Question

You are estimating a model explaining out-of-pocket health care spending as a function of age, number of health conditions, female dummy, and years of education. Note that coefficient for age is not significant with low t-score.

. reg health_care_cost age num_hconditions female raedyrs if age<=80

      Source |       SS           df       MS      Number of obs   =       552

-------------+----------------------------------   F(4, 547)       =      2.84

       Model |   859820811         4   214955203   Prob > F        =    0.0238

    Residual |  4.1427e+10       547 75734668.9   R-squared       =    0.0203

-------------+----------------------------------   Adj R-squared   =    0.0132

       Total |  4.2287e+10       551 76745344.3   Root MSE        =    8702.6

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

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

            age | -123.1563   219.3149    -0.56   0.575    -553.9588    307.6462

num_hconditions |   887.5861   330.8229     2.68   0.008     237.7472    1537.425

         female |   1698.277   808.0694     2.10   0.036     110.9782    3285.576

        raedyrs |   185.5531   108.8725     1.70   0.089    -28.30624    399.4124

          _cons |   8668.253   17063.78     0.51   0.612     -24850.3     42186.8

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		Remove age since it is an irrelevant variable.
		Age is neither omitted not irrelevant variable
		Keep age since it is theoretically important variable and removing age would lead to omitted variable bias.
		Age is both omitted and irrelevant variable

Answer 1

You are estimating a model explaining out-of-pocket health care spending as a function of age, number of health conditions, female dummy, and years of education.

Note that coefficient for age is not significant, with a low t-score.

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Correct answer:

Keep age since it is theoretically important variable and removing age would lead to omitted variable bias.

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In the specified model, age is a very important variable that may explain out-of-pocket health care expenditure. The results suggest that the coefficient is insignificant, and it has a low t-score.

However, this doesn't mean that the variable should be dropped. It can't be removed from the model, as it is theoretically relevant. Though statistically it has been proved to be insignificant, dropping it would lead to omitted variable bias.