the reader can see that the estimated probability is 0.4944. That is, given the income of $20,000, the probability of a family owning a house is about 49 percent. Table 15.6 shows the probabilities thus computed at various income levels. As this table shows, the probability of house ownership increases with income, but not linearly as with the LPM model.
Computing the Rate of Change of Probability. As you can gather from Table 15.6, the probability of owning a house depends on the income level. How can we compute the rate of change of probabilities as income varies? As noted in footnote 19, that depends not only on the estimated slope coefficient 02 but also on the level of the probability from which the change is measured; the latter of course depends on the income level at which the probability is computed.
To illustrate, suppose we want to measure the change in the probability of owning a house at the income level $20,000. Then, from footnote 19 the change in probability for a unit increase in income from the level 20 (thousand) is: 0(1 - P)P = 0.07862(0.5056)(0.4944) = 0.01965.
It is left as an exercise for the reader to show that at income level $40,000, the change in probability is 0.01135. Table 15.6 shows the change in probability of owning a house at various income levels; these probabilities are also depicted in Figure 15.3.
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