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# ProblemSet11 Answers - Professor Mumford [email protected]

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Professor Mumford Econ 360 - Fall 2010 Problem Set 11 Answers (Advanced Topics: Time Series and Panel Data) True/False (15 points) 1. FALSE The Dickey-Fuller test can be used to determine if there is evidence that the speciﬁed time series is highly persistent (also called a unit root) . 2. TRUE Regressing a highly persistent time series on another highly persistent time series produce spurious results. 3. TRUE Fixed-eﬀects estimation can be used to estimate causal eﬀects if the unobserved factors that are correlated with the dependent variable of interest are time invariant. 4. TRUE The validity of diﬀerences-in-diﬀerences estimation depends on the assumption that pre-existing trends in the treated and control groups are similar. 5. FALSE With panel data, estimation in ﬁrst diﬀerences and ﬁxed-eﬀects estimation are not computationally identical except when there are only two time periods . 1

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Long Answer Questions (84 points) 6. NYSE Index (a) In a regression of trade volume on day of the week indicators we ﬁnd that Monday has the lowest trade volume on average and Thursday has the highest trade volume on average. However, an F-test of the join signiﬁcance of the day of the week dummies produces a p-value of 0.1880 which is not statistically signiﬁcant. So, while there seems to be some evidence that the day of the week aﬀects volume, it is not strong evidence. (b) There is no evidence that the day of the week has any eﬀect on the closing price. The p-value from the F-test is 0.9974. We probably don’t ﬁnd a relationship because if it were true that the price tended to increase on a certain day of the week, people would try to buy it the day before, which would drive up the price then instead. Eﬃcient markets should not exhibit any predictable patterns because if they did they would be exploited. (c) Yes. In a regression of the adjusted close on the lagged value of adjusted close we get an estimate for ρ of 0.9967 which is very close to one. The Dickey-Fuller test gives a test statistic of -1.571 which gives a p-value of 0.4979. This means we cannot reject the null hypothesis that the series is a highly persistent series. (d) No. In a regression of the volume on the lagged value of volume we get an estimate for ρ of 0.7614 which is not very close to one. The Dickey-Fuller test gives a test statistic of -14.208 which gives a p-value of 0.000. This means we can reject the null hypothesis that the series is highly persistent and we conclude that it is simply a weakly-persistent or auto-correlated series. (e) The regression of closing price on trading volume gives a coeﬃcient estimate of -0.0305894 which seems to indicate that on days where there is a lot of trading, the price tends to drop. We may be concerned because closing price is a highly persistent series. However, even in the ﬁrst-diﬀerences regression we still ﬁnd a statistically signiﬁcant (at the 10 percent level) relationship, although it is much weaker. (f) No. In a regression of the rate of return on the lagged value of the rate of return
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ProblemSet11 Answers - Professor Mumford [email protected]

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