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# Econometrics

Submitted By missmariam
Words 1475
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Question no. 1
Y1= ∝0+∝1Y2+∝2X1+∈1
Y2= β0+β1Y1+β2X1+β3X3+ϵ2 i. Identification Status:
Equation 1: P1=1, P2=1 so that P1=P2 so, equation is Exactly identified.
Equation 2: P1=0, P2=1 so that P1<P2 so, equation is Unidentified.

ii. Reduced form equations:
Putting Y1 in Y2:
Y2= β0+β1(∝0+∝1Y2+∝2X1+∈1) +β2X1+β3X3+ϵ2
Y2= β0+β1α0+β1α1Y2+β1α2X1+β1ϵ1+β2X1+β3X3+ϵ2
Y21-β1α1= β0+β1α0+X1β1α2+β2+β3X3+β1ϵ1+ϵ2
Y2= β0+β1α01-β1α1+β1α2+β21-β1α1X1+β31-β1α1X3+β1ϵ1+ϵ21-β1α1
Y1=π20+π21X1+π22X3+ν2

Now putting this reduced form equation of Y2 in Y1 equation:
Y1= ∝0+∝1(π20+π21X1+π22X3+V2)∝2X1+∈1
Y1= ∝0+∝1π20+X1α1π21+α2+α1π22X3+α1V2+ϵ1
Y1= π10+π11X1+π12X3+V1

π10= ∝0+∝1π20 α0= π10-π12π22(π20) π11= α1π21+α2 α2= π11- π12π22(π21) π12= α1π22 α1= π12π22
Using STATA the reduced form equation (DATA set 1)

Y2= -1.57953 -.37781X1+1.744 X3
Y1= 14.245+ .67809 X1+ .99181 X3

Estimations of structural parameters
For equation 1:
Run the regression on reduced form equations in STATA and we calculated the following values of structural parameters: 1. α1= π12π22
= .99181 1.744 α1= 0.5688 2. α2= π11- π12π22π21
= .67809 - 0.5688 (-.37781) α2= 0.8930 3. α0= π10-π12π22(π20)
= 14.245-0.5688(-1.57953) α0= 15.1437

Question no. 2
Y1=αo+α1Y2+α2X1+α3X2+e1
Y2=βo+β1Y1+β2X1+β3X3+e2
Status Identification of equations:
For equation 1:
P1=1
P2=1
P1=P2This identifies that the equation 1 is “Exactly-identified”.
For equation 2: P1=1 P2=1
P1=P2 This identifies that the equation 2 is “Exactly-identified”
Transformation into reduced form equation:
Putting Y2 equation in Y1 equation
Y1=αo+α1[βo+β1Y1+β2X1+β3X3+e2]+α2X1+α3X2+e1
Y1 1-α1β1=αo+α1βo+α1β2X1+α1β3X3+α1e2+α2X1+α3X2+e1
Y1 =αo+α1βo1-α1β1+α1β2+α2X11-α1β1+α3X21-α1β1+α1β3X31-α1β1+α1e2+e11-α1β1
Y1=π10+π11X1+π12X2+π13X3+V1

Now putting this reduced form equation of Y1 in Y2 equation:
Y1=βo+β1[π10+π11X1+π12X2+π13X3+V1]+β2X1+β3X3+e2
Y1=βo+β1π10+ β1π11X1+β1π12X2+β1π13X3+β1V1+β2X1+β3X3+e2
Y1=(βo+β1π10)+(β1π11+ β2 )X1+β1π12X2+(β1π13+β3)X3+β1V1+e2

Y2=π20+π21X1+π22X2+π23X3+V2

π20=βo+β1π10 βo=π20- π22π12.π10 π21 = β1π11+β2 β2=π21- π22π12.π11 π22=β1π12 β1= π22π12 π23=β1π13+β3 β3=π23- π22π12.π13 Note: Equation Y2is exactly-identified because its structural parameters can be found out by one way so we can solve this equation through ILS.
Now putting Y1 in Y2 equation:
Y2=βo+β1[αo+α1Y2+α2X1+α3X2+e1]+β2X1+β3X3+e2
Y21-β1α1=βo+β1αo+β1α2X1+β1α3X2+β1e1+β2X1+β3X3+e2
Y2=βo+β1αo1-β1α1+β1α2+β21-β1α1X1+β1α31-β1α1X2+β31-β1α1X3+
β1e1+e2(1-β1α1)
Y2=π30+π31X1+π32X2+π33X3+V3

Putting reduced equation of Y2 in Y1
Y1=αo+α1[π30+π31X1+π32X2+π33X3+V3] +α2X1+α3X2+e1
Y1=π40+π41X1+π42X2+π43X3+V4

