title	author	date	output
Lecture 16 Instrumental Variables in Action	Nick Huntington-Klein	March 28, 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 - Instrumental Variables is sort of like the opposite of controlling for a variable - You isolate *just* the parts of `X` and `Y` that you can explain with the IV `Z` - If `Z` is related to `X` but all effects of `Z` on `Y` go THROUGH `X`, you've isolated a causal effect of `X` on `Y` by isolating just the causal part of `X` and ignoring all the back doors! - If `Z` is binary, get difference in `Y` divided by difference in `X` - If not, get correlation between explained `Y` and explained `X` ## Estimation - There are *lots* of details we could go into on how to estimate instrumental variables - 2SLS isn't the only game in town by far! - Generalized method of moments deals with heteroskedasticity better than 2SLS with robust SEs - Tests for weak instruments - Limited information maximum likelihood deals with weak instruments better ## Estimation - Considerations for binary dependent or endogenous variables, panel IV, bias corrections, etc. etc. etc. - There's a lot! - You can read about a lot of this in the assigned textbook chapter, and it's important to know about before attempting to actually use IV - But we're not going to focus on that much in this class. Instead, let's ask the real question: do the necessary conditions for IV really work? ## Today - We'll be seeing a few examples of instrumental variables in action in different studies - We'll ask what we think about the validity assumption, and how these studies actually work - Validity can be a hard sell sometimes! ## Today - We're going to be looking at several implementations of IV in real studies - We'll be looking at what they did and also asking ourselves what their causal diagrams might be ## Today - And whether we believe them! What would the diagram be for that expenditure/income example? Do we believe that there's really no back door from last year's investment to this year's expenditure? Really? - Every identification implies a diagram... and diagrams come from assumptions. We *always* want to think about whether we believe those assumptions - Remember, in any case, each of these is *just one study*. I could cite you equally plausible studies on these topics that found different findings in different contexts ## Common Macro-Type Example - In macroeconomics, how does US income affect US expenditures ("marginal propensity to consume")? - We can instrument with investment from LAST year. ```{r, echo=TRUE} library(AER) #US income and consumption data 1950-1993 data(USConsump1993) USC93 % mutate(lastyr.invest = lag(income) - lag(expenditure)) ``` ## Common Macro-Type Example ```{r, echo = TRUE} m % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## College Remediation - Bettinger & Long find positive effects of college remediation on persistence - But do we believe this IV? - Let's think - any possible other ways from `RemC` to `Pers`? - Keep in mind, `RemC` is based on the `loc`ation where you live, `loc -> RemC`. What else might be related to where you live? - How could we test the diagram? ## Medical Care Expenditures - One part of the health care debate is how much health care should be pair for by the person *using it* and how much should be paid for by *society* - One concern of taking the burden off of the user is that people might use way more medical care than they need if they're not paying for it - How does *the price you pay* for health care affect *how much you use it*? ## Medical Care Expenditures - So how does `price` affect `use`? - Something to keep in mind is that because of many varied insurance and social safety net programs, the `price` for the same procedure varies wildly between people - And might be affected by `inc`ome, `empl`oyment, what else? - Draw a diagram! - Before I show it, can you think of an instrument? ## Medical Care Expenditures - Kowalski (2016) notices that in many family insurance plans, if your family member is injured, the cost-sharing in the plan means that if *you* then get injured, you'll pay less for your care - So `fam`ily injury is an instrument for price ## Medical Care Expenditures ```{r, dev='CairoPNG', echo=FALSE, fig.width=6,fig.height=6} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Medical Care Expenditures - Kowalski (2016) finds that a 10% price reduction increases use by 7-11%. - So do we believe this one? - Can you imagine any ways in which a family member's use of medical care might affect your use of medical care except through the price you face? - Let's consider some that we might be able to control for (and she does) and some we might not - Any back doors we can imagine? What could we test? ## Stock Market Indexing - The Russell 1000 stock index indexes the top 1000 largest firms by market `cap`italization, and the Russell 2000 indexes the next top 2000 - Both indices are value-weighted, so "big fish-small pond" stocks at the top of the 2000 have more money coming to them than "small fish-big pond" stock at the bottom of the 1000 - Even though the price shouldn't be affected by something as immaterial as what stocks you're being compared to... maybe it does! ## Stock Market Indexing - Does *where you're listed* affect your `price`? - Draw that diagram! - Keep in mind that your listing is based on your `cap` - just big enough for the 1000 and you're on the 1000, not quite there and you're on the `R2000` - All sorts of firm qualities may affect your `cap` and also your `price` - Any guesses as to what might be a good instrument? ## Stock Market Indexing - Sounds like a regression discontinuity, not an IV! What gives? - It's BOTH! This is called "fuzzy RD" - When the regression discontinuity isn't perfect - crossing the cutoff takes you from, say, 40% treated to 60% rather than 0% to 100% - it's sort of like the experiments with imperfect assignment we covered - And the fix is the same - an IV! Being `above` is an IV for being listed on `R2000` ## Stock Market Indexing ```{r, dev='CairoPNG', echo=FALSE, fig.width=6,fig.height=6} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Company Tax Incentives - It's common for localities to offer tax incentives to bring companies to town - Economists tend not to like this, as that company probably would have been just as productive elsewhere, so it's a giveaway to them - But, selfishly, it's nice if that company is producing in *your* city rather than elsewhere, right? Jobs! - What are the impact of "Empowerment Zone (`EZ`)" tax incentives on `emp`loyment? Draw the diagram! ## Company Tax Incentives - This is looking pretty familiar by now ```{r, dev='CairoPNG', echo=FALSE, fig.width=6,fig.height=5.5} dag % tidy_dagitty() ggdag_classic(dag,node_size=20) + theme_dag_blank() ``` ## Company Tax Incentives - Hanson (2009) uses *the political power of your congressperson* as an IV for `EZ` - Did your representative make it onto a powerful `comm`ittee, increasing the chances of getting an EZ for their district? IV! (controlling for the `rep`, we're looking before/after here, like diff-in-diff) - Do we believe this? Any potential problems? What could we test? ## Others - Try to think of a decent IV - For *any* causal question - Remember, you must have: - `Z` is related to `X` - All back doors from `Z` to `Y` must be closed - All front doors from `Z` to `Y` must go through `X`