PANEL DATA REGRESSION MODELS IN EVIEWS: Pooled OLS, Fixed or Random effect model?

Transcription

1 PANEL DATA REGRESSION MODELS IN EVIEWS: Pooled OLS, Fixed or Random effect model? ADESETE, Ahmed Adefemi 12/6/2017

2 2 PANEL DATA REGRESSION MODELS IN EVIEWS: Pooled OLS, Fixed or Random effect model? Panel data refers to a type of data that contains observations of multiple phenomena collected over different time period for the same group of individuals, units or entities. In short, in econometrics panel data refers to a multidimensional data collected over a period of time. Panel data analysis on the other hand refers to a statistical method widely used in different disciplines such as social sciences, econometrics to analyze data that are collected for multiple periods and over the same individuals or entities. A simple panel data regression can specified thus: Y it = a + bx it + ε it Y...dependent variable X...independent or explanatory variable a, b...coefficients i, t...indices for individuals and time ε...error term Panel data regression analysis can be done in mainly three ways: (1) Independently Pooled OLS regression model. (2) Fixed effects model (3) Random effects model Independently Pooled OLS regression model This type of panel data model assumes homogeneity of all sections of data in a panel data study that is it does not treat each section differently. Alternatively, it treats all section as just a single section of data. In short, there are no unique characteristics of individuals within the measurement set and no universal effects over time. Example if Panel data is collected for six countries across , Pooled OLS does not distinguish between these six countries while also neglecting the cross section and time series nature of the data. Fixed effects model 2 This type of model allows for heterogeneity or individuality among different cross-sections allowing each cross-section to have its own intercept. In short, the intercept may be different for the crosssections but it is time invariant that is the intercept remains the same over time. The error term in a

3 3 fixed effects model is assumed to vary non-stochastically over each entity and time. There are unique attributes of individuals which do not vary across time and is correlated with independent variables. Summarily, we can conclude that in a fixed effects models, the parameters of the model are fixed alternatively, the group means are fixed. The fixed effect model can be estimated with the aid of dummy variables. Random effects model This model is also known as the variance components model. Random effect model also allows for heterogeneity and is also time invariant but the individual specific effect is uncorrelated with the independent variables. It can also refer to as a kind of hierarchical linear model which adopts the assumption of data being drawn from a hierarchy of different populations whose differences relates to that hierarchy. The Question is, How are these models estimated and how is the correct choice of model made? Panel data regression analysis in Eviews. The main objective of this tutorial is to learn how to estimate Pooled OLS regression model, Fixed effect model, Random effect model and also how to make the correct choice of model amongst the three models in a panel study. Data on GDP, Inflation rate, Export and Import for Nigeria, Ghana, Gambia and Togo over time period STEP 1 The first step is to Open navigate to the Eviews icon and click to open the eviews working environment. 3

4 4 STEP 2: Create a new workfile. Click on file in the eviews work environment ad navigate to New and then to Workfile. File > New > Workfile After clicking on workfile, you should have a workfile environment like this: 4 Under the Workfile structure type column, navigate to Balanced Panel. Under the date specification box, select the frequency of data. In this case we would select annual because we are making use of an annual panel data. After navigating to Balanced panel, there should be a display icon like this:

5 5 The start date for the data employed for this article is 1992 and the end date is 2000 while the number of cross sections is four(4). Panel data tutorial is the given workfile name. Click OK if these fields are already filled. The eviews created workfile environment should display as below: 5

6 6 STEP 3: Upload the panel data. Open the data in Microsoft excel package. Highlight the data and copy After copying the data, open the panel data workfile environment again, right click on the workfile environment and navigate to paste : 6

7 7 After finally clicking on paste, you should have this: Click on Next 7

8 8 Change the Basic Structure box from Dated panel to Dated-regular frequency then set the start date as highlighted in blue below. Finally Click Finish to complete uploading data. 8

9 9 Another method of uploading data is the IMPORT Method. From the created workfile, click file on the top left hand corner of the workfile environment and navigate to Import then finally click import from file. Navigate to the file where the data is saved After selecting the data, you should have a display screen like this: 9 The highlighted blue part signifies the sheet numbers in which the data is located. In this case, sheet 1 is selected. Other steps should follow as indicated in the copy and paste method.

10 10 STEP 4: Run the Panel Data regression. This regression analysis would be done using three different panel data regression models which are: (1) Pooled OLS Regression model (2) Fixed effects panel regression model (3) Random effects panel regression model 1) Pooled OLS regression model Step A: Go to the empty white space(it is highlighted with blue below) at the top of the created workfile and type POOL. Then click Enter on your computer/laptop Step B: After Clicking Enter, you should have a screen like this: 10

11 11 Then, List all the data to be used for the panel data study in the empty white space vertically. Click Define after listing the data STEP C: Then Navigate to Estimate and Click. A screen display like below would appear. 11

12 12 Specify the dependent variable and the independent variables as the common coefficients except there is a particular case where the effect of each cross section on another cross section would be studied, then cross-section specific coefficients would be specified. Click OK to have the estimation result. This is the final result of the Pooled OLS estimation technique. 12

