Instructions: For all questions, you must clearly show how you arrived at the answer in order to receive full credit

Instructions: For all questions, you must clearly show how you arrived at the answer in order to receive full credit. Show statistical output from Stata to support any claims that you make. For hypothesis tests, always state the null and alternative hypotheses and make it clear why you are rejecting or not rejecting the null hypothesis. Along with your answers, submit a STATA do file that produces all the output that you used to arrive at your answers. The data for this assignment is wage2.dta, and the file wage2_readme.txt contains variable definitions.
1. (50 points) In this question, you will perform an empirical analysis of IQ scores.
(a) Compute basic summary statistics for IQ, and also generate a histogram. Report the mean, standard deviation, minimum, and maximum.
(b) If your IQ is 120, and you meet a randomly selected person from the population, what is the probability that they have a lower IQ score than you? How does the answer change if your IQ is 80?
(c) Standardize the IQ variable by generating a new variable called std_IQ that has a mean of zero and a standard deviation of one. Verify that you have done this correctly by summarizing std_IQ. (Note that the mean and standard deviation will not be exactly equal to zero and one because of rounding error. This is fine.)
(d) In empirical research, information is typically missing for some observations. There are many reasons for this, but in survey data a person may not know the answer to a question, or may simply refuse to answer a question. Missing data in Stata is coded as a “.” (For example, type list if feduc == . to see all observations with a missing value for father’s education). The Stata command for finding out about missing data is tabmiss. To install this function, type net search tabmiss (hit enter) click on the link, then click (click here to install). Use the tabmiss command to find out which variables have missing data, and how common missing data is. For each variable with missing data, report the percentage of missing values.
(e) Is missing data on fathers education more or less likely as IQ increases? Show at least one statistic that conclusively supports your claim. Provide a possible explanation for this feature of the data. Note that in this dataset, father’s education level is reported by the child, after the child has grown up and entered the labor market.
(f) Regress standardized IQ scores (std_IQ) on the number of siblings that a person has (sibs). Interpret the coefficient on sibs, and test the null hypothesis that IQ is unrelated to number of siblings.
(g) Repeat the regression from (1f), but this time also include mother’s and father’s education as explanatory variables. How does the coefficient on sibs change compared to the estimate in (1f)? Explain why the estimate changes in this way.
(h) Based on your regression from (1g), test the joint hypothesis that mother’s and father’s education are both unrelated to the IQ of their child.
Based on your regression from (1g), test the hypothesis that mother’s and father’s education have the same relationship to the IQ of their child.
(i) The government is considering a policy to discourage people from having more than one child. Based on regression analysis, if this policy is effective in reducing family size, how will it affect IQ scores of the population?
2. This question is about the relationship between observable variables and earnings.
(a) Create an hourly wage variable (call it w) based on the variables wage and hours. To do this, assume that for each person, hours worked in a month = 4*(average weekly hours worked). Report the mean, standard deviation, and min and max for this new variable.
(b) Create a variable (lnw) that is the natural logarithm of the hourly wage (w). Report the mean, standard deviation, and min and max for this new variable.
(c) You are hired by a professor to assist in a research project on the determinants of wages. He asks you to regress lnw on the variables (educ, tenure, exper, age, married, black, south, urban). Interpret the coefficient on educ. Economically, is this a large relationship? Hint: review material in the text on regressions with dependent variables in log form.
(d) The professor realizes that he forgot to ask you to include standardized IQ scores in the regression as an explanatory variable. Repeat the regression with the addition of this variable. How does the coefficient on educ change? This estimate is referred to as βeduc for the rest of the assignment. Provide an explanation for the change in the estimate.
(e) Which of the Gauss Markov assumptions needed for OLS to be the Best Linear Unbiased Estimator do you think is most likely to be violated in the previous regression? If it is violated, what does this imply for your estimate of βeduc? Do you think that your estimate of βeduc is a good estimate of the “return to education”?
(f) Returning to your regression from (2d) that includes IQ scores, create a variable for experience2, add it to the regression, and estimate the model (this is called adding a quadratic in experience to the model). According to your estimates, after how many years of work experience does the log wage start to decrease with additional years of experience?
(g) A negative return to work experience is difficult to reconcile with the theory of human capital, and models of learning-by-doing on the job. Evaluate your estimates of β1exper +β2exper2, discussing both statistical and economic significance. Do you prefer a model with or without the quadratic term? Why?
(h) Return again to your regression from question 2d (explanatory variables are std_IQ, educ, tenure, exper, age, married, black, south, urban). According to these estimates, how many years of work experience is being married equivalent to, in terms of log wages?
(i) Do you think that your estimate of βmarried is an unbiased estimate of the causal effect of marriage on log wages? Why or why not? Think about which of the assumptions underlying the regression model might be violated by the marriage variable.