APROXIMACIÓN A UNA ESTIMACIÓN DE LAS IMPORTACIONES EN COLOMBIA: 1965-2005 UN ENFOQUE EN LOS ACONTECIMIENTOS POLÍTICO -ECONÓMICOS DE LA HISTORIA COLOMBIANA
JIMENA DELGADO SOTO*, ALEJANDRO MAYORGA ARBOLEDA * PONTIFICIA UNIVERSIDAD JAVERIANA, CALI MAYO DE 2011 RESUMEN A CONTINUACIÓN SE DESARROLLARÁ UN ANÁLISIS DE LAS DINÁMICAS DE IMPORTACIÓN COLOMBIANAS ACONTECIDAS ENTRE 1966 Y 2005. PARTIENDO DE UN FUNDAMENTO TEÓRICO Y CON LA COMPLEMENTACIÓN DE DATOS HISTÓRICOS, SE ESTIMA UN MODELO ECONOMÉTRICO QUE PRETENDE DAR CUENTA DE DICHA DINÁMICA EN TÉRMINOS DEL COMPORTAMIENTO DEL PIB REAL Y DE LA TASA DE CAMBIO REAL, CONSIDERANDO ADEMÁS ALGUNOS HECHOS POLÍTICO-ECONÓMICOS RELEVANTES EN LA HISTORIA COLOMBIANA, CUYA INFLUENCIA HA LOGRADO GENERAR CAMBIOS ESTRUCTURALES SIGNIFICATIVOS EN LA DINÁMICA DE CRECIMIENTO DE NUESTRO PAÍS, COMO ES EL CASO POR EJEMPLO DE LA IMPLEMENTACIÓN EN 1991 DE LA POLÍTICA DE APERTURA ECONÓMICA. PALABRAS CLAVE: IMPORTACIONES, PIB REAL, TASA DE CAMBIO REAL, APERTURA ECONÓMICA, ELASTICIDAD
________________________________________________________________________________________ * AGRADECEMOS LOS CONOCIMIENTOS ENTREGADOS POR EL PROFESOR LUIS EDUARDO GIRÓN CRUZ DURANTE EL PRIMER SEMESTRE DEL AÑO 2011 EN LA ASIGNATURA ECONOMETRÍA II, Y ADEMÁS SU ACOMPAÑAMIENTO Y ASESORÍA PARA LA ELABORACIÓN DEL PRESENTE TRABAJO .
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TABLA DE CONTENIDO OBJETIVOS.................................... ....................................................... ...................................... ...................................... ....................................... ....................................... ...................................... ............................... ............ 2 ....................................................... ...................................... ...................................... ...................................... ...................................... ...................................... ...................... ... 2 MARCO TEÓRICO .................................... ........................................................ ...................................... ...................................... ....................................... ....................................... ............................... ............ 5 MARCO REFERENCIAL ..................................... ........................................................ ...................................... ...................................... ...................................... ...................................... ...................... ... 6 FORMULACIÓN DEL MODELO .....................................
