slides_Ch2_W[1]

1 we assume 21 to hold in the population it denes the

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Unformatted text preview: 2.1) We assume (2.1) to hold in the population, it de…nes the SLRM. The key assumption embedded in (2.1) is that g is linear in the β. Melissa Tartari (Yale) Econometrics 3 / 93 De…nition: the SLRM II We choose to start by writing the following equation relating Y to X and U : Y = βo + β1 X + U (2.1) We assume (2.1) to hold in the population, it de…nes the SLRM. The key assumption embedded in (2.1) is that g is linear in the β. Another assumption embedded in (2.1) is that X has a linear e¤ect on Y : a unit change in X has the same e¤ect on Y regardless of the value of X : dY = β1 . dX Melissa Tartari (Yale) Econometrics 3 / 93 De…nition: the SLRM II We choose to start by writing the following equation relating Y to X and U : Y = βo + β1 X + U (2.1) We assume (2.1) to hold in the population, it de…nes the SLRM. The key assumption embedded in (2.1) is that g is linear in the β. Another assumption embedded in (2.1) is that X has a linear e¤ect on Y : a unit change in X has the same e¤ect on Y regardless of the value of X : dY = β1 . dX Is this realistic? Not always. Melissa Tartari (Yale) Econometrics 3 / 93 De…nition: the SLRM II We choose to start by writing the following equation relating Y to X and U : Y = βo + β1 X + U (2.1) We assume (2.1) to hold in the population, it de…nes the SLRM. The key assumption embedded in (2.1) is that g is linear in the β. Another assumption embedded in (2.1) is that X has a linear e¤ect on Y : a unit change in X has the same e¤ect on Y regardless of the value of X : dY = β1 . dX Is this realistic? Not always. Luckily, this restrictions will no longer obtain in the MLRM (while linearity in the β will still apply). Melissa Tartari (Yale) Econometrics 3 / 93 De…nition: the SLRM III U represents factors other than X that a¤ect Y ; we can think of U as standing, loosely, for “unobserved”; these may be factors that are: Melissa Tartari (Yale) Econometrics 4 / 93 De…nition: the SLRM III U represents factors other than X that a¤ect Y ; we can think of U as standing, loosely, for “unobserved”; these ma...
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