Causal Infraction and Network Marketing - Trends in Data Science

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1 Causality and Treatment Effects Prof. Jacob M. Montgomery Quantitative Political Methodology (L32 363) October 21, 2013 Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

2 Overview Thinking about causality Average treatment effects Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

3 We do not live in a bivariate world So far, we ve done univariate inference. Moving forward we will do bivariate inference. This is useful: With the right study design (e.g., experimental research) Why? (You should be able to answer this) This is a powerful, powerful way to do research (Take my class!) Building block for more advanced models NOTE: In many situations (e.g., civil war), we don t have experimental data. This means we need to think about all relevant predictors and control variables. We will finish the semester by talking about multiple regression as one method for attempting to deal with this. Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

4 Causality In political science we want to make causal claims. X Y What does this mean? Let s do this a bit more formally for the case of an experiment (the easiest way to think about it). Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

5 Causal inference We will use T to represent a treatment variable. For a categorical treatment T i = 1 if unit i receives the treatment 0 if unit i receives the control We let yi 1 represent the outcome of the ith unit if the treatment is given. We let yi 0 represent the outcome of the ith unit if the control is given. One of these is observed, the other is the counterfactual what would have been observed if the other treatment have been given? The causal effect of T i will then be yi 1 yi 0 Ex., My theory is that individuals who watched this TV ad will be more likely to vote for Ted Cruz than if they didn t watch it. Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

6 Average treatment effects We cannot measure individual level causal effects We can estimate the population average treatment effect by looking at those who received the treatment and those who did not. ATE = mean(yi 1 yi 0) Each group acts as a counterfactual for the other Ex., My theory is that those individuals who watched this TV ad will be more likely to vote for Mitt Romney on average than those who didn t watch it. Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

7 The fundamental problem of causal inference The fundamental problem of causal inference is that at most one of yi 0 and yi 1 can be observed. We can think of each of these as potential outcomes. However, we can only observe one. The other is the counterfactual. Estimation of causal effects requires some combination of: certain research designs that approximate potential outcomes randomization statistical adjustment Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

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9 Stand up if your student ID ends in: Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

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12 Take away Causal effects rely on unobserved counterfactuals At best, we can estimate average treatment effects comparing those who received a treatment with those who don t. In order for this to work, each group must be identical (on average) in every way except the treatment. The best way to achieve this is through random assignment (i.e., experiments) What if this assumption is not met? Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

13 Confounders and causality PROBLEM: This only works if the two groups are, on average, otherwise identical If the two groups differ on other factors that also cause yi 1 and y 0 this is a confounding relationship. If this is the case, our counterfactual is wrong and we can make no causal claim. Take Away If you aren t controlling for all other relevant variables (through randomization or statistical methods), you cannot make a valid causal claim. i, Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

14 Thinking about confounding variables Direct causal relationships: Spurious relationships: X 1 Y Chain relationships: Multiple causation: X 2 X 1 AND X 2 Y 2 X 1 X 2 Y X 1 Y AND X 2 Y Direct and indirect causation: X 1 Y AND X 1 X 2 AND X 2 Y Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

15 Write down one of each type of claim for this data. Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

16 At a minimum we need to show... Association What we will be doing this rest of the semester Correlation, contingency tables, regression coefficients,... Association = causation Temporal order For T i to cause Y i it must come before Y in time order Post hoc ergo propter hoc After this, therefore because of this Temporal order does = causation (e.g., every superstition ever) Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

17 At a minimum we need to show... Eliminate alternative explanations Suppose there is an association and a proper time order. We stil cannot infer causation. Rather, we must test for all alternative explanations. Only if all of these have been resolved can we claim causation. How can we do this? Experimental control (Take my class!) Statistical control (Stay tuned...) Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

18 Some ways to approximate potential outcomes Measure same unit for all treatments Are the effects the same? Divide unit into groups to receive treatments (e.g., close elections) Do the parts really behave identically? Pre-treatment / post-treatment analysis (e.g., policymaking) Would the unit have stayed the same in the control condition? We can match units into pairs that are very similar on covariates (e.g., twins) Are they really interchangeable? Instrumental variables Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19

19 Class business Midterms PS 4 posted wed. PS 6 Quiz for next class Lecture 13 (QPM 2013) Causality and Treatment Effects October 21, / 19