Boottest Interpretation

[Cansu Oymak]

Hello Dear Statalist users,

I am running an IV regression where I try to understand the effect of refugee influx on native children's health outcomes proxied by their height-for-age zscores (haz06). I am using 3 rounds of (pooled) DHS and refugee share, my treatment variable is as follows: Refugee Share = (Number of refugees in province c in the birth year od children (t) / Initial population of city c (which is 2010). Refugee share takes values of 0 for those who born in 2011 and before and it starts to take its actual values for those born in 2013 and onwards. It is simply because there were no refugees before 2011 in any province of interest. In other words, refugee share determines the children's exposure status to refugee shock based on their year of birth and province of residence. Note that refugee share and the IV are standardized variables (simply they are all z-scores).

Here is my code:

ivreg2 haz06 (z_refugee_share=z_instrument_scaled) i.plate i.survey_year i.child_sex i.child_birth_month i.SEDUC i.rural_ total totalrooms log_publicexpenditure_percapita hospital_percapita terrorindex_scaled [pweight=wgt] if child_birth_year!=2012, cluster(plate)

Plate stands for 81-provinces.

After performing my regression, I used "boottest" command but I fail to how to interpret this result. If anyone can help me in understanding the interpretation I would be really happy.
boottest z_refugee_share==0, nograph

Wild bootstrap-t, null imposed, 999 replications, Wald test, bootstrap clustering by plate, Rademacher weights:
z_refugee_share==0

z = 3.6594
Prob>|z| = 0.0030

95% confidence set for null hypothesis expression: [.1364, .6201]

I have deeply read David Roodman's article (https://journals.sagepub.com/doi/epu...36867X19830877). However, I could not fully understand the interpretation. What does it tell me in a precise way. I am literally confused.

Thank you in advance.

[David Roodman]

The z statistic should exactly match that displayed by ivreg2 for z_refugee_share. The p value and confidence interval may differ from ivreg2's but have the same interpretation.

[Cansu Oymak]

The z statistic should exactly match that displayed by ivreg2 for z_refugee_share. The p value and confidence interval may differ from ivreg2's but have the same interpretation.

Dear David,

Thank you very much for your answer.
In the following article, Dreher, Axel and Langlotz, Sarah and Matzat, Johannes and Parsons, Christopher Robert, Immigration, Political Ideologies and the Polarization of American Politics (2020). CESifo Working Paper No. 8789, Available at SSRN: https://ssrn.com/abstract=3754680 or http://dx.doi.org/10.2139/ssrn.3754680, they said that the standard errors are bootstrapped and clustered. This is what I actually look for. However, I could not figure out how to do this in my codes. My standard erros must be bootstrapped and clustered at the province level. If you can help me I would be really happy.
Thank you very much.

[David Roodman]

Well, those are apparently not "wild" bootstrapped. Probably they were done with Stata's bootstrap prefix command, which does the classic, nonparametric bootstrap, just resampling the data, has a cluster option, and does report standard errors, which are standard deviations of the simulated distributions.

boottest does not report standard errors because the theory behind their use assumes that the sampling distribution is z or t, but the reason for bootstrapping is that that assumption may be wrong.

[Cansu Oymak]

Well, those are apparently not "wild" bootstrapped. Probably they were done with Stata's bootstrap prefix command, which does the classic, nonparametric bootstrap, just resampling the data, has a cluster option, and does report standard errors, which are standard deviations of the simulated distributions.

boottest does not report standard errors because the theory behind their use assumes that the sampling distribution is z or t, but the reason for bootstrapping is that that assumption may be wrong.

Dear David,

Thank you very much for your reply. I am actually looking for the Stata's bootstrap prefix command you have just mentioned, which has a cluster option. I have look at this page:https://www.stata.com/manuals/rbootstrap.pdf but I could not understand the bootstrap as having a cluster option. If you know and can help, I will be truly glad!

[Rich Goldstein]

p. 2 of what you link to notes a cluster option and it can also be found in the help file

h bootstrap

[Maxence Morlet]

Dear David Roodman, thank you very much for the excellent boottest command.

I have a question related to this thread: is it econometrically wrong to take the upper and lower bounds of the confidence interval produced through your boottest command, and then compute a "bootstrapped" standard error in the following manner:

(Upper Bound of CI - Lower Bound of CI)/3.92

assuming a 95% confidence interval?

[Maxence Morlet]

Apologies for the disturbance, I have found the answer here: New paper explaining wild (cluster) bootstrapping with boottest - Statalist