In which of the following cases is an instrumental variable not used to obtain a consistent estimator of the unknown coefficients of the population regression function? O A. It is not used when there is an omitted variable bias due to the omission of a variable from the regression equation which is correlated with both the regressor and the regressand. O B. It is not used when there is correlation between the regressors. O C. It is not used when there is measurement errors in the regressors. O D. It is not used when there is simultaneous causality between the regressor and the regressand. Suppose an instrumental variable regression model with one regressor, X, and one instrument, Z, is of the form: Y, = Bo +B,X;+ uj, where u; and B, denote the error term which incorporates all the factors affecting the regressand which are not included in the model and the slope coefficient on X, respectively. Which of the following conditions need to be fulflled for the instrument to be valid? (Check all that apply.) O A. The instrument must be uncorrelated with the error term, i.e., corr (Z,, u;) = 0. O B. The instrument must be correlated with the regressor, i.e., corr (Z, X;)# 0. O c. The instrument must be uncorrelated with the regressand, i.e., corr (Zj, Y;) = 0. O D. The instrument must be uncorrelated with the regressor, i.e., corr (Z;, X;) = 0.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
do fast with explanation
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
