Difference-in-difference with multiple periods and continuous treatment

[John Bakker]

Hi all,

I want to estimate the effects of agricultural innovation subsidies on firm's R&D activities.
My dataset contains innovative agricultural firms, of which some received a subsidy (treated) and some did not (untreated)
I observe the activities (in number of R&D personnel) and other variables of these firms in 2007-2011 (balanced panel)
Grants were provided in 2009 and 2010 and the dataset contains the exact value of the subsidy

I want to use a difference-in-difference approach to estimate the effects of the subsidy on R&D activity.
As the subsidy relates to innovation projects with a minimum duration of 3 years, I assume the subsidy will have effect in all of these years.

Yet, I am not sure which equation i should use to estimate these effects. I think I need to estimate the following equation with fixed effects:

y_it = a_i + λ_t + β*Subsidy_t + μ*X_it + e_{it
where i = firm, t = year, X = other covariates, where 'Subsidy' has value 0 in pre-treatment years for both control and treatment firms and value of the subsidy in post-treatment years for treated firms.}
i.e. in Stata (in the case without covariates):
xtset firm year
xtreg r_d_personnel i.year subsidy, fe cluster(firm)

I wanted to replicate my results by estimating a standard 'DID' in a regression equation and estimated the following equation:
regress r_d_personnel i.year treated subsidy, vce(cluster firm)
_{where treated is a dummy variable equal to one when a firm is in the treamtent group (received subsidy in 2009 or 2010) and zero when a firm did not receive a subsidy in 2007-2011.}

Yet, the models do not produce the same results and I know it has something to do with the treatment being a continuous variable, because if I estimate the same equation with a dummy variable for treatment (which is equal to 1 for treated firms in post-treatment years and zero otherwise) I do get exactly the same results. I do however not know which equation is right and why.

Furthermore, when I include (time-varying) control variables I also obtain different results, even with the treatment being a dummy variable.

I hope you can answer my question(s)
Thanks in advance.

Kind regards,

John

[Erdem Yilmaz]

If you wanna use standard reg then code should be:

reg r_d_personnel i.post##i.treated, vce(cluster firm)

where treated group should always take the value of 1, and post should be switched to one in the year of treatment and kept to be one.
You should not include time-varying if they are likely to be affected from the treatment

[John Bakker]

Hi Erdem,

Thanks for the quick response.
I think this is the equation in case of the treatment being a dummy variable?
With time-varying you mean other control variables? I think the year dummies should be added to the equation right?

John

[Erdem Yilmaz]

Hello John,
So if the firm is treated at any time in the sample, it is always one, and the post takes the value of one if at that particular time t that particular firm is treated. Actually you even don't need "i." suffix.
Yes, I mean other control variables. Since you have more than one treatment year, you might add time dummies.

[John Bakker]

Hi Erdem,

Thanks for the reply, but I am still confused why I obtain different results with fixed effects regression compared to standard regression when I use the continuous subsidy variable instead of a treatment dummy. Do you have any idea on why that is the case?

John

[Erdem Yilmaz]

What do you mean by continuous? like 6 million dollars? Then of course you will get different results. With diff in diff you compare the increase in the r_d personal of treatment group with the control group. If you are interested in the heterogeneous treatment of different subsidy amounts, you could do something like this: Create a dummy variable that takes the value of if subsidy amount is below the median and 0 otherwise.