Formal Modeling

[ThisGuyRiteHere]

So formal modeling is:

"Applications of game theory—and an alternative strategic theory called “theory of moves”—as well as social-choice theory to a wide variety of strategic situations, principally but not exclusively in politics, will be examined. Uses of strategy in voting in committees and elections, in political campaigns, in the defense and deterrence policies of nations, and in bargaining and coalition-building situations will be among the topics discussed. Secrecy and deception as political strategies will also be analyzed."

I am debating on taking this with research design and statistics. Is this too much for your first semester? I do not want to overload myself and my funding is dependent on the first semester, so I cannot mess it up. Is formal modeling tough for someone with some statistics and game theory background (undergrad classes in each subject)

[jazzrap]

Formal modeling has little to do with statistics, although it is not PC to say it. 

[ThisGuyRiteHere]

So what does it have to do with? Can you give me some basic examples of the type of work it would consist of?

[jazzrap]

It has more to do with Calculus and probability. By statistics I meant regression models. 

[AmericanQuant]

I can't really say what your particular course will be like. But I don't think jazzrap is exactly correct, formal modeling is more like real analysis than calculus.

[wtncffts]

How many courses are you supposed to take? I ask because I'd think you're also required to take at least one substantive course (that is, not methodology), but maybe your program is structured that way. If it is the case that in addition to research design and a stats course you also are taking a substantive course, that should be a full course load right there.

[jazzrap]

I can't really say what your particular course will be like. But I don't think jazzrap is exactly correct, formal modeling is more like real analysis than calculus.

A lot of models require more calculus than regressions (they require no regressions). This is what I meant basically. But thanks for the reply. 

[jazzrap]

OP, 

 

A minor question about your status. Are you applying in the Fall while already attending a doctoral program? I am just curious:)

[catchermiscount]

Don't listen to anything in this thread so far.

 

Formal modeling is when you create and analyze a mathematical model of behavior of some kind.  It need not be game theoretic or social choice theoretic, though those are both very prominent in the business.  It could be something as simple as the Prisoner's Dilemma, which is a 2 by 2 strategic form game that most incoming students have heard of.  The Prisoner's Dilemma, despite being really simple, can be used to develop all sorts of insights about public good provision, and more complicated models of public good provision often boil down to Prisoner's Dilemma logic.  And so on.

 

A formal model, naively, has nothing to do with statistics.  People start seeing Greek letters and they figure "oh, quantitative is quantitative."  Not so.  Consider the social choice literature best represented by its exemplar, Arrow's Theorem.  Arrow's Theorem has nothing to do with the "real world."  It's not an empirical model at all.  There is no "testing" it to see whether or not it comports with the real world, because it isn't meant to and doesn't generate testable hypotheses.  Now, many people in political science would say that this means that Arrow's Theorem is flawed in that it doesn't tell us anything about the real world.  You might have seen arguments like that in your undergraduate courses---there's a well known book entitled Pathologies of Rational Choice Theory that goes into it in great detail.  Note also that not all quantitative analysis is alike:  Don Green, one of the authors of PRCT, has been highly influential by promoting field experiments and other causal research designs, and many of his influential papers are free of regression analysis.  After all, randomization does a lot of work if you let it.

 

Of course, not all formal models are like Arrow's Theorem (if only!).  For starters, Arrow's Theorem isn't game theoretic, and most applications of formal theory in political science are in fact game theoretic.  Not all of these are testable, either.  For example, James Fearon famously uses game theory to tease out three "Rationalist Explanations for War."  Very simple bargaining models, but certainly game theoretic.  He uses them to keep his logic tight and to facilitate the exposition---it's not like he gives us "Fearon's Theorem" out of it.  Some folks have tried testing Fearon's arguments, but it's hard to say "oh man, I just read Fearon's paper, and I got these hypotheses out of it."  In the study of American politics, you get a similar feel from the work of Riker, Shepsle, Ordeshook, Schofield, Calvert, McKevley, and so many others.  They're using formal models to describe and explain.  Often what they're doing interfaces with political philosophy as much as it does with "modern," empirical social science. 

 

So, formal models are not necessarily empirical, and not all Greek letters are the same.  One question that the business is grappling with is how formal theory informs empirical analysis.  You may have heard of the EITM (Empirical Implications of Theoretical Models) project, which offers summer courses and support.  While much of that is just dedicated toward good formal modeling, the name of the project itself should tell you what the idea is:  develop a formal model, derive testable empirical hypotheses, and test those assumptions.  For example, you might solve a model to determine the equilibrium expression of one parameter as a function of other parameters.  Then you can take a partial derivative of that function and determine whether it is positive or negative, which is an empirical hypothesis that can be tested in a regression setting. With apologies, some of the people that have taught me don't like that idea very much.  You might look into their book, which is entitled A Model Discipline.  One might also wonder how formal models can inform causal empirical models, which is a very difficult question to answer (and one I've been chewing on for a while---the answer gets messy in a hurry).