METODOLOGÍA PARA EL MANEJO DE LOS DATOS...................................... ......................................................... ...................................... ...................................... ............................ ......... 7 ESTIMACIÓN POR MCO Y ANÁLISIS DEL MODELO ..................................... ........................................................ ...................................... ...................................... ............................ ......... 9 PRUEBAS DE ESTACIONARIEDAD ..................................... ........................................................ ...................................... ...................................... ....................................... ................................. ............. 10 Serie
ln M t
...................................... ......................................................... ...................................... ...................................... ...................................... ...................................... ....................................... .................... 11
Serie
ln PIBt ..................................... ........................................................ ...................................... ...................................... ...................................... ...................................... .................................... ................. 14
Serie
ln TCRt ..................................... ........................................................ ...................................... ...................................... ...................................... ...................................... .................................... ................. 17
Prueba de Estacionariedad para el Término de Perturbación .......................................................................... 21
PRUEBAS DE HIPÓTESIS PARA LOS SUPUESTOS DEL MCRL.................................... ........................................................ ....................................... ............................. .......... 23 Pruebas Prueb as de Significancia Significan cia ..................................... ........................................................ ...................................... ...................................... ...................................... ....................................... .................... 23 Prueba Prueb a de d e White W hite - Heteroscedasticid Hetero scedasticidad ad ...................................... ......................................................... ....................................... ....................................... ................................ ............. 24 Prueba Prueb a de Normalidad Nor malidad de d e los Errores Err ores ..................................... ........................................................ ...................................... ...................................... .................................... ................. 24 Prueba de Breusch-Godfrey - Autocorrelación ................................................................................................. 25 Prueba Prueb a de Multicolinealidad Multicoline alidad ................................................ ................................................................... ...................................... ...................................... ...................................... ....................... .... 25 Prueba Prueb a RESET-Ramsey RESET-Ra msey - Especificación Especifica ción ................................ ................................................... ...................................... ...................................... .................................... ................. 26 Pruebas Prueb as de Datos Atípicos ............................... .................................................. ...................................... ...................................... ...................................... ...................................... ....................... .... 26 ......................................................... ...................................... ...................................... ...................................... ...................................... ..................... 29 ECUACIONES SIMULTÁNEAS ...................................... Sistema de Ecuaciones Ecuacion es Simultáneas Simultáne as .................................... ....................................................... ...................................... ...................................... ...................................... ..................... 29 Ecuaciones Ecuacion es Reducidas Reducid as................................................. .................................................................... ....................................... ....................................... ...................................... ............................. .......... 30 Reglas para la Identificació Ide ntificaciónn .................................... ....................................................... ....................................... ....................................... ...................................... ................................ ............. 30 Prueba Prueb a de Simultaneidad Simultaneida d de Hausman ...................................... ......................................................... ....................................... ....................................... ................................ ............. 32 Prueba Prueb a de Exogeneidad Exogene idad ...................................... ......................................................... ...................................... ...................................... ...................................... ....................................... .................... 33
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1. OBJETIVOS 1.2. GENERAL Analizar, por medio de la teoría económica y de algunas herramientas econométricas básicas, la dinámica de las importaciones colombianas experimentada durante el período 1966-2005, explicada ésta, por variables económicas como el PIB Real, la Tasa de Cambio Real y los niveles de Importaciones para períodos anteriores.
1.3. ESPECÍFICOS Plantear un modelo econométrico sobre las importaciones colombianas. Analizar el impacto de variables económicas como el PIB Real y la Tasa d Cambio Real sobre los niveles de Importación en Colombia. Analizar el efecto sobre las Importaciones, de la implementación de Políticas Económicas de Apertura Económica en el país. 2. MARCO TEÓRICO 2.1. COMERCIO INTERNACIONAL La interacción económica establecida entre diferentes naciones, conocida como Comercio Internacional, es el
