Ch 12 extra probs answers

# Ch 12 extra probs answers - Econ 120B Solutions to Chapter...

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Econ 120B Solutions to Chapter 12 Practice Problems 1. a. Instrumental validity has two components, instrument relevance ( ), and instrument exogeneity ( ). The individual’s postal zip code will certainly be uncorrelated with the omitted variable, ability, even though some zip codes may attract more able individuals. However, this is an example of a weak instrument, since it is also uncorrelated with years of education. 0 ) , ( i i X Z corr 0 ) , ( = i i u Z corr b. There is instrument relevance in this case, since, on average, individuals who do well in intelligence scores or other work related test scores, will have more years of education. Unfortunately there is bound to be a high correlation with the omitted variable ability, since this is what these tests are supposed to measure. c. A non-zero correlation between the mother’s or father’s years of education and the individual’s years of education can be expected. Hence this is a relevant instrument. However, it is not clear that the parent’s years of education are uncorrelated with parent’s ability, which in turn, can be a major determinant of the individual’s ability. If this is the case, then years of education of the mother or father is not a valid instrument. d. There is some evidence that the larger the number of siblings of an individual, the less the number of year of education the individual receives. Hence number of siblings is a relevant instrument. It has been argued that number of siblings is uncorrelated with an individual’s ability. In that case it also represents an exogenous instrument. However, there is the possibility that ability depends on the attention an individual receives from parents, and this attention is shared with other siblings.

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