Panel Data Regression Using Jamovi

This guide shows how to do a simplified Panel Data Regression analysis using Jamovi Panel data regression is a little different to the usual simple linear regression or multiple regression, since it often includes data, such as financial data, that changes over time for specific entities (like companies or countries).

Example

A finance researcher seeks to determine if aspects such as the frequency of board meetings, board size, firm size, total assets, and equity have an impact on Tobin’s Q (a financial measure of the value of a company) for a number of different banking institutions from 2010 to 2020. The data are shown below in Jamovi. The data shown below can be downloaded in a CSV file called panel_data_dbase_csv_v2.csv.

Note that the variable BoardSize has an icon with 3 circles next to it, indicating it is Nominal. However, we need it as Scale. Also, FrequencyofBoardMeeting is Nominal, we need it as Ordinal. To amend this, double click on the variable name. Select Measure type as the correct variable type.

The final dataset now looks like this:

Notice how the data are formatted. Each row represents one set of observations (in this case one year’s data) for each bank. Therefore we need two additional variables that identify the bank (Bank_id) and the year (years) the data comes from. This way of arranging the data is called “Long Format”. The data needs to be in this long format and not “Wide Format” where you have each year’s data in separate columns which is often how the data are presented in tables or when extracted from financial databases.

There are also variables for BoardSize, FirmSize, FrequencyofBoardMeeting, tot_asset_trill, and Equity_trill, which can vary from year to year within each bank. These are our predictor variables also referred to as independent variables. The dependent variable is Tobin’s Q since we are interested in how this depends on (are affected by) the other (predictor or independent) variables.

Running a panel regression in Jamovi

Step 1: Initial Data Visualization

We should always first explore our data visually, to assess the potential value of a panel regression model. Particularly useful is to analyse the relationship between our dependent variable, e.g. Tobin’s q and our main independent variables, particularly Equity_bill and Total_asset_bill. We can do that by generating scatter plots.

From the Exploration menu, click Scatterplot then move the independent variable ‘Equity_trill’ to the X-Axis box and ‘TobinQ’ to the Y-Axis box.

You should now have the following graph:

Repeat this time replacing ‘Equity_trill’ with ‘tot_asset_trill’ in the X-Axis and Y-Axis box to get:

Then repeat for all the other predictor variables.

In these graphs, we’re trying to spot trends or patterns in the data. A common thing we look for is whether there’s a linear relationship between the variables. Imagine you’re trying to draw a straight line through the data points. It can sometimes be tricky to determine this just by looking, but it’s a helpful first step to understanding your data.

In our example, there appears to be a reasonably linear relationship between Tobin’s Q and our two main factors, albeit with lots of variation. If needed, you can add a line to the graph to help see this relationship better. But for our example, just looking at the overall trend or pattern of the data is enough.

Step 2: Panel Data Regression

In panel data regression, it’s essential to control for specific unobserved effects that are specific to each bank and remain fairly constant over time. Examples might be the types of customers each bank attracts, as some may attract younger customers and some older customers. Another example might be the types of financial products the bank trades in. These might differ between banks but stay relatively constant over time but may explain some of the differences in Tobin’s Q.

Whilst Jamovi can’t handle advanced panel regression models very easily, we can use it to implement a fixed effects regression technique for panel regression. Whilst this is somewhat limited for panel data regression, this approach offers a practical and scientifically sound method for panel data analysis.

From the Jamovi Regression menu, click on Linear Regression:

Then, move our dependent variable, “TobinQ”, to the Dependent variable box:

Next, we need to select two key variables: “Bank_id” which identifies each bank, and “years” which specifies the time frame. These two types of variables are essential in panel data regression; one tells us about the individual entity (in this case, banks) and the other about the time period linking the same data to each bank together. These are both categorical (Nominal) variables and so place these two variables in the “Factors” box as shown below. If you have any other categorical predictors then these need to be in the Factors box as well (in our case we don’t).

Since all of our other variables are scale data these should go into the Covariates box:

Step 3: Results

One of the key parts of the Linear Regression output to look at is the Model Coefficients - TobinQ table. Our primary interest is in understanding how our predictor variables shown at the bottom of the table influence the outcome Tobin’s Q (labelled as “BoardSize” down to “Equity_trill”). This table includes a lot of results but we are often not interested in the row labelled “(Intercept”) or rows any labelled “Bank_id” or “years”. The parameter estimates for Bank_id are there to capture differences between banks and the parameter estimates for years are there to connect the data for each bank over time.

The column labelled Estimate gives us what are sometimes called the “beta coefficients” which describe the relationship each predictor has with Tobin’s Q. The column labelled p gives the associated p-value which tells us if there is evidence each relationship is statistically significant (i.e. represents a true relationship and not just a random chance relationship).

Step 4: Interpreting the Results

tot_asset_trill has a B (beta) value of -0.023 which indicates a negative relationship. i.e. Banks with larger assets are associated with having decreased values of Tobin’s Q. The p-value in this case is 0.05 which is right on the threshold of 0.05 (when working to the usual 5% level of significance) indicating that there is only borderline evidence that tot_asset_trill is a statistically significant predictor of Tobin’s Q.

Equity_till has a B (beta) value of .216 which indicates a positive relationship. i.e. Banks with larger equity are associated with having increased values of Tobin’s Q. The p-value here is 0.003 and hence very much below 0.05, and so there is actually a lot more evidence here that Equity_bill is a statistically significant predictor of Tobin’s Q.

For the remaining predictor variables (BoardSize, FirmSize and FrequencyofBoardMeeting) the p-values are all greater than 0.05 indicating that there is no evidence that these have any true association with Tobin’s Q. hence we do not try to interpret the B (beta) values as these represent random chance relationships.

We might write this up in a report by saying:

“The results suggest that the total assets of a company, as represented by tot_asset_trill, and the equity figures, denoted by Equity_bill, both have a statistically significant relationship with Tobin’s Q. However, it is important to note that the tot_asset_trill variable is negative, indicating that banks with higher total assets and equity do not necessarily have higher levels of Tobin’s Q. Conversely, there is no evidence that factors such as the size of the board (BoardSize), the overall size of the firm (FirmSize), and the frequency of board meetings (FrequencyofBoardMeeting) have any relationship with Tobin’s Q.”

For more resources, see sigma.coventry.ac.uk Adapted from material developed by Coventry University Creative Commons License