After estimating a probit model for the likelihood of a website visitor clicking through conditional on if the visit occurred on a weekday or not, you get the following results: ClickThrough_i = -1.2(0.4) + 0.8(0.2)WeekDay_i, where standard errors are reported in parenthesis. What would be the calculation that yields the marginal effect of a visit moving from a weekend to a weekday on click-throughs? A) -1.2 + 0.8 = -0.4 B) 0.8 C) Φ(-1.2 + 0.8) - Φ(-1.2) D) Φ(-1.2)

Question

Quizplus · Accepted Answer

The marginal effect is calculated as the derivative of the probability with respect to the variable of interest (in this case, weekday). However, because this is a probit model, the marginal effect is not directly observable and must be calculated using the formula:

Φ(α + βx) - Φ(α + βx - β)

where α is the intercept, β is the coefficient for the weekday variable, x is the average value of the weekday variable in the sample (which is 0.5 assuming a balanced sample), and Φ is the cumulative distribution function for the standard normal distribution.

Plugging in the values from the equation given in the question, we get:

Φ(-1.2 + 0.8*0.5) - Φ(-1.2) = Φ(-0.2) - Φ(-1.2) ≈ 0.079 - 0.115 ≈ -0.036

Therefore, the marginal effect of a visit moving from a weekend to a weekday on click-throughs is approximately -0.036, which represents a 3.6% decrease in the probability of clicking through.

After Estimating a Probit Model for the Likelihood of a Website