Consider the following estimated equation:
$\hat { \mathrm { C } } _ { \mathrm { t } } = 18.5 - 0.07 \mathrm { P } _ { \mathrm { t } } + 0.93 \mathrm { YD } _ { \mathrm { t } } - 0.74 \mathrm { D } _ { \mathrm { t } } - 1.3 \mathrm { D } _ { 2 \mathrm { t } } - 1.3 \mathrm { D } _ { 3 \mathrm { t } }$ where: C_t= per-capita pounds of pork consumed in the United States in quarter t
P_t =the price of a hundred pounds of pork (in dollars) in quarter t
YD_t =per capita disposable income (in dollars) in quarter t
D_1t =dummy equal to 1 in the first quarter (Jan.-Mar.) of the year and 0 otherwise
D_2t =dummy equal to 1 in the second quarter of the year and 0 otherwise
D_3t =dummy equal to 1 in the third quarter of the year and 0 otherwise
(a) What is the meaning of the estimated coefficient of YD?
(b) Specify expected signs for each of the coefficients. Explain your reasoning.
(c) Suppose we changed the definition of D₃_t so that it was equal to 1 in the fourth quarter and 0 otherwise and re-estimated the equation with all the other variables unchanged. Which
of the estimated coefficients would change? Would your answer to part (b) above change? Explain your answer.

Question

Consider the following estimated equation:

\hat { \mathrm { C } } _ { \mathrm { t } } = 18.5 - 0.07 \mathrm { P } _ { \mathrm { t } } + 0.93 \mathrm { YD } _ { \mathrm { t } } - 0.74 \mathrm { D } _ { \mathrm { t } } - 1.3 \mathrm { D } _ { 2 \mathrm { t } } - 1.3 \mathrm { D } _ { 3 \mathrm { t } }

where: C_t= per-capita pounds of pork consumed in the United States in quarter t
P_t =the price of a hundred pounds of pork (in dollars) in quarter t
YD_t =per capita disposable income (in dollars) in quarter t
D_1t =dummy equal to 1 in the first quarter (Jan.-Mar.) of the year and 0 otherwise
D_2t =dummy equal to 1 in the second quarter of the year and 0 otherwise
D_3t =dummy equal to 1 in the third quarter of the year and 0 otherwise
(a) What is the meaning of the estimated coefficient of YD?
(b) Specify expected signs for each of the coefficients. Explain your reasoning.
(c) Suppose we changed the definition of D₃_t so that it was equal to 1 in the fourth quarter and 0 otherwise and re-estimated the equation with all the other variables unchanged. Which
of the estimated coefficients would change? Would your answer to part (b) above change? Explain your answer.

Quizplus · Accepted Answer

The Answer is We'd expect pork consumption to be the highest in the fourth quarter due to holidays, so the expected signs of the dummy coefficients are negative. For part (c), the coefficients of P and YD shouldn't change, but the others should, because the omitted condition is now the third quarter and not the fourth quarter. Thus the expected signs of the coefficients of D₁ and D₂ are no longer negative. (Some of the best students will note that the estimate of the coefficient of D₂ will be almost exactly zero.)

Consider the Following Estimated Equation Where: Ct= Per-Capita Pounds of Pork Consumed in the United

Consider the Following Estimated Equation Where: C_t= Per-Capita Pounds of Pork Consumed in the United