You Are Studying The Tradeoff Between Time Spent Sleeping

You are studying the tradeoff between time spent sleeping and time spent working in a sample of individuals aged 23-65. Suppose the true model is:

sleep = β 0 + β 1 totwrk + β 2 age + u

where sleep and totwrk (total work) are measured in minutes per week and age is measured in years.

But rather than estimating the true model, you omit age:

sleep = α 0 + α 1 totwrk + u

Based on the estimates from the two regressions you ran in Stata, in what direction would you expect an OLS estimate of α 1 to be biased?

In reality, even the “true model” from the previous question:

sleep = β 0 + β 1 totwrk + β 2 age + u

may omit important variables. Name an additional omitted variable that may cause the OLS estimator of β 1 to be biased. Explain your reasoning.