a) Estimate the model nettfa = Bo+ Biinc+ B2inc + Bage + 4age + Bsmarr + Bofsize + B7e401k+u using OLS with default standard errors: reg nettfa c.inc#3 #c.inc c.age #23%2c.age marr fsize e401k Note: the specification with # or ## is less straightforward than "reg nettfa inc incsq age agesq marr fsize e401k" but it simplifies the estimation of predicted values and marginal effects (we indicate that the same variable is present in two or more terms). If you generate a separate variable incsq instead, Stata will treat inc and incsq as unrelated regressors when computing marginal effects. Term "c.inc##c.inc" denotes both inc and inc squared; you can also include these terms separately as "inc" 2 and "c.inc#c.inc". Prefix c. indicates a continuous variable. If you do not know how to refer to a particular factor variable or an interaction term in further hypothesis testing, run the regression command with option "coeflegend"; it will report the Stata name for each coefficient. Try "reg nettfa c.inc# #c.inc c.age##c.age marr fsize e401k, coeflegend" and then "test inc c.inc#c.inc". b) It is very likely that a linear specification is too restrictive for regressor "fsize" (family size). Examine the frequency distribution of fsize: tab fsize Create a new variable "nfsize" where all the categories with 7 and more persons are "top-coded" as 7: recode fsize (7/13=7), gen (nfsize) Re-run the regression treating nfsize as a set of dummy variables (i.nfsize) for each value of nfsize: reg nettfa c.inc%23 %3c.inc c.age%23%2c.age marr i.nfsize e401k Note: when working with #, prefix c is used for continuous variables and prefix i for categorical variables Q. Interpret the coefficients for i.nfsize. Explain why the table does not contain the coefficient for nfsize=1. Q. Briefly compare other coefficients in (a) and (b). c) Perform the misspecification test RESET (additional information is provided in module "Course project" >> "Course project tutorial"). estat ovtest Q. Briefly interpret the result. d) Re-estimate the model using the interaction terms age*inc and age*i.nfsize: reg nettfa c.inc#23 #c.inc c.age #23%2c.age c.inc#c.age marr i.nfsize i.nfsize #c.age e401k Repeat the RESET test and interpret the result (compare the RESET test statistics for the two specifications). Now run the Breusch-Pagan test for heteroskedasticity: estat hettest, fstat and White's test for heteroskedasticity: estat imtest, white Q. Briefly interpret the results. e) Re-estimate the model in (d) using robust errors: reg nettfa c.inc#23 #c.inc c.age%23%2c.age c.inc#c.age marr i.nfsize i.nfsize #c.age e401k, r Q. Write down the partial derivative of the fitted value with respect to inc; it estimates the effect of a one-unit ($1000) increase in income. Q. Find the difference in predicted wealth of the households with 1 person and 4 persons; assume that the respondent's age is 40. f) Plot the predicted wealth as a function of age for married respondents who are eligible for 401k plan, with family income of $33,000 and 4 persons in the household: margins, at (age= (25 (5) 65) marr=1 nfsize=4 e401k=1 inc=33) 3 and marginsplot Q. Explain the shape of the graph. Plot the marginal effects of age on wealth for married respondents who are eligible for 401k plan, with family income of $33,000 and 4 persons in the household: margins, dydx (age) at (age=(25 (5) 65) marr=1 nfsize=4 e401k=1 inc=33) marginsplot Q. Explain the shape of the graph. Note: you can save the graphs as przy mies and insert them in the text.