Assume That You Had Found Correlation of the Residuals Across $| \rho |$

question 17

Essay

Assume that you had found correlation of the residuals across observations. This may happen because the regressor is ordered by size. Your regression model could therefore be specified as follows:
Y_i = β₀ + β₁X_i + u_i
u_i = ρu_i-1 + v_i; $| \rho |$ < 1.
Furthermore, assume that you had obtained consistent estimates for β₀, β₁, ρ. If asked to make a prediction for Y, given a value of X(= X_j)and $\hat u$ _j-1, how would you proceed? Would you use the information on the lagged residual at all? Why or why not?

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Definitions:

Market Supply

The total quantity of a good or service that all producers in a market are willing and able to sell at various prices.

Market Supply Curve

A graphical representation showing the relationship between the price of a good and the quantity of that good that all suppliers are willing to produce and sell.

Competitive Industry

A market scenario where numerous producers compete to offer goods or services to consumers, ensuring no single entity dominates the market prices or supply.

Price-Quantity

Relationship between the price of a good and the quantity of the good supplied or demanded.