Estimating a Spatial Dynamic Panel Model with Two-Time Lags in Stata using xsmle

[Hermelino Souza]

Hi everyone,

I am trying to estimate the following spatial dynamic panel data model:

y_it = y_{i,t-2} + p_{i,t} + p_{i,t-1} + X_{i,t-2} + w*y_{i,t-2} + w*p_{i,t} + w*p_{i,t-1} + W*X_{i,t-2}

where:

• y is GDP,
• p represents a public regional policy,
• x includes other control variables,
• w is a spatial weight matrix.

I aim to test whether the effects of policy p persist for more than one year. I believe that appropriately arranging the time lags of the variables is crucial to eliminate correlations between p and X at the same time periods, as well as between p and y.

When attempting to implement this specification using the xsmle command in Stata, it appears that the command only allows for one lag of the dependent variable. Specifically, the model I can estimate seems restricted to:

y_it = y_{i,t-1} + p_{i,t} + p_{i,t-1} + X_{i,t-2} + w*y_{i,t-2} + w*p_{i,t} + w*p_{i,t-1} + W*X_{i,t-2}

Here is the code I used:

xsmle y lag1_p lag2_p x, fe wmatrix(w) model(sdm) difficult dlag(3) type(ind) eff

I truly appreciate any guidance or suggestions on how to correctly specify and estimate this model. Thank you in advance for your assistance!


PS. I still consider adding y_{i,t-2} manually, but if I do, it won't be treated as endogenous and effects estimates will will not be correct.

[Sebastian Kripfganz]

xsmle implements a bias correction procedure for space-time dynamic panel data models. The analytical bias correction would be different if there was a second lag of the dependent variable. This is not implemented in xsmle.

[Hermelino Souza]

Thank you, Prof. Sebastian Kripfganz!
Do you think it is feasible to implement bias correction in this multiple-lags model? And if I apply those lags only to the independent variables, will I encounter the same problem?

I really appreciated your attention.

[Sebastian Kripfganz]

In theory, it is feasible to extend the bias correction approach to multiple lags. However, this is not implemented in any of the existing packages. It would require programming the whole bias correction procedure from scratch in a new package (and, of course, working out how exactly the bias correction would need to look like).