A Partial Solution. To the Fundamental Problem of Causal Inference

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1 A Partial Solution To the Fundamental Problem of Causal Inference

2 Some of our most important questions are causal questions.

3 1,000 5,000 10,000 50, , Level of Democracy ( 10 = Least Democratic, 10 = Most Democratic) Gross National Income Per Capita

4 100,000 Qatar Kuwait Norway Luxembourg United States Switzerland Austria Germany Denmark Gross National Income Per Capita 50,000 10,000 5,000 1,000 Netherlands Canada Australia Singapore Belgium Saudi Arabia United Kingdom France Oman Italy Sweden Czech Republic New Zealand Ireland Finland Japan Malaysia Trinidad and Tobago Israel Slovenia Spain Bahrain Croatia Cyprus Latvia Estonia Equatorial Guinea Libya Argentina Cuba Mexico Poland Portugal Gabon Botswana Turkey Belarus Greece Kazakhstan Lebanon Brazil Romania Hungary Lithuania Azerbaijan Iraq Suriname Thailand Jordan Montenegro Panama Bulgaria Chile Colombia Algeria Ecuador Tunisia Turkmenistan China Egypt Serbia Peru South Africa Dominican Republic Namibia Uruguay Fiji Sri Lanka El Salvador Armenia Indonesia Angola Ukraine Mauritius Georgia Albania Swaziland Morocco Bhutan Guyana Guatemala Costa Rica Jamaica Uzbekistan Nigeria Pakistan Mongolia Paraguay Yemen Cape Verde Djibouti Kyrgyzstan Honduras Mauritania Cambodia India Cameroon Papua New Guinea Zambia Philippines Nicaragua Tajikistan Bangladesh Nepal Ghana Lesotho Haiti Chad Gambia Mali Senegal Rwanda Madagascar Kenya Burkina Faso Zimbabwe Sierra Leone Eritrea Benin Comoros Ethiopia Uganda Guinea Bissau Guinea Solomon Islands Togo Niger Mozambique Burundi Liberia Central African Republic Malawi Level of Democracy ( 10 = Least Democratic, 10 = Most Democratic)

5 100,000 Qatar Kuwait Norway Luxembourg United States Switzerland Austria Germany Denmark Gross National Income Per Capita 50,000 10,000 5,000 1,000 Netherlands Canada Australia Singapore Belgium Saudi Arabia United Kingdom France Oman Italy Sweden Czech Republic New Zealand Ireland Finland Japan Malaysia Trinidad and Tobago Israel Slovenia Spain Bahrain Croatia Cyprus Latvia Estonia Equatorial Guinea Libya Argentina Cuba Mexico Poland Portugal Gabon Botswana Turkey Belarus Greece Kazakhstan Lebanon Brazil Romania Hungary Lithuania Azerbaijan Iraq Suriname Thailand Jordan Montenegro Panama Bulgaria Chile Colombia Algeria Ecuador Tunisia Turkmenistan China Egypt Serbia Peru South Africa Dominican Republic Namibia Uruguay Fiji Sri Lanka El Salvador Armenia Indonesia Angola Ukraine Mauritius Georgia Albania Swaziland Morocco Bhutan Guyana Guatemala Costa Rica Jamaica Uzbekistan Nigeria Pakistan Mongolia Paraguay Yemen Cape Verde Djibouti Kyrgyzstan Honduras Mauritania Cambodia India Cameroon Papua New Guinea Zambia Philippines Nicaragua Tajikistan Bangladesh Nepal Ghana Lesotho Haiti Chad Gambia Mali Senegal Rwanda Madagascar Kenya Burkina Faso Zimbabwe Sierra Leone Eritrea Benin Comoros Ethiopia Uganda Guinea Bissau Guinea Solomon Islands Togo Niger Mozambique Burundi Liberia Central African Republic Malawi Level of Democracy ( 10 = Least Democratic, 10 = Most Democratic)

