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B ( ;: Op2$?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> 6. (    6 P  L cN NN}/kGrjL#j_    0`1   8 cN NN}/kGreW[#j_ ,{Nd\ ,{ Nd\ ,{Vd\ ,{Nd\    01   1 @ H  0޽h ? ̙33 Default Design0 jb( %{    0̌Y P   Y P*    0 Y    Y \* d  c $ ?  Y  0ȜY  @ Y 8 cN NN}/kGreW[#j_ ,{Nd\ ,{ Nd\ ,{Vd\ ,{Nd\    6Y `P  Y P*    6AU `  Y R*  H  0޽h ? ̙330 (    0(Y P   Y T*     0|Y    Y V*     6Y `P  Y T*     6hY `  Y V*   H  0޽h ? ̙33  0`(    6P1P  ~Variables Artificiales b,&     <  <T1z  \Son variables binarias o variables cero-uno diseadas para describir informacion cualitativa]Q 2E      H  0޽h ? ̙33p  @(  x  <A (??PxH (H  0޽h ? ̙33u %P @(     s *1 La muestra separada de Hombres  (2 , x   <A *??0 *H  0޽h ? ̙33g `(  x  <A ??`$h    s *$1@ La muestra separada de Mujeres  (2 6 H  0޽h ? ̙33_ pV( g( :   61 h Salario Y (2   61  xX Aos de enseanza,   <1_I3 V ! 2! ( 6ܪ1   ~Dos modelos separados: 2, T * 6S1  P  *Yi = a1 + b 1 Xi + ui3 3333333333( + 61 P   *Yj = a 2 + b2 Xj + uj| , 61   <(hombre) 2  - 61   ](mujer) 2` B c $A ??PP   C 0t1` @ 2  E <T1 P  @  F <1 PP  > 8 G 601 @ *Y = a 2 + b X (mujer)j 2 H 6`1 @`U G^*023 I 61  7n G^*0x23 J 61  D@ E^( 23dB K <DoQF 0  L P  M 0$10  *Y = a1 + b X (hombre)R 23333  N 0d1A a - 9^0x23 O 01 P k 9^023 P 0p1 - 9^0x23dB Q <D3o0 XB U 0DԔP@`XB V 0Dfo p @ H  0޽h ? ̙33 JB ( : Z  0$:  Supongamos que la relacion entre Y y X no cambia, es decir, las pendientes son las mismas: b 1 = b2 .Vg 2^33333    0 : ^ Modelo: 2   6<:  66Yi = a1 + a2 Di + b Xi + ui 0  6:Pp HYi = a1 + a2 Di + b Xi + b D*Xi + ui % >^B  6D @p g  0(: Py  5Yi = salario anual Xi = aos de esperiencia enseandoL6 2  !b  Xr   0` P@[   00:  UDi = 1 si hombre = 0 en caso contrario (mujer)2V 2 SP^B  @ 6D    0P8:  SVariable de control$ 23X  0<: Supongamos que la relacion entre Y y X cambia, es decir, las pendientes no son las mismas: b 1 b2.Vf 2^33333     0G:Pp UModelo: 2XB  0D@ XB  0D H  0޽h ? ̙33s #(    0P:@  h Salario Y (2   04U:  xX Aos de enseanza,   6lZ:_I3 V ! 2!3F  P    P  0^:   lDos modelos separados: 2V  0b:   *Yi = a1 + b 1 Xi + ui3 3333333333*  0Ll: 0 P  *Yj = a 2 + b2 Xj + uj|   0xv:   <(hombre) 2    0@y:0 P  ](mujer) 2`   c $A ??P   0 ~:` @ 2   6:P  @   6@:PP  > P  0:@ *Y = a 2 + b2X (mujer) 2  0\:@`U G^*023  0: 7n G^*0x23  0: &@ E^( 23^B  6DqF 0   P    0 :0  ,Y = a1 + b 1X (hombre)p 2333333   0:A a - 9^0x23  0: P k 9^023  0t: - 9^0x23  xB&C3DEF&3@`6   3 B4C0 DEF0 4@Z XB  0DfԔ p XB  0DԔ`@0H  0޽h ? ̙33 /' (     0<:`I D1 + D2 = 1 D1 = 1 - D2t 23 33 33 33 3x   <A ,??