Econ 603 Introduction to Econometrics
Faculty of Business
Econ 603 Introduction to Econometrics
Assignment 2, Semester 2, 2016
Question One (Total: 4 marks)
For each of the following statements indicate whether it is justified and explain your reasons.
(a) “Because multicollinearity lowers t-statistics, all of the insignificant regression coefficients should be dropped from the model because they are redundant”.
Solution: The statement is incorrect for the following reasons:
A. When there is multicollinearity, the high correlation between the explanatory variables makes it difficult to distinguish between their partial effects, resulting in high standard errors in the coefficients and low t-scores.
B. Thus, the insignificant t-scores do not necessarily indicate that the coefficients are redundant. Variables are redundant only if they essentially measure the same item, and this decision should be made based on theory.
(b) Consider the model: ,
where: Yi = The total cost of production of firm i.
Xi = The physical output of firm i.
“Since and are functions of , there is perfect collinearity”.
Solution: Perfect multicollinearity is the violation of Assumption that no explanatory variable is a perfect linear function of any other explanatory variables. If two or more independent variables have an exact linear relationship between them then we have perfect multicollinearity. In this case the major issue is that OLS cannot generate estimates of regression coefficients (error message).
Question Two (Total: 21 marks)
To answer this question, you may use STATA to analyse the data in the worksheet entitled “S2assignment2_data.dta” in “Assignment 2”. The intention is to investigate returns to education. The data contains the following variables collected for 935 working men in the United States:
WAGE = weekly earnings ($)
AGE = age in years
EDUC = years of education
EXPER = years of work experience
TENURE = years with current employer
MARRIED= 1 if married; and 0 otherwise
SOUTH=1 if living in the Southern region; and 0 otherwise (those living in the North)
URBAN=1 if living in an SMSA (Standard Metropolitan Statistical Area); and 0 otherwise
BLACK = “black” if black; and “otherwise” otherwise
IQ = IQ test scores
(HINT: please be noted that you need to generate a new dummy variable for variable “BLACK” in STATA. You may use “1” to represent black and “0” otherwise).
(a) Before running the regression, firstly obtain descriptive statistics (min, max, mean and standard deviation) of weekly earnings by ethnicity (BLACK). Please provide the summary of descriptive statistics from STATA. Do you observe any income gap between the two groups? Briefly comment.
Solution:
black = otherwise
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
wage | 815 990.6479 408.0027 115 3078
age | 815 33.1227 3.102612 28 38
educ | 815 13.61963 2.217333 9 18
exper | 815 11.46994 4.327646 1 23
tenure | 815 7.386503 5.117688 0 22
-------------+--------------------------------------------------------
south | 815 .2981595 .4577308 0 1
urban | 815 .7055215 .4560879 0 1
black | 0
married | 815 .8993865 .301001 0 1
iq | 815 103.5215 13.63635 54 145
Table-1: Summary statistics for black for weekly wages
The above table is evident that there is no gap in between the two groups as mentioned above.
. summarize
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
wage | 935 957.9455 404.3608 115 3078
age | 935 33.08021 3.107803 28 38
educ | 935 13.46845 2.196654 9 18
exper | 935 11.56364 4.374586 1 23
tenure | 935 7.234225 5.075206 0 22
-------------+--------------------------------------------------------
south | 935 .3411765 .4743582 0 1
urban | 935 .7176471 .4503851 0 1
black | 0
married | 935 .8930481 .3092174 0 1
iq | 935 101.2824 15.05264 50 145
Table-2: Summary statistics for all variables
(b) Use the data in “assignment2_data.dta” to estimate the following log(wage) equation:
Provide the output from Stata, and interpret the key results from your output. This includes interpreting all the slope coefficients, significance levels, and model fit criteria (HINT: please take a natural logarithm of weekly earnings).
Solution:
. logit wage age educ exper tenure south urban black married, offset(iq)
no observations
(c) Re-estimate the regression model with the addition of the variable IQ - a proxy variable for ability. Please provide the summary of your regression results from STATA. How is the re-estimated model different from b)? And why? (HINT: if you consider IQ as a relevant variable in determining an individual’s earnings, there might be a problem when excluding IQ. Define and explain the problem).
Solution: Note: wage not 0/1 valued; any nonzero, nonmissing value is treated as a
positive outcome
error obtaining starting values; try fitting a marginal model in order to
diagnose the problem
(d) Now, add an interacted regressor EDUC·BLACK to the regression model specified in (c). Please provide the summary of your regression results from STATA. Use your results to compare the estimated return to education between non-blacks and blacks and interpret the statistical significance of the results.
Solution: mprobit wage age educ exper tenure south black urban married iq
no observations
(e) What two other potential explanatory variables that may be missing from the model? Justify your answer with reference to existing studies in the literature on determinants of wage levels (HINT: you should use at least one academic journal paper and make sure you reference their findings and include discussions as to why these additional variables are relevant. 200 words minimum. Please use APA referencing, and you might find the following link useful: http://www.library.auckland.ac.nz/subject-guides/bus/topicguides/apa_for_business.htm).
Solution: The given data in the excel sheet, has not observations. The right equation is missing.