Comparing Coefficients from Two Independently Estimated Simultaneous Quantile Regression Models

[Jun Xu]

Dear Statalisters,

Hope someone could give me at least some pointers. I am estimating two simultaneous quantile regressions using sqreg with data collected from two cross-sectional surveys, one fielded around the turn of the century and another recently. Now I want to compare/test differences in some of the coefficients across time, for example the effect of education on logged income for the 25th quantile in time 1 and time 2. Is there any literature on how to do this? Can I use the classical method by calculating the test static z with the following formula?

z = (coef_time1 - coef_time2) / sqrt ((se(coef_time1))^2 + (se(coef_time2))^2)

My intuition says ok because asymtotically this makes sense. sqreg gets its standard errors using bootstrap, and bootstrapped errors should still follow properties prescribed in asymptotic theories.... Any thoughts or suggestions?

Jun Xu, PhD
Associate Professor
Department of Sociology
Ball State University

[Joao Santos Silva]

Dear Jun,

I am not sure to understand your problem because the way you describe it suggests that you are using -sqreg- to simultaneously estimate regressions using data from different samples and I do not think that is possible.

Anyway, the approach you suggest sounds sensible because I guess it is safe to assume that there is no correlation between the two estimates. An alternative is to write a small piece of code to bootstrap the joint estimation of both models and get the joint covariance matrix.

Best wishes,

Joao

[Jun Xu]

Joao,

Thank you very much for your comments and suggestion. The formula that I referred to was cited on p.1276 of the following paper

http://sites.stat.psu.edu/~ajw13/sta...odelSlopes.pdf

I will explore the method that you proposed, but it seems to me very much like a fully interactive model with both slopes estimated in the same model, and then use the Wald test, right?

[Joao Santos Silva]

Dear Jun,

As the paper says, the formula is valid if the samples are independent, which I guess is your case; so that may be enough. The bootstrap I suggested is indeed very much like the Wald test in the fully interactive model. I still do not fully understand what you are doing (why use sqreg?) so my advice needs to be taken with more than the usual pinch of salt.

Best wishes,

Joao

[Jun Xu]

Joao,

Sorry for being remiss of your initial question. Basically I am estimating two simultaneous quantile regressions of logged income. Since I want to estimating the effects of a set of indepvars on different quantile points of logged income simultaneously, I went with sqreg. Is this the right way to go? So I ran sqreg separately for two different years of a cross-sectional survey, one collected in 2003 and the other 2013. I then want to compare for example if the effect of gender was stronger on the 5th quantile in year 2003 than it was in 2013 or vice versa. Both sets of estimation use the same set of independent and dependent (logged income) variables, but collected in different years. In addition, I also need to control for clustering among the observations, so I used bs along with sqreg. So the codes go like:

loc lhs my_dependent_variable
loc rhs my_independent_variable_list

bs _b, cluster (cluster_var) seed(12345) reps (500): sqreg `lhs' `rhs_varlist', reps(2) q(0.05 0.10 0.25 0.50 0.75 0.90 0.95)

Hope this clarifies. Can you clarify your suggestion that "An alternative is to write a small piece of code to bootstrap the joint estimation of both models and get the joint covariance matrix"?Thanks a lot!

Jun

[Jun Xu]

By the way, the cross-sectional survey is like the general social survey conducted in the US. It is cross-sectional, but the variables and measures are quite comparable across years. The cases in different year samples are supposed to be different, since they don't follow the panel design.

[Joao Santos Silva]

Dear Jun,

Thanks for clarifying. Given the nature of your samples, I believe that the method you mention in your original post is a valid approach because it is reasonable to assume the samples are independent.

If you do not want to assume independence, then you can merge (stack) the two samples and run a single model interacting all regressors with an indicator of the, say, second sample. You can then use the Wald test you mentioned in #3. Given the nature of your problem, I do not think my idea of jointly bootstrapping the two regressions would work.

Finally, if you do not want to test restrictions involving different quantiles you can use -qreg2- to compute "clustered" standard errors and therefore avoid bootstrap.

Best wishes,

Joao

[Jun Xu]

Joao,

This is real helpful. Thanks a lot!

Jun