Testing preference parameters from 2 datasets

[suella_rodrigues]

Dear Professor,

I am trying to test the robustness of my willingness to pay estimates.
In a previous post, you had suggested a procedure for a test.
However, my problem is that I have two different datasets and I want to see whether the willingness to pay estimates are statistically different, given that prices are the same (in the two datasets).

In the earlier post, you had suggested that I should first calculate the standard error. But, how can the two coefficient have a common covariance matrix.

Am I correct to claim that since these estimates come from different datasets they are independent so their covariance is zero?

Thank you.

Maria

[Michiel Bliemer]

Yes correct, if you estimate separate models with vectors of parameters a and b respectively, then cov(a,b) = 0.
Of course, parameters within each data set have covariances, that is, cov(a1,a2) is not zero.

To calculate se(WTP) you need to apply the Delta method using the variances and covariances across the two vectors of parameters. You do this for each data set and then do a paired t-test.

Michiel

[suella_rodrigues]

professor, thank you very much.

Just to clarify.

Now that I want to calculate the SE(w) where w is the difference between the two coefficients (1 from each dataset).
SE(w)=sqrt([var(b1 )+var(b2 ) - 2*Cov(b1, b2 )])

assuming b1 here is the variance of the coefficient in dataset1 and b2 is the variance of the coefficient in dataset 2. Given that the prices are the same in both the dataset.
so here the cov is 0.

is it sufficient to use this t test to construct the confidence intervals and test whether the coefficients are statistically different in the two datasets?

[Michiel Bliemer]

Yes I believe that is the way to do it.

Computing var(b1) and var(b2) will require the Delta method if they are ratios of parameters (which is often the case with willingness to pay) or other combinations of parameters. If you are directly comparing parameters then the Delta method is not needed and var(b1) and var(b2) can be taken directly from the variance-covariance matrix.

[suella_rodrigues]

All clear now. Thank you very much for everything professor!
Have a lovely day!
Maria