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3.4: Multivariate Regression Examples

ECON 480 · Econometrics · Fall 2019

Ryan Safner
Assistant Professor of Economics
safner@hood.edu
ryansafner/metricsf19
metricsF19.classes.ryansafner.com

Sacerdote (2001) on Peer Effects

Paper Motivation I

  • What determines student outcomes in college? (GPAs, fraternity enrollment, alcohol/drug use, etc)

  • Effects of peer groups

Sacerdote, Bruce, (2001), "Peer Effects with Random Assignment: Results from Dartmouth Roommates" Quarterly Journal of Economics 116(2):681-704

Paper Motivation II

  • "Standard" way to estimate peer effects: regress student i's outcomes/behavior on other students' outcomes/behavior

GPAi=β0+β1OwnBehaviori+β2RoommateBehaviori+ui

Sacerdote, Bruce, (2001), "Peer Effects with Random Assignment: Results from Dartmouth Roommates" Quarterly Journal of Economics 116(2):681-704

Paper Motivation II

  • "Standard" way to estimate peer effects: regress student i's outcomes/behavior on other students' outcomes/behavior

GPAi=β0+β1OwnBehaviori+β2RoommateBehaviori+ui

  • Problems with this approach:
    1. Individuals self-select into peer groups
    2. If two roommates A and B influence each other, how do we disentangle causal effect of B→A vs. A→B?
    3. Are peer effects actually driven by students' own backgrounds, or by their actual choices?

Sacerdote, Bruce, (2001), "Peer Effects with Random Assignment: Results from Dartmouth Roommates" Quarterly Journal of Economics 116(2):681-704

Paper Motivation II

corr(OwnBehavior,u)≠0corr(RoomateBehavior,u)≠0E[u|OwnBehavior,RoommateBehavior]≠0

Sacerdote, Bruce, (2001), "Peer Effects with Random Assignment: Results from Dartmouth Roommates" Quarterly Journal of Economics 116(2):681-704

Sacerdotes' Identification Strategy

  • Freshmen entering Dartmouth College are randomly assigned to dorms & roommates

  • Removes self-selection of peer groups by shared characteristics

  • Random assignment: roommate A's background characteristics are uncorrelated with roommate B's background characteristics

Sacerdote, Bruce, (2001), "Peer Effects with Random Assignment: Results from Dartmouth Roommates" Quarterly Journal of Economics 116(2):681-704

Relevant Institutions

  • Freshmen entering Dartmouth College are randomly assigned to dorms & roommates
  • Each incoming freshman fills out a questionnaire:
    1. I smoke. (Y/N)
    2. I like to listen to music while studying. (Y/N)
    3. I keep late hours. (Y/N)
    4. I am more neat than messy. (Y/N)
    5. I am (Male/Female).
  • There are 25=32 combinatorial possibilities of answers to the questions
  • Students are assigned to roommates/dorms at random, conditional on their combination of answers to the 5 survey answers

The Data

  • Data from Dartmouth's database of students: history of dorm assignments & term-by-term academic performance

  • Data on pre-treatment characteristics (SAT scores, high school class rank, private/public HS, home state, academic index)

  • Outcome variables: GPA, time to graduation, frat membership, major choice, participation in athletics

  • Survey of Incoming Freshman: if student drank beer in last year and expectation of graduating with honors

  • Sample of 1589 students

  • Create dummy variable for each block to control for covariates (we'll talk later about dummy variables and fixed effects like this)

The Data: Summary Statistics I

The Data: Summary Statistics II

The Data: Demonstrating Random Assignment

The Data: Demonstrating Random Assignment

Sacerdote's Empirical Model (Basically)

GPAi=β0+β1ACAi+β2ACAj+ui

  • Student i and roommate j

  • ACA: Index of academic performance (broken down into different metrics)

  • Other outcomes of interest (besides GPA: graduation, major, fraternity, athlete

Regression Results

Regression Results

  • For every 1 point increase (decrease) in your roommate's GPA, your GPA increases (decreases) about 0.12 points

Regression Results

  • For every 1 point increase (decrease) in your roommate's GPA, your GPA increases (decreases) about 0.12 points

  • If you would have been a 3.0 student with a 3.0 roommate, but you were assigned to a 2.0 roommate, your GPA would be 2.88

Regression Results: Academic Performance

Regression Results: Social Outcomes

Conclusions

  • Peer effects are very strong!

  • Important influences in Freshman year performance (GPA) and activities (joining a social organization)

  • Not important for choosing a major

Sacerdote, Bruce, (2001), "Peer Effects with Random Assignment: Results from Dartmouth Roommates" Quarterly Journal of Economics 116(2):681-704

Duggan and Levitt (2002) on Corruption in Sumo Wrestling

Paper Motivation I

  • 2000 year history, national sport of Japan, extremely ritualistic

  • Japan is a country with low corruption (CPI: 75, Rank 18th best)

  • Good data available

  • Situation is ripe for cheating! So when/why does it happen?

Duggan, Mark and Steven D. Levitt, (2002), "Winning isn't Everything: Corruption in Sumo Wrestling" American Economic Review 92(5):1594-1605

Relevant Institutions I

  • Tournaments (basho), 66 wrestlers (rikishi), 15 bouts each

  • Wrestlers with 8+ wins (kachi-koshi) move up in rankings (banzuke)

  • Those with a losing record ($<$8 wins) (maki-koshi) fall in rankings

Duggan, Mark and Steven D. Levitt, (2002), "Winning isn't Everything: Corruption in Sumo Wrestling" American Economic Review 92(5):1594-1605

Relevant Institutions II

  • A marginal win generates a 2.5 rank increase

  • But movement from 7 to 8 wins produces almost an 11 rank increase!

