Coursework

The answers to the questions must be type-written. The preference is that symbols and equations should be inserted into the document using the equation editor in Word. Alternatively, they can be scanned and inserted as an image (providing it is clear and readable). Maximum words 1,500 excluding any Stata output and commands.

The  coursework  comprises  two  questions  where  the  second   is   a  short   Stata assignment. ANSWER ALL QUESTIONS. Both questions 1 and 2 carry equal weight and the marks shown within each question indicate the weighting given to component sections. Any calculations must show all workings otherwise full marks will not be awarded. In question 2 all Stata output should be shown.

Coursework must be submitted online through Blackboard using Turnitin and by no later than 12.00 noon on the deadline. Coursework submitted after the 12.00 noon deadline will have a late penalty applied. Details about the late penalty policy can be found in the Student Handbook.

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PLEASE    WRITE    YOUR    STUDENT    REGISTRATION     NUMBER    IN    THE

SUBMISSION TITLE BOX AND USE THIS AS THE FILENAME YOU UPLOAD.

1.                Using data from the U.S. Survey of Consumer Finances in 2019 the level of non-mortgage debt of 16,750 individuals was modelled as a function of: a cubic polynomial in age; whether the individual was married; their financial expectations about future income; whether they are very knowledgeable about their personal finances; and their log weekly wage rate,  as shown in equation (1):

debtsi  = β0  +β1 agei  +β2 agei(2) +β3 agei(3) +β4maTTiedi  +β5 expecti

+β6finknowi  +β7 log(wagei ) +Ei

(eq. 1) where i  is the unit of observation (individual) and log denotes the natural logarithm. Variables are defined as follows: maTTiedi  is equal to 1 if married and 0 otherwise; expecti  is equal to -1 if pessimistic (expect income to fall next year), 0 if no change in income expected, +1 if optimistic (expect income to increase next year); and finknowi equals 1 if the individual thinks they are very knowledgeable about their finances. The following Stata output shows the estimates.

regress debts c.age##c.age##c.age married expect finknow logwage

Source |       SS           df       MS

-------------+----------------------------------

Model |  13695

Residual |

-------------+----------------------------------

Total |  4137700

Number of obs

F( ,      )

Prob > F

R-squared

Adj R-squared

=    16,750

=

=

=

=

debts | Coefficient  Std. err.      t    P>|t|      [95% conf. interval]

------------------+----------------------------------------------------------------

sum debts age married expect finknow logwage

Variable |        Obs        Mean    Std. dev.       Min        Max

-------------+---------------------------------------------------------

debts |     16,750    531.6209    4970.326          0     175000

age |     16,750    45.64818    11.65751         18         65

expect |     16,750    .0501493    .7748462         -1          1

finknow |     16,750    .9225672     .26728105        0          1

+---------------------------------------------------------

logwage |     16,750    10.25585     3.45366          0   17.62217

Interpret the results and test whether the age effects are individually statistically significant at the 1% level.

At what two values of age is the level of debt minimised?

For financial expectations and the log wage calculate the respective elasticity, based upon the sample mean.

Calculate  the  value  of  the   RSS  and  the   degrees  of  freedom associated with the ESS, RSS and TSS.

Test whether the parameters on the explanatory variables are jointly statistically significant at the 5% level.

Showing your calculation in full find the adjusted R-squared.

An alternative specification for equation (1) is to model the debt-to- income ratio as follows (note: incomei  = wagei  + benefitsi , where benefitsi  represents benefit income, e.g. unemployment insurance):

= β0  +β1 agei  +β2 agei(2) +β3 agei(3) +β4marriedi

+β5 expecti  +β6finknowi  +β7 log(wagei ) +Ei

What particular problems might be found with this model?

The  initial  model  (equation  1)  is  now  re-estimated  changing  the functional form by replacing the cubic function in age with binary indicators for different age bands, as shown in equation (2):

debtsi  = β0  +Σk(3)=1βkageki  + β4marriedi  +β5 expecti  +β6finknowi

+β7 log(wagei ) +Ei

(eq. 2) Age  binary  indicators  are  defined  as  follows:  age1  = 1   if  the  individual  is  aged  between   18-34,  0  otherwise;  age2  = 1   if  the  individual is aged between 35-44, 0 otherwise; and age3  = 1  if the  individual is aged between 45 and 54, 0 otherwise. The reference  category is aged above 55. The following Stata output below shows  the estimates.

i)         Interpret the  age coefficients explaining how they affect the  level of debt. Are the  results consistent with those found under the original functional form of equation (1)? Explain your answer.

ii)        Which  model  is  preferred  (equation  1)  or  (equation  2), explain your answer? Show all calculations to reach your decision in full.

regress debts age1-age3 married expect finknow logwage

Source |       SS           df       MS      Number of obs   =    16,750

-------------+----------------------------------   F( ,      )     =      6.18

Model |                                     Prob > F        =

Residual |  4127000                             R-squared       =

-------------+----------------------------------   Adj R-squared   =

Total |

debts | Coefficient  Std. err.      t    P>|t|      [95% conf. interval]

-------------+----------------------------------------------------------------

age1 |              116.9167    -1.67   0.096    -423.9473    34.39083

age2 |              107.6893    -2.71   0.007     -502.494   -80.32902

age3 |              103.1392    -0.96   0.339     -300.687    103.6404

married |  -416.1489   81.63058    -5.10   0.000    -576.1534   -256.1443

expect |  -85.35759   49.65449    -1.72   0.086    -182.6856    11.97045

finknow |   276.0255   146.0629     1.89   0.059    -10.27332    562.3243

logwage |   37.13198   11.21791     3.31   0.001      15.1437    59.12026

_cons |   277.0043   186.8169     1.48   0.138    -89.17654    643.1852

Re-write the regression model shown in equation (2) to allow for differential wage effects with respect to age. The TSS and ESS from estimating this model are 4137700 and 12890 respectively. Based upon this information test whether there are differential wage effects across age groups at the 5% level. [15 marks]

STATA ASSIGNMENT