resultado de una importante dinámica ejercida por prácticas de oferta y demanda, en las que una nación ya no se limita a consumir estrictamente su producción, como ocurría en una situación de autarquía, sino que amplía significativamente su frontera de posibilidades de consumo para acceder a una cesta de bienes y servicios que además de satisfacer sus deseos y necesidades, es el reflejo de la especialización y las ventajas en una producción más eficiente por parte de otras naciones. Gracias al comercio, el gasto de una nación durante un año determinado, no resulta necesariamente igual a su producción de bienes y servicios, y en cambio surge la posibilidad de establecer relaciones internacionales fundamentadas en los intercambios eficientes. Un sinnúmero de teorías de manera recurrente tienden a cuestionar el comercio internacional, e incluso a plantear argumentos en su contra fundamentándose para ello en políticas proteccionistas que luchan una batalla constante con el librecambio; sin embargo, es muy importante reconocer la evidente importancia del comercio internacional al interior de una economía mundial; en este sentido, no hay peligro de afirmar que el ³comercio trae consigo ganancias´1. Pensando entonces en términos de los principales actores del comercio entre naciones (exportadores e importadores), los exportadores por medio de éste, logran encontrar nuevos canales de comercialización para sus productos, que no son vendidos al interior de sus países bien sea
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importadores se benefician al poder acceder a esos productos escasos a un precio significativamente más bajo. Se establecen entonces Patrones de Comercio fundamentados justamente en las ³ventajas comparativas´ que cada nación experimenta, logrando una producción más eficiente traducida en términos de excedentes en los beneficios logrados dentro de la dinámica del comercio internacional. Ahora bien, para objeto de estudio a lo largo de esta investigación, centraremos nuestro análisis en el comportamiento de las importaciones como componente esencial del comercio internacional. Para comenzar, vale la pena una aproximación a su definición más básica; al respecto, N. Gregory Mankiw dice: ³ Las importaciones, son todos aquellos bienes y servicios que se producen en el extranjero y se venden en nuestro país´2, mientras que Olivier Blanchard la complementa diciendo: ³Las importaciones son compras de bienes y servicios extranjeros por parte de los consumidores, las empresas y el Estado del país´ 3 . Y finalmente adaptando una definición para el contexto colombiano, Eduardo Lora propone: ³Las importaciones son la introducción legal de mercancías procedentes de otros países o de una zona franca industrial colombiana al resto del territorio aduanero nacional ´4. Se podría pensar entonces que el volumen de comercio internacional
explicado por parte de las importaciones, se dinamiza por factores como los gustos de los consumidores de un país determinado por los bienes extranjeros, los precios de los bienes en dicho país en relación con los precios en el exterior, los tipos de cambio a los que la moneda nacional permite comprar cierta cantidad de moneda extranjera, la renta de los residentes del país y del país extranjero, los costos de transporte en los que se debe incurrir para ingresar al país mercancías provenientes del exterior, y de manera muy especial, las políticas del país comprador con respecto al comercio internacional. ¿Pero, de qué dependen entonces las importaciones?, sería éste entonces nuestro siguiente punto, y para ello basta con analizar en primera instancia y de forma vasta la dinámica general de la economía del país importador, esto por medio de su Producto Interno Bruto -PIB-, y de las fluctuaciones experimentadas por el Tipo de Cambio a lo largo de un determinado período de tiempo. A priori y haciendo referencia tanto en la observación como en la teoría económica, es válido pensar en una relación positiva tanto entre las importaciones y el nivel del renta del país, así como también entre éstas y el tipo de cambio. En lo que respecta al PIB, dicha relación positiva se justifica analizando la Identidad de la Contabilidad Nacional5 para una economía abierta: PIB ! Y ! C I G X M
Donde, PIB ! Y ! Producto/Renta Nacional C ! Consumo
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I ! Inversión G ! Gasto
X ! Exportaciones
M ! Importaciones
Un incremento en el nivel de renta o de producción de un país, propicia un entorno donde la capacidad adquisitiva de sus agentes económicos se ve sustancialmente mejorada, se genera entonces un efecto riqueza y como consecuencia se experimentan incrementos en el consumo de las familias, en la inversión de las empresas y en el gasto del gobierno; en otros términos la demanda interna crece y un porcentaje de ésta es satisfecho por la oferta disponible de bienes y servicios extranjeros, representada por el volumen creciente de importaciones. Un claro ejemplo de esta situación se evidencia cuando al interior de un país se opta por implementar una política fiscal expansiva por medio de una reducción en los impuestos, lo que genera un incremento en la renta disponible, traducido en términos de un mayor consumo y de una disminución del ahorro nacional, lo que termina por reducir directamente las exportaciones netas, o en otras palabras, por incrementar el nivel de importaciones. Es muy importante tener en cuenta, que para efectos de un análisis y una comparación más eficientes de las dinámicas de importación en Colombia a lo largo del tiempo, debe considerarse el PIB Real, definido como la ³suma de las cantidades de bienes finales multiplicadas por los precios constantes´6 y que a diferencia del PIB Nominal que se presenta en términos de los precios corrientes para un año determinado, permite medir verdaderamente verdader amente la evolución de la producción de un país con el paso del tiempo eliminando los efectos de las fluctuaciones en los precios, esto debido a que se referencia a un año base. Pero éste análisis del mercado de bienes y servicios no puede p uede pensarse independiente al comportamiento del mercado de dinero, para el caso específico del comercio internacional, del mercado de divisas; y es entonces cuando entra en juego el Tipo T ipo de Cambio, o el precio al cual se realizan r ealizan los intercambios de bienes y servicios en el ámbito global. Dada la naturaleza misma del comercio exterior, consistente en el intercambio entre naciones, éste debe analizarse en términos del Tipo de Cambio Real, definido como ³un indicador amplio de los precios de los bienes y servicios de un país respecto a los de otros ´7, es decir que éste indica la relación de intercambio de bienes y servicios basada en sus precios relativos8, y técnicamente está definido por la siguiente expresión: I ! e
Donde, I !
