Question

You estimated the following model explaining “Years in the Labor Force” (experience) as a function of education, health status, and age. Your colleague suggested adding variables “female”. Using theory and 3 clues, would you follow your colleague’s advice?

r1jyears     = years in the labor force

raedyrs      = years of educational attainment     

pfhealth     = dummy for poor/fair health

age          = age measured in years

female       = dummy for being female

sibs         = number of siblings

. reg r1jyears raedyrs pfhealth age

      Source |       SS           df       MS      Number of obs   =     1,121

-------------+----------------------------------   F(3, 1117)      =     60.73

       Model |  28625.8233         3 9541.94111   Prob > F        =    0.0000

    Residual | 175505.633     1,117  157.122322   R-squared       =    0.1402

-------------+----------------------------------   Adj R-squared   =    0.1379

       Total |  204131.457     1,120 182.260229   Root MSE        =    12.535

------------------------------------------------------------------------------

    r1jyears |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]

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

     raedyrs |   .5696057   .1230842     4.63   0.000     .3281035     .811108

    pfhealth | -3.108815   .9230098    -3.37   0.001    -4.919843   -1.297787

         age |   .8371034   .0678502    12.34   0.000     .7039753    .9702315

       _cons | -24.99491    4.15634    -6.01   0.000    -33.15003    -16.8398

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. reg r1jyears raedyrs pfhealth age female

      Source |       SS           df       MS      Number of obs   =     1,121

-------------+----------------------------------   F(4, 1116)      =    132.55

       Model |  65746.5751         4 16436.6438   Prob > F        =    0.0000

    Residual |  138384.882     1,116   124.00079   R-squared       =    0.3221

-------------+----------------------------------   Adj R-squared   =    0.3196

       Total |  204131.457     1,120 182.260229   Root MSE        =    11.136

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    r1jyears |      Coef.   Std. Err.     t    P>|t|     [95% Conf. Interval]

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

     raedyrs |   .6095674   .1093685     5.57   0.000     .3949763    .8241585

    pfhealth | -3.083225   .8199744    -3.76   0.000     -4.69209    -1.47436

         age |   .5342491   .0627661     8.51   0.000     .4110962    .6574019

      female | -12.02953   .6952682   -17.30   0.000    -13.39371   -10.66535

       _cons | -2.288246   3.918656    -0.58   0.559     -9.97701    5.400518

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Would you say that “female” is omitted or irrelevant variable or niether?

		“Female” is an irrelevant variable
		“Female” is neither omitted nor irrelevant variable
		“Female” is an omitted variable
		“Female” is both omitted and irrelevant variable

Answer 1

Here the 1^st regression model is given as follows.

=> (Years in the Labor Force) = (-24.99) + 0.57*(Years of Educational Attainment) + (-3.12)*(Dummy for poor/Fair Health) + 0.84*(Age), with adjusted R-square “0.1379 = 13.79%”. So, the estimated equation explains 14% of variation in “Years in the Labor Force”.

The 2^nd regression model is given as follows.

=> (Years in the Labor Force) = (-2.29) + 0.61*(Years of Educational Attainment) + (-3.08)*(Dummy for poor/Fair Health) + 0.53*(Age) + (-12.03)*Female, with adjusted R-square “0.3196 = 31.96%”. So, the estimated equation explains around 32% of variation in “Years in the Labor Force” and the “p-value” of Female is close to zero implied it’s a relevant variable should be included.

So, here “Female” is a omitted variable, the correct option is “C”.