It's more direct to use the log(GDP) instead. Differences in log(GDP) are log ratios, a measure of relative change (that may be given as %). If you want unbiased estimates of mean GDPs and mean changes, you should use a Gamma- or quasi-Poisson model with log-link (rather than using the logarithms of the observed values).

I agree with Jochen Wilhelm . In addition to compare different models

First, I would run a linear model: GDP = a+household consumption growth rate+government expenditure growth rate

Second, I would run a log linear model: log(GDP)= a+household consumption growth rate+government expenditure growth rate

Finally, run a generalized linear model (GLM) with Gamma distribution: g(GDP)=a+household consumption growth rate+government expenditure growth rate

This link maybe useful to see gamma regression using R Programming

https://www.groups.ma.tum.de/fileadmin/w00ccg/statistics/czado/lec8.pdf

The choice of good transformations will be influenced by your sample (e.g., are all units equally populated), what the data are like, and research questions, but another useful transformation can be dividing by population. What are these? Another comment relates to using a growth measure, in general, as a predictor. If the original measures have much unreliability, you may get regression towards the mean (Galton, 1886). Are your measures fairly accurate?

I agree with Jochen, but you can also analyze by time series