A Partial Solution To the Fundamental Problem of Causal Inference - - PowerPoint PPT Presentation

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A Partial Solution To the Fundamental Problem of Causal Inference - - PowerPoint PPT Presentation

Dec 02, 2023 222 likes •856 views

A Partial Solution To the Fundamental Problem of Causal Inference Some of our most important questions are causal questions . 100,000 50,000 Gross National Income Per Capita

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A Partial Solution

To the Fundamental Problem of Causal Inference

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Some of our most important questions are causal questions.

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  • 1,000

5,000 10,000 50,000 100,000 −10 −5 5 10

Level of Democracy (−10 = Least Democratic, 10 = Most Democratic) Gross National Income Per Capita

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  • Albania
Algeria Angola Argentina Armenia Australia Austria Azerbaijan Bahrain Belgium Benin Burkina Faso Bhutan Belarus Bangladesh Botswana Brazil Burundi Bulgaria Cambodia Canada Cameroon Cape Verde Central African Republic Chad Chile China Colombia Comoros Costa Rica Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominican Republic Ecuador Egypt Equatorial Guinea Eritrea Estonia Ethiopia Finland Fiji France Gabon Gambia Ghana Germany Guinea−Bissau Greece Georgia Guatemala Guinea Guyana Haiti Honduras Hungary India Indonesia Ireland Iraq Israel Italy Jamaica Jordan Japan Kenya Kuwait Kyrgyzstan Kazakhstan Latvia Liberia Lebanon Lesotho Libya Lithuania Luxembourg Mauritania Madagascar Malaysia Mauritius Malawi Mexico Mali Montenegro Mongolia Morocco Mozambique Namibia Nepal New Zealand Nicaragua Nigeria Niger Norway Netherlands Oman Pakistan Panama Paraguay Peru Philippines Papua New Guinea Poland Portugal Qatar Romania Rwanda South Africa El Salvador Saudi Arabia Senegal Serbia Sierra Leone Singapore Slovenia Solomon Islands Spain Sri Lanka Suriname Swaziland Sweden Switzerland Tajikistan Thailand Turkmenistan Togo Trinidad and Tobago Tunisia Turkey Uganda United Kingdom Ukraine Uruguay United States Uzbekistan Yemen Zambia Zimbabwe

1,000 5,000 10,000 50,000 100,000 −10 −5 5 10

Level of Democracy (−10 = Least Democratic, 10 = Most Democratic) Gross National Income Per Capita

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  • Albania
Algeria Angola Argentina Armenia Australia Austria Azerbaijan Bahrain Belgium Benin Burkina Faso Bhutan Belarus Bangladesh Botswana Brazil Burundi Bulgaria Cambodia Canada Cameroon Cape Verde Central African Republic Chad Chile China Colombia Comoros Costa Rica Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominican Republic Ecuador Egypt Equatorial Guinea Eritrea Estonia Ethiopia Finland Fiji France Gabon Gambia Ghana Germany Guinea−Bissau Greece Georgia Guatemala Guinea Guyana Haiti Honduras Hungary India Indonesia Ireland Iraq Israel Italy Jamaica Jordan Japan Kenya Kuwait Kyrgyzstan Kazakhstan Latvia Liberia Lebanon Lesotho Libya Lithuania Luxembourg Mauritania Madagascar Malaysia Mauritius Malawi Mexico Mali Montenegro Mongolia Morocco Mozambique Namibia Nepal New Zealand Nicaragua Nigeria Niger Norway Netherlands Oman Pakistan Panama Paraguay Peru Philippines Papua New Guinea Poland Portugal Qatar Romania Rwanda South Africa El Salvador Saudi Arabia Senegal Serbia Sierra Leone Singapore Slovenia Solomon Islands Spain Sri Lanka Suriname Swaziland Sweden Switzerland Tajikistan Thailand Turkmenistan Togo Trinidad and Tobago Tunisia Turkey Uganda United Kingdom Ukraine Uruguay United States Uzbekistan Yemen Zambia Zimbabwe

1,000 5,000 10,000 50,000 100,000 −10 −5 5 10

Level of Democracy (−10 = Least Democratic, 10 = Most Democratic) Gross National Income Per Capita

