Econometric Methods and Applications I
WS 14/15
Martin Huber
PC 2, Questions 3g-i (Tobit model)
Consider now the number of hours worked per week and its dependence on the
given personal characteristics. The aim is to understand how the number of
children and their age are related the number of hours worked.
Estimate a linear regression model for hours using the treatment variables child
ych0_2 ych3_4 ych5_10 ych11_16 and the additional controls age age^2
educ_l educ_h married nwinc.
>
+
>
>
model_pc2_hours=hours~ child+ych0_2 +ych3_4+
I(age^2)+ educ_l+ educ_h+married+ nwinc
ols_hours=lm(model_pc2_hours)
coeftest(ols_hours, vcov=vcovHC)
ych5_10 + ych11_16 +age
t test of coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.2454458 3.2105587 -0.0764 0.939066
child
-4.5805291 0.4746190 -9.6510 < 2.2e-16
ych0_2
-5.9403766 1.4297272 -4.1549 3.337e-05
ych3_4
-4.4979978 1.5264608 -2.9467 0.003235
ych5_10
-2.4253756 1.2184776 -1.9905 0.046619
ych11_16
1.1121868 1.2813053
0.8680 0.385452
age
2.1298172 0.1481543 14.3757 < 2.2e-16
I(age^2)
-0.0298018 0.0015848 -18.8047 < 2.2e-16
educ_l
-0.3546690 0.7385247 -0.4802 0.631089
educ_h
2.5538452 0.6037553
4.2299 2.401e-05
married
-8.0291203 0.6007008 -13.3663 < 2.2e-16
nwinc
-0.0348820 0.0430283 -0.8107 0.417610
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’
***
***
**
*
***
***
***
***
0.1 ‘ ’ 1
g. Interpret the estimated coefficients on child and ych0_2. Explain why it may
be problematic to include wage in the regression. Obtain the OLS fitted
values. Are there any problems?

child: one more child reduces weekly hours worked on average by
about 4.6 hours, also here the effect depends on the age of the children;

ych0_2: having the youngest child in the age between 0 and 2 reduces
hours worked on average by about 6 hours;

wage cannot be an exogenous control variable, as it depends on the
hours worked. Only when hours worked is positive wage is observed;
wage depends on hours worked. If we include wage, we will face a
reverse causality problem.

OLS fitted values: see next page.
1
Econometric Methods and Applications I
WS 14/15
Martin Huber
OLS fitted values
The OLS model predicts negative values of hours worked. This is
unreasonable, given the character of the variable (hours worked).
h. Explain why hours worked is a reasonable candidate for a Tobit model?
Hours worked cannot be negative, thus a linear specification is not
reasonable, in particular for shorter hours. In a given set-up, hours=0
corresponds to a corner solution outcome. Thus, linear model doesn’t give
the correct approximation of the observed values. The linear model allows
only for constant partial effects which might not be very reasonable in this
case: hours of work might change differently for women depending on how
many children they already have.
Estimate a Tobit model for hours using the same variables as before.
i.
Are the signs and the statistical significance of the coefficients the same as in
the linear regression model for hours? What do you make of the different
magnitude of the coefficient on child in the Tobit and the linear model? Show
the fitted values of the Tobit model and compare them to the linear model.
2
Econometric Methods and Applications I
WS 14/15
Martin Huber
Call:
tobit(formula = hours ~ child + ych0_2 + ych3_4 + ych5_10 + ych11_16 +
age + I(age^2) + educ_l + educ_h + married + nwinc, data = data_pc2)
Observations:
Total
3300
Left-censored
834
Uncensored Right-censored
2466
0
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -25.401342
4.407507 -5.763 8.25e-09 ***
child
-5.683531
0.595552 -9.543 < 2e-16 ***
ych0_2
-7.107114
1.743928 -4.075 4.59e-05 ***
ych3_4
-5.078088
1.873887 -2.710 0.00673 **
ych5_10
-2.666295
1.504972 -1.772 0.07645 .
ych11_16
1.677888
1.551747
1.081 0.27957
age
3.528386
0.215950 16.339 < 2e-16 ***
I(age^2)
-0.047882
0.002462 -19.448 < 2e-16 ***
educ_l
-1.262477
0.894032 -1.412 0.15792
educ_h
2.851991
0.831140
3.431 0.00060 ***
married
-9.629721
0.757513 -12.712 < 2e-16 ***
nwinc
-0.046862
0.018944 -2.474 0.01337 *
Log(scale)
2.895029
0.015144 191.173 < 2e-16 ***
--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The signs of all the coefficients correspond to the ones obtained from the
linear regression. All the coefficients that were significant /not significant
before remain significant /not significant. The coefficients cannot be
interpreted directly from the table after the Tobit estimation. Thus the
magnitude in the Tobit and the OLS coefficients is not really comparable.
The predicted values obtained from the Tobit model are non-negative. They
are a better approximation of the observed values of the variable hours
worked.
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