Heterogeneity and Variability of variables for selected cases in Panel Data

[Yalfal Temesgen]

Dear All,
I have a panel data with three waves and i am comparing the mean difference (mean comparison) of consumption and or Income (both are dependent variable and are continuous variables) on sex, rural/urban households (both coded as 0 and 1). I am also comparing the variability of consumption and income (Coefficients of variations of consumption and income). Please, i request you a guidance on the above issue,

Thank you in Advance!
.

[Yalfal Temesgen]

Joerg Luedicke (StataCorp) Do you have any advice on this issue? Thank you.

[Carlo Lazzaro]

Yalfal:
bumping your question and/or trying to reach Stata list contributors does not fix the lack of any useful details that interesetd listers would consider in replying.
Please read (and act on) the FAQ to post more effectively. Thanks.

[Yalfal Temesgen]

Dear Carlo,

Thank you for suggestion, let me explain in detail with example. I am comparing mean difference of consumption on sex of the household head on panel data,

ttest food_cons_ann, by(Sex_hh)

Two-sample t test with equal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
0 | 7,350 17806.62 194.9903 16716.94 17424.39 18188.86
1 | 2,367 12187.81 253.1479 12316.11 11691.4 12684.23
---------+--------------------------------------------------------------------
combined | 9,717 16437.92 161.7196 15941.49 16120.91 16754.92
---------+--------------------------------------------------------------------
diff | 5618.809 372.4309 4888.767 6348.851
------------------------------------------------------------------------------
diff = mean(0) - mean(1) t = 15.0869
Ho: diff = 0 degrees of freedom = 9715

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000

is it valid to use the t test for panel data??

[Carlo Lazzaro]

Yalfal:
no, because -ttest- assumes that the observations are independent (but due to the panel structure of your dataset they aren't).
You should use the coefficients of the panel data regression and compare them via -test-.

[Yalfal Temesgen]

Dear Carlo,
I have estimated a fixed effect panel regression model (nonfarm income as dependent and continuous, and sex of the household head as independent and dummy variable 0/1) in my data set. And I want to test if the coefficients are significantly different for sex group.

xtreg nonfarm_income(i.Sex_hh), fe
test 1.Sex_hh

is is the correct ways of doing?

[Carlo Lazzaro]

Yalfal,
yes it is.
Please note that brackets are redundant:

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage i.msp i.year, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,518
Group variable: idcode                          Number of groups  =      4,711

R-sq:                                           Obs per group:
     within  = 0.1060                                         min =          1
     between = 0.0788                                         avg =        6.1
     overall = 0.0722                                         max =         15

                                                F(15,4710)        =      69.81
corr(u_i, Xb)  = 0.0283                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,711 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       1.msp |   .0025304   .0073558     0.34   0.731    -.0118904    .0169512
             |
        year |
         69  |   .0869055   .0104597     8.31   0.000     .0663996    .1074114
         70  |   .0725606   .0107678     6.74   0.000     .0514506    .0936706
         71  |   .1240816   .0114248    10.86   0.000     .1016837    .1464796
         72  |   .1356594   .0124313    10.91   0.000     .1112882    .1600306
         73  |   .1506002   .0125345    12.01   0.000     .1260268    .1751736
         75  |    .165097    .012694    13.01   0.000     .1402108    .1899832
         77  |   .2213591   .0131519    16.83   0.000     .1955752    .2471431
         78  |   .2570069   .0136809    18.79   0.000      .230186    .2838278
         80  |    .264297   .0139082    19.00   0.000     .2370305    .2915636
         82  |    .284492   .0139396    20.41   0.000     .2571638    .3118202
         83  |   .3089943   .0143706    21.50   0.000     .2808212    .3371674
         85  |   .3596244   .0140079    25.67   0.000     .3321623    .3870865
         87  |   .3765222   .0144541    26.05   0.000     .3481855     .404859
         88  |   .4348184   .0156146    27.85   0.000     .4042064    .4654304
             |
       _cons |   1.443117   .0105433   136.88   0.000     1.422447    1.463787
-------------+----------------------------------------------------------------
     sigma_u |  .40816356
     sigma_e |  .30286574
         rho |  .64491395   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. test 1.msp

 ( 1)  1.msp = 0

       F(  1,  4710) =    0.12
            Prob > F =    0.7309

[Yalfal Temesgen]

