Rich Makadok on Formal Modeling and Firm Strategy

14 October 2014 at 11:25 am 18 comments

[A guest post from Rich Makadok, lifted from the comments section of the Tirole post below.]

Peter invited me to reply to [Warren Miller’s] comment, so I’ll try to offer a defense of formal economic modeling.

In answering Peter’s invitation, I’m at a bit of a disadvantage because I am definitely NOT an IO economist (perhaps because I actually CAN relax). Rather, I’m a strategy guy — far more interested in studying the private welfare of firms than the public welfare of economies (plus, it pays better and is more fun). So, I am in a much better position to comment on the benefits that the game-theoretic toolbox is currently starting to bring to the strategy field than on the benefits that it has brought to the economics discipline over the last four decades (i.e., since Akerlof’s 1970 Lemons paper really jump-started the trend).

Peter writes, “game theory was supposed to add transparency and ‘rigor’ to the analysis.” I have heard this argument many times (e.g., Adner et al, 2009 AMR), and I think it is a red herring, or at least a side show. Yes, formal modeling does add transparency and rigor, but that’s not its main benefit. If the only benefit of formal modeling were simply about improving transparency and rigor then I suspect that it would never have achieved much influence at all. Formal modeling, like any research tool or method, is best judged according to the degree of insight — not the degree of precision — that it brings to the field.

I can’t think of any empirical researcher who has gained fame merely by finding techniques to reduce the amount of noise in the estimate of a regression parameter that has already been the subject of other previous studies. Only if that improved estimation technique generates results that are dramatically different from previous results (or from expected results) would the improved precision of the estimate matter much — i.e., only if the improved precision led to a valuable new insight. In that case, it would really be the insight that mattered, not the precision. The impact of empirical work is proportionate to its degree of new insight, not to its degree of precision. The excruciatingly unsophisticated empirical methods in Ned Bowman’s highly influential “Risk-Return Paradox” and “Risk-Seeking by Troubled Firms” papers provide a great example of this point.

The same general principle is true of theoretical work as well. I can’t think of any formal modeler who has gained fame merely by sharpening the precision of an existing verbal theory. Such minor contributions, if they get published at all, are barely noticed and quickly forgotten. A formal model only has real impact when it generates some valuable new insight. As with empirics, the insight is what really matters, not the precision.

So, the relevant question should be: Does formal modeling generate valuable new insights? And if so, where and how?

I am aware of some ways in which formal modeling can help a theorist generate new insights. I would never say that formal modeling is absolutely necessary for generating any particular theoretical insight. Nor would I ever say that any particular insight could not be generated through verbal theorizing. Nevertheless, there are some kinds of theoretical insights that are just easier to see with the aid of a formal model. By analogy, you can, at least in principle, chop down any tree with just an axe, but there are some trees for which you would really much rather have a chainsaw, as a matter of convenience. I once heard an obstetrician convince an expectant mother to accept an epidural anesthetic by saying that it’s just a modern convenience, like air conditioning in the Atlanta summer. You can certainly survive without such modern conveniences, but why not use them if they’re readily available? That’s roughly how I think about formal modeling — just a helpful modern convenience.

Here are three kinds of insights for which formal modeling can be particularly helpful:

1.) Decomposing an effect into separate parts that may sometimes oppose each other — e.g., direct and indirect effects, or intended and unintended effects.

For example, in economics, the effect of a change in the price of a good on the quantity of that good demanded is decomposed into two separate parts — the substitution effect (a fairly direct effect) and the income effect (a somewhat indirect effect). In most situations — i.e., for “normal goods” — these two components of the effect move in the same direction, but sometimes — i.e., for “Giffen goods” — they move in opposite directions. It’s just easier to understand this kind of decomposition with the aid of a little math. I suppose that one could envision the possibility of a Giffen good without a formal model, but I imagine that it would be a lot harder.

An example of this sort of decomposition in the strategy field is in my 2013 SMJ article with David Ross, where we decompose the effect of product differentiation on profit into separate parts — a competitive-advantage effect and a rivalry-restraint effect. Sometimes these two parts move in the same direction, and sometimes in opposite directions. The math in our model helps to clarify when each part is strengthened or weakened, when they oppose each other, and when one might overwhelm the other. Could these results have been generated via verbal theorizing? In principle, I suppose so, but I think it would have been a lot harder — and I certainly could never have done it.

2.) Interaction effects

It may be relatively easy to envision the main effect that A increases B, but it may be a bit trickier to envision the interaction effects of how C, D, and E influence the strength of the effect of A on B. Is the effect of A on B dampened/undermined or amplified/reinforced when C, D, and E increase? A formal model can be quite helpful in answering such questions about interaction effects. Without a formal model, it may be difficult to develop a clear unambiguous argument for such interaction effects to be either positive or negative. Indeed,
without a formal model, a theorist might never even think of the possibility that C, D, and E could have an effect on the relationship between A and B. But such unanticipated interactions may just naturally drop out of a formal model, without even looking for them. In this regard, a formal model may even suggest new insights that the theorist had not previously contemplated.

For example, a basic agency-theoretic model in economics (e.g., Grossman & Hart, 1983 Econometrica) is about the main effect of performance-based incentives motivating behavior from an agent that is more consistent with the principal’s interests. But how is this main effect altered when the agent’s assigned tasks differ in their measurability? And how does such an interaction effect influence the division of labor among different agents? While a formal model may not be absolutely required to answer these interaction-effect questions, the one developed by Holmstrom & Milgrom (1991 JLEO) sure helps a lot.

Likewise, in the strategy field, I have often used formal models to hypothesize interaction effects on profit that would have been difficult (at least for me) to envision otherwise. My 2001 SMJ article finds that there is a negative interaction effect between the profitability of information-based advantages and the profitability of deployment-based advantages. My 2003 SMJ article finds a positive interaction effect between the profitability of skills and the profitability of motivation. My 2010 Management Science article finds a negative interaction effect between the profitability of competitive advantage and the profitability of rivalry restraint. I suppose that, in principle, someone else might have been able to envision these results without relying on a formal model, but I definitely could not have.

3.) Boundary conditions

In extreme cases, if an interaction effect is particularly severe, it can completely overwhelm the main effect. For example, A may ordinarily increase B, but if A and C have a negative interaction effect on B, then it is possible that a sufficiently large value of C may totally erase the effect of A on B, or perhaps even reverse the ordinary effect of A on B so that A actually decreases B. We often call this a “boundary condition” of the positive effect of A on B (i.e., C must be sufficiently low).

In this regard, Peter is correct that one benefit of formal modeling is “bringing to light the hidden assumptions of the old-fashioned, verbal models” — insofar as a “hidden assumption” is just an unrecognized boundary condition. However, that is only half of the story. A formal model not only can identify the boundary condition, but it can also make predictions about what happens when the boundary condition gets violated.

In economics, there are many examples of such boundary conditions being identified through formal modeling. For instance, consider Bertrand’s response to Cournot oligopoly — i.e., two firms can be sufficient to eliminate all profit from an industry if their behavior toward each other is sufficiently aggressive. Likewise, Akerlof shows that asymmetric information can be a boundary condition on the ability of markets to improve welfare. Were the formal models absolutely essential to achieving these insights about boundary conditions? Maybe not. But do the formal models help an awful lot in visualizing and explaining these boundary conditions? Certainly.

In the strategy field, a formal model by Luis Cabral & Miguel Villas-Boas (2005 Management Science) demonstrates a boundary condition on the idea that publicly-available synergies would increase the profit of firms in an industry, by showing that sometimes they can actually decrease firms’ profits. My own forthcoming SMJ paper, coauthored with Jens Schmidt and Thomas Keil, takes this boundary condition one step further by showing that even private, proprietary synergies can sometimes backfire and reduce profit. I cannot speak for Luis, Miguel, or my coauthors Jens and Thomas, but I know that I certainly could neither have envisioned nor anticipated this boundary condition without the tool of formal modeling.

Anyway, that’s my defense of formal modeling as a research tool.

For myself, I work really hard to make my formal modeling papers accessible to earthlings. I try to write them in a way that any reasonably intelligent MBA student could read them, skip over the math, and still get all of the main points. Unfortunately, most game theorists in the economics discipline and even some of the modelers in strategy do not share my philosophy about this. In my humble opinion, they do a disservice to themselves, their field, and their citation counts by neglecting this duty.

Entry filed under: History of Economic and Management Thought, Methods/Methodology/Theory of Science, Myths and Realities, Strategic Management.

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18 Comments Add your own

  • 1. Joshua Gans  |  14 October 2014 at 11:51 am

    Good one. Damn straight.

  • 2. rmakadok  |  14 October 2014 at 3:41 pm

    Thanks, Josh.

  • 3. LR  |  14 October 2014 at 9:54 pm

    I don’t see Warren’s comment on the Tirole post.

    Interesting comments here, but I prefer Bryan Caplan’s analysis of “economath.”

  • 4. Peter Klein  |  14 October 2014 at 10:04 pm

    Sorry, this one:

  • 5. LR  |  15 October 2014 at 11:25 am

    Maybe I’m blind, but I just don’t see anyone named Warren in that thread. Deleted comment maybe?

  • 6. Peter Klein  |  15 October 2014 at 11:27 am

    OK, sorry again — it’s the comment linked above, authored by “beckmill,” the name of Warren Miller’s firm.

  • 7. @mdryall  |  15 October 2014 at 1:37 pm

    Nice discussion Rich. I agree that verbal theory and formal theory both provide insights – typically, the insight of formal theory is to grasp why the insight of verbal theory is wrong.

    An example close to my heart is the growing stream of work on value capture under competition (the one based upon cooperative game theory). Results in this line illustrate not only the falsity of many canonical theoretical “insights” in strategy, but also explain why this is so.

    Another, related, benefit is discovering relationships hidden to informal intuition (which is what verbal theory is). For example, the value capture work claims that competitive *intervals* are central to understanding firm performance. Maybe a sufficient period of loose, informal reflection could also have surfaced this insight … but, I honestly doubt it.

    Moreover, we now have young scholars actually using advanced empirical techniques to estimate these intervals based upon the theory. Even had the insight arisen via informal reasoning (which it didn’t), there is no way one could run the complex linear programs required to estimate interval boundaries in one’s head. In this case, the theory is required for the empirics.

    Having been an active participant in this debate over the last 20 years, I see Strategy as a field is moving away from its more incoherent biases wrt the efficacy of formal methods. So, I’m very optimistic.

    Keep up the good fight, Rich!

  • 8. RussCoff  |  15 October 2014 at 5:25 pm

    Let me begin by seconding Rich’s comments — probably not a surprise since we have worked together. One thing that strikes me is how quickly a model can yield insights that are not intuitive (interesting in a Murray Davis sense). Even partly relaxing an assumption or adding an interaction can lead to unanticipated findings because a small amount of complexity may quickly outstrip naive intuition. I use the term “finding,” which is often reserved for empirical research, because the resulting insight often reflects an aha moment. Of course, these depend on the model’s internal logic but these boundary conditions are a starting point for further inquiry (whether empirical, conceptual, or additional models).

    We are only held back by our failure to communicate with each other. Put another way, I agree with Rich that, to maximize impact, such papers should be written so the main insights is accessible to non-modelers. And, I might add, non-modelers must make an effort to incorporate this as well (like any other method).

    In sum, we can learn, ask more (and different) questions, and move the literature forward. Or we can form separate isolated communities and the literature will likely stagnate…

  • 9. Peter Klein  |  15 October 2014 at 11:55 pm

    I appreciate Rich’s thoughtful observations and the rich discussion in the comments. Mike Ryall’s formulation is a little strong for my tastes, however. It doesn’t follow from “I can write down a model in which X is true” that X is in fact true in a particular case. The models we’re discussing include myriad assumptions about players, preferences, endowments, payoffs, and the like, not to mention all sorts of ceteris paribus conditions. Insightful as any particular formal model may be, its judicious application to any real problem is as much an art as the application of verbal or any other kind of reasoning. Theoretical propositions, whether verbal or mathematical, consist of if-then statements. Strategists (like game theorists in economics) tend to focus on the thens, but may lose sight of the ifs. That was my point about Tirole. There is sometimes a tendency to overstate the usefulness of particular frameworks or modeling techniques because their proponents tend to concentrate on the internal consistency of the frameworks and techniques, not the conditions under which they apply, or whether the problems they solve are really the right problems. As Rich says, let’s evaluate each model or modeling strategy on the merits.

  • 10. LR  |  16 October 2014 at 2:00 pm

    What soured me on mathematical modeling was the tendency for research to emphasize mathematical clarity over economic rigor. Richard Levin’s article “On Farmers Who Solve Equations” way back in 1989 is very good on this issue. Another example that has been on my mind recently is the insistence in the literature that fertilizer is a risk-increasing input for farmers. Economists were baffled that producers over-apply this input, even though it is “risk-increasing.” What these economists missed is the reality that variance is not a good proxy for real-world risk. People treat risk as a downside issue, not as variability. Thankfully, a recent paper admitted this issue. We’ve had math programming tools for dealing with downside risk for 3 decades, but the elegant math, I suspect, was much too attractive to pass up and we’ve been wasting our time with the risk-as-variance paradigm for much longer than was necessary.

    Apparently not all that glitters is gold.

  • 11. rmakadok  |  17 October 2014 at 12:02 am

    Hi, LR.

    Thanks for suggesting the amusing “On Farmers” article by Levins, which I had not previously known about.

    For the benefit of others who are following this thread, I located an online copy of this article at the following address:

    I confess that I am unfamiliar with the fertilizer/risk literature that you mention, so perhaps I am missing or misunderstanding something important, but what you describe sounds more like an empirical measurement issue to me. Am I missing or misunderstanding something?

    Also, thanks very much for your pointer to Bryan Caplan’s “economath” blog posts, which I also had not previously known about. I stand behind my argument that insight, rather than precision or rigor, is really what matters. For that reason, I quite agree with you that when formal modeling is pursued so excessively that it no longer yields any meaningful insight, then its return on investment (i.e., investment in training and effort) can certainly be negative. Based on your comments and Caplan’s, it sounds like this may be the case in many subfields of economics, and perhaps even for the economics discipline as a whole. Even Paul Krugman’s DEFENSE of formal modeling (in response to Caplan) starts out by frankly admitting that this is true, as follows: “I don’t really disagree with this statement [i.e., the statement that ‘most economath badly fails the cost-benefit test’]; after all, Sturgeon’s Law — 90 percent of everything is crud — definitely applies to economics, and when it comes to elaborate mathematical models you probably want to up the percentage.”

    What makes me happy about this — because it gives me (and Josh and Mike and Olivier and a few others) job security — is the fact that I DON’T live inside an old discipline like economics where formal modeling has been the norm for 40 years and has been dramatically overused to the point where it no longer yields much new insight. Rather, I live in the relatively young field of strategic management where formal modeling is still very new and dramatically underused, so that there will remain, for many years to come, plenty of “low-hanging fruit” where genuinely new insights can be derived via formal models. So, if the “soil” for formal modeling in your area of research has been depleted due to excessive tillage, then I invite you to bring your plow over to our farm, where newly-cleared fields are still fresh and fertile. We could sure use more farmhands over here, so feel free to bring some friends along too.


  • 12. ochatain  |  17 October 2014 at 7:56 am

    Hi there, as I also make a living out of formal modeling in strategy, I guess I should chime in too. This debate has been very informative and I’d like to thank all the contributors, as this is the perfect complement to the PhD course I have just started to teach.

    Of course I agree with everything that was said about the role of formal modeling to generate insights that were unanticipated. This accords with my personal experience developing papers using game theoretical models. I’d just like to add two unrelated observations to this debate.

    First the role of the formal model as both a discipline and a spur for your intuition is not to be neglected. For one thing you cannot get any result you want unless you explicitly change your assumptions. This can tell a lot about the value of these assumptions. For another, you sometime get a result which you know is mathematically correct but for which you have absolutely no intuition. You just don’t know what is going on. All the work necessary to figure out where the result is coming from in terms of mechanism is really valuable. And it is tricky too because one can easily give the wrong interpretation to a formula that was correctly derived. But I often feel I learn the most in that phase.

    Second, I think it is extremely important to establish the connections between formal theory and empirical work, especially in strategy. When I write a theory paper one of my explicit goals is to help empiricists to do a better job. This can be by providing new hypotheses to test. More subtly, it can be about providing alternative explanations that may help us reconsider the usual interpretation given to empirical patterns (e.g., Lippman and Rumelt’s 1982 paper).
    Another way is to provide a toolbox to deeply integrate the theory and the empirics. This is what is starting to appear in the value-based literature as seen in recent workshops at the AOM and at SMS. That one has been a long run effort that seems just to start paying off.


  • 13. stevepostrel  |  17 October 2014 at 8:48 pm

    I’m on the record on this topic at this blog with past posts, so let me just state my general agreement with Rich’s main point. Let me also agree with the point in his comment above that if you believe in diminishing marginal returns, the strategy field is likely to be significantly under-formalized while econ is more likely to have overshot (I personally doubt this latter, though).

    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.

  • 14. Amer  |  18 October 2014 at 3:42 am

    Hi all,

    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.

    Amer khan
    Curtin university Malaysia

  • 15. LR  |  18 October 2014 at 11:14 am


    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).


    Levi Russell

  • 16. rmakadok  |  18 October 2014 at 12:16 pm

    Hi, Amer. Thanks for your note.

    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 ).

    Thanks again,

  • 17. Rafe Champion  |  19 October 2014 at 8:02 am

    Interesting old book! Truth versus Precision in Economics, by Thomas Mayer, 19993.

    Maths can be misleading even in the physical sciences

  • 18. David Hoopes  |  7 November 2014 at 9:17 pm

    It’s important to distinguish between the benefits of modeling to IO economics versus the influence of modeling in business strategy (or what modelers might call management strategy). Peter notes in his original post a book review by Sam Pelzman. Pelzmen contrasted a 1950s IO handbook with a 1980s handbook (with chapters by Tirole!). Pelzman noted in the 1950s book theory made up 33% in the 1980s book 80%. In the former book anti-trust was central in the latter it was peripheral.

    The problems facing 1990s business strategy were quite different than Pelzman’s concerns for IO. At the time, and to this day, there is a lot of “verbal” strategic management theorizing that gets published that can be conceptually sloppy. This doesn’t mean one can’t be very precise. It just so happens that in management and strategy a lot of “theory” and empirical work cashes in big on being vague and mushy. People can read into it whatever they want.

    In my opinion then, formal modeling’s marginal benefit to strategy is substantial. (Aside: economists have been doing a lot of solid empirical work relevant to strategy in the last 20 years).

    Thus, long time O&M friend S. Postrel is pretty handy to have around if you’re mucking through lots of qualitative theories since he happens to have some very nice models to aid thinking things through.

    As a few people above point out the models are more useful if there are some data and expectations grounded in observation to use with them. In the field of strategy this has not been a big problem. In 1980s IO perhaps it was.

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