Introductory Econometrics
Multiple Hypothesis Testing
by Hieu Nguyen
Fall 2024
1.
File wage.csv contains a cross-sectional dataset on 526 working individuals for the year 1976 in the US.
Using this labor market data, estimate a simple model describing the impact of years of education and
work experience on hourly wage in USD per hour:
wage = β0 + β1educ + β2exper + ϵ.
(a) Import data into Gretl from the .csv file. Carry out a basic inspection of data (display values,
visually, descriptive statistics).
(b) Comment on the expected signs of coefficients β1 and β2 first and then estimate the model.
(c) Evaluate the statistical significance of β1 and β2 based on the Gretl output.
(d) How much of the variation in wage for these 526 individuals is explained by educ and exper?
Explain.
(e) Estimate also the model without exper, compare R2
and R2
adj. Which is a better model? Why?
(f) Test formally the following hypotheses at the 5% significance level:
(i) Education has a significant impact on wages.
(ii) Workforce experience has a significantly positive impact on wages.
(iii) The regression is overall significant.
(g) Set up a 90% confidence interval for β2 (and a 99% confidence interval for β1).
(h) How would the estimated coefficients, standard errors, and t-statistics have differed if we transformed
the wage variable into monthly income and exper into decades? Explain.
2.
Answer the following questions about data on the sales prices of houses in the UK. The variables in this
study are:
• PRICEi: sales price for house i;
• ASSESSi: assessed price of house i;
• LOTSIZEi: size of lot (in square feet) for house i;
• BDRMSi: number of bedrooms for house i;
• BATHi: number of bathrooms for house i;
• OCEANi: a variable equal to 1 if house i is located within 10 miles of the ocean, 0 otherwise;
• URBANi: a variable equal to 1 if house i is located in an area classified as urban, 0 otherwise;
• LAKEi: a variable equal to 1 if house i is located within 10 miles of a lake, 0 otherwise;
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Table 1: Results of regressions
Dependent variable PRICEi, n = 238
(1) (2) (3) (4) (5) (6) (7)
ASSESSi 0.90 0.90 0.91 0.90 0.89 0.90 0.90
(0.03) (0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
LOTSIZEi 0.0035 0.00059 0.00059 0.00057 0.00058 0.00059 0.00060
(0.00002) (0.00002) (0.00002) (0.00002) (0.00002) (0.00002) (0.00002)
BDRMSi 11.5 9.74 7.65 8.74 10.43
(2.32) (3.11) (3.29) (3.54) (3.77)
BATHi 3.57 3.78
(2.24) (1.11)
OCEANi 15.6 14.32 16.76 15.32 14.56
(11.43) (5.21) (4.32) (4.98) (7.01)
URBANi 9.54 10.29 12.32
(8.99) (5.43) (5.22)
LAKEi 11.36 12.87 11.98
(4.28) (8.32) (6.43)
INTERCEPT 261.9 -38.91 -40.30 -43.21 -36.54 -42.37 -38.44
(11.98) (6.78) (7.32) (6.99) (5.87) (7.22) (9.43)
RSS 145.69 142.99 136.66 134.54 135.38 135.22 136.54
R2
0.143 0.159 0.196 0.209 0.204 0.205 0.197
• INTERCEPT: intercept in the model.
Table 1 lists estimated coefficients with standard errors in parentheses below.
(a) Using the reported regressions, could you test whether the value of the house near water was
different from the value of the house away from water at the 5% significance level, controlling for
assessed value, lot size, and the number of bedrooms? If so, perform the test. If not, explain what
results you would need to do the test.
(b) Could you test whether bathrooms change the house value, controlling for assessed value, lot size,
and the number of bedrooms at the 5% significance level? If so, perform the test. If not, explain
what results you would need to do the test.
(c) Can you test whether the assessed value and number of bedrooms are jointly significant, controlling
for lot size? If yes, perform the test at the 5% significance level. If not, explain what you would
need to perform this test.
(d) Could you test whether all 7 of the listed variables (excluding the intercept) are jointly significant
at the 5% significance level? Be sure to state any assumptions you are making.
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