Stochastic Models of Political Economy

Winter 2002

Department of Political Science

University of Michigan

Course Description: An introduction to probability-based models in political science and political economy. We will begin with an intensive review of the necessary probability theory and measure theory, including relevant distributions, moment generating functions and characteristic functions, Bayes estimators for sample functions, sufficient statistics, Laplace and Fourier transforms and other topics. We will then consider stochastic models of decisions and organizational processes, including models of budgetary decisionmaking and bounded rationality (Padgett, Carpenter), models of riots (Spilerman), and models of organizational failure (Bendor, Heimann). We will then turn to models of optimal stopping, optimal control and optimal experimentation (strategic experimentation and bandit models). Concepts covered will include Brownian motion, compound and simple Poisson processes, Ito's Lemma, smooth pasting, and others. Applications will include models of optimal product approval, optimal time to prosecution, bandit models of detente between two states, models of turf competition between states or bureaucracies, models of competitive adoption (the adoption of new policies by states in a federalist system, when to call an election or break a story in a competitive news market, etc), and optimal institutional termination (optimal stopping of Poisson processes, with applications to the lifetime of agencies).

 

 

 

Syllabus
Note: This syllabus will continue to be edited throughout the semester. Suggestions, especially additions of applied material, welcome.

 

Sessions

All Sessions will be given in Lorch 373, and will be based in a combination of PDF files and blackboard equations. After (sometimes before) class I will make the class slides available to students on the Internet (in PDF or in HTML format). You should not use these notes as a substitute for attending Sessions.

Session

Slides

PDF

Session 1 [1/9/2002] - Introduction, Random Variables and their Distributions I

 

Session 2 [1/16/2002] - Random Variables and their Distributions II

Session 3 [1/23/2002] - Conditional Probability, Conditional Expectation and Bayesian Updating

Session 4 [1/30/2002] - Markov Chains, Theory and Applications

Session 5 [2/6/2002] - Exponential and Poisson Processes, with Applications to Diffusion

Session 6 [2/13/2002] - Models of Organizational Attention and Memory

Session 7 [2/20/2002] - Models of Bounded Rationality

Session 8 [3/6/2002] - Reliability Theory and Institutional Redundancy I

Session 9 [3/13/2002] - Reliability Theory and Institutional Redundancy II

Session 10 [3/20/2002] - Brownian Motion

Session 11 [3/27/2002] - Optimal Stopping I

Session 12 [4/3/2002] - Optimal Stopping II

Session 13 [4/10/2002] - Bandits I

Session 14 [4/17/2002] - Bandits II

Session 14 [Alternate] - Wrap-Up and Finish

 

 

Some links

Yuval Peres' Papers and Session Notes on Brownian Motion

Joe Conlon's Papers on 3-D Wiener Processes, Green's Functions, and other stuff

Ernesto Mordecki's Notes on Poisson Processes

Rob Bradley's Self-Avoiding Walks Page

 

My Scattered Notes

A Heuristic for Understanding the Difference between lim sup and lim inf

Using Laplace Transforms in Stochastic Models [coming soon!]

Using Infinitesimal Markov Generators for Optimal Stopping of Poisson Processes (Simple and Compound) [coming soon!]