Standard error

[EL KIMON]

Dear all,
I used the above formula e=(Δh/h).(Δw/w) for the calculation of hours elasticity because of an increase to the wages.
For the above calculation i have a specific results which is just a number. Can i calculate the Confidence interval or S.E. by having just a number?
Because the articles i based on they mention bootstrap S.E. or bootstrap C.I. and i dont know how to deal with.
Thank you in advance,
Best EL.

[Carlo Lazzaro]

El:
as far as I can get your query, you can't, because -bootstrap- works by resampling with reintroduction the observations that composed a given sample (something that a point estimate is not).

[EL KIMON]

Dear sir.
Thank you for the reply. Besides bootstrap there is not a way to get the SE or the CI for one value. Correct?

[Carlo Lazzaro]

El:
correct.

[Jeff Wooldridge]

All estimates are numbers. The standard error is an estimate of the sampling standard deviation of the estimator.

You can bootstrap and compute the elasticity for each bootstrap sample. Or, you might be able to use the -nlcom- command. Show us your Stata commands and output.

[Carlo Lazzaro]

Jeff:
I was under the impression that the original poster was trying to replicate the results of a published research recalculating hours elasticity by hand.
That's why I thought that he could not obtain the related SE.

[EL KIMON]

Dear sir,
Actually as Carlo said i calculated the hours elasticity by hand.
Firstly i used the discrete choice model to estimate the labour supply, thus used the mixed logit command. Afterwards, i calculated the predicted hours for each choice hours.
For the specific model i had 3 choice hours.
So for the predicted hours i multiply the frequencies of each choice by the analogous hours of that choice and then sum them together.
By the same process i calculate the predicted hours if i increase the wage by 10%.
Finally for the elasticity i used the formula : e=[Δp/p]/0.1 (calculation by hand) which the outcome is just one number.
Could for that number find the S.E. or C.I. ? Or should i follow a different method?
Thank you both for your time.
El.

[Jeff Wooldridge]

It seems to me you need to review the notion of a standard error. When isn't an estimate just a number? When we run a multiple regression, every OLS coefficient is just a number. The standard deviation measures its sampling variance, where the thought experiment is that you sample the data over and over again. Carlo seemed to think you had only the estimates reported in a paper and did a calculation based on those numbers reported. But it's clear you have the underlying data, which means you can compute a standard error.

I recommend bootstrapping. You will see then how standard errors are measuring sampling variable across different bootstrap samples. You can find lots of examples on the Internet. You need to write a little program, in a Stata do file, that does the calculations that you list above. Then draw about 1,000 bootstrap samples. At each stage, the new elasticity will be estimated, so you'll have 1,000 numbers. You take the standard deviation of those numbers and that is your bootstrap standard error.

The good news is that once you have written your short code you can then call Stata's bootstrap routine and the calculations will be done for you. I don't think your model and calculations are so complicated that bootstrapping 1,000 times will be especially hard.

JW