  • Rank signals prestige, moving up a single rank is worth about $3,000/year

  • Top 5th-10th ranked wrestlers make $250,000/year

Duggan, Mark and Steven D. Levitt, (2002), "Winning isn't Everything: Corruption in Sumo Wrestling" American Economic Review 92(5):1594-1605

Relevant Institutions III

  • Consider 2 wrestlers: A (8-6) vs B (7-7) going into final (15th) match

  • Return to winning for B (7-7) is much higher than for A (8-6)

  • A (8-6) throws the match to B (7-7), who must return the favor in later tournaments if A finds himself in the same 7-7 position

Duggan, Mark and Steven D. Levitt, (2002), "Winning isn't Everything: Corruption in Sumo Wrestling" American Economic Review 92(5):1594-1605

The Data

  • All official top-rank sumo matches from January 1989-January 2000

  • Six tournaments per year, nearly 70 wrestlers per tournament

  • Tournaments last 15 days with one match per wrestler

  • 64,000 wrestler-matches

The Theoretical vs. Actual Probability of Winning

  • Theoretical (binomial) probability of winning 8 times: 19.6%

  • Actual probability (from data): 26%

  • Much higher probability for 8 wins than it should be! (& lower for 7)

    • Could this be from rampant cheating!?

The Model (Slightly Modified)

Winijtd=β1Bubbleijtd+β2Rankdiffijt+λij+δit+uijtd

  • Win=1 if wrestler i beats wrestler j in tournament t on day d

  • Bubble=1 if wrestler ($i$) is on margin (7-7), -1 if opponent ($j$) is on margin, =0 if neither are on margin

  • Rankdiff: difference in rank between wrestlers

  • Wrestler λ and tournament δ fixed effects

Initial Results

  • Frequency of rigging increases as tournament nears end (day 15)

  • On day 15, 7-7 wrestlers on margin win 25% more often than they otherwise should

Interpretation of Initial Results

  • Two alternative hypotheses to explain results:

    1. Match rigging (corruption)
    2. Effort: wrestlers on margin (7-7) just fight harder! Wrestlers with 8 wins are more complacent (already made it)

  • To test, look for evidence of reciprocity agreements over time

    • If these tacit agreements to rig matches exist, wrestlers from stable A should have very high win rates when on the margin against wrestlers from stable B, and vice versa

Interaction Effects

  • Last row (before R2): wrestler's success strongly increases with overall success rates of playing wrestlers on the bubble from other stables

  • For each 10% increase in success in other bubble matches between these two stables, the wrestler on the bubble is 2.7% more likely to win

Reciprocity?

  • Wrestlers who won a bubble match previously tend to do worse when playing same opponent - throw the match to them in reciprocity!

Fisman and Miguel (2007)

Paper Motivation

  • What determines the level of corruption?

    1. Legal environment of country
    2. Culture or social norms

  • How to identify the true source(s)?

Fisman, Raymond and Edward Miguel, (2007), "Corruption, Norms, and Legal Enforcement: Evidence from Diplomatic Parking Tickets," Journal of Political Economy 115(6): 1020-1048

Relevant Institutions

  • U.N. Diplomats are given immunity from prosecution or lawsuits in the U.S.

  • Reciprocal agreements with other countries, designed to protect diplomats in unfriendly environments

  • Diplomatic license plates in NYC are identified, get ticket, but no way to enforce

  • "The best free parking pass in town"

Fisman, Raymond and Edward Miguel, (2007), "Corruption, Norms, and Legal Enforcement: Evidence from Diplomatic Parking Tickets," Journal of Political Economy 115(6): 1020-1048

The Data

  • Between 11/1987 and 12/2002, 150,000 unpaid parking tickets, fines totaling $18,000,000

  • 30 Days to pay a fine, afterwards a 110% penalty. After 70 days, recorded as unpaid violation

  • Individual violation-level data: license plate, name, country of origin, date & time of violation, fine, amount paid (if any)

  • 43% were violations of "no standing/loading zone"

  • 20% of cases, the car was registered to the diplomatic mission (not personal)

  • Scale fines by the size of the country's mission

Identification Strategy I

  • Becker's (1968) rational crime model says with no punishment$\implies$ rational for all diplomats to never pay parking fines

  • But large variation in data! Unpaid fines are strongly correlated with country's score on corruption index!

  • Home country corruption norms are an important predictor of diplomats breaking the law

    • Low corruption countries' diplomats tend to pay the fine even where they are not legally compelled to
    • High corruption countries' diplomats rack up massive fines

Identification Strategy II

  • Natural experiment: post-9/11, NYC began cracking down on enforcement

  • Diplomats with 3+ unpaid parking tickets had diplomat plates revoked

  • Led to immediate 98% reduction in unpaid parking tickets

  • So enforcement matters as well as corruption norms

Data I

Data II

Empirical Model

Unpaid Violations=β0+β1Corruption+β2Enforcement+β3Diplomats+...+βkControls

Results I

Results II

Results III

Sacerdote (2001) on Peer Effects

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