Y1=αo+α1π30+α1π31X1+α1π32X2+α1π33X3+α1V3+α2X1+α3X2+e1

π43=α1π33 α1=π43π33 π40=αo+α1π30 αo=π40-π43π33. π30 π41=α1π31+α2 α2=π41-π43π33. π31 π42=α1π32+α3 α3=π42-π43π33. π32
Note: As the equation 1 is exactly identified so we can find out the structural parameters through ILS
Using STATA the reduced form equation (DATA set 1)
Y1=15.519+1.103X1+.384X2+.719X3
Y2=.892+.447X1+ .746X2+1.216X3

Estimations of structural parameters
For equation 1:
Run the regression on reduced form equations in STATA and we get the following values of structural parameters: 4. α1=0.59161 5. α2=0.83886 6. α3=-0.05674 7. α0=14.99196

For equation 2:
Now we compute the values of β from α values 1. β1=1.93972 2. β2=-1.69311 3. β3=1.93972 4. βo=-29.2117

Question # 3: Model
Y1=α0+α1Y2+α2X1+α3X2+ϵ1
Y2=β0+β1Y1+β2X1+β3X3+β4X5+ϵ2 iii. Identification Status:
Equation 1: P1=1, P2=2 so that P1<P2 so, equation is Over identified.
Equation 2: P1=1, P2=1 so that P1=P2 so, equation is Over Exactly identified. iv. Reduced form equations
Putting Y2 in equation Y1
Y1=α0+α1β0+β1Y1+β2X1+β3X3+β4X5+ϵ2+α2X1+α3X2+ϵ1
Y1=α0+α1β0+α1β1Y1+α1β2X1+α1β3X3+α1β4X5+α1ϵ2+α2X1+α3X2+ϵ1
Y1(1-α1β1)=α0+α1β0+(α1β2+α2)X1+α3X2+α1β3X3+α1β4X5+α1ϵ2+ϵ1
Y1=α0+α1β0(1-α1β1)+(α1β2+α2)(1-α1β1)X1+α3(1-α1β1)X2+α1β3(1-α1β1)X3+α1β4(1-α1β1)X5+α1ϵ2+ϵ1(1-α1β1)
Y1=π10+π11X1+π12X2+π13X3+π14X5+υ1
Now putting reduce equation of Y1 in equation Y2
Y2=β0+β1[π10+π11X1+π12X2+π13X3+π14X5+υ1]+β2X1+β3X3+β4X5+ϵ2
Y2=β0+β1π10+(β1π11+β2)X1+β1π12X2+(β1π13+β3)X3+(β1π14+β4)X5+β1υ1+ϵ2
Y2=π20+π21X1+π22X2+π23X3+π24X5+υ2
π20=β0+β1π10 | β0=π20-π10[π22π12] | π21=β1π11+β2 | β1=π22π12 | π22=β1π12 | β2=π21-π11[π22π12] | π23=β1π13+β3 | β3=π23-π13[π22π12] | π24=β1π14+β4 | β4=π24-π14[π22π12] |

v. Estimated reduced equations:
Y1=π10+π11X1+π12X2+π13X3+π14X5+υ1
Y1=-6.860086 +1.301827 (X1)+.7571526 (X2)+.4143187(X3)+.1310392(X5)
Y2=π20+π21X1+π22X2+π23X3+π24X5+υ2
Y2= 6.063845+.4011194 (X1)+.659783 (X2)+ 1.286288(X3)-.0302849 (X5) vi. Structural Parameters of Equation 2 ; by using ILS
Y2=β0+β1Y1+β2X1+β3X3+β4X5+ϵ2
β0=π20-π10[π22π12] β0=6.063845 -6.860086[.659783.7571526] β0=0.085964002 β1=π22π12 β1=.659783.7571526 β1=.8714003 β2=π21-π11π22π12 β2=.4011194-1.301827[.659783.7571526] β2=-.73329304 β3=π23-π13π22π12 β3=1.286288-.4143187 [.659783.7571526] β3=.92525056 β4=π24-π14π22π12 β4=-.0302849-.1310392[.659783.7571526] β4=-.1444725
Question no. 4
Y1=α0+α1Y2+e1
Y2=β0+β1Y1+β2X1+β3X5+e2
Status Identification of equations:
For equation 1:
P1=2
P2=1 P1>P2This identifies that the equation 1 is “over-identified”.
For equation 2: P1=0 P2=1 P1<P2 This identifies that the equation 2 is “un-identified”

