------------------------------------------------------------------------------- log: C:\Documents and Settings\salon\Escritorio\clase3-mar.log log type: text opened on: 4 Mar 2005, 16:14:33 ** REGRESIONES CON EFECTOS FIJOS O ALEATORIOS ** En esta sesión vimos los siguientes comandos: reshape wide reshape long xtreg ... , fe xtreg ..., re areg ..., abs(state) xi: xtreg ... xi: areg ... xttest0 (después de xtreg, re) hausman (después de xtreg, fe y re) . use "C:\Documents and Settings\salon\Escritorio\panelusa.dta", clear ** Esta base de datos ya está en formato “largo” (long)... ** El comando reshape transforma bases de formato “wide” a “long” y viceversa. ** Ejemplo: . help reshape . keep spend saletax popul state year . reshape wide spend saletax popul, i(state) j(year) (note: j = 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 > 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989) Data long -> wide ----------------------------------------------------------------------------- Number of obs. 2000 -> 50 Number of variables 5 -> 121 j variable (40 values) year -> (dropped) xij variables: spend -> spend1950 spend1951 ... spend1989 saletax -> saletax1950 ... saletax1989 popul -> popul1950 popul1951 ... popul1989 ----------------------------------------------------------------------------- ** Mira: . browse ** Regresando al formato “long” original: . reshape long spend saletax popul, i(state) j(year) (note: j = 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 > 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989) Data wide -> long ----------------------------------------------------------------------------- Number of obs. 50 -> 2000 Number of variables 121 -> 5 j variable (40 values) -> year xij variables: spend1950 spend1951 ... spend1989 -> spend saletax1950 ... saletax1989 -> saletax popul1950 popul1951 ... popul1989 -> popul ----------------------------------------------------------------------------- . browse ** Cargando la base panel original . use "C:\Documents and Settings\salon\Escritorio\panelusa.dta", clear . * Pooled regressions... (usando OLS sin efectos fijos ni temporales) . reg spend popul aper* persinc dem*, robust Regression with robust standard errors Number of obs = 1885 F( 7, 1877) = 330.33 Prob > F = 0.0000 R-squared = 0.5717 Root MSE = 412.17 ------------------------------------------------------------------------------ | Robust spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -36.73489 3.337699 -11.01 0.000 -43.28088 -30.1889 aper5_17 | 483.0721 389.0936 1.24 0.215 -280.0293 1246.174 aper65 | -5996.363 1742.111 -3.44 0.001 -9413.041 -2579.685 persinc | .1870054 .0110892 16.86 0.000 .1652569 .2087539 dem1 | 78.52772 82.82724 0.95 0.343 -83.91544 240.9709 demmaj1 | 55.40479 43.02319 1.29 0.198 -28.97352 139.7831 demgov | 21.5322 22.65587 0.95 0.342 -22.90114 65.96554 _cons | -221.353 189.3116 -1.17 0.242 -592.6363 149.9303 ------------------------------------------------------------------------------ ** Definiendo las variables que agrupan casos (i´s) y periodos (t´s): . iis stcode . tis year * Fixed Effects Regression - Regression con efectos fijos (estatales) . xtreg spend popul aper* persinc dem*, fe Fixed-effects (within) regression Number of obs = 1885 Group variable (i): stcode Number of groups = 49 R-sq: within = 0.8036 Obs per group: min = 14 between = 0.3771 avg = 38.5 overall = 0.4689 max = 40 F(7,1829) = 1069.16 corr(u_i, Xb) = 0.0235 Prob > F = 0.0000 ------------------------------------------------------------------------------ spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.51484 5.131464 -2.63 0.009 -23.57899 -3.450696 aper5_17 | -302.6328 199.2352 -1.52 0.129 -693.3852 88.11947 aper65 | 2275.595 597.6709 3.81 0.000 1103.406 3447.784 persinc | .1416308 .0034689 40.83 0.000 .1348275 .1484341 dem1 | 216.9176 53.46584 4.06 0.000 112.0571 321.7781 demmaj1 | -16.2362 17.60653 -0.92 0.357 -50.76722 18.29482 demgov | 34.17819 9.944188 3.44 0.001 14.67503 53.68134 _cons | -584.6617 79.68837 -7.34 0.000 -740.9515 -428.3719 -------------+---------------------------------------------------------------- sigma_u | 636.079 sigma_e | 185.56074 rho | .92157064 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(48, 1829) = 154.82 Prob > F = 0.0000 ** Con efectos fijos, la R2 que nos interesa es la “R2 within” (0.8036)... ** Otra forma de hacerlo es con el comando areg (absorbing regression): . areg