gen gr_rate = D.lnuclms
reg lnunclms ez y1982-y1988
Given this model, either the within transformation or the FD transformation could be applied to difference out the fixed effects for cities. But it is inappropriate to apply –cluster- to make standard errors robust to within group (within city) correlation of the error terms because the number of groups is small, just 22 cities. That we do not have a number of groups sufficiently large to apply –cluster- makes the choice of estimation methods, within transformation or FD transformation, especially important. Which transformation is preferable here?
* Example generated by -dataex-. To install: ssc install dataex
clear
input int year long uclms byte(ez city) float(lnuclms gr_rate) byte(y1980 y1981 y1982 y1983 y1984 y1985 y1986 y1987 y1988) float u_hat
1980 166746 0 1 12.024227 . 1 0 0 0 0 0 0 0 0 .
1981 83561 0 1 11.333332 -.6908951 0 1 0 0 0 0 0 0 0 -.3692632
1982 158146 0 1 11.971274 .6379423 0 0 1 0 0 0 0 0 0 .1808147
1983 83572 0 1 11.333464 -.6378107 0 0 0 1 0 0 0 0 0 -.2830596
1984 45949 1 1 10.735288 -.598176 0 0 0 0 1 0 0 0 0 -.07752831
1985 48848 1 1 10.79647 .06118107 0 0 0 0 0 1 0 0 0 .05973202
1986 46570 1 1 10.748712 -.04775715 0 0 0 0 0 0 1 0 0 -.018279206
1987 47205 1 1 10.762255 .01354313 0 0 0 0 0 0 0 1 0 .28122693
1988 37953 1 1 10.544104 -.2181511 0 0 0 0 0 0 0 0 1 .12053338
1980 115279 0 2 11.65511 . 1 0 0 0 0 0 0 0 0 .
1981 78278 0 2 11.268022 -.3870888 0 1 0 0 0 0 0 0 0 -.06545687
1982 126389 0 2 11.74712 .4790983 0 0 1 0 0 0 0 0 0 .021970706
1983 79666 0 2 11.285598 -.4615221 0 0 0 1 0 0 0 0 0 -.106771
1984 41376 0 2 10.630456 -.6551418 0 0 0 0 1 0 0 0 0 -.3163717
1985 53905 0 2 10.894979 .26452255 0 0 0 0 0 1 0 0 0 .2630735
1986 42037 0 2 10.646305 -.24867344 0 0 0 0 0 0 1 0 0 -.2191955
1987 44151 0 2 10.69537 .04906559 0 0 0 0 0 0 0 1 0 .3167494
1988 27088 0 2 10.206846 -.4885244 0 0 0 0 0 0 0 0 1 -.14983997
1980 61046 0 3 11.019383 . 1 0 0 0 0 0 0 0 0 .
1981 60959 0 3 11.017957 -.0014266968 0 1 0 0 0 0 0 0 0 .3202052
1982 90064 0 3 11.408276 .3903189 0 0 1 0 0 0 0 0 0 -.066808745
1983 61609 0 3 11.028563 -.3797121 0 0 0 1 0 0 0 0 0 -.024960995
1984 41869 0 3 10.6423 -.3862629 0 0 0 0 1 0 0 0 0 -.04749275
1985 49353 0 3 10.806754 .1644535 0 0 0 0 0 1 0 0 0 .16300446
1986 38632 0 3 10.561836 -.24491787 0 0 0 0 0 0 1 0 0 -.21543993
1987 37350 0 3 10.52809 -.033747673 0 0 0 0 0 0 0 1 0 .23393613
1988 31182 0 3 10.347596 -.1804924 0 0 0 0 0 0 0 0 1 .15819207
1980 91152 0 4 11.420283 . 1 0 0 0 0 0 0 0 0 .
1981 47337 0 4 10.765047 -.6552362 0 1 0 0 0 0 0 0 0 -.3336043
1982 102228 0 4 11.53496 .7699137 0 0 1 0 0 0 0 0 0 .3127861
1983 59709 0 4 10.997238 -.5377226 0 0 0 1 0 0 0 0 0 -.18297148
1984 30062 0 4 10.311017 -.6862211 0 0 0 0 1 0 0 0 0 -.347451
1985 41624 0 4 10.636433 .3254156 0 0 0 0 0 1 0 0 0 .3239666
1986 33688 0 4 10.424897 -.21153545 0 0 0 0 0 0 1 0 0 -.1820575
1987 23357 0 4 10.058652 -.3662453 0 0 0 0 0 0 0 1 0 -.09856146
1988 17190 0 4 9.752083 -.3065691 0 0 0 0 0 0 0 0 1 .032115374
1980 183095 0 5 12.11776 . 1 0 0 0 0 0 0 0 0 .
1981 100892 0 5 11.521806 -.5959549 0 1 0 0 0 0 0 0 0 -.274323
1982 121593 0 5 11.708435 .1866293 0 0 1 0 0 0 0 0 0 -.2704983
1983 61597 0 5 11.028368 -.6800671 0 0 0 1 0 0 0 0 0 -.32531595
1984 63997 0 5 11.06659 .03822327 0 0 0 0 1 0 0 0 0 .3769934
1985 82141 1 5 11.316193 .24960136 0 0 0 0 0 1 0 0 0 .4300299
1986 54092 1 5 10.89844 -.4177513 0 0 0 0 0 0 1 0 0 -.3882734
1987 37084 1 5 10.52094 -.3775005 0 0 0 0 0 0 0 1 0 -.10981672
1988 28978 1 5 10.274292 -.2466488 0 0 0 0 0 0 0 0 1 .09203568
1980 117090 0 6 11.670698 . 1 0 0 0 0 0 0 0 0 .
1981 131495 0 6 11.786724 .11602592 0 1 0 0 0 0 0 0 0 .4376578
1982 190727 0 6 12.158598 .3718739 0 0 1 0 0 0 0 0 0 -.08525376
1983 172074 0 6 12.05568 -.10291767 0 0 0 1 0 0 0 0 0 .25183344
1984 113250 1 6 11.637353 -.4183273 0 0 0 0 1 0 0 0 0 .10232036
1985 112460 1 6 11.630353 -.00699997 0 0 0 0 0 1 0 0 0 -.008449022
1986 95065 1 6 11.462317 -.16803646 0 0 0 0 0 0 1 0 0 -.13855852
1987 112507 1 6 11.63077 .16845417 0 0 0 0 0 0 0 1 0 .436138
1988 73704 1 6 11.207812 -.4229584 0 0 0 0 0 0 0 0 1 -.0842739
1980 172782 0 7 12.059786 . 1 0 0 0 0 0 0 0 0 .
1981 161154 0 7 11.990116 -.06966972 0 1 0 0 0 0 0 0 0 .25196218
1982 356613 0 7 12.784407 .7942905 0 0 1 0 0 0 0 0 0 .3371629
1983 255142 0 7 12.449575 -.3348312 0 0 0 1 0 0 0 0 0 .01991987
1984 125848 1 7 11.74283 -.7067451 0 0 0 0 1 0 0 0 0 -.18609746
1985 124783 1 7 11.73433 -.0084991455 0 0 0 0 0 1 0 0 0 -.009948198
1986 106736 1 7 11.578114 -.15621758 0 0 0 0 0 0 1 0 0 -.12673964
1987 95935 1 7 11.471426 -.10668755 0 0 0 0 0 0 0 1 0 .16099626
1988 72338 1 7 11.189105 -.28232098 0 0 0 0 0 0 0 0 1 .0563635
1980 123567 0 8 11.72454 . 1 0 0 0 0 0 0 0 0 .
