I'm working with time series panel data (30 years over 50 states). Let's say that the DV of interest is births per capita per state per year, and there is a policy that is implemented in about half of the states over these 30 years starting in different years to encourage births. This policy involves providing greater access to free fertility treatments. However, interested mothers need to apply to receive these benefits and it takes awhile for knowledge of these programs to get out and for applications to actually ramp up. For about a third of the states that implement this policy, I have data regarding how many women apply for free fertility treatments for every year after implementation. In the other states that adopt this policy, I have sparser data, sometimes only the number of applicants for the first year or two, or the last few years of the program. However, based on the states with full data, the growth in applicants appears to follow a standard growth curve, starting out slowly, then accelerating in later years before leveling off.
I want to estimate the effect of the number of applicants to this program (per capita) on births (per capita). I can generate estimates of missing application data by fitting a growth curve on existing data and then predicting missing values in states with data gaps. However, this would constitute a generated regressor and require correcting standard errors. Is it possible to deal with this in Stata for time series panel data using either bootstrapping or conceptualizing it as Two-Sample Instrumental Variable?
basic variables are:
year
state
births_per_cap
policy_implemented (binary)
years_policy_in_place
applicants_per_cap (with missing data)
x1 (exogenous regressor known in literature to predict birth rates)
The following nonlinear mixed-effects regression generates a growth curve that fits the application data very well and can be used to generate missing data:
menl applicants_per_cap = ({b1}+{U[state]})/(1+exp(-(years_policy_in_place-{b2})/({b3}+{U[state]}))) if years_policy_in_place>0, initial (b1 .30 b2 25 b3 6 )
predict complete_applicants_per_cap
replace complete_applicants_per_cap=0 if years_policy_in_place==0
However, I'm unclear how to deal with the problem of correcting standard errors when using these predicted values in a second stage regression in Stata either through bootstrapping or a Two-Sample Instrumental Variable approach. Any guidance would be much appreciated.
I want to estimate the effect of the number of applicants to this program (per capita) on births (per capita). I can generate estimates of missing application data by fitting a growth curve on existing data and then predicting missing values in states with data gaps. However, this would constitute a generated regressor and require correcting standard errors. Is it possible to deal with this in Stata for time series panel data using either bootstrapping or conceptualizing it as Two-Sample Instrumental Variable?
basic variables are:
year
state
births_per_cap
policy_implemented (binary)
years_policy_in_place
applicants_per_cap (with missing data)
x1 (exogenous regressor known in literature to predict birth rates)
The following nonlinear mixed-effects regression generates a growth curve that fits the application data very well and can be used to generate missing data:
menl applicants_per_cap = ({b1}+{U[state]})/(1+exp(-(years_policy_in_place-{b2})/({b3}+{U[state]}))) if years_policy_in_place>0, initial (b1 .30 b2 25 b3 6 )
predict complete_applicants_per_cap
replace complete_applicants_per_cap=0 if years_policy_in_place==0
However, I'm unclear how to deal with the problem of correcting standard errors when using these predicted values in a second stage regression in Stata either through bootstrapping or a Two-Sample Instrumental Variable approach. Any guidance would be much appreciated.
