1 Lecture One Econ 240C

2 Einstein’s blackboard, Theory of relativity, Oxford, 1931

3 Outline Pooling Time Series and Cross- Section Review: Analysis of Variance –one-way ANOVA –two-way ANOVA Pooling Examples

4 Pooling Often you may have data sets vary both across individuals and also over time. For example, you may have macro data such as GDP but for several countries. You could analyze this data country by country, but it is also possible to pool the data and analyze it jointly rather than individually.

5 The Rock Music Data In this data, individual teenagers are polled about how many minutes of rock music they listen to per day for each of the seven days of the week. There is variation across individual teenagers there is variation for a single teenager over time, i.e. the days of the week

6 Example: Rock Music Data Teen Sun.Mon.Tue.Wed.Th.Fri.Sat

8 One Way ANOVA Across Days of the Week

10 One Way ANOVA Across 200 Teenagers

Selection: First Ten Teenagers

13 Two-Way ANOVA Across both Days and Teens Controlling for both sources of variation reduces the unexplained sum of squares, “within groups” in EXCEL-speak, and hence makes the variation for days of the week and/or for teenagers, more significant since the F-statistic depends on the ratio of explained sum of squares to unexplained sum of squares and the latter is smaller per above.

Two-way ANOVA

15 Stacked Regressions GDP for two countries Canada and France, Estimating time trends: GDP i (t) = c i + d i t + e i, Note, on next slide, that there is a separate intercept for Canada, CAN that is one when the data is Canadian and zero when the data is French. Ditto for time and GDP

17 Stacked Data Separate intercepts can be typed in as well as separate time trends, but this becomes more laborious for 7 countries than for two. Pooling is a process in Eviews for automating stacked regressions

18 A Stacked Regression Time Trend (GDP_CAN + GDP_FRA) = c CAN CAN + d CAN TIME_CAN + c FRA FRA + d FRA TIME_FRA

Dependent Variable: GDPSTACKED Method: Least Squares Sample: 1 86 Included observations: 86 Variable CoefficientStd. Errort-StatisticProb CAN FRA TIME_CAN TIME_FRA R-squared Mean dependent var Adjusted R-squared 0.972S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

20 Stacked Regression Results Note the intercept for Canada is with a standard error of 183.3; the time trend is with a standard error of 7.51; What would result if we estimated each country separately, as illustrated for Canada on the next slide. The estimated intercept and slope is the same but the standard errors are larger and t-stats lower.

Dependent Variable: GDP_CAN Method: Least Squares Sample: 1 43 Included observations: 43 Variable CoefficientStd. Errort-StatisticProb. CAN TIME_CAN R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Durbin-Watson stat

22 Pooling in EViews So that is the motivation for pooling and in Lab One on Wednesday we will learn how to accomplish pooling using Eviews.

23 The Law of One Price If arbitrage is possible, then the price of a commodity will be the same everywhere, accounting for transportation and transactions costs

24 Concept: evolutionary time series, cointegration

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26 Concept: stationary time series,

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28 Reference Working Paper: John Pippenger and Llad Phillips, “Some Pitfalls in Testing the Law of One Price in Commodity Markets” Econ Home Page, Working Papers, 2005, series # 4-05 –Read pages 1-5, scan the rest –Note concepts: cointegration, unit roots etc., topics in this course.