6 100,000 Qatar Kuwait Norway Luxembourg United States Switzerland Austria Germany Denmark Gross National Income Per Capita 50,000 10,000 5,000 1,000 Netherlands Canada Australia Singapore Belgium Saudi Arabia United Kingdom France Oman Italy Sweden Czech Republic New Zealand Ireland Finland Japan Malaysia Trinidad and Tobago Israel Slovenia Spain Bahrain Croatia Cyprus Latvia Estonia Equatorial Guinea Libya Argentina Cuba Mexico Poland Portugal Gabon Botswana Turkey Belarus Greece Kazakhstan Lebanon Brazil Romania Hungary Lithuania Azerbaijan Iraq Suriname Thailand Jordan Montenegro Panama Bulgaria Chile Colombia Algeria Ecuador Tunisia Turkmenistan China Egypt Serbia Peru South Africa Dominican Republic Namibia Uruguay Fiji Sri Lanka El Salvador Armenia Indonesia Angola Ukraine Mauritius Georgia Albania Swaziland Morocco Bhutan Guyana Guatemala Costa Rica Jamaica Uzbekistan Nigeria Pakistan Mongolia Paraguay Yemen Cape Verde Djibouti Kyrgyzstan Honduras Mauritania Cambodia India Cameroon Papua New Guinea Zambia Philippines Nicaragua Tajikistan Bangladesh Nepal Ghana Lesotho Haiti Chad Gambia Mali Senegal Rwanda Madagascar Kenya Burkina Faso Zimbabwe Sierra Leone Eritrea Benin Comoros Ethiopia Uganda Guinea Bissau Guinea Solomon Islands Togo Niger Mozambique Burundi Liberia Central African Republic Malawi Level of Democracy ( 10 = Least Democratic, 10 = Most Democratic)

7 100,000 Qatar Kuwait Norway Luxembourg United States Switzerland Austria Germany Denmark Gross National Income Per Capita 50,000 10,000 5,000 1,000 Netherlands Canada Australia Singapore Belgium Saudi Arabia United Kingdom France Oman Italy Sweden Czech Republic New Zealand Ireland Finland Japan Malaysia Trinidad and Tobago Israel Slovenia Spain Bahrain Croatia Cyprus Latvia Estonia Equatorial Guinea Libya Argentina Cuba Mexico Poland Portugal Gabon Botswana Turkey Belarus Greece Kazakhstan Lebanon Brazil Romania Hungary Lithuania Azerbaijan Iraq Suriname Thailand Jordan Montenegro Panama Bulgaria Chile Colombia Algeria Ecuador Tunisia Turkmenistan China Egypt Serbia Peru South Africa Dominican Republic Namibia Uruguay Fiji Sri Lanka El Salvador Armenia Indonesia Angola Ukraine Mauritius Georgia Albania Swaziland Morocco Bhutan Guyana Guatemala Costa Rica Jamaica Uzbekistan Nigeria Pakistan Mongolia Paraguay Yemen Cape Verde Djibouti Kyrgyzstan Honduras Mauritania Cambodia India Cameroon Papua New Guinea Zambia Philippines Nicaragua Tajikistan Bangladesh Nepal Ghana Lesotho Haiti Chad Gambia Mali Senegal Rwanda Madagascar Kenya Burkina Faso Zimbabwe Sierra Leone Eritrea Benin Comoros Ethiopia Uganda Guinea Bissau Guinea Solomon Islands Togo Niger Mozambique Burundi Liberia Central African Republic Malawi Level of Democracy ( 10 = Least Democratic, 10 = Most Democratic)

