SOLUCIÓN DE LA PRIMERA PRÁCTICA CALIFICADA DE ECONOMETRIA I

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1 UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA SOLUCIÓN DE LA PRIMERA PRÁCTICA CALIFICADA DE ECONOMETRIA I 1º El investigador especifica el modelo siguiente: (7 puntos) M1(t) = a + b P(t) + c(0) PBI(t) + c(1) PBI(t-1) + c(2) PBI(t-2) u(t) se le pide estimar el modelo y obtenga los multiplicadores. Asumimos que: c(i) = (1-d) d i, se reemplaza y se obtiene: M1(t) = a + b P(t) + (1-d) PBI(t) + (1-d)d PBI(t-1) + (1-d)d 2 PBI(t-2) u(t) (1) Rezagamos un periodo: M1(t-1) = a + b P(t-1) + (1-d) PBI(t-1) + (1-d)d PBI(t-2) + (1-d)d 2 PBI(t-3) u(t-1) Multiplicamos por d: d M1(t-1) = ad + bd P(t-1) + (1-d)d PBI(t-1) + (1-d)d 2 PBI(t-2) + (1-d)d 3 PBI(t-3) d u(t-1) (2) (1) (2): M1(t) - d M1(t-1) = a ad + b P(t) - bd P(t-1) + (1-d) PBI(t) + (u(t) - d u(t-1)) M1(t) = a(1 d) + b P(t) - bd P(t-1) + (1-d) PBI(t) + d M1(t-1) + u*(t) M1(t) = a* + b P(t) + b* P(t-1) + d* PBI(t) + d M1(t-1) + u*(t) Sample (adjusted): 1977Q2 2010Q4 Included observations: 135 after adjustments C P P(-1) PBI M1(-1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) TEST DURBIN H N N. S. Prob % Sample: 1977Q2 2010Q4 Included observations: 135 Autocorrelation Partial Correlation AC PAC Q-Stat Prob **. ** md1qbp1=135*( )^2 = md1qbp2=135*(( )^ ^2 =

2 2 Breusch-Godfrey Serial Correlation LM Test: (1 lag) F-statistic Prob. F(1,129) Obs*R-squared Prob. Chi-Square(1) Breusch-Godfrey Serial Correlation LM Test: (2 lag) F-statistic Prob. F(2,128) Obs*R-squared Prob. Chi-Square(2) Method: Two-Stage Least Squares Sample (adjusted): 1977Q3 2010Q4 Included observations: 134 after adjustments Instrument list: C P P(-1) PBI P(-2) PBI(-1) C P P(-1) PBI M1(-1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Sum squared resid F-statistic Durbin-Watson stat Prob(F-statistic) Second-Stage SSR MULTIPLICADORES: M1(t) = a* + b P(t) + b* P(t-1) + d* PBI(t) + d M1(t-1) + u*(t) Sustituyendo: M1(t) = a* + b P(t) + b* P(t-1) + d* PBI(t) + d (a* + b P(t-1) + b* P(t-2) + d* PBI(t-1) + d M1(t-2) + u*(t-1)) + u*(t) M1(t) = a*(1+d) + b P(t) + (b* + bd) P(t-1) + db* P(t-2) + d* PBI(t) + dd* PBI(t-1) + d 2 M1(t-2) + (u*(t) + d u*(t-1)) Segunda sustitución: M1(t) = a*(1+d) + b P(t) + (b* + bd) P(t-1) + db* P(t-2) + d* PBI(t) + dd* PBI(t-1) + d 2 (a* + b P(t-2) + b* P(t-3) + d* PBI(t-2) + d M1(t-3) + u*(t-2)) + (u*(t) + d u*(t-1)) M1(t) = a*(1+d+d 2 ) + b P(t) + (b* + bd) P(t-1) + (db*+bd 2 ) P(t-2) + b*d 2 P(t-3) + d* PBI(t) + dd* PBI(t-1) + d 2 d* PBI(t-2) + d 3 M1(t-3) + (u*(t) + d u*(t-1) + d 2 u*(t-2)) MIP = b = c(2) = MIPBI = d* = c(4) = MD1RP = b* + bd = c(3)+c(2)*c(5) = MD1RPBI = d*d = c(4)*c(5) = MD2RP = db*+bd 2 = c(3)*c(5)+c(2)*c(5)^2 = MD2RPBI = d*d 2 = c(4)*c(5)^2 = MTP = b + bd + + b* + db* + bd = b (1 + d + d 2 +.) + b* (1 + d + d 2 +..) = (b + b*) (1 + d + d 2 +..) MTPBI = d* + d*d + d*d 2 +. = d* (1 + d + d 2 +.) Los multiplicadores totales para simplificarlos require que: 1 y la estimación del modelo se tiene: d = º Se tiene el modelo siguiente: (4 puntos) M1(t) = a + b P(t) + c(0) PBI(t) + c(1) PBI(t-1) c(8) PBI(t-8) + u(t)

3 3 se le pide estimar el modelo y obtener el retardo medio. C P PDL PDL PDL PDL PDL PDL PDL E R-squared Mean dependent var C P PDL PDL PDL PDL PDL PDL R-squared Mean dependent var C P PDL PDL PDL PDL PDL R-squared Mean dependent var

4 4 C P PDL PDL PDL PDL R-squared Mean dependent var C P PDL PDL PDL R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Lag Distribution of PBI i Coefficient Std. Error t-statistic. * * * * * * * * * Sum of Lags mod2rm = obs J B 1977Q Q Q Q Q Q Q Q

5 5 3º Determine la mejor estimación respecto al ítem 1 y 2. (2 puntos) CRITERIO MODELO 1 MODELO2 Adjusted R-squared Akaike info criterion Schwarz criterion Hannan-Quinn criter Sum squared resid La mejor estimación es el modelo 1 porque tiene el mayor R cuadrado ajustado y la menor suma residual. 4º Comente y fundamente su respuesta. (7 puntos) 4.1. El método de estimación de un modelo con retardos infinitos es máxima verosimilitud El estimador de mínimos cuadrados ordinarios es sesgado y no consistente en un modelo dinámico.