Maths can be misleading even in the physical sciences

http://www.the-rathouse.com/2010/Schwartz_on_mathematics.pdf

]]>I have never thought about how interviewing managers might yield data relevant to understanding the relationship between multiple mechanisms for generating profit (such as rivalry restraint and competitive advantage). If you have any ideas, let me know.

Meanwhile, if you want to learn more about this theory as it currently stands, then I would recommend reading the following recent articles (listed chronologically):

Makadok, Richard (2010). “The Interaction Effect of Rivalry Restraint and Competitive Advantage on Profit: Why the Whole Is Less Than the Sum of the Parts.” Management Science 56(2): 356-372.

Chatain, Olivier, & Zemsky, Peter (2011). Value creation and value capture with frictions. Strategic Management Journal, 32(11): 1206-1231.

Makadok, Richard (2011). “The Four Theories of Profit and Their Joint Effects.” Journal of Management 37(5): 1316-1334.

Makadok, Richard and Ross, David Gaddis (2013). “Taking Industry Structuring Seriously: A Strategic Perspective on Product Differentiation.” Strategic Management Journal 34(5): 509-532.

Also, Mike Ryall and his coauthors, Joao Montez and Francisco Ruiz-Aliseda, have written a very interesting not-yet-published working paper on this same topic, where they extend the value-capture style of modeling that he mentioned in his comment above (download from http://works.bepress.com/michael_ryall/20/ ).

Thanks again,

Rich

Thanks for your response, you’ve clarified several points for me. I can certainly appreciate the ability of mathematical models to generate, as you put it, useful insights, especially in relatively new fields of research. Though I didn’t learn much formal modeling in undergraduate B-school, the RBV, Porter’s 5 Forces, and other insights of strategy have had a tremendous impact on my thinking as an economist. I’m happy to work in a field (agricultural and applied economics) that respects B-school perspectives as well as “traditional” economics. While I don’t see myself “bringing my plow over to [your] farm,” I certainly appreciate the invitation and hope I can incorporate the insights of the strategy literature into my research program.

The risk issue originates, I think, with the “need” for developing mathematically-derived theoretical hypotheses for empirical work. Mean-variance modeling is prevalent in the literature likely because it is an elegant way of deriving mathematical hypotheses. If the requirement for mathematically-derived theoretical hypotheses weren’t in place we could begin from what is plainly obvious to all of us, namely that risk aversion is a down-side issue, and use “verbal” theory and whatever empirical method is in line with that theory. I think this is an example of mathematical rigor dictating our (theoretical) understanding of economics. Of course, this isn’t directed at you as a criticism, but at what we both criticize as an over-reliance on formal modeling.

I’m glad you enjoyed the Levins piece. It was presented to me in a research methods class in graduate school. The professor focused on criticisms of the article, but I found Levins’ article quite convincing (and, of course, humorous).

Best,

Levi Russell

]]>This discussion is really useful for early career researchers like me also contemplating adding new quant skills to increase ‘marketabilty’. I do case studies, interviews, ethnography, and follow grounded theory methodology. It appears this abstract model building goes against the grounded methodology where models need to emerge from empirics, and it should be beyond just a ‘relationship between models and data. Going back to Rich’s example on dividing effects into rovalry and comp advantage, wondered what comes in the way of discovering this through indepth interviews and field work. In other words, how could someone observe this dual effect through grounded theory work.

Thanks,

Amer khan

Curtin university Malaysia

What I would like to stress is that there are many theoretical fever-dreams that can only be dispelled with formal modeling. Some of these are my own: For example, I’ve had the idea of a tradeoff between the frequency and severity of downside events as a function of the degree of prevention undertaken, looking for an interior solution of optimal prevention. So far, no dice, and I can see where my initial primitive intuition was in error after trying to fit some functional forms and drawing some pictures. Some of these fever-dreams are others': I can’t tell you how many theory articles I’ve reviewed where I’ve wanted to shout at the page “Just build a model already!” Precise verbal theorizing is very, very hard to do, and many of the more successful practitioners (e.g. Williamson) freely resorted to drawing curves and diagrams which are–shhh–math. The idea that it’s easier to hide trivial or wrong ideas with math than with words strikes me as empirically false on a massive scale.

The same applies to Peter’s point about the “if” clauses of formal propositions not being verified in application. They are still less verified when they are never specified explicitly or when they can mutate through equivocation to seem to apply or not apply to any situation.

Formalism is a drag to both readers and writers when things that are easy to say in words (with perhaps a couple of hand gestures) must be turned into hard-to-encode-and-decode mathematical expressions. But if you are going to any depth with the analysis, you will quickly find that the things you can say by using the math are very, very hard to say in words without elaborate translation into awkward clauses, clarifications, examples, etc. A diagram may be your best bet. In fact, I’ve occasionally scared myself that some result I had formally derived earlier couldn’t be true based on erroneous verbal arguments or pictorial intuition; only going back to the math restored my understanding.

I certainly believe that formal models should be accompanied at all times by a bodyguard of hypothetical or real examples that keep the relation of the theoretical terms to aspects of reality in view. Oddly, I’ve found that most formal modelers in strategy are much more interested in such “storytelling” than are many purely verbal theorists, who often seem content to float on abstractions.

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