9:59:59.000,9:59:59.000 - [Instructor] The path from cause [br]to effect is dark and dangerous. 9:59:59.000,9:59:59.000 But the weapons [br]of Econometrics are strong. 9:59:59.000,9:59:59.000 [Attack] with fierce [br]and flexible instrumental variables 9:59:59.000,9:59:59.000 when nature blesses you [br]with fortuitous random assignment. 9:59:59.000,9:59:59.000 [gong rings] 9:59:59.000,9:59:59.000 Randomized trials are the surest [br]path to ceteris parabus comparisons. 9:59:59.000,9:59:59.000 Alas, this powerful tool [br]is often unavailable. 9:59:59.000,9:59:59.000 But sometimes, randomization [br]happens by accident. 9:59:59.000,9:59:59.000 That's when we turn [br]to instrumental variables, 9:59:59.000,9:59:59.000 IV for short. 9:59:59.000,9:59:59.000 - [Voice whispers] Instrumental [br]variables. 9:59:59.000,9:59:59.000 - [Instructor] Today's lesson [br]is the first of two on IV. 9:59:59.000,9:59:59.000 Our first IV lesson begins [br]with a story of schools. 9:59:59.000,9:59:59.000 - [Josh] Charter schools [br]are public schools 9:59:59.000,9:59:59.000 freed from daily district oversight[br]and teacher union contracts. 9:59:59.000,9:59:59.000 The question of whether charters [br]boost achievement 9:59:59.000,9:59:59.000 is one of the most important 9:59:59.000,9:59:59.000 in the history [br]of American education reform. 9:59:59.000,9:59:59.000 - The most popular charter schools[br]have more applicants 9:59:59.000,9:59:59.000 so the luck of the lottery draw [br]decides who's offered a seat. 9:59:59.000,9:59:59.000 A lot is at stake for the students [br]vying for their chance. 9:59:59.000,9:59:59.000 Waiting for the lottery results [br]brings up lots of emotions 9:59:59.000,9:59:59.000 as was captured [br]in the award-winning documentary 9:59:59.000,9:59:59.000 "Waiting For Superman." 9:59:59.000,9:59:59.000 - [Mother] Don't cry.[br]You're gonna make Mommy cry. 9:59:59.000,9:59:59.000 Okay? 9:59:59.000,9:59:59.000 - Do charters really provide[br]a better education? 9:59:59.000,9:59:59.000 Critics most definitely say no, 9:59:59.000,9:59:59.000 arguing that charters enroll [br]better students to begin with, 9:59:59.000,9:59:59.000 smarter or more motivated[br]so differences in later outcomes 9:59:59.000,9:59:59.000 reflects selection bias. 9:59:59.000,9:59:59.000 - [Kamal] Wait, this one seems easy. 9:59:59.000,9:59:59.000 In a lottery, winners [br]are chosen randomly, 9:59:59.000,9:59:59.000 so just compare winners and losers. 9:59:59.000,9:59:59.000 - [Student] Obviously. 9:59:59.000,9:59:59.000 - On the right track, Kamal, 9:59:59.000,9:59:59.000 but charter lotteries [br]don't force kids into 9:59:59.000,9:59:59.000 or out of a particular school. 9:59:59.000,9:59:59.000 They randomize offers [br]of a charter seat. 9:59:59.000,9:59:59.000 Some kids get lucky. 9:59:59.000,9:59:59.000 Some kids don't. 9:59:59.000,9:59:59.000 If we just wanted to know [br]the effect of charter school offers, 9:59:59.000,9:59:59.000 we could treat this [br]as a randomized trial. 9:59:59.000,9:59:59.000 But we we're interested [br]in the effects 9:59:59.000,9:59:59.000 of charter school attendance,[br]not offers. 9:59:59.000,9:59:59.000 And not everyone [br]who is offered, accepts. 9:59:59.000,9:59:59.000 IV turns the effect of being offered[br]a charter seat into the effect 9:59:59.000,9:59:59.000 of actually attending [br]a charter school. 9:59:59.000,9:59:59.000 - [Student] Cool. 9:59:59.000,9:59:59.000 - Oh nice. 9:59:59.000,9:59:59.000 - Let's look at an example, [br]a charter school from 9:59:59.000,9:59:59.000 the Knowledge Is Power [br]Program, or KIPP for short. 9:59:59.000,9:59:59.000 This KIPP school is in Lynn, 9:59:59.000,9:59:59.000 a faded industrial town [br]on the coast of Massachusetts. 9:59:59.000,9:59:59.000 The school has [br]more applicants than seats 9:59:59.000,9:59:59.000 and therefore picks its students[br]using a lottery. 9:59:59.000,9:59:59.000 From 2005 to 2008,[br]371 fourth and fifth graders 9:59:59.000,9:59:59.000 put their names [br]in the KIPP/Lynn lottery, 9:59:59.000,9:59:59.000 253 students won a seat at KIPP, 9:59:59.000,9:59:59.000 118 students lost. 9:59:59.000,9:59:59.000 A year later, lottery winners had [br]much higher match scores 9:59:59.000,9:59:59.000 than lottery losers. 9:59:59.000,9:59:59.000 But remember, [br]we're not trying to figure out 9:59:59.000,9:59:59.000 whether winning a lottery [br]makes you better at math. 9:59:59.000,9:59:59.000 We want to know if attending KIPP[br]makes you better at math. 9:59:59.000,9:59:59.000 Of the 253 lottery winners,[br]only 199 actually went to KIPP. 9:59:59.000,9:59:59.000 The others chose [br]a traditional public school. 9:59:59.000,9:59:59.000 Similarly of the 118 lottery losers,[br]a few actually ended up at KIPP. 9:59:59.000,9:59:59.000 They got an offer later. 9:59:59.000,9:59:59.000 So what was the effect of test scores[br]of actually attending KIPP? 9:59:59.000,9:59:59.000 - [Student] Why can't we just [br]measure their math scores? 9:59:59.000,9:59:59.000 - [Instructor] Great question. 9:59:59.000,9:59:59.000 Who would you compare them to? 9:59:59.000,9:59:59.000 - [Student] Those who didn't attend. 9:59:59.000,9:59:59.000 - [Instructor] Is attendance random? 9:59:59.000,9:59:59.000 - [Camilla] No. 9:59:59.000,9:59:59.000 - Selection bias. 9:59:59.000,9:59:59.000 - [Instructor] Correct. 9:59:59.000,9:59:59.000 - [Otto] What? 9:59:59.000,9:59:59.000 - [Instructor] The KIPP offers [br]are random so we can be confident 9:59:59.000,9:59:59.000 of ceteris parabus,[br]but attendance is not random. 9:59:59.000,9:59:59.000 The choice to accept the offer [br]might be due to characteristics 9:59:59.000,9:59:59.000 that are related [br]to math performance. 9:59:59.000,9:59:59.000 Say, for example, [br]that dedicated parents 9:59:59.000,9:59:59.000 are more likely [br]to accept the offer. 9:59:59.000,9:59:59.000 Their kids are also more likely [br]to do better in math, 9:59:59.000,9:59:59.000 regardless of school. 9:59:59.000,9:59:59.000 - [Student] Right. 9:59:59.000,9:59:59.000 - [Instructor] IV converts [br]the offer effect 9:59:59.000,9:59:59.000 into the effect of KIPP attendance, 9:59:59.000,9:59:59.000 adjusting for the fact [br]that some winners go elsewhere 9:59:59.000,9:59:59.000 and some losers manage [br]to attend KIPP anyway. 9:59:59.000,9:59:59.000 Essentially, IV takes [br]an incomplete randomization 9:59:59.000,9:59:59.000 and makes the appropriate [br]adjustments. 9:59:59.000,9:59:59.000 How? IV describes a chain reaction. 9:59:59.000,9:59:59.000 Why do offers affect achievement? 9:59:59.000,9:59:59.000 Probably because they affect [br]charter attendance 9:59:59.000,9:59:59.000 and charter attendance [br]improves math scores, 9:59:59.000,9:59:59.000 the first link in the chain[br]called the first stage 9:59:59.000,9:59:59.000 is the effect of the lottery [br]on charter attendance. 9:59:59.000,9:59:59.000 The second stage is the length [br]between attending a charter 9:59:59.000,9:59:59.000 and an outcome variable, 9:59:59.000,9:59:59.000 in this case, math scores. 9:59:59.000,9:59:59.000 The instrumental variable [br]or instrument for short 9:59:59.000,9:59:59.000 is the variable [br]that initiates the chain reaction. 9:59:59.000,9:59:59.000 The effect of the instrument [br]on the outcome is called 9:59:59.000,9:59:59.000 the reduced form. 9:59:59.000,9:59:59.000 This chain reaction can be [br]represented mathematically. 9:59:59.000,9:59:59.000 We multiply the first stage,[br]the effect of winning 9:59:59.000,9:59:59.000 on attendance, by the second stage, 9:59:59.000,9:59:59.000 the affect of attendance on scores. 9:59:59.000,9:59:59.000 And we get the reduced form, 9:59:59.000,9:59:59.000 the effect of winning [br]the lottery on scores. 9:59:59.000,9:59:59.000 Reduced form and first stage [br]are observable and easy to compute. 9:59:59.000,9:59:59.000 However, the effect of attendance[br]on achievement 9:59:59.000,9:59:59.000 is not directly observed. 9:59:59.000,9:59:59.000 This is the causal effect[br]we're trying to determine. 9:59:59.000,9:59:59.000 Given some important assumptions [br]we'll discuss shortly, 9:59:59.000,9:59:59.000 we can find the effect [br]of KIPP attendance 9:59:59.000,9:59:59.000 by dividing the reduced form[br]by the first stage. 9:59:59.000,9:59:59.000 This will become more clear [br]as we work through an example. 9:59:59.000,9:59:59.000 - [Student] Let's do this.