Delta method for standard error in stata?

[Shi Y. Yan]

How to use delta method to calculate standard error in stata

Run the regression Yi=aXi+other terms.

for example, i = product 1, product 2 and product 3
Increase of variable Xi= 12 30 15
sales increase Yi = 12a 30a 15a
Product price Pi = 3 6 8

I get sales-weighted average price/cost increase = (12a*3+30a*6+15a*8)/(12a+30a+15a)

How can I obtain the standard error for the sales-weighted average price increase


Thanks

[Clyde Schechter]

It is a bit difficult to relate what you have written to a specific data structure, variables and models, but, off hand, it looks like you are trying to evaluate a non-linear combination of regression coefficients. If that's the case, see -help nlcom-.

[Shi Y. Yan]

It is a bit difficult to relate what you have written to a specific data structure, variables and models, but, off hand, it looks like you are trying to evaluate a non-linear combination of regression coefficients. If that's the case, see -help nlcom-.

Thanks for your reply. I try to nlcom to solve it. seems it has some problems. I try to explain my question clearly with a simple example.

Data structure

Product	year	price	sales	size	...
product1	2001	200	20	1	...
product2	2001	150	14	2	...
product3	2001	300	30	3	...
product1	2002	145	16	1	...
product2	2002	134	14	2	...
product3	2002	310	29	3	...

-xtreg sales price

for example, I get the slope, 0.1(_b[price])

Use the slope, I can calculate the predicted sales, sales_hat for 2003

	year	price	sales_hat		size
product1	2003	160	16		1
product1	2003	140	14		2
product1	2003	300	30		3

The sales-weighted average size in 2001 and 2002 can be calculated exactly from the first table.


But I want to calculate the sales-weighted average size for 2003

(16*1+14*2+30*3)/(16+14+30)

Therefore, I use "nlcom" to obtain the se for this average size.

-nlcom sum(_b[price]*price*size)/sum(_b[price]*price)

But it doesn't work.

[Clyde Schechter]

OK. I think I get it now. You don't actually need to fiddle directly with the regression coefficients, because -predict- will do that all for you. You have sales and you have size as variables. So you can do this:

xtreg sales price
predict sales_hat
by product (year), sort: egen sales_weighted_total_size = total(sales_hat*size)
by product (year), sort: egen total_sales = total(sales_hat)
gen sales_weighted_average_size = sales_weighted_total_size/total_sales

[Clyde Schechter]

I realized just now that my previous post gives you a simpler way to calculate the sales weighted average size, but it does not address your original question about using the delta method to get the standard error of the latter. And I'm afraid I don't know the answer to it and I don't see how it would work. If I were in need of that standard error, I imagine I would probably try to get it by bootstrapping.

[Shi Y. Yan]

Thanks for your relies