class: center, middle, inverse, title-slide # Introduction to Causal Identification ### Jenni Putz ### 28 January 2022 --- class: inverse, middle # Causality --- name: intro # Intro Most tasks in econometrics boil down to one of two goals: $$ `\begin{align} y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \cdots + \beta_k x_k + u \end{align}` $$ -- 1. .hi-purple[Prediction:] Accurately and dependably .purple[predict/forecast] `\(\color{#6A5ACD}{y}\)` using on some set of explanatory variables. -- 1. .hi[Causal identification:] Estimate the actual data-generating process—learning about the true, population model that explains .pink[how] `\(\color{#e64173}{y}\)` .pink[changes when we change] `\(\color{#e64173}{x_j}\)` --- # Intro Generally, .hi[*causal*] relationships are complex and challenging to answer, _e.g._, -- - What .pink[causes] some countries to grow and others to decline? - What .pink[caused] President Trump's 2016 election? - .pink[How] does the number of police officers affect crime? - What is the .pink[effect] of better air quality on test scores? - Do longer prison sentences .pink[decrease] crime? - How did cannabis legalization .pink[affect] mental health/opioid addiction? --- # Correlation ≠ Causation You've likely heard the saying > Correlation is not causation. --  --- # Causality ## The challenges Determining and estimating the true model can be pretty difficult—both .purple[practically] and .pink[econometrically]. -- .pull-left[.purple[ **Practical challenges** - Which variables? - Which functional form(s)? - Do data exist? How much? - Is the sample representative? ]] -- .pull-right[.pink[ **Econometric challenges** - Omitted-variable bias - Reverse causality - Measurement error - How precise can/must we be? ]] -- <br>Causality requires us to .hi-slate[hold all else constant] (*ceterus paribus*). --- # Causality The ideal experiment would compare treatment and control .hi[for the same, exact unit]. -- `$$y_{\text{Treatment},i} - y_{\text{Control},i}$$` -- This .pink[*ideal experiment*] is clearly infeasible, as we cannot observe the same unit in .hi-pink[both] treatment and control. --- # Example The effect of de-worming on school attendance. -- ## Motivation Intestinal worms are common among school-age children in less developed countries. The symptoms can keep children at home from school, decreasing human capital accumulation. -- ## Research Question How much do de-worming interventions increase school attendance? --- # Example Suppose we want to know the causal effect of receiving de-worming medication on school attendance. -- **Q:** Could we simply compare attendance of those who have de-worming medication vs. attendance of those who don't? -- **A:** Probably not (if we want the causal effect). -- **Q:** Why not? -- **A:** Omitted-variable bias: Families with access to de-worming medication probably have healthier children for other reasons that may affect school attendance. .pink[Violates *all else equal*. Biased and/or spurious results.] -- **Q:** So what *should* we do? -- **A:** .hi[Run an experiment!] --- # Example Randomized experiments help us maintain *all else equal*. -- We often call these experiments .hi[*randomized control trials*] (RCTs) -- Imagine an RCT where we have two groups: - .hi-slate[Treatment:] Villages where children receive de-worming medication. - .hi-slate[Control:] Villages where children do not receive de-worming medication. -- By randomizing villages into .hi-slate[treatment] or .hi-slate[control], we will, on average, include all kinds of villages in both groups. --- # Example  --- # Example  --- # Example  --- # Causation We can estimate the .hi[causal effect] of de-worming on attendance by comparing the average attendance in the treatment group with the control group. $$ `\begin{align} \overline{\text{Attendance}}_\text{Treatment} - \overline{\text{Attendance}}_\text{Control} \end{align}` $$ -- Alternatively, we can use the regression -- $$ `\begin{align} \text{Attendance}_i = \beta_0 + \beta_1 \text{Trt}_i + u_i \tag{1} \end{align}` $$ where `\(\text{Trt}_i\)` is a binary variable (=1 if village `\(i\)` received the de-worming medication). -- On average, .hi[randomly assigning treatment should balance] treatment and control across the other dimensions that affect attendance. --- class: inverse, middle # Selection Bias --- name: rct # Randomization Can Go Wrong, Too!  --- # Selection Bias **Q:** What is .hi-purple[selection bias]? -- **A:** We have selection bias when our control group doesn't offer a good comparison for our treatment group. -- Specifically, the .pink[average *untreated* outcome for a member of our **treatment group**] (which we cannot observe) differs from the .purple[average *untreated* outcome for a member of our **control group**] -- Basically, the control group doesn't give us a good .hi-purple[counterfactual] for .purple[what our treatment group would have looked like if the members had not received treatment.] --- # Selection Bias .hi-slate[Practical problem:] Selection bias is also difficult to observe -- .hi-slate[Bigger problem:] If selection bias is present, our estimate for the effect of treatment is biased, preventing us from understanding the causal effect of treatment. --- # Selection Bias ## Solutions .hi-slate[Option 1:] .hi-pink[Distribute treatment] in a way such that the treatment and control groups are essentially identical (experiments with good randomization). -- .hi-slate[Option 2:] .hi-purple[Build a control] group that *matches* the treatment group --- # Example Labor economists, policy makers, parents, and students are all interested in the (monetary) *return to education.* -- .hi-slate[Thought experiment:] - Randomly select an individual. - Give her an additional year of education. - How much do her earnings increase? This change in earnings gives the .hi-slate[causal effect] of education on earnings. --- # Example **Q:** Could we simply compare the earnings of people with varying levels of education? -- **A:** Probably not if we want the true, causal effect. -- 1. People choose education based on ability and other factors 1. High-ability people tend to earn more and stay in school longer 1. Education likely reduces experience (time out of the workforce) -- These points illustrate the difficulty in learning about education while *holding all else constant*. --- # Example **Q:** So how can we estimate the returns to education? -- .hi-slate[Option 1:] Run an .hi[experiment]. -- - Randomly .pink[assign education] (might be difficult). - Randomly .pink[encourage education] (might work). - Randomly .pink[assign programs] that affect education (*e.g.*, mentoring). -- .hi-slate[Option 2:] Look for a .hi-purple[*natural experiment*]—a policy or accident in society that arbitrarily increased education for one subset of people. -- - Mandatory schooling laws - Admissions cutoffs - Lottery enrollment and/or capacity constraints --- # Real-world experiments Both examples consider .hi-slate[real experiments] that isolate causal effects. .hi-slate[Characteristics] - .purple[Feasible]—we can actually (potentially) run the experiment. - .purple[Compare individuals] randomized into treatment against individuals randomized into control. - .purple[Require "good" randomization] to get *all else equal*. -- The idea of differencing .hi-pink[treatment] and .hi-purple[control] to estimate causal effects extends into many other methodologies: -- - Difference-in-differences - Synthetic Control - Instrumental Variables - Machine Learning --- class: inverse, middle # Thank you!