Fama-Macbeth regression (problems)

[Erling Nisja]

Hi!
I am currently working on my master thesis and are trying to conduct a Fama-Macbeth regression. I want to use different gold mining stocks as the dependent variables, and the log changes in the gold price as the independent variable. I am able to do the regression, but only get "0(omitted)" for the independent variable:

Fama-MacBeth Estimation

panel variable: firmid Number of obs = 11280
time variable: date Number of date(s) = 120
R-squared = 0.0000
------------------------------------------------------------------------------
ERP | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
GOLD | 0 (omitted)
_cons | -.0076154 .0118524 -0.64 0.522 -.0310823 .0158516
------------------------------------------------------------------------------
120 date regressions


I suspect there could be something wrong with our data, or our sorting of data. Here is a samle:

firmid	year	Gold	ERP
1	1	-0.019431725	-0.0201138
1	2	0.035683520	-0.0176034
1	3	0.017367882	-0.0386295
1	4	-0.015468690	-0.0204544
1	5	0.022587536	-0.0324364
1	6	-0.008195546	0.04616726
1	7	-0.017356307	0.00836654
1	8	0.011955348	0.08899398
1	9	0.011144885	-0.0088698
1	10	0.105910796	0.23437753
1	11	0.057463168	0.02708793
1	12	-0.005003019	-0.036941
1	13	0.059881162	0.021038
1	14	0.085130960	0.1895452
1	15	0.074990192	0.04909454
1	16	-0.109518762	-0.2461444
1	17	-0.033997609	-0.1161874
1	18	0.053308553	0.07388602
1	19	0.050238875	0.13873372
1	20	-0.030692120	-0.1344284
1	21	-0.111466902	-0.1570298
1	22	0.070959272	0.07244675
1	23	-0.187802900	-0.5179759
1	24	0.061161992	0.16708275
1	25	0.108367687	0.33464153
1	26	0.060037715	-0.0215995
1	27	0.018558628	-0.2518928
1	28	-0.010237710	0.19148002
1	29	-0.042936447	-0.1558742
1	30	0.101315711	0.24459425
1	31	-0.054541318	-0.0567587
1	32	0.029922781	0.03109677
1	33	-0.003934844	-0.0298609
1	34	0.057754006	0.03170587
1	35	0.036250681	0.00905472
1	36	0.121169433	0.23250078
1	37	-0.073423431	-0.1569372
1	38	-0.001186835	-0.0759875
1	39	0.021686944	0.05197144
1	40	0.005837936	0.02554202
1	41	0.047382079	0.08185457
1	42	0.038940325	-0.0055025
1	43	-0.007281685	0.01177018
1	44	-0.027598580	-0.0512879
1	45	0.049165933	0.10148392
1	46	0.057980014	0.03626628
1	47	0.025583200	0.02176512
1	48	0.025074764	0.08728586
1	49	0.021735181	0.00276466
1	50	-0.062154752	-0.0860563
1	51	0.065795050	0.1080543
1	52	0.001418729	-0.0476349
1	53	0.075005928	-0.0321241
1	54	0.006166648	-0.0489444
1	55	-0.039769625	-0.0543341
1	56	0.093800061	0.06974765
1	57	0.113070937	0.07324308
1	58	-0.102180718	-0.1116895
1	59	0.031547793	0.06512512
1	60	0.025153997	0.06835422
1	61	-0.102858293	-0.1545062
1	62	0.105199189	0.08486806
1	63	-0.020847627	-0.0251367
1	64	-0.018148100	-0.0831247
1	65	-0.011923340	-0.0891899
1	66	-0.031196210	0.03568007
1	67	-0.008188135	-0.1125678
1	68	0.003366870	-0.1424405
1	69	0.054835924	0.17047807
1	70	0.048014569	0.08406657
1	71	-0.034283840	-0.1325591
1	72	-0.000687321	-0.0850906
1	73	-0.031855841	0.03782254
1	74	0.003836449	-0.0836839
1	75	-0.055623441	-0.0910301
1	76	0.010893814	-0.0130594
1	77	-0.098726210	-0.4125793
1	78	-0.025804222	0.10793495
1	79	-0.122232396	-0.3388198
1	80	0.052798369	0.09737778
1	81	0.058264315	0.1303121
1	82	-0.076846787	-0.060349
1	83	0.015122551	-0.0011349
1	84	-0.064775717	-0.1475265
1	85	-0.016333161	0.12617632
1	86	0.045360259	0.09046977
1	87	0.068853610	0.06028646
1	88	-0.055297677	-0.1361997
1	89	0.000881631	-0.0445955
1	90	-0.029158892	-0.0733773
1	91	0.064968501	0.13452788
1	92	-0.026178069	0.00109057
1	93	-0.005732051	0.00981948
1	94	-0.058700917	-0.2205723
1	95	-0.037492904	-0.2130504
1	96	0.022336194	0.0402766
1	97	-0.007817099	-0.1436218
1	98	0.069395714	0.18153773
1	99	-0.050665181	-0.0101532
1	100	-0.006382215	-0.0605923
1	101	-0.023571533	0.08457989
1	102	0.019123948	-0.1005432
1	103	-0.021419670	-0.1231994
1	104	-0.069160716	-0.4445195
1	105	0.043430954	0.00742665
1	106	-0.022608949	-0.0866074
1	107	0.017925306	0.22603891
1	108	-0.063028221	-0.0209924
1	109	-0.003392271	-0.0294913
1	110	0.058825708	0.31062873
1	111	0.090420986	0.27570347
1	112	-0.017172998	0.02806701
1	113	0.065415543	0.33638057
1	114	-0.067322704	-0.1231231
1	115	0.098979411	0.27302902
1	116	0.010432158	0.00073342
1	117	-0.027988457	-0.2224693
1	118	-0.000746820	-0.0235115
1	119	-0.017642947	0.05679867
1	120	-0.098512851	-0.203778
2	1	-0.019431725	-0.0407056
2	2	0.035683520	-0.0041583
2	3	0.017367882	-0.0182022
2	4	-0.015468690	-0.0549337
2	5	0.022587536	-0.0280577
2	6	-0.008195546	0.00299388
2	7	-0.017356307	-0.0460065
2	8	0.011955348	0.03752575
2	9	0.011144885	0.01263126
2	10	0.105910796	0.08230174
2	11	0.057463168	0.06984858
2	12	-0.005003019	0.00689
2	13	0.059881162	-0.0259781
2	14	0.085130960	0.08481894
2	15	0.074990192	-0.0177556
2	16	-0.109518762	-0.1576084
2	17	-0.033997609	-0.0366984
2	18	0.053308553	0.09824646
2	19	0.050238875	0.10925096
2	20	-0.030692120	-0.1226396
2	21	-0.111466902	-0.0483519
2	22	0.070959272	-0.1559209
2	23	-0.187802900	-0.384109
2	24	0.061161992	0.1378668
2	25	0.108367687	0.29862568
2	26	0.060037715	-0.0333823
2	27	0.018558628	-0.0387225
2	28	-0.010237710	0.22404896
2	29	-0.042936447	-0.2020577
2	30	0.101315711	0.21426983
2	31	-0.054541318	-0.1291548
2	32	0.029922781	-0.0082184
2	33	-0.003934844	-0.0405501
2	34	0.057754006	0.053754
2	35	0.036250681	0.02719548
2	36	0.121169433	0.24481792
2	37	-0.073423431	-0.1625734
2	38	-0.001186835	-0.0381723
2	39	0.021686944	0.09894132
2	40	0.005837936	0.05085164
2	41	0.047382079	0.03735062
2	42	0.038940325	-0.0054101
2	43	-0.007281685	0.07646839
2	44	-0.027598580	-0.0593014
2	45	0.049165933	0.08134719
2	46	0.057980014	0.05408182
2	47	0.025583200	-0.0393499
2	48	0.025074764	-0.0262848
2	49	0.021735181	0.02376237
2	50	-0.062154752	-0.0780639
2	51	0.065795050	-0.0075184
2	52	0.001418729	-0.03117
2	53	0.075005928	0.0571724
2	54	0.006166648	-0.0335935
2	55	-0.039769625	-0.0352921
2	56	0.093800061	0.02904932
2	57	0.113070937	0.12135452
2	58	-0.102180718	0.01271651
2	59	0.031547793	0.03661329
2	60	0.025153997	0.04729951
2	61	-0.102858293	-0.1368462
2	62	0.105199189	0.01828626
2	63	-0.020847627	-0.0240681
2	64	-0.018148100	-0.1355142
2	65	-0.011923340	-0.0811731
2	66	-0.031196210	0.04573794
2	67	-0.008188135	-0.0366975
2	68	0.003366870	-0.0879513
2	69	0.054835924	0.13199169
2	70	0.048014569	0.09440712
2	71	-0.034283840	-0.0455959
2	72	-0.000687321	-0.152882
2	73	-0.031855841	0.01648392
2	74	0.003836449	-0.0606009
2	75	-0.055623441	-0.0983012
2	76	0.010893814	0.04365526
2	77	-0.098726210	-0.2390588
2	78	-0.025804222	0.06788311
2	79	-0.122232396	-0.1447425
2	80	0.052798369	-0.0197597
2	81	0.058264315	0.07106932
2	82	-0.076846787	-0.1550212
2	83	0.015122551	-0.0462825
2	84	-0.064775717	-0.0863984
2	85	-0.016333161	-0.0341559
2	86	0.045360259	-0.0913567
2	87	0.068853610	0.11700939
2	88	-0.055297677	-0.0076633
2	89	0.000881631	0.0450097
2	90	-0.029158892	-0.0828656
2	91	0.064968501	0.10498116
2	92	-0.026178069	0.00476495
2	93	-0.005732051	0.07230399
2	94	-0.058700917	-0.1632441
2	95	-0.037492904	-0.185219
2	96	0.022336194	0.02784287
2	97	-0.007817099	-0.0394492
2	98	0.069395714	0.28409592
2	99	-0.050665181	0.03057395
2	100	-0.006382215	-0.1306279
2	101	-0.023571533	0.15352171
2	102	0.019123948	0.02532945
2	103	-0.021419670	-0.1609913
2	104	-0.069160716	-0.3426554
2	105	0.043430954	0.01869508
2	106	-0.022608949	-0.0546651
2	107	0.017925306	0.21451229
2	108	-0.063028221	-0.0654103
2	109	-0.003392271	-0.0221077
2	110	0.058825708	0.13288656
2	111	0.090420986	0.21125279
2	112	-0.017172998	0.04714075
2	113	0.065415543	0.25455638
2	114	-0.067322704	-0.0503848
2	115	0.098979411	0.21099244
2	116	0.010432158	0.0903092
2	117	-0.027988457	-0.1135175
2	118	-0.000746820	-0.034521
2	119	-0.017642947	-0.0041448
2	120	-0.098512851	-0.1623982
3	1	-0.019431725	-0.0791206
3	2	0.035683520	-0.0161854
3	3	0.017367882	-0.0774433
3	4	-0.015468690	-0.0573347
3	5	0.022587536	-0.0309149
3	6	-0.008195546	0.01489949
3	7	-0.017356307	-0.0152531
3	8	0.011955348	0.01697372

