Econometrics-I-6 - Econometrics I Professor William Greene...

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Part 6: Finite Sample Properties of LS Econometrics I Professor William Greene Stern School of Business Department of Economics
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Part 6: Finite Sample Properties of LS Econometrics I Part 6 – Finite  Sample Properties of  Least Squares ™    1/34
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Part 6: Finite Sample Properties of LS Terms of Art p Estimates and estimators p Properties of an estimator - the sampling distribution p “Finite sample” properties as opposed to “asymptotic” or “large sample” properties ™    2/34
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Part 6: Finite Sample Properties of LS Application: Health Care Panel Data German Health Care Usage Data , 7,293 Individuals, Varying Numbers of Periods Data downloaded from Journal of Applied Econometrics Archive. There are altogether 27,326 observations. The number of observations ranges from 1 to 7. (Frequencies are: 1=1525, 2=2158, 3=825, 4=926, 5=1051, 6=1000, 7=987). Variables in the file are DOCVIS = number of doctor visits in last three months HOSPVIS = number of hospital visits in last calendar year DOCTOR = 1(Number of doctor visits > 0) HOSPITAL = 1(Number of hospital visits > 0) HSAT = health satisfaction, coded 0 (low) - 10 (high) PUBLIC = insured in public health insurance = 1; otherwise = 0 ADDON = insured by add-on insurance = 1; otherswise = 0 HHNINC = household nominal monthly net income in German marks / 10000 . (4 observations with income=0 were dropped) HHKIDS = children under age 16 in the household = 1; otherwise = 0 EDUC = years of schooling AGE = age in years MARRIED = marital status For now, treat this sample as if it were a cross section, and as if it were the full population. ™    3/34
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Part 6: Finite Sample Properties of LS Population Regression ™    4/34
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Part 6: Finite Sample Properties of LS Sampling Distribution A sampling experiment : Draw 25 observations at random from the population. Compute the regression. Repeat 100 times. Display estimates. matrix ; beduc=init(100,1,0)$ proc$ draw ; n=25 $ regress; quietly ; lhs=hhninc ; rhs = one,educ $ matrix ; beduc(i)=b(2) $ sample;all$ endproc$ execute ; i=1,100 $ histogram;rhs=beduc $ ™    5/34
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Part 6: Finite Sample Properties of LS How should we interpret this variation in the regression slope? ™    6/34
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Part 6: Finite Sample Properties of LS The Statistical Context of Least Squares Estimation The sample of data from the population: Data generating process is y = x +  The stochastic specification of the regression model: Assumptions about the random . Endowment of the stochastic properties of the model upon the least squares estimator. The estimator is a function of the observed (realized) data. ™    7/34
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Part 6: Finite Sample Properties of LS Least Squares - - - - - = - - = - = = + = + = + ε + ε + ε β ε β ε ε β β β 1 1 1 1 n 1 i i i 1 1 n 1 i i i 1 n 1 i i i 1 i i i  ( )    =  ( ) ( )  =  The true parameter plus sampling error.
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