Keywords: Discrete choice; random utility model; choice probabilities; linear probability model;
How to construct a structural econometric model
- Discrete choice to maximize utility
- Random utility model
- Use different assumptions about the unobservables in the random utility model
Random utility model:
The agent gets some amount of utility from each of the alternatives, selects the alternative that provides the greatest utility.
(Models derived from RUM are consistent with utility (or profit) maximization, even if the decision maker does not maximize utility)
Decompose the utility of each alternative, U , into two components
usually, we specify the representative utility as a linear function
However, knowing the representative utility is not sufficient as there exists unobserved random component. Make probabilistic statements to model discrete choices:
The left side of the last formula is the cumulative distribution of the difference of unobserved random component, with assumptions of the distribution yield different models.
The general formula for choice probabilities reveals two properties:
- only difference in utility matter (other alternatives are not included)
- the scale of utility is arbitrary (scaling any utilities does not change the comparision)
Binary linear choice:
Pros and cons
- regression is fast and easy to run
- probabilities are not bounded by [0,1], coefficients are not structure parameters, error terms are heteroskedastic and not normally distributed.