Econometrics-I-3

Econometrics-I-3 - Applied Econometrics William Greene...

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Applied Econometrics William Greene Department of Economics Stern School of Business
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Applied Econometrics 3. Linear Least Squares
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Vocabulary Some terms  to be used in the discussion. Population characteristics and entities vs. sample  quantities and analogs Residuals and disturbances Population regression line and sample regression Objective :  Learn about the conditional mean  function.  Estimate  β  and  σ 2 First step:   Mechanics of fitting a line  (hyperplane) to a set of data
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Fitting Criteria The set of points in the sample Fitting criteria - what are they:   LAD Least squares and so on Why least squares ? (We do not call it ‘ordinary’ at this point.)   A fundamental result:           Sample moments are “good” estimators of          their population counterparts          We will spend the next few weeks using this principle and  applying it to least squares computation.
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    In the population     E[ y  |  X  ] =  X β    so                                    E[ y  -  X β  | X ] =  0     Continuing              E [x ε i ] = 0     Summing,                Σ i  E [x ε i ] =  Σ 0 = 0     Exchange  Σ and E   E [ Σ i  x ε i ] =  E[  X ′ ε   ] =  0                                  E[  X  ( y  -  X β ) ]  =   0     Choose  b , the estimator of  β  to mimic this population result:  i.e.,  mimic the population mean with the sample mean       Find  b  such that               As we will see, the solution is the least squares coefficient vector. = = 1
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Econometrics-I-3 - Applied Econometrics William Greene...

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