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The Two Conditions for Instrument Validity Are Corr(Zi, Xi)≠ 0

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The two conditions for instrument validity are corr(Zi, Xi)≠ 0 and corr(Zi, ui)= 0. The reason for the inconsistency of OLS is that corr(Xi, ui)≠ 0. But if X and Z are correlated, and X and u are also correlated, then how can Z and u not be correlated? Explain.


Definitions:

Lorenz Curve

A graphical representation used to show the distribution of income or wealth within a society.

Gini Ratio

A measure of income or wealth inequality within a population, ranging from 0 (perfect equality) to 1 (maximum inequality).

Income Inequality

The unequal distribution of household or individual income across the various participants in an economy, leading to various economic and social issues.

Lorenz Curve

A graphical representation of income or wealth distribution within a society, showing the proportion of the total income earned by various segments of the population.

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