Tipo de Cambio Real
P
P
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!
Tipo de Cambio Nominal
P ! Precio del Bien Nacional
P ! Precio del Bien Extranjero
El Tipo de Cambio Real, resulta pues del análisis inflacionario de cada nación involucrada en el intercambio y simultáneamente, del Tipo de Cambio Nominal 9 del país importador, que no es más que el precio relativo de su moneda con respecto a la moneda de su socio comercial. Así mismo es posible ver que esta relación de precios internacionales de bienes y servicios, resulta de la dinámica de las políticas económicas implementadas al interior de cada país. En este sentido, la política fiscal influye en una primera instancia sobre el comportamiento de los precios, mientras que la política monetaria determina los tipos de interés a los cuales cada nación dinamizará su mercado de dinero y consecuentemente el flujo de capitales permitiendo variaciones dentro del mercado de divisas. Recogiendo el análisis anterior, es posible validar dicha relación positiva entre el Tipo de Cambio Real y el nivel de importaciones de determinada nación, aceptando la hipótesis que plantea que si ³el Tipo de Cambio Real es alto, los bienes extranjeros son relativamente baratos y los nacionales son relativamente caros ´10
2.2. PROCESO DE APERTURA ECONÓMICA EN COLOMBIA11 La
Historia Económica Colombiana comprendida entre la década del cincuenta y la década del ochenta, refleja la poca cohesión entre las expectativas y objetivos de crecimiento y desarrollo de sarrollo económico del país, con las medidas adoptadas por el modelo vigente para lograrlo. Así, durante este período, Colombia experimentó no sólo una notable desaceleración en su ritmo de crecimiento económico, sino que además se sumergió en una de las más críticas situaciones de carácter sociopolítico e institucional por la que hubiera atravesado hasta entonces. Surgen entonces una serie de factores estructurales relevantes dentro de la economía colombiana, que le imponen la urgente necesidad de ser transformados y de reorientar sus políticas de desarrollo de forma tal que el país pudiera llegar a pensarse activo dentro de un ámbito económico global. Merecen ser destacados entonces, aspectos como el problema de la deuda externa, principal limitante de procesos de financiamiento internacional para el desarrollo, la limitada dinámica de los procesos de industrialización industrialización y su consecuente baja capacidad de generación de empleo y finalmente los altos y crecientes niveles de ³deuda social´ en dimensiones fundamentales para el desarrollo como la educación, la salud y los asuntos políticos. En la década de los noventa, en respuesta a esta crítica situación se cimientan los principales lineamientos de un proceso de ³ajuste estructural´ para la economía colombiana. Esta estrategia de crecimiento y desarrollo iniciada en los últimos momentos del gobierno de Virgilio Barco y finalmente implementada durante el gobierno de César Gaviria, se fundamentó en el desarrollo desar rollo a partir de la modernización del aparato a parato productivo de la economía nacional, de tal forma que ésta lograra adaptarse e incursionar a las dinamias del mercado
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internacional, atendiendo conjuntamente asuntos que respondieran a una gradual liberación del comercio y todas aquellas dimensiones determinantes del desarrollo enmarcadas en asuntos sociales y políticos.