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  • Albania
Algeria Angola Argentina Armenia Australia Austria Azerbaijan Bahrain Belgium Benin Burkina Faso Bhutan Belarus Bangladesh Botswana Brazil Burundi Bulgaria Cambodia Canada Cameroon Cape Verde Central African Republic Chad Chile China Colombia Comoros Costa Rica Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominican Republic Ecuador Egypt Equatorial Guinea Eritrea Estonia Ethiopia Finland Fiji France Gabon Gambia Ghana Germany Guinea−Bissau Greece Georgia Guatemala Guinea Guyana Haiti Honduras Hungary India Indonesia Ireland Iraq Israel Italy Jamaica Jordan Japan Kenya Kuwait Kyrgyzstan Kazakhstan Latvia Liberia Lebanon Lesotho Libya Lithuania Luxembourg Mauritania Madagascar Malaysia Mauritius Malawi Mexico Mali Montenegro Mongolia Morocco Mozambique Namibia Nepal New Zealand Nicaragua Nigeria Niger Norway Netherlands Oman Pakistan Panama Paraguay Peru Philippines Papua New Guinea Poland Portugal Qatar Romania Rwanda South Africa El Salvador Saudi Arabia Senegal Serbia Sierra Leone Singapore Slovenia Solomon Islands Spain Sri Lanka Suriname Swaziland Sweden Switzerland Tajikistan Thailand Turkmenistan Togo Trinidad and Tobago Tunisia Turkey Uganda United Kingdom Ukraine Uruguay United States Uzbekistan Yemen Zambia Zimbabwe

1,000 5,000 10,000 50,000 100,000 −10 −5 5 10

Level of Democracy (−10 = Least Democratic, 10 = Most Democratic) Gross National Income Per Capita

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  • Albania
Algeria Angola Argentina Armenia Australia Austria Azerbaijan Bahrain Belgium Benin Burkina Faso Bhutan Belarus Bangladesh Botswana Brazil Burundi Bulgaria Cambodia Canada Cameroon Cape Verde Central African Republic Chad Chile China Colombia Comoros Costa Rica Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominican Republic Ecuador Egypt Equatorial Guinea Eritrea Estonia Ethiopia Finland Fiji France Gabon Gambia Ghana Germany Guinea−Bissau Greece Georgia Guatemala Guinea Guyana Haiti Honduras Hungary India Indonesia Ireland Iraq Israel Italy Jamaica Jordan Japan Kenya Kuwait Kyrgyzstan Kazakhstan Latvia Liberia Lebanon Lesotho Libya Lithuania Luxembourg Mauritania Madagascar Malaysia Mauritius Malawi Mexico Mali Montenegro Mongolia Morocco Mozambique Namibia Nepal New Zealand Nicaragua Nigeria Niger Norway Netherlands Oman Pakistan Panama Paraguay Peru Philippines Papua New Guinea Poland Portugal Qatar Romania Rwanda South Africa El Salvador Saudi Arabia Senegal Serbia Sierra Leone Singapore Slovenia Solomon Islands Spain Sri Lanka Suriname Swaziland Sweden Switzerland Tajikistan Thailand Turkmenistan Togo Trinidad and Tobago Tunisia Turkey Uganda United Kingdom Ukraine Uruguay United States Uzbekistan Yemen Zambia Zimbabwe

1,000 5,000 10,000 50,000 100,000 −10 −5 5 10

Level of Democracy (−10 = Least Democratic, 10 = Most Democratic) Gross National Income Per Capita

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  • Albania
Algeria Angola Argentina Armenia Australia Austria Azerbaijan Bahrain Belgium Benin Burkina Faso Bhutan Belarus Bangladesh Botswana Brazil Burundi Bulgaria Cambodia Canada Cameroon Cape Verde Central African Republic Chad Chile China Colombia Comoros Costa Rica Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominican Republic Ecuador Egypt Equatorial Guinea Eritrea Estonia Ethiopia Finland Fiji France Gabon Gambia Ghana Germany Guinea−Bissau Greece Georgia Guatemala Guinea Guyana Haiti Honduras Hungary India Indonesia Ireland Iraq Israel Italy Jamaica Jordan Japan Kenya Kuwait Kyrgyzstan Kazakhstan Latvia Liberia Lebanon Lesotho Libya Lithuania Luxembourg Mauritania Madagascar Malaysia Mauritius Malawi Mexico Mali Montenegro Mongolia Morocco Mozambique Namibia Nepal New Zealand Nicaragua Nigeria Niger Norway Netherlands Oman Pakistan Panama Paraguay Peru Philippines Papua New Guinea Poland Portugal Qatar Romania Rwanda South Africa El Salvador Saudi Arabia Senegal Serbia Sierra Leone Singapore Slovenia Solomon Islands Spain Sri Lanka Suriname Swaziland Sweden Switzerland Tajikistan Thailand Turkmenistan Togo Trinidad and Tobago Tunisia Turkey Uganda United Kingdom Ukraine Uruguay United States Uzbekistan Yemen Zambia Zimbabwe

1,000 5,000 10,000 50,000 100,000 −10 −5 5 10

Level of Democracy (−10 = Least Democratic, 10 = Most Democratic) Gross National Income Per Capita

?

