This document is a summary of everything you need to know for the endterm (and midterm) of the course 'Econometrics' (6012B0453Y) at the University of Amsterdam, taught by Hans van Ophem. This document includes the following topics: log and ln, expected value, variance, covariance, estimators, simp...
SOLUTIONS MANUAL for Introduction to Econometrics, Global Edition 4th Edition James H. Stock; Mark Watson - (GET DOWNLOAD LINK FOR MULTIPLE FILES + EXCEL)
Estimators → are random!
We try to estimate a population parameter. This is usually unknown, except in a Monte Carlo
Analysis.
• Unbiasedness: 𝐸 (𝑋̅) = 𝜇
• Consistency: 𝑣𝑎𝑟(𝑋̅) → 0 as 𝑛 → ∞
AND the estimator is asymptotically (“as 𝑛 → ∞”) unbiased!
Simple regression
𝑌𝑖 = 𝛽0 + 𝛽1 𝑋𝑖 + 𝑢𝑖 (population)
→ 𝛽1 measures the unit change in 𝑌, per unit change in 𝑋
We estimate 𝛽0 and 𝛽1 by min ∑𝑒𝑖2
𝑌̂𝑖 = 𝛽̂0 + 𝛽̂1 𝑋𝑖 (fitted value)
𝑒𝑖 = 𝑢̂𝑖 = 𝑌𝑖 − 𝑌̂𝑖 = 𝑌𝑖 − 𝛽̂0 − 𝛽̂1 𝑋𝑖
2
min ∑𝑒𝑖2 = min ∑(𝑌𝑖 − 𝛽̂0 − 𝛽̂1 𝑋𝑖 )
1. Take the first derivative with respect to 𝛽0 and/or 𝛽1
2. Set equal to 0 and solve for 𝛽0 or 𝛽1
Least Squares Assumptions
1) 𝜀𝑖 is a random variable with 𝐸 (𝜀𝑖 |𝑋) = 0
2) (𝑌𝑖 , 𝑋𝑖 ) are i.i.d.
3) Large outliers are unlikely → finite nonzero 4th moments → kurtosis is finite
1
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