<p>I'm trying to estimate the effect of a treatment on prices.
I have a panel dataset on which I'm using a DiD to estimate treatment effect through a dummy variable that identifies the period during which the treatment was active.
The particular feature is that the treatment period is the initial period, while the control period is the latter one.
Practically the treatment_dummy=1 for t in [1,T] and treatment_dummy=0 for t in [T+1;end].</p>
<p>In the regression I added various controls, among which I added some cost items for the product of interest.
I expect to see a positive effect of the treatment, i.e. I expect prices to be higher during the treatment compared to the period after the treatment.</p>
<p>Since I'm considering a period that covers many years, I also added inflation as a control in the form of CPI.
I expected that adding CPI would have increased the estimation of treatment effect since over the period CPI has nearly always increased.
Contrary to my expectations, adding CPI reduces the treatment effect estimation.</p>
<p>I thought about a possible multicollinearity but the tests did not find evidence for it.
It may be possible that I am facing OVB and adding inflation reduces this bias.</p>
<p>Do you have any suggestions on what may cause this?
Do you have an economic interpretation to what is happening?</p>
<p>Thank you very much for any help!</p>

CC BY-SA 4.0
2023-12-15T11:49:24.477Z
If you ignore the CPI and omit it from the model, your estimate of the treatment effect subsumes the actual treatment effect and the effect of the inflation. If CPI happens to be positively correlated to the treatment, omitting the CPI increases the magnitude of the estimate of the treatment effect. Might this be the case here? I am probably just rephrasing what you already wrote...
Richard Hardy
CC BY-SA 4.0
2023-12-18T09:29:32.900Z
That is exactly the problem. That is what I would expect, but CPI is negatively correlated with the treatment, and adding it still increases the magnitude of the estimate of the treatment effect.
Sam
CC BY-SA 4.0
2023-12-18T09:34:49.050Z
I wrote *omitting the CPI increases the magnitude of the estimate of the treatment effect* and you wrote *adding it still increases the magnitude of the estimate of the treatment effect*. Are these two not the same thing?
Richard Hardy
<econometrics><inflation><difference-in-difference>
Unexpected effect of adding a variable to a multivariate regression. How to interpret it?
Sam
# Unexpected effect of adding a variable to a multivariate regression. How to interpret it?

(Asked by: username_0 on 2023-12-14)

I'm trying to estimate the effect of a treatment on prices.
I have a panel dataset on which I'm using a DiD to estimate treatment effect through a dummy variable that identifies the period during which the treatment was active.
The particular feature is that the treatment period is the initial period, while the control period is the latter one.
Practically the treatment\_dummy=1 for t in [1,T] and treatment\_dummy=0 for t in [T+1;end].

In the regression I added various controls, among which I added some cost items for the product of interest.
I expect to see a positive effect of the treatment, i.e. I expect prices to be higher during the treatment compared to the period after the treatment.

Since I'm considering a period that covers many years, I also added inflation as a control in the form of CPI.
I expected that adding CPI would have increased the estimation of treatment effect since over the period CPI has nearly always increased.
Contrary to my expectations, adding CPI reduces the treatment effect estimation.

I thought about a possible multicollinearity but the tests did not find evidence for it.
It may be possible that I am facing OVB and adding inflation reduces this bias.

Do you have any suggestions on what may cause this?
Do you have an economic interpretation to what is happening?

Thank you very much for any help!

**Tags:** econometrics, inflation, difference-in-difference

> **Comments:**
> **username_1**: If you ignore the CPI and omit it from the model, your estimate of the treatment effect subsumes the actual treatment effect and the effect of the inflation. If CPI happens to be positively correlated to the treatment, omitting the CPI increases the magnitude of the estimate of the treatment effect. Might this be the case here? I am probably just rephrasing what you already wrote...  
> **username_0**: That is exactly the problem. That is what I would expect, but CPI is negatively correlated with the treatment, and adding it still increases the magnitude of the estimate of the treatment effect.  
> **username_1**: I wrote *omitting the CPI increases the magnitude of the estimate of the treatment effect* and you wrote *adding it still increases the magnitude of the estimate of the treatment effect*. Are these two not the same thing?  

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## 0 answers

