I am comparing the trends of a variable between two time periods: 1950-1999 and 2000-2018. Since former has a length of 50 years and the latter 19 years, is it right to compare the trend values obtained via least-squares linear regression?
If you want to know if there are any differences in your trends, you could apply Gujarati method to run the model with dummy variables. if those dummies became significant, you can state the significant differences in your trends.
For comparison it is possible that the base should be the same, i.e., the length of data, which you don't have. Therefore you can not compare these the data span. In addition, the slope of trend would vary due to length of data in different direction.