The IV Regression Assumptions KEY CONCEPT 12.4 The variables and errors in the IV regression model in Key Concept 12.1 satisfy the following: 1. E(u;|W1; ..., W„) = 0; 2. (X1, ..., Xi, W1;, ..., Wi, Zi, . .., ZmY;) are i.i.d. draws from their joint distribution; 3. Large outliers are unlikely: The X's, W's, Z's, and Y have nonzero finite fourth moments: and 4. The two conditions for a valid instrument in Key Concept 12.3 hold.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Consider the instrumental variable regression model
Yi = β0 +β1Xi + β2Wi + ui,
where Xi is
three assumptions in Key Concept 12.4 are satisfied. Which IV assumption
is not satisfied when:
a. Zi is independent of (Yi, Xi, Wi)?
b. Zi = Wi?
c. Wi = 1 for all i?
d. Zi = Xi?
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