Consider the One-Variable Regression Model, Y_i = β₀ + β₁X_i $\tilde { Y } _ { i }$

question 25

Essay

Consider the one-variable regression model, Y_i = β₀ + β₁X_i + u_i, where the usual assumptions from Chapter 4 are satisfied. However, suppose that both Y and X are measured with error, $\tilde { Y } _ { i }$ = Y_i + z_i and $\widetilde { X } _ { i }$ = X_i + w_i. Let both measurement errors be i.i.d. and independent of both Y and X respectively. If you estimated the regression model $\tilde { Y } _ { i }$ = β₀ + β₁
$\widetilde { X } _ { i }$ + v_i using OLS, then show that the slope estimator is not consistent.

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Definitions:

IRRs

Internal Rate of Return; a financial metric used to estimate the profitability of potential investments, calculated as the discount rate that makes the net present value of all cash flows equal to zero.

Mutually Exclusive

A condition in which two or more propositions cannot both be true at the same time, often applied in scenarios of project selection or decision making.

IRR

Internal Rate of Return, a financial metric used to assess the profitability of investments by calculating the interest rate that makes the net present value of all cash flows equal to zero.

Decision Rules

Guidelines or criteria used to make choices among alternatives in decision-making processes.