For my master thesis, I am analyzing the impact of the legal system of a country (i.e. common law versus civil law) on the earnings' forecast accuracy of security analysts. My data is composed of 628 firms in 16 countries during 5 years. My model is as follows:
EPAi,t = β0 + β1*LegalSysti,t + β2*LnSizei,t+ β3*Coveri,t + β4*Lossi,t + β5*Flevi,t + β6*Roei,t + εi,t, where, i and t correspond to the firm i at the year t ; and LegalSyst and Loss are dummy variables.
I ran some diagnostic tests and it seems that a fixed effect model is appropriate. But the problem is that my variable of interest (LegalSyst) is omitted (collinearity + time-invariant, I suppose) with the fixed effect model. Therefore, I cannot examine the effect of the legal system on my dependant variable. I have seen some threads suggesting going for "hybrid models". But I don't know how to perform it because I have basic knowledges of econometrics and Stata/SE 16.0.
(1) Is there another alternatives to fix the problem of omitted variable in order to get an estimated coefficient value ?
I tried to run "xtset CountryID Year" but I got the message "repeated time values within panel data" because I have multiple firms for every Country and Year. Therefore, I went with the following code:
Code:
. xtset EnterpriseID Year
panel variable: EnterpriseID (strongly balanced)
time variable: Year, 2014 to 2018
delta: 1 unit(3) Furthermore, for example If I want to analyze jointly 2 common law and 2 civil law countries in my sample, should I use "cluster" ? If yes, could you suggest me the syntax code ? (Note: CountryID is the variable that refers to the country. It can take the value from 1 to 16 depending on the corresponding country)
Code:
. xtreg EPA LegalSyst LnSize Cover Loss Flev Roe, fe
note: LegalSyst omitted because of collinearity
Fixed-effects (within) regression Number of obs = 3,140
Group variable: EnterpriseID Number of groups = 628
R-sq: Obs per group:
within = 0.0704 min = 5
between = 0.0447 avg = 5.0
overall = 0.0331 max = 5
F(5,2507) = 37.99
corr(u_i, Xb) = -0.7049 Prob > F = 0.0000
------------------------------------------------------------------------------
EPA | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
LegalSyst | 0 (omitted)
LnSize | -.021504 .006088 -3.53 0.000 -.033442 -.009566
Cover | -.0022359 .0005592 -4.00 0.000 -.0033324 -.0011394
Loss | .0692554 .0056121 12.34 0.000 .0582506 .0802602
Flev | -.0004474 .0008064 -0.55 0.579 -.0020287 .0011339
Roe | -.0012693 .0010576 -1.20 0.230 -.0033431 .0008044
_cons | .2085857 .0481035 4.34 0.000 .114259 .3029124
-------------+----------------------------------------------------------------
sigma_u | .07222027
sigma_e | .06471257
rho | .55466326 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(627, 2507) = 2.30 Prob > F = 0.0000Code:
estimates store fixed
Code:
. xtreg EPA LegalSyst LnSize Cover Loss Flev Roe, re
Random-effects GLS regression Number of obs = 3,140
Group variable: EnterpriseID Number of groups = 628
R-sq: Obs per group:
within = 0.0601 min = 5
between = 0.2990 avg = 5.0
overall = 0.1551 max = 5
Wald chi2(6) = 411.26
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
EPA | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
LegalSyst | .0219064 .0046445 4.72 0.000 .0128033 .0310094
LnSize | .0045568 .0013606 3.35 0.001 .0018902 .0072235
Cover | -.0009433 .0002839 -3.32 0.001 -.0014997 -.0003869
Loss | .0848819 .0044507 19.07 0.000 .0761587 .0936052
Flev | .0006721 .0007244 0.93 0.353 -.0007476 .0020919
Roe | -.0008226 .0009642 -0.85 0.394 -.0027124 .0010673
_cons | -.0183203 .0088933 -2.06 0.039 -.0357508 -.0008897
-------------+----------------------------------------------------------------
sigma_u | .03070813
sigma_e | .06471257
rho | .18379327 (fraction of variance due to u_i)
------------------------------------------------------------------------------Code:
estimates store random
Code:
. hausman fixed random
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference S.E.
-------------+----------------------------------------------------------------
LnSize | -.021504 .0045568 -.0260608 .005934
Cover | -.0022359 -.0009433 -.0012926 .0004818
Loss | .0692554 .0848819 -.0156266 .0034186
Flev | -.0004474 .0006721 -.0011196 .0003544
Roe | -.0012693 -.0008226 -.0004468 .0004344
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg
Test: Ho: difference in coefficients not systematic
chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 58.99
Prob>chi2 = 0.0000Code:
. xtreg EPA LegalSyst LnSize Cover Loss Flev Roe i.Year,fe
note: LegalSyst omitted because of collinearity
Fixed-effects (within) regression Number of obs = 3,140
Group variable: EnterpriseID Number of groups = 628
R-sq: Obs per group:
within = 0.0736 min = 5
between = 0.0412 avg = 5.0
overall = 0.0310 max = 5
F(9,2503) = 22.10
corr(u_i, Xb) = -0.7333 Prob > F = 0.0000
------------------------------------------------------------------------------
EPA | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
LegalSyst | 0 (omitted)
LnSize | -.0249718 .0068277 -3.66 0.000 -.0383603 -.0115833
Cover | -.001942 .0005912 -3.28 0.001 -.0031013 -.0007827
Loss | .0696952 .0056099 12.42 0.000 .0586946 .0806957
Flev | -.0004988 .000807 -0.62 0.537 -.0020813 .0010837
Roe | -.0012968 .001058 -1.23 0.220 -.0033715 .000778
|
Year |
2015 | .0057079 .0036651 1.56 0.120 -.0014791 .0128949
2016 | .0094027 .0036612 2.57 0.010 .0022234 .016582
2017 | .0093605 .003829 2.44 0.015 .0018522 .0168688
2018 | .0077649 .0039683 1.96 0.050 -.0000166 .0155465
|
_cons | .2259927 .0527099 4.29 0.000 .1226332 .3293522
-------------+----------------------------------------------------------------
sigma_u | .07569337
sigma_e | .06465357
rho | .57817704 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(627, 2503) = 2.31 Prob > F = 0.0000Code:
. testparm i.Year
( 1) 2015.Year = 0
( 2) 2016.Year = 0
( 3) 2017.Year = 0
( 4) 2018.Year = 0
F( 4, 2503) = 2.14
Prob > F = 0.0729Code:
. xttest3 Modified Wald test for groupwise heteroskedasticity in fixed effect regression model H0: sigma(i)^2 = sigma^2 for all i chi2 (628) = 9.4e+08 Prob>chi2 = 0.0000
I would very appreciate if you could help me. Thanks in advance.
Thanh
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