Dear Statalisters,
I am currently writing my Masters thesis and estimate the effect of a bonus pay system for supervisors on store performance for a regional restaurant chain.
I have monthly data for each store including profits, the (externally and previously) planned profits and other control variables. I also have a dummy which is 1 for the treatment period (3 months) and 0 otherwise (i.treatment, see regression on the bottom) as well as a dummy for the stores in the treatment (1) and control (0) group.
The store supervisors receive a bonus when they meet a certain quarterly target which is set at about 90% of the planned profits.
The treatment and control group were set up randomized and I can pretty clearly see parallel trends already graphically for my dependent variable (the stores profits). For my first hypothesis H1, I see a positive effect on performance as literature suggests and I do not have further questions regarding H1.
However (and this is where my actual question starts), I also developed a second hypothesis H2 to show that this "incentive effect" varies, depending on how far away stores are from the 90% level. Therefore, I generated a variable which is the Profit Ratio (Profits/Planned Profits). Then, I calculated the average Profit Ratio for the 3 months prior to the treatment(Previous_Ratio). I used this average to categorize the stores into low performers (<0,8 Profit Ratio; they get the category dummy "1"), Standard (0,8-1,0; dummy "2") and High (>1,0; dummy "3). I then transfer the respective category dummy to all observations of the respective store.
The FE regression looks as follows
Now I'm wondering:
a) What Endogeniety problem might arise from using this Profit Ratio,
b) How I could account for it in this regression
and
c) How I could assess the Common Trends Assumption other than graphically for the second hypothesis (in Stata).
Regarding a/b) If I have both the previous levels and the interaction with the treatment in regression, I don't have a endogeneity problem here anymore, or do I? The levels themselves control for the unobservable factors. The interaction then measures whether there is also a treatment effect that is larger with a greater - or different - previous quota.
For c), I took a look at Angrist, J. D. and Pischke, J.-S. (2009): Mostly Harmless Econometrics. There is equation 5.2.7 on page 238 which seems to go into my direction; however I seem to lack the econometric understanding to transfer this onto my problem - or might just am too deep into my topic to comprehend it at th moment. I just read this thread as well from yesterday (https://www.statalist.org/forums/for...rends-question) but I'm not sure if it's the right way for this Profit Ratio.
I hope I provided everything you need and would be very happy if some of you guys could help me out!
All the best,
Martin
I am currently writing my Masters thesis and estimate the effect of a bonus pay system for supervisors on store performance for a regional restaurant chain.
I have monthly data for each store including profits, the (externally and previously) planned profits and other control variables. I also have a dummy which is 1 for the treatment period (3 months) and 0 otherwise (i.treatment, see regression on the bottom) as well as a dummy for the stores in the treatment (1) and control (0) group.
The store supervisors receive a bonus when they meet a certain quarterly target which is set at about 90% of the planned profits.
The treatment and control group were set up randomized and I can pretty clearly see parallel trends already graphically for my dependent variable (the stores profits). For my first hypothesis H1, I see a positive effect on performance as literature suggests and I do not have further questions regarding H1.
However (and this is where my actual question starts), I also developed a second hypothesis H2 to show that this "incentive effect" varies, depending on how far away stores are from the 90% level. Therefore, I generated a variable which is the Profit Ratio (Profits/Planned Profits). Then, I calculated the average Profit Ratio for the 3 months prior to the treatment(Previous_Ratio). I used this average to categorize the stores into low performers (<0,8 Profit Ratio; they get the category dummy "1"), Standard (0,8-1,0; dummy "2") and High (>1,0; dummy "3). I then transfer the respective category dummy to all observations of the respective store.
The FE regression looks as follows
Code:
xtreg Profit_Ratio i.Previous_Ratio##i.treatment i.month, fe
a) What Endogeniety problem might arise from using this Profit Ratio,
b) How I could account for it in this regression
and
c) How I could assess the Common Trends Assumption other than graphically for the second hypothesis (in Stata).
Regarding a/b) If I have both the previous levels and the interaction with the treatment in regression, I don't have a endogeneity problem here anymore, or do I? The levels themselves control for the unobservable factors. The interaction then measures whether there is also a treatment effect that is larger with a greater - or different - previous quota.
For c), I took a look at Angrist, J. D. and Pischke, J.-S. (2009): Mostly Harmless Econometrics. There is equation 5.2.7 on page 238 which seems to go into my direction; however I seem to lack the econometric understanding to transfer this onto my problem - or might just am too deep into my topic to comprehend it at th moment. I just read this thread as well from yesterday (https://www.statalist.org/forums/for...rends-question) but I'm not sure if it's the right way for this Profit Ratio.
I hope I provided everything you need and would be very happy if some of you guys could help me out!
All the best,
Martin