1981 84035 0 8 11.338988 -.3855505 0 1 0 0 0 0 0 0 0 -.06391859
1982 121736 0 8 11.70961 .3706217 0 0 1 0 0 0 0 0 0 -.08650593
1983 85812 0 8 11.359914 -.3496962 0 0 0 1 0 0 0 0 0 .005054951
1984 83180 0 8 11.328762 -.03115177 0 0 0 0 1 0 0 0 0 .3076184
1985 55967 1 8 10.932517 -.396245 0 0 0 0 0 1 0 0 0 -.2158165
1986 68651 1 8 11.13679 .20427418 0 0 0 0 0 0 1 0 0 .2337521
1987 33909 1 8 10.431436 -.7053556 0 0 0 0 0 0 0 1 0 -.4376718
1988 19190 1 8 9.862144 -.5692911 0 0 0 0 0 0 0 0 1 -.23060665
1980 164996 0 9 12.013677 . 1 0 0 0 0 0 0 0 0 .
1981 139598 0 9 11.846522 -.1671543 0 1 0 0 0 0 0 0 0 .1544776
1982 215534 0 9 12.280874 .4343519 0 0 1 0 0 0 0 0 0 -.022775693
1983 148060 0 9 11.905373 -.3755016 0 0 0 1 0 0 0 0 0 -.02075052
1984 107105 0 9 11.581565 -.3238077 0 0 0 0 1 0 0 0 0 .014962432
1985 86550 1 9 11.368478 -.2130871 0 0 0 0 0 1 0 0 0 -.03265859
1986 87191 1 9 11.375856 .007378578 0 0 0 0 0 0 1 0 0 .03685652
1987 50279 1 9 10.825343 -.55051327 0 0 0 0 0 0 0 1 0 -.28282946
1988 30843 1 9 10.336665 -.488678 0 0 0 0 0 0 0 0 1 -.1499935
1980 533598 0 10 13.187398 . 1 0 0 0 0 0 0 0 0 .
1981 435754 0 10 12.984833 -.2025652 0 1 0 0 0 0 0 0 0 .11906672
1982 667208 0 10 13.410857 .4260244 0 0 1 0 0 0 0 0 0 -.031103177
1983 545625 0 10 13.209687 -.20116997 0 0 0 1 0 0 0 0 0 .15358114
1984 340092 0 10 12.736972 -.4727154 0 0 0 0 1 0 0 0 0 -.13394523
1985 325797 0 10 12.69403 -.04294205 0 0 0 0 0 1 0 0 0 -.0443911
1986 303724 0 10 12.623875 -.070155144 0 0 0 0 0 0 1 0 0 -.0406772
1987 262512 0 10 12.478052 -.14582253 0 0 0 0 0 0 0 1 0 .12186129
1988 209103 0 10 12.250583 -.22746944 0 0 0 0 0 0 0 0 1 .11121503
1980 169747 0 11 12.042065 . 1 0 0 0 0 0 0 0 0 .
1981 95962 0 11 11.471707 -.5703573 0 1 0 0 0 0 0 0 0 -.2487254
1982 157129 0 11 11.964823 .4931154 0 0 1 0 0 0 0 0 0 .03598781
1983 67341 0 11 11.117524 -.8472986 0 0 0 1 0 0 0 0 0 -.4925475
1984 32549 0 11 10.390502 -.7270222 0 0 0 0 1 0 0 0 0 -.388252
1985 36576 0 11 10.507148 .11664581 0 0 0 0 0 1 0 0 0 .11519676
1986 65114 0 11 11.083895 .57674694 0 0 0 0 0 0 1 0 0 .6062249
1987 45005 0 11 10.71453 -.3693657 0 0 0 0 0 0 0 1 0 -.10168188
1988 29916 0 11 10.306149 -.4083805 0 0 0 0 0 0 0 0 1 -.06969604
1980 74306 0 12 11.215947 . 1 0 0 0 0 0 0 0 0 .
end
[/CODE]
reg lnunclms ez y1982-y1988
Given this model, either the within transformation or the FD transformation could be applied to difference out the fixed effects for cities. But it is inappropriate to apply –cluster- to make standard errors robust to within group (within city) correlation of the error terms because the number of groups is small, just 22 cities. That we do not have a number of groups sufficiently large to apply –cluster- makes the choice of estimation methods, within transformation or FD transformation, especially important. Which transformation is preferable here?
* Example generated by -dataex-. To install: ssc install dataex
clear
input int year long uclms byte(ez city) float(lnuclms gr_rate) byte(y1980 y1981 y1982 y1983 y1984 y1985 y1986 y1987 y1988) float u_hat
1980 166746 0 1 12.024227 . 1 0 0 0 0 0 0 0 0 .
1981 83561 0 1 11.333332 -.6908951 0 1 0 0 0 0 0 0 0 -.3692632
1982 158146 0 1 11.971274 .6379423 0 0 1 0 0 0 0 0 0 .1808147
1983 83572 0 1 11.333464 -.6378107 0 0 0 1 0 0 0 0 0 -.2830596
1984 45949 1 1 10.735288 -.598176 0 0 0 0 1 0 0 0 0 -.07752831
1985 48848 1 1 10.79647 .06118107 0 0 0 0 0 1 0 0 0 .05973202
1986 46570 1 1 10.748712 -.04775715 0 0 0 0 0 0 1 0 0 -.018279206
1987 47205 1 1 10.762255 .01354313 0 0 0 0 0 0 0 1 0 .28122693
1988 37953 1 1 10.544104 -.2181511 0 0 0 0 0 0 0 0 1 .12053338
1980 115279 0 2 11.65511 . 1 0 0 0 0 0 0 0 0 .
1981 78278 0 2 11.268022 -.3870888 0 1 0 0 0 0 0 0 0 -.06545687
1982 126389 0 2 11.74712 .4790983 0 0 1 0 0 0 0 0 0 .021970706
1983 79666 0 2 11.285598 -.4615221 0 0 0 1 0 0 0 0 0 -.106771
1984 41376 0 2 10.630456 -.6551418 0 0 0 0 1 0 0 0 0 -.3163717
1985 53905 0 2 10.894979 .26452255 0 0 0 0 0 1 0 0 0 .2630735
1986 42037 0 2 10.646305 -.24867344 0 0 0 0 0 0 1 0 0 -.2191955
1987 44151 0 2 10.69537 .04906559 0 0 0 0 0 0 0 1 0 .3167494
1988 27088 0 2 10.206846 -.4885244 0 0 0 0 0 0 0 0 1 -.14983997
1980 61046 0 3 11.019383 . 1 0 0 0 0 0 0 0 0 .
1981 60959 0 3 11.017957 -.0014266968 0 1 0 0 0 0 0 0 0 .3202052
1982 90064 0 3 11.408276 .3903189 0 0 1 0 0 0 0 0 0 -.066808745
1983 61609 0 3 11.028563 -.3797121 0 0 0 1 0 0 0 0 0 -.024960995
1984 41869 0 3 10.6423 -.3862629 0 0 0 0 1 0 0 0 0 -.04749275
1985 49353 0 3 10.806754 .1644535 0 0 0 0 0 1 0 0 0 .16300446
1986 38632 0 3 10.561836 -.24491787 0 0 0 0 0 0 1 0 0 -.21543993
1987 37350 0 3 10.52809 -.033747673 0 0 0 0 0 0 0 1 0 .23393613
1988 31182 0 3 10.347596 -.1804924 0 0 0 0 0 0 0 0 1 .15819207
1980 91152 0 4 11.420283 . 1 0 0 0 0 0 0 0 0 .
