Panel Data Regression with Two Dependent Variables

[David Wang]

Hello all,

I have a quick question about how to analyze a panel data set where I have two dependent variables and two main predictors (all of them are continuous variables). I want to assess the relative impacts of the two main predictors x1 and x2 on the two dependent variables y1 y2 by comparing the coefficients of y1 y2 simultaneously. I am aware that -xtreg- will not be suitable for this analysis because -xtreg- allows only one dependent variable. However, I am not sure what other alternatives I should choose for this multivariate panel data regression. Any help is much appreciated!

Many thanks,
David

[Clyde Schechter]

You could do something like this:

gen long obs_no = _n
reshape long y, i(obs_no) j(which_dv)

xtreg y i.which_dv##c.(x1 x2) // , fe or re, robust vce, whatever

The coefficient of 2.which_dv#x1 will estimate the difference between the coefficients for the y1:x1 and y2:x1 regressions. Analogous interpretation applied to the coefficient of 2.which_dv#x2.

That said, do remember that trying to compare two regression coefficients is a hazardous occupation. Unless y1 and y2 are measured in the same units, on the same scale, and have the same distribution, such comparisons are meaningless.

[David Wang]

Thanks much, Clyde! I have to say this is a very smart approach! Since my two dependent variables are not measured on the same scale, I first standardized the two dependent variables, and then applied your approach. It worked very well. Again, I really appreciate your help, Clyde!

Best,
David

[Hayuma Ami]

Hello, I can not run the code suggested by Clyde. I have a panel data with two continuous DVs and five continuous IVs for six countries and period of 26 years. Any help will be appreciated.

[Carlo Lazzaro]

Hayuma:
welcome to this forum.
Another approach might be:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. mvreg ln_wage wks_work= i.idcode i.year c.age##c.age if idcode<=5

Equation             Obs   Parms        RMSE    "R-sq"          F      P>F
--------------------------------------------------------------------------
ln_wage               60      21    .2595974    0.6501   3.622568   0.0003
wks_work              60      21    17.87903    0.7203   5.021056   0.0000

------------------------------------------------------------------------------
             | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
ln_wage      |
      idcode |
          2  |  -.3751495   .1104366    -3.40   0.002    -.5985287   -.1517704
          3  |   .1603017   1.898535     0.08   0.933    -3.679847     4.00045
          4  |   .6039827   1.924932     0.31   0.755    -3.289559    4.497524
          5  |   .4026861   1.911194     0.21   0.834    -3.463069    4.268441
             |
        year |
         69  |   .2081141   .4098055     0.51   0.614    -.6207959    1.037024
         70  |    .231393   .6704796     0.35   0.732     -1.12478    1.587566
         71  |   .2591752     .97434     0.27   0.792    -1.711613    2.229964
         72  |   .4146467   1.285236     0.32   0.749    -2.184989    3.014282
         73  |   .5367871   1.599101     0.34   0.739    -2.697699    3.771273
         75  |   .6129151   2.231424     0.27   0.785    -3.900565    5.126395
         77  |   .8047842   2.870449     0.28   0.781    -5.001247    6.610815
         78  |   1.085894   3.189191     0.34   0.735    -5.364854    7.536642
         80  |   1.139914   3.826443     0.30   0.767    -6.599797    8.879625
         82  |   1.314783   4.472338     0.29   0.770    -7.731375    10.36094
         83  |   1.567653   4.788419     0.33   0.745    -8.117838    11.25315
         85  |   2.064355    5.43326     0.38   0.706    -8.925449    13.05416
         87  |   2.465956   6.086959     0.41   0.688    -9.846081    14.77799
         88  |   2.824165   6.648009     0.42   0.673     -10.6227    16.27103
             |
         age |   .2352784   .3120618     0.75   0.455    -.3959262    .8664831
             |
 c.age#c.age |  -.0057469   .0010793    -5.32   0.000    -.0079301   -.0035638
             |
       _cons |   -1.11577   5.019817    -0.22   0.825    -11.26931    9.037768
-------------+----------------------------------------------------------------
wks_work     |
      idcode |
          2  |  -.3176303   7.606007    -0.04   0.967    -15.70223    15.06697
          3  |   37.28914   130.7562     0.29   0.777    -227.1902    301.7684
          4  |   28.61586   132.5742     0.22   0.830    -239.5407    296.7724
          5  |    33.0437    131.628     0.25   0.803    -233.1991    299.2865
             |
        year |
         69  |   -6.92705   28.22419    -0.25   0.807    -64.01586    50.16176
         70  |   9.155491   46.17737     0.20   0.844    -84.24706     102.558
         71  |   3.221527   67.10489     0.05   0.962    -132.5109     138.954
         72  |   16.51413   88.51697     0.19   0.853    -162.5283    195.5566
         73  |   1.172813   110.1335     0.01   0.992    -221.5932    223.9388
         75  |   11.98843   153.6829     0.08   0.938    -298.8646    322.8415
         77  |   39.23896    197.694     0.20   0.844    -360.6349    439.1128
         78  |   22.50841   219.6464     0.10   0.919    -421.7685    466.7853
         80  |   75.03396   263.5353     0.28   0.777    -458.0166    608.0845
         82  |   100.4684   308.0195     0.33   0.746      -522.56    723.4967
         83  |   75.70391   329.7887     0.23   0.820    -591.3567    742.7645
         85  |   129.7519   374.2003     0.35   0.731    -627.1396    886.6434
         87  |   140.0234    419.222     0.33   0.740    -707.9331    987.9798
         88  |   130.8923   457.8627     0.29   0.776    -795.2224    1057.007
             |
         age |   6.163943   21.49237     0.29   0.776    -37.30848    49.63636
             |
 c.age#c.age |  -.1830421   .0743361    -2.46   0.018    -.3334009   -.0326832
             |
       _cons |   -32.1808   345.7256    -0.09   0.926    -731.4768    667.1152
------------------------------------------------------------------------------

[Joseph Coveney]

I can not run the code suggested by Clyde. I have a panel data with two continuous DVs and five continuous IVs for six countries and period of 26 years.

I'm not sure why you cannot, but try something like that shown below, starting at the "Begin here" comment. (The stuff above is just to create a dataset for illustration.) Do-file and log file attached.

version 18.0

clear *

// seedem
set seed 215682931

// Six countries
quietly drawnorm lat0 lat1, double corr(1 0.5 \ 0.5 1) n(6)
generate byte cid = _n

// Period of 26 years
quietly expand 26
bysort cid: generate byte yea = _n

// Five continuous predictors
forvalues iv = 1/5 {
    generate double pre`iv' = runiform()
}

// Two types of continuous outcome
forvalues dv = 0/1 {
    generate double out`dv' = rnormal(lat`dv', 1)
}

*
* Begin here
*
quietly reshape long out, i(cid yea) j(typ)
mixed out i.typ##c.pre? i.yea || cid: , reml dfmethod(kroger) nolrtest nolog

exit