Hi!
I'm analysing the effect of gaining health insurance through Medicare Advantage (a federal health insurance program offered predominantly to elderly people via private insurers) in the US on the conditional distribution out-of-pocket health care spending.
In general, health insurance coverage is likely to be endogenous to out-of-pocket health care spending (e.g., people choose health insurance bearing in mind their future spending).
As a result, I restrict my sample to those who join the Medicare Advantage program "shortly after" becoming eligible at age 65 (e.g., joins in first month eligible; within 3 months; ...). This group's coverage is due to the arbitrary age cutoff and we would not expect at sharp change in their spending if they had continued with their previous insurance coverage only.
I have an unbalanced panel of monthly out-of-pocket spending for ten years (max: 10 x 12 =120 monthly observations for a given individual; mean = 88). The number of individuals depends on how I define "shortly after" but is at least 60,000 (those that join immediately upon becoming eligible).
To analyze the mean effect of Medicare Advantage coverage on out-of-pocket spending, I would use a timing-based (no control group) event study model, where the event is defined as enrolling in Medicare Advantage:
\[ m_{it} = \sum\gamma_j . D_{i,t-j} + \alpha_i + \delta_t + \beta.X_{it} + \epsilon_{it} \]
Where
\[ m_{it}, D_{i,t-j}, \alpha_i, \delta_t , X_{it} \] are out-out-pocket spending, event time dummies, individual fixed effects, time (e.g., year-month) fixed effects, and other covariates, respectively. Miller's (2023) review shows that this model can be estimated under certain parameter restrictions (due to multicollinearity).
I was hoping to get advice regarding how (and whether) one can estimate such a model using quantile regression.
Does it make sense to include time FEs (e.g. month-year or year) manually as dummies in the quantiles via moments approach (Machado and Santos-Silva, 2019) estimated via xtqreg (Joao Santos Silva), or using the absorb() option of mmqreg (Fernando Rios)? I hope to use the quantile via moments estimator since it allows the individual FEs to affect the entire distribution, instead of just being location shifters.
Alternatively, might it be possible to estimate this model via the Canay (2011) estimator, if one were willing to assume that the individual FEs are location shifters?
Any other advice relating to my methodology, or references to (theoretical/applied) papers on the topic of quantile regression with individual and time FEs (or specifically quantile regression in the case of event studies) would also be greatly appreciated.
Best,
Aidan Sloyan
(Stata 18.0 SE)
I'm analysing the effect of gaining health insurance through Medicare Advantage (a federal health insurance program offered predominantly to elderly people via private insurers) in the US on the conditional distribution out-of-pocket health care spending.
In general, health insurance coverage is likely to be endogenous to out-of-pocket health care spending (e.g., people choose health insurance bearing in mind their future spending).
As a result, I restrict my sample to those who join the Medicare Advantage program "shortly after" becoming eligible at age 65 (e.g., joins in first month eligible; within 3 months; ...). This group's coverage is due to the arbitrary age cutoff and we would not expect at sharp change in their spending if they had continued with their previous insurance coverage only.
I have an unbalanced panel of monthly out-of-pocket spending for ten years (max: 10 x 12 =120 monthly observations for a given individual; mean = 88). The number of individuals depends on how I define "shortly after" but is at least 60,000 (those that join immediately upon becoming eligible).
To analyze the mean effect of Medicare Advantage coverage on out-of-pocket spending, I would use a timing-based (no control group) event study model, where the event is defined as enrolling in Medicare Advantage:
\[ m_{it} = \sum\gamma_j . D_{i,t-j} + \alpha_i + \delta_t + \beta.X_{it} + \epsilon_{it} \]
Where
\[ m_{it}, D_{i,t-j}, \alpha_i, \delta_t , X_{it} \] are out-out-pocket spending, event time dummies, individual fixed effects, time (e.g., year-month) fixed effects, and other covariates, respectively. Miller's (2023) review shows that this model can be estimated under certain parameter restrictions (due to multicollinearity).
I was hoping to get advice regarding how (and whether) one can estimate such a model using quantile regression.
Does it make sense to include time FEs (e.g. month-year or year) manually as dummies in the quantiles via moments approach (Machado and Santos-Silva, 2019) estimated via xtqreg (Joao Santos Silva), or using the absorb() option of mmqreg (Fernando Rios)? I hope to use the quantile via moments estimator since it allows the individual FEs to affect the entire distribution, instead of just being location shifters.
Alternatively, might it be possible to estimate this model via the Canay (2011) estimator, if one were willing to assume that the individual FEs are location shifters?
Any other advice relating to my methodology, or references to (theoretical/applied) papers on the topic of quantile regression with individual and time FEs (or specifically quantile regression in the case of event studies) would also be greatly appreciated.
Best,
Aidan Sloyan
(Stata 18.0 SE)
