INTRODUCTION TO ECONOMETRICS II
ECO 306
NOUN
112 variables that are difficult to measure, such as technical progress or changes in tastes.
Nonstochastic explanatory variables are unusual in regression analysis. A rationale for making the nonstochastic assumption has been one of simplifying the analysis of the properties of the regression estimators. For example, we saw that in the regression model
…[4.01] the OLS estimator of the slope coefficient maybe decomposed as follows
( )
( )
( )
( )
…[4.02]
Here, if X is nonstochastic, so is
( ) and the expected value of the error term can be written , ( )- ( ). Also if X is nonstochastic,
, ( )- is 0. Which easily helps us to prove that b
2
is an unbiased estimator of
The desirable properties of the OLS estimators remain unchanged even if the descriptive variables have stochastic components, provided that these components are distributed independently of the disturbance term, and provided that their distributions do not depend on the parameters
u
Let us demonstrate the unbiasedness and consistency properties and as typical, taking an efficient approach.
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