Can lagged explanatory variable correct endogeneity?

[George Tim]

I want to estimate a model:
retail price of a product in a week = state dummy * holiday dummy * gas price in that week + state FE + month FE + product FE
Endogeneity is likely since crude oil price affects retail product prices and gasoline prices. Ideally I would instrument gas prices with crude oil price but weekly crude oil price data is only available at country level and not at state level. Will including lag of gas price in the model correct for endogeneity? Or can I instrument gas price with lag gas price? Or is there any other solution?

[George Ford]

People do it, but it depends on persistence of the series. A few good papers out there analyzing the issues. There's also a state-level wholesale gas price variable in STEO, if you're looking at retail prices. Might be able to construct an interesting IV from the wholesale/crude spread.

[George Ford]

bad weather or refiner shut downs might be a useful IV. that would presumably affect prices only through crude costs.

[George Tim]

bad weather or refiner shut downs might be a useful IV. that would presumably affect prices only through crude costs.

Thank you. I found weekly crude refiner input prices by states. Do you think I could use that as IV? Also can you please direct me to wholesale gas price data? I only found retail data by EIA

[George Ford]

As you say, crude oil in an input into gas and other products. Nothing related to crude oil is going to be a good IV. I'd be looking at things that affect prices at the pump but not "manufacturing". Gas taxes, regional gas disruptions, and maybe seasonal gas demand. It may depend on what you are trying to demonstrate. Is it that retail gas prices paid by people are sub/comp to other products, or there's an income effect? Or, how much to transportation costs related to transport are passed through?

IV choice is going to be very important here. My mind is thinking that truck transportation PPI might be useful in some way--not sure why and it could be a dead end.

[George Tim]

As you say, crude oil in an input into gas and other products. Nothing related to crude oil is going to be a good IV. I'd be looking at things that affect prices at the pump but not "manufacturing". Gas taxes, regional gas disruptions, and maybe seasonal gas demand. It may depend on what you are trying to demonstrate. Is it that retail gas prices paid by people are sub/comp to other products, or there's an income effect? Or, how much to transportation costs related to transport are passed through?

IV choice is going to be very important here. My mind is thinking that truck transportation PPI might be useful in some way--not sure why and it could be a dead end.

this article attempts something similar. What could possibly be a reason they don't use IV? https://acrobat.adobe.com/id/urn:aai...3-917a1fe23279

[George Ford]

not sure why milk prices and gas prices would be jointly determined