spend popul aper* persinc dem*, a(stcode) Number of obs = 1885 F( 7, 1829) = 1069.16 Prob > F = 0.0000 R-squared = 0.9154 Adj R-squared = 0.9129 Root MSE = 185.56 ------------------------------------------------------------------------------ spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.51484 5.131464 -2.63 0.009 -23.57899 -3.450696 aper5_17 | -302.6328 199.2352 -1.52 0.129 -693.3852 88.11947 aper65 | 2275.595 597.6709 3.81 0.000 1103.406 3447.784 persinc | .1416308 .0034689 40.83 0.000 .1348275 .1484341 dem1 | 216.9176 53.46584 4.06 0.000 112.0571 321.7781 demmaj1 | -16.2362 17.60653 -0.92 0.357 -50.76722 18.29482 demgov | 34.17819 9.944188 3.44 0.001 14.67503 53.68134 _cons | -584.6617 79.68837 -7.34 0.000 -740.9515 -428.3719 -------------+---------------------------------------------------------------- stcode | F(48, 1829) = 154.823 0.000 (49 categories) ** Noten como areg arroja las mismas “betas” que xtreg, fe. ** Pero la R2 es distinta (0.9154)... ** Esto es porque el comando areg “calcula” (sin reportar) las dummies de cada ** estado, mientras que xtreg, fe usa el método de “sustracción de medias” de ** cada estado en la base de datos, y luego estima un modelo sin dummies. ** Por ello, la suma de errores cuadrados (SST) de xtreg es diferente a la de ** areg, y por consiguiente la R2 difiere. ** ¿PERO DONDE ESTAN LAS DUMMIES? ** Otra forma de estimar FIXED EFFECTS es usando regresiones normales con ** el comando xi para “expansion de dummies”. . set matsize 400 // Para calcular muchas betas, hay que ampliar el matsize. ** Este comando genera una dummy para cada estado y corre la regresion: . xi: reg spend popul aper* persinc dem* i.state i.state _Istate_1-50 (_Istate_1 for state==AK omitted) Source | SS df MS Number of obs = 1885 -------------+------------------------------ F( 55, 1829) = 359.90 Model | 681579900 55 12392361.8 Prob > F = 0.0000 Residual | 62977567.6 1829 34432.7871 R-squared = 0.9154 -------------+------------------------------ Adj R-squared = 0.9129 Total | 744557468 1884 395200.354 Root MSE = 185.56 ------------------------------------------------------------------------------ spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.51484 5.131464 -2.63 0.009 -23.57899 -3.450696 aper5_17 | -302.6328 199.2352 -1.52 0.129 -693.3852 88.11947 aper65 | 2275.595 597.6709 3.81 0.000 1103.406 3447.784 persinc | .1416308 .0034689 40.83 0.000 .1348275 .1484341 dem1 | 216.9176 53.46584 4.06 0.000 112.0571 321.7781 demmaj1 | -16.2362 17.60653 -0.92 0.357 -50.76722 18.29482 demgov | 34.17819 9.944188 3.44 0.001 14.67503 53.68134 _Istate_2 | -4067.682 93.84831 -43.34 0.000 -4251.743 -3883.621 _Istate_3 | -4167.242 101.765 -40.95 0.000 -4366.83 -3967.654 _Istate_4 | -4118.284 81.79228 -50.35 0.000 -4278.7 -3957.868 _Istate_5 | -4068.71 126.1927 -32.24 0.000 -4316.207 -3821.213 _Istate_6 | -4272.479 77.93379 -54.82 0.000 -4425.328 -4119.631 _Istate_7 | -4637.761 79.46028 -58.37 0.000 -4793.604 -4481.919 _Istate_8 | -4075.513 74.52802 -54.68 0.000 -4221.682 -3929.344 _Istate_9 | -4473.39 107.9155 -41.45 0.000 -4685.041 -4261.74 _Istate_10 | -4192.437 87.36316 -47.99 0.000 -4363.779 -4021.095 _Istate_11 | -3594.643 81.81263 -43.94 0.000 -3755.099 -3434.187 _Istate_12 | -4256.489 95.75107 -44.45 0.000 -4444.282 -4068.696 _Istate_13 | -4038.208 85.53409 -47.21 0.000 -4205.962 -3870.453 _Istate_14 | -4486.597 97.41563 -46.06 0.000 -4677.655 -4295.54 _Istate_15 | -4345.066 87.9454 -49.41 0.000 -4517.55 -4172.582 _Istate_16 | -4391.016 91.4031 -48.04 0.000 -4570.282 -4211.751 _Istate_17 | -4038.798 92.82073 -43.51 0.000 -4220.844 -3856.752 _Istate_18 | -3883.852 87.8844 -44.19 0.000 -4056.217 -3711.488 _Istate_19 | -4369.294 91.06521 -47.98 0.000 -4547.897 -4190.691 _Istate_20 | -4397.883 78.1669 -56.26 0.000 -4551.189 -4244.577 _Istate_21 | -4100.055 93.21709 -43.98 0.000 -4282.878 -3917.232 _Istate_22 | -4172.191 89.01268 -46.87 0.000 -4346.768 -3997.613 _Istate_23 | -4028.221 93.35303 -43.15 0.000 -4211.311 -3845.131 _Istate_24 | -4492.268 95.67876 -46.95 0.000 -4679.919 -4304.617 _Istate_25 | -3955.29 96.69578 -40.90 0.000 -4144.936 -3765.644 _Istate_26 | -4056.97 86.44783 -46.93 0.000 -4226.516 -3887.423 _Istate_27 | -4077.689 88.77088 -45.93 0.000 -4251.792 -3903.587 _Istate_28 | -3835.737 89.12654 -43.04 0.000 -4010.538 -3660.937 _Istate_29 | (dropped) _Istate_30 | -4423.467 87.7357 -50.42 0.000 -4595.54 -4251.395 _Istate_31 | -4601.741 