Transformation into reduced form equation:
Putting Y1 equation in Y2 equation:
Y2=β0+β1[α0+α1Y2+e1]+β2X1+β3X5+e2
Y2=β0+β1α0+β1α1Y2+β1e1+β2X1+β3X5+e2
Y2[1-β1α1]=β0+β1α0+β2X1+β3X5+β1e1+e2
Y2=β0+β1α01-β1α1+β21-β1α1X1+β31-β1α1X5+β1e1+e2 1-β1α1
Y2=π20+π21X1+π22X5+v2

Now putting this reduced form equation of Y2 in Y1 equation:
Y1=α0+α1[π20+π21X1+π22X5+v2]+e1
Y1=α0+α1π20+α1π21X1+α1π22X5+α1v2+e1 Y1=π10+π11X1+π12X5+v1

π10= α0+α1π20 α0=π10-π11π21*π20 π11=α1π21 α1=π11π21 π12=α1π22 α1=π12π22 Note: Equation Y1is over-identified because its structural parameters can be found out by more than one ways so we can solve this equation through 2 stage least square (2SLS). Estimations of structural parameters
For equation 1:
Run the regression on reduced form equation of Y2 in stata in first step and we get the values of π :
Y2=37.125+2.745X1+.043X5
Then in second step run the regression Y1 on Y2hat then get the following values of structural parameters 1. α0=0.3354 2. α1=0.89298

Question no. 5
Y1=α0+α1Y2+α2X1+e1
Y2=β0+β1Y1+β3X5+e2
Status Identification of equations:
For equation 1:
P1=1
P2=1 P1=P2This identifies that the equation 1 is “exactly-identified”.
For equation 2: P1=1 P2=1 P1=P2 This identifies that the equation 2 is “exactly-identified”
Putting Y1 equation in Y2 equation:
Y2=β0+β1[α0+α1Y2+α2X1+e1]+β3X5+e2
Y2=β0+β1α0+β1α1Y2+β1α2X1+β1e1+β3X5+e2
Y2[1-β1α1]=β0+β1α0+β1α2X1+β3X5+β1e1+e2
Y2=β0+β1α01-β1α1+β1α21-β1α1X1+β31-β1α1X5+β1e1+e2 1-β1α1
Y2=π20+π21X1+π22X5+v2

Now putting this reduced form equation of Y2 in Y1 equation:
Y1=α0+α1π20+π21X1+π22X5+v2+α2X1+e1
Y1=π10+π11X1+π12X5+v1

Y1=α0+α1π20+(α1π21+α2)X1+α1π22X5+α1v2+e1 π10= α0+α1π20 α0=π10-π11π21*π20 π11=α1π21+α2 α2= π11-π12π22 *π21 π12=α1π22 α1=π12π22 Estimations of structural parameters
For equation 1:
ILS
By using STATA:
Y2=37.125+2.745X1+.043X5
Y1=18.263+ 2.243X1+ 0.120X5 1. α0= -85.467 2. α1= 2.749 3. α2= -5.427
2SLS:
Run the regression on reduced form equation of Y2 in STATA in first step and we get the values of π :
Y2=37.125+2.745X1+.043X5
Then in second step run the regression Y1 on Y2hat then get the following values of structural parameters 4. α0= -85.467 5. α1= 2.749 6. α2= -5.427
Thus, prove that ILS and 2SLS provide identical results for exactly identified equations.

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#### Stock Market Relation

...International Conference On Applied Economics – ICOAE 2010 299 DOES STOCK MARKET DEVELOPMENT CAUSE ECONOMIC GROWTH? A TIME SERIES ANALYSIS FOR BANGLADESH ECONOMY MD. SHARIF HOSSAIN (PH. D.)1 - KHND. MD. MOSTAFA KAMAL2 Abstract In this paper the principal purpose has been made to investigate the causal relationship between stock market development and economic growth in Bangladesh. To investigate long-run causal linkages between stock market development and economic growth the Engle-Granger causality and ML tests are applied. In this paper another attempt has been made to investigate the non-stationarity in the series of stock market development and economic growth by using modern econometric techniques. The co-integrated tests are applied to know whether this pair of variables shares the same stochastic trend or not. From our analysis it has been found that the stock market development strongly influences the economic growth in Bangladesh economy, but there is no causation from economic growth to stock market development. Thus unidirectional causality has prevailed between stock market development and economic growth in the Bangladesh economy. Also it has been found that all the variables are integrated of order 1, and both the variables stock market development and economic growth share the same stochastic trend in Bangladesh economy. JEL Code: C010 Key Words: Stock Market Development, Causal Relationship, Non-stationarity, Unit Root Test, Co-integrated......

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