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PS6solutions - Econ 103 UCLA Fall 2010 Problem Set 6...

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Econ 103 UCLA, Fall 2010 Problem Set 6 Solutions by Diego Ubfal Part 1: True or False and explain briefly why. 1. Estimation of the IV regression model requires exact identification or overidentification. TRUE. The model cannot be estimated if it is not identified, which is the case when the number of available instruments is smaller than the number of endogenous variables. 2. Two Stage Least Squares is calculated as follows: In the first stage Y is regressed on the exogenous variables only. The predicted value of Y is then regressed on the instrumental variables. FALSE. In the first stage the endogenous X is regressed on the exogenous variables (including the instrumental variables). In the second stage Y is regressed on the pre- dicted values of X from the first stage and on all the exogenous variables (excluding the instrumental variables). 3. The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor, the first stage F must be statistically significant to indicate a strong instrument. FALSE. The rule-of-thumb for checking for weak instruments is to check whether the first stage F is larger than 10 or not. A value larger than 10 indicates strong instru- ments. 4. The J -statistic tells you if the instruments are exogenous. FALSE. The J statistic can only tell us whether at least one of several instruments is endogenous. A small value of the J -statistic (smaller than the corresponding critical value) tells you that there is no evidence to reject the null hypothesis that all the instru- ments are exogenous. If the value of the J -statistic is larger than the critical value we can only say that there is evidence to claim that at least one instrument is not exoge- nous. This is an indirect and not a direct test for endogeneity (which is not feasible) since we are testing for correlation between the instruments and the residuals and not the population error terms. 5. The distinction between endogenous and exogenous variables is that exogenous variables are determined inside the model and endogenous variables are determined outside the model. FALSE. Exogenous variables are are those that are uncorrelated with u and endogenous ones are those that are correlated with u . 6. The two conditions for a valid instrument are Corr ( Z i , X i ) = 0 and Corr ( Z i , u i ) = 0 . FALSE. In the simple case of one endogenous regressor and one instrument, the correct conditions are Corr ( Z i , X i ) 6 = 0 and Corr ( Z i , u i ) = 0 . 1
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Econ 103 UCLA, Fall 2010 7. Instrument relevance means that the instrument is one of the determinants of the dependent variable. FALSE. The instrument should be one of the determinants of the endogenous inde- pendent variable. 8. The TSLS estimator is unbiased, consistent, and has a normal distribution in large samples.
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