psviii245b

# psviii245b - University of California Department of...

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University of California D. Steigerwald Department of Economics Economics 245B Problem Set VIII 1. Consider the regression model y t = β 0 + β 1 y t-1 + ε t where { ε t } t=1,. ..,T is a mean zero white noise process. a. For β 1 < 1, find what the OLS estimator of β 1 converges to in probability. Is \$ β 1 unbiased? b. Suppose β 1 < 1 and ε t = ρε t-1 + u t , where ρ < 1 and {u t } t=1,. ..,T is a sequence of independent identically distributed random variables. Find what \$ β 1 converges to in probability. How does your answer change if ε t = ρε t-1 + u t ? If your answer differs from those given in parts a. or b., explain intuitively why it differs. c. Suppose β 1 = 1, and ε t is a white noise process. Find what \$ β 1 converges to in probability. How does your answer change if ε t = ρε t-1 + u t ? If your answer differs from those given in parts a. or b., explain intuitively why it differs. d.

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psviii245b - University of California Department of...

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