# Notes

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Chapter 16 Models with Binary Dependent Variables
An interesting group of applications uses a dependent variable (y) that takes the values of either 0 or 1 (a binary variable – commonly known as a dummy variable or indicator variable). Example A problem in transportation economics is to explain the choice between driving a car and taking the bus when commuting to work. For a random sample of N = 21 workers who commute to work the mode of transport is coded as the dummy variable:

1  yi =  0 

individual i drives a car to work individual i takes the bus to work

The choice of transportation may be influenced by a variety of factors. A key variable is:

xi

the extra time in minutes needed for a bus journey compared to travel by car (this may be negative to indicate that a bus journey is faster than using a car), for i = 1, . . . , N.

1

Econ 326 - Chapter 16

The linear probability model explains the choice variable by the linear regression equation:

y i = β1 + β 2 x i + e i

for

i = 1, 2, . . . , N

Estimation by the least squares principle (OLS) gives parameter estimates of β1 and β 2 as b1 and b2 . For some value of interest x 0 a prediction is calculated as:

y 0 = b1 + b 2 x 0 ˆ ˆ The predicted value y 0 has the interpretation as the probability that the event will occur ( y = 1 ) given the value x 0 .
For the transportation to work example, y 0 is the probability that an ˆ individual will drive a car to work given a difference in travel time for a bus journey compared to a car trip.

2

Econ 326 - Chapter 16

For the data set with transportation travel times least squares (OLS) estimation of the linear probability model is:

y i = 0.48 + 0.007 x i ˆ

R 2 = 0.61

The intercept estimate gives the probability that a worker chooses to drive a car to work when there is no difference in travel time between a car trip and a bus journey (that is, the...

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