st: Re: Appropriate estimation method to use with panel data with lagged endogenous variables occurring in different time periods?

["Rodrigo A. Alfaro" <raalfaroa@gmail.com>]

///
Think wide:

(1) Run a linear model without taking in account the nature of the 
variables. This will give you some idea about the sign of the coefficients. 
(2) Use ANOVA or MANOVA procedures to analyze your data. You can obtained 
the combined effect of smoking and breastfeeding. This is a modified 
Maarten's suggestion (... always... there is a much simpler way of answering 
the research question). (3) About timing, note that breastfeeding (x1) is 
relevant just to one year (it would be good to have a more specific 
description, like up to 3 months, 6 months, etc. Research has showed that 
6/9 months are fine for the development of the brain. I read in a Pediatric 
magazine!!), but smoking (x2) is relevant up to age 3 then you claimed that 
both are associated with income (it seems to be education, but I guess that 
income is a good proxy here). I guess that income in the first year is 
similar to income in the second and third year, regardless of your field I 
can thin that even income(t) = cons + rho*income(t-1) + u(t), with rho very 
close to one, then I think that using lagged income is fine for both 
variables. You can also try both income, but they could be highly 
correlated. (4) For sufficient number of data, you could work in small 
groups, like doing your analisis for some particular quartile of income or 
some percentile of low birthweight. (5) IV+probit sounds good, you could try 
it... maybe Woolridge (2002) "Cross Sectional and Panel Data Econometrics", 
MIT Press (also known as "The Black Book", because it is black... not other 
reasons) could give you some help in how to deal with that problem in the 
case of IV+probit. (6) Using logit instead of probit you could "solve" for 
the binary-endogenous variables as it was done for the case of conditional 
logit. With that and probably assuming that also the binary-endogenous 
variables are generated by a logit-process you could (I am not sure) rewrite 
the model such that it looks like a system of the equation. Otherwise, under 
probit, you need to deal with complication of the non-linearities that are 
ver very hard (the cdf of a normal distribution has not a closed-form, then 
how you can compute the inverse function of that cdf?).

Rodrigo.




----- Original Message ----- 
From: "Tiffany Green" <t_green1920@yahoo.com>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, June 12, 2007 2:42 PM
Subject: st: Appropriate estimation method to use with panel data with 
lagged endogenous variables occurring in different time periods?



> I have a 3 period model which estimates the effect of
> maternal behaviors (smoking and breastfeeding) on
> child health (asthma). Childhood asthma at age three
> is a function of smoking at (up to) age 3 and
> breastfeeding up to age 1.  Low birthweight is also
> treated as endogenous.   So, I have three endogenous
> (and dichotomous) RHS variables:
>
> asthma at age 3=f(smoking at (up to) age 3,
> breastfeeding at age 1, low birth weight, various
> socioeconomic characteristics).
>
> I was advised to use IV probit, but from what I
> understand, because all of endogenous regressors are
> binary and not continuous, this would not be
> appropriate to use in this case.  I also gather that
> mvprobit would apply more to SURE types of models.
>
> The other issue is that I am unclear how to account
> for the fact that my endogenous variables appear in
> different time periods, and so using a simple ivreg
> type of command would not seem to be appropriate.  For
> example, breastfeeding at year 1 would be a function
> of say, income at year 1, while smoking at year 3
> would obviously be a function of say, income in year
> 3.
>
> I would appreciate any advice on what estimation
> method  or methods would be more appropriate in this
> case.
>
>
> If the facts don't fit the theory, change the facts.
> -Albert Einstein
>
>
>
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