Now That Your Synapses are Firing…. A Look Ahead at Things to Come

Edmund Malesky, Ph.D., UCSD Now That Your Synapses are Firing….A Look Ahead at Things to Come Quantitative Methods II Lecture 19

What Have We Done? • In this course we have learned the basic techniques of regression analysis • We have also learned some of the central problems in using regression on political science data • But there are many other tools and estimators used in political science

Maximum Likelihood Estimation • MLE is a broader method for conceptualizing statistical inference • We have estimated a model and asked the question what is the probability that the true data differ from this model? • MLE asks, what is the likelihood of this model given the data we observe?

Pervasive Endogeneity Problems • Endogeneity is one of most pervasive problems in social science research • Fundamental problem is the lack of experimental data • “Causes” can almost always be “effects” • Most common response is to ignore this problem • We can do better than that!

Examples of Ignored Endogeneity • Trade is a cause of international peace • OR…states trade if they anticipate peace • Democracy causes economic growth • OR…economic growth causes democracy • Campaign money causes candidates to win elections • OR…donations go to anticipated winners

Why Is Endogeneity a Problem? • We have equation y=Xβ+u • We observe covariation between an x and y • We attribute this covariation to β – the impact of x on y β x y

The Causal Indeterminacy of Covariation • But if y may also be a cause of x, how are we to assess the overlap of x and y • Should covariation be attributed to β, or a second coefficient “φ” reflecting the impact of y on x? β/ φ y x

The Sources of Endogeneity Bias • The size and direction of endogeneity bias is a function of the covariance between u1 and u2 • IF x causes y and y also causes x, but the error terms are not correlated across these equations, we can analyze the equations separately • BUT…this scenario is quite unlikely

When Do We Estimate Endogeneity?An Example from Public Opinion Demographics (Age, Race, Gender) Party Identification Education Tolerance For Casualties US Right to Attack US Will Succeed

Solutions to Endogeneity Bias • There are two major strategies for coping with endogeneity • First, define and measure observations so as to avoid endogeneity • Second, specify the endogenous system and account for the covariance of e1 and e2 in the estimation using instrumental variables regression.

Solution 1: Experimental Research • Endogeneity bias illustrates one of the great strengths of experimental research • Think about whether your causal mechanism could be addressed through experiments • Could be used in combination with other types of “real world” data • Prof. McIntosh is the IR/PS expert on this research strategy.

Solution 2: Instrumental Variables Steven Levitt of Freakonomics Fame is the master of this approach (i.e. using fire department spending to instrument for police spending.) Our own Chris Woodruff has a famous instrumental variable to his name as well (distance of villages from railway line in Mexico). • The basic strategy is to find an estimator (z) that is both contemporaneously uncorrelated with the error term from the original model and that is correlated (preferably highly so) with the regressor for which it is to serve as an instrument (Kennedy 1992, Bound, Jaeger, and Baker 1995, Timpone 2001). • If so, we can IDENTIFY the parameter φ. y x Z

Time-Series Analysis • We have modeled structural relationships in our data and made assumptions about the stochastic term • Time-series analyses model the stochastic variation and then ask whether structural effects matter given this pattern

Cross-Sectional Time Series • Here the approach is structural like our class • Similar to autocorrelation issues • But much more complex when we have spatial and temporal issues at the same time • Increasingly common tool

Event History Analysis • Many political phenomena occur over time • This approach keeps to structural modeling approach but addresses dependent variables relating to time (asks the question “how long?”) • Also known as survival analysis or hazard analysis

Latent Variables • Many political science theories relate to unobserved concepts • Latent variables models can explicitly model these complex variables • Also good for coping with measurement error • LISREL models – common in survey work

Bayesian Statistics • Models dynamic processes based on assumptions about prior distributions of probabilities and the updating of new information

Th-Th-Th That’s All Folks! • All these things and many more are awaiting you in QM3 and beyond. • Thanks for a great quarter!

Now That Your Synapses are Firing…. A Look Ahead at Things to Come