Reading

• Olga V. Chyzh. 2024. How to stop contagion: Applying network science to evaluate the effectiveness of covid-19 vaccine distribution plans. Journal of Politics 86 (1): 18-35.

• Karthik Rajkumar, Guillaume Saint-Jacques, Iavor Bojinov, Erik Brynjolfsson, and Sinan Aral. A causal test of the strength of weak ties. Science, 377(6612):1304--1310, 202

Very Healthy Cereal

Empirical Observation

• This cereal sticks to a magnet.

Why Did it Stick?

• Propose a theoretical model (that includes a causal mechanism) to explain the observation.

• Suppose our causal mechanism is that this cereal sticks to a magnet because of its iron content.

• A testable hypothesis: cereals that are high in iron stick to a magnet.

Test

Does It Stick?

• This cereal does not stick to a magnet.

Causal Effect

• Unit of analysis: cereal type

• Treatment variable (causal variable of interest) $T$: iron content (high/low)

• Treatment group (treated units): Total cereal

• Control group (untreated units): Honey Smacks cereal

• Outcome variable (response variable) $Y$: whether it sticks to a magnet (yes/no).

Causality

• Counterfactual: Would Total cereal stick to a magnet if it did not have iron?

• Two potential outcomes: $Y\left(1\right)$ and $Y\left(0\right)$

• Causal effect: $Y\left(1\right)-Y\left(0\right)$

• Fundamental problem of causal inference: only one of the two potential outcomes is observable.

• Cannot calculate individual causal effect $Y\left(1\right)-Y\left(0\right)$!

• Can calculate the average treatment effect by comparing the means of a treatment and a control group.

• Importance of control group: must be identical to the treatment group on all factors but the treatment.

The Problem

• Causal inference is predicated on comparing the observed to the counterfactual.

  • Example: To show that the Medici rose to power due to their high network centrality, we must compare the Florentine network to a counter-factual, in which the Medici did not hold a central position.

• Often cannot change one aspect of the network while holding all else constant

  • Cannot change an actor centrality without changing centrality of other actors.
  • Example 1: Cannot observe what a policy diffusion process across US states would look like in the absence of New York and California.
  • Example 2: What would the post-World War II international alliance network would look like without the United States?

A Causal Approach

• Experiment

  • Randomly assign features to nodes/edges in networks

  • Examples: LinkedIn experiment

• Natural experiment

  • Find a sample of social networks, such that some features (e.g.the central nodes' transmission potential) are disabled in some of the networks, but not the others.

  • Examples: Covid-19 vaccine prioritization policies in the US, censorship on Twitter

• Simulations to study different scenarios

Assumptions

• Unconfoundedness

• SUTVA--stable unit treatment value assumption: treatment assignments for other units do not affect the outcome for unit i and that each treatment defines a unique outcome for each unit

• Parallel trends

Natural Experiment

• Most similar cases: California and Oregon counties

• Matching on demographic and economic variables

• Treatment: California opened vaccine eligibility to grocery workers (central nodes) about 1 month earlier than Oregon.

Field Experiment

• Randomly vary friend suggestions: weak vs. strong links

• Study the effect of the treatment on job applications and new jobs