Omitted Variable Bias

(Video) Omitted Variable Bias

by Marginal Revolution University

This video by Marginal Revolution University explains omitted variable bias and provides an example to understand the concept.

Summary

Omitted variable bias is a type of selection bias in regression analysis (regression models) that occurs because we do not use the right controls.

For example, you want to understand variables that contribute to higher salary. You know that higher education can lead to higher salary. If we dive deeper, we know that having more books at home increases academic achievement.

So, we've determined that:

$$\text{More books at home} \rightarrow \text{doing better in school} \rightarrow \text{higher salary}$$

But are the number of books at home the only factor to consider when considering academic achievement? Maybe parental IQ could bias our results.

Leaving out the variable of parental IQ when considering the relationship between academic achievement and salary is an example of omitted variable bias. We've omitted this important variable from our analysis.

Background

In the previous lessons, we learned about the importance of sampling in experiments and statistics. We dove into types of sampling. We also learned about different types of sampling biases, including self-selection and observer bias. We also learned about different methods of avoiding sampling bias in our research, including blinding and random sampling.

This lesson will cover another type of sampling bias, called omitted variable bias.

Omitted Variable Bias

This type of bias is when a statistical analysis leaves out specific variables from the analysis. The result is a potentially invalid statistical analysis, as there may be relevant variables that are not included within the analysis.

We often see this bias when we are dealing with regression analysis, looking at multiple factors' variability with each other, specifically cause and effect. If there were some third variable we didn't consider, it could be affecting our results (i.e., the dependent variable). This third variable may be an omitted variable.

It may be easier to understand with an example.

Example

You want to understand the relationship between drinking orange juice and feeling energized. You notice that on the mornings that you drink orange juice, you feel like you have more energy throughout the day. This increased energy makes you feel more productive!

$$\text{drinking orange juice} \rightarrow \text{more energy} \rightarrow \text{more productive}$$

You tell everyone about your new secret weapon for increasing your productivity! When you tell your mom, she asks how you know it is the orange juice. You say that you noticed that when you wake up on time in the morning, you have time to drink orange juice.

But maybe waking up on time is also affecting your energy. Having more energy could then affect your productivity. This means that drinking orange juice and having more energy may be correlated, but that does not mean orange juice caused you to have more energy.

Waking up on time is an example of an omitted variable. You did not originally consider it when looking at your energy throughout the day, but it may be affecting your energy levels and your productivity. Leaving out an important variable can create bias in your analysis. This idea can also be called an error term.

That is why, in statistics, you should not only consider the variables that seem relevant at first. You may not know which variables are important until you complete a full analysis. Always consider as many possible variables and conditions as you can.

Omitted Variable Bias

Now that we've learned about sampling bias, let's dive into omitted variable bias.

Omitted variable bias happens when an important factor is left out of an analysis.

Imagine that we notice that children with larger shoe sizes are often better readers. At first, it might seem like having bigger feet is connected to better reading skills. But shoe size does not actually make someone a better reader. There is another important variable that we have left out: age.

As children get older, their feet usually grow, so their shoe size increases. At the same time, older children have had more time to practice and improve their reading skills. This means that age helps explain why shoe size and reading ability seem to be related.

If we leave age out of our analysis, we might reach the wrong conclusion about the relationship between shoe size and reading ability. Looking for omitted variables helps us better understand what the data is really telling us.

Learning about bias will become especially important as we learn about the different types of research studies: observational studies, surveys, and experiments.