Saturday, June 6, 2009

Suppressing Causally Relevant Factors in the Special Sciences

Can I beg your indulgence? Here is a little parable (712 words). It is meant to undermine Hempel's requirement of maximal specificity in IS-explanation. I would be very interested to know how people react to it:

"Imagine an economist interested in the price elasticity of demand. She finds that price changes have different effects on demand for different kinds of commodity. For necessities such as staple food items, it has very little effect; for small conveniences such as dry-cleaning, the effect of price increases is linear; for luxury items with pretensions of exclusivity, it is inverted – the higher the price, the greater the demand – and so on. She also discovers that hitherto overlooked transaction-factors are relevant: elasticity takes on different values in business-to-business transactions, in on-line purchases, and so forth. Such additional determinants would interest our economist – though she may not have been aware of or interested in different categories of transaction until they turned up in her surveys, such factors are relevant to her question. She is interested in a complete economic theory of price elasticity, not just in some pre-selected set of factors. Her discipline defines the relevant features by its methodology; she does not define them by idiosyncratic interests.

"Let’s suppose that at a certain point in her investigation, the economist has discovered all the economic determinants – even those that she did not anticipate at first. But she has also stumbled upon a non-economic factor involved in some sales transactions. Say, for instance, that for reasons having to do with colour perception, some women’s willingness to tolerate a higher cost varies with the colour and size of the font in which the price of an item is displayed and with the kind of light shining on the price ticket. (Many women are more sensitive to colour differences than men.) In different stores, where the price happens to be displayed differently, price increases affect demand differently on average, because women are differently affected.

"I conjecture that the economist will not count this as an admissible factor. The effect arises situationally; it may vary simply with the prevailing light at different times of day, and with the purely accidental use of different price-tickets in different stores. Such accidental variation has nothing to do with the kinds of interaction that the economist is trying to understand. It affects elasticity, but to include its effects would distort the economist’s understanding of the transactional influences she is investigating. Because this data is irrelevant from her point of view; the economist would average over the perceptual variations – or perhaps even “correct for” them as government economic statisticians correct for seasonal variation in unemployment rates – rather than building them into her model. Of course, she may change her mind about this: she, or economists in general, may come to think that perceptual oddities are actually of economic interest (just as they have recently come to believe that the psychological oddities of consumers are of economic interest). However this may be, the point that I wish to make here is that there are usually some factors of this sort in the “special sciences” – factors that make a causal difference to the explanandum, but are deemed outside of the concern of the investigator.

"A moment ago, I mentioned “averaging over” perceptual variation. This is what I mean. The economist is trying to predict demand: this is the outcome that interests her. Her model predicts how demand varies with price, given certain other characteristics of transactions. Let C be a type or class of transactions that are indistinguishable from an economic point of view. Every transaction in C is, in other words, the same as every other with respect to the factors that interest our economist. The demand for a commodity will be the sum of the demand for it in various types of transaction. However, within a given type, demand will depend (in part) on how transactions happen to be influenced by the perceptual factors just mentioned. The economist ignores this variation in C: she simply lumps these transactions together, and calculates elasticity for C as an average over different modes of display, men and women, and different lighting conditions. In this manner, the economist tolerates a source of variation in instances of C. Consequently, elasticity is predicted only probabilistically. Given an increase of price, there is a probability function associated with various values of demand for C. Some of that uncertainty comes from a suppression of a causally relevant, but theoretically inadmissible, factor."


  1. Mohan, I think most economists would be unlikely to accept an upward sloping demand curve (as you seem to suggest). They can get very dogmatic about this (in my experience).
    On the other hand, much of empirical economics in labor theory or some area of applied (whatever it is called these days) consists of building up a working knowledge of and modeling precisely the interaction between standard economic factors and such non economic factors as you call attention to. In fact, most economists work in such areas and learn to become quite sophisticated in recognizing such local factors. The problem is that there is (well was) a big gap (i.e., no feedback mechanism) between extremely formal high theory and much applied work--so that the applied work neither or barely (implicitly) tested high theory or could help refine it. Much knowledge within economics is of engineering type.
    So, the parabel accurately describes the situation from the vantage point of high theory but not from the vantage point of the living, empirical economist.

