Econometrics Question

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:

𝑔𝑎𝑠𝑖 =𝛽0 +𝛽1𝑡𝑎𝑥𝑖 +𝛽2𝑥1𝑖 +𝛽3𝑥2𝑖 +⋯+𝛽𝑘+1𝑥𝑘𝑖 +𝜀𝑖

Where 𝑔𝑎𝑠𝑖 is per-person gasoline consumption in state 𝑖, 𝑡𝑎𝑥𝑖 is the per-gallon tax on gasoline in state 𝑖, and the 𝑥 variables are other variables that you think should be held fixed when estimating the effect of 𝑡𝑎𝑥𝑖 on 𝑔𝑎𝑠𝑖. We do not have a measure of the level of concern about climate change in a state. How do you expect the omission of concern about climate change to bias the estimate of 𝛽1?

Answer 1

Hi there! A couple of ideas here, because it could really go either way. As long as you can justify your answer, you should be good to go. I'll give the example involving concern about climate change, since they mention it in the question:

Within a state, the average concern about climate change is likely correlated with the amount of gas tax: states where the population is more concerned about climate change might vote for higher gas taxes. If we could include a variable that helps "tease out" how much of the variation of gas consumption comes from concern about climate change (separate from the tax itself), the effect of the tax itself on consumption might decrease. Therefore, I'd say omitting the climate change variable biases answers away from the null.