Discrete choice and correlated error terms To be or not to be | Professor M

Discrete choice and correlated error terms

To be or not to be? An economist would compare the utility of “to be” and the utility of “not to be” and pick the choice yielding the highest utility. When predicting the choices of others, decompose the utility into an observed component and an unobserved component. The former depends on a choice’s attributes and the sensitivities of a person’s utility to these attributes—both can be quantified. The unobserved component captures the unquantifiable qualities and tastes. Well, if you know nothing about something, you might as well call it the error term that will—keeping the choice attributes and sensitivities to those fixed—push some people to choose “to be” more often and others—“not to be.”

It gets interesting—and realistic—if the error terms persist over time. In other words, the same person would lean in the same direction when faced with a similar choice—even if observable characteristics change a bit.

It gets even more interesting—and more realistic—when we acknowledge that how you do anything is how you do everything. This is just a catchy way of conveying a simple idea—Individual errors terms in a discrete choice model are correlated not only in the time series but also in the cross-section of choices.

Scratch a lie, find a thief? Choosing to lie is consistent with a person’s error term for lying being, say, sufficiently positive—contributing to the person’s decision to lie. If the error terms for lying and stealing are positively correlated, which they likely are, then yes—a liar may be hiding some stolen skeletons in the closet.