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Review Question 1.3.2 (Example of a linear estimator)
For the consumption function example in Example 1.1, propose a linear and unbiased estimator of $$ \beta_2 $$ that is different from the OLS estimator.
Solution
We propose an estimator $$ \widehat{\beta}_2 = ( CON_2 - CON_1 ) / ( YD_2 - YD_1 ) $$.
When $$ YD_1, \ldots, YD_n $$ is known, $$ \widehat{\beta}_2 $$ is a linear combination of $$ CON_1, \ldots, CON_n $$.