### Discussant comments

Posted:

**Thu May 30, 2019 12:53 pm**Congratulations to team,

the paper is quite interesting, well written and pleasant to read.

the paper is quite interesting, well written and pleasant to read.

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Posted: **Thu May 30, 2019 12:53 pm**

Congratulations to team,

the paper is quite interesting, well written and pleasant to read.

the paper is quite interesting, well written and pleasant to read.

Posted: **Thu May 30, 2019 2:36 pm**

Thanks, Jorge. Very useful and thoughtful comments.

There is only one issue that I wanted to verify with you - but we can also talk about it tomorrow - I wanted to check whether the issue with the paid labour bivariate probit was about the simultaneity of education decision, fertility decision and labour market prospects, thus requiring that we need to model it at the same time. (we did do bivar probit, with IV in the first stage, but education is not modelled. we however have done this in a previous version of the paper and reconsider this.) We opted for bivar probit because of big gap between results with this approach and when we do linear approximation. Wooldridge's advice was that in such cases we needed to then use bivar probit.

I hope we can chat more tomorrow. John said that you were going to be here for the individual discussions with the teams.

Best wishes,

Ronelle

There is only one issue that I wanted to verify with you - but we can also talk about it tomorrow - I wanted to check whether the issue with the paid labour bivariate probit was about the simultaneity of education decision, fertility decision and labour market prospects, thus requiring that we need to model it at the same time. (we did do bivar probit, with IV in the first stage, but education is not modelled. we however have done this in a previous version of the paper and reconsider this.) We opted for bivar probit because of big gap between results with this approach and when we do linear approximation. Wooldridge's advice was that in such cases we needed to then use bivar probit.

I hope we can chat more tomorrow. John said that you were going to be here for the individual discussions with the teams.

Best wishes,

Ronelle

Posted: **Fri May 31, 2019 3:28 am**

Jorge, I thought about your comment about the direction of bias and I think the confusion has been about naming (smaller vs. larger coefficient in an absolute coefficient magnitude sense vs. upward vs. downward on a timeline). You are of course absolutely correct about the direction of the bias. But the consolation is that we have meant the same thing and have been using it consistently so in the text (to clear we understood that the omitted heterogeneity would cause the coefficient to be larger/inflated, but of course because it is a neg coefficient this will be downward bias and not upward bias). I will check my logic with you when we meet later today. I have also read more about measurement error and because our explanation is not aligned with the classical approach, but talks about systematic bias, the direction of the error cannot be determined ex-ante. Thanks again for your super-useful comments - they were fantastic. Ronelle

Posted: **Fri May 31, 2019 5:44 am**

Hi Ronellerburger wrote: ↑Thu May 30, 2019 2:36 pmThanks, Jorge. Very useful and thoughtful comments.

There is only one issue that I wanted to verify with you - but we can also talk about it tomorrow - I wanted to check whether the issue with the paid labour bivariate probit was about the simultaneity of education decision, fertility decision and labour market prospects, thus requiring that we need to model it at the same time. (we did do bivar probit, with IV in the first stage, but education is not modelled. we however have done this in a previous version of the paper and reconsider this.) We opted for bivar probit because of big gap between results with this approach and when we do linear approximation. Wooldridge's advice was that in such cases we needed to then use bivar probit.

I hope we can chat more tomorrow. John said that you were going to be here for the individual discussions with the teams.

Best wishes,

Ronelle

Thanks for the clarification. Indeed, I will be in Skype during the individual presentations. Please contact me when the time comes so that we continue the exchange (my user is jdavalos1).

There were two comments on the biprobit. The first only suggested to go LPM to avoid the convergence issues (empirical identifiability) that you seem to encounter in some estimates.

In the second, I was referring to the simultaneity of education decision (years of education and literacy) and fertility. In principle, you can easily replicate biprobit estimates using the CMP package (Stata). You can also append new non-linear equations (education) as long as the system is written as a recursive one. I am not very optimist of this since the convergence and empirical identification issues risk to increase exponentially, but it may be worth trying. My main goal was to emphasize that, from your own arguments, there is endogeneity in the education regressors.

talk to you soon

Posted: **Fri May 31, 2019 6:50 am**

Hi Ronelle,rburger wrote: ↑Fri May 31, 2019 3:28 amJorge, I thought about your comment about the direction of bias and I think the confusion has been about naming (smaller vs. larger coefficient in an absolute coefficient magnitude sense vs. upward vs. downward on a timeline). You are of course absolutely correct about the direction of the bias. But the consolation is that we have meant the same thing and have been using it consistently so in the text (to clear we understood that the omitted heterogeneity would cause the coefficient to be larger/inflated, but of course because it is a neg coefficient this will be downward bias and not upward bias). I will check my logic with you when we meet later today. I have also read more about measurement error and because our explanation is not aligned with the classical approach, but talks about systematic bias, the direction of the error cannot be determined ex-ante. Thanks again for your super-useful comments - they were fantastic. Ronelle

Thanks for the clarification regarding the direction of the bias, it was just a misunderstanding. I agree with your logic as per your clarification.

Regarding the attenuation bias due to measurement error, I had to infer from you description of the OLS and IV estimates(where OLS is closer to zero) that the systematic measurement error should behave like this:

x* = x + a +u.

[Here 'a' is supposed to be a negative constant (non-random) representing the systematic underreporting, while u is the non-systematic error. So a+u represent the systematic plus non-systematic errors]. Under this setup attenuation bias still holds (this would explain your results).

In contrast, changing the setup to allow x and u to be negatively correlated (while dropping 'a') leads to what you just accurately mentioned i.e. that the sense of the bias is undetermined.

I wrote my comment as a question since I was aware that these biases (endogeneity and measurement error) are not easy to disentangle. You motivated them so well that It was natural to me to keep pushing an explanation to the OLS-IV gap.