After estimating a probit model for the likelihood of a website visitor clicking through conditional on the average income from the county in which the visit's IP address came from, you get the following results: ClickThrough_i = -1.8(0.75) + 0.06(0.005)Income_i, where standard errors are reported in parenthesis. What would be the calculation that yields the marginal effect of income moving from $40,000 to $41,000 on the click-through rate? A) -1.8 + 0.06 = -1.74 B) Φ[0.06(41 - 40)] C) Φ(-1.8 + 0.06 × 41) - Φ(-1.8 + 0.06 × 40) D) 0.8

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Quizplus · Accepted Answer

To calculate the marginal effect of income moving from $40,000 to $41,000, we need to calculate the difference in click-through rates between the two income levels. The formula for the marginal effect of a continuous variable in a probit model is Φ(βx). In this case, x is 41,000 - 40,000 = 1, so we need to calculate Φ(-1.8 + 0.06 × 41) - Φ(-1.8 + 0.06 × 40) to get the marginal effect. This yields a value of approximately 0.008, which indicates that a one-unit increase in income (i.e. $1,000) is associated with a 0.8 percentage point increase in the click-through rate.

After Estimating a Probit Model for the Likelihood of a Website