1. Review

• causality as counterfactual
• potential outcomes

2. Types of Causal Claims

• deterministic causal claims
• probabilistic causal claims

3. Testing Causal Claims

• Fundamental Problem of Causal Inference

All causal claims are claims about how the world would be changed in an alternate timeline in which some thing (or things) were different than they actually are.

These alternate timelines/universes are counterfactuals

“The expansion of NATO into Eastern Europe caused Russia to invade Ukraine”

implicitly claims that…

in the counterfactual world where NATO did not expand (the “cause” is not present), Russia would not have invaded Ukraine in February 2022 (the “effect” would be different).

potential outcomes are values for variables that describe the factual world (that has occurred) and counterfactual worlds (that have not).

• a variable corresponding to what is “affected” or the “outcome” (e.g. Russia invasion: yes or no)
• the values that variable would take for a particular case (e.g. Ukraine) in different potential “universes” where the variable for the “cause” (e.g. # of E. European countries in NATO) were to take different values

\(\mathrm{Russian \ Invasion}_{Ukr}(\mathrm{E. \ Europ. \ NATO \ Memb.} = 0) = ?\) \(\mathrm{Russian \ Invasion}_{Ukr}(\mathrm{E. \ Europ. \ NATO \ Memb.} = 14) = ?\)

Which of these potential outcomes is factual? Counterfactual?

\(\mathrm{Russian \ Invasion}_{Ukr}(\mathrm{E. \ Europ. \ NATO \ Memb.} = 0) = ?\) \(\mathrm{Russian \ Invasion}_{Ukr}(\mathrm{E. \ Europ. \ NATO \ Memb.} = 14) = ?\)

What are the values of these potential outcomes if the following claim is true?

“The expansion of NATO into Eastern Europe caused Russia to invade Ukraine”

“The expansion of NATO into Eastern Europe caused Russia to invade Ukraine”

If this causal claim were true: then it implies these potential outcomes:

\(\color{red}{\mathrm{Russian \ Invasion}_{Ukr}(\mathrm{E. \ Europ. \ NATO \ Memb.} = 0) = \mathrm{No}}\) \(\mathrm{Russian \ Invasion}_{Ukr}(\mathrm{E. \ Europ. \ NATO \ Memb.} = 14) = \mathrm{Yes}\)

(red indicates \(\color{red}{\mathrm{counterfactual}}\))

It follows that, all causal claims can be re-stated as counterfactual claims

• They contain a conditional clause, starting with “If” (always in the subjunctive mood)
• A “then” clause, stating what would happen if the conditional/“If” clause were true (always in the conditional mood)
• May be in past, present, or future tense.

Example:

“News coverage of the discovery of unmarked graves at the Kamloops Residential School increased settler Canadian support for Truth and Reconciliation.”

\[\overbrace{\text{If there had not been news coverage of the graves}}^{\text{If-clause in Subjunctive Mood}}, \\ \underbrace{\text{there would be less support for Truth and Reconciliation}}_{\text{Then-clause in Conditional Mood}}\]

Note: Counterfactual claims get increasingly complicated, the more complicated your causal claim is

• On assignments/final exam do not come up with overly complex causal claims.

With your neighbors: turn these causal claims into counterfactual claims.

1. “The rise of social media ‘echo chambers’ increased political polarization.”
2. “The purchase of 20% rental housing units by private equity firms has increased the cost of rent.”
3. “Remote learning during the pandemic increased mental health issues among students.”

