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Variables Instrumentales

Variables Instrumentales. Econometría UDESA. Example 15.1 - Wooldridge. We use the data on married working women in MROZ.RAW to estimate the return to education in the simple regression model (15) For comparison, we first obtain the OLS estimates :.

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Variables Instrumentales

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  1. Variables Instrumentales Econometría UDESA

  2. Example 15.1 - Wooldridge • We use the data on married working women in MROZ.RAW to estimate the return to education in the simple regression model (15) • For comparison, we first obtain the OLS estimates: The estimate for β1 implies an almost 11% return for another year of education.

  3. Example 15.1 - Wooldridge • Next, we use father’s education (fatheduc) as an instrumental variable for educ. • We have to maintain that fatheducis uncorrelated with u. • The second requirement is that educand fatheducare correlated. The t statistic on fatheducis 9.43, which indicates that educand fatheduchave a statistically significant positive correlation. (In fact, fatheducexplains about 17% of the variation in educin the sample.)

  4. Example 15.1 - Wooldridge • Using fatheducas an IV for educgives:

  5. Example 15.1 - Wooldridge • The IV estimate of the return to education is 5.9%, which is about one-half of the OLS estimate. • This suggests that the OLS estimate is too high and is consistent with omitted ability bias. • But we should remember that these are estimates from just one sample: we can never know whether 0.109 is above the true return to education, or whether 0.059 is closer to the true return to education. • The 95% confidence interval for β1 using OLS is much tighter than that using the IV. • The IV confidence interval actually contains the OLS estimate. • We cannot say whether the difference is statistically significant.

  6. Example 15.2 - Wooldridge • We use WAGE2.RAW to estimate the return to education for men: (15) • We want to use the variable sibs (number of siblings) as an instrument for educ. • These are negatively correlated, as we can verify from a simple regression: This equation implies that every sibling is associated with, on average, about 0.23 less of a year of education.

  7. Example 15.2 - Wooldridge • If we assume that sibs is uncorrelated with the error μ, then the IV estimator is consistent. Estimating equation (15) using sibs as an IV for educgives:

  8. Example 15.2 - Wooldridge • For comparison, the OLS estimate of β1 is 0.059 with a standard error of 0.006. • Unlike in the previous example, the IV estimate is now much higher than the OLS estimate. • While we do not know whether the difference is statistically significant, this does not mesh with the omitted ability bias from OLS. • It could be that sibs is also correlated with ability: more siblings means, on average, less parental attention, which could result in lower ability. • Another interpretation is that the OLS estimator is biased toward zero because of measurement error in educ.

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