Dear carlo,

Thank you for the detail example and Here is my result

. xtreg nonfarm_income i.Sex_hh, fe vce(cluster HHID_Panel)

Fixed-effects (within) regression Number of obs = 9,717
Group variable: HHID_Panel Number of groups = 3,239

R-sq: Obs per group:
within = 0.0000 min = 3
between = 0.0000 avg = 3.0
overall = 0.0000 max = 3

F(1,3238) = 0.68
corr(u_i, Xb) = -0.0196 Prob > F = 0.4107

(Std. Err. adjusted for 3,239 clusters in HHID_Panel)
------------------------------------------------------------------------------
| Robust
nonfarm_in~e | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.Sex_hh | -5665.164 6885.619 -0.82 0.411 -19165.78 7835.448
_cons | 5863.905 1677.294 3.50 0.000 2575.241 9152.569
-------------+----------------------------------------------------------------
sigma_u | 108823.74
sigma_e | 181372.37
rho | .26470703 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.
end of do-file

. test 1.Sex_hh

( 1) 1.Sex_hh = 0

F( 1, 3238) = 0.68
Prob > F = 0.4107


Thank you again

[Carlo Lazzaro]

Yalfal:
as reported in -xtreg- outcome table, -test- highlighgts that, other things being equal, -gender- does not expain variation in the regressand.
But I do think that you have more relevant issues with your model:
- lack of informative predictors (it is hard to believe that -gender- is the only predictor of the data generating process you're investigating);
- as aconsequence of what above, your model is misspecified.
The chunks of code in the following toy-example (that elaborated on the previous one) can be tweaked to your code to test whether your model is (as I would bet) misspecified:

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage i.msp i.year, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,518
Group variable: idcode                          Number of groups  =      4,711

R-sq:                                           Obs per group:
     within  = 0.1060                                         min =          1
     between = 0.0788                                         avg =        6.1
     overall = 0.0722                                         max =         15

                                                F(15,4710)        =      69.81
corr(u_i, Xb)  = 0.0283                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,711 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       1.msp |   .0025304   .0073558     0.34   0.731    -.0118904    .0169512
             |
        year |
         69  |   .0869055   .0104597     8.31   0.000     .0663996    .1074114
         70  |   .0725606   .0107678     6.74   0.000     .0514506    .0936706
         71  |   .1240816   .0114248    10.86   0.000     .1016837    .1464796
         72  |   .1356594   .0124313    10.91   0.000     .1112882    .1600306
         73  |   .1506002   .0125345    12.01   0.000     .1260268    .1751736
         75  |    .165097    .012694    13.01   0.000     .1402108    .1899832
         77  |   .2213591   .0131519    16.83   0.000     .1955752    .2471431
         78  |   .2570069   .0136809    18.79   0.000      .230186    .2838278
         80  |    .264297   .0139082    19.00   0.000     .2370305    .2915636
         82  |    .284492   .0139396    20.41   0.000     .2571638    .3118202
         83  |   .3089943   .0143706    21.50   0.000     .2808212    .3371674
         85  |   .3596244   .0140079    25.67   0.000     .3321623    .3870865
         87  |   .3765222   .0144541    26.05   0.000     .3481855     .404859
         88  |   .4348184   .0156146    27.85   0.000     .4042064    .4654304
             |
       _cons |   1.443117   .0105433   136.88   0.000     1.422447    1.463787
-------------+----------------------------------------------------------------
     sigma_u |  .40816356
     sigma_e |  .30286574
         rho |  .64491395   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict fitted, xb
(16 missing values generated)

. g sq_fitted=fitted^2
(16 missing values generated)

. xtreg ln_wage i.msp i.year fitted sq_fitted , fe vce(cluster idcode)
note: fitted omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =     28,518
Group variable: idcode                          Number of groups  =      4,711

R-sq:                                           Obs per group:
     within  = 0.1097                                         min =          1
     between = 0.0781                                         avg =        6.1
     overall = 0.0725                                         max =         15