Usually… different focus leads to different kinds of causal claims

1. causes of effects \(\to\) deterministic causal claims
2. effects of causes \(\to\) probabilistic causal claims

And different types of causal claims imply different counterfactuals/potential outcomes, different forms of evidence.

deterministic causal claims

claims about what happens with certainty under specific causal conditions

• whenever some cause (or set of causes) is present, the effect always happens
• or whenever some cause (or set of causes) is absent, the effect never happens
• usually make these claims when we are interested in causes of effects

There are several varieties and combinations

• necessary conditions
• sufficient conditions
• conjunctural/multiple causation (combinations of multiple necessary/sufficiency conditions)

necessary conditions

A causal claim that there is some cause \(C\) without which the effect \(E\) cannot occur

• A cause \(C\) must happen in order for effect \(E\) to happen.
• Does not mean if the cause \(C\) is present, effect \(E\) must happen

A claim: “If Canada had not signed the UN Declaration on the Rights of Indigenous Peoples, the Blueberry River First Nation would not have been able to successfully challenge BC’s permitting of industrial activities on their ancestral lands.”

Also can be stated: “The signing of the UNDRIP by Canada was a necessary condition for the Blueberry River First Nation to be able to successfully challenge BC’s permitting of industrial activities on their ancestral lands.”

Head to menti.com and use code \(4959 \ 5430\)

If this claim is true: “The signing of the UNDRIP by Canada was a necessary condition for the Blueberry River First Nation to be able to successfully challenge BC’s permitting of industrial activities on their ancestral lands.”…

The fact that Canada signed the UNDRIP does not mean that the the BRFN’s legal victory over BC was inevitable.

• Presence of necessary condition \(\not\to\) effect must happen. Instead, absence of necessary condition \(\to\) effect does not happen

Claims about necessary conditions have specific implications about potential outcomes:

If we say that: “economic crisis is a necessary condition for populist dictatorship to replace democracy”

It implies the potential outcomes in for democratic country \(i\):

\(\mathrm{Dictatorship}_i \ (\mathrm{Economic \ Crisis = No}) = \mathrm{No}\)

\(\mathrm{Dictatorship}_i \ (\mathrm{Economic \ Crisis = Yes}) = \mathrm{Yes} \ or \ \mathrm{No}\)

Something else might need to happen, in addition to economic crisis, for dictatorship to arise.

(In contrast to necessary conditions)

sufficient conditions

• cause \(C\) always produces an effect \(E\) when it is present
• do not depend on other factors being present; cause \(C\) can produce \(E\) by itself
• Sufficient conditions imply: every time \(C\) is present, then \(E\) will happen

“A military coup that overthrows a democratically elected government is a sufficient condition for large public protests.”

• This might be the case every time
• Does not appear to depend on other factors

Generally, single causes that are sufficient conditions are rare in social sciences

Sufficient conditions also imply specific potential outcomes:

“A military coup that overthrows a democratically elected government is a sufficient condition for large public protests.” implies that for every democratic country \(i\):

\(\mathrm{Protests}_i \ (\mathrm{Military \ Coup = No}) = \mathrm{No \ or \ Yes}\)

\(\mathrm{Protests}_i \ (\mathrm{Military \ Coup = Yes}) = \mathrm{Yes}\)

What can be done to limit the spread of misinformation on social media?

• Educating people about strategies used to spread misinformation (“inoculation”) may make them less susceptible to these techniques.
• Does showing people a short video explaining a misinformation tactic increase their ability to recognize the tactic?

Aired this ad on YouTube and then surveyed people in “treatment” and “control” conditions to see if they recognize the misinformation tactic

menti.com \(7452 \ 3898\)

Does it make sense to say that “being inoculated” is a necessary condition for spotting misinformation?

• No. Clearly some people recognized misinformation without being inoculated.

Does it make sense to say that “being inoculated” is a sufficient condition for spotting misinformation?

• No. Clearly some people were inoculated but did not recognize misinformation.

• It is simpler to state this as probabilistic: being “inoculated” increases likelihood of recognizing misinformation

probabilistic causal claims

are claims that the presence/absence of a cause \(C\) makes an effect \(E\) more or less likely to occur. Or cause \(C\) increases/decreases effect \(E\) on average

• In contrast to deterministic causal claims this implies
  • effect \(E\) can happen when \(C\) is absent
  • effect \(E\) may not happen when \(C\) is present
• NOT a claim that politics has some inherent randomness (e.g. quantum mechanics)
• Usually make these claims when interested in effects of causes

Causality may be deterministic… there are exact conditions for when effect always/never happens.

