In the Context of a Controlled Experiment, Consider the Simple $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \text {. Let the } Y _ {i}$

question 14

Multiple Choice

In the context of a controlled experiment, consider the simple linear regression formulation $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \text {. Let the } Y _ {i}$ be the outcome, $X _ { \mathrm { i } }$ the treatment level, and $u _ { i }$ contain all the additional determinants of the outcome. Then

• A) the OLS estimator of the slope will be inconsistent in the case of a randomly assigned \(X _ { i }\) since there are omitted variables present.
• B) \(X _ { \mathrm { j } } \text { and } u _ { \mathrm { i } }\) will be independently distributed if the \(X _ { \mathrm { i } }\) be are randomly assigned.
• C) \(\beta _ { 0 }\) represents the causal effect of X on Y when X is zero.
• D) \(E ( Y \mid X = 0 )\) is the expected value for the treatment group.

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Definitions:

Productivity

A measure of the efficiency of production, often quantified as the ratio of outputs (goods and services) produced per input used (such as labor, materials, and capital).

Resource

An economic or productive factor required to accomplish an activity, often considered in terms of time, labor, capital, and materials.

Complementary Resource

refers to inputs or goods that are used together with another resource or good to produce a product or service.

Marginal Revenue Product

This is the additional revenue generated from employing one more unit of a factor of production, such as labor.