85.47294 -53.84 0.000 -4769.376 -4434.106 _Istate_32 | -3677.96 77.72744 -47.32 0.000 -3830.404 -3525.516 _Istate_33 | -4331.12 68.59048 -63.14 0.000 -4465.644 -4196.596 _Istate_34 | -4134.043 120.3731 -34.34 0.000 -4370.126 -3897.96 _Istate_35 | -4358.659 97.47217 -44.72 0.000 -4549.827 -4167.49 _Istate_36 | -4124.432 93.96077 -43.90 0.000 -4308.714 -3940.151 _Istate_37 | -4156.617 87.36063 -47.58 0.000 -4327.954 -3985.28 _Istate_38 | -4269.809 105.7342 -40.38 0.000 -4477.181 -4062.436 _Istate_39 | -4273.609 89.18346 -47.92 0.000 -4448.521 -4098.697 _Istate_40 | -4024.445 85.34474 -47.16 0.000 -4191.828 -3857.061 _Istate_41 | -4045.203 94.75151 -42.69 0.000 -4231.035 -3859.37 _Istate_42 | -4178.205 90.2744 -46.28 0.000 -4355.256 -4001.153 _Istate_43 | -4315.767 104.5119 -41.29 0.000 -4520.742 -4110.791 _Istate_44 | -3864.298 76.918 -50.24 0.000 -4015.154 -3713.441 _Istate_45 | -4308.729 83.14398 -51.82 0.000 -4471.796 -4145.662 _Istate_46 | -3853.145 90.95341 -42.36 0.000 -4031.528 -3674.761 _Istate_47 | -4109.69 83.46422 -49.24 0.000 -4273.385 -3945.995 _Istate_48 | -4134.712 90.33262 -45.77 0.000 -4311.878 -3957.546 _Istate_49 | -3979.989 93.02953 -42.78 0.000 -4162.444 -3797.534 _Istate_50 | -3679.343 76.74978 -47.94 0.000 -3829.869 -3528.816 _cons | 3548.728 84.87612 41.81 0.000 3382.264 3715.193 ------------------------------------------------------------------------------ ** Noten como esta R2 es igual a la de areg—la unica diferencia es que esta vez sí vemos las dummies. ** Noten que las betas de nuestras variables de interés son idénticas en los tres métodos. ** ¿Qué tan distintas son las dummies estatales? (Noten que Alaska es el estado ** de comparación de todas las dummies estatales—esto puede cambiarse). . test _Istate_44 = _Istate_19 ( 1) - _Istate_19 + _Istate_44 = 0 F( 1, 1829) = 99.46 Prob > F = 0.0000 ** ... las dummies del estado 44 y el 19 son estadisticamente distintas... ** FIXED AND TIME EFFECTS - Un modelo con efectos estatales y temporales ** xtreg sólo permite absorber una categoria. Las dummies temporales deben ** introducirse con la expansión xi: . xi: xtreg spend popul aper* persinc dem* i.year, fe i.year _Iyear_1950-1989 (naturally coded; _Iyear_1950 omitted) Fixed-effects (within) regression Number of obs = 1885 Group variable (i): stcode Number of groups = 49 R-sq: within = 0.8389 Obs per group: min = 14 between = 0.6530 avg = 38.5 overall = 0.5361 max = 40 F(46,1790) = 202.67 corr(u_i, Xb) = 0.1647 Prob > F = 0.0000 ------------------------------------------------------------------------------ spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.85073 4.822282 -2.87 0.004 -23.30863 -4.392839 aper5_17 | -321.2967 368.2342 -0.87 0.383 -1043.511 400.9175 aper65 | -2189.024 631.5634 -3.47 0.001 -3427.703 -950.3452 persinc | .0370278 .0073554 5.03 0.000 .0226017 .0514539 dem1 | 143.3822 51.69292 2.77 0.006 41.99742 244.7671 demmaj1 | -7.802901 16.28596 -0.48 0.632 -39.74439 24.13859 demgov | 26.84782 9.226615 2.91 0.004 8.751748 44.94389 _Iyear_1951 | 7.089081 35.57766 0.20 0.842 -62.68903 76.86719 _Iyear_1952 | -8.734004 35.76774 -0.24 0.807 -78.88493 61.41692 _Iyear_1953 | 19.36336 36.16764 0.54 0.592 -51.57187 90.2986 _Iyear_1954 | 34.73218 36.18379 0.96 0.337 -36.23474 105.6991 _Iyear_1955 | 35.40622 36.46374 0.97 0.332 -36.10976 106.9222 _Iyear_1956 | 57.71247 37.03808 1.56 0.119 -14.92995 130.3549 _Iyear_1957 | 89.59729 37.55865 2.39 0.017 15.93389 163.2607 _Iyear_1958 | 127.7902 38.11307 3.35 0.001 53.03937 202.5409 _Iyear_1959 | 144.9234 38.4262 3.77 0.000 69.55844 220.2883 _Iyear_1960 | 150.4599 39.66643 3.79 0.000 72.66256 228.2573 _Iyear_1961 | 174.6079 39.81461 4.39 0.000 96.51986 252.6959 _Iyear_1962 | 193.6857 40.93713 4.73 0.000 113.3961 273.9752 _Iyear_1963 | 232.9573 41.92327 5.56 0.000 150.7336 315.181 _Iyear_1964 | 258.2838 43.89358 5.88 0.000 172.1957 344.3718 _Iyear_1965 | 280.9553 44.93091 6.25 0.000 192.8328 369.0779 _Iyear_1966 | 330.7593 46.87435 7.06 0.000 238.8251 422.6935 _Iyear_1967 | 417.6653 48.65774 8.58 0.000 322.2334 513.0973 _Iyear_1968 | 454.5834 50.36069 9.03 0.000 355.8115 553.3553 _Iyear_1969 | 477.9342 51.52263 9.28 0.000 376.8833 578.985 _Iyear_1970 | 494.6204 51.23363 9.65 0.000 394.1364 595.1044 _Iyear_1971 | 607.5863 51.49973 11.80 0.000 506.5804 708.5922 _Iyear_1972 | 648.5896 53.36667 12.15 0.000 543.9221 753.2571 _Iyear_1973 | 640.6648 55.88472 11.46 0.000 531.0586 750.271 _Iyear_1974 | 591.9319 53.3496 11.10 0.000 487.2979 696.566 _Iyear_1975 | 698.8696 52.71709 13.26 0.000 595.4761 802.2631 _Iyear_1976 | 704.7435 55.04716 12.80 0.000 596.78 812.7069 _Iyear_1977 | 703.7375 58.46254 12.04 0.000 589.0755 818.3995 _Iyear_1978 | 688.0794 58.31866 11.80 0.000 573.6996 802.4592 _Iyear_1979 | 732.7374 52.26395 14.02 0.000 630.2326 835.2421 _Iyear_1980 | 753.1609 55.95589 13.46 0.000 643.4152 862.9067 _Iyear_1981 | 761.3285 57.04873 13.35 0.000 649.4394 873.2176 _Iyear_1982 | 812.0485 56.50898 14.37 0.000 701.218 922.879 _Iyear_1983 | 785.5975 57.62831 13.63 0.000 672.5716 898.6233 _Iyear_1984 | 823.311 60.36248 13.64 0.000 704.9227 941.6993 _Iyear_1985 | 892.2298 63.21699 14.11 0.000 768.243 1016.217 _Iyear_1986 | 925.6809 65.93699 14.04 0.000 796.3593 1055.002 _Iyear_1987 | 950.0674 67.70635 14.03 0.000 817.2756 1082.859 _Iyear_1988 | 947.7948 69.61648 13.61 0.000 811.2567 1084.333 _Iyear_1989 | 941.72 71.50241 13.17 0.000 801.483 1081.957 _cons | 397.7871 120.5648 3.30 0.001 161.3245 634.2498 -------------+---------------------------------------------------------------- sigma_u | 630.17213 sigma_e | 169.87032 rho | .93225877 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(48, 1790) = 160.21 Prob > F = 0.0000 ** Noten cómo al introducir efectos fijos y temporales, cambian algunas betas ** de interés calculadas antes. ** Otra forma (muy larga) de calcular FIXED + TIME EFFECTS es generar ambos ** conjuntos de dummies con xi: . xi: reg spend popul aper* persinc dem* i.state i.year i.state _Istate_1-50 (_Istate_1 for state==AK omitted) i.year _Iyear_1950-1989 (naturally coded; _Iyear_1950 omitted) Source | SS df MS Number of obs = 1885 -------------+------------------------------ F( 94, 1790) = 255.45 Model | 692905360 94 7371333.62 Prob > F = 0.0000 Residual | 51652107.7 1790 28855.9261 R-squared = 0.9306 -------------+------------------------------ Adj R-squared = 0.9270 Total | 744557468 1884 395200.354 Root MSE = 169.87 ------------------------------------------------------------------------------ spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.85073 4.822282 -2.87 0.004 -23.30863 -4.392839 aper5_17 | -321.2967 368.2342 -0.87 0.383 -1043.511 400.9175 aper65 | -2189.024 631.5634 -3.47 0.001 -3427.703 -950.3452 persinc | .0370278 .0073554 5.03 0.000 .0226017 .0514539 dem1 | 143.3822 51.69292 2.77 0.006 41.99742 244.7671 demmaj1 | -7.802901 16.28596 -0.48 0.632 -39.74439 24.13859 demgov | 26.84782 9.226615 2.91 0.004 8.751748 44.94389 _Istate_2 | -4348.526 92.74127 -46.89 0.000 -4530.419 -4166.634 _Istate_3 | -4376.184 99.44407 -44.01 0.000 -4571.223 -4181.145 _Istate_4 | -4278.477 78.71352 -54.36 0.000 -4432.857 -4124.096 _Istate_5 | -3955.418 121.7435 -32.49 0.000 -4194.192 -3716.643 _Istate_6 | -4346.316 74.57754 -58.28 0.000 -4492.584 -4200.047 _Istate_7 | -4370.066 76.87123 -56.85 0.000 -4520.833 -4219.3 _Istate_8 | -3987.833 70.50696 -56.56 0.000 -4126.118 -3849.549 _Istate_9 | -4372.031 105.657 -41.38 0.000 -4579.255 -4164.807 _Istate_10 | -4441.307 86.12261 -51.57 0.000 -4610.219 -4272.396 _Istate_11 | -3690.692 77.36356 -47.71 0.000 -3842.425 -3538.96 _Istate_12 | -4222.852 91.55759 -46.12 0.000 -4402.423 -4043.281 _Istate_13 | -4267.159 82.80293 -51.53 0.000 -4429.559 -4104.758 _Istate_14 | -4349.645 93.7984 -46.37 0.000 -4533.611 -4165.679 _Istate_15 | -4403.14 84.37607 -52.18 0.000 -4568.626 -4237.654 _Istate_16 | -4353.329 87.31162 -49.86 0.000 -4524.573 -4182.086 _Istate_17 | -4261.11 90.75439 -46.95 0.000 -4439.105 -4083.114 _Istate_18 | -4162.665 86.7247 -48.00 0.000 -4332.758 -3992.573 _Istate_19 | -4187.858 88.65751 -47.24 0.000 -4361.741 -4013.975 _Istate_20 | -4375.622 75.29844 -58.11 0.000 -4523.304 -4227.94 _Istate_21 | -4218.656 89.70619 -47.03 0.000 -4394.596 -4042.716 _Istate_22 | -4184.93 85.14179 -49.15 0.000 -4351.917 -4017.942 _Istate_23 | -4012.801 88.85657 -45.16 0.000 -4187.075 -3838.528 _Istate_24 | -4459.275 92.61793 -48.15 0.000 -4640.926 -4277.625 _Istate_25 | -4318.458 96.31771 -44.84 0.000 -4507.365 -4129.551 _Istate_26 | -4186.487 82.86409 -50.52 0.000 -4349.008 -4023.967 _Istate_27 | -4358.217 88.10071 -49.47 0.000 -4531.008 -4185.426 _Istate_28 | -3983.947 85.46457 -46.62 0.000 -4151.568 -3816.326 _Istate_29 | (dropped) _Istate_30 | -4440.018 83.6269 -53.09 0.000 -4604.035 -4276.001 _Istate_31 | -4411.551 82.61819 -53.40 0.000 -4573.589 -4249.512 _Istate_32 | -4019.86 77.12819 -52.12 0.000 -4171.13 -3868.589 _Istate_33 | -4309.776 65.14366 -66.16 0.000 -4437.542 -4182.01 _Istate_34 | -3939.69 116.6159 -33.78 0.000 -4168.407 -3710.972 _Istate_35 | -4369.435 93.93154 -46.52 0.000 -4553.662 -4185.208 _Istate_36 | -4213.781 91.19261 -46.21 0.000 -4392.636 -4034.926 _Istate_37 | -4173.309 83.72535 -49.85 0.000 -4337.519 -4009.099 _Istate_38 | -4231.877 102.5071 -41.28 0.000 -4432.923 -4030.831 _Istate_39 | -4211.172 86.31118 -48.79 0.000 -4380.453 -4041.89 _Istate_40 | -4398.767 85.58384 -51.40 0.000 -4566.622 -4230.912 _Istate_41 | -4193.71 91.07419 -46.05 0.000 -4372.333 -4015.087 _Istate_42 | -4423.312 88.9942 -49.70 0.000 -4597.855 -4248.768 _Istate_43 | -4458.238 101.8077 -43.79 0.000 -4657.913 -4258.564 _Istate_44 | -4199.984 76.02993 -55.24 0.000 -4349.101 -4050.867 _Istate_45 | -4448.364 81.29445 -54.72 0.000 -4607.806 -4288.922 _Istate_46 | -3974.707 87.25045 -45.56 0.000 -4145.831 -3803.584 _Istate_47 | -4081.377 79.94533 -51.05 0.000 -4238.173 -3924.581 _Istate_48 | -4145.989 86.52006 -47.92 0.000 -4315.68 -3976.298 _Istate_49 | -4196.085 90.71669 -46.25 0.000 -4374.007 -4018.163 _Istate_50 | -3801.175 73.0156 -52.06 0.000 -3944.38 -3657.97 _Iyear_1951 | 7.089081 35.57766 0.20 0.842 -62.68903 76.86719 _Iyear_1952 | -8.734004 35.76774 -0.24 0.807 -78.88493 61.41692 _Iyear_1953 | 19.36336 36.16764 0.54 0.592 -51.57187 90.2986 _Iyear_1954 | 34.73218 36.18379 0.96 0.337 -36.23474 105.6991 _Iyear_1955 | 35.40622 36.46374 0.97 0.332 -36.10976 106.9222 _Iyear_1956 | 57.71247 37.03808 1.56 0.119 -14.92995 130.3549 _Iyear_1957 | 89.59729 37.55865 2.39 0.017 15.93389 163.2607 _Iyear_1958 | 127.7902 38.11307 3.35 0.001 53.03937 202.5409 _Iyear_1959 | 144.9234 38.4262 3.77 0.000 69.55844 220.2883 _Iyear_1960 | 150.4599 39.66643 3.79 0.000 72.66256 228.2573 _Iyear_1961 | 174.6079 39.81461 4.39 0.000 96.51986 252.6959 _Iyear_1962 | 193.6857 40.93713 4.73 0.000 113.3961 273.9752 _Iyear_1963 | 232.9573 41.92327 5.56 0.000 150.7336 315.181 _Iyear_1964 | 258.2838 43.89358 5.88 0.000 172.1957 344.3718 _Iyear_1965 | 280.9553 44.93091 6.25 0.000 192.8328 369.0779 _Iyear_1966 | 330.7593 46.87435 7.06 0.000 238.8251 422.6935 _Iyear_1967 | 417.6653 48.65774 8.58 0.000 322.2334 513.0973 _Iyear_1968 | 454.5834 50.36069 9.03 0.000 355.8115 553.3553 _Iyear_1969 | 477.9342 51.52263 9.28 0.000 376.8833 578.985 _Iyear_1970 | 494.6204 51.23363 9.65 0.000 394.1364 595.1044 _Iyear_1971 | 607.5863 51.49973 11.80 0.000 506.5804 708.5922 _Iyear_1972 | 648.5896 53.36667 12.15 0.000 543.9221 753.2571 _Iyear_1973 | 640.6648 55.88472 11.46 0.000 531.0586 750.271 _Iyear_1974 | 591.9319 53.3496 11.10 0.000 487.2979 696.566 _Iyear_1975 | 698.8696 52.71709 13.26 0.000 595.4761 802.2631 _Iyear_1976 | 704.7435 55.04716 12.80 0.000 596.78 812.7069 _Iyear_1977 | 703.7375 58.46254 12.04 0.000 589.0755 818.3995 _Iyear_1978 | 688.0794 58.31866 11.80 0.000 573.6996 802.4592 _Iyear_1979 | 732.7374 52.26395 14.02 0.000 630.2326 835.2421 _Iyear_1980 | 753.1609 55.95589 13.46 0.000 643.4152 862.9067 _Iyear_1981 | 761.3285 57.04873 13.35 0.000 649.4394 873.2176 _Iyear_1982 | 812.0485 56.50898 14.37 0.000 701.218 922.879 _Iyear_1983 | 785.5975 57.62831 13.63 0.000 672.5716 898.6233 _Iyear_1984 | 823.311 60.36248 13.64 0.000 704.9227 941.6993 _Iyear_1985 | 892.2298 63.21699 14.11 0.000 768.243 1016.217 _Iyear_1986 | 925.6809 65.93699 14.04 0.000 796.3593 1055.002 _Iyear_1987 | 950.0674 67.70635 14.03 0.000 817.2756 1082.859 _Iyear_1988 | 947.7948 69.61648 13.61 0.000 811.2567 1084.333 _Iyear_1989 | 941.72 71.50241 13.17 0.000 801.483 1081.957 _cons | 4608.055 134.5466 34.25 0.000 4344.17 4871.94 ------------------------------------------------------------------------------ ** Noten otra vez como la R2 de este metodo difiere de la “within R2” de antes ** Por si no se han dado cuenta, xtreg no permite la opcion robust. ** Una ventaja de usar el método areg o xi es que te permite la opcion robust: . xi: reg spend popul aper* persinc dem* i.state i.year, robust i.state _Istate_1-50 (_Istate_1 for state==AK omitted) i.year _Iyear_1950-1989 (naturally coded; _Iyear_1950 omitted) Regression with robust standard errors Number of obs = 1885 F( 94, 1790) = 353.56 Prob > F = 0.0000 R-squared = 0.9306 Root MSE = 169.87 ------------------------------------------------------------------------------ | Robust spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.85073 5.106137 -2.71 0.007 -23.86535 -3.836118 aper5_17 | -321.2967 368.25 -0.87 0.383 -1043.542 400.9485 aper65 | -2189.024 708.8155 -3.09 0.002 -3579.217 -798.8315 persinc | .0370278 .0173177 2.14 0.033 .0030629 .0709928 dem1 | 143.3822 69.79076 2.05 0.040 6.502315 280.2622 demmaj1 | -7.802901 19.59238 -0.40 0.690 -46.22924 30.62344 demgov | 26.84782 9.602359 2.80 0.005 8.014805 45.68083 _Istate_2 | -4348.526 451.3065 -9.64 0.000 -5233.669 -3463.384 _Istate_3 | -4376.184 457.0444 -9.57 0.000 -5272.581 -3479.788 _Istate_4 | -4278.477 425.0973 -10.06 0.000 -5112.216 -3444.737 _Istate_5 | -3955.418 447.7113 -8.83 0.000 -4833.509 -3077.326 _Istate_6 | -4346.316 418.7997 -10.38 0.000 -5167.703 -3524.928 _Istate_7 | -4370.066 415.0355 -10.53 0.000 -5184.072 -3556.061 _Istate_8 | -3987.833 413.8141 -9.64 0.000 -4799.443 -3176.224 _Istate_9 | -4372.031 453.505 -9.64 0.000 -5261.486 -3482.577 _Istate_10 | -4441.307 441.8414 -10.05 0.000 -5307.887 -3574.728 _Istate_11 | -3690.692 422.0924 -8.74 0.000 -4518.538 -2862.847 _Istate_12 | -4222.852 433.4316 -9.74 0.000 -5072.937 -3372.767 _Istate_13 | -4267.159 425.4032 -10.03 0.000 -5101.498 -3432.82 _Istate_14 | -4349.645 433.2818 -10.04 0.000 -5199.436 -3499.854 _Istate_15 | -4403.14 428.7787 -10.27 0.000 -5244.099 -3562.18 _Istate_16 | -4353.329 427.0843 -10.19 0.000 -5190.966 -3515.693 _Istate_17 | -4261.11 443.2411 -9.61 0.000 -5130.434 -3391.785 _Istate_18 | -4162.665 444.0557 -9.37 0.000 -5033.587 -3291.743 _Istate_19 | -4187.858 433.2494 -9.67 0.000 -5037.586 -3338.13 _Istate_20 | -4375.622 424.5254 -10.31 0.000 -5208.239 -3543.004 _Istate_21 | -4218.656 431.9966 -9.77 0.000 -5065.927 -3371.385 _Istate_22 | -4184.93 428.3834 -9.77 0.000 -5025.114 -3344.745 _Istate_23 | -4012.801 426.4865 -9.41 0.000 -4849.265 -3176.338 _Istate_24 | -4459.275 438.778 -10.16 0.000 -5319.846 -3598.704 _Istate_25 | -4318.458 456.5986 -9.46 0.000 -5213.98 -3422.936 _Istate_26 | -4186.487 427.0165 -9.80 0.000 -5023.99 -3348.984 _Istate_27 | -4358.217 443.1918 -9.83 0.000 -5227.445 -3488.989 _Istate_28 | -3983.947 425.0229 -9.37 0.000 -4817.54 -3150.353 _Istate_29 | (dropped) _Istate_30 | -4440.018 425.2054 -10.44 0.000 -5273.969 -3606.067 _Istate_31 | -4411.551 423.1844 -10.42 0.000 -5241.538 -3581.563 _Istate_32 | -4019.86 428.3824 -9.38 0.000 -4860.042 -3179.678 _Istate_33 | -4309.776 409.2026 -10.53 0.000 -5112.341 -3507.211 _Istate_34 | -3939.69 447.334 -8.81 0.000 -4817.042 -3062.338 _Istate_35 | -4369.435 435.2609 -10.04 0.000 -5223.108 -3515.762 _Istate_36 | -4213.781 442.4646 -9.52 0.000 -5081.583 -3345.98 _Istate_37 | -4173.309 426.5945 -9.78 0.000 -5009.985 -3336.634 _Istate_38 | -4231.877 443.4765 -9.54 0.000 -5101.663 -3362.091 _Istate_39 | -4211.172 431.6579 -9.76 0.000 -5057.778 -3364.565 _Istate_40 | -4398.767 442.9802 -9.93 0.000 -5267.58 -3529.954 _Istate_41 | -4193.71 430.4544 -9.74 0.000 -5037.956 -3349.465 _Istate_42 | -4423.312 441.0378 -10.03 0.000 -5288.315 -3558.308 _Istate_43 | -4458.238 451.6789 -9.87 0.000 -5344.112 -3572.365 _Istate_44 | -4199.984 420.2014 -10.00 0.000 -5024.121 -3375.847 _Istate_45 | -4448.364 433.1574 -10.27 0.000 -5297.912 -3598.817 _Istate_46 | -3974.707 427.2521 -9.30 0.000 -4812.673 -3136.742 _Istate_47 | -4081.377 424.3554 -9.62 0.000 -4913.661 -3249.093 _Istate_48 | -4145.989 430.9333 -9.62 0.000 -4991.174 -3300.804 _Istate_49 | -4196.085 443.3591 -9.46 0.000 -5065.641 -3326.529 _Istate_50 | -3801.175 417.624 -9.10 0.000 -4620.257 -2982.093 _Iyear_1951 | 7.089081 28.07061 0.25 0.801 -47.96552 62.14368 _Iyear_1952 | -8.734004 25.81642 -0.34 0.735 -59.3675 41.89949 _Iyear_1953 | 19.36336 26.66912 0.73 0.468 -32.94252 71.66925 _Iyear_1954 | 34.73218 25.93513 1.34 0.181 -16.13414 85.59849 _Iyear_1955 | 35.40622 27.41062 1.29 0.197 -18.35396 89.16639 _Iyear_1956 | 57.71247 30.95496 1.86 0.062 -2.99919 118.4241 _Iyear_1957 | 89.59729 30.73995 2.91 0.004 29.30734 149.8872 _Iyear_1958 | 127.7902 30.89706 4.14 0.000 67.19206 188.3882 _Iyear_1959 | 144.9234 30.81454 4.70 0.000 84.48712 205.3596 _Iyear_1960 | 150.4599 33.08697 4.55 0.000 85.56677 215.3531 _Iyear_1961 | 174.6079 34.60412 5.05 0.000 106.7391 242.4766 _Iyear_1962 | 193.6857 38.77322 5.00 0.000 117.6401 269.7312 _Iyear_1963 | 232.9573 41.36686 5.63 0.000 151.8249 314.0897 _Iyear_1964 | 258.2838 48.44903 5.33 0.000 163.2612 353.3064 _Iyear_1965 | 280.9553 51.16311 5.49 0.000 180.6096 381.301 _Iyear_1966 | 330.7593 58.49729 5.65 0.000 216.0291 445.4894 _Iyear_1967 | 417.6653 66.67318 6.26 0.000 286.8999 548.4308 _Iyear_1968 | 454.5834 71.11299 6.39 0.000 315.1102 594.0566 _Iyear_1969 | 477.9342 74.65035 6.40 0.000 331.5232 624.3452 _Iyear_1970 | 494.6204 112.0509 4.41 0.000 274.8561 714.3846 _Iyear_1971 | 607.5863 74.94515 8.11 0.000 460.5971 754.5755 _Iyear_1972 | 648.5896 81.02993 8.00 0.000 489.6664 807.5128 _Iyear_1973 | 640.6648 92.71626 6.91 0.000 458.8213 822.5083 _Iyear_1974 | 591.9319 94.11077 6.29 0.000 407.3534 776.5104 _Iyear_1975 | 698.8696 78.82228 8.87 0.000 544.2762 853.4629 _Iyear_1976 | 704.7435 74.95906 9.40 0.000 557.727 851.7599 _Iyear_1977 | 703.7375 95.67481 7.36 0.000 516.0915 891.3836 _Iyear_1978 | 688.0794 95.88364 7.18 0.000 500.0238 876.135 _Iyear_1979 | 732.7374 83.01162 8.83 0.000 569.9275 895.5472 _Iyear_1980 | 753.1609 88.00861 8.56 0.000 580.5505 925.7714 _Iyear_1981 | 761.3285 90.72941 8.39 0.000 583.3818 939.2752 _Iyear_1982 | 812.0485 84.63231 9.60 0.000 646.0599 978.037 _Iyear_1983 | 785.5975 87.7446 8.95 0.000 613.5049 957.6901 _Iyear_1984 | 823.311 100.5615 8.19 0.000 626.0807 1020.541 _Iyear_1985 | 892.2298 112.9034 7.90 0.000 670.7935 1113.666 _Iyear_1986 | 925.6809 114.6316 8.08 0.000 700.855 1150.507 _Iyear_1987 | 950.0674 119.5133 7.95 0.000 715.6671 1184.468 _Iyear_1988 | 947.7948 118.7496 7.98 0.000 714.8923 1180.697 _Iyear_1989 | 941.72 121.1547 7.77 0.000 704.1004 1179.339 _cons | 4608.055 439.5628 10.48 0.000 3745.945 5470.165 ------------------------------------------------------------------------------ *** COMPARANDO EFECTOS FIJOS VS. EFECTOS ALEATORIOS ** xtreg tiene opciones fe (fixed effects) y re (random effects): ** FIXED EFFECTS REGRESSION . xtreg spend popul aper* persinc dem*, fe Fixed-effects (within) regression Number of obs = 1885 Group variable (i): stcode Number of groups = 49 R-sq: within = 0.8036 Obs per group: min = 14 between = 0.3771 avg = 38.5 overall = 0.4689 max = 40 F(7,1829) = 1069.16 corr(u_i, Xb) = 0.0235 Prob > F = 0.0000 ------------------------------------------------------------------------------ spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.51484 5.131464 -2.63 0.009 -23.57899 -3.450696 aper5_17 | -302.6328 199.2352 -1.52 0.129 -693.3852 88.11947 aper65 | 2275.595 597.6709 3.81 0.000 1103.406 3447.784 persinc | .1416308 .0034689 40.83 0.000 .1348275 .1484341 dem1 | 216.9176 53.46584 4.06 0.000 112.0571 321.7781 demmaj1 | -16.2362 17.60653 -0.92 0.357 -50.76722 18.29482 demgov | 34.17819 9.944188 3.44 0.001 14.67503 53.68134 _cons | -584.6617 79.68837 -7.34 0.000 -740.9515 -428.3719 -------------+---------------------------------------------------------------- sigma_u | 636.079 sigma_e | 185.56074 rho | .92157064 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(48, 1829) = 154.82 Prob > F = 0.0000 ** RANDOM EFFECTS REGRESSION . xtreg spend popul aper* persinc dem*, re Random-effects GLS regression Number of obs = 1885 Group variable (i): stcode Number of groups = 49 R-sq: within = 0.8034 Obs per group: min = 14 between = 0.4192 avg = 38.5 overall = 0.4870 max = 40 Random effects u_i ~ Gaussian Wald chi2(7) = 7354.02 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ spend | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -17.10089 4.933078 -3.47 0.001 -26.76955 -7.432238 aper5_17 | -337.3402 200.7367 -1.68 0.093 -730.7769 56.09651 aper65 | 1620.119 592.9956 2.73 0.006 457.8687 2782.369 persinc | .145831 .0034421 42.37 0.000 .1390845 .1525774 dem1 | 199.1189 53.60937 3.71 0.000 94.04649 304.1913 demmaj1 | -11.14637 17.7557 -0.63 0.530 -45.9469 23.65417 demgov | 33.53881 10.05574 3.34 0.001 13.82993 53.2477 _cons | -466.4247 102.9804 -4.53 0.000 -668.2627 -264.5868 -------------+---------------------------------------------------------------- sigma_u | 453.92823 sigma_e | 185.56074 rho | .85681858 (fraction of variance due to u_i) ------------------------------------------------------------------------------ ** Noten que las betas, p-values y R2 son distintos... ** EVALUANDO SI EFECTOS FIJOS VS. ALEATORIOS: ** xttest0 se corre inmediatamente despues de random effects, y prueba la ** hipotesis nula de que no hay varianza entre las dummies estatales. ** Si Ho se rechaza, descartamos la hipotesis de que no hay efectos fijos a ** controlar--es decir, quizá necesitamos fixed effects. ** Si Ho no se rechaza, no podemos descartar la hipotesis de que los efectos ** son aleatorios. . xttest0 Breusch and Pagan