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###### 日期：2019-10-24 11:33

ECO-5006A: Introductory Econometrics

Take-Home Written Exercise 1

A researcher has been provided with a random sample of 2,658 married female employees.

The data set contains information on the following variables:

salary : monthly labour income, \$1000s

kids : number of dependent children in the household (hhd)

age : age in years

educ : years of education

The researcher is interested in estimating the effect of having an additional kid in the hhd on

labour income. For this reason, the following MLR model is specified:

salaryi = β0 + β1kidsi + β2agei + β3educi + ui

, i = 1, 2, . . . , 2658 (1)

where βj

for j = 0, 1, 2, 3 are unknown coefficients to be estimated and ui

is the error term.

Estimating this model by OLS provides the following results: (2)

with standard errors in brackets.

(a) Using the results above, interpret the estimated coefficient of variable kids, β?1 and the

estimated coefficient of variable age, β?

2. Also test whether these coefficients are statistically

different from 0.

[25 marks]

(b) Do the estimated coefficients of variables kids and age have the expected sign? Justify

[15 marks]

(c) Construct a 99% confidence interval estimate for β3 and interpret it.

[10 marks]

(d) Are the results of your hypotheses tests in part (a) and the confidence interval estimate

in part (c) valid if assumptions MLR1 to MLR5 hold, but the error term in equation one

is not normally distributed?

[10 marks]

(e) A variable that strongly explains labour income but has been omitted from the model

is ‘hours of work per month’ (hours). Suppose that this variable is now added to the

regression model of eq (1) and the new model is estimated by OLS. How will the addition

of this variable affect the estimated value of the coefficient of variable kids? In addition,

how will the addition of this variable affect the standard error of this coefficient? Justify