IV Application (card)

College proximity as IVs for education

Author

Kevin Hu(胡华平)

Case Description

Research Interests:

With data set Card1995.dta, researchers were interest in the return (log(Wage)) to education (edu) .

In the wage example (wage, or log wage lwage), Let’s consider some of the variables shown below (see Table 1 ).

Table 1: variables and definition
variable definition
obs index
lwage quantity variable: log of wage
edu quantity variable: education years
exp quantity variable: working years
exp2 quantity variable: square working years/100
black dummy: 1=black; 0=nonblack
south dummy: 1=southern area; 0= other
urban dummy: 1=live in urban; 0= other
college dummy: 1=college nearby; 0= other
public dummy: 1=public college nearby; 0= other
private dummy: 1=private college nearby; 0= other
age quantity variable: age (years)
age2 quantity variable: age square /100
momedu quantity variable: mother’ education years
dadedu quantity variable: father’ education years

Models

Origin model

The origin model is

\[ \begin{aligned} lwage & = \hat{\alpha}_0 +\hat{\alpha}_1 {educ} + \hat{\alpha}_3 exp +\hat{\alpha}_4 exp2 \\ & +\hat{\alpha}_5 black +\hat{\alpha}_6 south +\hat{\alpha}_7 urban + u_i \end{aligned} \]

TSLS1: edu V.S. college

we will use college as instruments for educ in our IV model setting.

\[\begin{cases} \begin{align} {edu} &= \hat{\gamma}_0 +\hat{\gamma}_1exp + \hat{\gamma}_2exp2 + \hat{\gamma}_3black + \hat{\gamma}_4south + \hat{\gamma}_5urban + \hat{\theta}_1college +v_i && \text{(stage 1)}\\ lwage & = \hat{\eta}_1 +\hat{\eta}_2\widehat{edu} + \hat{\eta}_3exp +\hat{\eta}_4exp2 +\hat{\eta}_5 black +\hat{\eta}_6 south +\hat{\eta}_7 urban+ e_i && \text{(stage 2)} \end{align} \end{cases}\]

TSLS2: (edu,exp,exp2) V.S. (college, age, age2)

we use (college, age, age2) as instruments for (edu,exp,exp2) in our IV model setting.

\[\begin{cases} \begin{align} {edu} &= \hat{\gamma}_0 +\hat{\gamma}_1age + \hat{\gamma}_2age2 + \hat{\gamma}_3black + \hat{\gamma}_4south + \hat{\gamma}_5urban + \hat{\theta}_1college +v_{1i} && \text{(1 of stage 1)}\\ {exp} &= \hat{\lambda}_0 +\hat{\lambda}_1age + \hat{\lambda}_2age2 + \hat{\lambda}_3black + \hat{\lambda}_4south + \hat{\lambda}_5urban + \hat{\lambda}_1college +v_{2i} && \text{(2 of stage 1)}\\ {exp2} &= \hat{\delta}_0 +\hat{\delta}_1age + \hat{\delta}_2age2 + \hat{\delta}_3black + \hat{\delta}_4south + \hat{\delta}_5urban + \hat{\delta}_1college +v_{3i} && \text{(3 of stage 1)}\\ lwage & = \hat{\eta}_1 +\hat{\eta}_2\widehat{edu} + \hat{\eta}_3exp +\hat{\eta}_4exp2 +\hat{\eta}_5 black +\hat{\eta}_6 south +\hat{\eta}_7 urban+ e_i && \text{(stage 2)} \end{align} \end{cases}\]

TSLS3: edu V.S. (public,private)

we use both (public,private) as instruments for educ in our IV model setting.

\[\begin{cases} \begin{align} {edu} &= \hat{\gamma}_0 +\hat{\gamma}_1exp + \hat{\gamma}_2exp2 + \hat{\gamma}_3black + \hat{\gamma}_4south + \hat{\gamma}_5urban + \hat{\theta}_1public + \hat{\theta}_2private +v_i && \text{(stage 1)}\\ lwage & = \hat{\eta}_1 +\hat{\eta}_2\widehat{edu} + \hat{\eta}_3exp +\hat{\eta}_4exp2 +\hat{\eta}_5 black +\hat{\eta}_6 south +\hat{\eta}_7 urban+ e_i && \text{(stage 2)} \end{align} \end{cases}\]

TSLS4: (edu, exp,exp2) V.S. (public,private,age,age2)

we use both (public,private,age,age2) as instruments for (edu, exp,exp2) in our IV model setting.

\[\begin{cases} \begin{align} {edu} &= \hat{\gamma}_0 +\hat{\gamma}_1age + \hat{\gamma}_2age2 + \hat{\gamma}_3black + \hat{\gamma}_4south + \hat{\gamma}_5urban + \hat{\theta}_1public + \hat{\theta}_2private +v_{1i} && \text{(1 of stage 1)}\\ {exp} &= \hat{\lambda}_0 +\hat{\lambda}_1age + \hat{\lambda}_2age2 + \hat{\lambda}_3black + \hat{\lambda}_4south + \hat{\lambda}_5urban + \hat{\lambda}_1public + \hat{\lambda}_2private +v_{2i} && \text{(2 of stage 1)}\\ {exp2} &= \hat{\delta}_0 +\hat{\delta}_1age + \hat{\delta}_2age2 + \hat{\delta}_3black + \hat{\delta}_4south + \hat{\delta}_5urban + \hat{\delta}_1public + \hat{\delta}_2private +v_{3i} && \text{(3 of stage 1)}\\ lwage & = \hat{\eta}_1 +\hat{\eta}_2\widehat{edu} + \hat{\eta}_3exp +\hat{\eta}_4exp2 +\hat{\eta}_5 black +\hat{\eta}_6 south +\hat{\eta}_7 urban+ e_i && \text{(stage 2)} \end{align} \end{cases}\]

Reproducible Sources

Hansen, B. Econometrics[M]. Princeton: Princeton University Press, 2022. Chapter 12: Instrumental Variables.

  • Table 12.1: Instrumental Variable Wage Regressions

  • Table 12.2: Reduced Form Regressions

Learning Targets

  1. Understand the nature of Endogeneity.

  2. Know the steps of running TSLS method.

  3. Be familiar with R package function systemfit::systemfit() and ARE::ivreg().

Exercise Materials

You can find all the exercise materials in this project under the file directory:

D:/github/course-em-eng/02-homework/IV-wage-card
├── card1995.dta
└── code-card-hansen.R