FOR MORE HIGH-QUALITY PAST PAPER MODEL ANSWERS, ONLINE TUTORING AND
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
ECN225 Econometrics 2 – 2012
Questions and Answers
Question 1
a)
𝐸[𝑌 | 𝑋 ] = 𝐸[𝛽 + 𝛽 𝑋 + 𝑢 | 𝑋 ] (By definition)
𝐸[𝑌 | 𝑋 ] = 𝐸[𝛽 | 𝑋 ] + 𝐸[𝛽 𝑋 | 𝑋 ] + 𝐸[𝑢 | 𝑋 ] (Splitting up the expectation on the right-hand
side)
𝐸[𝑌 | 𝑋 ] = 𝛽 + 𝛽 𝐸[𝑋 | 𝑋 ] + 0 (Because 𝐸[𝑢 | 𝑋 ] = 0, and because the expectation of a
fixed parameter is just that parameter).
𝐸[𝑌 | 𝑋 ] = 𝛽 + 𝛽 𝑋 (Because the expected value of X conditional on X, is just X).
b) The estimator of 𝛽 seeks to minimize the sum of squared errors, which is defined as:
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
ECN225 Econometrics 2 – 2012
Questions and Answers
Question 1
a)
𝐸[𝑌 | 𝑋 ] = 𝐸[𝛽 + 𝛽 𝑋 + 𝑢 | 𝑋 ] (By definition)
𝐸[𝑌 | 𝑋 ] = 𝐸[𝛽 | 𝑋 ] + 𝐸[𝛽 𝑋 | 𝑋 ] + 𝐸[𝑢 | 𝑋 ] (Splitting up the expectation on the right-hand
side)
𝐸[𝑌 | 𝑋 ] = 𝛽 + 𝛽 𝐸[𝑋 | 𝑋 ] + 0 (Because 𝐸[𝑢 | 𝑋 ] = 0, and because the expectation of a
fixed parameter is just that parameter).
𝐸[𝑌 | 𝑋 ] = 𝛽 + 𝛽 𝑋 (Because the expected value of X conditional on X, is just X).
b) The estimator of 𝛽 seeks to minimize the sum of squared errors, which is defined as:
