Applied Microeconometrics I

Transcription

1 Applied Microeconometrics I Lecture 6: Instrumental variables in action Manuel Bagues Aalto University September Lecture Slides 1/ 20 Applied Microeconometrics I

2 A few logistic reminders... Tutorial on R: Today at 15:15, Room C-250 On Tuesday (Sep. 26) we will discuss problem set 1 in class Grades will be available online In the lecture, we will hand you back your problem sets with grades and comments. Problem set 2 will be available Friday night. Next week, we will be available at the computer room for questions on Tuesday and Thursday (15:15-16:45). Reminder: the book Mastering metrics is an excellent way to prepare the course. 2/ 20 Applied Microeconometrics I

3 Yesterday Interpretation of estimates Matching Regression analysis Main threats the validity of regression analysis Omitted variable bias Bad controls Measurement error 3/ 20 Applied Microeconometrics I

4 Today Measurement error (slides lecture 5, pages 8-10) Examples (slides lecture 5, pages 12-42) The impact of social networks The impact of computers on the wage structure Introduction to IV (lecture 6) 4/ 20 Applied Microeconometrics I

5 Outline 1 IV 5/ 20 Applied Microeconometrics I

6 Motivation Sometimes (often) the regression we have is not the regression we want... That is, we do not have a rich enough data to eliminate the selection bias... Possible solution: look for an instrumental variable But good instruments are hard to find... 6/ 20 Applied Microeconometrics I

7 Schooling example Our aim is still to estimate the causal effect of schooling on wages Lets assume we do not observe everything that affects both selection into schooling and earnings (ablity) The relationship between earnings and schooling and earnings Y i = α 0 + ρs i + η i η i = A i γ + v i The variables A i are assumed the only reason why η i and S i are correlated, i.e. E[S i v i ] = 0 7/ 20 Applied Microeconometrics I

8 Schooling example If we could observe the variables A i we could simply include them to the regressions and estimate Y i = α + ρs i + A i γ + v i How to estimate ρ without observing A i? Instrumental variable (IV) allows us to estimate ρ when A i is unobserved 8/ 20 Applied Microeconometrics I

9 With a valid instrumental variable we can consistently estimate ρ in Y i = α + ρs i + A i γ + v i We can write ρ in terms of the population moments Cov(Z i, Y i ) = ρcov(z i, S i )+Cov(Z i, η i ) Given the exclusion restriction, Cov(Z i, η i ) = 0, it follows that ρ = Cov(Z i,y i ) Cov(Zi,Yi) Cov(Z i,s i ) = V (Z i ) Cov(Z i,s i ) V (Z i ) The coefficient of interest, ρ, is the ratio between regression of Y i on Z i (the reduced form) and regression of S i on Z i (the first stage). 9/ 20 Applied Microeconometrics I

10 What is (a valid) instrumental variable? Instrumental variable (IV) is a variable that: 1 Is correlated with causal variable of interest, S i, Cov(Z i, S i ) 0 2 Is uncorrelated with any other determinants of Y i Cov(Z i, η i ) = 0 This requirement can be decomposed in two: 2.1 Exogeneity: None of the unobserved factors affects the instrument [η i Z i] 2.2 Exclusion restriction: Z i only affects Y i through its effect on S i [Z i η i] 10/ 20 Applied Microeconometrics I

11 Why IV works? Intuitive idea behind IV is as follows: 1 You found a variable (the instrument) that affects who is assigned to the treatment 2 This variable is unrelated to other factors that affect the outcome 3 And you know that your instrument has no direct impact on the outcome, it can only affect the outcome through its impact on the treatment. In sum, an IV strategy is equivalent to an RCT without full compliance 11/ 20 Applied Microeconometrics I

12 Can we test validity of IV? Can we test the assumptions needed for valid IV: 1 Is correlated with causal variable of interest, S i, Cov(Z i, S i ) 0 YES: Significance of first stage, F-statistics 2 Is uncorrelated with any other determinants of Y i Cov(Z i, η i ) = 0 NO! The validity of the instrument relies on theory! (Note that tests of overidentification just tell you whether instruments are consistent with each other, but they can still be invalid) 12/ 20 Applied Microeconometrics I

13 Can you think about a good instrument for schooling? What about the last digit of social security number? What about IQ? Month of birth Angrist and Krueger (QJE 1991) Family background? Geographical proximity? Altonji, Elder and Taber (JHR 2005) Working status? 13/ 20 Applied Microeconometrics I

14 Some additional remarks: We used omitted variable to motivate IV, but note that IV can fix every form of endogeneity (more on this later!) Note that IV identifies the impact of the treatment on a very particular group of people: people that only "take" the treatment when they are induced by the treatment to do it. In other words, IV helps to estimate the local average treatment effect (more on this later!) Again: the validity of an instrument relies on theoretical assumptions that must be discussed very carefully. 14/ 20 Applied Microeconometrics I

15 Good instruments are hard to find Good instruments come from a combination of three ingredients: Good institutional knowledge Economic theory Last but not least: Originality Some usual sources of instruments: Nature Assignment rules So-called Natural experiments (e.g. the quarter of birth, Vietnam lottery, electoral timing...) Note that, in general, choice variables of the agent tend to be bad instruments (unless agents are completely irrational or, somehow, they are unaware of the impact their actions) 15/ 20 Applied Microeconometrics I

16 Examples: nature The effect of family size on children s education Twins, gender of the first born, gender of the two first born (Black, Devereux and Salvanes, QJE 2005; Angrist, Lavy and Schlosser, JOLE 2009) The impact of your sibling s gender How would you estimate it? 16/ 20 Applied Microeconometrics I

17 Examples: assignment rules Class size Maimonedes rules (Angrist and Lavy 1999) Assignment based on alphabetical order Foster care Time in prison Other ideas? 17/ 20 Applied Microeconometrics I

18 Examples: natural experiments Immigration Networks of immigrants (Card 1991) Does police decrease crime? Electoral cycles (Levitt 1997) The impact of violent movies on crime Blockbuster movies (Dahl and DellaVigna 2009) 18/ 20 Applied Microeconometrics I

19 Examples (continued) The effect of preschool television exposure on standardized test scores during adolescence: Historical Evidence from the Coleman Study (Gentzkow and Shapiro 2008) The Potato s Contribution to Population and Urbanization: Soil (Nunn and Nancy Qian 2011) 19/ 20 Applied Microeconometrics I

20 (Bad) examples Parental socioeconomic characteristics as an instrument for children education South of Italy as an instrument for CEO s gender Generally: Lagged variables as instruments 20/ 20 Applied Microeconometrics I