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EXERCISE ON POOLING OF CROSS SECTIONAL AND TIME SERIES DATAWhen you have data in both the time and cross sectional dimensions, this opens up new challenges for estimation and opportunities for inference. Typically we expect heteroscedasticity across the cross section and autocorrelation over time, so these problems must be addressed. Alsothe availability of observations over time allows one to estimate error covariances across the crosssection, so it is possible to treat spatial autocorrelation. Eviews has all of these capabilities, and additional options for flexible estimation with pooled data.The easiest way to understand how to set up a pooled data set is to look at an example. Inthis exercise you will be working with the Grunfeld investment data set, which contains three variables observed across five firms over the 20 years 1935-1954. The variables are market value of the firm at the end of the previous year (f), the value of plant and equipment at the end of the previous year (cs) and gross investment (i; the dependent variable). This data set has been saved inan Excel file, identified by the name [email protected] Begin in the usual way creating an Eviews workfile for annual data, 1935-1954. Then use Procs/Import/Read Text-Lotus-Excel, give the name of the file, and indicate that 15 variables are to be read (the other defaults should work). You should see the following list of variables.C CS1 CS2 CS3 CS4 CS5 F1 F2 F3 F4 F5 I1 I2 I3 I4 I5 The number appended to each variable name is the firm number so that the variables for one firm are distinct from those of another. Notice that each variable is given a base name (i, f or cs) so that you can easily refer to the entire set of observations on a given variable. You will refer to each Apool [email protected] with the base name plus the character ?. For example, i? Refers to the entire set of 5*20 observations on investment.Manipulating data in the pool.First you must create a Apool [email protected] Click on Object/New/Pool, and in this pool window enter the firm identifiers: 1 2 3 4 5. Click on Define to save this object. There is a toolbar at the top of this window for working with this pooled data set. Using the base names, you can perform operations on the entire pooled data set. For example, if you want to generate the logarithms of every investment time series, select pooledGenr from the toolbar, and enter the equationli?=log(i?)You can also mix generic and specific variable names as infratio=f?/f1Pooled EstimationThere are a number of ways that you can use your pooled data in estimating an equation. You might estimate a fixed or random intercept model, or perhaps a model with selected variablesthat have different coefficients across cross-sections, as well as separate AR(1) coefficients. Or you could estimate a separate equation for each cross-sectional unit. EViews pool objects allow you to estimate your model using least squares, weighted least squares with estimated cross-section weights, or seemingly unrelated regressions, all without rearranging or reordering your data.In this exercise we will focus on the most straightforward estimation problems. Some of the extensions mentioned above or in the Eviews help menu may be appropriate for your own data analysis. Press the Estimate button on your pool toolbar and the Pool Estimation dialog will open. You need to specify the following:1. Dependent Variable: List a pool variable, in this case i?, in the Dependent Variable box.2. Sample: Enter your sample specification in the edit window at the upper right. For this analysis we will use the complete sample, 1935 - 1954. By default, EViews will use the largest sample possible in each cross-section. An observation will be excluded if any of the explanatory or dependent variables for that cross-section are unavailable in that period.The checkbox for Balanced Sample instructs EViews to perform the exclusion over all cross-sections. EViews will eliminate an observation if data are unavailable for any cross-section in that period. This exclusion ensures that estimates for each cross-section will be based on a common set of dates.3. Explanatory Variables: Next, you will list your regressors. There are two edit boxes where you will enter your explanatory variables: Common coefficients: C enter variables that are to have the same coefficient across all cross-section members of the pool. EViews will force the coefficients on these variables to be identical across the firms in this pool, and will label the output using the ordinary or pool name, asappropriate. For this exercise enter cs? In the Common coefficients box. Cross-section specific coefficients: C list variables with different coefficients for each member of the pool. EViews will include a different coefficient for each cross-sectional unit, and will label the output using the cross-section identifier followed by [email protected] and then the ordinary series name. Enter f? in this box.You may include AR terms in your specification if you need to treat autocorrelation. For example, adding the term AR(1) to either list of explanatory variables above causes Eviews to implement the Cochrane-Orcutt correction for first order autoregressive errors. If the terms are entered in the common coefficients list, EViews will estimate the model assuming a common AR error. If the AR terms are entered in the cross-section specific list, EViews will estimate separate AR terms for each member. You may experiment with this feature if you wish.4. Intercept. In the area labeled Intercept: you can choose among the following alternative specifications:None no intercepts; Common identical intercept for all pool members; Fixed effects different intercepts estimated for each pool member; Random effects treats intercepts as random variables across pool members: You cannot estimate random effects models with cross-section specific coefficients, AR terms, or weighting.Choose the fixed effects option for this estimation. 5. Weights. EViews does not weight observations in pooled estimation by default, but you have the option of estimating weighted versions of your specifications. These weighting options invoke alternative GLS models for heteroscedasticity and/or cross sectional autocorrelation. There are three options for weights:No weighting. all observations are given equal weight.Cross section weights. GLS using estimated cross-section residual variances.SUR. analog to Seemingly Unrelated RegressionCGLS using estimated