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# We now study the statistical properties of ols we

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Unformatted text preview: for nonlinearities. The key is that y = βo + β1 x + u is linear in the parameters βo and β1 . There are no restrictions on how y and x relate to the original dVar and eVars of interest. Melissa Tartari (Yale) Econometrics 47 / 93 The Meaning of Linear Regression What does LINEAR mean in SLRM? We have just seen that we can allow for nonlinearities. The key is that y = βo + β1 x + u is linear in the parameters βo and β1 . There are no restrictions on how y and x relate to the original dVar and eVars of interest. However, the interpretation of the coe¢ cients does dependent on their de…nition. Melissa Tartari (Yale) Econometrics 47 / 93 The Meaning of Linear Regression What does LINEAR mean in SLRM? We have just seen that we can allow for nonlinearities. The key is that y = βo + β1 x + u is linear in the parameters βo and β1 . There are no restrictions on how y and x relate to the original dVar and eVars of interest. However, the interpretation of the coe¢ cients does dependent on their de…nition. Here is an example of a NONLINEAR SRM: y= Melissa Tartari (Yale) 1 +u βo + β1 x Econometrics 47 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u . Melissa Tartari (Yale) Econometrics 48 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u . We now study the statistical properties of OLS: Melissa Tartari (Yale) Econometrics 48 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u . We now study the statistical properties of OLS: ˆˆ we view βo , β1 as estimators of the parameters ( βo , β1 ), i.e. as random variables, Melissa Tartari (Yale) Econometrics 48 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u . We now study the statistical properties of OLS: ˆˆ we view βo , β1 as estimators of the parameters ( βo , β1 ), i.e. as random variables, ˆˆ we study the properties of the distributions of βo , β1 over di¤erent random samples from the population. Melissa Tartari (Yale) Econom...
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