Consider the Following Population Regression Model Relating the Dependent Variable $Y _ { i }$

question 11

Essay

Consider the following population regression model relating the dependent variable $Y _ { i }$ and regressor $X _ { i }$ ,
$$\begin{array} { c } Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } , i = 1 , \ldots , n . \\X _ { i } \equiv Y _ { i } + Z _ { i }\end{array}$$ where Z is a valid instrument for X.
(a) $$\text { Exlain why you should not use OLS to estimate } \beta _ { 1 } \text {. }$$

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Definitions:

Allowance Method

An accounting technique used to estimate the amount of uncollectible accounts receivable that will not be paid by debtors, allowing companies to record these anticipated losses as an expense.

Bad Debt Expense

An expense reported on the income statement, representing the estimate of receivables that a company does not expect to collect.

Allowance for Doubtful Accounts

A contra-asset account that represents the estimated portion of accounts receivable that may not be collectible.

Uncollectible Receivables

Refers to money owed to a company by its debtors that is unlikely to be paid and is considered a loss.