Resumen
Summary Chapter15-Econometrics-InstrumentalVariable
- Grado
- Institución
Introduction to basic Econometrics.It containing certain chapters. It give a detailed study of Econometrics Chapter15-Econometrics-InstrumentalVariable
[Mostrar más]Vista previa 2 fuera de 5 páginas
Vista previa 2 fuera de 5 páginas
Añadir al carrito
Añadir al carrito
Vendedor
Seguir
partwi085
Vista previa del contenido
Chapter 15Instrumental Variables Estimation
A basic assumption in analyzing the performance of estimators in multiple regression is that the explanatory
variables and disturbance terms are independently distributed. The violation of such assumption disturbs the
optimal properties of the estimators. The instrumental variable estimation method helps in estimating the
regression coefficients in the multiple linear regression model when such violation occurs.
Consider the multiple linear regression model
y X
where y is (n 1) vector of observation on study variable, X is ( n k ) matrix of observations on
X 1 , X 2 ,..., X k , is a (k 1) vector of regression coefficient and is a (n 1) vector of disturbances.
Suppose one or more explanatory variables is correlated with the disturbances in the limit, then we can write
1
plim X ' 0.
n
The consequences of such an assumption on ordinary least squares estimator are as follows:
b X 'X X 'y
1
X ' X X ' X
1
b X ' X X '
1
1
X ' X X '
n n
1
X 'X X '
plim b plim plim
n n
0
X 'X
assuming plim XX exists and is nonsingular. Consequently plim b and thus the OLSE
n
becomes an inconsistent estimator of .
To overcome this problem and to obtain a consistent estimator of , the instrumental variable estimation can
be used.
Econometrics | Chapter 15 | Instrumental Variables Estimation | Shalabh, IIT Kanpur
1
, Consider the model
1
y X with plim X ' 0.
n
Suppose that it is possible to find a data matrix Z of order n k with the following properties.:
Z'X
(i) plim ZX is a finite and nonsingular matrix of full rank. This interprets that the variables in
n
Z are correlated with those in X , in the limit.
Z '
(ii) plim 0,
n
i.e., the variables in Z are uncorrelated with , in the limit.
Z 'Z
(iii) plim ZZ exists.
n
Thus Z variables are postulated to be
uncorrelated with , in the limit and
to have a nonzero cross product with X .
Such variables are called instrumental variables.
If some of X variables are likely to be uncorrelated with , then these can be used to form some of the
columns of Z and extraneous variables are found only for the remaining columns.
First, we understand the role of the term X ' in the OLS estimation. The OLSE b of is derived by
solving the equation
y X ' y X
0
or X ' y X ' Xb
or X ' y Xb 0.
Econometrics | Chapter 15 | Instrumental Variables Estimation | Shalabh, IIT Kanpur
2
Los beneficios de comprar resúmenes en Stuvia estan en línea:
Garantiza la calidad de los comentarios
Compradores de Stuvia evaluaron más de 700.000 resúmenes. Así estas seguro que compras los mejores documentos!
Compra fácil y rápido
Puedes pagar rápidamente y en una vez con iDeal, tarjeta de crédito o con tu crédito de Stuvia. Sin tener que hacerte miembro.
Enfócate en lo más importante
Tus compañeros escriben los resúmenes. Por eso tienes la seguridad que tienes un resumen actual y confiable. Así llegas a la conclusión rapidamente!
Preguntas frecuentes
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
100% de satisfacción garantizada: ¿Cómo funciona?
Nuestra garantía de satisfacción le asegura que siempre encontrará un documento de estudio a tu medida. Tu rellenas un formulario y nuestro equipo de atención al cliente se encarga del resto.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller partwi085. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for 4,39 €. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
45,681 summaries were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now