Faculty of Liberal Arts and Professional Studies
Department of Economics
Use of Economic Data – AP/ECON3210.03A
Assignment #2: Questions and Solutions
Date: October 9 , 2013
Due Date: October 16 , 2013
Course Director: Ida Ferrara
Weight of Assignment: 5% of the final grade.
NOTES: (1) assignments will have to be submitted electronically within MOODLE by the
end of October 16 ; (2) students failing to submit the assignment on the due date will receive
a grade of zero for the assignment; (3) the data files for the two questions are provided as
dat files if STATA is used and as xlsx files if EXCEL is used (either software is acceptable);
(4) computer outputs have to be included in the submission and as part of the submission
(e.g., everything should be in one file).
1. (4.10) The file london.dat is a cross section of 1509 households drawn from the 1980-1982 British
Family Expenditure Surveys. Data have been selected to include only households with one or two
children living in Greater London. Self-employed and retired households have been excluded. Variable
definitions are in the file london.def. The budget share of a commodity, say food, is defined as
expenditure on food
A functional form that has been popular for estimating expenditure functions for commodities is
𝑊𝐹𝑂𝑂𝐷 = 𝛽 + 1 ln 2𝑂𝑇𝐸𝑋𝑃 + 𝑒 )
(a) Estimate this function for households with one child and households with two children. Report and
comment on the result. (You may find it more convenient to use the files lon1.dat and lon2.dat that
contain the data for households with one and two children, respectively).
(b) It can be shown that the expenditure elasticity for food is given by
𝛽 + 𝛽 ln 𝑇𝑂𝑇𝐸𝑋𝑃 + 1) ]
𝜀 = 1 2
𝛽1+ 𝛽 2n 𝑇𝑂𝑇𝐸𝑋𝑃 )
Find estimates of this elasticity for one- and two-child households, evaluated at the average total
expenditure in each case. Do these estimates suggest food is a luxury or a necessity? (Hint: Are the
elasticities greater than one or less than one?)
(c) Analyze the residuals from each estimated function? Is it reasonable to assume that the errors are
(d) Using the data on households with two children (lon2.dat), estimate budget share equations for
fuel (WFUEL) and transportation (WTRANS). For each equation, discuss the estimate of 𝛽 and
carry out a two-tail test of statistical significance. 2 (e) Using the regression results from part (d), compute the elasticity 𝜀 for fuel and transportation first
at the median of total expenditure (90) and then at the 95 percentile of total income (180). What
differences do you observe? Are any differences you observe consistent with economic reasoning?
2. (4.15) Does the return to education differ by race and gender? For this question, use cps4.dat; you will
have to extract subsamples of observations consisting of (i) all males, (ii) all females, (iii) all whites,
(iv) all blacks, (v) white males, (vi) white females, (vii) black males, and (viii) black females.
(a) For each sample partition, obtain the summary statistics of WAGE.
(b) A variable’s coefficient of variation is 100 times the ratio of its sample standard deviation to tis
sample mean. For a variable 𝑦, it is
𝐶𝑉 = 100 𝑦
It is a measure of variation that takes into account the size of the variable. What is the coefficient
of variation for 𝑊𝐴𝐺𝐸 within each sample partition?
(c) For each sample partition, estimate the log-linear model
𝑙𝑛 𝑊𝐴𝐺𝐸 = 𝛽 + 𝛽 1𝐷𝑈𝐶 +2𝑒
What is the approximate percentage return to another year of education for each group?
(d) Does the model fit the data equally well for each sample partition?
(e) For each sample partition, test the null hypothesis that the rate of return to education is 10% against
the alternative that it is not, using a two-tail test at the 5% level of significance. Chapter 4, Exercise Solutions, Principles of Econometrics, 4e 109
(a) For households with 1 child
WFOOD 1 .0099 0.1495ln(TOTEXP)
(se) (0.0401) (0.0090) R 0.3203
(t) (25.19) (16.70)
For households with 2 children:
WFOOD 0 .9535 0.1294ln(TOTEXP)
(se) (0.0365) (0.0080) R 0.2206
(t) (26.10) ( 16.16)
For 2 we would expect a negative value because as the total expenditure increases the
food share should decrease with higher pr oportions of expenditure devoted to less
essential items. Both estimations give the expected sign. The standard errors for1 2band
from both estimations are relatively small resulting in high values of t ratios and
(b) For households with 1 child, the average total expenditure is 94.848 and
b b ln TOTEXP 1
1 2 1.00990 .1495 (94.848) 1
b1 2 ln EXP 1.00990 .1495 ln(94.848)
For households with 2 children, the average total expenditure is 101.168 and
b1 2 ln EXP 1 0.95350 .12944 l 01.168) 1
b b ln EXP 0.95350 .12944 ln(101.168)
Both of the elasticities are less than one; therefore, food is a necessity.
Figure xr4.10(c) Plots for 1-child households
3 4 5 6 3 4 5 6
Fitted equation Residual plot Chapter 4, Exercise Solutions, Principles of Econometrics, 4e 110
Exercise 4.10(c) (continued)
(c) The fitted curve and the residual plot for hous eholds with 1 child suggest that the function
linear in WFOOD and ln( TOTEXP) seems to be an appropriate one. However, the
observations vary considerably around th e fitted line, consistent with the low R value.
Also, the absolute magnitude of the residuals appears to decline as ln(TOTEXP) increases.
In Chapter 8 we discover that such behavior suggests the existence of heteroskedasticity.
The plots of the fitted equation and the residua ls for households with 2 children lead to
The values of JB for testing H 0 the errors are normally distributed are 10.7941 and
6.3794 for households with 1 child and 2 ch ildren, respectively. Since both values are
greater than the critical value 5.991 , we reject H . The p-values obtained are
0.0045 and 0.0412, respectively, confirming that H is rejected. We conclude that for
both cases the errors are not normally distributed.
Figure xr4.10(c) Plots for 2-child households
3.5 4.0 4.5 5.0 5.5 6.0 3.5 4.0 4.5 5.0 5.5 6.0
Fitted equation Residual plot
(d) The estimated equation for the fuel budget share is
WFUEL 0 .3009 0.0464ln(TOTEXP)
(se) (0.0198 ) (0.0043) R 0.1105
(t) (15.22) (10.71)
The estimated slope coefficient is negative, and statistically significant at the 5% level.
The negative sign suggests that as total expenditure increases the share devoted to fuel will
decrease. Chapter 4, Exercise Solutions, Principles of Econometrics, 4e 111
Exercise 4.10(d) (continued)
The estimated equation for the transportation budget share is
WTRANS 0.0576 + 0.0410ln( TOTEX)P
(se) (0.0414) (0.0091) R 0.0216
(t) ( 1.39) ( 4.51 )
The estimated slope coefficient is positive, and statistically significant at the 5% level. The
positive sign suggests that as total expend iture increases the share devoted to
transportation will increase.
(e) The elasticity for quantity of fuel with resp ect to total expenditure, evaluated at median
total expenditure is
0.300873 6409 ln(90) 1
0.300873 0 6409 ln(90)
and at the 95 percentile of total expenditure it is
0.300873 409 ln(180) 1
0.300873 0 6409 ln(180) 0.2249
These elasticities are less than one, indicating that fuel is a necessity. The share devoted to
fuel declines as tot