1987Starting with the data for problem 6 and the data on the price of a related
ID: 1095075 • Letter: 1
Question
1987Starting with the data for problem 6 and the data on the price of a related commodity for the years 1986 to 2005 given below, we estimated the regression for the quantity demanded of a commodity (which we now relabel QX), on the price of the commodity (which we now label PX), consumer income (which we now label Y), and the price of the related commodity (PZ), and we obtained the following results. (If you can, run this regression yourself; you should get results identical or very similar to those given below.)
QX = 121.86 - 9.50PX + 0.04Y - 2.21PZ
(-5.12) (2.18) (-0.68)
R2 = 0.9633 F = 167.33 W = 2.38
(b) is to evaluate the above regression results in terms of the signs of the coefficients, the statistical significance of the coefficients, and the explanatory power of the regression (R2). The number in parentheses below the estimated slope coefficients refer to the estimated t values. The rule of thumb for testing the significance of the coefficients is if the absolute t value is greater than 2, the coefficient is significant, which means the coefficient is significantly different from 0. For example, the absolute t value for Px is 5.12, which is greater than 2; therefore, the coefficient of Px, (-9.50) is significant. In other words, Px does affect Qx. If the price of the commodity X increases by $1, the quantity demanded (Qx) will decrease by 9.50 units.
(c) Are X and Z complements or substitutes?
Year 1986 1987 1988 1989 1990 PZ ($) 14 15 15 16 17 Year 1991 1992 1993 1994 1995 PZ ($) 18 17 18 19 20 Year 1996 1997 1998 1999 2000 PZ ($) 20 19 21 21 22 Year 2001 2002 2003 2004 2005 PZ ($) 23 23 24 25 25Explanation / Answer
(a) Explain why you think we have chosen to include the price of commodity Z in the above regression.
Z is a related good with X as the results show the coefficient of price of Z is negative which means that as Pz rises demand for X falls. Both these goods are complementary to each other.
As Pz rises the demand for Z falls ( law of demand ) . as demand for Z falls demand for X is shown to fall so that they complement each other.
(b) Evaluate the above regression results.
These results and interpretations are based on the regression equation given. The coefficient f each variable is the incremental effect of this variable on the dependent variable ( Qx), assuming all other variables remain unchanged.
If Px rises by 1 unit ( $1)demand falls by 9.5 units. Demand falls as the sign is negative.
If income rises by $1 demand rises by .04 units. Demand will rise due to income rise as the sign is positive.
If price of Z rises by $1, demand for X falls by 2.21 units. Demand of X falls when price of Z rises as the sign is negative.
In terms of significance Px and Y are significant as t value is >2. ( 5.12>2 and 2.18>20)we compare absolute values of t statistic only with 2
Pz is not a significant explanatory variable as t value < 2 (.68<2)
X is a normal good that obeys the law of demand as the coefficient of Px is negative.
X is normal god as its demand rises with income, as shown by the positive coefficient of Y
Z is complementary to X
c) Are X and Z complements or substitutes?
Complementary as the coefficient of Pz is negative. As PZ rise, Qz falls (due to law of demand ) and Qx also falls. As Qx and Qz both fall together they are complementary to each other.
Notes:
1. P15(b) is to evaluate the above regression results in terms of the signs of the coefficients, the statistical significance of the coefficients, and the explanatory power of the Regression (R2) The number in parentheses below the estimated slope coefficients refer to the estimated t values. The rule of thumb for testing the significance of the coefficients is if the absolute t value is greater than 2, the coefficient is significant, which means the coefficient is significantly different from zero. For example, the absolute t value for Px is 5.12 is greater than 2, therefore, the coefficient of Px, (-9.50) is significant. In other words, Px does affect Qx. If the price of the commodity X increases by $1, the Quantity demanded (Qx) will decrease by 9.50 units.
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