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Public Lectures on Structural Econometrics - CEMMAP masterclass - Shared screen with speaker view
Kevin Lee
27:51
Is a factor of 1/2 missing in the 2nd line?
Elena Pastorino
29:51
@Kevin: are you satisfied with Bob's explanation?
Kevin Lee
29:57
yes
XIAOXIA SHI
29:58
It looks like it.
Zhuotong Xie
46:23
the formula for fx^(N) (x) looks very similar with f(x,y)=f(x)f(y). Why is this still true when x_1 and x_k are not independent?
Arie Beresteanu
47:55
y and x are not assumed to be independent. f(y,x)/f(x) = f(y|x)
Arie Beresteanu
48:30
Then the integral of y*f(y|x) dy gives E(y|x)
XIAOXIA SHI
48:35
@Zhuotong, are you asking about why the product kernel is used in the multi-variate case?
Giuseppe Forte
48:38
Zhuotong is referring to the two-dimensional kernel fn I think
Kevin Lee
49:01
sum of product =/= product of sum
Zhuotong Xie
49:04
yes. the formula in page 5
XIAOXIA SHI
49:56
@Zhuotong, that is a common way to handle multivariate kernel regression. It's simpler than using a more general multivariate kernel. It does not require the variables to be independent from each other.
XIAOXIA SHI
50:43
The main reason is for simplicity as I understand it.
Elena Pastorino
50:52
@Zhuotong: Bob is going over it now. Let us know if it still not clear after this slide
Arie Beresteanu
50:53
It's a way to measure the distance between x_n and x.
Zhuotong Xie
51:09
I see. Thanks a lot!
Shunan Zhao
01:23:12
I am not familar with the estimators of eq (2) and (3). Is there any reference I can read more about them? Thank you?
Joan Llull
01:27:07
I don't know on top of my head, but, unless others have one, we can ask him maybe at the end of the class, what do you think?
Shunan Zhao
01:29:06
Sounds good. Thank you, Joan.
Joan Llull
01:29:22
No problem! Remind us if we forget!
Vladimir Yankov
01:31:59
is this equivalent to Frisch Waugh Lovell theorem
Elena Pastorino
01:33:32
@Vladimir: if you wish, it is the analogue in a way in this partially linear model. The function g(z) here is unknown
Joan Llull
01:33:42
I would say, Vladimir, the intuition would be the same indeed
Kevin Lee
01:43:52
Is g known here?
XIAOXIA SHI
01:44:17
@Kevin, it is unknown.
Elena Pastorino
01:44:56
@Kevin: it is a special monotonic version of the previous partially linear model -- g(.) is monotone
Shunan Zhao
01:45:18
Is eq (8) identified if you have x in both par and nonpar parts?
Elena Pastorino
01:46:34
@Shunan: it depends on the restrictions you place on g(.). I believe Bob will take about this but … please ask more if this is not the case!
Elena Pastorino
01:47:40
Note that before the covariates were partitioned in x and z. Now they are not but we are placing a strong restriction on g(.) we did not before. There is certainly a trade-off
Shunan Zhao
01:52:28
Thank you!
Elena Pastorino
01:58:45
Dole, D. (1999): “Cosmo: A Constrained Scatterplot Smoother for Estimating Convex,Monotonic Transformations,” Journal of Business & Economic Statistics, 17, 444–455
Elena Pastorino
02:00:34
this is what I had in mind in case anyone is interested
JAYANTI BEHERA
02:01:18
@Elena, thank you.
Joan Llull
02:02:27
WRIGHT, F. T. (1981), “The Asymptotic Behavior of Monotone Regression Estimates”,Annals of Statistics,9, 443–448