3. MARCO REFERENCIAL La literatura económica acerca del comportamiento de las importaciones en una economía abierta es bastante
basta, seguido a esto se han desarrollado varios modelos econométricos en vías de lograr identificar el comportamiento de las mismas con fines de acción o recomendación para las futuras políticas económicas que se implementen en los países objeto de estudio. En el trabajo ³La demanda para importaciones en Colombia´ de Hugo Oliveros y Luisa Fernanda Silva del Banco de la República, se puede confirmar la consideración a priori de que las importaciones dependen indudablemente de el ingreso (PIB) y de la tasa de cambio real (TCR); que entre estas existe una relación de largo plazo además en equilibrio y que las fluctuaciones en el consumo de bienes extranjeros entonces estarán dadas principalmente las acciones que los responsables de la política económica efectúen sobre estas. Un estudio mas recienten en el 2005 es el trabajo realizado por Juan Nicolás Hernández, ³Demanda de importaciones para el caso colombiano: 1980-2004 ³del Banco de la República; en éste trabajo se recopila el planteamiento no solo de Oliveros y Silva, sino de muchos otros importantes análisis sobre la estimación de las importaciones en el país como lo es Igor Esteban Zuccardi Huertas con ³Demanda por importaciones en Colombia: Una estimación ³en el 2001. El denominador común en estos trabajos además de las variables ya mencionadas es la relevancia que algunos a lgunos hechos históricos han tenido sobre la economía, y en nuestro caso claramente sobre las importaciones. La variable Dummy para diferenciar el cambio que significo para la economía economía del país la apertura económica se suma a ese denominador común.
4. FORMULACIÓN DEL MODELO
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dinámicas del comercio exterior colombiano, y que en respuesta a este suceso, toma el valor de cero para el período comprendido entre 1966-1991, mientras que para el período 1992-2005, esta variable indicadora adquiere el valor de 1. A priori, contrastando el Modelo con la teoría económica, esperamos que finalmente nos lleve a concluir una relación positiva entre el nivel de Importaciones y el PIB Real, la Tasa de Cambio Real y las Importaciones Rezagadas. Así mismo, esperamos encontrar que el impacto de la Política de Apertura Aper tura Económica, haya sido significativo para los años posteriores a 1991, hecho que se reflejaría en un crecimiento del nivel de Importaciones durante el período 1992-2005. El Modelo de Importaciones Colombianas que formulamos pretende evidenciar entonces el efecto conjunto medido en términos de crecimiento porcentual, del PIB Real, la Tasa de Cambio Real y las Importaciones Rezagadas un período, sobre el nivel de Importaciones, considerando además los posibles impactos de la implementación de una Política de Apertura Económica; en este sentido, la forma funcional que adopta nuestro modelo es ³log log´, el cual mide ³el cambio porcentual en Y (M) ante un pequeño cambio porcentual en X (PIB, TCR, Importaciones Rezagadas) dado´ 12 y nos permitirá medir dichos efectos por medio de elasticidades. En este sentido el Modelo resulta ser el siguiente: M t
!
F
F
F
F
F 4 APEC
e 0 PIBt 1 TCRt 2 M t 31e
e
ut
Que linealizado equivale a: ln M t !
F0
F 1 ln PIBt F 2 ln TCR t F 3 ln M t 1 F 4 APEC t u t
Donde: M t ! Importaciones Colombianas
PIBt !
PIB Real
TCR
Tasa de Cambio Real
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Aunque contamos con datos históricos comprendidos en el período 1965-2005, vale la pena aclarar que para objetos de estimación y análisis de nuestro modelo, tendremos en cuenta únicamente el período 1966-2005, esto como consecuencia de la forma autoregresiva del Modelo, que implica la pérdida de una observación por efecto del período rezagado. Originalmente tuvimos tres series de PIB Real, cada una con año base 1975, 1994 y 2000 respectivamente. Decidimos trabajar con precios constantes a 2000 dada la relativa actualidad de dichos precios y su consecuente facilidad para ser interpretados en relación con los vigentes hoy en día en Colombia, por esta razón fue necesario llevar a cabo un procedimiento de ³Empalme de Series del PIB´, cuyos cálculos se encuentran anexados en la Tabla 1, y mediante la aplicación de la siguientes fórmulas para cada año comprendido en el período en el período de estudio: B
B
I.
