Instrumental Variables
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1 Instrumental Variables Prof. Jacob M. Montgomery Quantitative Political Methodology (L32 363) December 6, 2016 Lecture 26 (QPM 2016) IV Analysis December 6, / 27
2 Class business PS8 due Wednesday (?) Lecture 26 (QPM 2016) IV Analysis December 6, / 27
3 Class business PS8 due Wednesday (?) Poster files will be due before the final lecture period on December 7. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
4 Class business PS8 due Wednesday (?) Poster files will be due before the final lecture period on December 7. OPTIONAL poster session will be held on during reading period. Specific time and location TBD. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
5 Class business PS8 due Wednesday (?) Poster files will be due before the final lecture period on December 7. OPTIONAL poster session will be held on during reading period. Specific time and location TBD. 1% extra credit for the best poster as chosen by the faculty Lecture 26 (QPM 2016) IV Analysis December 6, / 27
6 Class business PS8 due Wednesday (?) Poster files will be due before the final lecture period on December 7. OPTIONAL poster session will be held on during reading period. Specific time and location TBD. 1% extra credit for the best poster as chosen by the faculty Cookies! Lecture 26 (QPM 2016) IV Analysis December 6, / 27
7 Class business PS8 due Wednesday (?) Poster files will be due before the final lecture period on December 7. OPTIONAL poster session will be held on during reading period. Specific time and location TBD. 1% extra credit for the best poster as chosen by the faculty Cookies! Show off your hard work to your friends and professors Lecture 26 (QPM 2016) IV Analysis December 6, / 27
8 Class business PS8 due Wednesday (?) Poster files will be due before the final lecture period on December 7. OPTIONAL poster session will be held on during reading period. Specific time and location TBD. 1% extra credit for the best poster as chosen by the faculty Cookies! Show off your hard work to your friends and professors Questions/concerns? Lecture 26 (QPM 2016) IV Analysis December 6, / 27
9 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
10 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Lecture 26 (QPM 2016) IV Analysis December 6, / 27
11 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Lecture 26 (QPM 2016) IV Analysis December 6, / 27
12 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible Lecture 26 (QPM 2016) IV Analysis December 6, / 27
13 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work Lecture 26 (QPM 2016) IV Analysis December 6, / 27
14 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work It matters for me Lecture 26 (QPM 2016) IV Analysis December 6, / 27
15 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work It matters for me Used for annual evaluations Lecture 26 (QPM 2016) IV Analysis December 6, / 27
16 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work It matters for me Used for annual evaluations Used for tenure/promotion Lecture 26 (QPM 2016) IV Analysis December 6, / 27
17 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work It matters for me Used for annual evaluations Used for tenure/promotion It really matters for your TAs Lecture 26 (QPM 2016) IV Analysis December 6, / 27
18 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work It matters for me Used for annual evaluations Used for tenure/promotion It really matters for your TAs They are beginners Lecture 26 (QPM 2016) IV Analysis December 6, / 27
19 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work It matters for me Used for annual evaluations Used for tenure/promotion It really matters for your TAs They are beginners They need jobs Lecture 26 (QPM 2016) IV Analysis December 6, / 27
20 Course evaluations Online course evals are now available You get 1% extra credit for filling them out Why bother? I read every comment. Tell me what you like Tell me what should be improved Be as constructive and specific as possible I really want this class to work It matters for me Used for annual evaluations Used for tenure/promotion It really matters for your TAs They are beginners They need jobs Your evaluations will be included in their applications Lecture 26 (QPM 2016) IV Analysis December 6, / 27
21 Road map Where we have been: What is regression? How to interpret coefficients? Interactions/Dummies Regression assumptions Using regression for causal inference Using difference-in-differences to make causal claims Regression discontinuity Today: Instrumental variables Lecture 26 (QPM 2016) IV Analysis December 6, / 27
22 Lecture 26 (QPM 2016) IV Analysis December 6, / 27
23 Instrumental variables (IV) analysis: Two frameworks How to handle non-compliance in experiments Lecture 26 (QPM 2016) IV Analysis December 6, / 27
