ECON4004 - Econometrics 2 Tutorial 1
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ECON4004 - Econometrics 2
Tutorial 1
1. We have data for individuals in the US that contain information on: i) wage rate per hour worked (measured in US dollars and denoted by the variable WAGE); ii) years of education (denoted by the variable EDUC); iii) race (denoted by the dummy variable BLACK that takes the value 1 if the individual is black and 0 otherwise; iv) gender (denoted by the dummy variable FEMALE that takes the value 1 if the individual is a female, and 0 otherwise).
We want to estimate the following model to explain the hourly wage earned by the individuals in the sample:
WAGE = β 1 +β2EDUC+ β3BLACK+ β4FEMALE+ β5(BLACK × FEMALE) + e (1. 1)
The estimated coefficients of equation (1. 1) can be found in Table 1:
Table 1. Coefficient estimates
Variable Coefficient Std. Error t‐Statistic p‐value
|
|
‐9.482 |
1.958 |
‐4.843 |
0.000 |
|
EDUC |
2.474 |
0.135 |
18.310 |
0.000 |
|
BLACK |
‐ 2.065 |
2.162 |
‐0.955 |
0.340 |
|
FEMALE |
‐4.224 |
0.825 |
‐5.120 |
0.000 |
|
BLACK × FEMALE R2 = 0.2277 |
0.533 |
2.802 |
0.190 |
0.849 |
(a) Calculate the conditional expectation of the hourly wage of a person with 16 years of education who is:
i) a white male
ii) a white female
iii) a black male
iv) a black female
Calculate the difference between i) and ii), i) and iii) and iii) and iv) and show how they are related to the estimated coefficients.
(b) Interpret the coefficient of the interaction effect BLACK × FEMALE
(c) How would you test for the joint significance of the variables BLACK, FEMALE and their interaction?
(d) As can be seen from the results in Table 1, neither the coefficient of BLACK nor the coefficient of BLACK × FEMALE is statistically significant. As a result, can we conclude that race does not affect hourly wages?
2. The following model allows the return to education (as measured by the logarithm of hourly wages) to depend upon one’s years of education (denoted by the variable EDUC), the total of both parents’ education (measured in years, denoted by the variable PAREDUC), labor experience (measured in years and denoted by the variable EXPER), and tenure in the firm/institution of current employment (measured in years and denoted by the variable TENURE):
log(WAGE) = β 1 + β2EDUC + β3(EDUC×PAREDUC) + β4EXPER + β5TENURE + e (2. 1) (a) Show that the return to another year of education in this model is
ΔE[log(WAGE)]/ΔEDUC = β2 + β3PAREDUC (2.2)
What sign do you expect for β3? Why?
(b) The coefficient estimates of equation (2.2) can be found in Table 2:
Table 2. Coefficient estimates
Variable Coefficient Std. Error t‐Statistic p‐value
|
|
5.650 |
0.130 |
43.462 |
0.000 |
|
EDUC |
0.047 |
0.010 |
4.700 |
0.000 |
|
EDUC × PAREDUC |
0.00078 |
0.00021 |
3.714 |
0.000 |
|
EXPER |
0.019 |
0.004 |
4.750 |
0.000 |
|
TENURE |
0.010 |
0.003 |
3.333 |
0.001 |
|
R2 = 0.169 |
|
|
|
|
Using two specific values for PAREDUC—for example, PAREDUC=32 if both parents have a college education, and PAREDUC=24 if both parents have a high school education, interpret the coefficient on the interaction term.
(c) When PAREDUC is added as a separate variable to equation (2. 1), we get the coefficient estimates shown in Table 3:
Table 3. Coefficient estimates
Variable Coefficient Std. Error t‐Statistic p‐value
|
|
4.940 |
0.380 |
13.000 |
0.000 |
|
EDUC |
0.097 |
0.027 |
3.593 |
0.000 |
|
PAREDUC |
0.033 |
0.017 |
1.941 |
0.053 |
|
EDUC × PAREDUC |
‐0.00160 |
0.00120 |
‐ 1.333 |
0.183 |
|
EXPER |
0.020 |
0.004 |
5.000 |
0.000 |
|
TENURE |
0.010 |
0.003 |
3.333 |
0.001 |
|
R2 = 0.174 |
|
|
|
|
Does the log hourly wage now depend positively on parent education? How are the coefficients related to parent education different from those in Table 2?
2022-04-27