Positive coefficient on price/cost

[sj_tan_]

Hi all,

I am using some choice experiment data in which the choice model is as follows:

choice = b1*statusquo + b2*v1 + b3*v2 + b4*v3 +b5*pricepermonth + b0 + eps

I am running latent class models and in most 2-class models there is a class whose price per month coefficient is positive and significant. In 3-class models, there is one class with a positive and significant price per month coefficient, and one with an insignificant price per month coefficient.

Is there any meaningful way to interpret the results of a model with positive and significant cost parameters?

Thanks so much.

[Michiel Bliemer]

I am not sure I understand your choice model, I assume your alternatives are statusquo, choice1, choice2, etc, such that you have utility functions

U(statusquo) = ...
U(choice1) = ...
U(choice2) = ...

And that you have 0-1 data for choices for one of these alternatives, not that you are using the choice variable directly as an endogenous variable.

Positive price parameters could be the result of improperly defined utility functions, or could be sign that there is a relevant variable not captured in the model and therefore the error term is not orthogonal with the data. For example, if people associate price with higher quality or more comfort, but quality or comfort are not included in the model, then this may lead to a positive price coefficient.

You could try to estimate income effects in the utility function, e.g. b5*price*incomeindex^gamma, where incomeindex = income/mean(income) and you estimate gamma as the income elasticity, or use income in the class assignment model.

Michiel



Michiel

[sj_tan_]

Hi Michiel,

Yes, each respondent had a choice between three alternatives, choice 1, choice 2, and a status quo.

In this very hastily written equation: choice = b1*statusquo + b2*v1 + b3*v2 + b4*v3 +b5*pricepermonth + b0 + eps

- choice is a binary variable equal to 0 if an alternative (choice 1, choice 2, or status quo) is chosen, and 0 otherwise
- statusquo is a binary variable equal to 0 if an alternative is the status quo and 0 otherwise
- v1, v2, and v3 are the varying attributes of the choice experiment; the status quo had defined levels approximating a current local policy
- pricepermonth is some positive number, varying for the two choice alternatives, but the same every time for the status quo


Here is the actual context:

There is a local fee imposed on utility bills that funds a rebate program for installing water conservation equipment. Since individuals must apply for the program, but all residents are taxed, there is no reason to believe that higher fees would be associated with an average individual's comfort or quality -- the vast majority of residents don't participate in this program.

I am using income in the class membership model already (a numeric variable created from 4 possible income categories).

I'm not sure how to estimate the income elasticity, is gamma estimated first with the survey data only, or simultaneously?

Thanks

[Michiel Bliemer]

I am not sure I understand the need for the status quo dummy, I would think that you have (assuming that alt1 and alt2 are unlabelled alternatives, or are they labelled?):

U(statusquo) = b0 + b2*v1 + b3* v2 + v4 * v3
U(alt1) = b2*v1 + b3* v2 + v4 * v3
U(alt2) = b2*v1 + b3* v2 + v4 * v3

You seem to have both b0 as well as b1 for the status quo, I am not sure what that means to have two constants and how that can be estimated. Your positive price parameter may have to do with the fact that your constants are not properly defined, can you perhaps explicitly write down all three utility functions that you have defined in your estimation software?

You would estimate gamma simultaneously, it is just another parameter in your utility function.

Michiel

[sj_tan_]

Sorry, I am a bit confused because I have not worked with a choice experiment with a well defined status quo. These are unlabeled alternatives.

When I look at the estimates from a 2-class I see the following:

In each class, estimated coefficients on the status quo dummy variable, price, and the other attribute variables. There is no constant in the utility models for each class.

There are also estimated coefficients on each of the demographic variables used to determine class membership, including income, as well as a constant in the class membership model.

So I believe I have what you defined:

U(statusquo) = b0 + b2*v1 + b3* v2 + b4 * v3
U(alt1) = b2*v1 + b3* v2 + b4 * v3
U(alt2) = b2*v1 + b3* v2 + b4 * v3