Trying to recreate other authors results.

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 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.

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.