8 100,000 Qatar Kuwait Norway Luxembourg United States Switzerland Austria Germany Denmark Gross National Income Per Capita 50,000 10,000 5,000 1,000 Netherlands Canada Australia Singapore Belgium Saudi Arabia United Kingdom France Oman Italy Sweden Czech Republic New Zealand Ireland Finland Japan Malaysia Trinidad and Tobago Israel Slovenia Spain Bahrain Croatia Cyprus Latvia Estonia Equatorial Guinea Libya Argentina Cuba Mexico Poland Portugal Gabon Botswana Turkey Belarus Greece Kazakhstan Lebanon Brazil Romania Hungary Lithuania Azerbaijan Iraq Suriname Thailand Jordan Montenegro Panama Bulgaria Chile? Colombia Algeria Ecuador Tunisia Turkmenistan China Egypt Serbia Peru South Africa Dominican Republic Namibia Uruguay Fiji Sri Lanka El Salvador Armenia Indonesia Angola Ukraine Mauritius Georgia Albania Swaziland Morocco Bhutan Guyana Guatemala Costa Rica Jamaica Uzbekistan Nigeria Pakistan Mongolia Paraguay Yemen Cape Verde Djibouti Kyrgyzstan Honduras Mauritania Cambodia India Cameroon Papua New Guinea Zambia Philippines Nicaragua Tajikistan Bangladesh Nepal Ghana Lesotho Haiti Chad Gambia Mali Senegal Rwanda Madagascar Kenya Burkina Faso Zimbabwe Sierra Leone Eritrea Benin Comoros Ethiopia Uganda Guinea Bissau Guinea Solomon Islands Togo Niger Mozambique Burundi Liberia Central African Republic Malawi Level of Democracy ( 10 = Least Democratic, 10 = Most Democratic)

9 correlation correlation

10 Four Ways to Get a Correlation

11 causation

12 causation

13 key explanatory variable causation

14 causation key explanatory variable outcome variable

15 causation key explanatory variable outcome variable causes

16 spuriousness

17 spuriousness

18 key explanatory variable spuriousness

19 spuriousness key explanatory variable outcome variable

20 spuriousness key explanatory variable outcome variable confounder

21 spuriousness key explanatory variable outcome variable causes confounder

22 spuriousness key explanatory variable outcome variable causes causes confounder

23 Note: a confounder is a variable that causes both X and Y. spuriousness key explanatory variable outcome variable causes causes confounder

24

25 reverse causation

26 reverse causation

27 reverse causation key explanatory variable outcome variable causes

28 reverse causation key explanatory variable outcome variable causes Notice the the arrow goes the wrong direction!

29

30 chance

31 chance

32 chance key explanatory variable outcome variable

33 Sometimes, X and Y will be correlated just by chance, even when there is no systematic relationship between the two. chance key explanatory variable outcome variable Notice there is no causal arrow!

34 2 0 2 Y Y Y Y X Y X X X X Pure Noise Generated by a Computer

35 causation spuriousness reverse causation chance no systematic relationship; correlation simply due to chance

36 Ruling Out the Alternatives spuriousness and reverse causation a compelling theoretical model randomization spuriousness controlling for confounders chance box model and statistical inference

37 Ruling Out the Alternatives spuriousness and reverse causation a compelling theoretical model randomization spuriousness controlling for confounders chance save for later box model and statistical inference

38 Ruling Out the Alternatives spuriousness and reverse causation a compelling theoretical model randomization Discuss Today spuriousness controlling for confounders chance save for later box model and statistical inference

39 A Compelling Theoretical Model

40 A Compelling Theoretical Model Simply explain why spuriousness and reverse causation make little theoretical sense.

41 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?

42 Randomization

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

44

45 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.

46 R hyp T : The hypothetical turnout Rate if everyone was in the Treatment group. R hyp C : The hypothetical turnout Rate if everyone was in the Control group. R hyp T R hyp : average treatment effect (ATE) C

47

48 RT obs : The observed turnout Rate in the Treatment group. RC obs : The observed turnout Rate in the Control group. R obs T R obs C {z } estimate ATE z } { R hyp T R hyp C

49 RT obs : The observed turnout Rate in the Treatment group. RC obs : The observed turnout Rate in the Control group. R obs T R obs C {z } estimate ATE z } { R hyp T R hyp C

50 X causation spuriousness Coin Flip reverse causation X chance no systematic relationship; correlation simply due to chance Coin Flip

51

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58

59

60

61 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 obtain a correlation.

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