Can I use estimated coefficients to compute ratios?

[frederick lim]

I would like to observe the weekly spent and weekly mileage to Store A and Store B after a managerial intervention. To do so, I estimate the following DiD model specification (noted that the model would be unidentified and have taken the necessary steps to address this):

Log(spent_store_a)= household fixed effect+weekly fixed effects+B1AFTER+B2TREAT+B3AFTERXTREAT+Error
Log(mileage_store_a)= household fixed effect+weekly fixed effects+B1AFTER+B2TREAT+B3AFTERXTREAT+Error

Log(spent_store_b)= household fixed effect+weekly fixed effects+B1AFTER+B2TREAT+B3AFTERXTREAT+Error
Log(mileage_store_b)= household fixed effect+weekly fixed effects+B1AFTER+B2TREAT+B3AFTERXTREAT+Error

With the estimates obtained in B3 above (four estimated coefficients), I take the following ratios:

(Spent/Mileage) of Store a and (Spent/Mileage) of Store b.

Analysis: Ratio of Store a is > Ratio of Store b (1)

I then draw the conclusion that households, on average, are spending more per mile at Store a compared to Store b.

My question: By computing ratios using the estimated coefficients from the DiD model, is the interpretation and procedures given above correct for the purpose of making the comparison in (1)? Thanks.

Best,
Fred

[Phil Bromiley]

You'll increase your chances of a helpful answer by following the FAQ on asking questions - provide Stata code in code deimiters, Stata output, and sample data using dataex. Also, try to reduce the code you include to what is needed to demonstrate your problem. You should also have searched for the major terms in your question from the command window of Stata (findit majorterm) and in the subject index in the documentation (under index at the bottom of the list of documentation).

Since Spent and Millage don't appear on the rhs of your equations, I have no idea what you are asking. It looks like the equations are just irrelevant if you just want to compare to ratios.

If you want to work with predicted values, you use predict after each equation, then you can calculate your ratios and use a ttest to see if they differ. Whether that makes sense or not, I'm not sure.

[frederick lim]

Hi Phil,

Thanks for the advice. Noted.

Basically, this is a difference-in-difference model specification. So the dependent variables of interest (i.e. Spent and Mileage) will not appear in the RHS? I'm using the DiD regression to estimate B3, and then take ratio using the estimated B3s for retail store a and retail store b for comparison.