Your Textbook Derives the OLS Estimator As $\hat { \beta }$

question 31

Essay

Your textbook derives the OLS estimator as $\hat { \beta }$ = $\left( X ^ { \prime } \right.$ X)^-1
$X ^ { \prime }$ ^Y.
Show that the estimator does not exist if there are fewer observations than the number of explanatory variables, including the constant. What is the rank of $X ^ { \prime }$ X in this case?

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Definitions:

Depreciates

Describes a decrease in value over time, often used in reference to currency or physical assets.

Imports

Goods and services purchased from other countries and brought into a country.

Inflation

The speed at which the overall price level for goods and services increases, thereby diminishing buying power.

Floating Exchange Rates

A system in which currency values are allowed to fluctuate according to foreign exchange market mechanisms without direct intervention by the country’s government.