`   ,H  0޽h ? ̙33H     ,X x ( : X X 0h:  (La Trampa de la Variable Dummy)*! 2   "X 6:pv 8Si se introducen dos variables dummies en un modelo como9 29H " #X 6x:Pp JYi = a1 + a2 D1i + a2 D2i + b Xi + uI"& 2 33,  $X 6:@  ;donde D1i = 1 hombre = 0 lo contrario$<3$-   %X 6,:@  <donde D2i = 1 mujer = 0 lo contrario,$=46   &X 6<: @  Fzentonces este modelo no se puede estimar debido a la existencia de multicolinealidad perfecta entre la constante, D1 y D2.{ 2{3    F   (X ` `h )X c $A ??:p  *X 0:x ; D1 = 1 - D2 2  +X 0:x  ?o D2 = 1 - D1 2 ,X 0:  5o D1 + D2 = 1 ( Multicolinealidad Perfecta)6 26 H X 0޽h ? ̙33    A0 A (  b  6>@P,  Para evitar la multicolinealidad perfecta, si una variable cualitativa tiene  m categorias, introducir solo  m-1 variables dummies.H 2M33     . <:  B3  / <L>   B3  0 <8> `  B3  1 <>  B3  3 <>@ B3  4 <>P   B3  6 < >` B3  8 6H#>P @ @  > 6&>p@` 31 ? <*>Z z >  @ 6P->` pP  32 A <0>0 }  Cuando a una de las categorias de una variable dummy se le asigna el valor de cero se la llama categoria-control (o grupo omitido). < 2`%    H  0޽h ? ̙33 >0 (     6?>PP FVolvamos al ejemplo del principio: Model: Yi = a1 + a2 Di + b Xi + uI p 2" 3R  # 8     <   6`P>    ;Hombre: 2  BS>  @  |t==> Yi = (a1 + a2 Di) + b Xi Di = 1;  333 33  <8a>     P ^2  <e>   D ^&  <j> P   P ^2 $ <n>   G ^(F ( 6s>    XMujer: ==> 2  * B,w>   VYi = a1 + b Xi Di = 0A-3 338 + <>    ;^ , <>p 0 P  D ^& - <> P  F ^(P 5 0>`  (Di = 1 hombre = 0 en caso contrario:) 3 &, H  0޽h ? ̙33  (    C fANC:\COURSE\ECON2170\GUJARA\tab1501d.bmp   C fANC:\COURSE\ECON2170\GUJARA\tab1501e.bmp@ 0  6Ě>  aMujeres `    6>` SHombres `  ,  6Ԣ>p Regresiones Separadas por sexo `h          H  0޽h ? ̙33  (    C fANC:\COURSE\ECON2170\GUJARA\tab1501a.bmpP  !  6>P -Regresiones via dummies para el mismo ejemplo. .`N         F @,    @ T  L   # @,f   <б> L  .Yi = (a1 + a2 D) + b Xi3 3333333333   6H>0   C^&33  6> @  ?^"3  6>` @  ?^"3  6> p@ A^$F3  6>0P F `   6h> P f= (19.937-1.2810) + 1.561X `    0>` SD1:M =1 `  X2  0   C fA NC:\COURSE\ECON2170\GUJARA\tab1501c.bmpP@   0>`  SD2:H =1 `    6\>  P f= (16.656+1.2810) + 1.561X `  F @,   lT  L  # @,f  <> L  .Yi = (a1 + a2 D) + b Xi3 3333333333  6>0   C^&33  6> @  ?^"3  6h>` @  ?