[R] Time Series Count Models

[Brett Gordon]

Hello,

I'm trying to model the entry of certain firms into a larger number of
distinct markets over time. I have a short time series, but a large
cross section (small T, big N).

I have both time varying and non-time varying variables. Additionally,
since I'm modeling entry of firms, it seems like the number of
existing firms in the market at time t should depend on the number of
firms at (t-1), so I would like to include the lagged cumulative count.

My basic question is whether it is appropriate (in a statistical
sense) to include both the time varying variables and the lagged
cumulative count variable. The lagged count aside, I know there are
standard extensions to count models to handle time series. However,
I'm not sure if anything changes when lagged values of the cumulative
dependent variable are added (i.e. are the regular standard errors
correct, are estimates consistent, etc....).

Can I still use one of the time series count models while including
this lagged cumulative value?

I would greatly appreciate it if anyone can direct me to relevant
material on this. As a note, I have already looked at Cameron and
Trivedi's book.

Many thanks,

Brett