This chapter proposes semiparametric estimation of the relationship between growth rate of GDP per capita, growth rates ofphysical and human capital, labor as well as other covariates and common trends for a panel of 23 OECD countries observed over the period 1971-2015. The observed differentiated behaviors by country reveal strong heterogeneity. This is the motivation behind using a mixed fixed- and random coefficients model to estimate this relationship. In particular, this chapter uses a semiparametric specification with random intercepts and slopes coefficients. Motivated by Lee and Wand (2016), the authors estimate a mean field variational Bayes semiparametric model with random coefficients for this panel of countries. Results reveal nonparametric specifications for the common trends. The use of this flexible methodology may enrich the empirical growth literature underlining a large diversity of responses across variables and countries.