1981 47337 0 4 10.765047 -.6552362 0 1 0 0 0 0 0 0 0 -.3336043
1982 102228 0 4 11.53496 .7699137 0 0 1 0 0 0 0 0 0 .3127861
1983 59709 0 4 10.997238 -.5377226 0 0 0 1 0 0 0 0 0 -.18297148
1984 30062 0 4 10.311017 -.6862211 0 0 0 0 1 0 0 0 0 -.347451
1985 41624 0 4 10.636433 .3254156 0 0 0 0 0 1 0 0 0 .3239666
1986 33688 0 4 10.424897 -.21153545 0 0 0 0 0 0 1 0 0 -.1820575
1987 23357 0 4 10.058652 -.3662453 0 0 0 0 0 0 0 1 0 -.09856146
1988 17190 0 4 9.752083 -.3065691 0 0 0 0 0 0 0 0 1 .032115374
1980 183095 0 5 12.11776 . 1 0 0 0 0 0 0 0 0 .
1981 100892 0 5 11.521806 -.5959549 0 1 0 0 0 0 0 0 0 -.274323
1982 121593 0 5 11.708435 .1866293 0 0 1 0 0 0 0 0 0 -.2704983
1983 61597 0 5 11.028368 -.6800671 0 0 0 1 0 0 0 0 0 -.32531595
1984 63997 0 5 11.06659 .03822327 0 0 0 0 1 0 0 0 0 .3769934
1985 82141 1 5 11.316193 .24960136 0 0 0 0 0 1 0 0 0 .4300299
1986 54092 1 5 10.89844 -.4177513 0 0 0 0 0 0 1 0 0 -.3882734
1987 37084 1 5 10.52094 -.3775005 0 0 0 0 0 0 0 1 0 -.10981672
1988 28978 1 5 10.274292 -.2466488 0 0 0 0 0 0 0 0 1 .09203568
1980 117090 0 6 11.670698 . 1 0 0 0 0 0 0 0 0 .
1981 131495 0 6 11.786724 .11602592 0 1 0 0 0 0 0 0 0 .4376578
1982 190727 0 6 12.158598 .3718739 0 0 1 0 0 0 0 0 0 -.08525376
1983 172074 0 6 12.05568 -.10291767 0 0 0 1 0 0 0 0 0 .25183344
1984 113250 1 6 11.637353 -.4183273 0 0 0 0 1 0 0 0 0 .10232036
1985 112460 1 6 11.630353 -.00699997 0 0 0 0 0 1 0 0 0 -.008449022
1986 95065 1 6 11.462317 -.16803646 0 0 0 0 0 0 1 0 0 -.13855852
1987 112507 1 6 11.63077 .16845417 0 0 0 0 0 0 0 1 0 .436138
1988 73704 1 6 11.207812 -.4229584 0 0 0 0 0 0 0 0 1 -.0842739
1980 172782 0 7 12.059786 . 1 0 0 0 0 0 0 0 0 .
1981 161154 0 7 11.990116 -.06966972 0 1 0 0 0 0 0 0 0 .25196218
1982 356613 0 7 12.784407 .7942905 0 0 1 0 0 0 0 0 0 .3371629
1983 255142 0 7 12.449575 -.3348312 0 0 0 1 0 0 0 0 0 .01991987
1984 125848 1 7 11.74283 -.7067451 0 0 0 0 1 0 0 0 0 -.18609746
1985 124783 1 7 11.73433 -.0084991455 0 0 0 0 0 1 0 0 0 -.009948198
1986 106736 1 7 11.578114 -.15621758 0 0 0 0 0 0 1 0 0 -.12673964
1987 95935 1 7 11.471426 -.10668755 0 0 0 0 0 0 0 1 0 .16099626
1988 72338 1 7 11.189105 -.28232098 0 0 0 0 0 0 0 0 1 .0563635
1980 123567 0 8 11.72454 . 1 0 0 0 0 0 0 0 0 .