                                                F(16,4710)        =      68.97
corr(u_i, Xb)  = 0.0213                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,711 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       1.msp |   .6518011   .0937206     6.95   0.000     .4680649    .8355374
             |
        year |
         69  |   20.09825   2.903486     6.92   0.000     14.40606    25.79045
         70  |   16.69646   2.411894     6.92   0.000     11.96802     21.4249
         71  |   29.05008     4.1968     6.92   0.000     20.82239    37.27777
         72  |   31.88262   4.606077     6.92   0.000     22.85255    40.91268
         73  |   35.56855   5.138789     6.92   0.000     25.49412    45.64298
         75  |   39.17903   5.660572     6.92   0.000     28.08166     50.2764
         77  |   53.50018   7.730238     6.92   0.000     38.34529    68.65506
         78  |   62.82777   9.078397     6.92   0.000     45.02986    80.62567
         80  |   64.75995   9.357575     6.92   0.000     46.41472    83.10517
         82  |   70.15422   10.13723     6.92   0.000      50.2805    90.02794
         83  |   76.78349   11.09553     6.92   0.000     55.03106    98.53591
         85  |   90.77676   13.11868     6.92   0.000     65.05801    116.4955
         87  |   95.53557   13.80649     6.92   0.000     68.46839    122.6027
         88  |   112.2912   16.22976     6.92   0.000     80.47332    144.1092
             |
      fitted |          0  (omitted)
   sq_fitted |  -77.39406   11.22923    -6.89   0.000     -99.4086   -55.37952
       _cons |   162.5849   23.38089     6.95   0.000     116.7474    208.4223
-------------+----------------------------------------------------------------
     sigma_u |  .40811829
     sigma_e |  .30225362
         rho |  .64578926   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. test sq_fitted

 ( 1)  sq_fitted = 0

       F(  1,  4710) =   47.50
            Prob > F =    0.0000

.

The -test- outcome proves the model to be misspecified.

[Yalfal Temesgen]

Carlo:
Households in the study sub-sample exhibited marked heterogeneity in terms of
sex, residence, literacy and whether a household had a single member. what i was try to see is
the differences in mean incomes (farm income, nonfarm income and total income) by sex, residence, literacy and whether a household had a single member, to confirm the heterogeneity.

[Yalfal Temesgen]

Here is my result based on your example
. predict fitted, xb

. g sq_fitted=fitted^2

. xtreg nonfarm_income i.Sex_hh i.Wave fitted sq_fitted, fe vce(cluster HHID_Panel)

Fixed-effects (within) regression Number of obs = 9,717
Group variable: HHID_Panel Number of groups = 3,239

R-sq: Obs per group:
within = 0.0009 min = 3
between = 0.0000 avg = 3.0
overall = 0.0003 max = 3

F(5,3238) = 1.11
corr(u_i, Xb) = -0.0257 Prob > F = 0.3521

(Std. Err. adjusted for 3,239 clusters in HHID_Panel)
------------------------------------------------------------------------------
| Robust
nonfarm_in~e | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.Sex_hh | 964.7182 8346.265 0.12 0.908 -15399.78 17329.21
|
Wave |
2 | 140.4106 2246.216 0.06 0.950 -4263.738 4544.559
3 | 185.2449 7342.39 0.03 0.980 -14210.96 14581.45
|
fitted | 1.383383 .8698441 1.59 0.112 -.3221172 3.088884
sq_fitted | -.0000339 .0000394 -0.86 0.390 -.0001112 .0000434
_cons | -269.862 3429.959 -0.08 0.937 -6994.972 6455.248
-------------+----------------------------------------------------------------
sigma_u | 108879.53
sigma_e | 181351.82
rho | .26495072 (fraction of variance due to u_i)
------------------------------------------------------------------------------

. test sq_fitted

( 1) sq_fitted = 0

F( 1, 3238) = 0.74
Prob > F = 0.3896

is that the -test- outcome proves the model misspecified?

[Carlo Lazzaro]

Yalfal:
no, the opposite holds: your model seems well specified (or, more technically speaking, the functional form of the regressand seems to be correctly specified; see -linktest- entry in Stata .pdf manula for further details).

[Yalfal Temesgen]

Carlo
thank you very much and I am also comparing the Coefficients of variations of income (total income, nonfarm income and farm income) across percentiles, did you have suggestion, please

[Carlo Lazzaro]

Yalfal:
hwhy not considering a panel data quantile regression instead of looking at CV (that has lost most of its appealing from 2000 on; https://www.routledge.com/Principles.../9781138593145).