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602 PART THREE: TOPICS IN ECONOMETRICS

Odds Interpretation. Remember that Li = ln[Pi/(1 — Pi)]. Therefore, taking the antilog of the estimated logit, we get Pi/(1 — Pi), that is, the odds ratio. Hence, taking the antilog of (15.7.1), we obtain:

Using a calculator, you can easily verify that e007862 = 1.08 1 7. This means that for a unit increase in weighted income, the (weighted) odds in favor of owing a house increases by 1.0817 or about 8.17%. In general, if you take the antilog of the jth slope coefficient (in case there is more than one regressor in the model), subtract 1 from it, and multiply the result by 100, you will get the percent change in the odds for a unit increase in the jth regressor.

Incidentally, if you want to carry the analysis in terms of unweighted logit, all you have to do is to divide the estimated L* by *Jwl. Table 15.6 gives the estimated weighted and unweighted logits for each observation and some other data, which we will discuss shortly.

Computing Probabilities. Since the language of logit and odds ratio may be unfamiliar to some, we can always compute the probability of owning a house at a certain level of income. Suppose we want to compute this probability at X = 20 ($20,000). Plugging this value in (15.7.1), we obtain: L* = —0.09311 and dividing this by *Jwl = 4.2661 (see Table 15.5), we obtain Li = —0.02226. Therefore, at the income level of $20,000, we have

TABLE 15.6 LSTAR, XSTAR, ESTIMATED LSTAR, PROBABILITY, AND CHANGE IN PROBABILITY*

Probability,

TABLE 15.6 LSTAR, XSTAR, ESTIMATED LSTAR, PROBABILITY, AND CHANGE IN PROBABILITY*

Probability,

Lstar

Xstar

ELstar

Logit

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