.........

We have been stuck for several days, and all help are really appreciated.

[Attaullah Shah]

Fama and McBeth regressions are cross-sectional regressions estimated in each time period. If you look at your data, first three periods of firmid 1 and 2 as an example, the values are the same, which might be the case for other firmids as well. Regressing ERP on a constant, regression will omit the constant. No surprise at all.

 
old
ERP

1
1
-0.019431725
-0.0201138

1
2
0.035683520
-0.0176034

1
3
0.017367882
-0.0386295


    
2
1
-0.019431725
-0.0407056

2
2
0.035683520
-0.0041583

2
3
0.017367882
-0.0182022

2
4
-0.015468690
-0.0549337

[Erling Nisja]

Thank you so much for your quick reply.
How do you suggest we do a Fama Macbeth regression with macro variables (Gold price changes) ? All macro variables will only vary over time and not over firm. (Thats why they are constant over firms, right?)

[Attaullah Shah]

Yes, this is true that macro variables are constant across firms, but not across time periods, therefore Fama and Mcbeth regression on macro variables in a single country is a bad idea. You might consider time series or panel regression instead. FB regression lends itself more easily to cases where the variable varies across cross-sectional units and is relatively constant over time within each cross-sectional unit

[Erling Nisja]

Okey, thank you. I hear what you are saying, but at the same time i have seen several studies where they use macro-factors (only varying across time, and not firms) in Fama Macbeth regression. We want to check if there is a premium for investing in gold stocks with a high gold beta, similar to the CAPM beta and risk premium. Didn't Fama-French test CAPM using the Fama-Macbeth approach?

Like the study in this thesis:
http://dare.uva.nl/cgi/arno/show.cgi?fid=635358

Thank you so much for the help, sir.

[Attaullah Shah]

The said thesis as well as Fama and French first calculate betas, then in the second stage (cross-sectional )regression, betas are used as independent variables to explain observed returns.

[Erling Nisja]

Okey, so in our first step we do a time series regression and obtain n(number of firms) betas, and then use those betas to conduct t cross sectional regressions to get t gammas(beta to beta)?