PIBt !
A
PIBt 1 * PIBt A
PIBt 1 C
C
II.
PIBt !
B
PIBt 1 * PIBt B
PIBt 1
Donde: A
!
B
!
Precios constantes con año base 1975 Precios constantes con año base 1994
C ! Precios constantes con año base 2000 t
!
Año de análisis
t 1 ! Año inmediatamente posterior al año
de análisis
Ahora bien, en lo referente al cálculo del Tipo de Cambio Real, fue necesario en primer lugar contar con una serie del Tipo de Cambio Nominal correspondiente al período 1966-2005, además del Índice de Precios al
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________________________________________________________________________________ TCR
!
Tipo de Cambio Real
TCN ! Tipo de Cambio Nominal Los cálculos correspondientes se encuentran anexados en la Tabla 2.
Finalmente, para la variable Importaciones, se utilizó una serie del valor de las Importaciones nacionales en Pesos Colombianos, ajustadas ajustadas al Tipo de Cambio Camb io vigente para cada año del período per íodo de análisis. Las
cifras consolidadas de las 40 observaciones para cada una de las variables a incluir en nuestro Modelo, se anexa en la Tabla 3.
6. ESTIMACIÓN POR MCO Y ANÁLISIS DEL MODELO13
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el modelo nos indica entonces que para el caso hipotético de la ausencia de las variables explicatorias, la variación porcentual en las importaciones importaciones sería del -29.78970%, esto para el período comprendido comprendido entre 1966 y 1991, mientras que con el cambio institucional dado por el proceso de apertura económica en 1991, a partir de 1992 se contaría con un diferencial en el intercepto in tercepto de 0.162325% como lo indica la variable Dummy APEC (Apertura Económica), lo cual está acorde con el boom del consumo evidenciado en los años posteriores a dicho proceso de apertura económica. Debido al cambio en el intercepto que define la variable APEC se establece que para los años siguientes a 1991, en ausencia de las demás variables explicatorias, las importaciones colombianas experimentarían un crecimiento negativo del 29.627375%. Del mismo modo, de acuerdo a la elasticidad de m con respecto al ingreso incremento del 1% en la variable
TCRt ,
PIBt ,
se presenta que ante un
es decir el tipo de cambio real, ceteris paribus, las importaciones
colombianas crecerían 0.328968%; de acuerdo a la elasticidad de M con respecto a la
TCRt
ante un
incremento del 1% en el PIBt , ceteris paribus, las importaciones crecerían un 1.929972% y finalmente, ante un cambio del 1% en las importaciones en el año inmediatamente anterior al estimado, manteniendo todo lo demás constante, las importaciones crecerían en 0.449647%. Para fines prácticos, dado el coeficiente de determinación lineal de 0.9984, se entiende que el 99.84% de las variaciones presentadas en las importaciones son explicadas por las variables explicativas del modelo.
7.
PRUEBAS DE ESTACIONARIEDAD
En primer lugar, es importante anotar que la condición de Estacionariedad esta referida a la posibilidad de que una serie de tiempo presente ³media y varianza que no experimenten variaciones sistemáticas a lo largo del tiempo´ 14 . En otras palabras, una serie de tiempo es Estacionaria si su media y su varianza son constantes a lo largo del tiempo. Ahora bien, el trabajo empírico supone que las series de tiempo empleadas en la formulación de modelos econométricos son estacionarias. En este sentido, para probar la Estacionariedad de nuestras series de tiempo, recurrimos a dos métodos; el
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lapso de días, para nuestro caso en el que tenemos 40 observaciones anuales ya incluyendo la perdida de una por el rezago, decimos que la potencia de nuestra Prueba de Estacionariedad es muy confiable. 7.1. SERIE ln M t
Como observamos en la siguiente gráfica la serie ln M t no tiene una tendencia parecida a la de un proceso de ruido blanco, es decir, que mediante su grafica podemos observar en un primer momento que ni su media ni su varianza son constantes a lo largo del tiempo, lo cual significa que la serie ser ie no es estacionaria.
