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日期:2019-08-12 10:20

ECO 321 Summer 2019

Homework 4

Due August 10th

Cut and paste at the end of your submission the R code you have used in problem

2 to show your work.

1. Consider the following nonlinear multivariable regression model:

log(yi) = β0 + β1x1i + β2x2i + β3x1i × x2i + β4 log(x3i) + ui

, i = 1, . . . , n. (1)

This model satisfies the least-squares assumptions. Use either first differences or

calculus to show the following.

(a) The effect of a change in x1i on log(yi) is equal to,

(b) The effect of a change in x2i on yi

is equal to,

(c) The effect of a change in x3i on log(yi) is equal to,

(d) The effect of a change in x3i on yi

is equal to,

2. The data set data ksubs.csv contains information on net financial wealth (nettf a),

age of the survey respondent (age), annual family income (inc), family size (fsize),

and participation in certain pension plans for people in the United States. The wealth

and income variables are both recorded in thousands of dollars. In particular, the

variable e401k is equal to 1 is the person is eligible for 401k, a retirement savings

plan sponsored by the employer, and 0 otherwise.

(a) Create a scatter plot of nettf a against inc. Can you observe any visible correlation

between nettf a and inc? Do you think that a regression of nettf a on inc

may feature heteroskedasticity? Explain.

1

(b) Suppose that the Least-Squares assumptions are satisfied and estimate the following

regression model:

nettf ai = β0 + β1male + β2e401k + β3inci + β4agei + ui

, i = 1, . . . , n. (2)

Report the estimated values of the regression coefficients and discuss their signs

(if it is or it is not as expected), their (heteroskedasticity robust) standard errors,

and significance level.

(c) We now introduce some additional variables and some nonlinearities in the

model. We add the square of age (agesq), the square of income (incsq), a

dummy for the individual being married (marr), and the household size (fsize).

We thus estimate the following model.

nettf ai =β0 + β1male + β2e401k + β3inci + β4agei (3)

+β5incsqi + β6agesqi + β7marri + β8fsizei + ui

, i = 1, . . . , n.

Obtain the OLS estimators of the regression coefficients and their (heteroskedasticity

robust) standard errors. Compare the new estimators with those obtained

in (b). How have they changed? Compare the adjusted R2

in this model and in

model (2).

(d) Based on the model specified in (c), derive the marginal effect of age on netff a,

and explain its meaning. What is the effect of increasing age of one unit on net

financial assets for a person that is 30 year old? How about the same effect for

a person that is 65 year old? Comment.

2


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