title	author	date	output
Lecture 15 Instrumental Variables	Nick Huntington-Klein	March 20, 2019	revealjs::revealjs_presentation theme transition self_contained smart fig_caption reveal_options solarized slide true true true slideNumber true

```{r setup, include=FALSE} knitr::opts_chunk$set(echo = FALSE, warning=FALSE, message=FALSE) library(tidyverse) library(dagitty) library(ggdag) library(gganimate) library(ggthemes) library(Cairo) library(fixest) library(modelsummary) theme_set(theme_gray(base_size = 15)) ``` ## Recap - We've covered quite a few methods for isolating causal effects! - Controlling for variables to close back doors (explain X and Y with the control, remove what's explained) - Matching on variables to close back doors (find treated and non-treated observations with ) - Using a control group to control for time (before/after difference for treated and untreated, then difference them) - Using a cutoff to construct a very good control group (treated/untreated difference near a cutoff) ## Today - We've got ONE LAST METHOD to go deep on! - Today we'll be covering *instrumental variables* - The basic idea is that we have some variable - the instrumental variable - that causes `X` but has no other open back doors! ## Natural Experiments - This calls back to our idea of trying to mimic an experiment without having an experiment. In fact, let's think about an actual randomized experiment. - We have some random assignment `R` that determines your `X`. So even though we have back doors between `X` and `Y`, we can identify `X -> Y` ```{r, dev='CairoPNG', echo=FALSE, fig.width=6,fig.height=3} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Natural Experiments - The idea of instrumental variables is this: - What if we can find a variable that can take the place of R in the diagram despite not actually being something we randomized in an experiment? - If we can do that, we've clearly got a "natural experiment" - When we find a variable that can do that, we call it an "instrument" or "instrumental variable" - Let's call it `Z` ## Instrumental Variable So, for `Z` take the place of `R` in the diagram, what do we need? - `Z` must be related to `X` (typically `Z -> X` but not always) - There must be *no open paths* from `Z` to `Y` *except for ones that go through `X`* In other words "`Z` is related to `X`, and all the effect of `Z` on `Y` goes THROUGH `X`" ## Instrumental Variable - This doesn't relieve us of the duty of identifying a causal effect by closing back doors - But it *moves* that duty from the endogenous variable to the instrument, which potentially is easier to identify - (and then adds on the additional requirement that there are also no open *front* doors from $Z$ to $Y$ except through $X$ ) ## Instrumental Variable How? - Explain `X` with `Z`, and keep only what *is* explained, `X'` - Explain `Y` with `Z`, and keep only what *is* explained, `Y'` - [If `Z` is logical/binary] Divide the difference in `Y'` between `Z` values by the difference in `X'` between `Z` values - [If `Z` is not logical/binary] Get the correlation between `X'` and `Y'` ## Estimation - We will be doing this mostly by hand today (until the end part) but most commonly this is estimated using *two stage least squares* - We basically just do what we described on the last slide: 1. Use the instruments and controls to explain $X$ in the first stage 1. Use the controls and the predicted (explained) part of $X$ in place of $X$ in the second stage 1. (do some standard error adjustments) Many ways to do this in R, we'll be doing 2SLS with `feols()` from **fixest** ## Graphically ```{r, dev='CairoPNG', echo=FALSE, fig.width=8,fig.height=7} df 100), W = rnorm(200)) %>% mutate(X = .5+2*W +2*Z+ rnorm(200)) %>% mutate(Y = -X + 4*W + 1 + rnorm(200),time="1") %>% group_by(Z) %>% mutate(mean_X=mean(X),mean_Y=mean(Y),YL=NA,XL=NA) %>% ungroup() #Calculate correlations before_cor % mutate(mean_X=NA,mean_Y=NA,time=before_cor), #Step 2: Add x-lines df %>% mutate(mean_Y=NA,time='2. What differences in X are explained by Z?'), #Step 3: X de-meaned df %>% mutate(X = mean_X,mean_Y=NA,time="3. Remove everything in X not explained by Z"), #Step 4: Remove X lines, add Y df %>% mutate(X = mean_X,mean_X=NA,time="4. What differences in Y are explained by Z?"), #Step 5: Y de-meaned df %>% mutate(X = mean_X,Y = mean_Y,mean_X=NA,time="5. Remove everything in Y not explained by Z"), #Step 6: Raw demeaned data only df %>% mutate(X = mean_X,Y =mean_Y,mean_X=NA,mean_Y=NA,YL=mean_Y,XL=mean_X,time=afterlab)) #Get line segments endpts % group_by(Z) %>% summarize(mean_X=mean(mean_X),mean_Y=mean(mean_Y)) p Y, With Binary Z as an Instrumental Variable \n{next_state}')+ transition_states(time,transition_length=c(6,16,6,16,6,6),state_length=c(50,22,12,22,12,50),wrap=FALSE)+ ease_aes('sine-in-out')+ exit_fade()+enter_fade() animate(p,nframes=175) ``` ## Instrumental Variables - Notice that this whole process is like the *opposite* of controlling for a variable - We explain `X` and `Y` with the variable, but instead of tossing out what's explained, we ONLY KEEP what's explained! - Instead of saying "you're on a back door, I want to close you" we say "you have no back doors! I want my `X` to be just like you! I'm only keeping that part of `X` that's explained by you!" - Since `Z` has no back doors, the part of `X` explained by `Z` has no back doors to the part of `Y` explained by `Z` ## Imperfect Assignment - Let's apply one of the common uses of instrumental variables, which actually *is* when you have a randomized experiment - In normal circumstances, if we have an experiment and assign people with `R`, we just compare `Y` across values of `R`: ```{r, echo=TRUE} df % mutate(X = R, Y = 5*X + rnorm(500)) #The truth is a difference of 5 df %>% group_by(R) %>% summarize(Y=mean(Y)) ``` ## Imperfect Assignment - But what happens if you run a randomized experiment and assign people with `R`, but not everyone does what you say? Some "treated" people don't get the treatment, and some "untreated" people do get it - When this happens, we can't just compare `Y` across `R` - But `R` is still a valid instrument! ## Imperfect Assignment ```{r, echo=TRUE} df % #We tell them whether or not to get treated mutate(X = R) %>% #But some of them don't listen! 20% do the OPPOSITE! mutate(X = ifelse(runif(500) > .8,1-R,R)) %>% mutate(Y = 5*X + rnorm(500)) #The truth is a difference of 5 df %>% group_by(R) %>% summarize(Y=mean(Y)) ``` ## Imperfect Assignment - So let's do IV (instrumental variables); `R` is the IV. ```{r, echo=TRUE} iv % group_by(R) %>% summarize(Y = mean(Y), X = mean(X)) iv #Remember, since our instrument is binary, we want the slope (iv$Y[2] - iv$Y[1])/(iv$X[2]-iv$X[1]) #Truth is 5! ``` ## Another Example - Justifying that an IV has no back doors can be hard! - Usually things aren't as clean-cut as having actual randomization - And sometimes we may have to add controls in order to justify the IV - Think hard - are there really no other paths from `Z` to `Y`? - This will often require *detailed contextual knowledge* of the data generating process ## Pollution and Driving - If air quality is really bad, you may choose to drive instead of walk/bike/bus in order to avoid breathing it - So do particularly smoggy days lead people to drive more? - Pan He and Cheng Xu ask this question using Shanghai as an example! ## Pollution and Driving - Plenty of back doors - seasons, whether factories are running, smog levels last week... ```{r, dev='CairoPNG', echo=FALSE, fig.width=6,fig.height=4.5} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Pollution and Driving - The *direction of the wind* could be an IV - Shanghai faces the water, and so when the wind blows West, it brings pollution into the city ```{r, dev='CairoPNG', echo=FALSE, fig.width=6,fig.height=4.5} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Pollution