EViews Training Series and Groups: Statistical Analysis Note: Data and workfiles for this tutorial are provided in: Data: Data.xls Results: Results.wf1 Practice Workfile: Data.wf1

Data and Workfile Documentation Data.wf1 and Data.xlsx consist of two pages (tabs) with the following data: Workfile Page: coss_section (Data.xlsx tab cross_section) data on 4,137 individuals GPA – Cumulative GPA in high school SAT – combined SAT score Black – indicator variable =1 if black, 0 otherwise Female – indicatore variable=1 if female, 0 otherwise Hsize – size of graduating class, (in hundreds of people) Hsrank – rank in graduating class 2 * This data is from Wooldridge, Introductory Econometrics (4 th Edition).

Data and Workfile Documentation (con’t) Workfile Page: TimeSeries (Data.xlsx tab TimeSeries) monthly data Jan1959-March2013 CPI – CPI index, level (source: Bureau of Labor Statistics) bond10Y – 10-year Treasury bond yield (source: the Federal Reserve Board of Governors) Hstarts – housing starts (thousands of units) (source: the Census Bureau) Series_NA – created series. 3

Group View Menu

View Menu for Groups You can use the View menu item to perform a number of analysis, display views, etc. for a collection of series in a group. 5 View menu for Groups: 1.To see the available actions for a group, click on the TimeSeries page, highlight series cpi and bond10y, right click and select Open → as Group. 2.Click on the View menu item. A drop- down menu appears with a number of options grouped in 4 sections. The first section/block provides various ways of looking at the data in the group. The second bloc provides general statistics. The third block provides general statistics for time series. The fourth block allows you to modify/display the group labels.

Basic statistical summaries of the series contained in one group can be found in EViews under the View → Descriptive Statistics. 6 Descriptive Statistics: Common Sample Descriptive Statistics: Common Sample 1.Click on the TimeSeries page and create a group containing cpi, bond10y and bond10y_real. Name this group group02. 2.Click View → Descriptive Statistics → Common Sample. General stats for all the series in the sample are shown here. Note that statistics are computed using a common sample. This means that if a series has missing observations, stats for all series are computed over the common sample for which all series have non-missing observations.

You can also compute Descriptive Statistics for the series in one group over the sample of each individual series. 7 Descriptive Statistics: Individual Sample Descriptive Statistics: Individual Sample 1.Click on the TimeSeries page and open group02. 2.Click View → Descriptive Statistics → Individual Sample. Notice that this table differs slightly from the previous one. This is because the stats for CPI and Bond10Y are computed over the entire sample (651 observations) whereas stats for bond10y_real are computed over 650 observations (bond10y_real is missing the first observation). In the previous example, statistics for all series were computed over the smaller sample (650 observations).

The Covariance Analysis view is a very useful tool to obtain different measures of association (covariances/correlations) for the series in a group. There are four general classes in EViews from which you can compute measures of association: Ordinary (Pearson), Ordinary (uncentered), Spearman rank-order, and Kendall’s tau-a and tau-b. 8 Covariance Analysis: Example 1 Covariance Analysis: Example 1 1.Click on the cross_section, select series GPA and SAT, right click and open as group. Let’s name this group01. 2.Click View → Covariance Analysis. The Covariance Analysis dialog box opens up. Under Method, click the drop-down menu choose the type of measure (let’s select Ordinary here). 3.Click the Covariance box (the default). 4.Under Saved results basename, name your results so they are saved in the workfile (here cov1) 5.Click OK.

The covariance between the two series is shown here. Note that the covariance is displayed in a spreadsheet format (the default). Note also that the covariance is now saved in the workfile with name cov1cov. The extension cov is added by EViews to indicate that this is a measure of covariance. Note that the saved covariance matrix does not show the name of the original series but only the matrix elements (R1, R2, C1, C2). 9 Covariance Analysis: Example 1 (cont’d)

Let’s consider some of the options in the Covariance Analysis in more detail. 10 Covariance Analysis: Example 2 Covariance Analysis: Example 2 1.Click on the cross_section, select series GPA SAT, and black, right click and open as group. Let’s name this group02. 2.Click View → Covariance Analysis. The Covariance Analysis dialog box opens up. Under Method, select Ordinary uncensored. 3.Check the Correlation, t-statistic, Probability and Number of obs boxes. 4.Select Single table under Layout. 5.Under Saved results basename, name your results so they are saved in the workfile (here cov2). 6.Click OK.