^"3  6> p@ A^$F3X  0JH  0޽h ? ̙33  (    C fA NC:\COURSE\ECON2170\GUJARA\tab1501b.bmpL  @ # p0 6  <C @ Yi = a1 + b Xi   6 C    C^&  6Cp 0  P ^2  6C  F ^(F  6Cp  [= 17.095+1.608X `    <C*JJ >   6C  !Regresion sin distincion de sexos""@       H  0޽h ? ̙33@     (    C fANC:\COURSE\ECON2170\GUJARA\tab1501f.bmp0   0#C0`  r D1: Mujer =1   `&    8 @     0(C@ HMujer: Y = (a1 + a2 D) + (b1 + b2D)X% 2  :  0d2C@  6Hombre: Y = a1 + b1 Xi  2  6P:C0 P . _^. d`     6>C  _^. d`     6XBCh   _^. d`     6 FC  ~ _^. d`     6IC ` _^. d`     6MC4j _^. d`    6xQC 0 ^= 18.689 + 1.373 X `    6UCpP ]= 16.255 +1.677 X `  -  <TC  UInterpreta esta regresion donde se permite la pendiente sea diferente para cada sexoVV2   ;  H  0޽h ? ̙330    d ( Z   C fANC:\COURSE\ECON2170\GUJARA\tab1501g.bmp`@`   0`C  X D2: Hombre=1   `  @8 @    P p  6dC@ HHombre: Y = (a1 + a2 D) + (b1 +b2D)X% 2 ^  6mC@  :Mujer: Y = a1 + b1 Xi  2  <$vC  _^. d`    <zCF f $ _^. d`     <~Ch   _^. d`     <C  ~ _^. d`     <,C ` _^. d`     <C4j _^. d`    6ȎC  ]=16.255 + 1.677 X `    6hCp0 ]=18.689 + 1.373 X `  H  0޽h ? ̙33m 0(( : (* ( 0$C 2Una variable cualitativa con mas de dos categorias,3 22H  8 0p (p  ( 0PC0` `(Gasto medico) = a1 + a2 D2 + a3 D3 + bRenta + u1 23333,! ( 0XCp 7(Y) 23 ( 0C`p 7(X) 23 ( 0C  UgD2 = 1 Educacion secundaria = 0 otros D3 = 1 Educacion universitaria = 0 otrosVh3 313 33t  H ( 0޽h ? ̙33 @(-,9( {@s@ , , 6C`f Z Gasto Medico  ^B , 6Dpp ^B , 6D pP  , 6CP Srenta 2^ , 63p ^B  , 6D3p p ^B  , 6Dp ^B  , 6D@p 0 X  , 0 p , 0HC HD3 = 1& 2F    !,     , 6C   $\Educacion Universitaria Y = (a1 + a3 D3) + b X/ 2$   , <LC0   E^( , <C p@ E^(x , <`C`@ E^(x , <C@ R ^4PF  i  ,  i  , 6pC i  VEducacion Secundaria Y = (a1 + a2 D2) + b X, 2$   , <C @` p C^& , <LCP p  F ^( , <Hp` R ^4 , <hHp0 R ^4ZF  G   #, G  N , 60 H G   BMenos que Secundaria Y = a1 + b XD" 233336  , <H  C^&33 , <H@  C^&33 , <pH P  C^&33  , <DH P  B3  ", 0x HPp HD2 = 1& 28 pP &,pP $, 0 #HpP Xa18 2333 %, 6'H0 5^3F pP ', ` P  (, 0,HpP Xa28 2 ), 6/H0 5^Xr *, 00 pF pP +, @ p`  ,, 03HpP Xa38 2 -, 67H0 5^H , 0޽h ? ̙33+ P0k(  0 0 0?H  $D2 = 1 Secundaria = 0 otros0%3 3#3, 0 0CH  &D3 = 1 Universitaria = 0 otros<' $3,  0 0KH ========================================= obs Y X D2 D3 ========================================= 1 6.000000 40.00000 0.000000 1.000000 2 3.900000 31.00000 1.000000 0.000000 3 1.800000 18.00000 0.000000 0.000000 4 1.900000 19.00000 0.000000 0.000000 5 7.200000 47.00000 0.000000 1.000000 6 3.300000 27.00000 1.000000 0.000000 7 3.100000 26.00000 1.000000 0.000000 8 1.700000 17.00000 0.000000 0.000000 9 6.400000 43.00000 0.000000 1.000000 10 7.900000 49.00000 0.000000 1.000000 11 1.500000 15.00000 0.000000 0.000000 12 3.100000 25.00000 1.000000 0.000000 13 3.600000 29.00000 1.000000 0.000000 14 2.000000 20.00000 0.000000 0.000000 15 6.200000 41.00000 0.000000 1.000000 ========================================= NK831. DP @ L<H 0 0޽h ? ̙33N `4( : 4 4 6XbH0  >Z  4 6cH0  X . 