Introduction to econometrics II eco 356 faculty of social sciences course guide course Developers: Dr. Adesina-Uthman

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Introduction to Econometrics ECO 356 Course Guide and Course Material

4.1.3.6 Measurement Errors in the Dependent Variable
INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN

INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
115 Looking at the error term, we can see that it is going to behave badly. By [4.07] and
[4.09], both X
i
and depend on
. The population covariance between X and u is nonzero and, so b
2
is an inconsistent estimator of
. Even if you had a very large sample, your estimate would be inaccurate. In the limit it would underestimate by an amount
…[4.12]
4.1.3.6 Measurement Errors in the Dependent Variable
These measurement errors in the dependent variable do not matter as much. In practice, they can bethought of as contributing to the disturbance term. They are undesirable, because anything that increases the noise in the model will tend to make the regression estimates less accurate, but they will not cause the regression estimates to be biased. By assumption, let the true value of the dependent variable be Q, and the true relationship be
…[4.13] wherev is a disturbance term. If is the measured value of the dependent variable in observation i, and is the measurement error,
…[4.14] which maybe rewritten
…[4.15] whereu is the composite disturbance term (v + r) The only difference from the usual model is that the disturbance term in [4.15] has two components the original disturbance term and the error in measuring Y. The important thing is that the explanatory variable X has not been affected. Hence OLS still yields unbiased estimates provided that X is nonstochastic or that it is distributed

INTRODUCTION TO ECONOMETRICS II

ECO 306

NOUN
116 independently of v and r. The population variance of the slope coefficient will be given by
…[4.16] and so will be greater than it would have been in the absence of measurement error, reducing the precision of the estimator. The standard errors remain valid but will be larger than they would have been in the absence of the measurement error, reflecting the loss of precision.

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