1. Met 2651 Instrument variabler (sider: 539,543, 544,545,549,550,551,559,560,561,564) Ulf H. Olsson Professor of Statistics

2. Ulf H. Olsson IV and TSLS

3. Ulf H. Olsson IV and TSLS If the ”errror term” is correlated with one or more of the x- variables, OLS is not consistent. It is biased even if the sample is large. The bias can either be postive or negative, large or small dependeing on the correlation between the ”error term” an the x- variables. Suppose some INSTRUMENT variables z1,z2,x3, …xq are availabel (q >=k). All z are uncorrelated with the error term.

4. Ulf H. Olsson IV and TSLS It does not require any distributional assumptions, is valid if the estimated relationships is linear, the required variances and covariances exist and the inverse exist.

5. Ulf H. Olsson Two steps Step 1: estimate each xi with respect to z Step 2: Replace x with x-hat and estimate the OLS regression of y with respect to x-hat For every x-variable correlated with ”the error term” there must be at least one instrumental variable outside the set of x-variables.

6. Ulf H. Olsson Econometric Model

7. Ulf H. Olsson Econometric Model Klein’s Model (1950 )

8. Ulf H. Olsson Econometric Model Klein’s Model (1950 )

9. Ulf H. Olsson Econometric Model Klein’s Model (1950 )