Any ideas on examining how much an effect reduces in a given period?

[Matthew Williams]

Dear all,

I have a question that need your advice and suggestions. Specifically, I am examining the effect of maternal education on child mortality in a given country from 1990 to 2010 using instrumental variables (IV) method. The outcome is a binary variable indicating child mortality (1=yes), maternal education is measured by years of schooling and a timing of a secondary education reform in the country is used as an IV for maternal years of schooling. Models are estimated using 2SLS.

Results show that increased maternal education induced by the education reform reduces the probability of child mortality by 0.12 percentage points. According to the World Bank data (or other sources), I also observe the mortality rates of that country, reducing from 120 deaths in 1990 to 50 deaths per 1,000 live birth in 2010. Based on the results of IV estimates, my idea is that I want to link the results of my study to the country mortality reduction, i.e., something like to see how much effect that maternal education accounts for the reduction in the country from 1990 to 2010 (e.g., 120 deaths to 50 deaths per 1,000 live births). Please note that data used in my study is nationally representative of the study subject.

I would be highly appreciated if anyone can give me advice/suggestions on how to do such analysis or any relevant references to my questions would also be very helpful.

Thank you.

[Joro Kolev]

You do not provide enough information regarding what you have done. But it seems to me that the key challenge in your study will be to identify the causal effect of maternal education while controlling for time trends. In other words, to separate the effect of maternal education from the time trends. For example if this education reform you re using is aggregate, that is, affects every woman in the country, I would say that things are not looking good.

Otherwise assuming that you have estimated the causal effect of maternal education on child mortality, you can use the actual increase in maternal education in the aggregate data from 1990 to 2010, and predict what decrease in aggregate child mortality this causes. Then compare the prediction to the actual reduction in child mortality that took place.

[Matthew Williams]

Hi Joro,

Thank you so much for your useful advice. I appreciate that.

Otherwise assuming that you have estimated the causal effect of maternal education on child mortality, you can use the actual increase in maternal education in the aggregate data from 1990 to 2010, and predict what decrease in aggregate child mortality this causes. Then compare the prediction to the actual reduction in child mortality that took place.

As for this point, could you please guide me bit on how to proceed your suggestions step-by-step? Assuming that Y (1=child dead) is the child mortality, Edu is the year of maternal education, Z is the IV, and X is a set of covariates.
Here is my first stage regression

reg Edu Z X, robust

and my 2SLS

ivregress Y (Edu=Z) X, robust

Thank you.

[Joro Kolev]

What I mean is a back of the envelope calculation. What you are estimating in your IV regression is the marginal effect d[E(Y|Edu,X)]/d[Edu], the marginal effect is your slope parameter on Edu.

Because your dependent variable is binary the d[E(Y|Edu,X)]/d[Edu] = d[Prob(Y=1|Edu,X)]/d[Edu].

So I am suggesting that you calculate the aggregate average education of mothers in 1990, then calculate the aggregate average education of mothers in 2010, and then use the derivative from the IV regression to predict what fall in aggregate average probability of a child death should have happened between 1990 and 2020. And then compare this to the actual fall in aggregate child mortality.

Hi Joro,

Thank you so much for your useful advice. I appreciate that.


As for this point, could you please guide me bit on how to proceed your suggestions step-by-step? Assuming that Y (1=child dead) is the child mortality, Edu is the year of maternal education, Z is the IV, and X is a set of covariates.
Here is my first stage regression

reg Edu Z X, robust

and my 2SLS

ivregress Y (Edu=Z) X, robust

Thank you.