Hello everyone,

I have concerns for several days about the validity of the results I obtain with my regression and I'm writing in the forum to find someone that can give an answer to my question.

In my paper I analyze the impact of an intervention on my variable of interest y. The explanatory variable "Intervention" is equal to 1 when there is an intervention and 0 when there is no intervention. My observations are cells (about 200,000) that are located in 40 countries in total during 19 years. As the interventions are not randomized across cells I use an instrumental variable and a 2SLS regression. My second-stage is the following one:

y_ict = \beta_0 + \beta_1*Intervention_ict + FE_i + FE_ct + u_ict

The regression is controlled for cell fixed effects (FE_i) and for country X year fixed effects (FE_ct) , while the errors are clustered at a country level.

I managed to find an IV for "Intervention" which is exogenous and relevant, but using it I get a coefficient \beta_1 which seems to me a little too high. I therefore thought of controlling my regression for the lagged value of my dependent variable. Because in fact a variation in my dependent variable in t-1 could increase the probability of having an intervention in t, but could also have an impact on my dependent variable in t. In my case, a war in a cell in t-1 may increase the probability of receiving humanitarian aid in t but may also increase the probability of having a war in t. When I control for this variable my instrument remains relevant and \beta_1 remains significant but is almost divided by two, which is much more credible. So I wonder how statistically correct it is to control my regression for the lagged value of my dependent variable. I read some articles talking about the Nickell Bias in this situation, but I have some difficulties to understand if the decrease of my coefficient \beta_1 when I control for the lagged value is due to this bias or if in my case it could be justified to control for this variable.

Thank you in advance for your answers,
David