Using the variable names in the CPS85 data set, suppose we are interested in the following wage equation: LN W AGE = β0 + β1ED + β2EX + β3EX SQ + u where LN W AGE denotes the log of aver
Trang 1Alastair Hall ECON60622: Further Econometrics Spring 2009
Problem Set for Tutorial 1
You will work through these problems in Tutorial 1 So please work through the problems before hand and bring your answers to the tutorial The answers do not need to be handed in
This tutorial involves four questions relating to our discussion of categorical variables in Lecture 2 Questions 1, 3 and 4 use the data set CPS85 that can be downloaded from the class web page
1 Using the variable names in the CPS85 data set, suppose we are interested in the following wage equation:
LN W AGE = β0 + β1ED + β2EX + β3EX SQ + u
where LN W AGE denotes the log of average hourly earnings, ED denotes the number of years of education, EX denotes experience and EX SQ is the square of experience.
(a) Why do you think that both EX and EX SQ have been included?
(b) Estimate the model using the data in CPS85 Do the OLS estimates of β1, β2 and β3
have the signs you would expect?
(c) Calculate the semi-elasticity of the wage with respect to education
(d) Calculate the semi-elasticity of the wage with respect to experience
2 Suppose we have a cross-sectional sample of observations on the log(wage) of n individuals Further suppose that the first n1 in the sample are men; that is, letting yi denote the log(wage)
of the ithperson (observation) in the sample, we have that {y1 , y2, yn1} are the observations
for the men and {yn1+1, yn1+2, yn} are the observations on the women The number of
men in the sample is, therefore, n1 and the number of women is n − n1 = n2, say As in class,
we introduce a dummy variable to indicate gender which is defined as follows:
x = 0, if individual is male
= 1, if individual is female Now consider the regression model:
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Trang 2(a) Show that the normal equations associated with OLS estimation of (1) can be written as:
where the sample mean of y is given by ¯ y = n−1P n
i=1yi and the sample mean of y for
women is ¯yf = n−12 P n
i=n1+1yi (b) Using (2)-(3), show that ˆβ0= ¯ym and ˆβ1 = ¯yf − ¯ym
3 Suppose that we wish to study the relationship between log(wage) and the number of years
of education, and suspect that the relationship depends on the gender and marital status (i.e married or non-married) of the individual
(a) Propose a linear regression model for this relationship in which both the intercept and slope depend on gender and marital status
(b) Write down the conditional expectation of log(wage) for each of the four types (in terms
of gender and marital status) of individual in the sample, and use this to deduce the interpretation in the coefficients in the model
(c) Estimate this model by OLS using the data in CPS85 and report your results
(d) Test whether the relationship is affected by marital status Be sure to state the null and alternative hypothesis and the decision rule of the test
4 In the Lecture, we considered a wage equation of the form
and discussed how this formulation allows the intercept to be different for men and women Another way to parameterize such a relationship is to introduce a dummy variable for males,
M A = 1 − F E, and estimate the model
(a) What is the interpretation of the coefficients γ1 , γ2 and γ3?
(b) Estimate the models in (4) and (5) using the CPS85 data Given your answer to part (a) and the discussion in the lecture, are the OLS estimates from the two models logically consistent? Explain
(c) Are the reported R2’s in the Stata analysis the same? If not then which should we believe? Explain
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