Testing preference parameters

[suella_rodrigues]

professor,

I would like to test a hypothesis that preferences for certain attributes are different/equal between two demographics i.e. the parameter values are different/equal between 2 models.
One way would be comparing WTP. Is there any other method that would be more suitable? for instance likelihood ratio test?

Thank you
Maria

[Michiel Bliemer]

Suppose that you would like to test the following null and alternative hypothesis:

H0: beta1 = beta2
H1: beta1 <> beta2

Comparing WTP would be testing whether beta1/betac = beta1/betac, which involves cost/price parameter bc. But you can simply directly compare beta1 and beta2 using the test above as follows.

First, you rewrite the hypothesis above using new variable w,

H0: w=beta1-beta2 = 0
H1: w=beta1-beta2 <> 0

In other words, w is the difference in estimates beta1 and beta2, which you can compute based on your estimation results.
Next, you need to determine the standard error of w, which can be computed as:

se(w) = sqrt (var(beta1) + var(beta2) - 2*cov(beta1,beta2)),

where sqrt is the square root, var is the variance, and cov is the covariance. You can get the variance and covariance from the covariance matrix that also comes out of model estimation.

Finally, you compute the relative confidence intervals,

[ w - t(alpha)*se(w), w + t(alpha)*se(w) ],

where t(alpha) is the critical t-value for significance level alpha. For example, t(0.05) = 1.96. If value 0 does NOT lie within this confidence interval, then the null hypothesis can be reject and therefore you can reject the null hypothesis that beta1 = beta2, i.e. beta1 and beta2 are statistically different at the 5% (or your t(alpha) value) significance level.

Michiel

[suella_rodrigues]

Thank you Professor.