Answered: E(ui) = E(ui|X2i)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Consider a regression with two variables, in which X1i is the variable of interest and X2i is the control variable. The zero conditional mean assumption requires

Group of answer choices

E(ui|X1i) = E(ui|X2i)

E(ui|X1i, X2i) = E(ui|X1i)

E(ui|X1i, X2i) = 0

E(ui) = E(ui|X2i)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1: Explanation of the correct option

$E (u_{i} | X_{1 i}, X_{2 i}) = 0$
This means that, for each combination of $X_{1 i}$ and $X_{2 i}$ values, the expected value of the error term is zero. In other words, the error term is not systematically related to either $X_{1 i}$ or $X_{2 i}$ , and there is no conditional bias in the model due to omitted variables or endogeneity.

The key point is that the zero conditional mean assumption requires the error term to be unrelated to both $X_{1 i}$ and $X_{2 i}$ , which is expressed as $E (u_{i} | X_{1 i}, X_{2 i}) = 0$