Instrumental Variable: Examples

Eduard Bukin

Questions about questions

Research FAQs:

Before running a regression, ask the following four questions (see J. D. Angrist & Pischke, 2009, Ch. 1)

  1. What is the causal relationship of interest?

  2. What is the experiment that could ideally be used to capture the causal effect of interest?

  3. What is your identification strategy?

  4. What is your mode of statistical inference?

FAQ 1. What is the causal relationship of interest?

FAQ 2. What is the experiment…?

  • Describe an ideal experiment.

  • Highlight the forces you’d like to manipulate and the factors you’d like to hold constant.

  • FUQs: fundamentally unidentified questions

    • Causal effect of race or gender;

    • Do children that start school 1 year later learn more in the primary school?

      • Because older kinds are in general better learners there is not counter factual.
      • However, it is possible to establish this school starting effect on adults (Black, Devereux, & Salvanes, 2008).

FAQ 3. What is your identification strategy?

Identification strategy

is the manner in which a researcher uses observational data (i.e., data not generated by a randomized trial) to approximate a real experiment (J. D. Angrist & Krueger, 1991)

  1. Use theory!

  2. Analyze, what were/are the policies/environments that could mimic the experimental setting?

FAQ 4. What is your mode of statistical inference?

  • describes the population to be studied,

  • the sample to be used,

  • and the assumptions made when constructing standard errors.

  • choose appropriate statistical methods

  • apply them diligently.

Examples

Example 1. wage, education and random nature of the date of birth

Angrist, J. D., & Krueger, A. B. (1991). Does Compulsory School Attendance Affect Schooling and Earnings? The Quarterly Journal of Economics, 106, 979–1014. https://doi.org/10.2307/2937954

Identification strategy:

  • Policy required students to enter school in the calendar year in which they turned six years old;

  • Children born in the fourth quarter enter school at age 5 and 3⁄4 , while those born in the first quarter enter school at age 6 3⁄4;

  • Compulsory schooling laws require students to remain in school until their 16th birthdays;

Combination of school start age policies and compulsory schooling laws creates a natural experiment in which children are compelled to attend school for different lengths of time depending on their birthdays.

Average schooling by quarter of birth

Source: (J. D. Angrist & Krueger, 1991)

Average wage by quarter of birth

Source: (J. D. Angrist & Krueger, 1991)

Fantastic instrumental variable:

  • Quarter of birth;

  • The intuition is:

    • Only a small part of variance in education (the one linked to the quarter of birth) is used to identify the return to education.

    • This small part of variance occurs due to random natural experiment, thus the ceteris paribus holds here.

Estimates

Conclusions

  • IV estimates are very close to the OLS;

  • What does it mean?

    • Ability bias was small in the OLS!

Example 2. Children and their parents’ labor supply: Evidence from exogenous variation in family size

(J. Angrist & Evans, 1998) Angrist, J., & Evans, W. N. (1996). Children and their parents’ labor supply: Evidence from exogenous variation in family size.

Research question and the problem

  • What is the effect of additional child on women labor market participation?

  • Conventional wisdom:

    • More children require more time therefore, women used to sacrifice own employment opportunities.

Endogeneity problem

What would the ideal experiment here?

  • Families without children are inappropriate counter factual

  • Rich families can afford more children: inappropriate counter factual

  • Family usually plan for having an additional children

    • thus, a families with 1 children are also inappropriate counter factual

  • we need a source of exogenous variation in children

Identification strategy

People may plan for a second child, but they cannot plan for having twins!!!

  • We can use dummy variable for a twin birth as instrument for the number of children.

Results

References

MP223-Applied Econometrics (SoSe 2023). Author: Eduard Bukin (2023). | GitHub | StudIP | ILIAS.

Angrist, J. D., & Krueger, A. B. (1991). Does Compulsory School Attendance Affect Schooling and Earnings? The Quarterly Journal of Economics, 106(4), 979–1014. http://doi.org/10.2307/2937954
Angrist, J. D., & Pischke, J.-S. (2009). Mostly harmless econometrics. Princeton University Press. http://doi.org/10.1515/9781400829828
Angrist, J., & Evans, W. (1998). Children and their parents labor supply: Evidence from exogenous variation in family size. He American Economic Review, 88(3), 450–477. Retrieved from https://www.jstor.org/stable/116844
Bertrand, M., & Mullainathan, S. (2004). Are emily and greg more employable than lakisha and jamal? A field experiment on labor market discrimination. American Economic Review, 94(4), 991–1013. http://doi.org/10.1257/0002828042002561
Black, S. E., Devereux, P. J., & Salvanes, K. G. (2008). Staying in the classroom and out of the maternity ward? The effect of compulsory schooling laws on teenage births. The Economic Journal, 118(530), 1025–1054. http://doi.org/10.1111/j.1468-0297.2008.02159.x