and Driving - This gives us an IV we can use! - Of course, we need to control for Season to block out the back door. - The authors do indeed find that additional smog, brought in by the wind, increases the number of people who choose to drive - making the problem worse later!! ## Trade and Manufacturing - Another example: did Chinese imports reduce US manufacturing employment? - Employment in the US manufacturing sector has been dropping for decades - (note - *manufacturing itself* isn't dropping, we're manufacturing more than ever, we're just doing it without as many actual people) ## Trade and Manufacturing - The timing of the drop in manufacturing jobs coincides with us importing a lot more Chinese stuff - But did the Chinese imports *cause* the decline or was it a coincidence? Automation is another good explanation! - Or general declining US competitiveness in the global market, vs. everyone (not just China) ## Trade and Manufacturing - Autor, Dorn, & Hanson use Chinese exports *to other countries* (`CEXoth`) as an IV for Chinese exports *to the US* (`CEXus`) in order to estimate the impact of Chinese exports *to the US* on US manufacturing employment (`mfg`) - Let's think about whether this makes sense as an IV - any back doors from `CEXoth` to `mfg` we can imagine? Or front doors that don't go through `CEXus`? - Also, important, do we think that the arrow from `CEXoth` to `CEXus` is actually there? ## Trade and Manufacturing `D` is global demand for US manufactures, `L` is US labor supply, `Close` measures how similar the kinds of things the US manufactures are to China manufactures ```{r, dev='CairoPNG', echo=FALSE, fig.width=8,fig.height=4} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Trade and Manufacturing - So we need to control for `D` in some way to close `CEXoth D -> mfg` but other than that we have a good instrument - (they do this, and also use information like "what does `Close` look like on a regional level?" to improve their estimate) - Autor, Dorn, & Hanson found that Chinese exports elsewhere predicted them in the US (China was opening up and becoming more effective as a producer, making their products attractive everywhere) ## Trade and Manufacturing - And when you limit `mfg` and `CEXus` to just what's explained by `CEXoth`, you do see that some decline in `mfg` is because of Chinese imports  ## Practice - Does the price of cigarettes affect smoking? Get AER package and data(CigarettesSW). Examine with help(). - Get JUST thecigarette taxes `cigtax` from `taxs-tax` - Draw a causal diagram using `packs`, `price`, `cigtax`, and some back door `W`. What might `W` be? - Adjust `price` and `cigtax` for inflation: divide them by `cpi` - Explain `price` and `packs` with `cigtax` using `cut(,breaks=7)` for `cigtax` - Get correlation between the explained parts and plot the explained parts - does price reduce packs smoked? ## Practice Answers ```{r, echo=TRUE} library(AER) data(CigarettesSW) CigarettesSW % mutate(cigtax = taxs-tax) %>% mutate(price = price/cpi, cigtax = cigtax/cpi) %>% group_by(cut(cigtax,breaks=7)) %>% summarize(priceexp = mean(price), packsexp = mean(packs)) %>% ungroup() cor(CigarettesSW$priceexp,CigarettesSW$packsexp) ``` ## Practice Answers Plot ```{r, echo=TRUE, fig.width=6,fig.height=4} plot(CigarettesSW$priceexp,CigarettesSW$packsexp) ``` ## Practice Diagram Answers ```{r, dev='CairoPNG', echo=FALSE, fig.width=6,fig.height=4} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Practice - Doing it with Regression! - Common 2SLS estimators: `ivreg` in **AER**, `iv_robust` in **estimatr**, and `feols()` in **fixest**. We'll use the latter since it's fast easy to combine with fixed effects and all kinds of error adjustments ```{r, echo = TRUE, eval = FALSE} m % mutate(cigtax = taxs-tax) %>% mutate(price = price/cpi, cigtax = cigtax/cpi) first_stage