Question

Consider the model ln(Yi)=β0+β1Xi+β2Ei+β3XiEi+ui, where Y is an individual's annual earnings in dollars, X is years of work experience, and E is years of education. Consider an individual with a high-school degree (E=12yrs) who has been working for 20 years. The expected increase in log earnings next year (when X=21yrs) compared to this year is, dropping units,

β1

β1+12β3

β1+β3

β0+21β1+12β2+252β3

Answer 1

Given model is ln(Yi)=β0+β1Xi+β2Ei+β3XiEi+ui

according to the question, we have X= 20, E=12 for the current year

setting these values, we get

ln(Yi)=β0+β1(20)+β2(12)+β3(20*12)+ui = β0+β1(20)+β2(12)+β3(240) + ui......equation 1

and model equation for next year when X= 21 and E = 12 is given as

ln(Yi)=β0+β1(21)+β2(12)+β3(21*12)+ui = β0+β1(21)+β2(12)+β3(252) + ui....equation 2

Expected increase in log earnings next year compared to this year is given as equation 2 minus equation 1

we get

Expected increase = β0+β1(21)+β2(12)+β3(252) + ui -  β0-β1(20)-β2(12)-β3(240) - ui = β1 + 12β3

All remaining variable are cancelled out

So, answer is option B