1981 84035 0 8 11.338988 -.3855505 0 1 0 0 0 0 0 0 0 -.06391859
1982 121736 0 8 11.70961 .3706217 0 0 1 0 0 0 0 0 0 -.08650593
1983 85812 0 8 11.359914 -.3496962 0 0 0 1 0 0 0 0 0 .005054951
1984 83180 0 8 11.328762 -.03115177 0 0 0 0 1 0 0 0 0 .3076184
1985 55967 1 8 10.932517 -.396245 0 0 0 0 0 1 0 0 0 -.2158165
1986 68651 1 8 11.13679 .20427418 0 0 0 0 0 0 1 0 0 .2337521
1987 33909 1 8 10.431436 -.7053556 0 0 0 0 0 0 0 1 0 -.4376718
1988 19190 1 8 9.862144 -.5692911 0 0 0 0 0 0 0 0 1 -.23060665
1980 164996 0 9 12.013677 . 1 0 0 0 0 0 0 0 0 .
1981 139598 0 9 11.846522 -.1671543 0 1 0 0 0 0 0 0 0 .1544776
1982 215534 0 9 12.280874 .4343519 0 0 1 0 0 0 0 0 0 -.022775693
1983 148060 0 9 11.905373 -.3755016 0 0 0 1 0 0 0 0 0 -.02075052
1984 107105 0 9 11.581565 -.3238077 0 0 0 0 1 0 0 0 0 .014962432
1985 86550 1 9 11.368478 -.2130871 0 0 0 0 0 1 0 0 0 -.03265859
1986 87191 1 9 11.375856 .007378578 0 0 0 0 0 0 1 0 0 .03685652
1987 50279 1 9 10.825343 -.55051327 0 0 0 0 0 0 0 1 0 -.28282946
1988 30843 1 9 10.336665 -.488678 0 0 0 0 0 0 0 0 1 -.1499935
1980 533598 0 10 13.187398 . 1 0 0 0 0 0 0 0 0 .
1981 435754 0 10 12.984833 -.2025652 0 1 0 0 0 0 0 0 0 .11906672
1982 667208 0 10 13.410857 .4260244 0 0 1 0 0 0 0 0 0 -.031103177
1983 545625 0 10 13.209687 -.20116997 0 0 0 1 0 0 0 0 0 .15358114
1984 340092 0 10 12.736972 -.4727154 0 0 0 0 1 0 0 0 0 -.13394523
1985 325797 0 10 12.69403 -.04294205 0 0 0 0 0 1 0 0 0 -.0443911
1986 303724 0 10 12.623875 -.070155144 0 0 0 0 0 0 1 0 0 -.0406772
1987 262512 0 10 12.478052 -.14582253 0 0 0 0 0 0 0 1 0 .12186129
1988 209103 0 10 12.250583 -.22746944 0 0 0 0 0 0 0 0 1 .11121503
1980 169747 0 11 12.042065 . 1 0 0 0 0 0 0 0 0 .
1981 95962 0 11 11.471707 -.5703573 0 1 0 0 0 0 0 0 0 -.2487254
1982 157129 0 11 11.964823 .4931154 0 0 1 0 0 0 0 0 0 .03598781
1983 67341 0 11 11.117524 -.8472986 0 0 0 1 0 0 0 0 0 -.4925475
1984 32549 0 11 10.390502 -.7270222 0 0 0 0 1 0 0 0 0 -.388252
1985 36576 0 11 10.507148 .11664581 0 0 0 0 0 1 0 0 0 .11519676
1986 65114 0 11 11.083895 .57674694 0 0 0 0 0 0 1 0 0 .6062249
1987 45005 0 11 10.71453 -.3693657 0 0 0 0 0 0 0 1 0 -.10168188
1988 29916 0 11 10.306149 -.4083805 0 0 0 0 0 0 0 0 1 -.06969604
1980 74306 0 12 11.215947 . 1 0 0 0 0 0 0 0 0 .
end
[/CODE]
Comment