tailieunhanh - Further Econometrics

Tài liệu cao học tham khảo môn kinh tế bằng Tiếng Anh . 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. | Alastair 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 LNWAGE 3o 31ED 32EX 33EXSQ u where LNWAGE denotes the log of average hourly earnings ED denotes the number of years of education EX denotes experience and EXSQ is the square of experience. a Why do you think that both EX and EXSQ have been included b Estimate the model using the data in CPS85. Do the OLS estimates of 31 32 and 33 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 ith person observation in the sample we have that y1 y2 .yni are the observations for the men and yni 1 Vn1 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 y 3o 31X u 1 1 a Show that the normal equations associated with OLS estimation of 1 can be written as ny - n 3o - A 0 2 n yy - 2 3 - 2 3 0 3 where the sample mean of y is given by y n-1 n 1 y and the sample mean of y for women is yy n-1 Xn i y . b Using 2 - 3 show that v ym and 3 yy - ym. 3. Suppose that we wish to