Panel data. Variable change with cross section but fix over the years for each cross section

[waseem sajjad]

Dear All.

i am the new to stata . i am working on my research as under .
I am using the panel data model with 120 cross sections (individuals) who are following 40 firms for 9 years of data (2014 to 2022). My data has following data .

dependent variable:Y
performance (Yijt) of financial analysts.

independent varaiable :
experience (ijt) X1
qualification (ijt) X2
discretionary accruals (jt) X3
ownership concentration (jt) X4
Echange rate volatility (t) X5

Control variables

Horizon( ijt) cv1
brokersize(ijt) cv2
Firm size(jt), cv3
leverage(jt) cv4
coverage(jt) cv5
roe(jt). Cv6


My model selection is as under as per BPLM test ols is better than re model.
as per hausman test is fe better over re. so i selected fe for my model . Then to correct heteroskedasticity, xtreg ,fe vce(robust) is used .


Following problems
xtset i t
Model: xtreg y x1 x2 x3 x4 x5 cv1 cv2 cv3 cv4 cv5 cv6 i.year, fe vce(robust) . (I consider only individual and time effect)

1. My qualification variable omitted. (NOTE : QUAKIFICATION IS DICHOTOMOUS VARIABLE. I.E CFA(1) and non CFA(2). CFA is a professional certification for financial analysts.

2. If i use lsdv with time effect, individual effect with cluster at individual level, then it shows the coefficient .

regress y x1 x2 x3 x4 x5 cv1 cv2 cv3 cv4 cv5 cv6 i.panelid i.year, cluster (panelid)

3. If i use reghde command to consider fixed effects of i,j,t then exchange rate volatiliy is omitted.

Reghdfe Y x1 x2 x3 x4 x5 cv1 cv2 cv3 cv4 cv5 cv6 , absorb( panelid firm year) cluster (panelid)


Please if any one may help the model selection and ita output. I will be grateful.

[Carlo Lazzaro]

Waseem:
welcome to this forum.
The issue seems to rest on the fact that the omitted variables are time-invariant and, as such, they cannot be estimated by the -fe- estimator.
That said, I fail to get how you could get the -CFA- coefficient in 2), as it simply a different (and less efficient way) of going -fe-:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage age i.race if idcode<=3, fe
note: 2.race omitted because of collinearity.

Fixed-effects (within) regression               Number of obs     =         39
Group variable: idcode                          Number of groups  =          3

R-squared:                                      Obs per group:
     Within  = 0.3795                                         min =         12
     Between = 0.6496                                         avg =       13.0
     Overall = 0.1214                                         max =         15

                                                F(1,35)           =      21.40
corr(u_i, Xb) = -0.2960                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0307608   .0066489     4.63   0.000     .0172629    .0442588
             |
        race |
      Black  |          0  (omitted)
       _cons |   .8796702   .1939752     4.53   0.000     .4858795    1.273461
-------------+----------------------------------------------------------------
     sigma_u |  .30623358
     sigma_e |  .25645513
         rho |  .58777837   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(2, 35) = 17.07                      Prob > F = 0.0000

. reg ln_wage age i.race i.idcode if idcode<=3
note: 2.race omitted because of collinearity.

      Source |       SS           df       MS      Number of obs   =        39
-------------+----------------------------------   F(3, 35)        =     14.57
       Model |   2.8738157         3  .957938567   Prob > F        =    0.0000
    Residual |  2.30192326        35  .065769236   R-squared       =    0.5552
-------------+----------------------------------   Adj R-squared   =    0.5171
       Total |  5.17573896        38  .136203657   Root MSE        =    .25646

------------------------------------------------------------------------------
     ln_wage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0307608   .0066489     4.63   0.000     .0172629    .0442588
             |
        race |
      Black  |          0  (omitted)
             |
      idcode |
          2  |  -.3831397   .1049083    -3.65   0.001    -.5961148   -.1701645
          3  |  -.6053814   .1044625    -5.80   0.000    -.8174516   -.3933112
             |
       _cons |   1.230398   .1900956     6.47   0.000     .8444837    1.616313
------------------------------------------------------------------------------

.

Your third code is actually a different specification; therefore, no wonder that a different variable was omitted (by the way: are you sure that you need 3 different fixed effects for your research?).

[waseem sajjad]

Dead sir carlo,

Thank you for your response.

if CFA is omitted due to time invariant in fixed effect. Then what is the best possible way forward to study impact of CFA on performance. Like as under mentioned or any other way
1. Any other model considering CFA and other variables ?
2. To remove CFA from the main model and estimate other variables in fe estimator ?
3. Only run ttest to see mean differences anf its significance for CFA separarely?
4. Combine the experience and qualification to create index to estimate combine effect of experience and qualification. This option is suggested to change nature of qualification from time invariant to time variant. Is it would be ok?

Sir, for the third reghdfe is only if i consider the third effect(firm). But that is not necessary. Som studies considered firm effect and some studies did not in prior literature.

Thank you sir.

[Carlo Lazzaro]

Waseem:
if you're really interested in estimating the coefficient of the time-invariant predictor -CFA-, you may want to consider the Mundlak approach (see The Stata Blog » Fixed effects or random effects: The Mundlak approach).
Your option #4 does not take into account that -experience-might have a non-linear relationship with the regressand.
As far as your last point is concerned, I would stop at a two-way fixed effect.
Last but not least, Carlo is enough. Thanks.