8(T` X x 4 <A ?? P XB 4 0D  H 4 0޽h ? ̙33   p80 I (  0OI  8h8 Pp 8Pp 8 0sHPpp Menos que secundaria:$ 236 @ pPp 8pPp 8 0xHpPp Yi = -1.2859 + 0.1722 Xix 23 3333 33 8 6DHP0  C^&33 8 6HPp %Yi = (-1.2859 - 0.068 ) + 0.1722 XiL& 23 3"3 33 8 < HP`  C^&33  8 6DHp @ H= -1.3539 + 0.1722 X 23^2  8 6P p^B  8 6D` `  8 6H  \= -1.2859 + 0.1722 X, 2   8 6HP p e Secundaria:$ 2 3 8   @`  8 Pp@  8 6lHp @ $Yi = (-1.2859 + 0.447 ) + 0.1722 XiL% 23 3!3 33 8 <DH 0  C^&33 8 0H` @@`  c= -0.8389 + 0.1722 Xi2 23 33 8 0 edad > 25 = 0 otros$/->   \ 0H   )A2 = 1 si edad > 55 = 0 otros$*(>   \ 0H@ `  dA1 + A2 12 28 ` p   \p `  `B  \ 0D`  `B \ 0D` ` ` `B \ 0D`  `B \ 0D`  `B \ 0D`   \ 0lHp   aA2 =1@ 2  \ 0Hp p  aA1 =1@ 2  \ 0J p p  C0& 2 \ 0lJ `  625 2 \ 00J `  655 2H \ 0޽h ? ̙33a  `0 (  ` ` 0Jp @ #Entonces los modelos estimados son:$ 2$H  ` 0lJ  A(Cont.)(2  ` 0J g Menos de 25& 2 A8 p  `p ` 0Jp Y = a0 + b XR 2 ` 6"J0  7^ ` 6%J   8 ^ ` 6)Jp   : ^P,  ` 6,J@p` *Y = (a0 + a1A1) + b X 2  ` <X4J@0 p 7^  ` <$.JpP  7^ ` <07Jp `  7^ ` <>JpR 9^P ` 08AJ@` r25 < edad < 55& 2 ` 0FJ e edad > 55& 2 , ` 6JJp *Y = (a1 + a2A2) + b X 2 ` <RJ0  7^ ` <VJP  7^ ` <ZJ `  7^ ` <T]JO 9^F ` 6_J &  LPensad que hipotesis pueden ser interesantes para contrastar y como hacerloMM2    7  H ` 0޽h ? ̙33 ,1x  (  x x 0iJ  En un diagrama de puntos Y-X: 2,8   1x B  xB Z?D3?p B  xB Z?D3?p  `r  x 03p @ p 0  xp 0  x 0jJp 0  Va06 2333 x 6rJ@ 0  5^3N p 0  x    x 0dvJp 0  Va16 2333 x 6zJ@ 0  C^&33N p 0  x p  x 0xJp 0  Va26 2333 x 6 J@ 0  C^&33@ 0  0x0  x <J0 1YfB x 6D  P fB x 6D P P  x 6J   1X 2fr x 63 P fr x 63  `B x 0D  `B x 0D @`B x 0D ` x 65@J W edad < 25 2  x 650Jpp d25 < edad < 55 2 x 65LJ` W edad > 55 2 JN  #x   x 6 J (Y = ( a0 + a2) + b Xn 2 x <TJP0 7^ x <ȦJ0` 7^  x < @ 6 @ <܀K 0 `  C^& @ <(K  p`  C^& @ <K 0   C^& @ <K  0  C^&H @ 0޽h ? ̙33 VN D0 (  D8   D D 6K ?D = 1 si 1946-1954 = 0 demas (1955-1963)@?,  r D <4K >   D 6Kp p 1. Identica:& 2 Z  D 6K` :Y = b1 + b2 X + b3 D + b4 D*X 2&  D 6Kp (H0 : b3 = 0 y b4 = 0| 23 3333333F Pp D p D 04KP0  p 2. Paralela:& 2 \ D 0K p :Y = b1 + b2 X + b3 D + b4 D*X 2 D 0K0 H0 : b4 = 0^ 23 33333F Pp  D 0  D 6KP  o 4. Cruzada:& 2 b D 6pK  p  :Y = b1 + b2 X + b3 D + b4 D*X 2. D 6|K0   (H0 : b3 0 y b4 0| 23 3333333F Pp  D   D 0lsKP  s3. Concurrente:& 2  \ D 0HK  p  :Y = b1 + b2 X + b3 D + b4 D*X 2 D 0K0   H0 : b3 = 0^ 23 33333 D 6K0 3Diferentes tipos de regresion con variables dummies44$ H D 0޽h ? ̙33r ""XHP(  H H 0K ZPeriodo (46-54): Yt = A1 + A2 Xt + u1t Periodo (55-63): Yt = B1 + B2 Xt +u2t [           $  ! H <LPT 1Y^B H 6DT ^B H 