How to calculate the marginal effect of X1 in the equation? How to write stata commands?

[Huang Yingqian]

After evaluating the time invariant variables using the xtseqreg command (equation is ln(y)=b0+b1X1+b2(X1)^2+b3*X1*X2+other time variable), how do I find ∂y/∂X1 with the manual setting command? What is Stata's command to find the marginal effect and elasticity?

[Clyde Schechter]

Assuming you correctly coded your -xtseqreg- command as

xtseqreg ln_y c.X1##c.X1 c.X1#c.X2 // + other time variable

you can run

margins, dydx(X1) // MARGINAL EFFECT OF X1
margins, eyex(X1) // ELASTICITY

Very important: the coding of the -xtseqreg- command must use factor variables appropriately. If you instead calculated a separate variable for X1² and a separate variable for X1*X2, then -margins- will give you incorrect answers, because it will not know that these variables are actually related to X1.

I should also note that -xtseqreg- is not an official Stata command. I do not know it, and so I can't be sure that it supports factor-variable notation. As the help file shows it was written in 2019 by Sebastian Kripfganz, I strongly suspect it does. But if it doesn't, then you can't use -margins- after it. I would not know how to calculate marginal effects or elasticities after this estimator "by hand," so I hope you can use -margins-.

[Huang Yingqian]

Assuming you correctly coded your -xtseqreg- command as

xtseqreg ln_y c.X1##c.X1 c.X1#c.X2 // + other time variable

you can run

margins, dydx(X1) // MARGINAL EFFECT OF X1
margins, eyex(X1) // ELASTICITY

Very important: the coding of the -xtseqreg- command must use factor variables appropriately. If you instead calculated a separate variable for X1² and a separate variable for X1*X2, then -margins- will give you incorrect answers, because it will not know that these variables are actually related to X1.

I should also note that -xtseqreg- is not an official Stata command. I do not know it, and so I can't be sure that it supports factor-variable notation. As the help file shows it was written in 2019 by Sebastian Kripfganz, I strongly suspect it does. But if it doesn't, then you can't use -margins- after it. I would not know how to calculate marginal effects or elasticities after this estimator "by hand," so I hope you can use -margins-.

Thank you very much for your reply, but the xtseqreg command cannot use c.X1##c.X1 c.X1#c.X2. Do you have any other solutions?

[FernandoRios]

You can use do manual estimation (see any textbook on how to estimate marginal effects) and use lincom to get the right numbers.
Or use -f_able- from SSC

[Huang Yingqian]

You can use do manual estimation (see any textbook on how to estimate marginal effects) and use lincom to get the right numbers.
Or use -f_able- from SSC

Thank you for your reply. Is there any specific operation method?