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
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