13 13 2) Fixed effects panel regression model STEP A: Navigate to Quick. From Quick, navigate to Estimate Equation and click. After clicking Estimate Equation, there should be a display like this. 13

14 14 STEP B: Specify the equation log(gdp) c log(import) log(export) log(pop) STEP C: Click Panel Options and change Cross Section Box under Effects Specification to Fixed. 14

15 15 STEP D: Click OK This is the Fixed effect panel regression estimation result 3) Random effects panel regression model STEP A: Navigate to Quick. From Quick, navigate to Estimate Equation and click. 15

16 16 After clicking Estimate Equation, there should be a display like this. STEP B: Specify the equation log(gdp) c log(import) log(export) log(pop) STEP C: Click Panel Options and change Cross Section Box under Effects Specification to Random. 16

17 17 STEP D: Click OK This is the Random effect panel regression estimation result How is the right Choice of model made between these three models? The answer to this, is the Correlated Random effects-hausman test and the Wald test. Correlated Random effects-hausman test: This is used as a test to determine the right model between the fixed and random effects model. Hypothesis: Null hypothesis(h 0 )...Random effects model is appropriate Alternative hypothesis(h A )...Fixed effects model is appropriate 17 Decision Criterion: Reject H 0 if probability value is less than 5%, Accept H 0 if probability value is greater than 5%.

18 18 Steps for computing the Correlated Random effects-hausman test STEP 1 Open the Random effects model estimation result in the eviews workfile STEP 2 Click on View and navigate to Fixed/Random Effects Testing and finally select Correlated Random effects-hausman Test as demonstrated in the picture below. View > Fixed/Random Effects Testing > Correlated Random effects-hausman Test. 18

19 19 STEP 3 After Clicking Correlated Random effects-hausman Test, this should be the estimation result Check the probability value and make decision based on the decision criterion. The probability value here is which is greater than 5% thereby we accept null hypothesis and conclude that the random effects model is appropriate. Assume the Fixed effects model is the right model, To determine the right model between the Fixed effect model and the Pooled OLS regression model, the Wald test is adopted. Hypothesis: Null hypothesis(h 0 )...Pooled OLS regression model is appropriate(all dummy variables equal zero) Alternative Hypothesis(H A )...Fixed effect model is appropriate(all dummy variables does not equal zero) Decision criterion: Reject H 0 if probability value of the Wald test is less than 5%, Accept H 0 if the probability value of the Wald test is greater than 5%. 19

20 20 STEP 1 Estimate a Fixed effect model using dummy variables with one dummy variables to each coefficient. Here we have three variables, so we are going to have three dummy variables too. Specify the equation as below with the Panel Options left unchanged. 20

21 21 STEP 2 Click OK and have the Fixed effects model estimation result STEP 3: Click View and navigate to Coefficient diagnostics and then to Wald test STEP 4: Click on the Wald test 21

22 22 List the Coefficients of the dummy variables as listed below and equate all to Zero Click OK and get the estimation result Decision: Reject Null hypothesis and conclude that the fixed effect model is the appropriate model because the probability value(0.0040) is less than 5%. 22 NOTE: The first step is to test between the Fixed effect model and the Random effect model. If the Fixed effect model is the appropriate model after the test, then you should test further for the choice of model between the Fixed effect model and Pooled OLS regression model.if the Random effect model is the appropriate model then a further test would not be required. But if it is the other way round, the first step would be to determine the choice of model between the fixed effect model and Pooled OLS regression model, if the Fixed effect model is the appropriate model then you would use the Hausman test to check further the appropriate model between the

23 23 Fixed effect and the Random effect model. If Pooled OLS regression model is preferred then a further test would not be necessary. Any further research questions or questions regarding this article should be forwarded to adeseteahmed@gmail.com. Use of information on this publication/website is at your own risk. No part of this publication may be reproduced, downloaded or transmitted in any form or by any means published somewhere without the author permission. All publications are copyrighted by the author and publications are used for research and understanding purposes. DATA USED 23 YEARS COUNTRY GDP POP EXPORT IMPORT D2 D3 D BENIN 1.7E E E BENIN 2.27E E E BENIN 1.6E E E BENIN 2.17E E E BENIN 2.36E E E BENIN 2.27E E E BENIN 2.46E E E BENIN 2.69E E E BENIN 2.57E E E GAMBIA 5.04E E E GAMBIA 5.19E E E GAMBIA 5.2E E E GAMBIA 5.24E E E GAMBIA 5.36E E E GAMBIA 5.62E E E GAMBIA 5.82E E E GAMBIA 6.19E E E GAMBIA 6.53E E E GHANA 6.41E E E GHANA 5.97E E E GHANA 5.44E E+09 2E GHANA 6.47E E E GHANA 6.93E E E GHANA 6.89E E E GHANA 7.48E E E GHANA 7.72E E E GHANA 4.98E E E TOGO 1.69E E E TOGO 1.23E E E

24 TOGO 9.83E E E TOGO 1.31E E E TOGO 1.47E E E TOGO 1.5E E E TOGO 1.59E E E TOGO 1.58E E E TOGO 1.29E E E