Financial Econometrics Lecture Notes 5 University of Piraeus Antypas Antonios

Panel Data Analysis

Panel Data Analysis Data have two dimensions They evolve both in time and in cross sectional. Examples of cross sectional units Countries, Regions, Individuals, Residents Companies, etc. We refer to time with the index t= 1,2,3, … ,T We refer to cross sections with the index i=1,2,3,…,N. Total Number of Observations: NxT. Usually, we come across with cases with large N and small (T). For example, in most developing countries, they have started collecting statistical data in the early ’80 and most frequently in an annual basis. Therefore, in 2011 we would only have 31 observations for one country, but there exist a sufficient number of developing countries. The combination of these observations can create a adequate sample size for econometric analysis

Panel Data Analysis An example of the structure of Panel Data Cross Section Units: Countries. Time Unit: Years. Country Year Y X1 X2 … ASL 1955 1 2 3 … ASL 1956 2 3 4 … ASL 1957 3 4 5 … . . . . . … AUS 1955 1 2 3 … AUS 1956 2 3 4 … AUS 1957 3 4 5 … If all cross section units have the same number of time series observations, we say that we have a balanced panel. Otherwise we refer to our data to unbalanced panel.

Panel Data Analysis Importing Panel Data to gretl from Excel Some additional steps compare to the usual procedure. Step 1: Prepare the Excel file to an appropriate format Use file PanelDataStructureConverter.xlsm In Sheet DataNew save your data following the same structure Put Dates in Column A Put Variable Names in Row 1 Put Cross Sectional Identifiers in Row 2 Make sure that variables are grouped together and that cross sectional entities come in the same order at each group Once all data has been collected press ‘Run’ This Macro will restructure your data in the appropriate format in sheet Panel Data

Panel Data Analysis Importing Panel Data to gretl from Excel Some additional steps compare to the usual procedure. Step 1: Prepare the Excel file to an appropriate format Use file PanelDataStructureConverter.xlsm Copy sheet PanelData to a new Excel workbook and save it as csv Open gretl and import data as usually When prompted to set a Panel interpetation to your data press Yes and follow the steps

Panel Data Analysis Importing Panel Data to gretl from Excel Some additional steps compare to the usual procedure. Step 1: Prepare the Excel file to an appropriate format Use file PanelDataStructureConverter.xlsm Copy sheet PanelData to a new Excel workbook and save it as csv Open gretl and import data as usually When prompted to set a Panel interpretation to your data press Yes and follow the steps

Panel Data Analysis Importing Panel Data to gretl from Excel Some additional steps compare to the usual procedure. Step 1: Prepare the Excel file to an appropriate format Use file PanelDataStructureConverter.xlsm Copy sheet PanelData to a new Excel workbook and save it as csv Open gretl and import data as usually When prompted to set a Panel interpretation to your data press Yes and follow the steps

Fill the number of cross sectional entities you have in your sample Panel Data Analysis Importing Panel Data to gretl from Excel Some additional steps compare to the usual procedure. Step 1: Prepare the Excel file to an appropriate format Use file PanelDataStructureConverter.xlsm Copy sheet PanelData to a new Excel workbook and save it as csv Open gretl and import data as usually When prompted to set a Panel interpretation to your data press Yes and follow the steps Fill the number of cross sectional entities you have in your sample

Panel Data Analysis Like before, our starting point is the linear regression mode. Observe however that in the case of Panel Data, series are indexed both by i and t What are the main assumptions in a Panel Regression? Usual assumptions for the error term must hold (zero mean, homoscedasticity, no autocorrelation, exogeneity) Intercept coefficient β0 is the same across time and cross sections All X factors have the same effect on Y across time and cross sections The assumption that β0 is the same very restrictive and we have reasons to allow some flexibility and permit variation either cross sectional (Cross Section Effects) or in time (Period Effects)

