Dears,

I have a question about the model specification that I wonder if people can share their thoughts about it. I estimate a model using a panel dataset including 144 countries.
Code:
𝑦𝑖,𝑡+𝑘 = 𝛼𝑖𝑘 + 𝛾𝑡𝑘 + 𝛽𝑘𝐷𝑖,𝑡 + 𝜃𝑘𝑋𝑖,𝑡 + 𝜀𝑖,𝑡+𝑘
where
where 𝑦𝑖,𝑡 is the fertility rate for country 𝑖 in year 𝑡; 𝛼𝑖 are country fixed effects, included to
take account of differences in countries’ average fertility; 𝛾𝑡 are time fixed effects, included
to take account of global shocks and global business cycle; 𝐷𝑖,𝑡 is a dummy variable
indicating a pandemic recession event in country 𝑖 at year t. 𝑋𝑖,𝑡 is a vector that includes two
lags of the dependent variable and the pandemic recession dummy
I am interested to do a placebo test, but unfortunately, as I am searching but I do not know how can I do this.


any comments about this will be appreciated!
Thanks,