24 Instrumental variables (IV) analysis: Two frameworks How to handle non-compliance in experiments What do you do if some people in an experiment don t do what they are told? Lecture 26 (QPM 2016) IV Analysis December 6, / 27
25 Instrumental variables (IV) analysis: Two frameworks How to handle non-compliance in experiments What do you do if some people in an experiment don t do what they are told? How to make causal inference in the presence of endogenous regressors Lecture 26 (QPM 2016) IV Analysis December 6, / 27
26 Instrumental variables (IV) analysis: Two frameworks How to handle non-compliance in experiments What do you do if some people in an experiment don t do what they are told? How to make causal inference in the presence of endogenous regressors An approach that can sometimes work when you can t do anything else Lecture 26 (QPM 2016) IV Analysis December 6, / 27
27 Framework 1: Who get s the milk? Lecture 26 (QPM 2016) IV Analysis December 6, / 27
28 A non-hypothetical example: The setup Let s imagine a nutrition intervention: Randomly assign schools to get extra provisions of school milk at lunch At all schools teachers allocate milk and keep track of who gets it After one year, follow up and measure weights of all children Lecture 26 (QPM 2016) IV Analysis December 6, / 27
29 A non-hypothetical example: The hitch Two-sided noncompliance People in the treatment condition failed to receive the treatment Lecture 26 (QPM 2016) IV Analysis December 6, / 27
30 A non-hypothetical example: The hitch Two-sided noncompliance People in the treatment condition failed to receive the treatment Some kids don t like milk Lecture 26 (QPM 2016) IV Analysis December 6, / 27
31 A non-hypothetical example: The hitch Two-sided noncompliance People in the treatment condition failed to receive the treatment Some kids don t like milk More importantly, who would you give milk to? Lecture 26 (QPM 2016) IV Analysis December 6, / 27
32 A non-hypothetical example: The hitch Two-sided noncompliance People in the treatment condition failed to receive the treatment Some kids don t like milk More importantly, who would you give milk to? People in the control condition receive the treatment Lecture 26 (QPM 2016) IV Analysis December 6, / 27
33 A non-hypothetical example: The hitch Two-sided noncompliance People in the treatment condition failed to receive the treatment Some kids don t like milk More importantly, who would you give milk to? People in the control condition receive the treatment Some people have cows Lecture 26 (QPM 2016) IV Analysis December 6, / 27
34 A non-hypothetical example: The hitch Two-sided noncompliance People in the treatment condition failed to receive the treatment Some kids don t like milk More importantly, who would you give milk to? People in the control condition receive the treatment Some people have cows Rich people Lecture 26 (QPM 2016) IV Analysis December 6, / 27
35 Hypothetical experimental results Weight Got milk No milk Control Treatment Lecture 26 (QPM 2016) IV Analysis December 6, / 27
36 Instrumental variables We are going to solve two equations at the same time: x i = τ + T i γ + ɛ i1 (1) y i = α + x i β + ɛ i2 (2) ( ɛi1 ɛ i2 ) N(0, Σ) Lecture 26 (QPM 2016) IV Analysis December 6, / 27
37 How does this work? In the abstract 1 We have an endogenous regressor x and we want to know how it affect y. 2 We have a randomly assigned variable T that has a strong effect on x 3 T only affects y through x (exclusion restriction) 4 No one does the opposite on purpose (no defiers) If we have all of these, we can correctly estimate β... Lecture 26 (QPM 2016) IV Analysis December 6, / 27
38 How does this work? In the abstract 1 We have an endogenous regressor x and we want to know how it affect y. 2 We have a randomly assigned variable T that has a strong effect on x 3 T only affects y through x (exclusion restriction) 4 No one does the opposite on purpose (no defiers) If we have all of these, we can correctly estimate β but only for the subset of observations that are compliers. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
39 How does this work? In our example 1 We have an endogenous regressor x (milk consumption) and we want to know how it affect y (weight). 2 We have a randomly assigned variable T (which schools get lunch) that has a strong effect on x (milk consumption) 3 T only affects y through x (assignment not related to weight except through milk) 4 No one does the opposite on purpose (no one drinks extra milk because their school was added to the control) If we have all of these, we can correctly estimate β. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
40 How does this work? In our example 1 We have an endogenous regressor x (milk consumption) and we want to know how it affect y (weight). 2 We have a randomly assigned variable T (which schools get lunch) that has a strong effect on x (milk consumption) 3 T only affects y through x (assignment not related to weight except through milk) 4 No one does the opposite on purpose (no one drinks extra milk because their school was added to the control) If we have all of these, we can correctly estimate β.... but only for the subset of observations that are compliers. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
