1.         The saving behaviour of individuals is modelled using UK cross sectional data  for  2017  from   Understanding   Society   based   upon   18,117 employees. The table below describes the variables in the data.

Variable Definitions

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saver             =         1 if saved last month, 0 otherwise

lsaved           =        natural logarithm of the amount saved last month

work_fin        =         1 if employed in financial sector, 0 otherwise

ghealth          =         1 if currently in good or excellent health, 0 otherwise

sex                =         1 if male, 0=female

lincome         =        natural logarithm of income last month

age               =        age of individual in years

agesq            =        age squared

degree          =         1 if university degree, 0 = below degree level education

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a.     The following Stata output shows an analysis of modelling the probability that an individual saved in the previous month using a Logit regression. Summary statistics on variables used in the analysis are also provided.

sum work_fin ghealth sex lincome

Variable |        Obs        Mean    Std. Dev.       Min        Max

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i)      Showing  your  calculations  in  full,  find  the  marginal  effects evaluated at the mean from the above output.

ii)     Provide an economic interpretation of the marginal effects found in (a(i)).

b.     Using  the  same  data  the  amount  saved  is  estimated  by  a  Tobit regression censoring on zero savings. The Stata output is shown below.

tobit lsaved age agesq lincome sex degree, ll(0)

Tobit regression

Limits: lower = 0

upper = +inf

Number of obs     =

Uncensored     = Left-censored  = Right-censored =

18,117

7,744

10,373

0

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lsaved |      Coef.   Std. Err.      t    P> |t |     [95% Conf. Interval]

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/sigma |   5.240645   .0493397                      5.143935    5.337355

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i)     Calculate   the   predicted   monthly   savings   for   the   following individual: aged 40, gross income last month was £4,000, female, highest educational qualification degree level.                      [5 marks]

ii)     For the individual described in b(i) what is the probability that they saved between £10 and £1,000 per month?               [20 marks]

c.     An alternative approach to modelling the amount saved per month is to use  the  Heckman  sample  selection  estimator.  The  Stata  output  is shown below.

heckman lsaved age agesq lincome sex degree, select(saver = work_fin ghealth sex lincome)

Heckman selection model

(regression model with sample selection)

Log likelihood = -22844.85

Number of obs

Selected

Wald chi2(5)

Prob > chi2

18,117

7,744

10,373

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0.0000