Fama Macbeth regression with weighted coefficients

[Benedikt Dieker]

Hello statalist community

I am trying to run the following regression in stata:

where the excess return (EXRET) is my dependent variable, a proxy for difference of opinion (INCVOL) and a proxy for institutional ownership (INSOWN) are my independent variables, and I am controlling for the size effect (LnMV) and the market to book effect (LnMB).
i identifies the firm (permno) and q identifies the quarter (num_QUARTER).

I am trying to estimate each model by the calendar year-quarter (num_QUARTER) and output the precision-weighted Fama and Macbeth (1973) coefficient estimates, where the weights correspond to the number of observations available in each num_QUARTER.

Here is a sample of my data:

Example generated by -dataex-. For more info, type help dataex
clear
input double permno float(num_QUARTER EXRET ln_MV ln_MB) double INCVOL float INSOWN
10008 11 -3.613648 3.837628 .6660116 . 50.70855
10008 9 2.3320007 3.935141 .8268394 . 29.77759
10008 6 2.867223 3.898507 .8512741 . 34.233788
10008 8 .4817073 3.788159 .7337805 . 36.70713
10008 13 -.9682727 3.7018266 .4458091 . 44.39114
10008 7 5.464943 3.522456 .4682188 . 43.14516
10008 12 5.849236 3.432163 .2463477 . 51.50757
10008 10 -1.7264075 3.788159 .59201974 . 42.59423
10008 14 4.1000843 3.9286 .5639282 . 45.09671
10010 39 3.996558 3.979242 1.7785792 3.243112060436777 20.236296
10010 32 12.792796 4.535048 1.6222625 3.9632545293359813 8.989085
10010 35 .9209003 3.903807 1.8974736 3.730587269986754 10.883036
10010 12 -5.483268 2.555605 .6282953 . .3308768
10010 30 -1.7342974 4.343682 1.4674653 . 7.709942
10010 29 -5.497581 4.4030538 1.4837706 . 10.38042
10010 11 2.9390564 2.385821 .4960281 . 9.4157
10010 16 -2.424029 2.7355816 .6487922 . .7752287
10010 41 5.316243 4.3014655 2.079982 3.143430414516524 12.29525
10010 14 -4.1153455 2.859547 .8459778 . .4511957
10010 21 17.96718 2.906968 .6482305 . 1.549211
10010 25 -5.758246 4.707672 2.1232975 . 28.631784
10010 36 3.8106065 4.067744 2.003289 3.5763718828762605 6.736435
10010 27 4.899927 4.5394745 1.7059673 . 15.765204
10010 17 -3.61082 3.019382 .8926992 . .6788278
10010 28 -.9291086 4.6668105 1.7868258 . 11.099987
10010 33 -7.396168 4.2913423 1.3862462 3.882547117782703 7.857353
10010 38 -.49252 3.9549484 1.831729 3.340686017305362 16.595228
10010 22 -6.025785 4.436899 2.093364 . 12.177193
10010 42 -3.5942485 . . 3.2307917212785124 0
10010 31 11.832273 4.154188 1.278648 4.205261673947921 7.944925
10010 34 -1.1528807 4.011162 1.1025683 3.82539639632745 8.12151
10010 37 3.75514 4.4388576 2.2043371 3.4520890957179944 12.125244
10010 13 -3.490855 2.8352535 .8611723 . .3399007
10010 26 -22.12851 4.855687 2.1711104 . 24.2808
10010 40 -14.593055 3.996084 1.7676836 3.1438398217238763 12.346858
10010 19 3.907184 2.623242 .4089416 . .9546611
10010 20 4.5179973 2.7089984 .4877318 . 1.0325191
10010 23 6.075223 3.926768 1.467436 . 8.285469
10010 18 .3539547 2.9566655 .7894421 . 1.0134529
10010 15 -3.5315084 2.7891355 .7392515 . .47340825
10010 24 -1.8002476 4.501533 1.9816613 . 14.55777
10011 51 -3.56842 4.446916 .5785106 2.334583952508747 14.916426
10011 46 6.99464 4.776778 1.0684394 . 20.15268
10011 37 -2.8352714 3.5961645 1.5601523 . 2.707788
10011 44 3.627314 4.579211 .9194773 . 12.897806
10011 42 -1.09913 4.455161 1.7652068 . 3.182189
10011 38 -3.223763 4.1214304 2.0016873 . 2.7191024
10011 50 -5.325699 4.463703 .6218236 2.4463803968178697 19.195
10011 52 -.11500657 4.491021 .5861638 2.25453858594281 39.19349
10011 47 -7.960851 4.6077433 .8482187 2.717672115669003 17.707294
10011 36 3.944739 3.699705 1.7451184 . 2.3
10011 41 3.076095 4.331108 1.7054982 . 2.8928895
10011 40 -1.430903 4.5160847 1.9600986 . 2.913332
10011 48 .23876584 4.4052424 .6102028 2.67519623302301 25.705116
10011 43 7.620689 4.475688 1.6873487 . 5.335223
10011 35 -13.390417 3.2955816 1.4056373 . 1.879015
10011 49 -3.2104526 4.1643367 .3479661 2.532721266515545 34.033783
10011 39 4.7234454 3.935095 1.64438 . 2.679057
10015 4 -2.116692 3.6982975 1.1322718 . 7.276555
10015 1 .2713797 2.975351 .7527837 . 8.153242
10015 2 -.029075697 3.2543395 .836909 . 3.864492
10015 3 -13.90464 3.461979 .9384125 . 15.327478
10016 22 2.715161 6.139966 .3224233 . 0
10016 31 .3153377 5.626577 -.3344666 .7665897111991958 0
10016 60 2.0315082 5.812871 1.2374282 2.7224301578201575 72.10319
10016 63 10.072694 5.704714 1.0895839 .6080836900541465 78.52301
10016 15 5.258823 6.15718 .25509027 . .
end
[/CODE]

For some quarters, data for INCVOL is missing, whilst for INSOWN, some quarters are missing and some are 0, by design.

I have tried to run the following code, but I do not think it is correct:

xtset permno num_QUARTER
egen NQTR = count(num_QUARTER) if !mi(EXRET , ln_MV ,ln_MB ,INCVOL ,INSOWN), by(num_QUARTER)
foreach var in EXRET ln_MV ln_MB INCVOL INSOWN {
    g w`var' = `var'*sqrt(NQTR)
}
byso num_QUARTER: asreg wEXRET wln_MV wln_MB wINCVOL wINSOWN, fmb noconstant

Would appreciate any input, thanks in advance.

[George Ford]

Not exactly clear what's up here, but a thought.

You're estimating by quarter using a N weight by quarter. It seems to me this might make more sense if you had a single regression producing a single set of coefficients, where the quarters with more data get weighted more heavily.

I'm not sure what your getting by the byso num_QUARTER: asreg, unless you plan on aggregating in some way (and then, I'd estimate without the weight and use the weight in the aggregation).

xtfmb is an option (ssc install xtfmb), which allows aweights

[Benedikt Dieker]

appreciated, thanks.