Deck 1: Sample Exam for Chapters 1-3

Question 1

A source of constant discussion among applied econometricians is the degree to which measures of the overall fit of an estimated equation also measure the quality of that regression. To date, we have introduced something like four different measures of overall fit, but the two most used are $\mathrm { R } ^ { 2 }$ and $\overline { \mathrm { R } } ^ { 2 }$ .
(a) Carefully distinguish between $\mathrm { R } ^ { 2 }$ and $\overline { \mathrm { R } } ^ { 2 }$ .
(b) Of the two, which do you recommend typically using? Why?
(c) What drawbacks are there to the use of the measure you chose (as your answer to part (b) above) as the primary determinant of the overall quality of a regression?

Answer 1

See Section 2.4.

Question 2

Two of the most important econometric concepts to date have been the stochastic error term and the residual. Carefully distinguish between these two concepts, being sure to:
(a) Define both terms.
(b) State how they are similar.
(c) State how they are different.
(d) Give an example of an equation that contains a stochastic error term.
(e) Give an example of an equation that contains a residual.

Answer 2

See Sections 1.2 and 1.3.

Question 3

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 D_3t 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.

Answer 3

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.)

Question 4

Briefly identify the following in words or equations as appropriate:
(a) Degrees of freedom
(b) Estimated regression equation
(c) The Six Steps in Applied Regression Analysis
(d) Ordinary Least Squares
(e) The meaning of $\beta$ ₁ in:
Y_i = $\beta$ ₀ + $\beta$ ₁ X_1i+ $\beta$ ₂ X_2i + $\varepsilon$ _i