Suppose You Are Interested in Explaining the Effect That Family

question 7

Essay

Suppose you are interested in explaining the effect that family income (thousands)has on child birth weight and you are concerned that the true marginal effects differ for at different points in the birth weight distribution.In a sample of 22,365 live births,you estimate following $\begin{array}{llll}10^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =&5.583+0.086 \text { Income }_{i}&+0.084 \text { Education }_{i} \\&& (1.473)(0.032)&( (0.029)\\25^{\text {th }}\text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 6.012+0.073 \text { Income }_{i}&+0.076 \text { Education }_{i}\\&& (2.533) (0.027)& (0.038) \\50^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 6.309+0.069 \text { Income }_{i}&+0.091 \text { Education }_{i}\\&& (1.925)(0.022)&(0.042) \\75^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 6.733+0.057 \text { income }_{i}&+0.074 \text { Education }_{i}\\&& (2.437)(0.026)& (0.029) \\90^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 7.024+0.033 \text { Income }_{i}&+0.065 \text { Education }_{i}\\&& (1.847)(0.013) & (0.031) \\\end{array}$

a)What is quantile regression? Which variable is the quantile of?
b)In what circumstances would quantile regression be preferable to OLS?
c)Discuss the results presented above.

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Definitions:

Fixed Costs

Costs that do not change with the level of production or sales activities, such as rent, salaries, and insurance premiums.

Variable Costs

Costs that change in proportion to the level of production or business activity.

Unit Contribution Margin

The amount each unit sold contributes to fixed costs and profit after variable costs are subtracted.

Operating Income

The revenue accrued from a firm's foundational business activities, prior to the removal of interest and tax charges.