## Output gap, polynomial trends and gretl

Posted by Vitalie Ciubotaru

A while ago I needed to estimate Moldova’s output gap. The only data series that covered a long enough period of time and had quarterly frequency was gross domestic product. It can be downloaded from the online database of Moldova’s National Bureau of Statistics. So I used quarterly data on Moldova’s GDP and employed Gretl. In order to model the potential level of output I chose a third-order polynomial trend.

1. Get the data and save it as CSV file. The file should contain two columns: the dates and the values.
2. Import your data to gretl (File -> Open data -> Import -> Text/CSV). If the datafile is formatted properly, no additional treatment is required. Otherwise, one might need to explicitly specify the dataset structure, frequency, and the starting and ending dates.
```open /path/to/your/file.csv setobs 4 1995:1 --time-series```
3. Generate the time index and it’s powers. Since I estimated the third-order polynomial trend, I needed squares and cubes of the time index:
```genr index genr index_2 = index*index genr index_3 = index*index*index```
4. Run the regression. In my case it looked like this:
`ols gdp const index index_2 index_3`
5. Retrieve the coefficients for further use. For example, I wanted to compare them to what MS Excel and Libreoffice Calc compute when creating trends in their charts:
`b = \$coeff`
6. Retrieve the absolute values of the deviation from trend (the output gap in my case):
`gap = \$uhat`
To see the result, one can type something like:
`gnuplot gap --time-series --with-lines`
7. Compute the fitted values, i.e. the trend itself:
`trend = gdp - gap`
To see the input data and the trend line on one graph, one can type something like:
`gnuplot gdp trend --with-lines --time-series`

Here is my result: