Rich Makadok on Formal Modeling and Firm Strategy
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.