Econometrics help

Question

Determine the sign of the expected bias introduced by omitting a relevant variable. State your assumptions and provide a very brief rationale for your assumptions.

We plan to estimate the following regression:

𝑎𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒𝑡 = 𝛽0 + 𝛽1𝑠𝑎𝑡𝑢𝑟𝑑𝑎𝑦𝑡 + 𝛽2𝑥1𝑡 + 𝛽3𝑥2𝑡 + ⋯ + 𝛽𝑘+1𝑥𝑘𝑡 + 𝜀𝑡

Where 𝑎𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒𝑡 is the number of people who attend an outdoor farmer’s market in Wheaton on day 𝑡, 𝑠𝑎𝑡𝑢𝑟𝑑𝑎𝑦𝑡 is a dummy variable indicating whether day 𝑡 is a Saturday, and the 𝑥 variables are other variables that you think should be held fixed when estimating the effect of 𝑠𝑎𝑡𝑢𝑟𝑑𝑎𝑦𝑡 on 𝑎𝑡𝑡𝑒𝑛𝑑𝑎𝑛𝑐𝑒𝑡. We do not observe whether or not it rained on day 𝑡 so this cannot be included as a regressor. How do you expect the omission of a “rainy day” variable from the regression to bias the estimate of 𝛽1?

Answer 1

The omission of a rainy day variable will not bias the estimate of β₁, since rainy day and Saturday are independently distributed. Since the covariance of rainy day and Saturday is zero in expectation, the omitted variable bias is zero.