  2. I make a distinction later in the paper about the difference between explaining generalities and explaining individual occurrences. If I want to explain why price elasticity was lower in Toronto than in Chicago, it may well be relevant to cite the perceptual oddity mentioned. But if I am trying to build a model of price elasticity it won't be. Is this the kind of difference that you have in mind between "high theory" and "empirical economics"?

  3. No, I find your distinction unhelpful because it does not do justice to the kind of 'engineering' knowledge applied economists develop.
    Basically, I am saying that it is largely 'applied' economists that build empirically rich models; these are generally attentive to the kind of issues you mention. But I would say they produce models that are trying to capture (not sure I would use explain) more than 'individual' occurrences, but often less than what you call 'general' occurrences. General price elasticity models (if these exist) are probably inferred from other data (via proxies). At least this is the case in the work that I have studied.

  4. Eric, I think economists dogmatic about upward sloping demand curves should go out more. Case in point: A relative of mine sold the complete stock earrings for €20 after selling almost none of them for €2. If an economist does not accept that there can be such demand curves she should consider that she thereby gives a meaning postulate for `demand curve'. A bit like economists who state that everyone always behaves selfish because everyone follows her preferences.

    One may now say that my story about the earrings is just anecdotal, but the important thing is that demand curves sometimes slope upward. If I wanted to explain my relative's success with the earrings, I think I'd have to take that into account.

    Now, Mohan, I'm not sure how your point about influences of perceptual variations is meant to relate to Hempel's criterion for IS-explanations, because you are describing an economist's search for a law, while IS-explanation are about the application of a law to a specific explanandum.

    And with respect to finding a law for demand curves, would that not be determined by the sought-for domain of applicability? This might be what your distinction between `explaining generalities' and `explaining individual occurrences' is about, but I am not sure that such a bipartition is helpful. Rather, each intended domain of application will introduce different dependencies for the demand curves.

    Once I have my demand curves for the different domains of application, it seems that the specific explanandum determines which demand curve to use: If I want to explain the shift in demand on a national level for product X to a certain level of precision, I take the demand curve for X on the national level with enough dependencies taken into account to achieve that level of precision. Analogously for the earrings: If I just want to explain the increase in sales, very few dependencies may be enough (luxury items and ill-informed buyers maybe). If I want to explain the curve's specific shape per hour, even the amount of sunlight and each customer's psychology may be relevant. I assume that's why there are no per-hour-demand curves for specific products in specific shops.

  5. To be honest, I am unsure how majority of economists view upward sloping demand curves. They may be less dogmatic than I portray.
    I don't think economists need to be very impressed by anecdotal evidence of the sort Sebastian reports (hi!). (Scholastics had much better evidence against Galileo's views on falling bodies or Copernicanism.) Did your relative package the earrings differently, use different marketing, was there a seasonal effect, etc?

  6. Hi Eric,

    I agree that my anecdote is only that (but it isn't all that terrible: My relative really only changed the price tag on the display stand). I did want to note, though, that being dogmatic enough about the shape of demand curves can easily make the shape into a truth by convention.

  7. I don't understand the parable. The economist is looking for a law (of some kind) that connects price and demand. But the perceptual factors presumably affect demand regardless of price. If changing lighting affect demand throughout the course of the day, or if one store experiences higher demand than another because of the colour of their signage, then these effects will be observable at any price. They are therefore rightly "aggregated" out of the law.

    Now, if they are so significant that you would have to ask "what colour are the price tickets for this product?" (or "what font is it printed in?") before you could say anything about the price elasticity of demand for the product then that's essentially on par with knowing enough about the product to put it in the right category.