6D   H <@Li ` 9  1X^B  H 6D^  H 6   H 6@L1 @Q  [A1 = B18 2^B  H 6D(,^B  H@ 6D,`, H <L`  =1  H 6D L0  [A2 = B28 2 H 68%L3 p  Q Identica  (2   )H <x)LP @ 1Y^B *H 6D@` ` P ^B +H 6DP ` P  ,H <P-L @  1X^B .H 6D`` `p^ /H 6p` P  0H 61L p  EA1 & 2^B 1H 6D^B 2H@ 6D@ 3H <`6Lp =1  4H 6D;L` EA2 & 2 5H 6>L3   XParalela (2 : 7H 6XBLP p   A1 B1, A2 = B2 2 ^B 8H 6D` `^B 9H 6D@0^B :H@ 6D0 0 ;H <LLp@ PB22  H 6 UL 0  PB12 2 H H 0޽h ? ̙33 '2L0 (  L L <P_Lph 1Y^B L 6Dp ^B L 6Dp p  L <dbL   1X^B L 6D4P ^ L 6P hp   L 6fL hd  [A1 = B18 2^B  L 6D`^B  L@ 6D` `  L <kLP  11  L 6loLP  DB2& 2 L 6rL3 x  [ Concurrente (2  ^B L 6D`P ^B L 6D@88^B L@ 6D 8 L <wL@8(0 PA22  L <|L  51 L <pLp \  1Y^B L 6D p ^B L 6Dp p  L <L   1X^B L 6D P ^ L 6P \ p  L 6L \ <  QA1 2 2 ^B L 6DXX^B L@ 6DX L < L 51  L 6LXt QA2 2 2  !L 60L3 D WCruzada(2. #L 6Lp \    A1 B1, A2 B2 2 ^r )L 6p p  *L 6 2 3333$,  6L0   Efecto Interactivo:, d3`4       0N P Da 2 = efecto diferenciador de ser mujer a 3= efecto diferenciador de ser estudiante universitario a 4 = efecto diferenciador de ser mujer estudiante universitariaX &9=     H  0޽h ? ̙33 OG#&d( :  dL d s *N3  <Modelo Concurrente (o modelo con variacion en la pendiente)8=;Z    d 00L Ejemplo: Como podemos contrastar la hipotesis de que el consumo de gasolina es diferente en un coche nuevo que en un coche usado??? 2    d 0 !N T^Supongamos que al comienzo no hay ninguna diferencia de consumo entre los dos tipos de coches:_ 2^   d 0P*NP  eConsumo gasolina 2XB d@ 0D `XB d 0D``  d 0/Np Pmillas 2  d 6h3N   6Y 3  d 06N 5X 23XB  d 0D  XB  d 0D Xr d 03 p`8   d  d 08;N  Va06 2333 d 6?N p@ C^&33 d 6{LDNp 00  R * * * * * * S 2S d 6{HN C  Q * * * * * R 2R d 6; V h 0ԞN`  O Entonces  2   h 0Np0 sVariable dummy multiplicativa 23 h 0hN`  D8Yi = a0 + (g0 + g1 D) Xi +ui 2  h 0\N`  p> = a0 + g0 Xi + g1 D*Xi +ui 2 h 0N`  <: = a0 + g0 Xi + g1 Zi +ui 2333 h 0(NP0  Las relaciones estimadas son: 2,    h 6N `  @Usado: Yi = a0 + (g0 + g1 Di) Xi donde Di = 1 6Y 2  3 33 6%  h <N @@  8 ^ h <N 0 p  C^& h <N  p  C^& h < N ` p  C^&  h 6N` P  .LNuevo : Yi = a0 + g0 Xi' 2   h <$O`   7^  h <O 0  7^ h <O   C^&vL P   h#  P   h 6 OP   8== 23lB h <D3  L p <  !h#  p<  h <|O <  Yi = a0 + b Xin 2 lN P   h P  h 0OP   8== 23fB h 6D3   h 6 O @`  8 ^ h 6O0 0  7^ h 6O @ `  7^ h 0p#Op   5o 2XB (h 0D3@ H h 0޽h ? ̙33 qi0 l (  l8    l @B l 0+O   pQueremos contrastar si g1 = 0 o no. Se pueden utilizar dos estrategias:PI 2/l   l 0\4O@ D 2 8 l 66O@ ` D(i) Comparar : (a) Y = a0 + b XP# 2 l 6 0j 2  l 6|O  B  l 0,O0 w  Si t* > tcP, N-3H 2  l 0O   ~=> rechazar H02 2     l 0ЖO `  o (g1 0)P 2H l 0޽h ? ̙33e    @|  (  |^B | 6D@@^B | 6D@@ | <O  @ & ... 