Dear all,

I am trying to estimate the following equation:

ln⁡ m_nc=α_n + ∑α_nk *C_c^k + β_nc^core *CORE_nc + β_ns^ds + ln⁡DS_nc + ϵ_nc ln⁡〖(1+τ_nc)〗+e_nc (1)

the thing is the above equation received much modification, so the final equation to estimate is:

ln⁡ m_nc - ϵ_nc ln⁡〖(1+τ_nc)〗 =α_n+∑α_nk C_n^k+(-e^((β_n^core+∑β_k^core C_n^k ) ) )CORE_(n,c)+(-e^((β_n^DS+∑β_k^DS C_n^k ) ) ) ln⁡DS〗_nc + κ_nc

the terms in bold are my concern, as I'm seeing this for the first time, and I am unable to figure out how this can be done especially in STATA, and the more I go deeper in the attached references pages 4-7 the more I get confused, I'm really out of solution as I read many papers and looked everywhere, kindly if anyone can help me to understand the methodology in the paper, I really appreciate it.
sorry I don't have data to attach as I'm trying first to understand how to estimate that equation before collecting data and apologies for the messy equations.
Thank you.