Lagrangian multiplier test for random effects: spend[stcode,t] = Xb + u[stcode] + e[stcode,t] Estimated results: | Var sd = sqrt(Var) ---------+----------------------------- spend | 395200.4 628.6496 e | 34432.79 185.5607 u | 206050.8 453.9282 Test: Var(u) = 0 chi2(1) = 8171.29 Prob > chi2 = 0.0000 ** Se rechaza Ho: Parece ser que sí hay varianza entre las dummies estatales... ** La prueba Breusch y Pagan es muy fácil de rechazar, pero no es concluyente. ** Antes de descartar random effects necesitamos probar además si ** los efectos fijos bajo sospecha están correlacionados o no con las X´s. ** Si no hay correlación entre Ui y Xs, no hace falta usar ** efectos fijos—pues no hay ningún sesgo que eliminar, y ** random effects es más eficiente (pues no tiene que calcular tanta ** dummy). ** Primero estimamos fixed effects: . xtreg spend popul aper* persinc dem*, fe Fixed-effects (within) regression Number of obs = 1885 Group variable (i): stcode Number of groups = 49 R-sq: within = 0.8036 Obs per group: min = 14 between = 0.3771 avg = 38.5 overall = 0.4689 max = 40 F(7,1829) = 1069.16 corr(u_i, Xb) = 0.0235 Prob > F = 0.0000 ------------------------------------------------------------------------------ spend | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -13.51484 5.131464 -2.63 0.009 -23.57899 -3.450696 aper5_17 | -302.6328 199.2352 -1.52 0.129 -693.3852 88.11947 aper65 | 2275.595 597.6709 3.81 0.000 1103.406 3447.784 persinc | .1416308 .0034689 40.83 0.000 .1348275 .1484341 dem1 | 216.9176 53.46584 4.06 0.000 112.0571 321.7781 demmaj1 | -16.2362 17.60653 -0.92 0.357 -50.76722 18.29482 demgov | 34.17819 9.944188 3.44 0.001 14.67503 53.68134 _cons | -584.6617 79.68837 -7.34 0.000 -740.9515 -428.3719 -------------+---------------------------------------------------------------- sigma_u | 636.079 sigma_e | 185.56074 rho | .92157064 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(48, 1829) = 154.82 Prob > F = 0.0000 ** ... y guardamos los resultados: . est store fijos ** Luego estimamos random effects: . xtreg spend popul aper* persinc dem*, re Random-effects GLS regression Number of obs = 1885 Group variable (i): stcode Number of groups = 49 R-sq: within = 0.8034 Obs per group: min = 14 between = 0.4192 avg = 38.5 overall = 0.4870 max = 40 Random effects u_i ~ Gaussian Wald chi2(7) = 7354.02 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ spend | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- popul | -17.10089 4.933078 -3.47 0.001 -26.76955 -7.432238 aper5_17 | -337.3402 200.7367 -1.68 0.093 -730.7769 56.09651 aper65 | 1620.119 592.9956 2.73 0.006 457.8687 2782.369 persinc | .145831 .0034421 42.37 0.000 .1390845 .1525774 dem1 | 199.1189 53.60937 3.71 0.000 94.04649 304.1913 demmaj1 | -11.14637 17.7557 -0.63 0.530 -45.9469 23.65417 demgov | 33.53881 10.05574 3.34 0.001 13.82993 53.2477 _cons | -466.4247 102.9804 -4.53 0.000 -668.2627 -264.5868 -------------+---------------------------------------------------------------- sigma_u | 453.92823 sigma_e | 185.56074 rho | .85681858 (fraction of variance due to u_i) ------------------------------------------------------------------------------ ** Y ahora sí, comparamos ambos: . hausman fijos . ---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | fijos . Difference S.E. -------------+---------------------------------------------------------------- popul | -13.51484 -17.10089 3.586053 1.413034 aper5_17 | -302.6328 -337.3402 34.70735 . aper65 | 2275.595 1620.119 655.4765 74.60985 persinc | .1416308 .145831 -.0042002 .0004298 dem1 | 216.9176 199.1189 17.79867 . demmaj1 | -16.2362 -11.14637 -5.089834 . demgov | 34.17819 33.53881 .6393724 . ------------------------------------------------------------------------------ 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(6) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 93.31 Prob>chi2 = 0.0000 ** El comando hausman compara los resultados de fixed y random effects ** y prueba la Ho de que las betas de fe y re son indistintas. ** Si rechazas Ho, las betas difieren y entonces apoyas fixed effects ** Si no rechazas Ho, no hay evidencia de correlacion entre Ui y las Xs, ni ** sesgo a corregir en las betas, por lo tanto apoyas random effects. . log close log: C:\Documents and Settings\salon\Escritorio\clase3-mar.log log type: text closed on: 4 Mar 2005, 17:15:29 ---------------------------------------------------------------------------------