2 | <xOp @ & ... 2 | <OA @ & ... 2 | <hO A  @ & ... 2  | <OP  @ & ... 2  | 00O0  $@Y = a0 + g0 Xi + g1 Zi + ! 2  | 0O@ 0 `  aCalcular el t-valor 23 ` | c $A ??  dB | <DԔ @  | 6O@0P`  M^ `   | 6O^~  M^ `   | 6DOZz  M^ `   | 6OZ! A z  M^ `  H | 0޽h ? ̙33 JBP!!(  :  s *,O3 6Variaciones tanto en la constante como en la pendiente,7 263Z     0OW -Ejemplo: Estimacion de efectos estacionales :. 2.H    0Op lE = a + b T + u2 2   0DOp  E : consumo de electricidad 2,   0Op  eT : temperatura 2 <  0O >Para capturar los efectos estacionales solo en la constante: ? 2?b    0Q0  bNE = a0 + a1 D1 +a2 D2 + a3 D3 + b T + u( 2   0Q @@  Sdonde 28  0    0 ,   0 Q 0  0D1 = 1 invierno 0 otros21P /, `r   0  F  0     0   04Q 0  1D2 = 1 primavera 0 otros22P 0, `r  0  F  0   0 *  0Q 0  .D3 = 1 verano 0 otros2/P -, `r  0  98   ! `B  0D    00Q ` 8prim 2  0)Q  Tverano 2  0,Qp  Qoto 2  0(0Q  Tinvier 2`B  0D P `B  0DP  `B  0DpP p `B  0DP    044Q   6Q1 2  07Q` @  6Q2 2  0$;Q@   6Q3 2  0>QP 0  6Q4 2`B   0DP  H  0޽h ? ̙33    p X ( `L ! D  0 0Q@`   ,E = a0 + b0 T (Otoo)n 233333 33 B 6Q 0 p  7^3 C 6Q0`   7^3 D 6(Q` @  9^P3G@    U   ? 0Q   *BE = (a0 + a1) + (b0 +b2)T(Invier)" 2  E 6Q0 @  7^ F 6DQ @p  7^ G 6LQ0 p  7^ H 6Q@ p  9^F I 68R p  9^F@    N   A 0R   2JE = (a0 + a1) + (b0 + b2)T (Primaver)& 2  J 6R 0  9^Z K 6R    9^P L 6pR   8 ^ M 6R  9^N    O   P 0R   .FE = (a0 + a3) + (b0 + b3)T (Verano)$ 2  Q 6&R 0  9^P R 6P*R    9^F S 6-R   8 ^ T 60R  9^xH  0޽h ? ̙33D (  a  s *d-10 ELos efectos estacionales a veces se modelan como efectos trimestralesF 2F3    0@41  'D2 = 1 2-- Trimestre = 0 otros ( 2($   0891  'D3 = 1 3-- Trimestre = 0 otros ( 2($   0=17   'D4 = 1 4-- Trimestre = 0 otros ( 2($   6XB1 P` "Trimestre de control es el primero# #`N        H  0޽h ? ̙33!  a(    C rAZD:\COURSE\ECON2170\GUJARA\dummy_seasonal.bmp  6ԃR@ w1. En E-views dummy = 1 si estamos en el 1-er trimestre = 0 otrosZx ` dP`d`        8    dB  <D3> p ` ^B  6DԔ\ dB   <D3> XB  @ 0D3L ` H  0޽h ? ̙33 4, ( : x   <A ???   ?   6R  &Como son las variables artificiales?' '`@        H  0޽h ? ̙339 m(  +  s *ЛR3 Z ;Contraste de Cambio Estructural basado en variables dummies*< 2;H    0Rp 0 m Modelo Basico 2$  0pR`p $YT = a + b XT + uTz 2 &8    fB  6DfB  6D0  6lR  81974 23  6̲Rp 81960 23   68R 0 81989 23  0@Rp  RSe define la variable dummy : 2@  0нR  DD = 1 para el periodo que va de 1974 al 1989 = 0 el restoEEb Xr  0    0dR  igPra contrastar si las estructuras de los dos periodos son diferentes, la especificacion debe