SEM Application (mroz)

Labor market of married, Working Women

Author

Kevin Hu(胡华平)

Case Description

Let’s consider the labor market for married women already in the workforce.

We will use the data on working, married women in wooldridge::mroz to estimate the labor supply and wage demand equations by 2SLS.

The full set of instruments includes educ, age, kidslt6, nwifeinc, exper, and exper2.

Models setting

The structrual equations

\[ \begin{aligned} \text { hours } & =\alpha_1 \log ( wage)+\beta_{10}+\beta_{11} { educ }+\beta_{12} age+\beta_{13} { kidslt6 } &&\\ &+\beta_{14} { nwifeinc }+u_1 &&\text{(supply)}\\ \log ({ wage }) &=\alpha_2 { hours }+\beta_{20}+\beta_{21} { educ }+\beta_{22} { exper } +\beta_{23} { exper }^2+ u_2 && \quad \text{(demand)} \end{aligned} \]

  • In the demand function, we write the wage offer as a function of hours and the usual productivity variables.

  • All variables except hours and log(wage) are assumed to be exogenous.

  • educ might be correlated with omitted ability in either equation. Here, we just ignore the omitted ability problem.

The reduced equations

\[ \begin{alignedat}{8} \text { hours } & =\pi_{10}+\pi_{11} { educ }+\pi_{12} age+\pi_{13} { kidslt6 } +\pi_{14} { nwifeinc }\\ &+\pi_{15} { exper } +\pi_{16} {exper}^2 +v_1 \\ \log ({ wage }) &=\pi_{20}+\pi_{21} { educ }+\pi_{22} age+\pi_{23} { kidslt6 } +\pi_{24} { nwifeinc } \\ &+\pi_{25} { exper } +\pi_{26} {exper}^2+ v_2 \end{alignedat} \]

Reproducible Sources

Wooldridge, J.M. Introductory econometrics: a modern approach[M]. Seventh edition. Australia: Cengage, 2020.

  • Example 16.5: labor Supply of married, Working Women

Learning Targets

  1. Understand the nature of SEM.

  2. Know the steps of running TSLS method.

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

Exercise Materials

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

D:/github/course-em-eng/02-homework/sem-wage-mroz
└── code-sem-mroz.R