Trying to recreate other author's results. E.g. this paper. Introduction to the model is on page 10, while table with results is presented on page 13. Under the table there's a small note that SE were calculated via "delta method".
I am estimating a model: $\log{Y_{it}}= \alpha \cdot dummy_{it} + \beta_1\log{Y_{it-1}}+\beta_2\log{X_{it}}+u_{it}$ where $dummy_{it}$ is a binary variable indicating some kind of policy introduction. I am using autoregressive term, and therefore I can capture both short-run and long-run effect of the policy. The short-run is given by $\alpha$ while the long-run is $\frac{\alpha}{1-\beta_1}$. Standard error for the short run is printed by R. But to get standard errors for the long-run effect, author suggests using "delta method" and is not saying anything else.
Want to know how to calculate the standard errors in such a setting. Ideally both, "on paper" and in R using the "delta method".
So far I have tried alr3 package and its deltaMethod() function. I tend get to the right estimate but the SE is 0.00000. And when using msm package and its deltamethod() function I also get 0. Does that mean the SE is so minimal? I don't think so, as the author reports a higher value.