asumir queh 2h  F8 PP `  P P`   0RPP p  a = a0 + a1 Db 2  0HRP@ `  b = b 1 + b2 DV 2\  0R pi El modelo de regresion: YT = a0 + a1 D + b 1 XT + b2 D XT + uTU 2/ , ?H  0޽h ? ̙33 0 ,( @0@   s *XR3 \nEjemplo: El contraste de Chow en el modelo que relaciona tasa de desempleo y tasa de utilizacion de capacidad oo     8 0  0G  0 R`0 %Var Depend. Constante CAPt R2 F RSS nL& 2   $ $ H`B  0DPP  6R  ` 5_  6 U  *TMuestra : 60 - 89 desemplt 30.0 -0.293 0.761 93.6 17.15 30 (12.1) (9.7) RSSRbU  6 $ :$(| <  <R0 E^((^2  63  6U p  )SMuestra : 60 - 73 desemplt 19.64 -0.175 0.59 19.7 4.69 14 (5.9) (4.4) RSS1bT  5 $ 9$(| <  <R`   E^((^2  630 P`   6 U  +UMuestra : 74 - 89 desemplt 30.63 -0.296 0.871 102.1 3.29 16 (13.1) (10.1) RSS2bV  7 $ ;$(| \ <  <8$U P  E^((^2  63 P` XB  0D0`0  03Ui #Notae : en parentesis los t-valores$ 2$H H  0޽h ? ̙33Q (  A  08:U0 6 #H0 : No cambio estructural H1 : Sin$  ,  0BUP  Para el modelo no restringido:: 2 , -  0FU@` KRSSNR = RSS1 + RSS2 = 4.69 + 3.29 = 7.98fL 2   9C8 Pp  pP   0U  SF* = 2 2 `B  0D`p p  0 Fc ==> rechazar H0f    ,  6$U 0 p  R= 3.37 `  "  6tU@ .Contraste de cambio estructural via un test F:/ /`N        H  0޽h ? ̙33 ZR@( : -  0U 7 3Tasa de desempleo- tasa de utilizacion de capacidad4 24Z     0U@0 ` cMuestra : 1960 - 1989 2  0U`f w+Dt = 1 1974 a 1980 = 0 antes de 19740, *  6 & ...&  2H  0޽h ? ̙33B  (  ^  0 V <  $ Ao ut CAPt Dt DtCAPt 79 1 80 1 81 1 82 1 83 1 84 1 85 1 86 1 87 1 88 1 89 1h 2Fz,X x` Lx  6#V@  H& & & & & & & & .&  2 3  64V@&  H& & & & & & & & .&  2 3  67VpF  H& & & & & & & & .&  2   0h;V   B8U = a0 + a1 CAP + a2 Dt*CAPt 2,XB  0D  XB  0D @  XB  0D @  H  0޽h ? ̙33w '( : B  0XT RLa interpretacion de variables dummies en modelos de regresion Semilog (o Log-Lin)S 2SP  6  0 X  .ln Y = b1 + b2 X + b3 D 2  0lX (Salario) (aos de ensear) 2 3>  0X  *D1 = 1 hombre = 0 demas0+ )%8 @p @p   6pX@p $ln Y = 2.9298 + 0.0546 X2 + 0.1341 Db% 2 3   <X [ ^:$   0LX`  X$t=(481.5) (48.3) (27.2)% 2%  0YPp 'R2 = 0.995 dw = 2.512( 2 &   0Y  -Tomando antilogaritmos de of 0.1341 = 1.1435<. 2 33$  0X Y 0  |Esto significa que el salario inicial de un profesor-hombre es mas alto que el de una profesora-mujer en un 14.35 porciento.   XB  0D  P  0Y   @El modelo estimado para el salario de los profesores-hombres es:A 2At )8      0@Y @ W#ln Y = (2.9298 + 0.1341) + 0.0546 X$ 2$  0Y Lln Y = 3.0639 + 0.0546 X 2  6Y@   = ^  6Y@p = ^H  0޽h ? ̙33+x,ETDTT9 (*TDYsNs95gEs91o];_ߪڻvYsͩڵjs|/t޶ۏk7[7.o봝ڰ5V|bܼ -m-(tz! gxf,ЎYhvv:'t.nyBv] t!EB.]$t)eB. ]"t%UBW]&tji]7t}h_h? 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