17.9 - Sample Selection and the Heckman model (Example in R)

Summary

This video discusses the issue of sample selection bias and introduces the Heckman two-step selection model as a solution. The presenter explains how missing data on non-working individuals in labor economics can lead to biased wage estimates. Through an example from World War II, the video illustrates the concept of sample selection. The Heckman model helps correct for this bias by regressing a profit model in the first stage to calculate the inverse Mills ratio. The second stage tests whether sample selection is present, with practical implementation demonstrated using R.

Takeaways

• 😀 Sample selection bias occurs when we only observe data from a non-random subset of a population, leading to inaccurate results if not corrected.
• 😀 In labor economics, wage analysis can be biased because we only observe wages for individuals who are employed, ignoring those not working.
• 😀 Omitted data from non-working individuals creates a non-random sample, making ordinary least squares (OLS) regression inappropriate for estimating wage determinants.
• 😀 A well-known example of sample selection bias is the World War II British plane analysis, where bullet holes led to incorrect conclusions about where to add armor on planes.
• 😀 The correct approach to address sample selection bias involves two steps: First, use a probit model to estimate the probability of an observation being part of the sample.
• 😀 The second step involves applying the Heckman two-step model to regress the outcome of interest (e.g., wages) while including the inverse Mills ratio.
• 😀 The inverse Mills ratio, derived from the probit model in the first step, helps correct for the bias in the second stage regression.
• 😀 If the inverse Mills ratio is statistically significant, it indicates sample selection bias and the need for correction. If it's not significant, the sample is likely random.
• 😀 In the example with working women in labor force data, a significant inverse Mills ratio would indicate sample selection bias, but in this case, the null hypothesis was not rejected.
• 😀 The Heckman selection model is a useful tool for correcting sample selection bias, but careful testing of the inverse Mills ratio is crucial to determine its presence.

Q & A

What is sample selection bias?

Sample selection bias occurs when only a portion of the population is observed, leading to a non-random sample. This can happen when data is only collected from individuals who meet specific criteria, such as those who are working, while excluding others, such as those who are not working.

How does sample selection bias affect statistical analysis?

Sample selection bias can lead to incorrect or biased estimations in statistical models, especially if methods like Ordinary Least Squares (OLS) regression are used. When a non-random sample is used, OLS may produce unreliable results because the sample doesn't accurately represent the entire population.

What is the Heckman selection model, and how does it address sample selection bias?

The Heckman selection model is a two-step statistical approach used to correct for sample selection bias. The first step involves regressing a probit model to calculate the probability of an individual being part of the observed sample (e.g., being employed). The second step includes the inverse Mills ratio from the first step in the main regression model to account for the selection bias.

What does the inverse Mills ratio represent in the Heckman selection model?

The inverse Mills ratio is a term calculated in the first step of the Heckman model, representing the relationship between the likelihood of being in the sample and the outcome variable. It adjusts for the bias caused by non-random sample selection when included in the second stage regression.

Why is the null hypothesis tested in the Heckman selection model?

The null hypothesis in the Heckman selection model tests whether the inverse Mills ratio is equal to zero. If the null hypothesis is rejected, it suggests that there is sample selection bias present. If it fails to be rejected, it implies that sample selection bias is not a significant issue in the model.

What is the importance of the probit model in the first step of the Heckman selection model?

The probit model in the first step of the Heckman selection model estimates the probability of an individual being in the labor force (or another specific group). This model provides the data needed to calculate the inverse Mills ratio, which helps adjust for potential selection bias in the second stage.

How can the Heckman selection model be applied to wage data in labor economics?

In labor economics, the Heckman selection model can be used to correct for sample selection bias when studying wage determinants. For example, data might only be available for individuals who are employed, leading to a biased estimation of the impact of factors like education and experience on wages. The Heckman model corrects for this by incorporating selection probability and adjusting for the missing data from unemployed individuals.

What are the potential consequences of not correcting for sample selection bias?

Not correcting for sample selection bias can lead to biased estimates and incorrect conclusions. For instance, using OLS regression with a non-random sample might result in underestimating or overestimating the effects of certain variables, leading to flawed policy decisions or misguided conclusions in research.

In the example presented in the video, why did Ibrahimov argue that the British planes needed armor on a different part of the plane?

Ibrahimov argued that the planes with bullet holes in certain areas were more likely to return to Britain, while the planes hit in other areas were more likely to be shot down. Therefore, the armor should be added to the areas with no bullet holes, as the absence of damage in those areas indicated that planes with damage there did not make it back. This is an example of sample selection bias—only planes that survived were observed.

What does the video suggest about the statistical significance of the Heckman selection model compared to OLS?

The video suggests that when comparing the Heckman selection model to OLS, the slope coefficients are nearly identical, and the statistical significance is similar between the two methods. This indicates that in this particular case, after correcting for selection bias, the results of the two models were consistent, suggesting no significant bias in the sample.