 

The use of such models in economics is pretty much unquestioned.  You don't have to be a super duper technician to be able to use or create basic models.  Hell, deriving a demand function is formal modeling.  Many famous economists use relatively simple formal models to make very sophisticated arguments.  Stiglitz comes immediately to mind.  Mancur Olson kinda sorta used formal models, though his arguments inspired many formal modelers.  For a really cool paper in that vein, you might look for Esteban and Ray's "The Group Size Paradox Revisited," which is kind of microeconomic theory and kind of game theory. 

 

OK, that's more answer than you wanted, but this is a hobby horse of mine and I'm sitting around convalescing after surgery anyway.  If you're looking to read some formal work, you might look into some basic social choice stuff (even though it isn't all that applicable now).  Arrow's Social Choice and Individual Values, Riker's Liberalism versus Populism, and Ordeshook's Game Theory and Political Theory are nice books.  To see a very direct interface between formal theory and political philosophy, you might read some of Sen's Rationality and Freedom.  Or even more directly, you might skim some (deep, technical) work by John Harsanyi, who basically developed models aimed at getting after Rawls' initial position.  Fearon's famous "Rationalist Explanations for War" is an amazing paper always worth reading, and again, you'll note that it interfaces with qualitative work---this time history.  Many, many formal folks in IR and comparative have done similar things with history or qualitative security studies; many of them cite Schelling or Clausewitz or Waltz.  Indeed, two of the most prominent formal modelers in IR---James Fearon and Robert Powell---were Waltz students.  To see some argumentation and testing, you might look at Krehbiel's Pivotal Politics versus Cox and McCubbin's Legislative Leviathan.  Those guys disagree about how to model Congress, and as such disagree about predictions, and as such disagree about empirics. 

 

If you have more specific questions, feel free to IM with the sort of things you like reading and I'll see what I can come up with.

Edited May 21, 2013 by coachrjc

[catchermiscount]

And to answer your question:  you can do design, stats, and theory in one semester, though it'd be pretty tough.

[ThisGuyRiteHere]

Thank you for the answers. I am more mathematically prepared than the average student (I think), but I am going to sit formal methods out (for now at least). Comparative it is!

And to jazzrap, I am starting in August.

[jazzrap]

On 5/21/2013 at 7:55 AM, coachrjc said:

Don't listen to anything in this thread so far.

 

Formal modeling is when you create and analyze a mathematical model of behavior of some kind.  It need not be game theoretic or social choice theoretic, though those are both very prominent in the business.  It could be something as simple as the Prisoner's Dilemma, which is a 2 by 2 strategic form game that most incoming students have heard of.  The Prisoner's Dilemma, despite being really simple, can be used to develop all sorts of insights about public good provision, and more complicated models of public good provision often boil down to Prisoner's Dilemma logic.  And so on.

 

A formal model, naively, has nothing to do with statistics.  People start seeing Greek letters and they figure "oh, quantitative is quantitative."  Not so.  Consider the social choice literature best represented by its exemplar, Arrow's Theorem.  Arrow's Theorem has nothing to do with the "real world."  It's not an empirical model at all.  There is no "testing" it to see whether or not it comports with the real world, because it isn't meant to and doesn't generate testable hypotheses.  Now, many people in political science would say that this means that Arrow's Theorem is flawed in that it doesn't tell us anything about the real world.  You might have seen arguments like that in your undergraduate courses---there's a well known book entitled Pathologies of Rational Choice Theory that goes into it in great detail.  Note also that not all quantitative analysis is alike:  Don Green, one of the authors of PRCT, has been highly influential by promoting field experiments and other causal research designs, and many of his influential papers are free of regression analysis.  After all, randomization does a lot of work if you let it.

 

Of course, not all formal models are like Arrow's Theorem (if only!).  For starters, Arrow's Theorem isn't game theoretic, and most applications of formal theory in political science are in fact game theoretic.  Not all of these are testable, either.  For example, James Fearon famously uses game theory to tease out three "Rationalist Explanations for War."  Very simple bargaining models, but certainly game theoretic.  He uses them to keep his logic tight and to facilitate the exposition---it's not like he gives us "Fearon's Theorem" out of it.  Some folks have tried testing Fearon's arguments, but it's hard to say "oh man, I just read Fearon's paper, and I got these hypotheses out of it."  In the study of American politics, you get a similar feel from the work of Riker, Shepsle, Ordeshook, Schofield, Calvert, McKevley, and so many others.  They're using formal models to describe and explain.  Often what they're doing interfaces with political philosophy as much as it does with "modern," empirical social science. 

 

So, formal models are not necessarily empirical, and not all Greek letters are the same.  One question that the business is grappling with is how formal theory informs empirical analysis.  You may have heard of the EITM (Empirical Implications of Theoretical Models) project, which offers summer courses and support.  While much of that is just dedicated toward good formal modeling, the name of the project itself should tell you what the idea is:  develop a formal model, derive testable empirical hypotheses, and test those assumptions.  For example, you might solve a model to determine the equilibrium expression of one parameter as a function of other parameters.  Then you can take a partial derivative of that function and determine whether it is positive or negative, which is an empirical hypothesis that can be tested in a regression setting. With apologies, some of the people that have taught me don't like that idea very much.  You might look into their book, which is entitled A Model Discipline.  One might also wonder how formal models can inform causal empirical models, which is a very difficult question to answer (and one I've been chewing on for a while---the answer gets messy in a hurry).

 

The use of such models in economics is pretty much unquestioned.  You don't have to be a super duper technician to be able to use or create basic models.  Hell, deriving a demand function is formal modeling.  Many famous economists use relatively simple formal models to make very sophisticated arguments.  Stiglitz comes immediately to mind.  Mancur Olson kinda sorta used formal models, though his arguments inspired many formal modelers.  For a really cool paper in that vein, you might look for Esteban and Ray's "The Group Size Paradox Revisited," which is kind of microeconomic theory and kind of game theory. 

 

OK, that's more answer than you wanted, but this is a hobby horse of mine and I'm sitting around convalescing after surgery anyway.  If you're looking to read some formal work, you might look into some basic social choice stuff (even though it isn't all that applicable now).  Arrow's Social Choice and Individual Values, Riker's Liberalism versus Populism, and Ordeshook's Game Theory and Political Theory are nice books.  To see a very direct interface between formal theory and political philosophy, you might read some of Sen's Rationality and Freedom.  Or even more directly, you might skim some (deep, technical) work by John Harsanyi, who basically developed models aimed at getting after Rawls' initial position.  Fearon's famous "Rationalist Explanations for War" is an amazing paper always worth reading, and again, you'll note that it interfaces with qualitative work---this time history.  Many, many formal folks in IR and comparative have done similar things with history or qualitative security studies; many of them cite Schelling or Clausewitz or Waltz.  Indeed, two of the most prominent formal modelers in IR---James Fearon and Robert Powell---were Waltz students.  To see some argumentation and testing, you might look at Krehbiel's Pivotal Politics versus Cox and McCubbin's Legislative Leviathan.  Those guys disagree about how to model Congress, and as such disagree about predictions, and as such disagree about empirics. 

 

If you have more specific questions, feel free to IM with the sort of things you like reading and I'll see what I can come up with.

 

Hi, 

 

Sorry for stepping on someone's toe. I was kind of being sarcastic in the beginning. I wonder if you are doing formal model and have thought about the prospects of testing models. If so, I am on you side. I believe that models can be tested, although it remains a difficult challenge. However, the reality has put modelers in an odd position. Qualis and Quantis don't seem to care about modelers as much as modelers care about them.This is what I meant by saying "formal model has little to do with statistics, though it is not PC to say it". My apologies to OP, because I was being sarcastic in answering your question.

 

Now back to the original question: what mathematical background you would have to survive the intro course. My position remains the same: you need no stats, only a few probability rules and a sense of how to take derivatives. This is what would take for an intro course in a PhD program. However, if you are in NYU, Rochester, UCSD, WashU, you might need more beforehand. I don't know much about those schools. They just have a reputation for very heavy emphasis on math. Perhaps the 10th floor can address this better.

 

That said, game theory is not all about math, it requires some forms of thinking (as I feel personally) other than typical math. In other words, it is time consuming to digest. If you are taking stats, design, substantive classes, then it might be wise to wait for another semester or two to take the intro to formal modeling. 

[catchermiscount]

Jazzrap is right to mention that theory isn't just about math.  It's very much a way of thinking about things.  But, many theory classes are all about math, be they "how to do theory" or "how to read important theory papers." 

 

I am a student at one of the schools jazzrap enumerated, and we don't have any mathematical prerequisites for our theory sequence.  We've got a two-week math boot camp that brings you up to speed on basics like sets, functions, sequences and series, continuity, and derivatives and integrals.  The theory sequence itself starts with a few weeks of formal logic and builds up from there. 

 

Think of it this way.  If you read Simon and Blume's textbook, Mathematics for Economists, they refer to the chapters on optimization as the heart of the book.  After all, it's the heart of theory---people are maximizing something more often than not.  To understand optimization, you need to understand functions, continuity, and enough calculus to get first- and second-order conditions (derivatives, understanding Hessians and so on).  You might also need to know something about concavity and quasi-concavity for basic programming issues.  But no class I can think of takes that kind of knowledge as given.  The point of graduate training is...you know...training.  Now, if you intend to be a capital-T Theorist, you might come in with more knowledge.  But the average applied user can certainly pick that much up while being trained. 

 

How well you can balance that with design at once...who knows.  We take four classes per semester in the first year---one methods, one theory, one philosophy or research design, and one substantive.  It can be a bit of a time crunch, to be sure.  You might not want to self-inflict that much work.