  8. Sebastiaan, well, at one point the downward slope of the demand curve was up for empirical debate. It is my sense that things became settled/dogmatic on this score in the 1940s and 50s. (But again, I have not done research on the topic.) This did become conventional. Of course, the shape of the slope and the extent of price-elasticities remained up for empirical debate (with the proviso that these are very hard to establish).

  9. OK, OK, enough already about which way the demand curve slopes -- that was just an example!! ;>)

    Seriously though, these comments are very useful. I think Eric and Sebastian are going in the same direction: Eric's "empirically rich" models, and Sebastian's differing domains of application and concommitant degrees of precision both refer to models for predictive use. And I think Eric is surely right to say that the distinction between individual events and event types is not what is at question in this case.

    As you might have suspected, economics was not what I was after here. I'll come back to this in a moment, but let me try a slightly different suggestion. What the above comments convinced me of, as well as Thomas's, is that there is another way of looking at things. You could have an economist who is interested in economic explanation (not just prediction) -- by which you might gloss as "explanation in terms of economic factors". This economist is interested only in how economic factors change things.

    So understood, the economist doesn't restrict explanations by explananda but by explanantia. That is, she doesn't say: here is a price increase, what caused it? Rather she says: here is my general conception of an economic factor: what will they explain?

    So I want to concede that the perceptual variations make a difference. I want to assume that you'll get some relevant information if (as Thomas suggests)you'll get relevant information if you ask "what colour are the price tickets printed in?". What I want to claim -- or I could phrase this as a question) -- is that there are instances where this explanans-oriented economist will say: Look I know that colour will help me predict price, but this doesn't provide me with the kind of understanding I am looking for.

    Perhaps some of this intuition can be captured in a contrastive theory of explanation. Let's put that to one side. My question is: is the explanans-oriented economist just wrong?

    My real interest is in the theory of natural selection. Does it exclude certain factors as being of no interest and hence average over the variation relative to those factors? Hopefully the general theoretical considerations are not dependent on this context, however.

  10. Might the economist first try to isolate the 'perceptual effect', to determine just how variable it is or, if you like, how much probability it is responsible for introducing into class C. With that she would know how much significance it has relative to all other known, potentially causally relevant factors.
    If it is not a desireable expalanans (perhaps because it has low relevance and/or to factor it into the model would make the model too cumbersome), then she can abstract it (average over it). If it is desirable (ie. significantly affective), then it merits inclusion in the model.

  11. I think this idea of an "explanans-oriented" researcher is very, very interesting. In fact, I think the history of the philosophy of explanation (at least up to about 1989) can be understood as a shift from explanandum-oriented accounts (emphasizing deduction and predition) to explanans-oriented ones (emphasizing, say, "mechanisms").

    Interestingly, the I-S account has, to my mind, always been unnecessary. A statistical regularity can always be recast as an ordinary law + a measure of epistemic uncertainty (but I know that this "ignorance interpretation" doesn't fly with philosophers of physics.) And I-S accounts, Mohan seems to be saying, are what start us down the road to explanans-oriented explanations.

    Yes, I think the explanans-oriented economist is simply wrong. But I have to admit that I'm an unreconstructed D-N'er when it comes to explanation. (Scratch me and I'll claim that no progress has been made on explanation since ... Poppper!)

    The only imperative that drove us beyond simple D-N models that also accepted that we always have limited knowledge to base our explanation on was what Mohan is here, very astutely, identifying as "explanans-oriented" research. That is, explanations that have no ambition of predictive power.

    I think the statement "Look I know that colour will help me predict price, but this doesn't provide me with the kind of understanding I am looking for" involves a dubious, perhaps even specious, concept of "understanding". But I do grant that much post WWII science has proceeded in quest of this kind of understanding. Look where that got us!

  12. Thanks for all these comments. The excerpt was from an article entitled "Drift and 'Merely Statistical Explanation'". This paper was recently conditionally accepted at Philosophy of Science, but I began to rethink some of the central theses. The crispness of the responses encourage me in that I think the example must have been clear -- but I see how I need to rejig some of the ideas.