have no place in a dynamic analysis because the economic system is an evolutionary one. I will develop this point further in a subsequent post.

Peter Dorman said...

A different way to slice it is to identify CP with so-called atomistic methodology. (I hate this term, which is soaked in confusion. Are atoms atomistic?) One could argue that a complex question could be reduced to a set of independent questions about its elements. We might have 50 factors that affect an outcome, and we could analyze each separately, CP. Then, putting together these 50 relationships, we might suppose we have an analysis of the whole system. The problem, of course, is interaction between these factors. To the extent such interactions exist the methodology is invalid, unless there are case-specific reasons for believing they do not operate. (This is what I argued in my previous post.)

The additional claim you are adding is that change over time is always systemic, in the sense that interaction effects between elements have to be taken into account. The Marxist analog is the famous saying by Lukacs that “totality is the territory of the dialectic”. (My response was, well yes, but all totalizations are premature.) I think this is basically right. At the same time, however, it may be useful as a first approximation to examine subsystems separately, bearing in mind the qualifications.

Also, the distinction between statics and dynamics is not as awful as one might think. There is something to be said for the analysis of forces whose simultaneous effects constitute a system at a given moment in addition to systemic evolution over time.