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Ahora observemos que la grafica del correlograma cor relograma nos muestra unos coeficientes de autocorrelación bastante altos que además comienzan en un nivel significativamente alto y van disminuyendo muy lentamente hacia cero, lo que visualmente sugiere de nuevo que ln M t es una serie de tiempo que no es estacionaria.
Ahora bien, cuando observamos el correlograma de la serie
ln M t
en primeras diferencias, encontramos que
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________________________________________________________________________________
Al graficar la nueva serie dada por ln M t en primeras diferencias (DLNM), observamos claramente la diferencia que se presenta con la grafica de la serie
ln M t ,
ahora según se puede observar su media o
varianza parecieran ser constantes a lo largo del tiempo, lo que confirma que la serie estacionaria. 7.1.2.
DICKEY-FULLER
H0= La serie
ln M t
tiene Raíz Unitaria (es no Estacionaria)
Ha= La serie
ln M t
no tiene Raíz Unitaria (es Estacionaria)
ln M t
en I (1) es
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________________________________________________________________________________
En primeras diferencias la serie ln M t es decir, D(LNM) ahora es estacionaria, pues con un valor p de 0.0000 menor a 0.05 se rechaza la hipótesis nula y se establece que la serie no tiene raíz unitaria, es decir es estacionaria. 7.2. SERIE ln PIBt
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El anterior correlograma también es típico de una serie que no presenta estacionariedad, es decir los coeficientes de autocorrelación son bastante altos, comenzando por un valor grande que decrece muy lentamente, lo que da la interpretación entonces de ln PIBt como una serie no estacionaria.
Esta imagen del correlograma de la serie de tiempo D ( LNPIB) es típica de una serie de tiempo estacionaria en la cual se muestra cómo las autocorrelaciones con distintos rezagos se ubican alrededor de cero. Esto
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________________________________________________________________________________
Graficando la serie ln PIBt en primeras diferencias obtenemos una serie que visualmente parece tener media y varianza constantes a lo largo del tiempo, lo que indica que la serie ahora es estacionaria. 7.2.2.
DICKEY-FULLER
H0= La serie
ln PIBt
tiene Raíz Unitaria (es no Estacionaria)
Ha= La serie
ln PIBt
no tiene Raíz Unitaria (es Estacionaria)
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________________________________________________________________________________
7.3. SERIE ln TCRt
Al graficar la serie ln TCRt como se muestra a continuación, deducimos que no se trata de una serie estacionaria, pues su media y varianza no parecen constantes en el tiempo. tiempo.
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rezagos, lo cual es evidencia que quizás su media y varianza no son constantes a lo largo del tiempo, muestra de que la serie ln TCRt no es estacionaria.
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sin un proceso en orden 1; en términos prácticos la serie ahora tiene un mejor comportamiento, sin embargo es necesario que la serie sea integrada de orden ord en 2 para corregir totalmente la presencia de raíz r aíz unitaria.
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________________________________________________________________________________
7.3.2.
DICKEY-FULLER
H0= La serie
ln TCRt tiene Raíz Unitaria (es no
Ha= La serie
ln TCRt
Estacionaria)
no tiene Raíz Unitaria (es Estacionaria)
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Con el fin de confirmar lo que la simple observación nos sugiere, sugier e, analizaremos a continuación el correlograma de la serie u t y aplicaremos a ésta además, la Prueba Dickey-Fuller para conocer si presenta o no Raíz Unitaria.
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________________________________________________________________________________
En la anterior prueba de Dickey Fuller, el valor p de 0.0000 menor a 0.05 nos indica que se rechaza la hipótesis nula, lo cual significa que el término de perturbación u t no presenta raíz unitaria y es por lo tanto estacionario.
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________________________________________________________________________________
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________________________________________________________________________________
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