Panel Data Analysis Most of the time we allow the intercept to vary within cross units. There are two alternative methods on how to achieve this: Fixed effects In this case, the model uses the method of dummy variables to estimate N intercepts (β0), one for each cross unit. Pros: Easy and straight interpretation – Cons: Too many new parameters for estimation Random effects In this case, the model estimates only an average value and a variance for the intercept (β0) and assigns N different intercepts from a random distribution. Pros: Only 2 new parameters – Cons: No practical interpretation

Panel Data Analysis Estimating a Panel Regression in gretl Now that we are dealing with Panel Data, all procedures we discussed so far in gretl remain the same. Any additional toll for Panel Data Analysis is already enabled since we took care to create a Panel Balanced Workfile. An Example of a Panel Data Analysis: The Laffer Curve The Laffer Curve shows the relationship between government revenues raised by taxation and all possible rates of taxation. Some economists suggest that the Laffer Curve has negative slope from a tax rate and above suggesting that a decrease in the tax rates is possible to create an increase in government revenues from taxes. To test this theory we collected data from 12 countries and 11 years We would prefer to test the theory in each country separately, but unfortunately we would not have sufficient data to estimate efficiently our models (we would only have 11 observations per country).

Panel Data Analysis For this reason we choose to combine data from all countries and proceed with a Panel Data Analysis The model that will help us test our theory (the Laffer Curve) is the following: Two Main Questions: Is the coefficient β1 of Rates significant? If Yes, that means that governments can alternate their tax revenues by changing the tax rates. If β1 is found to be significant, what is its sign? Primary question of interest in specifying correctly a panel model is if we should include random or fixed effects in our model or should we exclude both of them. The following procedure can answer this question

Panel Data Analysis Random effects or Fixed effects? Or No effects? Estimate your model with Random Effects Go Model – Panel – Fixed or random effects, specify your model, select Random effects

Panel Data Analysis Random effects or Fixed effects? Or No effects? Estimate your model with Random Effects Go Model – Panel – Fixed or random effects, specify your model, select Random effects Test the Null Hypothesis of Valid Random Effects using the Hausman Test If you do not reject the null, include random effects in your model If you reject the null you must not include random effects in your model

Panel Data Analysis Random effects or Fixed effects? Or No effects? Estimate your model with Random Effects Go Model – Panel – Fixed or random effects, specify your model and select Random effects Test the Null Hypothesis of Valid Random Effects using the Hausman Test If you do not reject the null, include random effects in your model If you reject the null you must not include random effects in your model If you rejected the random effects, estimate your model with Fixed Effects Go Model – Panel – Fixed or random effects, specify your model and select Fixed effects

Panel Data Analysis Random effects or Fixed effects? Or No effects? Estimate your model with Random Effects Go Model – Panel – Fixed or random effects, specify your model and select Random effects Test the Null Hypothesis of Valid Random Effects using the Hausman Test If you do not reject the null, include random effects in your model If you reject the null you must not include random effects in your model If you rejected the random effects, estimate your model with Fixed Effects Go Model – Panel – Fixed or random effects, specify your model and select Fixed effects Test the Null Hypothesis of Groups having a common intercept If you reject the null, include fixed effects in your model If you did not rejected the Null Hypothesis of Groups having a common intercept , estimate your model with no effects (OLS)

Panel Data Analysis Random effects or Fixed effects? Or No effects? Estimate your model with Random Effects Go Model – Panel – Fixed or random effects, specify your model and select Random effects Test the Null Hypothesis of Valid Random Effects using the Hausman Test If you do not reject the null, include random effects in your model If you reject the null you must not include random effects in your model If you rejected the random effects, estimate your model with Fixed Effects Go Model – Panel – Fixed or random effects, specify your model and select Fixed effects Test the Null Hypothesis of Groups having a common intercept If you reject the null, include fixed effects in your model If you did not rejected the Null Hypothesis of Groups having a common intercept, estimate your model with no effects (OLS)