But in reality, it is almost always complex

• multiple factors might be necessary (conjunctural causality)
• different causes produce same effect (multiple causality)
• different groups of factors might, together be sufficient (multiple and conjunctural)
• (INUS/SUIN conditions: see here)

Because causality is complex, we do not fully know the deterministic rules…

\(C\) appears to only cause a change in the probability or likelihood of seeing the effect \(E\).

• e.g. coin flips

Which are probabilistic causal claims?

A) It’s probably true that leftwing government reduce student tuition fees

B) Electing a leftwing, rather than rightwing, government increases the likelihood that tuition fees will be reduced

C) Tuition fees are reduced more frequently under leftwing governments than rightwing governments

Which is a probabilistic causal claim?

A) It’s probably true that leftwing government reduce student tuition fees

B) Electing a leftwing, rather than rightwing, government increases the likelihood that tuition fees wil be reduced

C) Tuition fees are reduced more frequently under leftwing governments than rightwing governments

Not every probabilistic statement is causal

1. “Oppression is likely to cause a rebellion”

• Says oppression is probably a cause out rebellion
• Should say: cause \(C\) changes likelihood of outcome \(E\)

2. “Rebellions are more likely to occur in places where the population is oppressed”

• Says we are more likely to see rebellion where population is oppressed
• Not clearly causal; just a descriptive claim.

In this course, we focus on how to provide evidence that that pertain to claims about effects of causes rather than causes of effects.

• difficult to provide evidence of either
• easier to address effects of causes
• this means we focus on evidence of probabilistic causal claims

A claim for today:

NDP’s Bill 44 (abolishing single-family zoning restrictions to permit multi-family units) reduced the average cost of buying a house.

• Why is this a probabilistic claim?
• restate this as a counterfactual claim
• what kind of empirical evidence would help you decide whether this claim is true?

Causal claims imply relationships between potential outcomes

\(\text{Housing Price}_{BC}(\text{Bill 44}) < \\ \color{red}{\text{Housing Price}_{BC}(\text{No Bill 44})}\)

\(\mathrm{Black}\) indicates factual potential outcomes (we observe this state of the world)

\(\color{red}{\mathrm{Red}}\) indicates counterfactual potential outcomes (we do not observe this state of the world)

Average housing price: \(\text{Housing Price}_{BC}(\text{Bill 44}) = \$990,500\)

\(\color{red}{\text{Housing Price}_{BC}(\text{No Bill 44})} = \ \mathbf{????}\):

• How could we know what this is?
• We can never know what housing prices in BC would have been today absent the zoning legislation.

Fundamental Problem of Causal Inference

1. For BC, we can only observe the potential outcome of \(\text{Housing Price}_{BC}\) for where the value of \(\text{Bill 44} = Yes\): the actual policy that occurred in BC.

2. We can never observe the other, counterfactual, potential outcomes of \(\color{red}{\text{Housing Price}_{BC}}\) where \(\color{red}{\text{Bill 44} = No}\), because that was not the actual policy.

3. We can never empirically observe, for BC, whether \(\text{Bill 44}\) caused \(\downarrow \text{Housing Price}\).

Fundamental Problem of Causal Inference

1. By definition, \(X\) causes \(Y\) if the value of \(Y\) were different if we changed \(X\) for the exact same case.

2. For a specific case, we can only observe the potential outcome of \(Y\) for the value of \(X\) it actually takes.

3. We never observe the counterfactual potential outcomes of \(Y\) for different possible values of \(X\) that the case did not experience.

4. We can never empirically observe, for a specific case, whether \(X\) causes \(Y\).

I thought evidence for empirical claims based on observing the world?!

Does this mean that all evidence for causal claims fails weak severity?

Are there “solutions” to this fundamental problem?