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correlation ↛ correlation

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Four Ways

to Get a Correlation

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causation

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causation

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causation

key explanatory variable

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causation

key explanatory variable

  • utcome variable
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causation

key explanatory variable

  • utcome variable

causes

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spuriousness

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spuriousness

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spuriousness

key explanatory variable

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spuriousness

key explanatory variable

  • utcome variable
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spuriousness

key explanatory variable

  • utcome variable

confounder

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spuriousness

key explanatory variable

  • utcome variable

confounder

c a u s e s

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spuriousness

key explanatory variable

  • utcome variable

confounder

c a u s e s c a u s e s

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spuriousness

key explanatory variable

  • utcome variable

confounder

c a u s e s c a u s e s

Note: a confounder is a variable that causes both X and Y .

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reverse causation

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reverse causation

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reverse causation

key explanatory variable

  • utcome variable

causes

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reverse causation

key explanatory variable

  • utcome variable

causes

N

  • t

i c e t h e t h e a r r

  • w

g

  • e

s t h e w r

  • n

g d i r e c t i

  • n

!

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chance

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chance

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chance

key explanatory variable

  • utcome variable
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chance

key explanatory variable

  • utcome variable

N

  • t

i c e t h e r e i s n

  • c

a u s a l a r r

  • w

!

Sometimes, X and Y will be correlated just by chance, even when there is no systematic relationship between the two.

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SLIDE 34 −2 2 Y
  • −2
2 Y
  • ●
  • −2
2 Y
  • ●
  • −2
2 Y
  • −3
−2 −1 1 2 3 X −2 2 Y
  • −3
−2 −1 1 2 3 X
  • −3
−2 −1 1 2 3 X
  • −3
−2 −1 1 2 3 X
  • −3
−2 −1 1 2 3 X
  • Pure Noise Generated by a Computer
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causation spuriousness reverse causation chance

no systematic relationship; correlation simply due to chance

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Ruling Out the Alternatives

spuriousness and reverse causation

  • a compelling theoretical model
  • randomization

spuriousness

  • controlling for confounders

chance

  • box model and statistical inference
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Ruling Out the Alternatives

spuriousness and reverse causation

  • a compelling theoretical model
  • randomization

spuriousness

  • controlling for confounders

chance

  • box model and statistical inference

save for later…

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Ruling Out the Alternatives

spuriousness and reverse causation

  • a compelling theoretical model
  • randomization

spuriousness

  • controlling for confounders

chance

  • box model and statistical inference

save for later…

Discuss Today

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A Compelling Theoretical Model

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A Compelling Theoretical Model

Simply explain why spuriousness and reverse causation make little theoretical sense.

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A Compelling Theoretical Model

Simply explain why spuriousness and reverse causation make little theoretical sense.

  • Could it be that some other variable causes both

democratic institutions and GNI? What might this be?

  • Could it be that GNI causes democratic

institutions?

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Randomization

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What is the effect of a campaign mailer on a citizen’s decision to turn out and vote?

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Imagine we’re in the following ideal situation:

  • A. we have n potential voters,
  • B. the election hasn’t yet happened, and
  • C. we can control the assignment of the treatment.
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Rhyp

T

: The hypothetical turnout Rate if everyone was in the Treatment group. Rhyp

C : The hypothetical turnout Rate if everyone was in the Control group.

Rhyp

T

− Rhyp

C : average treatment effect (ATE)

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Robs

T : The observed turnout Rate in the Treatment group.

Robs

C : The observed turnout Rate in the Control group.

Robs

T

− Robs

C

| {z }

estimate

≈

ATE

z }| { Rhyp

T

− Rhyp

C

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Robs

T : The observed turnout Rate in the Treatment group.

Robs

C : The observed turnout Rate in the Control group.

Robs

T

− Robs

C

| {z }

estimate

≈

ATE

z }| { Rhyp

T

− Rhyp

C

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causation spuriousness reverse causation chance

no systematic relationship; correlation simply due to chance

Coin Flip

X X

Coin Flip

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Review Exercises

  • 1. I write that, under randomization,
  • A. What do each of these four quantities refer to? What do we call

the left-hand side? The right-hand side?

  • B. Notice that the equality is not exact. Instead, it is approximate.

What is the only reason it is not exact?

  • C. Explain why randomization allows us to rule out spuriousness

and reverse causation.

  • 2. Describe the design of Gerber and Green’s turnout experiment.

Describe the results (i.e., what percent of each group voted?). Discuss whether you can rule out any of the four possible ways to

  • btain a correlation.