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# The Linear Probability Model (1 pages)

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## The Linear Probability Model

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Lecture 16

Lecture number:
16
Pages:
1
Type:
Lecture Note
School:
Cornell University
Course:
Econ 3120 - Applied Econometrics
Edition:
1
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Unformatted text preview:

Econ 3120 1st Edition Lecture 16 Outline of Current Lecture I. Dummy Variables Current Lecture II. The Linear Probability Model The Linear Probability Model What if y is a binary variable? For example, consider the chlorine experiment in Zambia discussed earlier. Single bottles were sold to households at random prices ranging from 300-800 Kwacha. We want to measure the effect of price on purchase. We can run the OLS regression purchasei = Î²0 +Î²1 pricei +ui How do we interpret Î²1 in this case? Here, E(purchase|price) = P(purchase = 1|price). That is, the expectation is equivalent to the probability that the dependent variable equals 1. Now, 4 letâ€™s look at the CEF: E(purchase|price) = Î²0 +Î²1 price P(purchase = 1|price) = Î²0 +Î²1 price Differentiating with respect to price yields âˆ‚P(purchase = 1|price) âˆ‚ price = Î²1 Thus, Î²1 can be interpreted as the change in purchase probability associated with a 1-unit change in price. When price is measured in hundreds of Kwacha, we get: P(Purchased= 1|price) = 0.96 (0.052) âˆ’ 0.066 (0.0093) price Exercises: Can we rule out the prediction that everyone would have accepted a free distribution? At what price do we predict zero purchase? 5 These notes represent a detailed interpretation of the professorâ€™s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.

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