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Understanding Simultaneous Equations in Presidential Popularity and Military Force

This overview explores advanced techniques in POLS 603, focusing on the interplay between presidential popularity and the use of military force. It delves into the concept of endogeneity, clarifying the distinction between endogenous and exogenous variables. Emphasizing the simultaneous causation between popularity and military decisions, the text outlines the essential conditions for estimating simultaneous models, including identification criteria. Methods such as 2-Stage Least Squares and FIML are highlighted, along with the course's focus on complex mathematical modeling and advanced analytical techniques.

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Understanding Simultaneous Equations in Presidential Popularity and Military Force

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Presentation Transcript

  1. More advanced techniques & A quick look at POLS 603

  2. Simultaneous Equations • There are times when we are unsure of causation • Consider the following hypotheses • Presidents use military force intentionally to boost their popularity • When popularity is high, presidents are les restrained in their decisions to use force • Does use of force cause changes in popularity, or do changes in popularity cause presidents to elect the use of force?

  3. A Model of Presidential Popularity • So: • Note that since Use of Force is related to ut, and Popularity is related to et, there are correlated errors. • We sometimes refer to this as an endogeneity problem.

  4. Variable types • This leads us to classify the variables in a model as one of three types: • Endogenous variables – those that are determined within the model structure. The dependent variable is endogenous. • Exogenous variables – those that are determined outside the model. The independent variables are exogenous. • Lagged endogenous variables, which are often treated as exogenous variables due to their prior causation.

  5. Simultaneous Causation • Because of our prior hypotheses, we can infer that Presidential Popularity and the decision to use Military Force cause each other. • They are simultaneously determined. • For a sociologist, this is a non-recursive model.

  6. Conditions to estimate Simultaneous models • In order to estimate such a model, we have to satisfy certain conditions, which we call Identification: • Order Condition: In order for an equation to be identified, it must exclude at least M-1 variables. • Just Identified • Over identified • Rank Condition: An equation is identified if and only if at least one non-zero determinant of order (M-1)(M-1) can be constructed from the coefficients of the variables excluded from that equation.

  7. Methods of estimation • 2 Stage Least Squares (2SLS) • 3SLS • FIML

  8. Uses • Macroeconomic models of the economy. • Sometimes, thousands of equations.

  9. POLS 603 • Easier course than 602 • Readings harder in that they are more complex models, with more complex math • Expectations about math are less • Requirements • Take home final with general comp style questions • Paper using 1 advanced method

  10. Topics for 603 • Matrix Algebra • Time Series • Univariate • Multivariate • Polled Cross sectional time series • Vector Autoregression • Others

  11. Event History analysis • Duration • Survival • Count Models • Social Network Analysis • Bootstrapping • Computational Models (AI)

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