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Econometric models are statistical models used in econometric. This modelling tool help economist develop future economy plan for the company. This lecture note discuss important points for understanding Econometric modelling, it includes Equation, Modeling, Problems, Condition, Identification, Form, References
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3 1 2 3 3
2 3 3 2
1 2 1 2 1
1 2 3 1 2 3 3
1 2 3 1 2 3 2
1 2 3 1 2 3 1
y y y x x x u
y y y x x x u
y y y x x x u
1 1 1 0 0 2 0 1 1 0 0 1
11 32 03 21 12 03
y y y x x x
Equation 1: Order Condition: K=6; M=4; G= (K‐M) = 6 ‐4= (G‐1) = 3 ‐1= Exactly identified
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Rank condition:
1 1 1 0 0 2
0 1 1 0 0 1
1 3 0 2 1 0
1 2
1 1
As this is non‐zero, equation 1 is exactly identified.
Equation 2:
Order Condition: K=6; M=3; G= (K‐M) = 6 ‐3= (G‐1) = 3 ‐1= Over‐identified
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1 1 1 0 0 2
0 1 1 0 0 1
1 3 0 2 1 0
0 0
2 1
As this is zero, equation 3 is not identified. ESTABLISING IDENTIFICATION FROM THE REDUCED FORM
Order condition:
Rank condition
G* = number of endogenous variables contained in a particular equation.
An equation containing G* endogenous variables is identified if it is possible to construct at least one non‐zero determinant of order (G*‐1) from the reduced form coefficients of the exogenous variables excluded from that particular equation.
3 1 2 3 3
2 3 3 2
1 2 1 2 1 2
3 2
y y y x u
y y x u
y y x x u
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The reduced form for this model is:
3 1 2
2 1 2 3
1 1 2 3 2
y x x
y x x x
y x x x
Equation 1: Order Condition: K=6;M=4;G= (K‐M) = 6 ‐4= (G‐1) = 3 ‐1= Exactly identified
Rank condition: Excluded endogenous: y (^3) Included exogenous: x 1 , x (^2)
13 G=2, (G‐1)= As both 3 and 1 are non‐zero, equation 1 is exactly identified.
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Equation 3:
Order Condition: K=6; M=4; G= (K‐M) = 6 ‐4= (G‐1) = 3 ‐1= Exactly identified
Rank condition: Excluded endogenous: None Included exogenous: x (^3)
Equation 3 is not identified.
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Montgomery, D. C., Peck, E. A., and G. G. Vining: Introduction to Linear Regression Analysis , Wiley India, New York, 2006.
Dielman, Terry E.: Applied Regression Analysis for Business and Economics, PWS-Kent, Boston, 1991.
Draper, N. R., and H. Smith: Applied Regression Analysis, 3d ed., John Wiley & Sons, New York, 1998.
Frank, C. R., Jr.: Statistics and Econometrics, Holt, Rinehart and Winston, New York, 1971.
Goldberger, Arthur S.: Introductory Econometrics, Harvard University Press, 1998.
Graybill, F. A.: An Introduction to Linear Statistical Models , vol. 1, McGraw- Hill, New York,
Greene, William H.: Econometric Analysis, 4th ed., Prentice Hall, Englewood Cliffs, N. J., 2000.
Griffiths, William E., R. Carter Hill and George G. Judge: Learning and Practicing Econometrics, John Wiley & Sons, New York, 1993.
Gujarati, Damodar N.: Essentials of Econometrics, 2d ed., McGraw-Hill, New York, 1999.
Hill, Carter, William Griffiths, and George Judge: Undergraduate Econometrics, John Wiley & Sons, New York, 2001.
Johnston, J.: Econometric Methods, 3d ed., McGraw-Hill, New York, 1984.
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Ct = β 10 + β 11 Yt + u (^) 1t
I (^) t = β 20 + β 22 Yt + β 22 Yt− 1 + u2t