The table shows all statistics in the order in which they appear at the top of the table. Note also that results are now saved in a number of matrices: cov2corr (containing correlations), cov2prob (containing p-values), cov2tstat (containing t-stats), cov2obs (containing the number of observations). 11 Covariance Analysis: Example 2 (cont’d)

Had we selected Multiple Tables, under the Layout section (instead of Single Table), the output would change as shown here. All statistics are tabulated here in multiple tables. Note that the multiple tables view makes it easier to compare correlations across variables but more difficult to relate a given correlation to the corresponding probability and t-stats. 12 Covariance Analysis: Example 2 (cont’d)

Sometimes you may want to control for other variables while computing a measure of association between two or more series. EViews allows you to carry out this type of analysis by performing Partial Analysis. 13 Covariance Analysis: Example 3 Covariance Analysis: Example 3 1.Click on the cross_section page and open series GPA and hsize. Save this as group03. Let’s first compute unconditional analysis. 2.Click View → Covariance Analysis. The Covariance Analysis dialog box opens up. Under Method, select Ordinary. Also, check the Correlation and Probability boxes. 3.Select Single Table under Layout. 4.Click OK. GPA is negatively correlated with the size of the high school, but this is not statistically significant at the 5% significance level.

Now let’s condition this over a conditioning variable. Let’s control for an individual’s race (black). EViews automatically balances the sample, computes statistics and displays the partial covariances/correlations, controlling for all variables in the conditioning set. 14 Covariance Analysis: Example 3 (cont’d) Covariance Analysis: Example 3 1.Open group03. Click View → Covariance Analysis. The Covariance Analysis dialog box opens up. Under Method, select Ordinary. Also, check the Correlation and Probability boxes. 2.Select Single Table under Layout. 3.Under the Partial Analysis field, type the conditioning variable (black in this case). 4.Click OK.

Note that once we control for the race of the individuals the negative correlation between GPA and high school size becomes more pronounced (larger in magnitude) and is statistically significant at the 5% significance level. 15 Covariance Analysis: Example 3 (cont’d)

Another useful tool when analyzing data is the N-Way tabulation in the group View. This allows us to classify the observations into subgroups, check for independence among the series in the group, etc. 16 N-Way Tabulation: Example 1 1.Click on the cross_section page and open series GPA and black. Save this as group04. 2.Click View → N-Way Tabulation. The Crosstabulation dialog box opens up. Under Output, check Count, Overall %, and Chi-square tests. 3.Select Table under Layout. 4.Click OK.

The top portion of the table EViews displays information on the overall categories, measures of association (correlations) and Pearson’s Chi-squares for testing the independence among all series in the group. The bottom panel of the table shows the number of count (as number and as % of Total) for each of the subgroups. 17 N-Way Tabulation: Example 1 (cont’d) Top Panel Bottom Panel

Similarly, we can compute N-way Tabulation statistics for more than 2 series. 18 N-Way Tabulation: Example 2 1.Click on the cross_section page and open series GPA, female and black. Save this as group05. 2.Click View → N-Way Tabulation. The Crosstabulation dialog box opens up. Under Output, check Count and Overall % and Table %. 3.Select Table under Layout. 4.Click OK. EViews produces an output consisting of 4 parts. In the top panel, EViews produces the Tabulation summary, indicating the total number of categories.

The second and third panels show conditional tables for BLACK=0 and BLACK=1. They show the total number of observations that fall in each category (count), the percentage of observations in the category as percent of total observations (% total), and the percentage of the number of observations in category as percent of observations in the conditional table (%Table). 19 N-Way Tabulation: Example 2 (cont’d) Panel 2Panel 3

The bottom panel of the table shows the unconditional table (unconditional on race BLACK=0 or BLACK=1). 20 N-Way Tabulation: Example 2 (cont’d) Bottom Panel

The Tests of Equality item of the View menu tests the null hypothesis that all series in a group have the same mean (or median or variance). 21 Tests of Equality: Example 1 1.Click on the TimeSeries page and type in the command window: show cpi cpi(-12) 2.This creates a new group with two series: CPI and its 12 th lag. We can save this group as group03. 3.Click View → Tests of Equality. The Test Equality of dialog box opens up. Select Mean and check the Common Sample box. 4.Click OK.

Based on the provided statistics, we cannot reject the null that the series have equal means. This should not be surprising given that the group consists of CPI series and its 12 th lag. 22 Tests of Equality: Example 1 (cont’d)

We can also test as to whether the series in a group have equal median. 23 Tests of Equality: Example 2 1.Click on the TimeSeries page and type in the command window: group group04 hstarts hstarts(-12) hptrend01 2.This creates a new group with three series: hstarts its 12 th lag and the hptrend series derived from the Hodrick-Prescott filter. As the command indicates, this is saved as group04. Now open group04. 3.Click View → Tests of Equality. The Test Equality of dialog box opens up. Select Median and check the Common Sample box. 4.Click OK.

Based on the provided statistics, we cannot reject the null that the series have equal medians. This should not be surprising given that the group consists of the housing starts series, its 12 th lag, and a smooth series that denotes its long-term trend. 24 Tests of Equality: Example 2 (cont’d)

The Cross Correlation entry on the group's View menu shows the table of cross-correlations between the series in the group. 25 Cross Correlogram Cross Correlation: 1.Click on the TimeSeries page and open inflation, bond10Y and bond10y_real as a group. Let’s name this group06. 2.Click View → Cross Correlation (2). The Lag Specification box opens up. Specify here the number of lags (36, the default is fine). 3.Click OK. EViews computes cross-correlations only between the first and second series in the group.