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
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.
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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