41 Generally speaking, do you think that (your countrys) membership of the European Community [common market] is: (1) a bad thing, (2) neither good nor bad, or (3) a good thing. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
42 Framework 2: Guns and money Lecture 26 (QPM 2016) IV Analysis December 6, / 27
43 Some things can t be randomized Bad economy more war Lecture 26 (QPM 2016) IV Analysis December 6, / 27
44 Some things can t be randomized Bad economy more war More war bad economy Lecture 26 (QPM 2016) IV Analysis December 6, / 27
45 Some things can t be randomized Bad economy more war More war bad economy Bad government more war, bad economy Lecture 26 (QPM 2016) IV Analysis December 6, / 27
46 Instrumental variables We are going to solve two equations at the same time: x i = τ + T i γ + ɛ i1 (3) y i = α + x i β + ɛ i2 (4) ( ɛi1 ɛ i2 ) N(0, Σ) Lecture 26 (QPM 2016) IV Analysis December 6, / 27
47 How does this work? In the abstract 1 We have an endogenous regressor x and we want to know how it affect y. 2 We have a randomly assigned variable T that has a strong effect on x 3 T only affects y through x (exclusion restriction) 4 No one does the opposite on purpose (no defiers) If we have all of these, we can correctly estimate β... Lecture 26 (QPM 2016) IV Analysis December 6, / 27
48 How does this work? In the abstract 1 We have an endogenous regressor x and we want to know how it affect y. 2 We have a randomly assigned variable T that has a strong effect on x 3 T only affects y through x (exclusion restriction) 4 No one does the opposite on purpose (no defiers) If we have all of these, we can correctly estimate β but only for the subset of observations that are compliers. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
49 Using rainfall as an instrument Lecture 26 (QPM 2016) IV Analysis December 6, / 27
50 Using rainfall as an instrument Lecture 26 (QPM 2016) IV Analysis December 6, / 27
51 How does this work? In our example 1 We have an endogenous regressor x (economy) and we want to know how it affect y (civil war). 2 We have a randomly assigned variable T (rainfall in the previous year) that has a strong effect on x (economic growth) 3 T only affects y through x (rain does not directly affect civil war) 4 No one does the opposite on purpose (countries do not have negative economic growth as a consequence of lot s of rain) If we have all of these, we can correctly estimate β. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
52 How does this work? In our example 1 We have an endogenous regressor x (economy) and we want to know how it affect y (civil war). 2 We have a randomly assigned variable T (rainfall in the previous year) that has a strong effect on x (economic growth) 3 T only affects y through x (rain does not directly affect civil war) 4 No one does the opposite on purpose (countries do not have negative economic growth as a consequence of lot s of rain) If we have all of these, we can correctly estimate β.... but only for the subset of observations that are compliers. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
53 R code for two staged least squares library(aer) ivreg(y ~ x T, data = mydata) Lecture 26 (QPM 2016) IV Analysis December 6, / 27
54 Negative ads and turnout Ansolabehere, Iyengar, and Simon (1999), Replicating Experiments Using Aggregate and Survey Data: The Case of Negative Advertising and Turnout, American Political Science Review. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
55 The basic approach Using survey data from the 1992 election y: Self-reported probability of voting Lecture 26 (QPM 2016) IV Analysis December 6, / 27
56 The basic approach Using survey data from the 1992 election y: Self-reported probability of voting x: Self-reported ad tone Lecture 26 (QPM 2016) IV Analysis December 6, / 27
57 The basic approach Using survey data from the 1992 election y: Self-reported probability of voting x: Self-reported ad tone T: Date of the interview Lecture 26 (QPM 2016) IV Analysis December 6, / 27
58 Check our assumptions Assumption 1: We have a randomly assigned variable T that has a strong effect on x Self reported ad tone Early respondents Late respondents Lecture 26 (QPM 2016) IV Analysis December 6, / 27
59 Check our assumptions T only affects y through x No one does the opposite on purpose Lecture 26 (QPM 2016) IV Analysis December 6, / 27
60 2SLS Results Lecture 26 (QPM 2016) IV Analysis December 6, / 27
61 2SLS Results Remember, this is the effect of the treatment on compliers. Lecture 26 (QPM 2016) IV Analysis December 6, / 27
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