Probelem Set 1
Determine if each of the following statement is true or false. Briefly explain you answer.
(i) If the population regression function is where for male and zero for female. If , it’s possible to have a female who have higher earnings than any male.
(ii) The larger the error variance , the higher the variance of given , holding other things constant.
(iii) When sample size is large enough, the OLS estimator is distributed as multivariate normal even when the error term is not normally distributed. (Assume other standard assumptions hold.)
(iv) For two linear regression models with the same dependent variable, must be larger for the one with a larger number of regressors, where the larger model don’t necessarily include all the variables of the smaller model.
We have data collected from a random sample of 220 home sales from a community in 2003. Let Price denote the selling price (in $1000), BDR denote the number of bedrooms, Bath denote number of bathrooms, Hsize denote the size of the house (in square feet). Lsize denote the lot size (in square feet), Age denote the age of the house (in years), and Poor denote the condition of the house where 1 means the house is in poor condition, and 0 for not. An estimated regression equation yields
(i) Interpret each of the coefficient estimates. Do they make economic sense?
(ii) What factors may contribute to the disturbance term?
(iii) What is the expected price of a house with 3 bedrooms, 2 bathrooms, 2000 square feet large with a 1000 square feet of the lot, 10 years old and in good condition?
(iv) Number of bedroom and house size are likely to be positively correlated. What is the consequence of such correlation?
The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleeping. The model is where sleep is the minutes of sleeping per week, totwork is the minutes of working per week, educ is the year of education and age is years of age.
(i) What do you expect about the sign for , and ? Why? (There is no right answer, but you should give a reason for your prediction) With data collected, the estimated equation is
(ii) Interpret the estimated coefficients.
(iii) If one works 10 hours more per week, and other things are the same, what is the change in expected sleeping time?
(iv) How do the coefficients will change if both hours of sleep and total time of work are measured in hours instead?
(v) is quite small in this model. What do you think we may have missed in this regression?
(vi) If our main interest is to look at the causal effect of age on time to sleep, do you think of any reason why the above specification is inadequate?
The following regression is estimated as a production function
where Q is output level, K is the amount of capital input and L is the amount of labor input. Standard errors are given in the parenthesis.
(i) Interpret the coefficient estimates.
(ii) Is each of the coefficients statistically significant at 5% level?
(iii) Use the information given above, test the following hypothesis: (a) The capital and labor elasticity of output are the same. (b) The production function is constant return to scale. (Denote the coefficients and respectively. State the hypothesis in terms of model coefficients, then calculate the test statistic and check with the corresponding distribution to decide whether to accept or reject the null hypothesis.)
Software Question (optional)
card.dta ( which can be found on Internet) is a database which consists of 3010 observations for individuals between 24 to 34 years old. We’re interested in the education return on log hourly wage.
(i) Which variables you think should be included in the regression function? Why?
(ii) Estimate coefficients of the following regression by software.
(iii) Explain the following hypothesis and test them: (a) , (b) .
(iv) Do you think we should include age as an independent variable in this regression? Why?
(v) Which factor you think may be a part of the error term? Are them correlated with the independent variables?
java assignment help, java homework help, programming homework help, python assignment help, programming assignment, computer science assignment help, computer science homework help, python homework help, do my programming homework, computer science assignment, computer science homework, c++ homework help, java programming assignment help, php assignment help,