The Two Conditions for Instrument Validity Are $\operatorname { corr } \left( Z _ { i } , X _ { i } \right) \neq 0 \text { and } \operatorname { corr } \left( Z _ { i } , u _ { i } \right) = 0$

question 24

Essay

The two conditions for instrument validity are $\operatorname { corr } \left( Z _ { i } , X _ { i } \right) \neq 0 \text { and } \operatorname { corr } \left( Z _ { i } , u _ { i } \right) = 0$
The reason for the inconsistency of OLS is that $\operatorname { corr } \left( X _ { i } , u _ { i } \right) \neq 0$
But if X and Z are correlated, and X and u are also correlated, then how can Z and u not be correlated? Explain.

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Definitions:

Disaggregate Forecasts

Involve breaking down aggregate forecasts into more detailed and specific forecasts, often by product, location, or time period.

Collaborative Forecast

A method where multiple stakeholders work together to predict future demand or trends, often involving the sharing of information to improve accuracy.

Supply And Demand

The fundamental economic model describing the interaction between the quantity of goods available for sale and the consumers' willingness to purchase them at a certain price.

Plant/Equipment Investment

Capital expenditure on the physical assets of a company to increase its capacity or improve its efficiency.