# Classical Natural Experiments Twins Borders Others

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```					Classical Natural Experiments: Twins · Borders · Others

Course: Applied Econometrics Lecturer: Zhigang Li

What is the value of Schooling? What is the value of famous schools? Do people really learn useful things in schools? Do people learn more in college than in high school? Should government spend more money on schools? What level of schools should get more funding?

A naïve regression Incomei=α·Educationi+εi Problems
Measurement Errors (Income, Education)? Underspecification? Functional form misspecification? Endogeneity?

Key Issue
Endogeneity is the key issue
Due to the correlation between education and omitted variables that affect income (talents, family environment, …) Due to measurement errors in education

The problem may not be solved by adding more control variables or using panel data.

Solution with identical twins
Arguments for using twins data
Identical twins should be equally smart; they should look similar; and they should have the same family background. Therefore, if we could find twins with different education, we can compare their income. The difference should reflect only the effect of education but not of omitted variables. Strictly speaking, we assume there is no unobserved difference between twins that is correlated with education. Is this assumption valid?

Solution with identical twins
A rule: If one has two independent measures of a variable and both measures contain classical measurement errors, then she can use one measure as the instrumental variable of the other. Hence, one possible way to address the potential measurement errors in schooling is to ask the twins to report their co-twin’s education levels.

An Empirical Study (Bonjour et al., 2003)
Data: 3,300 same-sex twins in 1999 in U.K.
Detailed medical information Socioeconomic information

Method
ln(wif)=βSif+Aif+εif ln(w1f)-ln(w2f)=βWTP(S1f-S2f)+(a1f -a2f)+(ε1f-ε2f)

aif is the ability net of family and genetic effects. Why identical twins may have different years of schooling?

Do Better Schools Matter?
A naïve regression
Scorei=α·School_Qualityi+εi

Problems
How to measure school quality? Score is only one many aspects of school value Do good schools train good students or do smarter students go to good schools?
Again, student quality is unobserved

Solution Using Borders (Black, 1999)
Compare prices of houses on opposite sides of attendance district boundaries
Assumption: the houses share similar neighborhood characteristics ln(price)=α+X’β+Z’δ+γtest+ε Problem: Not all relevant house or neighborhood characteristics can be observed (e.g. public goods, neighborhood characteristics) Solution: Replace the district characteristics variable Z by a full set of boundary dummies indicating houses with common borders.

Data
Housing prices All purchases and sales from 1993 through 1995 for three counties in suburbs of Boston, Massachusetts. Massachusetts is chosen because of its small school districts, reducing heterogeneity of population within districts. Focus on elementary schools because only this level allows for enough within-district variation. Neighborhood characteristics School district characteristics School Quality is measured by the fourth grade Educational Assessment Program.

Sensitivity Tests
Concern: Districts on opposite sides of the boundaries are very different.
Exclude boundaries that were railroad tracks, highways, major streets. An artificial natural experiment to account for progressions in neighborhoods towards good schools. Compare the effects of including more neighborhood controls on estimates. Compare housing characteristics across borders.

Compare the effect of larger and smaller houses.

Is Minimum Wage Good or Bad? (Card and Krueger, 1994)
How do employers in a low-wage labor market respond to an increase in the minimum wage? Design

Event: Minimum wage in New Jersey rose from \$4.25 to \$5.05/hour on April 1, 1992. Design 1: The treatment group includes stores in NJ and the control group includes stores in PA, which was not (directly) affected by the wage rise. Design 2: Treatment includes stores paying high wage and control group includes stores paying low wage prior to the wage rise, all in NJ.

Empirical Implementation
Data: Survey (employment, wage, prices) of 410 (100%) fast-food restaurants in NJ and eastern PA before and after the wage rise. Information on store closing also available. ΔEi=a+bXi+cGAPi+εi

ΔEi: Employment change at store i Xi: Characteristics of store i GAP: 0 for PA stores and high-wage NJ stores; (5.05-W1i)/W1i for other NJ stores

Issues
Other things happening in NJ?
Recession in NJ about the same time

Other things happen in PA? Are NJ and PA comparable?
Seasonal patterns and market structure similar

Measurement
Impact on store closing and opening.

Findings
No evidence that the rise in NJ’s minimum wage reduced employment
In both design, increase in minimum wage increase employment.

Prices of fast-food meals increased in NJ relative to PA. Within NJ, no evidence that prices increased more in stores most affected by the minimum-wage rise.

Re-evaluating the Evidence by Card and Krueger (Neumark and Wascher, 2005) Data
Actual payroll (work hours) from 230 Burger King, KFC, Wendy’s, and Roy Rogers restaurants in NJ and PA. Data sample matched to the same zipcodes and restaurant chains of CK’s study.

Findings
Standard deviation of employment change in CK’s data is three times as large as the NW data, suggesting potential quality problem of the CK data. Estimates of the employment effect of the NJ wage rise lead to opposite conclusion from that of CK. Employment decrease in NJ after the wage rise.

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