# ch17 - Limited Dependent Variables P(y = 1|x = G(0 x y = 0...

This preview shows pages 1–6. Sign up to view the full content.

Economics 20 - Prof. Anderson 1 Limited Dependent Variables P ( y = 1| x ) = G ( β 0 + x β ) y* = β 0 + x β + u, y = max ( 0,y* )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Economics 20 - Prof. Anderson 2 Binary Dependent Variables Recall the linear probability model, which can be written as P( y = 1| x ) = β 0 + x β A drawback to the linear probability model is that predicted values are not constrained to be between 0 and 1 An alternative is to model the probability as a function, G ( β 0 + x β ), where 0< G ( z )<1
Economics 20 - Prof. Anderson 3 The Probit Model One choice for G ( z ) is the standard normal cumulative distribution function (cdf) G ( z ) = Φ ( z ) ≡ ∫ φ ( v )d v , where φ ( z ) is the standard normal, so φ ( z ) = (2 π ) -1/2 exp(- z 2 /2) This case is referred to as a probit model Since it is a nonlinear model, it cannot be estimated by our usual methods Use maximum likelihood estimation

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Economics 20 - Prof. Anderson 4 The Logit Model Another common choice for G(z) is the logistic function, which is the cdf for a standard logistic random variable G ( z ) = exp( z )/[1 + exp( z )] = Λ ( z ) This case is referred to as a logit model, or sometimes as a logistic regression Both functions have similar shapes – they are increasing in z , most quickly around 0
Economics 20 - Prof. Anderson 5 Probits and Logits Both the probit and logit are nonlinear and

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern