Consider the following simple regression model: y = ₀ + ₁x₁ + u. In order to obtain consistent estimators of ₀ and ₁, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z,x) 0 and Cov (z,u) = 0. The variable z is called a(n) _____ variable. A)dummy B)instrumental C) lagged dependent D) random

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The variable z introduced in the model that satisfies the conditions of Cov(z,x)≠0 and Cov(z,u)=0 is called an instrumental variable. This is because it serves as an instrument for estimating the effect of the endogenous variable x on the outcome variable y, while also addressing the issue of endogeneity (correlation between x and u). Dummy variables are used to represent categorical variables in regression analysis, lagged dependent variables are used to control for autocorrelation, and random variables are not relevant in this context. Variable z is called an instrumental variable since Cov(z,x) 11eab06d_2547_aee6_beed_61b87f7ccf2f_TB2133_11 0 and Cov(z,u) = 0.

Consider the Following Simple Regression Model: Y = 0

Consider the Following Simple Regression Model: Y = ₀