Week 9

Closing The Back Doors

Readings

• The Effect, Chapter 8: Closing Back Doors

• Rohrer, Julia M. “Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data.” Advances in Methods and Practices in Psychological Science 1:1 (2018): 27–42.

• Moore & Siegel, Chapter 12. Ignore sections 12.3.6 and 12.3.7 on computing determinants and inverses by hand. We have computers that do that for us now.

Overview

This week, we discuss the linear model as a general purpose tool for conditioning on confounding variables and recovering causal estimands. We will highlight the strengths and limitations of this approach, and show how to estimate the model’s parameters using matrix algebra.

Slides

(Full Screen Version)

3D Plots

Some three-dimensional plots illustrating the “plane of best fit”.

Midterm Survey

Problem Set

1. In class, we showed that GDP per capita was partly confounding the observed relationship between democracy and corruption. Can you think of any other back door paths that need to be closed? What variable would you need to measure and condition upon to close that path? Try your hand at finding a dataset with that variable, merging it with the country-level corruption dataset we created in R/week-09/cleanup-data.R, and adding it to the linear model. (You may find the countrycode package useful for that merge.)

2. Cohn et al. (2019) left wallets in cities around the world to see how many of them would be returned. It’s a very ambitious study. You can read about it here and you can find the replication data in our repository at data/cohn-2019/. You want the “behavioral data”; check out the codebook to see what all the variables mean. The experimenters varied a few things at random, including the type of institution they left it at (public, bank, etc.) and how much money was in the wallet. Your task is this: I want to know what fraction of wallets were returned in each country when they were left at public institutions (this could be another measure of public corruption; if bureaucrats just tend to steal wallets instead of returning them). Are government officials less likely to steal wallets in countries that have been democracies for longer periods of time (c_PIV_years_democracy)? What’s the slope of that relationship? And can you interpret that relationship as causal? Why or why not?

3. Optional Challenge: Replicate Figure 1 in the Cohn et al. (2019) paper using ggplot.