I have an unbalanced panel and want to estimate if war (a binary variable) has an effect on different outcomes, for example labor force participation. But the outcome variable is clearly path-dependant. My data consists of about 140 countries and 27 years.
I know that including a lagged dependent variable will bias the estimates, but Judson and Owen (link one) write that the bias is not too big for T=30, and the bias is bigger for the regression coefficient of the lagged dependent variable than for the regression coefficients of the other independent variables (which is what I'm interested in). So I'm thinking about estimating a fixed effects model with a lagged dependent variable. Did I understand Judson and Owens suggestion correctly? And do I have to use robust standard errors, because of course there is serial correlation, but sometimes it's written that "lagged dependent variables take care of serial correlation" (and if yes, which robust standard errors? Arellano's?)?
Then Angrist and Pischke suggest in Mostly Harmless Econometrics on page 184 (second link) that it is possible to give an upper and lower bound of the "true" effect. Do I understand it correctly that a pooled OLS with a lagged dependent variable and a fixed effects estimation without a lagged dependent variable will give me a bound in which the true effect of war on labor force participation should lie? They always talk about a positive beta (regression coefficient), but the variable I'm interested in (war) has a negative effect on the outcome variable (e.g. labor force participation). Can I still use these bounds? And again, which type of errors would i have to include?
I would be very grateful for any help in making sure that I understood the above-mentioned suggestions of the authors correctly!