In Chapter 10 of Your Textbook, Panel Data Estimation Was $$\left( X _ { i t } , Y _ { i t } \right) , i = 1 , \ldots , n \text { and } t = 1 , \ldots , T$$

question 12

Essay

In Chapter 10 of your textbook, panel data estimation was introduced.Panel data consist
of observations on the same n entities at two or more time periods T.For two variables,
you have $$\left( X _ { i t } , Y _ { i t } \right) , i = 1 , \ldots , n \text { and } t = 1 , \ldots , T$$ where n could be the U.S.states.The example in Chapter 10 used annual data from 1982
to 1988 for the fatality rate and beer taxes.Estimation by OLS, in essence, involved
"stacking" the data.
(a)What would the variance-covariance matrix of the errors look like in this case if you
allowed for homoskedasticity-only standard errors? What is its order? Use an example of
a linear regression with one regressor of 4 U.S.states and 3 time periods.

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Definitions:

Contractionary Gap

A situation where an economy's real GDP is lower than its potential GDP, indicating underutilization of resources.

Cyclically Balanced

An economic situation where fiscal policy is designed to be neutral over the business cycle, allowing for temporary deficits or surpluses but aiming for a long-term balance.

Federal Deficits

The financial situation in which a government's expenditures exceed its revenues within a given fiscal year, leading to borrowing or the issuance of debt.

Deficit Financing

The practice of funding government operations beyond the amount raised through taxation and other revenues by issuing debt or creating new money.